The Pennsylvania State University

The Graduate School

Department of Engineering Science and Mechanics

FINITE ELEMENT ANALYSIS FOR SURGICAL DECISION SUPPORT OF

INTRAMEDULLARY NAIL FIXATION FOR PROXIMAL FEMUR FRACTURES

A Dissertation in

Engineering Science and Mechanics

by

Scott M. Tucker

© 2019 Scott M. Tucker

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2019

The dissertation of Scott M. Tucker was reviewed and approved* by the following:

Gregory S. Lewis

Assistant Professor, Department of Orthopaedics and Rehabilitation, Department

of Engineering Science and Mechanics

Dissertation Advisor

Chair of Committee

Lisa Shantz

Associate Professor, Department of Cellular and Molecular Physiology

John Elfar

Michael and Myrtle Baker Professor and Vice Chair of Research Director, Center for Orthopaedic Research and Translational Science Professor of Orthopaedics and Rehabilitation, Public Health Sciences, and Neural

and Behavioral Sciences

Judith Todd

P.B. Breneman Chair, Department of Engineering Science and Mechanics

Professor of Engineering Science and Mechanics

Head of the Department of Engineering Science and Mechanics

*Signatures are on file in the Graduate School

J. Spence Reid

Special Member

Professor and Chief

Division of Orthopaedic Trauma

iii

ABSTRACT

Intramedullary nails are the most commonly used implant for surgical fixation of proximal

femur fractures. Although these fracture fixation procedures are generally successful with fewer

than 15% of intramedullary nailing cases progressing to nonunion,1 hip fracture cases represent

nearly 75% of the annual $19 billion spent on fracture management in the United States.2 Clinical

and research efforts to reduce these costs focus on mitigating failure risk and optimizing patient

outcomes to reduce the incidence of costly hospital readmissions and secondary surgeries. Surgeons

play a role in optimizing nailing constructs through selection of appropriate implant features as

well as recommendation of postsurgical return-to-function limitations. However, quantitative data

to support implant selection criteria are generally lacking.

Chapter 1 provides a broad overview of the biomechanics and biomaterials of fracture

fixation, including clinical considerations, fracture healing biology, biomechanics, biomaterials,

and experimental approaches to fracture biomechanics. Chapter 2 narrows the reader’s focus to a

review of intramedullary nail-fixed long bone fractures with emphasis on the femur. Relevant

literature was collected, reviewed, and organized to provide a comprehensive picture of recent

discoveries regarding intramedullary nail biomechanics. A discussion of some limitations of

application of biomechanical results to clinical practice is presented in Chapter 2 to remind readers

that the laboratory environment often requires simplification of authentic scenarios for proper

variable control.

Finite element computational models of proximal femur fractures fixed by intramedullary

nailing were developed, validated, and interpreted in Chapters 3 and 4. Specifically, a wide array

of clinically relevant intramedullary nail design variable combinations was simulated for nine

common femur fracture types under peak gait loading conditions with a generic femur model.

Biomechanical influences of implant features such as nail diameter, nail length, use or disuse of

iv

distal fixation screws, and material stiffness were assessed for each fracture type. Custom-written

code was developed to automate model assembly for a commercial finite element solver. Model

validation was achieved through comparison of predicted construct stiffness to previously reported

mechanical testing data with similar design variables. Reported outcome measures of peak implant

stress and motion at the fracture site are surrogates of relative construct failure risk and offer

insights into optimizing construct selection to reduce failure rates and promote fracture healing.

The results of parametric modeling are summarized here and presented in full detail in

Chapter 3 of this work. Filling the reamed endosteal canal with the largest fitting nail diameter

reduced axial and shear interfragmentary motion for all modeled fracture types. Nail length was

less predictive of shear interfragmentary motion for most simulated fracture types than other

construct variables such as nail diameter, distal fixation screws, and nail material properties.

Furthermore, gapping at the fracture site predisposed the construct to higher implant stresses and

larger interfragmentary motions. The biomechanical outcomes from this computational study can

directly aid in surgical decision-making for optimizing hip fracture fixation with intramedullary

nailing.

The work presented in Chapter 4 utilizes a subset of gapped fracture models from Chapter

3 to provide insight into safe loadbearing levels based on shear motion at the fracture site.

Successful union following fracture fixation surgery is partially dependent on how the fixation

construct resists shear motion as the patient returns to functional activities. Orthopaedic surgeons

attempt to optimize these biomechanics via implant selection as well as the ability to recommend

specific loadbearing limits for the patient postoperatively. We show the loadbearing percentage

that maintains shear motions at the fracture site below a literature-reported threshold for each

construct. Specifically, the data show that full weightbearing achieves the shear motion threshold

for short nails with distal fixation screws for all tested nail diameters in a pertrochanteric and an

v

intertrochanteric fracture type but not for a subtrochanteric fracture. Increasing nail diameter

increases the safe loadbearing limit for nearly all tested configurations, while removing distal

fixation screws has mixed results depending on if the nail is short or long.

Some assumptions of nonspecific modeling are then challenged in Chapter 5 though

introduction of patient-specific fracture type to the otherwise generic simulations. A patient image

based fracture shape-specific model was generated and demonstrated a clinically relevant decrease

in peak implant stress of over 50%, suggesting that simulation results are indeed sensitive to

patient-specific modeling. This Chapter 5 pilot study provides motivation for future investigation

into how results of generic models can be utilized, offers suggestions for directing future modeling

efforts, and questions the functionality of simplistic fracture classification for certain applications.

Results from such efforts have direct implications on surgical resident training, offering

previously unavailable detail on the specific biomechanical influences of implant selection in

parametric fashion, as well as utility in presurgical planning. Overall, the work presented in this

dissertation provides a clinically oriented comprehensive understanding of the biomechanics of

intramedullary nailing of proximal femur fractures.

vi

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................. viii

LIST OF TABLES ................................................................................................................... xi

ACKNOWLEDGEMENTS ..................................................................................................... xii

Chapter 1 Introduction to Fracture Fixation Biomechanics and Biomaterials ........................ 1

Overview .......................................................................................................................... 1

Clinical Aspects ............................................................................................................... 2

Introduction .............................................................................................................. 2

Types of Implants ..................................................................................................... 3 Anatomical Constraints ............................................................................................ 8

Fracture Healing Biology ................................................................................................. 9

Fracture Healing ....................................................................................................... 9 Infection ................................................................................................................... 13

Biomechanics ................................................................................................................... 13

Implant Loading ....................................................................................................... 13 Implant Stress and Failure ........................................................................................ 15 Fracture Gap Strain .................................................................................................. 18 Biomechanical Variables .......................................................................................... 20

Biomaterials ..................................................................................................................... 21

Stainless Steel vs. Titanium Alloys & Other Materials ............................................ 21 Biocompatibility ....................................................................................................... 22

Corrosion .................................................................................................................. 24

Experimental and Computational Modeling of Fracture Fixation Mechanics ................. 25

Experimental ............................................................................................................ 26 Computational .......................................................................................................... 28

Internal Plating ................................................................................................................. 30

Intramedullary Nailing ..................................................................................................... 32

Summary/Perspective ....................................................................................................... 37

Acknowledgments ............................................................................................................ 37

Chapter 2 A Review of Finite Element Modeling within Orthopaedics with Focus on

Femur Intramedullary Nails ............................................................................................. 38

Overview .......................................................................................................................... 38

Experimental and Computational Modeling of Femur Intramedullary Nails .................. 40

Applied Loads, Boundary Conditions, and Constraints ........................................... 40

Interfacial Modeling ................................................................................................. 43 What Biomechanics Research Has Taught us About Femur Intramedullary

Nailing .............................................................................................................. 43

Selecting an Implant ......................................................................................... 45 To Ream or Not to Ream.................................................................................. 48 Nail Diameter and Material .............................................................................. 49

vii

Static vs. Dynamic Distal Locking Screw Fixation .......................................... 50

Techniques Accounting for Biological Variability .......................................................... 53 Finite Element Mesh Generation ..................................................................................... 54 Modeling Applications ..................................................................................................... 55 Coordinate Systems for Description of Motion ............................................................... 57

Chapter 3 Parametric Finite Element Analysis of Intramedullary Nail Fixation of

Proximal Femur Fractures ................................................................................................ 58

Abstract ............................................................................................................................ 58

Introduction ...................................................................................................................... 59 Materials and Methods ..................................................................................................... 61

Bone and Fracture Model ......................................................................................... 61 Implant, Reaming, and Construct Configuration ..................................................... 62 Loading and Boundary Conditions .......................................................................... 63 Finite Element Simulation Parameters ..................................................................... 65 Validation, Outcome Measures, and Statistical Methods ......................................... 65

Results .............................................................................................................................. 66 Discussion ........................................................................................................................ 71

Chapter 4 Return to Function After Intramedullary Nail Proximal Femur Fracture

Fixation: Effects of Fixation Construct and Weightbearing on Shear Motion at the

Fracture Site ..................................................................................................................... 76

Abstract ............................................................................................................................ 76

Introduction ...................................................................................................................... 77 Materials and Methods ..................................................................................................... 78

Results .............................................................................................................................. 80 Discussion ........................................................................................................................ 82

Chapter 5 Examples of Precision Medicine in Orthopaedics.................................................. 84

Precision Finite Element Modeling for Intramedullary Nail Femur Fracture Fixation.... 84

Custom 3D Printed Implant Desing and Modeling for Pediatric Orthopaedic

Oncology .................................................................................................................. 88

Chapter 6 Conclusions, Discussion, and Future Work ........................................................... 93

Appendix A An Unsupervised Machine Learning Method for Discovering Patient

Clusters Based on Genetic Signatures ............................................................................. 97

Reference List .......................................................................................................................... 117

viii

LIST OF FIGURES

Figure 1-1: Applications of internal plating (B) and combined internal plating and

intramedullary nailing (D) to fix complex femur fractures (A, C). (Images from

cases in Hershey Medical Center). ................................................................................... 4

Figure 1-2: Bone screws used to stabilize a femoral neck fracture. Two of the screws

employ partial threading to achieve compression of the bone fragments. (Images

from cases in Hershey Medical Center).. ......................................................................... 6

Figure 1-3: (A) 3D CT-based models created in the Lewis laboratory of proximal

humerus fracture patients. (B) 3D-printed models were anatomically reduced to

simulate intraoperative reduction, prior to (C) computer modeling of stresses and

biomechanical stability with plate and screw fixation. (Images from the Lewis

laboratory.). ...................................................................................................................... 6

Figure 1-4: (A) Periprosthetic internal plate fixation on a synthetic bone model. (B-D)

Intramedullary nail implant with helical blade demonstrating nail curvature and

screw holes. (Images from the Lewis laboratory.). .......................................................... 7

Figure 1-5: We are currently conducting a clinical study in which the forces in vertical

struts of ring-type external fixators are measured. Force data from the struts, as well

as foot forces, are transmitted wirelessly (A) during the patient’s gait. A decrease

over time in normalized strut forces was observed in this patient (B), and in other

patients, consistent with offloading due to bone healing. In (B), ‘W37D’ indicates

dynamization of the frame. (Image from Hershey Medical Center.). .............................. 7

Figure 1-6: Careful considerations of biomechanics is needed when treating difficult

fractures. Surgeons attempt to create conditions at the fracture site that will promote

healing while allowing functional use of the extremity. Radiographs from our center

show a loss of fixation, plate, and/or screw failure in the (left) proximal tibia,

(middle) proximal humerus, and (right) distal dibia. (Images from our medical

center.).............................................................................................................................. 18

Figure 1-7: Plot to quantify the race between bone healing (callus stiffness: blue) and

implant fatigue (stresses: orange), with data based on simulations with callus. The

red line represents the fatigue strength of the material. (Data from our laboratory). ....... 28

Figure 1-8: Examples of finite element models of subtrochanteric fracture fixation with a

lateral plate and screws subject to axial loading, showing effects of screw

configuration and fracture gap size on resulting implant stresses (colors) and fracture

gap strains. (Right) Callus was represented with springs having various stiffness.

Blue represents low stress, red represents high stress. (Data from our laboratory.). ....... 32

Figure 1-9: Finite element models of intramedullary nailed long bones subject to axial

force and bending. Effects on fracture gap motions and stresses due to construct

ix

configuration are evident. Blue represents low stress, red represents high stress.

(Data from our laboratory.). ............................................................................................. 36

Figure 1-10: Stress color map of an implanted IM nail within an unfractured femur under

loading simulating the stance phase of gait. Blue represents low stress, red

represents high stress. (Data from our laboratory.). ......................................................... 36

Figure 2-1: Nail dynamization by removing distal locking screws allows for closure of

the fracture gap under axial loading. Image from Shih et al.3 .......................................... 51

Figure 2-2: Finite element models of a femoral head trabecular specimen created at a

voxel resolution of 84 μm (left) and 168 μm (right) using either voxel-based

meshing (top) or a tetrahedral meshing approach (bottom) from Ulrich et al.4. .............. 55

Figure 2-3: Cadaveric femur instrumented with a host of strain gauges for computational

model validation from Huiskes et al.5 .............................................................................. 56

Figure 3-1: Simulated proximal femur fracture types (type 31A-X.X). Types 31A-1.1,

2.1, and 3.2 were additionally modeled with gaps that remained open under the

applied load. Point pairs used to calculate interfragmentary motions are shown. ........... 62

Figure 3-2: Two design configurations under maximum applied load with the A32 (top)

and A11 (bottom) fracture types demonstrating a long, 10mm diameter nail with

distal fixation screws (top) and a short, 13mm diameter nail without distal fixation

screws (bottom). Applied loads and boundary conditions at the center of the femoral

head and implant meshes are shown. A sphere of bone is visible in the medial

femoral condyle to indicate where femoral boundary conditions are applied. All

bone models were pre-drilled for both long and short nail distal fixation screws,

regardless of configuration. .............................................................................................. 64

Figure 3-3a: Simulation outcomes for titanium implant material configurations for

reduced fractures. Maximum screw stress results are shown in the superior fixation

screw for cases that included fixation screws. ................................................................. 68

Figure 3-3b: Simulation outcomes for titanium implant material configurations for

gapped fractures. Maximum screw stress results are shown in the superior fixation

screw for cases that included fixation screws. Note vertical axis scales have a larger

range than in Figure 3-3a. ............................................................................................... 69

Figure 4-1: IM nails included in this study ranged from 10mm in diameter (left) up to

13mm and nail length was modeled as either short (26.9cm) or long (43.3cm) .............. 79

Figure 4-2: Gapped fractures modeled for analysis at intermediate load levels. Of note is

the difference in fracture gap size between the subtrohanteric 3.2 type (10mm) as

opposed to the others (5mm). Black circles represent point pairs at which

interfragmentary motions are determined. ....................................................................... 80

x

Figure 5-1: Patient fracture x-radiograph (left) superimposed over generic 3D bone model

(right). The fracture line at the superior aspect of the distal fragment is highlighted

with a spline which was used to create the fracture. ........................................................ 86

Figure 5-2: Solid model reconstructed from 3D CT data (left) shown as a gold standard

alongside patient-specific fracture from 2D x-ray alignment (right) demonstrating

good agreement in fracture shape. Reconstruction was graciously completed by

medical student Marcus Erdman. ..................................................................................... 87

Figure 5-3: Tumor volume visualization for the proximal tibia case with segmented

medical image (left) and resulting 3D reconstruction (right). Tumor is highlighted by

the red circle. .................................................................................................................... 90

Figure 5-4: Workflow for custom implant design for distal femur and proximal tibia

osteosarcomas. Patient imaging data (A, G) is reconstructed into a solid model with

virtual tumor removal (B, H) and an implant is designed to fill the bone defect (C, I).

Implant fit is then assessed (D, J). Finite element simulation stress results of implant

mechanical loading from low (blue) to high (red) under compressive loads (E, K).

Additively manufactured Ti-6Al-4V implants (F, L). ...................................................... 91

Figure 5-5: Detailed views of the proximal tibia articular-sparing implant design

demonstrating porous architecture and cortical contour. ................................................. 92

Figure 6-1: Example system load-displacement response shown (green). The piecewise

nature of the green curve demonstrates a change in system stiffness at each of the

two vertices, such as what could happen if bodies came into contact and

subsequently separated. The curve drawn in red indicates the behavior of the

simulation when contact controls is engaged. Dampening, which helps to smooth the

load-displacement relationship, introduces error in the approximated solution but

aids numerical convergence. ............................................................................................ 95

xi

LIST OF TABLES

Table 3-1: Fracture fixation construct configurations modeled. All combinations of

depicted design variables were simulated. ....................................................................... 63

Table 3-2: Results of multiple linear regression of all simulations for maximum implant

stress, axial interfragmentary motion, and shear interfragmentary motion grouped by

fracture type. Design variables with statistically significant predictive value (p<0.05)

are shaded green. Average results ± standard deviation for each outcome variable are

presented in the rightmost column. .................................................................................. 70

Table 4-1: Loadbearing percentiles (shaded) that did not induce greater than 1.5mm of

average shear interfragmentary motion. Data are separated by fracture type, nail

length, nail diameter, and presence or absence of distal screw fixation. Blank space

indicates that the shear motion cutoff is exceeded for a configuration at the

corresponding loadbearing level. ..................................................................................... 81

xii

ACKNOWLEDGEMENTS

I am grateful for my mentor Greg – I would not have been successful without his

commitment to excellence in science, unwavering support, friendship, and belief in my personal

mission. Hwa Bok Wee sustained my research efforts by teaching me many of the tools required

to conduct my thesis work, and is a valued friend.

To my wife Abby, who I feel has earned this degree just as much as I have. Thank you for

believing in me and including my journey in yours.

To my parents, for their wonderful example.

To my sister and friends for their endless support.

I am thankful for the Penn State Medical Scientist Training Program, Department of

Engineering Science and Mechanics, and Department of Orthopaedics and Rehabilitation for their

time, attention, and assistance in helping me achieve this degree. Furthermore, I thank my thesis

committee members for their guidance, time, and commitment to my success. I am proud of the

multidisciplinary path we have forged together and am encouraged that it remains open for future

students to explore.

Chapter 1

Introduction to Fracture Fixation Biomechanics and Biomaterials

Reprinted by permission from Springer Nature Customer Service Center GmbH: Springer Nature

eBook: Tucker SM, Reid, JS, Lewis, GS, Fracture Fixation Biomechanics and Biomaterials,

Springer, 15, 401-26 (2018).

Overview

Surgical fracture fixation is an important part of modern orthopaedic care. Implants

are designed by engineers, and selected and applied by surgeons, with careful consideration

of clinical, biological, biomechanical, and biomaterials principles. Clinically, a large

variety of screws, plates, intramedullary nails, and external fixation devices are used.

Fracture healing is a biologically complex process that may proceed down one of multiple

possible pathways. Successful fracture healing, as well as implant survival, is dependent

on three-dimensional biomechanics as the patient resumes activity. These biomechanics

are dependent on patient variables as well as the fracture fixation construct chosen by the

surgeon. Implant biomaterials must satisfy stringent biomechanical and biocompatibility

requirements. Experimental and computational models enable advances in implant design,

as well as our understanding of how surgeons may best apply these implants for each

patient.

2

Clinical Aspects

Introduction

Fracture management constitutes a very large portion of modern orthopaedic care. Many

fractures can be managed by non–surgical methods such as splinting, casting, and functional

bracing. This type of fracture management is particularly applicable in nondisplaced or minimally

displaced fractures – often in the pediatric population whose healing times are quite short and the

remodeling potential after healing can correct residual deformity. Nonetheless, operative fracture

care is being used increasingly as it has been shown to reduce disability, improve outcome, and

improve the quality of life following a significant fracture. There are three areas in which surgical

facture care has been shown to make a major impact on patient recovery from injury, and is pivotal

in the restoration of function and quality of life.

Displaced fractures of the femur and tibia in the adult are now usually treated surgically as it

has been well-demonstrated that this method is safe, promotes the rapid return to function including

ambulation, preserves joint function, and avoids the condition associated with non-operative

treatment previously coined “fracture disease” which is a complex of problems such as joint

stiffness, pressure ulcers, disuse osteopenia, formation of deep vein thrombosis, and muscle

atrophy.

The second area in which operative fracture care has resulted in dramatic improvement in

clinical outcomes is the fracture of the articular surfaces of joints. The surfaces of most joints (e.g.

hip, knee, ankle, and elbow) are highly congruent with each other such that distortion of the shape

of either side of a joint from a fracture can dramatically alter the load transmission across the

surface and raise cartilage contact pressures to the point that the cartilage will breakdown and lead

to post-traumatic degenerative arthritis. Often, this will result in joint destruction within several

3

years of the injury. Modern orthopaedic care of the injured joint rests on the concept of restoration

of the shape of bones on both sides of the joint as well as restoration of axial alignment and

ligamentous stability of the joint. This approach restores the normal pressures across the joint

during functional use of the limb. A joint that has been restored surgically in this way can undergo

very early motion which prevents stiffness and optimally promotes recovery of the injured articular

cartilage.

The final arena in which surgical treatment of fractures has made a dramatic improvement in

outcome is the multiple injury trauma patient. In this group, rapid stabilization of long bone and

pelvis fractures is viewed as part of the overall resuscitation of the patient since it helps control

bleeding, pain, and facilitates overall management of the multisystem injuries. Often, this is

accomplished initially using external fixation in a “damage control” mode. Then, after the patient

is stable and through the initial period of bleeding, these external fixation frames are replaced with

more definitive internal fixation to allow progressive mobilization and ambulation.

Types of implants

The common element in the entire spectrum of surgical fracture care is the use of orthopaedic

implants to restore skeletal stability that has been lost by the fracture or joint dislocation. It is the

thoughtful application of these devices that allows the modern fracture surgeon to create conditions

at the fracture site that will promote healing as well as allow functional use of the extremity during

the period of healing (Figure 1-1).

4

Four basic types of implants are used in the surgical treatment of fractures: screws, plates,

nails, and external fixators. The most basic type of orthopaedic implant is the bone screw (Figure

1-2). Modern orthopaedic bone screws are available in a vast variety of sizes (1-8mm diameter)

and thread designs which allow use in a wide variety of clinical situations. Screws can be used as

stand-alone fracture fixation devices which are placed across fracture fragments to generate

compression and create stability and promote fracture union. These “compression screws” employ

two different design techniques to achieve compression. The partially threaded bone screw gains

purchase in the bone fragment away from where the screw is placed with no screw threads in the

near fragment. Compression is generated when the head of the screw contacts the near bone

fragment and the threads engage the far bone fragment in essence “pulling” them together. A fully

threaded bone screw can also generate compression by the method of application (compression by

technique). A hole is drilled in the near bone fragment that is slightly larger than the outer diameter

of the screw (gliding hole) and the far bone fragment is drilled with a size equal to the core diameter

of the screw (threaded hole). When the screw is placed, the threads gain purchase only in the far

fragment and as the screw head contacts the bone surface, compression is generated. The same

fully threaded screw can be placed across bone fragments without the use of a gliding hole. In this

Figure 1-1: Applications of internal plating (B) and combined internal plating and intramedullary

nailing (D) to fix complex femur fractures (A, C). (Images from cases in Hershey Medical Center.)

5

situation, the screw engages threads on both sides of the fracture. Compression cannot be generated,

and this construct is termed a “static” or “position” screw.

Plates are placed on the outer aspect of the bone surface and are mechanically linked to the bone

via the use of screws. These bone screws can be mechanically joined to the plate either by a

frictional method (non-locked), or designed in such a way to allow the screw head to engage the

holes in the plate via a series of threads in the head of the screw (locked) such that movement of

the screw-plate interface is highly constrained. A plate designed to stabilize a fracture must fit

within the local anatomy such that muscles and tendons and the adjacent joints can function

normally while the plate is in place (Figures 1-3, 1-4A).

The third major type of fixation device is the intramedullary (IM) nail (Figure 1-4B-D). These

devices are placed into the medullary cavities of diaphyseal bones (e.g. femur, tibia, and humerus),

and act as internal splints across the fractures. IM nails can span the length of the bone and be large

devices, up to 50 cm. in length. Modern IM nails allow screws to be placed perpendicular to the

nail through the ends of the bone and the ends of the nail on either side of the fracture to control

motion and displacement. This type of device is termed an “interlocked” nail and is the workhorse

device in the treatment of adult femur and tibia fracture.

The fourth category of fixation device is the external fixator (Figure 1-5Error! Reference source

not found.). In this type of device, threaded bone pins (3-6 mm in diameter) are percutaneously

placed into the bone on either side of the fracture and then connected outside the body using clamps

and bars. External fixation can be constructed across an entire spectrum of stability (under the

surgeon’s control), to solve many clinical problems in orthopaedic fracture care up to the creation

of stability to allow definitive fracture healing. By its very design, external fixation is temporary

and will have to be removed. Screws, plates and intramedullary nails do not have to be removed

per se, but may be at a secondary procedure for a large variety of clinical reasons.

6

Figure 1-2: Bone screws used to stabilize a femoral neck fracture. Two of the screws employ partial

threading to achieve compression of the bone fragments. (Images from cases in Hershey Medical

Center.).

Figure 1-3: (A) 3D CT-based models created in the Lewis laboratory of proximal humerus fracture

patients. (B) 3D-printed models were anatomically reduced to simulate intraoperative reduction,

prior to (C) computer modeling of stresses and biomechanical stability with plate and screw

fixation. (Images from the Lewis laboratory.)

B C A

7

Figure 1-4: (A) Periprosthetic internal plate fixation on a synthetic bone model. (B-D)

Intramedullary nail implant with helical blade demonstrating nail curvature and screw holes.

(Images from the Lewis laboratory.)

Figure 1-5: We are currently conducting a clinical study in which the forces in vertical struts of

ring-type external fixators are measured. Force data from the struts, as well as foot forces, are

transmitted wirelessly (A) during the patient’s gait. A decrease over time in normalized strut forces

A B

Ratio of Total Strut

Forces to Injured

Limb Foot Force

Week (W) Clinical Visit

8

Variations in fixation implant design and surgical application may enhance overall mechanics

and promote healing. Features such as improved stability, reduced anatomical interference, and

more robust fixation to bone may be achieved through implant design modification, and careful

planning by the surgeon.

Anatomical Constraints

The biomechanical and anatomic design constraints on orthopaedic fracture implants are quite

rigorous. They must be biologically compatible, and meet the biomechanical requirements of the

situation in which they are used. Since they are used to support the bone and not replace it during

the period of healing, the implants must fit the local anatomy which varies among patients. IM

nails must fit within the intramedullary canal. Plates must fit on the external surface of bone and

not impede important muscles, tendons, and ligaments surrounding them. Implants are also

designed with consideration of the surgical exposure needed to apply them. Although many plates

and screws are applied with an open approach that exposes the bone fragments, IM nails, external

fixators and certain plates can be applied with a minimally invasive approach that avoids disturbing

the soft tissues surrounding the fracture that are important for blood supply and the healing process.

Plates designed to reduce the area of contact with bone via geometric modification of the contact

surface are termed minimum contact plates. Reducing contact area at the bone-plate interface may

enhance fracture healing by mitigating disruption to the periosteum and bone blood supply.6

As a result of the aforementioned stringent geometric design requirements, fracture fixation

implants typically do not have an infinite fatigue life. Since the fixation device may initially (at

was observed in this patient (B), and in other patients, consistent with offloading due to bone

healing. In (B), ‘W37D’ indicates dynamization of the frame. (Image from Hershey Medical

Center.)

9

the time of the acute fracture and before bone healing) be load bearing to allow the patient to begin

functional use of the extremity or ambulation, there will be accumulated damage in the

microstructure of the implant. It is well understood by both orthopedic clinicians and implant

designers that there is a “race” between bone healing and implant fatigue fracture. The clinical

presentation of a fatigue fracture of an orthopedic implant may imply some pathology of bone

healing.

Fracture Healing Biology

Fracture Healing

Fracture healing is a complex biomechanical process with multiple possible endpoints. The

most desirable endpoint, termed ‘union’ in the medical vernacular, is complete fusion of the

fractured components into one continuous osseous structure. A union may be achieved through one

of two well-described mechanisms.7 Primary or intramembranous bone healing occurs through

Haversian remodeling which requires absolute stability between bony fragments. On a cellular

level, primary healing involves direct healing of bone without the presence of intermediary tissues.

A very stable interface between two bone fragments is necessary because there is creation of

bridging capillaries as part of the Haversian remodeling which is intolerant of shear forces due to

its mostly linear morphology.8 Primary healing also requires contact between the fracture

fragments, or only a very small gap (on the order of 1 mm). The degree of stability required for

primary bone healing can usually only be achieved via compression between fragments. Thus,

primary bone healing usually only occurs for simpler fractures in which the fragments can readily

be fixed back in their anatomical position, usually with plates and/or lag screws.

10

Secondary healing or enchondral ossification is characterized by formation and evolution of

progressively stiffening intermediary tissues in a relative stability mechanical environment.

Secondary fracture healing progresses through three biological stages. The inflammation phase

begins the moment fracture occurs and can last up to five days. This first phase is characterized by

an immune response in which damaged, necrotic tissues are scavenged by immune cells and the

fibrinous hematoma formed during injury is organized into granulation tissue. Fibroblasts produce

type III collagen. Inflammatory mediators are released resulting in pain, swelling, and an increase

in local blood flow. A chondroid stage then begins enhancing the vascularity and cellularity of the

granulation tissue via mesenchymal stem cells from the nearby periosteum. The chondroid matrix

is then replaced by osteoblasts creating type I collagen. The replacement and removal of the

cartilage intermediate is the hallmark of endochondral ossification. At this point in the healing

process, mechanical loads can be transmitted from one fragment to the other, but there is no internal

organization of the callus. As normal loading returns, the woven bone characteristic of early callus

is remodeled into lamellar bone in response to the loading pattern. This remodeling process can

take months to years and is accompanied by a decrease in the size of the callus mass often closely

re-approximating the diameter of the normal surrounding bone. Coincident with the decrease in

size during remodeling, is an optimization of the mechanical properties of the bone.

The biological stages of secondary bone healing are intimately linked to the local mechanical

environment. The interfragmentary strain theory, first described by Stephen Perren in 1991,9 states

that a tissue type cannot exist in a region in which the mechanical forces exceed its strain tolerance.

The elegant interplay of biology and mechanics described in the strain theory provides the fracture

surgeon and implant designer a framework to understand these seemingly unrelated concepts. For

example, recent research on bone healing has found immature myeloid cell-mediated angiogenic

cascade to enhance bone healing in a mouse model.10

11

By definition, a fracture involves damage to the local blood supply of the bone often extending

to the local tissue. As a result, bleeding occurs around the bone ends creating a fracture hematoma.

As might be expected, conditions within this clotted hematoma are acidotic, hypercarbic, and have

a low oxygen tension. The first tissue to appear histologically in this region is type III collagen

made by fibroblasts. The syncytia of loosely organized collagen fibers and fibroblasts within the

clotted fracture hematoma is called granulation tissue. Mechanically, granulation tissue has a strain

tolerance of about 100%. Metabolically, granulation tissue survives in this region because it has a

low oxygen requirement which can be met via diffusion. The granulation tissue organizes into an

early fracture callus and conditions for the second stage of fracture healing are created. The second

tissue type to appear is cartilage, which is composed of type II collagen, is made by chondroblasts.

The presence of chondrocytes implies that the region has become mechanically stiffer as the strain

tolerance of cartilage is about 10%. At this time, the local blood supply is improving in response

to the release of angiogenic pyrogens. This larger more organized callus composed of granulation

tissue and cartilage further stiffens the region to the point where enchondral ossification can occur.

In regions of exceptionally low strain, osteoblasts will differentiate from mesenchymal stem cells

and begin production of an osteoid. The histological appearance of osteoblasts implies significant

mechanical stability has been achieved, as this tissue type has a strain tolerance of only about 2%.

An important concept is that osteoblasts are quite metabolically active and have a high oxygen

requirement. This requires the co-development of a rich capillary network. Bone cannot form in

regions of high strain because the supplying capillaries cannot survive. The strain theory informs

that each tissue type that appears in a healing fracture prepares the region both mechanically and

biologically for the next tissue. Bone formation implies that stability to maintain a capillary network

has been achieved. A histological hallmark of fracture healing is capillaries crossing the fracture

gap. In the case of primary bone healing, a surgical procedure has created stability between bone

fragments such that a capillary can cross the gap without the appearance of precursor tissues.

12

The different stability requirements between primary and secondary fracture healing are

functions of the strain tolerance of the local biological tissues. Although the strain tolerances for

relative stability are less defined, secondary healing has been shown to be induced by

interfragmentary motion on the order of millimeters.11

Impaired fracture healing can have biological and mechanical origins. Focusing on mechanical

causes, nonunions or delayed unions are generally a result of insufficient stability at the healing

site. Excessive strain during healing can rupture nascent capillaries and prevent nutrient transport

to the metabolically active healing site. Poor stability can have multiple origins including

inadequate initial surgery, implant hardware failure, or an unforeseen traumatic mechanical event.

Biologically, a patient may have decreased bone density that will affect the stability that can be

achieved at surgery. Tissue damage, infection12, medications, smoking13, nutrition, and genetic

factors14 influence the healing response following a fracture. Surgically, a risk of nonunion is

created if the local tissues are damaged by the procedure especially if secondary bone healing is

relied upon. In this situation, callus formation is impaired as a result of the tissue damage, and the

healing may not be able to proceed to union. In nonunion cases, stresses on the implant are never

relieved by bone unions, eventually resulting in a fatigue failure of the implant.

Residual bone deformity can result from a failed fracture fixation or improper bone healing.

Residual deformity can occur when the fracture is not reduced to its original anatomical position

or orientation, bone migrates through partial implant loosening, or implants partially fail through

yield. Most common in comminuted and bone loss fractures, residual deformity can leave a fracture

patient with pain, joint stiffness, limb-length discrepancies, and posttraumatic arthritis (in addition

to the deformity) associated with insufficient reduction of fractures affecting a joint. Residual

deformity outcomes may require medical or even surgical attention and reduce a patient’s quality

of life. The close relationship of local mechanics to successful bone healing necessitates that proper

care and consideration be given to all fractures.

13

Infection

Infection is a devastating complication following surgery, and implanted materials lead to

greater risk of infection. Open fractures where the skin is broken increase the risk for infection.

This risk can reach 30% in certain high grade open fractures with severe contamination and damage

to muscle and bone. Surgery further increases the risk for infection, although most infection rates

during surgery on non-immunocompromised patients are below 1%. Diabetes mellitus, HIV, and

rheumatoid arthritis are common examples of chronic conditions which can also increase the risk

for infection during fracture fixation. Additionally, lifestyle characteristics such as smoking,

obesity, and poor nutrition can also predispose patients to higher infection risks. Novel approaches

for reducing bacterial colonization and biofilm formation on fracture fixation biomaterials are an

active area of research.

Biomechanics

The biomechanics of the fracture fixation construct are integral to understanding how to

develop an optimal implant and surgical approach to fracture repair. The term ‘implant’ herein will

refer to the large fixation component that stabilizes the fracture often via attachment with screws.

The term ‘construct’ refers to the entire system encompassing the implant, screws, fracture site,

bone, and healing tissues. ‘Configuration’ will refer to surgical variables, i.e. number of screws

used, implant position, type of screw fixation, etc.

Implant Loading

The initial stress born by a fracture implant following surgery is quite variable across patients.

At one end is the scenario in which bone fragments have been anatomically reduced and

14

compressed (absolute stability). Load transmission will occur from one bone fragment to the other

directly and result in low implant stresses. At the other end of the stability spectrum is the situation

in which there is no initial contact between bone fragments and the implant carries the entire initial

load of the construct. A bridge plating across a large zone of comminution would be an example of

this.

Fracture fixation constructs are subjected to a variety of loading conditions ranging from

singular high force loading, such as due to an accidental patient fall, to repeated functional

activities. These load patterns are classified as either static or cyclic, respectively, and may lead to

either material yield or fatigue failure mechanisms. Orthopaedic implants can be subject to

surprisingly large mechanical loads within the body. For example, instrumented arthroplasty

implant studies show that implant reaction forces in the knee, hip, and spine can reach nearly three

times the bodyweight during simple gait.15 Furthermore, instrumented fracture fixation implant

studies can show the strain in an implant and use strain data as a surrogate for fracture healing over

time.16 A study using an instrumented femoral nail demonstrated that the load in that implant was

almost exclusively parallel to the implant’s primary axis in four different postures.17

Before a fractured bone has begun healing, the fixation construct may be responsible for up to

all of the load transferred across the fracture gap. This is particularly true in situations in which

there is no contact between the major bone fragments of the fracture. As time progresses,

intermediate bone tissues form across the fracture site which gradually reduce the load carried by

the implant. The construct must maintain mechanical integrity during the course of bone healing as

the mechanical environment at the fracture site plays a large role in achieving union. As discussed

previously, excessive motion at the fracture gap can result in local tissue strain that exceeds the

tolerance of nascent capillary networks that are attempting to bridge these gaps.3 Thus, we must

understand the mechanical responses of fixation constructs to physiological loads within the scope

of the stability tolerance required for a biological fracture healing process.

15

Bone, as a living material, adapts its composition and shape over time in response to its

mechanical stimulus history. Stress shielding refers to decreased bone density in regions that are

subjected to lower stress levels due to loads borne by the implant. The fixation implant effectively

offloads some of the forces that normally pass through the bone. Such a decrease in stress is

believed to engage biomechanical signals and either stimulate bone resorption or inhibit bone

formation.

Although limited or non-weightbearing is often appropriate in the early stages of fracture

healing, sometimes to protect the implant itself, prolonged limited weightbearing in a patient can

result in disuse osteopenia. Disuse osteopenia is a decrease in bone mineral density as a result of

prolonged periods of unloading in the bone. Bone remodeling processes, perhaps with sensing by

osteocyte cells, detect the relatively low loading profile of bone and favor resorption over

deposition, resulting in a bone density that decreases with time. Osteopenia decreases bone mineral

density and increases the risk of implant-bone loosening or bone fracture during activity.18,19

Implant Stress and Failure

Stress is a measure of internal forces in a localized region of material and has units of force

divided by area. Most often in orthopedic biomaterials stresses are generated in an implant in

response to applied external loads. Stress causes a material to deform, creating strain which is a

measure of internal displacement in a localized region of material. Strain is a unitless ratio of final

length to initial length. Basic yield and fatigue failure theories for engineering materials such as

orthopaedic implants primarily utilize stress to predict failure. Most current fracture fixation

implants are usually considered as linear elastic materials, meaning that while they undergo

deformation below failure thresholds, a linear relationship between stress and strain is maintained.

Young’s Modulus or elastic modulus is equivalent to the ratio of stress to strain. Examples of linear

16

elastic materials include steel, carbon fiber, and glass. Once the yield stress is reached, the material

begins to fail plastically and the Young’s Modulus no longer accurately describes the stress-strain

relationship.

Stress in a fracture fixation construct, like in other mechanical applications, is subject to

concentration effects. Stress concentration describes the localized magnification of stress due to

geometric features such as holes and sharp corners. Changes in cross sectional area are common

along fracture fixation implants and are frequently caused by variable implant design, holes in the

implant intended for screw placement, tapers, fillets, and edge characteristics. Most fracture

fixation plates have unique underside geometries that limit areas of contact with the periosteum in

order to reduce damage to blood supply. Variable cross sections are introduced in some cases to

avoid interference with anatomical structures and reduce the weight of the implant. In most modern

plates, the removal of material under the plate to limit bone contact area is done in such a way as

to keep the cross-sectional moment area of inertia of the implant the same throughout the plate

length. This allows the surgeon to easily bend the plate if needed during the surgical procedure.

Fracture fixation construct failure can occur within the implant. If the failure occurs under a

static load, yield can occur at the location of maximum shear stress in ductile materials. The yield

strengths for common fracture fixation implant materials such as cold-worked stainless steel, hot-

forged CoCr alloy, and forged, heat treated titanium are 792, 1600, and 1034 MPa, respectively.

Bone screws are typically made of annealed stainless steel which has a yield strength of 331 MPa.

Typically, shear stress is maximized in the implant region near an unsupported fracture gap where

there are fewer points of fixation and where the largest bending moments are likely to occur. When

the applied load is not sufficient to cause yield failure, the implant may still accumulate damage in

the form of microcracks. Cyclic loading at sub-yield stress levels causes fatigue failure via

progressive crack propagation and eventual brittle fracture within the implant. At stresses above a

material’s endurance limit (a cyclic stress amplitude below which failure will never occur), one can

17

calculate the number of fully reversed loading cycles required to reach fatigue failure. The resulting

data are plotted on an S-N curve to characterize the material’s response to cyclic loading. A

Goodman Diagram may be used to consider the fact that implant mechanical loading is often not

fully reversed, and is instead repeated with a non-zero mean stress.

However, the amplitude of cyclic loading of fracture fixation implants is often variable,

dependent on a variety of functional activities (e.g. walking, climbing stairs, jumping, etc.). Under

Miner’s rule, the total damage is defined as the sum of incremental damages calculated for each

load amplitude.20 Each incremental damage can be calculated as the ratio of the number of cycles

at a given stress or strain range to the total number of cycles required for failure at that range. Some

commercial finite element software include more advanced algorithms for predicting fatigue, e.g.

‘fe-safe’, a durability finite element software suite from Dassault Systemes. Fixation and contact

points between the implant, screws, and bone are of special interest for biomechanical

characterization as these locations are common sites of construct failure. Screw head shearing has

been documented to occur. In this case, screw fractures typically occur near the screw-implant-

bone junction (Figure 1-6). Shear stresses in this region can be influenced by decreasing the

distance between the fracture gap and the closest screws (working length), increasing the screw

count, and biological stiffening across the fracture site via healing.21 Local bone micro-fracture at

the screw-bone interface can also occur, typically leading to screw pullout from the bone.22

18

Fracture Gap Strain

Bone is remarkable in its ability to regenerate following a fracture. Unlike most other

tissues which produce scar tissue, a fractured bone, adequately stabilized and with sufficient

vascularization and other biological factors, is able to ultimately regain its near-original form.23

Nonoperative treatment relies on some degree of stability from soft tissues including muscles,

ligaments, fat, and skin, whereas operative treatment increases stability through implant fixation.

Various theories have been proposed for how mechanical stimulus affects differentiation

and adaptation of healing tissues. These theories are based on mechanical stimulus in the form of

hydrostatic pressure, deviatoric stress, and even fluid flow velocity, the latter viewing the tissue as

a poroelastic material.

Interfragmentary displacement or strain (displacement divided by fracture gap width)

measures provide a useful and intuitive means of characterizing mechanics at the fracture gap.

Based on available evidence, moderate strains of approximately 10-50% have been proposed as

Figure 1-6: Careful considerations of biomechanics is needed when treating difficult fractures.

Surgeons attempt to create conditions at the fracture site that will promote healing while allowing

functional use of the extremity. Radiographs from our center show a loss of fixation, plate,

and/or screw failure in the (left) proximal tibia, (middle) proximal humerus, and (right) distal

dibia. (Images from our medical center.)

19

being beneficial to healing.24,25 This strain is often split into two components: axial or longitudinal,

acting along the long bone axis, and shear, acting perpendicular to the long bone axis. There is

some consensus that shear strains can be detrimental to fracture healing, whereas moderate axial

strains are beneficial.26,27 Dynamized intramedullary nails and certain new plate technologies

promote additional axial strain.28 Excessively high strains are inhibitory to fracture healing and may

result in nonunions.29–31 Compressive interfragmentary displacements are superior to distractive

displacements in creating callus.32 Bone formation is linked with vascularization, and

interfragmentary movements early in fracture healing to promote revascularization, but in the later

stages of healing can inhibit blood flow.29,33 Some investigators have demonstrated clinically the

influence of biomechanical and biomaterial choices on fracture healing and callus formation.34

However much of the evidence supporting these theories are from studies in animals, especially

sheep. In these studies, fractures, often in the tibia, were simulated with osteotomy cuts leaving a

gap. The fractures were stabilized with external fixators. In one such study,26 five sheep were fixed

with a device that allowed only axial interfragmentary displacements, and five sheep were fixed

with a device that allowed only shear displacements. Displacement magnitudes were 1.5 mm with

a 3 mm fracture gap (50% strain) in both groups. The group with shear displacements experienced

significantly delayed healing of the osteotomies, with one third stiffness of the healing site after

eight weeks.

Although there is some consensus that axial and shear strain influence fracture healing

differently, unfortunately control of these two strain components by changes in fracture fixation

construct are not always intuitive. For example, increasing the working length (or bridge span)

between the inner-most screws in a plate construct seems that it would mostly affect axial

interfragmentary strain; however recent predictions from finite element models of 66 supracondylar

femoral fracture fixations in patients (with supporting data from synthetic bone experiments)

revealed that increasing working length primarily affected interfragmentary shear motions, not

20

axial motions.27 Changing the plate from stainless steel to titanium increased both types of motion.

Callus formation in the patients was not associated with comorbidities including smoking or

diabetes, but was promoted by longitudinal motions and inhibited by shear motions at the fracture

site.27 Additionally, improvements in one aspect of biomechanics may lead to concerns in another

aspect; the scenario of large longitudinal strains combined with small shear strains may be achieved

with smaller plate bridge spans, but unfortunately these smaller spans lead to larger plate stresses

and a risk of plate failure.27,35

Biomechanical Variables

Bone strain and displacement at the fracture gap are influenced by the stiffness of the construct,

interfragmentary contact, and load transfer at the fracture gap. The stiffness of a fixation construct

is its resistance to deformation in response to applied loads. Stiffness is a function of several

construct variables: design, orientation, material composition, working length, screw count, and

biological material properties in the fracture gap. Construct stiffness can be measured in multiple

modes: bending, torsion, and compression. The bending stiffness for plate constructs in long bones

often dictates most of the displacement at the fracture gap, whereas circular-type external constructs

rely more on the compression stiffness mode. Torsional stiffness can become important clinically

in all types of fracture repair constructs (plate, intramedullary nails, and external fixation).

Various fracture fixation devices provide stiffness to the fracture. For example, a bridge plate is

a construct in which a plate implant acts as an extramedullary splint spanning a complex fracture

and bends and compresses in response to axial loads on the bone. The bending stiffness of a bridge

plate can be calculated as an applied bending moment divided by lateral deflection. Similarly, the

compressive stiffness of the bridge plate can be determined by dividing the applied axial load by

axial displacement. All loading modes (compression, bending, and torsion) work in unison to

21

dictate the bony displacement and strain at the fracture site, critical for fracture healing, under a

given load scenario.

Graded-stiffness and composite material compositions can modify construct stiffness although

currently they do not see much clinical use. The working length of a fixation construct is the

distance between the two fixation points closest to the fracture gap. The stiffness of the construct

can be approximately inversely proportional to the working length.36 Surgical decisions such as

screw placement can cause construct stiffness to be too extreme in either direction (too stiff or too

compliant) to promote healing.

Use of either locking or nonlocking screws will influence the fracture fixation biomechanics.

Locking screws maintain a fixed angle with the plate and do not enable motion at the screw-plate

interface. Nonlocking screws compress the plate and the bone together creating a frictional

interface between them. Over time, especially in unicortical screw fixation, normal stresses in the

cancellous bone surrounding screws may cause loosening at the bone-screw interface, allowing the

screws to toggle at the implant-screw junction. Thus, the biomechanics of nonlocking screws allow

for some motion at the screw-plate interface, potentially resulting in a decreasing construct stiffness

over time.37

Biomaterials

Stainless Steel vs. Titanium Alloys and Other Materials

Although a vast array of metallic alloys are available for titanium and stainless steel, the

mechanical, chemical, and biocompatibility properties dictate that a small subset of these alloys are

appropriate for use in fracture fixation applications. Metallurgical alloying can influence multiple

material properties of the base metal. Specifically relevant to fracture fixation are the toughness,

22

manufacturability, oxidative potential, corrosion resistance, and biocompatibility. Most modern

implants are manufactured through forging.38

The current most common stainless steel alloy used in orthopaedic fracture fixation

applications is designated as 316L. This low carbon content alloy is manufactured to follow ASTM

F138 and F139 standards which specify: ≤ 0.03% carbon, ≤ 2% manganese, ≤ 0.03% phosphorous,

≤ 0.75% silicon, 17-20% chromium, 12-14% nickel, 2-4% molybdenum, with the remainder being

iron. The carbon and chromium content contribute to corrosion resistance while nickel and

molybdenum improve the mechanical toughness of the alloy. 316L is amenable to cold-working

strengthening which can potentially increase the yield strength from 330 MPa to a maximum of

1200 MPa.38 The elastic modulus for stainless steel is 190 GPa.

Titanium and titanium alloys have an elastic modulus of 110 GPa, considerably lower than that

of stainless steel and closer to that of bone, which explains why titanium alloy implants mitigate

the risk of bone loss associated with stress shielding. Titanium is commonly alloyed with aluminum

and vanadium, the most common being Ti-6AL-4V (5.5-6.5% aluminum and 3.5-4.5% vanadium).

Biocompatibility

All components of internal fracture fixation implants and percutaneous components of external

implants must be biocompatible. Because fracture healing typically occurs on the order of weeks

to months, biocompatibility must be maintained long after the materials have been implanted.

Although a complex topic, the biocompatibility of an implant refers to the local and systemic

physiological changes undertaken by host tissues in response to the implant’s presence. Potential

biocompatibility hazards of orthopedic implants include toxicity, immunogenicity, mutagenicity,

and infection propensity. Most assessments of biocompatibility of fracture fixation constructs focus

on immune responses to the implant. Immune responses can be triggered by material composition,

23

surface topography, as well as size, depending on the local implant environment, and can activate

traditional innate, complement, and humoral immunological pathways.

The implant surface-tissue interface is the single most important driver of biocompatibility in

metallic implants.39 Morphological features such as porosity, surface modification, and smoothness

as well as chemical characteristics such as hydrophobicity, wettability, surface charge, and polarity

influence an implant’s immunogenicity.40 Furthermore, corrosion (see below) may modify an

implant’s morphology, produce small particles from the implant, and ultimately reduce long term

biocompatibility. Soluble corrosion products can be immunogenic and can also be associated with

local cytotoxic and tissue toxicity reactions.

Biomaterials may be classified as inert, interactive, or viable.41 Inert biomaterials such as

cobalt-chromium alloys generate little or no biological response in the absence of wear and

corrosion. Titanium and stainless steel are classified as inert biomaterials. Titanium and titanium

alloys typically exceed the biocompatibility of stainless steel42 as well as have lower infection rates

over steel.43 Both titanium and stainless steel alloys commonly used in fracture fixation have very

good biocompatibility modulated by an inert, insoluble oxide layer that forms on the surface and is

chemically impermeable.

Interactive biomaterials differ in that they are designed to trigger biological responses such as

osteoinduction or osteointegration. Viable biomaterials contain a biological component and may

be resorbed or biodegraded. Fracture fixation implants are currently most commonly comprised of

inert biomaterials, but a construct that can adapt its mechanical properties as a fracture heals may

be desired. Early investigation into resorbable plates and screws shows potential in a rising field of

research.44,45

Biodegradable polymeric biomaterials, such as synthetic polyesters, are emerging as candidates

for orthopedic implant applications as biodegradation may eliminate the need for surgical removal

24

of implants. Degradation of synthetic polymeric biomaterials causes foreign-body reactions that

are measured using histopathology and currently their immunogenic hazards have little clinical

significance.46 Current research finds biomaterials such as polyetheretherketone (PEEK) to have

good strength and radiolucent properties that enable improved visualization of fracture healing by

computed tomography and standard radiographs. However, PEEK suffers from inferior fixation

strength and stability compared to titanium.47 Advances in polymer manufacturing and fracture

fixation technology may yet have clinical applications in fracture fixation.

Corrosion

Metallic materials used for fracture fixation in the body are susceptible to chemical attack,

termed corrosion. Corrosion is a collection of degradative processes resulting from metals reacting

with charged particles in solution. An oxidation reaction in which the metal loses electrons to the

surrounding solution starts a corrosive process. Metallic surface particles then either dissolve or

form an oxide on the material surface. Corrosion initiation is driven by the thermodynamics of

redox reactions and inhibited by kinetic barriers. For a given implant material, the thermodynamics

of reduction/oxidation reactions are fixed within a biological milieu. Therefore, a metallic implant’s

defense against corrosion is through development of kinetic barriers through passivation.

Passivation typically characterizes formation of a passive metal-oxide layer on the outer surface of

the metal. A continuous passive film presents a physical obstacle for the ion transfer necessary to

begin a corrosive process.

Broadly, corrosion can occur through several main mechanisms described as uniform attack,

galvanic corrosion, intergranular corrosion, crevice corrosion, and fretting corrosion.48 Fracture

fixation implants, however, are typically susceptible to galvanic, crevice, and fretting corrosion

pathways.

25

Galvanic corrosion is driven by an electrochemical potential gradient of metals in contact with

each other. While a larger problem for modular implants, galvanic corrosion can occur in fracture

fixation implants, for example, if the screws are made of a metal with a different electrochemical

potential than that of the implant metal. For this reason it is uncommon for a fracture fixation

construct to vary in composition between screws and implant.

Stress corrosion cracking is a subset of crevice corrosion in which pits grow on the surface of

the material. The ionic microenvironment in pits serves as a barrier between the local implant

surface and the surrounding tissues. The net effect of the pit microenvironment is to facilitate

corrosion through ionic exchange between the implant metal and nearby tissue. Additionally pit

geometry concentrates stress and promotes crack formation. When the stress intensity in a pit

reaches the critical value for crack propagation under corrosive conditions, a crack can propagate

and cause component failure. Unfortunately, the critical value for crack propagation under

corrosive conditions is typically lower than the fracture toughness of the material, making stress

corrosion cracking difficult to predict.

Fretting corrosion is corrosive damage resulting from cyclic motion between two opposing

surfaces. In this mechanism, grooves and oxide debris develop on the surface as a result of toggling

between contacting components. Fretting corrosion exposes the material beneath the passive oxide

layer. For example, nonlocking fracture fixation designs are at risk for fretting corrosion whereas

locking screws do not experience motion at the screw-plate interface and are less susceptible.

Experimental and Computational Modeling of Fracture Fixation Mechanics

The growth of orthopedic fracture knowledge facilitates a shift from hypothesis-based

medicine to evidence based medicine. This change in approach accompanies technological

developments in computer science, manufacturing, materials research, and mathematical methods

26

which combine to create more accurate laboratory models of interactions between biology and

medical devices than past iterations. Medical decisions should be made based on the best known

available models which, sometimes, are still clinically observation-based. As research efforts

expand to meet the evidence needs of modern fracture fixation, two distinct modalities emerge.

Experimental research in this context will refer to physical experiments, often involving mechanical

loading, kinematics, kinetics, or chemical phenomena. Computational experiments will encompass

those experiments conducted predominantly in silica, although experimental research accompanies

them as validation frequently.

Mechanical and biological environments involved in clinical fracture fixation are very

complex. Despite substantial advances in lab-based experimental and computational models,

clinical studies remain a vital part of modern investigation.

Experimental

Most lab-based experimental research in fracture fixation biomechanics and biomaterials

focuses on mechanical testing and/or bone healing. Mechanical testing involves a direct application

of load or displacement and is valuable because it enables direct measurement of a construct’s

response. The mechanical testing setup includes a loading apparatus, implant hardware, a fixation

mechanism, and a bone model. The most commonly used loading machines are either uniaxial or

biaxial standard mechanical testing frames retrofitted with fixtures to accommodate a fracture

construct. Implant hardware used during testing is commercially available hardware or, in the case

of testing new devices, custom made. Regardless of hardware, most fixation mechanisms selected

for testing are those that would be also used in clinical cases analogous to the experimental model.

Depending on the research question, the bone model can range in complexity from cylindrical

plastic pipe to compound synthetics to human cadaveric specimens. Such studies are typically

27

focused on the ‘time-zero’ mechanical response before any fracture healing occurs, unless the

fracture callus or bone healing is artificially simulated. Advanced composite fiber glass, epoxy

resin, and polyurethane synthetic bones can adequately represent certain bone mechanical

properties, but adequacy in representation of screw or implant fixation and loosening is still

controversial. A question regarding specific implant stresses and strains may be answered without

the need for expensive cadaveric bone specimens but a question focused on screw-bone fixation or

involving a complex fracture pattern may be best answered by recreating the fracture in a true bone

in the laboratory setting. These cadaver bones are typically stored frozen, not formalin-fixed

because of potential changes in mechanical properties associated with chemical preservation.

Experimental research can be used to test fracture construct performance during functional

activities or to simulate traumatic construct yield events. Generally of interest are failure scenarios

in the implant, the fixation mechanism, or in the bone. Static loading patterns are effective ways to

test yield failure modes, whereas cyclic loads can be applied to simulate fatigue failure. Both failure

modes are usually possible in a patient; yield if a patient has an accidental fall or other high load

event, and fatigue associated with long term physiological loading, especially if the fracture does

not heal quickly and the implants bear larger loads for longer time (Figure 1-7). Outcomes such as

construct stiffness and strength are commonly measured under loading conditions including axial

compression, torsion, bending, or a physiological combination thereof.49 Motion of bone fragments

or implant components during mechanical testing can be measured using infrared cameras, DVRTs,

or simple optical measurement methods using a digital camera.

28

Lab-based experimental research aimed at fracture healing is often conducted in animal

models. Animal models can be used to assess the impact of novel fixation constructs or biological

therapies on the healing response. For example, a recent study demonstrates a faster and stronger

healing response with active plating over conventional compression plating in sheep.50 Although

larger animal models are costly and time consuming they have the ability to simulate a biological

environment with similarities to that of a fractured human bone. Animal models can be exposed to

loading protocols in custom loading devices to simulate the mechanics of activities with ties to

human function.51,52 Furthermore, studies in smaller species enable the use of genetic modification

to understand mechanotransduction of fracture healing on a cellular and molecular level,53,54

although the metabolism and anatomy of these animals is often very different than humans, a hurdle

to clinical translation.

Computational

Computational fracture fixation research aims to simulate the mechanical environment of a

fixation construct. Due to limitations in computational power and modern characterizations of

biological materials it is not yet possible to accurately model all biological, chemical, and physical

Figure 1-7: Plot to quantify the race between bone healing (callus stiffness: blue) and implant

fatigue (stresses: orange), with data based on simulations with callus. The red line represents the

fatigue strength of the material. (Data from our laboratory)

bone

cartilage

granulation Cal

lus

Mat

eria

l Sti

ffn

ess

29

properties of implant hardware and biological tissue, however these features may have limited

impact on specific aspects of construct behavior. Therefore, major assumptions are made to

simplify development and run time of computational models of fracture fixation. The most

commonly used computational approach is the finite element method.

Computational models from previous studies focus on the effects of varying implant design,55

implant material composition,56–58 implant alignment and positioning,59,60 implant fixation,3,61,62 and

bone and fracture characteristics.63–65 Similar to experimental models, computational models often

focus on predicting implant failure, fracture gap strain, and implant load transmission.

Computational models have an important advantage of being able to predict displacement, stress,

and strain throughout all 3D points of a construct, whereas experimental measurements are often

limited to selected external points of a construct. Computational models may also simulate the time-

dependent effects of fracture healing on local mechanics, a challenging scenario to recreate in an

experimental model. Computational models enable comparison of results associated with variation

in a single model parameter, which may not be easily facilitated by experimental models, especially

if expensive biological specimens are involved. Computational models allow for multiple levels of

data interrogation while the physical nature of experimental models limit analysis to specifically

measured outcomes. However, computational models depend on user-defined inputs to run

simulations whereas experimental models allow for direct measurement of a physical system. A

computational model developer must understand and justify all inputs to the model. Experimental

models generally can provide better realism, especially when using cadaver tissues, and are thus

often used to validate computer models. In some cases though, experimental setups are less

accurate such as when measurements are sensitive to boundary conditions that are difficult to

precisely control experimentally but not computationally. Both computational and experimental

modeling modes can be very time consuming depending on setup and research question.

30

Internal Plating

Internal plating is a common method of treatment for many types of fractures. Plate

fixation can provide stability by transferring all of the load across a fracture or by sharing some of

the load burden with bone. Depending on the technique of application and design, plates can be

used for multiple functions: compression, bridging, buttress, protection, and tension band.66

Screw fixation between the plate and the bone must have sufficient strength to resist

failure. Screws can be locked or compression, uni- or bi- cortical, fixed angle or variable angle, and

can be inserted into as many or as few screw holes as desired. Locking screws are threaded into the

implant as well as the bone to maintain a gap between the two, whereas conventional screws rely

on frictional compression to hold the plate to the bone. Unicortical screws anchor in the cortex

closest to the implant and into any trabecular bone present beyond the cortex. Unicortical fixation

is necessary around articular joints and pre-existing prostheses, but is more susceptible to loosening

over time and may lead to construct failure via screw pullout from the bone.67 Bicortical fixation is

more rigid because the screws pass through the other dense cortex after crossing trabecular bone.

Variable angle locking screw holes allow for user-directed angulation of the screw relative to the

plate up to ~17o. Varying screw angle can allow the surgeon to accommodate for local anatomy

and other implants, or to avoid regions of poor bone quality for screw fixation. Unfortunately

variable angle locking plate-screw interfaces are not as strong as standard threaded locking

mechanisms,68 presenting an opportunity for additional improvements in plate systems.

Additionally, screw holes within a plate can be elastically suspended to enable dynamization of the

fracture in what are called active plates. Furthermore, the screw holes in the implant may be

designed to be slots instead of circular holes. Slot-shaped screw holes allow the plate to slide around

the screw which, like active plating, enables motion at the fracture.

31

Internal fixation plates are most commonly made of either stainless steel or titanium

alloys. It has been shown that stainless plates create a stiffer construct with a longer fatigue life

than titanium plates for applications at the distal femur.69 Other plate materials such as carbon fiber

PEEK composites have been shown to have comparable torsional stiffness to stainless steel but

inferior failure characteristics for distal fibula fractures.70 New hybrid materials such as

glass/flax/epoxy composites demonstrated higher ultimate strengths than conventional metals in

tension, compression, and bending while also having a lower axial stiffness,71 however, they are

not yet commonly used in the clinic.

Considering some of the subjective variables involved in internal plating construct

implantation (plate length, plate material, number of screws, screw fixation, fracture shape, plate

working length, etc.), it is evident that an optimization scheme could facilitate mechanically-

informed surgical decisions.72 Parametric models that iterate construct design variables have been

employed to observe the 3D mechanical effects of design changes under axial as well as combined

axial, torsional, and bending loads (Figure 1-8).21,73 Although the number of possible design

variable combinations is exponentially large, consideration of the surgical environment and local

anatomy and biology can focus the solution space and eliminate analysis of unlikely or impossible

construct designs such as one in which no screws are implanted. Model outputs such as implant

and screw stresses and fracture gap strain can also be used to predict construct failure and to observe

the mechanical influences of simulated healing. Thus, the utility of such models extends beyond

surgical decision support and preoperative planning into training applications for clinicians and

implant designers.

32

Intramedullary Nailing

Intramedullary (IM) nailing is a common method of treatment for adult shaft fractures

in diaphyseal bones. Nails are commonly used to provide relative stability for secondary

bone healing for fractures in the femur, tibia, and sometimes even the humerus. IM nailing

entails multiple decision points which may influence the healing course and even success

of a fixation construct. For example, the nail implant diameter can be selected to achieve a

tight or loose fit within the medullary canal. Additionally, the canal can be reamed to

accommodate a larger nail diameter and increase the contact area between the nail and the

bone. IM nails may be solid or cannulated. Solid nails were shown to have a lower risk of

infection in rabbits,74 whereas the more common cannulated nails may be surgically guided

by wire via their cannula during installation. IM nail length can dictate whether or not the

Figure 1-8: Examples of finite element models of subtrochanteric fracture fixation with a lateral

plate and screws subject to axial loading, showing effects of screw configuration and fracture gap

size on resulting implant stresses (colors) and fracture gap strains. (Right) Callus was represented

with springs having various stiffness. Blue represents low stress, red represents high stress. (Data

from our laboratory.)

33

nail engages bone in the distal metaphysis for stability. IM nails are often constrained

relative to the bone both proximal and distal to the fracture with screws (static locking).

Screws confer rotational as well as longitudinal stiffness to the construct.

Some femur nail designs accommodate two screws both proximal and distal to the

fracture. A common design to stabilize a proximal femur fracture incorporates a helical

blade which embeds within cancellous bone in the femoral head. Another design feature

common to femur nails is a dynamic interlocking screw slot. A dynamic screw slot allows

for guided translation of the fracture gap along the direction of the slot (inducing desirable

axial interfragmentary strain) while still conferring torsional shear stability with bicortical

screw fixation. Sometimes screws may not be installed on one side of the fracture to allow

for dynamic compression at the fracture site, although care must be taken in these cases to

ensure the nail does not perforate the bone on the unfixed side.

The first IM nail implants were made of stainless steel for their strength and

biocompatibility. However, stainless steel nails were too stiff to accommodate shape

mismatch between the nail and bone. These features were enhanced by a change to a Ti-

6AL-7NB titanium alloy which is now standard as a nail material. Titanium nails

demonstrate less slipping, more even stress distributions, and increased contact area within

the medullary canal over stainless steel nails in a computational model.56 Furthermore,

titanium nails reduce interfragmentary shear motion to better promote fracture healing over

stainless steel nails.75 Another study found that titanium nails are more stable than stainless

steel in torsion and axial compression, although both nail materials resisted failure at non-

weight-bearing loads.76

34

The mechanics of IM nails spanning a fracture are complex. The type and comminution

of the fracture dictates how much of the load applied through the bone must pass through

the nail. A fully comminuted fracture will require the nail to transfer all of the load across

the gap via the locking screws and represents the worst-case scenario in terms of implant

load bearing. Other factors that influence nail construct mechanics are the material

properties of the nail and screws, the cross sectional shape and anterior bow of the nail,

nail diameter, nail length, medullary canal reaming, and screw configuration. For example,

it has been shown that longer nails can generate higher contact stresses with the bone

medullary canal surface than shorter nails, and that the contact stresses can be mitigated by

increasing the flexibility of the distal end of the nail.77 An experimental model in cadavers

indicated that distal screws significantly increase maximum rotational load to failure in

unstable intertrochanteric fractures and recommended their use due to the improved

torsional strength.78

Contact within the medullary cavity is a significant mechanism for nail load transfer.79

The location and area of contact are influenced by nail size and shape, canal reaming, and

implant position and orientation. If the contact area is small, the load transferred to the

bone is concentrated and can generate high stress. This is thought to be a primary cause of

bone pain which some patients report after IM nail implantation. Increasing the area of

contact between the implant and the bone may reduce pain through design of the nail cross

section and radius of curvature, selecting an appropriate diameter nail for the bone, and

canal reaming. It has been shown that an 11mm-diameter nail with static interlocking

reduces motion at the fracture site up to 59% compared with a 9mm-diameter nail.80 Nail

implant modifications such as diameter, material, and cannulation as well as screw material

35

and area have been shown to reduce interfragmentary shear motion up to 54%.75 Prior work

combining computational and experimental modeling has validated finite element models

of an IM nailed femur at four stages of gait and suggested future improvements in implant

design and surgical implantation.81

Research in our laboratory using the finite element method has demonstrated

some effects of surgical and implant alterations on IM nail biomechanics (Figure 1-9).

These models utilize idealized bone and implant geometries. Additionally, more realistic

bone and IM nail geometries have been modeled for the femur. The femur model was built

using Mimics software suite from a patient CT scan. Separate materials are defined to

represent cortical bone and adjacent cancellous bone. The nail geometry is generated in

Solidworks software using the manufacturer’s design specifications. The nail implant is

aligned with the bone to represent surgical positioning and then the bone canal is reamed.

The implant and bone models are then imported into Abaqus software for finite element

analysis. The models are meshed and boundary conditions, contact constraints, and applied

loads are defined. Screws elements are positioned to align with screw holes in the nail and

are embedded within the surrounding bone mesh. A fracture can then be modeled by

defining a cutting plane and removing elements that intersect the plane. A complex 3D

model with physiological boundary conditions and applied loads can provide insight into

the location and magnitude of stresses in the implant, screws, and bone (Error! Reference

source not found. 1-10). Surgical variables such as nail positioning, bone quality, type and

number of fixation screws, applied loads, and fracture type may all be varied to view the

influence of these features on resultant stresses.

36

Figure 1-9: Finite element models of intramedullary nailed long bones subject to axial force and

bending. Effects on fracture gap motions and stresses due to construct configuration are evident.

Blue represents low stress, red represents high stress. (Data from our laboratory.)

Figure 1-10: Stress color map of an implanted IM nail within an unfractured femur under loading

simulating the stance phase of gait. Blue represents low stress, red represents high stress. (Data

from our laboratory.)

Addition of distal

screw

Single proximal

screw

Larger diameter

nail

Switch to dynamic

screw hole

Use of all four screws

37

Summary/Perspective

The 21st century has heralded advancement toward personalized medicine for the field

of orthopaedics. As computational technologies become more accessible and advanced for medical

applications, researchers identify novel challenges that can drive improvements in patient care.

Specifically for the field of fracture fixation, developed computational methods can be used to

iterate implant design concepts and suggest geometric, positional, and material variations to

achieve better optimization of construct mechanics. Furthermore, the detailed, accurate

approximations of mechanics now available from simulated fracture fixation experiments can be

used in conjunction with fabrication techniques such as additive manufacturing to create implant

concepts that were previously impractical to develop. As the one-implant-fits-all approach loses

traction in lieu of case-specific implant designs, it is expected that patient outcomes will continue

to improve, resulting in reduced time required for fixation, enhanced healed bone mechanics, and

fewer negative outcomes such as residual deformity and implant/fixation failure.

Acknowledgments

The authors gratefully acknowledge support from the AO Foundation, Switzerland (Project

S-15-196L), and the National Science Foundation/Penn State Center for Health Organization

Transformation. Hwabok Wee, PhD performed many of the finite element simulations shown in

figures. We also acknowledge contribution from April D. Armstrong, MD.

Chapter 2

A Review of Finite Element Modeling within Orthopaedics with Focus on

Femur Intramedullary Nails

Overview

Operative fracture fixation is being used increasingly to reduce disability, improve

outcomes, and improve quality of life following bony fracture. While fracture fixation is a generally

successful procedure, fracture management for the U.S. population over 50 years of age is estimated

to cost over $19 billion annually, with hip fractures accounting for 72% of these costs.2 Fracture

fixation failure occurs in up to 13.9% of patients and can result in nonunion, residual deformity,

and disuse osteopenia, with lasting impact on patients and their families.1,82 Revision of failed hip

fracture fixation is more costly than initial fixation, increases mortality risk, and significantly

lowers patient quality of life.83 These staggering numbers and debilitating morbidities motivated

development of research priorities for precision medicine in fracture management among leading

national orthopaedic focus groups.84

Surgical fracture fixation is achieved through the use of orthopaedic implants to stabilize

the fracture for bone healing.27,85 The fixation process involves reduction of bony fragments, when

possible, followed by implant positioning and fixation. Unfortunately, the surgical process is more

complex than this as fracture location and shape are driven by various causal injuries and local

bone quality. Furthermore, a surgeon’s toolkit includes multiple implants and fixation techniques

which must be narrowed to a single configuration for each case.86 Early fracture classification

strategies87 have evolved and informed the most recent AO Foundation Fracture and Dislocation

Compendium88 and can help to categorize common fracture patterns to assist in planning fracture

39

management. However, fracture fixation construct selection remains a largely subjective topic

among surgeons.

For example, most hip fractures are surgically fixed using a compression hip screw or an

IM nail. In such a case, the surgeon must select nail type and appropriate length, diameter, and

material, as well as decide whether or not to use fixation screws. Though there may be multiple

successful combinations of these design variables for a given case, each combination may have

relatively higher or lower risk of failure. In the case of the IM femur nail, failures are reported with

fixation screw bending and fatigue,89 screw cutout, and nail fatigue.90–92 Clinical outcomes of

fracture fixation are often binary: successful union or failure. However, an optimized fixation

construct might reduce the time required to achieve union or prove to be more capable of

withstanding unexpected loading than other constructs. Furthermore, early patient mobilization and

weightbearing is linked to better patient outcomes, especially for hip fractures in the elderly. Thus,

there is a need for systematic evaluation of fixation constructs as it could improve the financial,

physical, and emotional burden of failed fracture fixation in the U.S. healthcare system.93

Computational simulation provides an opportunity to determine specific treatment

recommendations based on individual case characteristics in numerous medical fields.94 Recent

advances in computational power and resource allocation have enabled multiple levels of

specificity in mechanical simulations, including bone geometry, fracture shape, and material

properties.95,96 However, there is not yet a process for taking patient imaging data and generating

model outputs on a clinically relevant timescale. Simplified computational models can be created

with relative ease, whereas precision modeling requires significant time and computational

resource allocation. There are various degrees of precision modeling that may or may not affect

clinically relevant outcomes. Therefore, the sensitivity of model outcomes to hierarchical levels of

precision modeling should be evaluated.

40

The most commonly used computational approach is the finite element method. The general

process of the finite element method for a mechanical problem is to discretize the system into a

finite number of smaller elements connected at nodes, approximate shape functions to describe

each element’s shape in all configurations of the system, implement boundary conditions, loading,

material properties, and contact formulations, develop the mass and stiffness matrices for the

problem, and solve a linear system of equations that represent the finite element approximation for

the system equations of motion. The resulting configuration of the system is defined in terms of

calculated values for degrees of freedom at nodes in the system. Once the configuration of the

system in both the reference and deformed configurations is known the desired output measures

can be calculated.

Experimental and Computational Modeling of Femur Intramedullary Nails

IM nails are the most commonly used femur fracture fixation implant and have been

studied in experimental and computational models since the early 2000s. Despite the numerous

variables present in a clinical femur fracture case, most research studies are limited by

computational power to assess one or only a few variables in an overly simplified framework.

Applied Loads, Boundary Conditions, and Constraints

It has been shown that FE femur nail simulation results are very sensitive to boundary

conditions and applied loads, and thus careful modeling choices are necessary.97,98 Because walking

is the most common functional activity for patients,99 simulations of femur fracture fixation often

use the maximum joint reaction force at the hip during gait as their applied load. A landmark paper

by Bergmann et al. established in vivo loads acting at the hip joint using instrumented total hip

41

arthroplasty implants during gait (as well as walking at variable speeds, stair ascent and descent,

knee bend, and standing from a chair) and expressed them as a percentage of patient bodyweight

for personalization in computational models.100 Most finite element femur models developed since

the Bergmann paper was published have used this loading convention.

Muscle forces are understood to significantly influence femoral loading101 but are

challenging to measure and model accurately, unlike joint reaction forces which can be measured

with implants instrumented with measuring devices.15 The most commonly used muscle loading

configuration in FE simulations of the femur was developed and simplified in a dynamic

musculoskeletal computational model of the hip by Heller et al.98 Their minimization scheme

systematically pared down the number of muscles contributing to their musculoskeletal model of

the hip until the calculated hip joint reaction force started to become ‘unphysiological.’

In addition to the influence of applied loads on simulation mechanics, some research

groups have focused on the mechanical influences of boundary conditions. For example, Speirs et

al. explored the sensitivity of motion in a finite element femur model to commonly used boundary

conditions.102 Their findings indicate that constraints that mimic closely the physiological

constraints on the biological system minimized large reaction forces near the points of constraint

application and minimized overall deflection of the hip. A more recent study evaluated the effect

of different constraint mechanisms on the femur during simulation.97 This study compared a

constraint in which the distal condyles are fixed in place (both with and without muscle loading) to

the physiological case suggested in the Speirs paper in which the center of the femoral head is

limited to one translational degree of freedom along the axis defining the applied load. This study

further confirmed the findings of Speirs et al., suggesting that physiologically similar constraints

enhance simulation validity and produce more realistic mechanics than nonphysiological

constraints.

42

The finite element modeling efforts described in Chapters 3 & 4 of this work are no

exception to the rule that applied loads and boundary conditions have great influence on simulation

behavior. For example, the mechanical testing experiments which are used for validation of the

models developed in this dissertation pot the distal femur in bone cement and fixturing such that

all translational degrees of freedom are locked and one rotational degree of freedom is limited.

However, the bone in the mechanical testing experiments was able to rotate in two degrees of

freedom about a pivot point within the medial condyle. The virtual nature of computational models

enabled implementation of a physical rotational constraint directly on this point in the finite element

model. However, on inspection the computational model appeared to be rotating in the locked

degree of freedom which was occurring because the boundary constraint was being applied to

trabecular bone elements which have low stiffness and were undergoing large deformations about

the constrained point. To remedy this, we kinematically chained a full circumference of points on

the nearby cortical bone to a reference point and enforced the boundary conditions at the reference

point. The resulting simulations were finally undergoing motion similar to the experiments on

which they would be validated after correction of this error.

Similarly, early simulations enforced the point of applied load within the center of the

femoral head because that is the location from which joint reaction forces were calculated in an

instrumented implant study.100 Anatomically, the hip relies on contact between the outer surface of

the femoral head and the acetabulum to transfer load to the femur. Thus, we adjusted our

simulations to kinematically chain a collection of points at the cortical surface of the femoral head

along the line of action of applied load to a reference point located at the center of the femoral head,

to which load was applied. However, it can be difficult to detect nuances such as these without

careful attention to boundary conditions and applied loads.

43

Interfacial Modeling

Choice of interfacial modeling strategies can also influence simulation outcomes. For

example, peak minimum principle strain in fixation screws decreased 75% when comparing a

thermal expansion/undersized pilot hole method to a simple cylindrical interface with friction.62

Because screw cutout from bone is a common mode of implant failure, especially in cases of poor

bone quality such as osteopenia and osteoporosis, it has been suggested that high-resolution finite

element models are needed to accurately model the local non-linear mechanical behavior at the

screw-bone interface.103 Furthermore, failure predictions at the screw-implant interface for plated

fracture fixation models are significantly influenced by interaction properties between the screw

head and the implant.104

However, sophisticated screw modeling approaches are computationally intensive and

may be unnecessary in some cases. Specifically, literature supports that complex screw modeling

such as including thread geometry or a simpler pseudo-threaded model both offer a more accurate

depiction of local bone strain than a bonded interface.105 However, the results of the same study by

Inzana et al. also indicate that relative comparisons of implant stability were not affected by the

modeling choice for the bone-screw interface, even when a simple bonding interaction was used.

Thus, the precision of interfacial modeling techniques can be selected based on desired outcome

measures and the degree of accuracy required to address the research questions.

What Biomechanics Research Has Taught us About Intramedullary Femur Nailing

Surgical femur fracture fixation involves multiple decision points, many of which are the

focus of current surgical debate. Specifically, surgeons first select the type of implant to be used in

the construct. The IM nail is the most commonly used implant for femur fractures and is often

44

preferred over other implants such as the distal hip screw due to better short term outcomes.106 If

an IM nail is to be used, however, the surgeon then needs to decide if they will ream the endosteal

canal to accommodate the nail. Data to support a preference for either reamed or unreamed nailing

is inconclusive and reaming remains an unanswered question.107 Furthermore, the size of the native

and/or reamed endosteal canal presents a challenge when selecting nail diameter which will dictate

the size of the gap between the implant and the endosteal canal. Femur nails are most commonly

made of titanium alloy but are also available in stiffer stainless steel. A nail can be long, spanning

nearly the full length of the femur, or short, extending only into the diaphyseal region. The nail can

be locked in place by distal fixation screws to constrain motion or can be dynamized through

removal of screws or use of slots rather than holes on the implant.

Most FE modeling studies of femur fracture fixation measure similar outcome variables:

maximum von Mises stress in the implant and screws, strain in the bone (often measured as

minimum principle strain), and a quantification of motion at the fracture site (measured as

displacement or strain). Von Mises stress is a theoretical predictor of material yielding for ductile

materials. The elastic limits of materials are tested under single dimensional load conditions under

which their stress-strain behaviors are described. However, the stress state on 3D bodies in complex

FE models is almost never one-dimensional. Thus, the von Mises stress is a criterion calculated

from the full 3D stress tensor that is approximated to predict yielding at a material point if the von

Mises stress equals or exceeds the simple tension yield limit stress.

Strain in the bone is commonly represented as minimum principle strain. The minimum

principle strain is the largest normal compressive strain at the material point being evaluated. Thus,

the minimum principle strain can be compared to the strain limit of a brittle material such as bone

as a predictor of yield.

Motion at the fracture site is a complex quantity to describe because there are many ways

it can be represented. The motion of individual point pairs can be measured but this can be

45

obfuscated by rotation of the two fragments relative to each other. A central virtual common point

between fracture fragments can be rigidly fixed to each fragment and motion of one fragment’s

point can be described as a translation from the other fragment’s point. In the case of gapped

fractures, fracture gap strain can be calculated and is thought to have a link to secondary fracture

healing (see Perren Strain Theory in Chapter 1). However, strain can be a confusing measure

because it is biased by the size of the initial gap (1mm of motion in a 10mm gap gives 10% strain,

whereas the same motion in a 5mm gap shows 20% strain). In cases with little or no fracture gap

and high stability between fragments that are expected to heal by primary bone healing, strain is

less meaningful and displacements are favored. In general, the description of motion used in

literature is customized from the above options based on the research question(s) being explored.

Selecting an Implant

Several FE studies have been conducted to assess biomechanical differences between

potential implants for femur fracture fixation. One study, focusing on distal diaphyseal femoral

fractures, compared the stresses between a laterally placed osteosynthesis plate and an IM nail

when used to fix the same fracture.108 Their findings indicated that the IM nail experienced higher

von Mises stress with distal femur fractures than the osteosynthesis plate but that this effect was

mitigated as the fracture gap was increased from 1 to 3mm. They further discuss that their model

indicated that the plate induced fracture healing through intramembranous ossification, maintaining

absolute stability at the fracture site, while the IM nail would induce endochondral ossification,

maintaining only relative stability at the fracture site. A later, similar study by a different research

group compared retrograde IM nailing to locking plate fixation for periprosthetic distal femur

fracture following total knee arthroplasty.109 This study by Shih-Hao et al. finds agreement that the

IM nail experiences higher stress than plate fixation and finds that both constructs sufficiently

46

stabilize a distal femur fracture. However, despite higher stresses in the nail, a biomechanical and

computational series of studies demonstrated that locking plate fixation had a higher probability of

fracture (21.8%) than IM nail fixation (0.019%).110,111 Conventional wisdom suggests that nails

have smaller stresses than plates for diaphyseal and proximal femur fractures have smaller peak

stresses than plates due to their positioning closer to the axis of load application.

Furthermore, if an IM nail has been decided upon for hip fracture fixation, there are still

several styles of nail available from each major implant manufacturer. As an example of this, a

study from 2009 evaluated bone strain and implant stress when a trochanteric fracture was virtually

fixed with a Gamma-Nail (Stryker), Gliding-Nail (Plus Orthopedics), Proximal Femoral Nail-A

(Synthes), and Targon-Proximal Femoral Nail (Aesculap) in a FE model.55 In this study similar

loads (including muscle forces) and boundary conditions were used as previously described by the

Bergmann and Duda research groups and the implants were compared to each other in ‘ideal’ and

slightly misaligned positions. The findings from the study indicate that, despite many geometric

similarities, each nail has a unique positioning error tolerance but that overall caudal alignment

should be preferred to cranial alignment to provide more favorable fracture healing conditions. This

finding is further supported by the results of a 2013 paper which evaluated the influence of implant

alignment in an intertrochanteric fracture finite element model.112 The study was limited to sliding

hip screw implants rather than IM nails and demonstrates that increasing the tip-apex distance

(TAD) of the lag screw (the distance between the tip of the screw and the apex of the femoral head),

decreased the risk for screw cut-out from the proximal femur. Although the risk of failure via screw

cutout is much higher in the sliding hip screw (80%) than in IM nails (8.5%),113 cutout remains an

important failure mode for all cephalomedullary devices.114

Thus, not only must an appropriate implant be selected, but it must also be implanted in an

optimized orientation and position. For this reason, a device called the variable angle nail was

developed which enables motion between the lag screw and the nail intraoperatively thus

47

influencing the TAD. A FE study compared the variable angle nail to a traditional nail design

(Gamma 3) and showed similar stiffness and fatigue characteristics between the two.115 However,

a 2018 retrospective case study of 83 patients with pertrochanteric femur fractures treated with

cephalomedullary nails showed that cases treated with a higher TAD did not increase the risk for

lag screw cutout.

Furthermore, surgically there are 2 common approaches for antegrade nailing – trochanter

tip and piriformis entry. Some nails are designed specifically for one type of entry or the other. The

surgical entry point used to install a cephalomedullary IM nail was studied in a FE model.60 It was

shown that the trochanter tip starting point exhibits higher bone strains than the piriformis entry

point, increasing the risk of iatrogenic fracture of the proximal femur when using a trochanter tip

entry point.

An additional consideration when selecting implant design features for fracture fixation is

the type of fracture. Specifically, it has been shown that “IM nails fail at a lower load in an unstable

fracture situation in the proximal femur than in a stable fracture.”116 Specifically, nails spanning

gapped fractures failed at 72% of the load at which they failed in reduced fractures. This study

further indicates the location of maximum stress is at the aperture of the lag screw, where fatigue

fracture of the nail is likely to begin. Another study by the same research group simulated a

pertrochanteric fracture, a lateral neck fracture, and a subtrochanteric fracture fixed by a

cephalomedullary nail.117 All three fractures were similar in global construct stiffness but differed

in maximum stress (665MPa for the subtrochanteric fracture, 621MPa for the pertrochanteric

fracture, and 480MPa for the lateral neck fracture). This further supports the idea from their

previous study that nails bear higher stresses in unstable fractures cases than in those that are stable.

In such cases, additional fixation techniques (i.e. supplemental plating) may be considered to

mitigate failure.

48

To Ream or Not to Ream

A question of constant clinical debate surrounding IM nailing for femur fracture fixation

is whether or not to ream the intramedullary canal.118 Reaming a canal can enable easier

implantation of an IM nail, reduce the risk of nonunion, and can facilitate usage of a stiffer, larger

diameter implant.119 However, reaming the bony canal decreases diaphyseal cortical thickness and

can increase the risk for bony fracture and nail punch-through. Reaming can also disrupt local

vascularization, essential for healing, in the innately poorly vascularized bone tissue.120 FE studies

are particularly well positioned to elucidate some of the biomechanical differences between reamed

and unreamed nailing but, unfortunately, canal reaming is typically not considered nor even

mentioned in most FE nailing studies.

One FE study published in the Journal of Orthopaedic Research in 2006 used an FE model

to predict interfragmentary strain at the fracture site, von Mises stress in an IM nail with locking

screws, and bony strain distributions for reamed and unreamed nailing of 3 different tibia

fractures.121 Their findings show that the unreamed nail is more likely to fatigue fail than the reamed

nail because the stresses at the interlocking bolts were higher in the unreamed case. The two cases

showed nearly equivalent maximum von Mises stresses in the locking screws with a proximal tibial

fracture but the mid-diaphyseal and distal fractures were both accompanied by higher screw stresses

in the unreamed case.

Another study specifically targeting the effect of reaming assesses how the mechanical

contact interface between the implant and the bone is affected by gap geometry and thickness.79

Specifically, their study used a simple transverse subtrochanteric fracture fixed by a

cephalomedullary nail under simulated maximum gait loading. Their model included a scenario

with perfect contact between implant and bone for the entire length of the nail (unreamed) as well

as a case in which there is initially no contact between the implant and bone (reamed). Their

49

findings indicate that larger endosteal reaming gaps lead to greater medial stress concentrations in

the implant while the unreamed case provides a more uniform stress distribution on the implant.

Nail Diameter and Material

IM nails are clinically available with multiple shaft diameters commonly between 9-12mm,

although ranging up to 17mm. Nail diameter influences the cross-sectional area moment of inertia

such that an increase in diameter increases the bending stiffness of the nail. One FE study using a

human tibia model demonstrated that shear motion at a diaphyseal gapped fracture site could be

reduced by adjusting nail alignment in the anteroposterior and mediolateral directions and by

increasing nail diameter and/or elastic modulus.75 Another FE study found a 51% decrease in

maximum nail stress in a subtrochanteric fracture model by increasing the diameter of a gamma

nail from 15.5mm to 17mm.122 It is intuitive that increasing nail diameter increases construct

stiffness and decreases motion at the fracture site. However, variations in reaming, patient bone

geometry, and bone quality can limit the opportunity for a large diameter nail. Under such

circumstances the two aforementioned computational studies evaluating nail diameter can provide

insight into the biomechanical costs of using smaller diameter nails.

Similar to nail diameter, nails made of materials with high modulus of elasticity such as

stainless-steel increase total construct stiffness. Early IM nails were nearly exclusively made of

stiff stainless steel (elastic modulus ~190GPa). However, this is much stiffer than healthy cortical

bone (~16 GPa) and thus these nails experienced high compressive and bending stresses.

Furthermore, the stiff stainless steel nails can stress shield the bone, thus reducing bony internal

and leading to bone resorption. Titanium alloy is now the market standard for nail material and has

been shown to decrease slipping, produce even stress distributions, and increase contact area within

the medullary canal over stainless steel nails in computational models.56,75 It has also been shown

50

that titanium nails are more stable than stainless steel in torsion and axial compression, although

both nail materials resisted failure at non-weight-bearing loads.76,123 Furthermore, titanium alloy is

more biocompatible than stainless steel, thus decreasing unintended immune responses. Additional

materials for intramedullary nails such as polymers and composites have been tested. A bovine

femur model demonstrated that polymeric femur nails resisted failure under static conditions,

however, maximum von Mises stress during walking exceeded the yield stress for each polymer.124

Polymeric materials are not yet strong and durable enough to withstand the dynamic loading of

fractured long bones.

Static vs. Dynamic Distal Locking Screw Fixation

IM nailing constructs can be dynamized by removing or adjusting the static fixation

enforced by distal fixation screws. This makes the distal fixation dynamic, allowing relative motion

between the implant and the distal fixation. In some cases dynamization is thought to be preferred

because bone heals in response to mechanical stimuli. Construct dynamization would promote

secondary bone healing with relative stability rather than primary bone healing which requires

absolute stability. Secondary healing is utilized especially in fractures with high comminution or

loss of bone in which absolute stability may not be attainable.

In 2004 a Synthes retrograde nailing system was evaluated in an unfractured femur model

under simplified gait loads with a 6 degree-of-freedom (DOF) constraint at the distal femur.81 The

initial focus of this study was to validate the FE model with mechanical testing in a composite bone

instrumented with strain gauges positioned along the outer cortical surface. Once agreement

between computationally predicted and mechanically tested strains was confirmed, the authors

assessed the effects of dynamization via screw removal and implant material on forces, moments,

and von Mises stress in the implant and screws. The study concluded that reamed, statically locked

51

retrograde IM nails should be used with all screws in place due to concerns about the effects of

screw removal on fracture healing that had been raised previously with a telemetrized (instrumented

with sensors capable of reporting force, pressure, and positional data) IM nail.17 However, the

unfractured nature of the bone model in their simulations is likely to have influenced their results,

particularly reducing stresses in the implant and screws due to decreased deformation relative to a

model which includes a fracture.

A more recent FE study also looked at nail dynamization but in the context of a fractured

bone model.3 While still employing the same distal boundary condition as the previously described

model, these simulations included an approximation for the gluteus medius muscle in addition to

the applied reaction force at the hip joint. Furthermore, the fracture models in this study were

diaphyseal with initial fracture gaps which closed when the system was dynamized by removing

the distal locking screws (Figure 2-1). The results show that dynamization increased contact area

and contact pressure at the fracture site in both proximal and distal diaphyseal femoral fractures,

eliminated potential failure at the distal screws, and decreased the maximum stress on the implant.

52

A 2013 biomechanical study challenged the findings of the above two presented FE studies

by assessing performance of static and dynamic distal locking screw fixation in long

cephalomedullary nails with unstable subtrochanteric fractures under torsional loading.125 Their

results showed, not surprisingly, that distal locking increases the rotational load to failure.

However, they found that the maximum torsional load to failure in the unlocked group falls within

the functional range of adult hip loading. Thus, they highly recommend use of the distal

interlocking screws due to the rotational failure not previously considered in the FE studies.

A clinical study in 2016 further demonstrated the complexity of the locking vs. unlocking

debate by evaluating removal of distal locking screws in the setting of short IM nails in stable

pertrochanteric fractures.126 The findings here indicate that removal of the distal locking screws in

stable fracture patterns was no different than the group treated with locking screws in terms of

walking function, residual pain, and overall satisfaction at one year followup. Furthermore, the

group without screws was associated with shorter operation time, less radiation from imaging,

shorter surgical incision length, and less blood loss and thigh pain than the locking group.

Thus, short nails spanning stable fractures appear to be preferred without distal locking

screws while long nails spanning unstable fractures likely require the use of distal locking screws

to avoid rotational failure. But what about long nails in stable fracture patterns? Short nails across

a gapped fracture? How would the recommendations from the FE studies differ if torsional loading

had also been considered? The disconnect between the early FE studies and the biomechanical

study is explained by the disregard for rotational loading in the FE studies but serves as an important

reminder to consider the context in which the results of both experimental and computational

Figure 2-1: Nail dynamization by removing distal locking screws allows for closure of the fracture

gap under axial loading. Image from Shih et al.3

53

studies will be considered. The results of the studies are validated within the experiments tested

but, when taken into a real-world clinical setting, will be extrapolated beyond the overly simplistic

conditions the experiments were conducted in. It is essential that the findings of clinically-relevant

work are presented within the constraints of their experimental framework so that their results are

not easily misinterpreted. To this end, it is essential that the gap between translational research and

clinical practice be shortened such that the research questions can be designed to have clinical

relevance and that clinical practice can be informed from research findings.

Techniques Accounting for Biological Variability

Biological tissues can be a challenge to model virtually due to variability in shape,

mechanical properties, and complex interactions between tissues. For example, although a majority

of long bone fractures fall into categories identified by the AO Foundation, nuanced geometry in a

specific fracture or implant can influence the mechanical outcomes of the system. Model geometry

for fracture fixation problems can be challenging to obtain due to variability and background noise

in medical imaging data. When available, 3D imaging data such as Magnetic Resonance Imaging

(MRI) or Computed Tomography (CT) can be used to generate a virtual description of the anatomy.

Several methods are available for image segmentation, during which efforts are made to delineate

signal from noise as well as distinguish tissues which may vary in mechanical properties (e.g.

muscle, bone, tendon, cartilage, etc.).95,127,128 Previous research into optimization strategies for

isolating refined geometric models from medical imaging data has yielded results, although no

single software or process is universally accepted.127,129,130

Due to radiation exposure with CT imaging and high cost and time inherent in both MRI

and CT imaging modalities, they may not be indicated for all patients. In such cases X-ray imaging

54

is the most commonly used diagnostic tool for fracture cases and thus only a 2D image set is

available. Strategies for developing 3D representations of geometry from plain film X-rays have

been developed but are more error-prone than MRI and CT.131,132

Recently, population-based methods have been developed for estimating patient-specific

features in computational models. For example, statistical shape modeling (SSM), which will be

discussed further in Chapter 5, can be used to estimate patient-specific femur geometry based on

demographic descriptors such as sex, age, BMI, and height.133–135

Finite Element Mesh Generation

Finite element meshes for musculoskeletal tissue geometry are sometimes generated in a

voxel-based manner, with resolution up to the resolution of available imaging data.136 Trabecular

bone has a complex structure that is sometimes modeled as a series of repeated units137 but has also

been represented with meshes generated from high-resolution MicroCT scans.138 All elements in a

voxel-based mesh are equal in size. Enhanced resolution in a voxel-based mesh can be achieved

via MicroCT scanning over traditional CT imaging. Voxel-based models typically require

additional processing to delineate boundaries and smooth surfaces. Small features may become lost

in a voxel-based mesh with poor resolution compared to relatively smoother tetrahedral meshes

(Figure 2-2).4 High-resolution voxel models may contain many elements and result in a very large

global stiffness matrix for the finite element formulation. One technique to obtain a

computationally efficient model from a dense voxel mesh is to use an element-by-element

technique which never assembles a global stiffness matrix.139 Several strategies have been

developed for automated mesh generation from object boundary data, voxel-based data, and hybrid

combinations of the two.140

55

Modeling Applications

The field of orthopedic medicine has many various applications for computational modeling.

Bone has been simulated in computational models for crack propagation141, plasticity142, and

microstructural143 analyses. As mentioned in the overview, orthopaedic joints have been modeled

extensively in native and medically-intervened states. In such models, stress and strain fields are

valuable for calculating and predicting outcomes such as translation and rotation under load,

contact pressure, contact area, and others in response to medical interventions such as joint

replacement, soft tissue repair, and fracture fixation. Cartilage and soft tissue have been modeled

in finite element formulations using a biphasic theory with fluid modeled without viscosity and

solids modeled as incompressible.144 Beyond biology, orthopedic implants themselves are also

Figure 2-2: Finite element models of a femoral head trabecular specimen created at a voxel

resolution of 84 μm (left) and 168 μm (right) using either voxel-based meshing (top) or a tetrahedral

meshing approach (bottom) from Ulrich et al.4

56

modeled for geometric design iteration, failure analysis, predicting stress and strain profiles, and

predicting mechanical interactions with biological tissues.

Painstaking validation of a femur bone model was conducted by Huiskes et al using 112

rosette strain-gauges glued to a cadaveric femur during mechanical loading.5 Previous work such

as this demonstrates why a computational model can be preferred to physical experimentation

(Figure 2-3).

Figure 2-3: Cadaveric femur instrumented with a host of strain gauges for computational model

validation from Huiskes et al.5

57

Coordinate Systems for Description of Motion

A common challenge for translating results from computational simulation to patient care

is to express the results in terms of anatomical coordinates. Human bones rarely conform to

common engineering geometries and our joints often undergo combined motions that are

sometimes not well approximated by simple definitions such as hinge and sliding joints. For this

reason Grood and Suntay, in a landmark paper, established recommendations for systematic

determination of coordinate systems for bones and joints.145 In this paper specific anatomic

landmarks are used to construct axes for describing translations and rotations relative to clinically

relevant orientations such as anteroposterior, mediolateral, and inferosuperior. For computational

models, anatomical landmarks are often digitized relative to each other or to fiducials and reference

frames to store relative position and orientation data between model components.

Further development of anatomic coordinate system concepts have been established for

specific joints such as the knee146, although modifications have been suggested recently to account

for errors in flexion angles lower than 0o and higher than 90o.147 An in-depth technical description

of the joint coordinate system convention published by MacWilliams and Davis 35 years after the

Grood and Suntay paper equates the convention to a x-y-z Cardan angle sequence, enforcing

sequence dependency and orthogonality.148 Understanding common conventions for describing

motion in medically relevant contexts is essential for computational model utility.

58

Chapter 3

Parametric Finite Element Analysis of Intramedullary Nail Fixation of

Proximal Femur Fractures

Text in this chapter has been submitted to the Journal of Orthopaedic Research and is

pending review (invited for resubmission following revisions).

Authors: Scott M. Tucker, Hwa Bok Wee, Edward Fox, J. Spence Reid, Gregory S. Lewis

Abstract

Proximal femur fracture fixation with intramedullary nailing relies on stability at the

fracture site and integrity of the fixation construct to achieve union. The biomechanics that dictate

fracture site stability and implant stress depend on fracture type as well as implant features such as

nail length, nail diameter, presence of distal fixation screws, and material composition of the

implant. When deciding how to fix a fracture, surgeons have choices in these implant-related design

variables. This study models all combinations of a range of implant variables for nine standard

AO/OTA proximal femur fractures using finite element analysis. Under simulated maximum load

during gait, the maximum stress in the implant and screws as well as interfragmentary motions at

the fracture site in the axial and shear directions were computed. The results were separated by

fracture type to show the influence of each design variable on measured biomechanical outcomes.

Filling the reamed canal with the largest fitting nail diameter reduced axial and shear

interfragmentary motion for all fracture types. Nail length was less predictive of shear

interfragmentary motion for most simulated fracture types than other construct variables.

Furthermore, gapping at the fracture site predisposed the construct to higher implant stresses and

larger interfragmentary motions. Clinical Significance: Biomechanical outcomes from this

59

computational study can directly aid in surgical decision-making for optimizing hip fracture

fixation with intramedullary nailing.

Introduction

Surgical fracture fixation is achieved through the use of orthopaedic implants to stabilize

the fracture for bone healing.27,85 The fixation process involves reduction of bony fragments

followed by implant positioning and fixation. Unfortunately, the biomechanics of fracture fixation

can be complex, in part due to variations in bone quality, anatomy, and local loading conditions.

Furthermore, a surgeon’s toolkit includes multiple implants and fixation techniques which must be

narrowed to a single configuration for each case.86 Despite a general understanding that fracture

geometry and fixation construct influence the biomechanics essential for proper and timely healing,

fracture fixation construct selection remains a largely subjective topic among surgeons and is often

linked to surgical training experience.149

At present, most hip fractures are surgically stabilized using an intramedullary (IM) nail.

The surgeon selects nail type, length, and diameter, as well as whether or not to use distal locking

screw fixation. Though there may be multiple successful combinations for a given case, each

configuration has a relatively higher risk of failure when compared to a theoretically optimal

construct.150 In the case of the intramedullary nail fixation, clinical failures are reported in up to

14% of patients1 via, most commonly, fixation screw bending and fatigue,89 cut-out, and nail

failure.90–92 Excessive interfragmentary motion at the fracture site resulting from instability can

result in high strain and disrupt healing, leading to nonunion.151 However, especially for patients

with unstable fractures or compromised healing capacity, an optimized fixation construct can

reduce the time required to achieve union and mitigate the risk of implant failure and nonunion

60

events. Thus, there is a need for systematic evaluation of fixation constructs to improve the

estimated $13.7 billion financial burden of hip fracture management in the U.S.93

Computational simulation provides an opportunity to determine specific treatment

recommendations based on individual case characteristics.94 Previous work evaluating

computational biomechanics of IM femur nails has been almost exclusively limited to variations in

a single construct variable such as fracture type,117 bone canal reaming,79,121 implant

positioning,60,152 nail material properties,153,154 nail size,155 and fixation screw use.3,125 A recent

study investigated multiple IM nail design variables but only evaluated transverse fracture types.123

Furthermore, physiological muscle loads may influence construct biomechanics but are only

sometimes considered in finite element femur fracture models.156,157 Thus, it is imperative that IM

femur fixation nail design variables be modeled with a holistic approach to evaluate synergistic

effects of combinations of fracture type and construct variables on biomechanics.

To our knowledge, this study provides the most comprehensive investigation of IM nail

biomechanics for proximal femur fractures to date. Utilizing a novel parametric high-throughput

modeling and analysis pipeline, this study investigates the effects of hip fracture type, IM nail

diameter, IM nail length, IM nail material, and use of distal fixation screws in a finite element

model of the heel strike phase of gait on maximum implant stress and interfragmentary motion.

The results of this study can be utilized toward optimizing clinical implant decisions based on

simple fracture classification.

61

Materials and Methods

Bone and Fracture Model

Simulations were developed using a previously validated generic virtual femur model.158

The femur was modeled as a composite of homogeneous isotropic linear elastic materials: cortical

bone (elastic modulus 17GPa, Poisson’s ratio 0.3) and trabecular bone (elastic modulus 155MPa,

Poisson’s ratio 0.3). Planar fractures were cut into the femur model using Solidworks (Dassault

Systèmes, Waltham, MA). Simulated fracture patterns were modeled after the AO/OTA fracture

classification scheme88 (Figure 3-1) and were selected to include common pertrochanteric,

intertrochanteric, and subtrochanteric fracture types. Specifically, fracture types 31A-1.1, 2.1, 2.2,

3.1, 3.2, and 3.3 were modeled. Fractures 31A1.1 and 31A2.1 were modeled as perfectly reduced

as well as with a 5mm gap simulating comminution. Subtrochanteric fracture type 31A3.2 was also

modeled with a 10mm gap. Gap sizes were selected such that the major fracture fragments did not

make contact under the maximum applied load.

62

Implant, Reaming, and Construct Configuration

A cannulated femur nail was modeled in Solidworks based on geometry of a popular IM

nail (Synthes Trochanteric Femoral Nail). The helical blade and lag screw (modeled as cylinders)

as well as the 15mm diameter proximal nail region were present in all cases. However, clinically

relevant variations in distal nail diameter (10, 11, 12, and 13mm) and nail length (long 43.3cm and

short 26.9cm) were implemented. The nail was centered relative to the femoral isthmus with the

proximal entry point located just medial to the superior tip of the greater trochanter. All bone

models were reamed to a distal diameter of 13.5mm, creating a concentric gap between the nail and

bone ranging between 0.25mm (for the 13mm diameter nail) and 1.25mm (for the 10mm nail).

Additional implant construct variations were modeled by adjusting the material properties to those

of titanium alloy (elastic modulus 110GPa, Poisson’s ratio 0.3) or of stainless steel (elastic modulus

Figure 3-1: Simulated proximal femur fracture types (type 31A-X.X). Types 31A-1.1, 2.1, and

3.2 were additionally modeled with gaps that remained open under the applied load. Point pairs

used to calculate interfragmentary motions are shown.

63

195 GPa, Poisson’s ratio 0.3) and by removing the two 5mm diameter distal fixation locking

screws. Fixation screw holes were present in the bone for both the long and short nail in all

simulations, even when fixation screws were not used (Figure 3-2). Model input file generation

was automated using custom Matlab (MathWorks, Natick, MA) code (Table 3-1).

Loading and Boundary Conditions

Finite element analysis was conducted using Abaqus (Dassault Systèmes, Waltham, MA)

software. Applied loads and boundary conditions were modeled for an 85.7kg person consistent

with previous FE simulation and mechanical testing experiments117 using a previously described

femur coordinate system.159 Briefly, a 2000N compressive load was applied at the center of the

femoral head oriented with a 13° abduction angle and directed 8° posteriorly from the long axis of

the femur to represent the maximum hip reaction force during human gait.100 The center of the

femoral head was constrained in translations orthogonal to the load vector. Distally, all translational

degrees of freedom as well as rotation about the epicondylar (knee flexion) axis were constrained

Table 3-1: Fracture fixation construct configurations modeled. All combinations of depicted

design variables were simulated.

Design Variable Options Cumulative

Combinations

Fracture Type/Gap

Status

31A-1.1, 2.1, 2.1, 2.2, 3.1, 3.2, 3.3,

and gapped fractures 31A-1.1, 2.1,

3.2

9

Nail Length Long, Short 18

Nail Diameter (mm) 10, 11, 12, 13 72

Distal Fixation Yes, No 144

Material Stainless Steel, Titanium 288

64

at a pivot point 23mm medial to the shaft axis in the medial condyle160 (Figure 3-2). Femur

internal/external rotation and rotation in the frontal plane were left unconstrained.

Based on pilot study simulations that demonstrated effects associated with ignoring muscle

forces, simulations included physiological muscle loads. Heller et al. determined a simplified

muscle-loading scheme for walking that maintains physiological hip-joint loading.98 Specifically,

body weight-scaled contributions from the gluteus medius, minimus, and maximus, vastus lateralis,

and the proximal and distal part of the tensor fascia latae were simulated. Muscle loads were applied

to single nodes translated onto the geometric femur model using the closest proximity nodes to the

muscle point-of-action coordinates described by Heller et al.

Figure 3-2: Two design configurations under maximum applied load with the A32 (top) and A11

(bottom) fracture types demonstrating a long, 10mm diameter nail with distal fixation screws (top)

and a short, 13mm diameter nail without distal fixation screws (bottom). Applied loads and

boundary conditions at the center of the femoral head and implant meshes are shown. A sphere of

bone is visible in the medial femoral condyle to indicate where femoral boundary conditions are

applied. All bone models were pre-drilled for both long and short nail distal fixation screws,

regardless of configuration.

65

Finite Element Simulation Parameters

Hard contact with Coulomb friction was simulated between IM nail and bone (µ=0.42), IM

nail and fixation screws (µ=0.20), and bony fragments at the fracture site (µ=0.46) based on

literature-reported values.112 Tie constraints were implemented between fixation screws and bone

to simulate the effect of screw threads and between the simplified cylindrical proximal head screw

and proximal trabecular bone. Quadratic tetrahedral elements were used to mesh all components

and totaled around 170,000 elements for each simulation. Mesh convergence analysis was

conducted by increasing the mesh to approximately 250,000, 300,000, and 400,000 elements.

Maximum implant stress differed by no more than 16MPa, axial motion differed by 0.17mm at

most, and shear interfragmentary motion differed by 0.07mm at most in convergence trials.

Validation, Outcome Measures, and Statistical Methods

The model validation was supported through comparison of global axial stiffness to

literature reported values from a study with very similar loads and boundary conditions, and small

differences in implant geometry.117 For pertrochanteric and subtrochanteric AO/OTA fracture types

31A1.1 and 31A3.2 the computational model resulted in a global axial stiffness 16% and 15%

stiffer than mechanical testing results, respectively.

The computational model outputs included maximum implant vonMises stress for the nail

and superior distal locking screw as well as interfragmentary motion. Interfragmentary motion was

calculated by averaging absolute displacements between 4 point pairs distributed about the fracture

plane in the anterior, posterior, medial, and lateral directions (Figure 3-1), a method adapted from

the literature.161 These displacements were transformed into axial and shear motions with respect

to the fracture type.

66

Statistical analysis was performed with JMP software (SAS, Cary, NC) using standard least

squares multiple linear regression for each fracture type with four design variables as regressors

(nail diameter, nail length, nail material, and distal screw fixation). Statistical significance was

determined at p<0.05.

Results

Individual simulation outcomes are shown in Figures 3-3a-b to demonstrate trends for

each design variable. Results for multiple linear regression for each outcome across all models

grouped by fracture type are presented in Table 3-2. Outcomes for configurations with stainless

steel nail material properties are omitted from the figure (available in supplemental figures) but

share similar trends as the shown configurations with titanium nail material properties.

Gapped fractures generally showed larger maximum implant stresses, as well as axial and

shear interfragmentary motions compared to their reduced counterparts. Stable fracture patterns

such as reduced 31A1.1, 31A2.1, and 31A3.1 showed smaller peak stresses and interfragmentary

motions than the gapped fracture patterns.

Increasing nail diameter decreased maximum implant stress and both axial and shear

interfragmentary motion, or had minimal effects in all simulated cases. In the A3.1, A3.2, and A3.3

fracture types adding distal fixation screws generally decreased axial and shear interfragmentary

motion, but increased maximum implant stresses due to the kinematic contact constraints imposed

by the screws on the nail. These effects were especially substantial in the A32 Gap fracture type.

Nail length had variable effects on outcomes which were dependent on fracture type.

From the regression analysis, nail diameter was statistically significant in predicting

maximum implant stress for the pertrochanteric and subtrochanteric reduced fractures but not for

the intertrochanteric fractures. Conversely, nail length was only statistically significant in

67

predicting implant stresses for the intertrochanteric fractures and was not a significant predictor of

maximum stress in the pertrochanteric and subtrochanteric fractures. Screw fixation was nearly

always a significant predictor of all outcome variables.

68

Figure 3-3a: Simulation outcomes for titanium implant material configurations for reduced

fractures. Maximum screw stress results are shown in the superior fixation screw for cases that

included fixation screws.

69

Figure 3-3b: Simulation outcomes for titanium implant material configurations for gapped

fractures. Maximum screw stress results are shown in the superior fixation screw for cases that

included fixation screws. Note vertical axis scales have a larger range than in Figure 3-3a.

70

Table 3-2: Results of multiple linear regression of all simulations for maximum implant stress,

axial interfragmentary motion, and shear interfragmentary motion grouped by fracture type. Design

variables with statistically significant predictive value (p<0.05) are shaded green. Average results

± standard deviation for each outcome variable are presented in the rightmost column.

Maximum Implant Stress

Regression

Fit (r2)

Nail

Diameter

Nail

Length

Nail

Material

Screw

Fixation

Average

(MPa)

31A1.1 0.53 503 ± 183

31A2.1 0.72 782 ± 320

31A2.2 0.71 830 ± 292

31A3.1 0.92 710 ± 348

31A3.2 0.92 894 ± 477

31A3.3 0.84 1013 ± 504

31A1.1 Gap 0.51 1654 ± 56

31A2.1 Gap 0.70 1364 ± 208

31A3.2 Gap 0.96 1346 ± 655

Axial Interfragmentary Motion

Regression

Fit (r2)

Nail

Diameter

Nail

Length

Nail

Material

Screw

Fixation

Average

(mm)

31A1.1 0.97 0.3 ± 0.0

31A2.1 0.96 1.3 ± 0.4

31A2.2 0.96 1.6 ± 0.3

31A3.1 0.86 0.9 ± 0.5

31A3.2 0.81 1.0 ± 0.6

31A3.3 0.91 1.2 ± 0.5

31A1.1 Gap 0.67 1.3 ± 0.3

31A2.1 Gap 0.93 1.8 ± 0.5

31A3.2 Gap 0.66 2.8 ± 2.8

Shear Interfragmentary Motion

Regression

Fit (r2)

Nail

Diameter

Nail

Length

Nail

Material

Screw

Fixation

Average

(mm)

31A1.1 0.88 0.4 ± 0.0

31A2.1 0.96 0.8 ± 0.3

31A2.2 0.96 1.4 ± 0.3

31A3.1 0.95 1.2 ± 0.4

31A3.2 0.80 1.5 ± 0.7

31A3.3 0.91 2.2 ± 0.6

31A1.1 Gap 0.96 1.3 ± 0.2

31A2.1 Gap 0.92 1.2 ± 0.6

31A3.2 Gap 0.80 6.0 ± 5.2

71

Discussion

To our knowledge, this study provides the most comprehensive investigation of IM nail

biomechanics for proximal femur fracture to date. This study demonstrates which implant

parameters are most important in determining construct biomechanics, and how these influences

vary among nine standardized fracture types. For some fractures such as 31A11, 31A11 Gap, and

31A22 Gap, biomechanics appear predetermined and under little control by the surgical construct.

However in the other fractures, certain decisions play a critical role in determining implant stresses

and interfragmentary motion (Figures 3-3a-b and Table 3-2).

The results suggest that nail diameter is an important predictor of both axial and shear

interfragmentary motion across all fracture types. Combining this with the inverse trends between

nail diameter and interfragmentary motions, the data suggest that larger diameter nails reduce

interfragmentary motions in both the shear and axial directions regardless of fracture type.

Furthermore, nearly all data lines in Figures 3-3a-b show downward slopes with increasing nail

diameter, demonstrating that increasing nail diameter tends to reduce stress in the implant, reduce

interfragmentary motions at the fracture site, as well as reduce stress in the fixation screws, when

present.

Excessive shear motion at a fracture site is thought to disrupt healing through rupture of

nascent capillaries that attempt to bridge the fracture151,162 and is important to mitigate. Nail length

was shown to be a statistically insignificant predictor of shear motion at the fracture site in all but

the 31A1.1 and 31A3.2 fracture types. This suggests that short nails can potentially be used without

deleterious effect on shear motion at the fracture site, an important consideration especially in

clinical cases where a long nail could interfere with distal hardware such as a total knee

arthroplasty. Furthermore, the 31A1.1 fracture type in which nail length was a significant predictor

is a stable fracture type that exhibited less than 1mm average shear motion in all cases, indicating

72

that optimization for shear motion has only a small effect in the 31A1.1 fracture type. In fact,

adjusting nail length had only small effects on axial interfragmentary motion (the vertical gap

between blue and orange lines in Figure 3-3a-b) in all cases which nearly always diminished as

nail diameter increased.

Distal screw fixation is an interesting design variable because of the competing effects it

had on maximum stress and interfragmentary motion. Specifically, adding the fixation screws

increased maximum implant stress for all fracture types but reduced interfragmentary motion in

both axial and shear directions in all cases except for shear motion in subtrochanteric fracture

31A3.1. Although our models suggest that screw fixation was a significant predictor of both axial

and shear interfragmentary motion, the differences in motion with and without screw fixation were

small except for in subtrochanteric fracture types. Furthermore, clinical data from 333 patients

indicated that stable pertrochanteric and intertrochanteric fractures can be treated with short

intramedullary nails without distal locking screws without increasing mortality nor hospital length

of stay, supporting the nail length and screw fixation findings of our model.126

The importance of nail diameter should be considered also in context of the gap between

the implant and the intramedullary canal, since prior work indicates that increasing canal fill

increases fracture site stability 163. Because all bones were reamed for a 13.5mm diameter canal,

the effect of nail diameter on stabilizing the fracture could depend on the gap between implant and

endosteal canal rather than implant diameter alone. Our data suggest at least that emphasis be

placed on filling the reamed canal as much as possible and may also indicate, pending further study,

that larger nail diameter itself reduces interfragmentary motions. A previous review of clinical

studies indicates that, by unknown mechanisms, union is more likely to occur in reamed cases than

in unreamed despite disruption in endosteal vascularity.164 It is thought clinically that reaming may

create a diffuse inflammatory response, or distribute bone debris into the fracture site and augment

union. Perhaps the unexplained healing mechanism is also linked to kinematics at the fracture site

73

which are predicted, in part, by nail diameter across all fracture types. Further investigation can

isolate effects of increasing nail diameter from filling the endosteal canal to provide further surgical

guidance on canal reaming.

Although nail failure by either yield or fatigue is reported in fewer than 2-5% of clinical

cases,92,165 the above analysis provides useful information on how fracture type and implant

construct influence the maximum implant stress. Specifically in cases where a clinician suspects

the patient may be slow to heal a fracture, such as with tobacco smokers166 and diabetics,167 the

yield strength and fatigue life of the implant can become factors in mitigating fixation failure under

the cyclic loads of gait. The location of maximum vonMises stress was at the superior aspect of the

junction between the cephalomedullary screw and the nail, consistent with previous

studies.55,116,117,122 The data available in Figures 3-3a-b and Table 3-2 can be used to optimize the

fixation construct to protect against high stress in the implant. Generally, increasing nail diameter

and omitting distal fixation screws leads to lower maximum stress in the implant. Observation of

simulation kinematics as load is increased to 2000N shows that addition of fixation screws limits

rotation and translation of the nail within the endosteal canal. The kinematic contact constraints

applied by the screws onto the nail result in a stiffer construct which concentrates stress on the

proximal nail more than when the fixation screws are omitted. The problem of IM nail fatigue is

quite complex. Ideally, a fracture construct that minimizes stress in the implant while optimizing

interfragmentary strain will result in rapid union of the fracture and minimal cycles on the implant.

Optimizing this combination for each patient, is the goal of fracture surgery and should be the

guiding principle.

Severely unstable 31A3.2 Gap fracture shape cases are not treated clinically without distal

fixation screws. In 31A3.2 simulations that omitted fixation screws, the translational boundary

conditions at the point of applied load artificially constrained motion of the proximal fragment.

Specifically, without the proximal boundary condition, rotation of the proximal fragment about the

74

long axis of the femur would only have been constrained by friction between the nail and the

endosteal canal, prohibiting simulation convergence. Therefore, the results reported for

interfragmentary motion in 31A3.2 Gap fracture models that do not include distal fixation screws

are underestimates. However, simulations confirm that addition of fixation screws in such cases

drastically reduces all interfragmentary motion, necessitating distal fixation with the 31A3.2 Gap

fracture type.

The computational nature of finite element studies requires validation. In direct comparison

our simulations were about 15% stiffer than literature-reported values based on mechanical testing,

as mentioned above in the methods section. Because of this we include additional comparisons of

vonMises stress data to previously validated studies. Eberle et al. report maximum nail stresses of

749MPa for the 31-A3.1 fracture with simplified muscle loading and 2367MPa for the 31-A3.3

fracture.122 The 11mm diameter, long, titanium alloy Gamma3 implant used with distal fixation

screws in the Eberle study as well as the applied muscle loads are not identical to those in our study,

however, our reported maximum stresses (1027MPa for the 31-A3.1 fracture and 1334MPa for the

31-A3.3 fracture) fall between their reported values.

Our study has several limitations. Although the AO/OTA fracture classification scheme

has utility in identifying similarities among common femur fracture patterns, the scheme itself is a

simplification of the complex 3D geometry of femur fractures. Our results indicate dependence of

outcomes on fracture type, and differences between simplified and complex fracture geometry

should be investigated in future work. However, we suggest that while the exact magnitudes

reported for our outcome measures would likely change with more accurate representations of

fracture type, the relative effects of design variable changes would likely persist. Similarly, the use

of a single femur geometry with a homogeneous material distribution for both cortical and

trabecular bone is a simplification that encourages analysis of relative effects rather than absolute

75

effects. Properly accounting for bone geometry and material heterogeneity may require use of

emerging statistical shape models of the femur.

Common to most other finite element modeling studies, our model used a single static load

representing heel strike in the gait cycle under full weightbearing. Clinically, patients are

commonly prescribed limited weightbearing following surgery. An additional limitation is that all

cases, regardless of fracture type and implant diameter, were reamed to a 13.5mm diameter canal

that was perfectly concentric with the implanted nail. This resulted in a perfect ream such that the

IM nails always began each simulation without distal endosteal contact. However, the friction and

contact formulations included in the model allowed for endosteal gap closure and normal and shear

reaction forces at sites of contact. Furthermore, our simulations assess fracture stability at ‘time

zero’ where no healing has occurred, thus modeling a worst-case scenario for biomechanics.

Chapter 4

Return to Function After Intramedullary Nail Proximal Femur Fracture

Fixation: Effects of Fixation Construct and Weightbearing on Shear Motion

at the Fracture Site

Abstract

Successful union following fracture fixation surgery is partially dependent on

biomechanics at the fracture site. The biomechanics are influenced by the stability of the fracture

fixation construct, specifically in how it resists shear motion, as well as the loads that pass across

the construct as the patient returns to functional activities. Orthopaedic surgeons attempt to

optimize these biomechanics via implant selection as well as the ability to recommend specific

loadbearing limits for the patient postoperatively. In this study we utilize finite element simulations

of 3 gapped or comminuted proximal femur fractures fixed by intramedullary nailing under gait

loads to explore the effects of construct selection on shear motion at the fracture site at multiple

levels of loadbearing. Construct variables include nail diameter, nail length, and presence of distal

fixation screws. We show the loadbearing percentage that maintains shear motions at the fracture

site below a literature-reported threshold for each construct. Specifically, the data show that full

weightbearing achieves the shear motion threshold for short nails with distal fixation screws for all

tested nail diameters in a pertrochanteric and an intertrochanteric fracture type but not for a

subtrochanteric fracture. Increasing nail diameter increases the safe loadbearing limit for nearly all

tested configurations, while removing distal fixation screws has mixed results depending on if the

nail is short or long. Clinical Significance: Biomechanical outcomes from this computational study

can build intuition about how construct selection and loadbearing prescriptions influence the

amount of shear motion at a proximal femur fracture fixed by an intramedullary nail.

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Introduction

The primary goal of surgical fixation of fractures is to stabilize the bony fragments to

promote bone healing. However, surgeons have to make many choices regarding the fixation

construct from implant type to implant fixation which will influence biomechanics at the fracture

site. Furthermore, surgeons commonly recommend limited weightbearing following fracture

fixation to promote healing and reduce the risk of construct failure. To this end, it is important to

understand the relative stability of various fracture fixation constructs and how surgical design

variables combined with patient weightbearing levels influence this stability.

Secondary fracture repair is characterized by bridging of a fracture gap by progressively

stiffening healing tissues. While these tissues form, they must endure the local mechanical and

chemical environment. Fracture repair tissues are thought to have a strain tolerance beyond which

their vascular supply is too disrupted to promote normal biological healing responses.9 Gapped

fractures predispose the bone fragments to excessive motion which can delay the healing process.

An important metric has been developed that shear motion of 1.5mm significantly delayed healing

in an ovine diaphyseal tibia fracture model.26

This unsafe limit for shear motion can be combined with recent advances in computational

modeling technology to understand the relative safety of combinations of fixation construct

variables and prescribed weightbearing in terms of shear motion at the fracture site. Most proximal

femur fractures, for example, are fixed with an antegrade intramedullary (IM) nail. These implants

can vary in shape, length, diameter, and material stiffness, and also offer multiple screw fixation

strategies. Using a previously developed computational finite element model of IM nailing in

proximal femur fractures (Chapter 3), we compare a wide array of combinations of common IM

nail design variables under simulated gait loading to the preestablished shear motion limit to assess

the relative weightbearing safety limit for each construct. The findings of this study can be used to

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build clinical intuition for how fracture fixation construct design variables influence shear motion

at gapped fracture sites, advance implant design, and customize weightbearing strategies based on

fixation features.

Materials and Methods

The 48 titanium nail simulations for gapped fracture types A11, A21, and A32 from

Chapter 3 are used in this section. However, rather than analyzing the results at the point of

maximum applied load, these data focus on the path of deformation as the applied load is ramped

up. Specifically, data were collected at 200N intervals between 0-2,000N of applied load. Because

of convergence considerations during the numerical solver each load level is measured within

±50N. The average shear interfragmentary motion of four pairs of points evenly spaced around the

fracture site was then calculated for each load level. The resulting shear motions were compared to

the literature-established 1.5mm shear motion limit and the maximum weightbearing percentile that

maintains shear interfragmentary motion below this limit is reported.

Experimental groups are defined by configuration name: short nail (S) vs. long nail (L) and

with screws (+) vs. without (-). It is worth repeating from Chapter 3 that the gap sizes were designed

such that they do not close under the maximum applied load of 2,000N. Specifically, a gap size of

5mm was used for the A11 and A21 fracture types while the A32 type had a 10mm gap (Figure 4-

2). The applied load and muscle forces were designed to represent the maximum load at the hip

during gait for an 85.7kg individual in the 100% load level.

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Figure 4-1: IM nails included in this study ranged from 10mm in diameter (left) up to 13mm and

nail length was modeled as either short (26.9cm) or long (43.3cm)

80

Results

The S+ configuration consistently limited mean shear motion to less than 1.5mm at the

same or higher load level as other configurations for all fracture types and nail diameters (Table 4-

1). For fracture types A11 Gap and A21 Gap, the S+ group was within the shear motion threshold

at full weightbearing for all nail diameters. The L- configuration appears similar to the S+

Figure 4-2: Gapped fractures modeled for analysis at intermediate load levels. Of note is the

difference in fracture gap size between the subtrohanteric 3.2 type (10mm) as opposed to the others

(5mm). Black circles represent point pairs at which interfragmentary motions are determined.

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configuration, with only small differences in weightbearing limit in the A11 and A32 fracture types.

Additionally, the L+ configuration shares similar trends with the S- configuration.

Implant diameter has a positive correlation with maximum loadbearing limit across all

configurations and fracture types. However, it is less noticeable in the A32 gapped fracture, in

which the safe loadbearing limit is often below the 25% cutoff. The A32 gapped fracture is unstable,

in general, with only 4 of the 16 design constructs achieving a loadbearing limit that maintains

mean shear motion below 1.5mm. Neither nail length nor screw fixation show independent trends

with maintaining below 1.5mm shear motion across fracture types.

Table 4-1: Loadbearing percentiles (shaded) that did not induce greater than 1.5mm of average shear

interfragmentary motion. Data are separated by fracture type, nail length, nail diameter, and presence

or absence of distal screw fixation. Blank space indicates that the shear motion cutoff is exceeded

for a configuration at the corresponding loadbearing level.

A11 Gap Fracture

Load

Level

Short Nail, No

Screws (S-)

Short Nail, Screws

(S+)

Long Nail, No

Screws (L-)

Long Nail, Screws

(L+)

100%

75%

50%

25%

Diameter

(mm)

10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13

A21 Gap Fracture

100%

75%

50%

25%

Diameter

(mm)

10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13

A32 Gap Fracture

100%

75%

50%

25%

Diameter

(mm)

10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13

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Discussion

To our knowledge this is the first finite element study evaluating IM nail shear motion in

the context of partial weightbearing. This study demonstrates the load level at which mean shear

motion at the fracture site remains below a cutoff which was found to impact healing. Implant

diameter has a clear relationship with the safe load level for all tested fracture types, although

fracture A32 exceeds the shear motion threshold in most cases. Nail length and screw fixation

appear to have a more complex relationship with the safe load level and seem to be dependent on

each other for their effects.

Specifically, the S+ and L- are the most shear motion-stabilized constructs for higher nail

diameters at 100% load bearing in all 3 fracture types. In the A11 and A21 fracture types. It might

be expected that constructs matched in nail length or in screw fixation would behave similarly to

each other but actually the contrary is true in this data. The S+ scenario resists shear motion well

across all nail diameters at high loads because the nail is well-constrained by the fixation screws,

the bending moment on the nail is low due to its short length, and the resulting construct is stiff.

Similarly, the L- scenario enables the long nail to toggle within the medullary canal, thus enabling

axial displacement which starts to reduce the fracture gap and, therefore, the shear interfragmentary

motion. However, toggle in the S- case due to the lack of screw fixation results in high

displacements of the proximal fragment which are not so well compensated for by axial

displacement at the fracture site. The L+ case does not enable nail toggle but the moment arm is

long due to the nail length and thus bending deformation of the nail results in high shear motions

at the fracture site.

In fact, the complex interplay between nail length and screw fixation could explain why,

in Chapter 3, nail length was found to be an insignificant predictor of shear motion at the fracture

site. Perhaps the effect of nail length on interfragmentary shear motion is also dependent on screw

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fixation and should not be considered separately. Previous clinical data indicate minimal

complications when stable femoral and tibial fractures were fixed using intramedullary nails

without interlocking, although the analysis did not consider nail length.168 Another study indicated

that short nails without distal interlocking demonstrated no increase in mortality nor hospital length

of stay when used to fix stable pertrochanteric and intertrochanteric fractures.126 It is likely that the

inherent stability of the fractures evaluated played a role in these outcomes and that similarly treated

unstable fracture types could behave differently.

In the literature, most findings indicate that shear motion delays or prohibits

healing.26,27,151,169 Although some studies have found that shear motion promotes healing,170,171

arguments have been made to suggest improperly controlled and measured results among studies

that found healing enhanced healing.172 A recent clinical study found no difference in outcomes of

healing and time to union in nail-fixed simple tibial shaft fractures but the non-gapped nature of

these fractures is a likely source of stability.173 Controversy aside, it is generally agreed that some

shear motion may be tolerated (or even beneficial) but also that there is an upper limit of shear

motion beyond which fracture healing is negatively impacted.

A limitation of this study is that the applied muscle loads are linearly scaled with the

applied reaction force at the hip. Due to the dynamic nature of these loads during gait it is difficult

to obtain an accurate representation of both the hip joint contact force and the applied muscle loads

under limited weightbearing. However, the applied muscle forces contribute to the overall hip joint

reaction force and it may be reasonable to assume they scale linearly together under limited

weightbearing.

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Chapter 5

Examples of Precision Medicine in Orthopaedics

Precision medicine is a growing focus within the medical community which encourages a

detailed examination of individual clinical case details to inform treatment decisions, rather than

the formerly popular one-size-fits-all approach. Advances in technology have facilitated deeper

understanding of disease, improvements in diagnostic capabilities, and knowledge to potentially

treat two patients with the same condition differently, because their cases may be distinct. As

precision medicine continues to gain traction it creates a need to better understand and optimize

fracture fixation. Surgical plans can be optimized based on modeling results with a goal of reducing

failure and improving patient outcomes.

Precision Finite Element Modeling for Intramedullary Nail Femur Fracture Fixation

As mentioned previously, many assumptions and simplifications are employed to facilitate

finite element fracture model development and computation on a reasonable timescale. However,

recent advances in computational power and resource allocation have enabled multiple levels of

specificity in mechanical simulations, including bone geometry, fracture shape, and material

properties.95,96 However, there is not yet a process for taking patient imaging data and generating

model outputs on a clinically relevant timescale. Simplified computational models can be created

with relative ease, whereas precision modeling requires significant time and computational

resource allocation. There are various degrees of precision modeling that may or may not affect

clinically relevant biomechanical measures. Therefore, the sensitivity of model outcomes to

precision modeling was evaluated in a case study of one model.

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Institutional Review Board approval was obtained to collect deidentified x-ray images from

patients with proximal femur fractures. A case was selected which had only 1 proximal femur

fracture line producing 2 bony fragments, similar to a fracture modeled in Chapter 3. Specifically,

the fracture type in the selected case was classified as an A21 fracture according to the AO/OTA

classification scheme.88 The generic bone model used for model development in Chapters 3 and 4

was again used but the model was initially unfractured. The 2D patient x-radiograph was

superimposed over the 3D generic bone model such that the bony cortices aligned (Figure 5-1).

The fracture line was then identified on the distal fragment from the x-ray and was used to create a

fracture in the 3D bone model.

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Although the patient’s fracture was not perfectly recapitulated with a straight cut,

reconstruction of the same patient’s CT scan into a solid model and comparison to the cut generic

bone demonstrates good agreement in shape (Figure 5-2).

Figure 5-1: Patient fracture x-radiograph (left) superimposed over generic 3D bone model (right).

The fracture line at the superior aspect of the distal fragment is highlighted with a spline which was

used to create the fracture.

87

The patient-specific fracture model was then reamed to accommodate an IM nail and a

long, 13mm diameter titanium nail was implanted with distal fixation screws present. The model

was then run under the same simulation conditions as the previous generic models. The results from

the patient-specific fracture model were then compared to the A22 fracture simulation from the

generic modeling library in Chapter 3 with the same construct variables. Although interfragmentary

motions and global stiffnesses were very similar between the two simulations, the patient specific

model showed a 57.9% decrease in maximum nail stress over the generic model (228.2MPa vs

541.9MPa).

The drastic difference in maximum stress between the patient-specific fracture model and

the generic raises some interesting points. First, generic modeling is perhaps limited in scope to

discuss relative trends in design variables rather than specific magnitudes. However, there are still

multiple levels of patient specificity lacking from the patient specific fracture model. Specifically,

full bone geometry, customized applied loads that scale with patient body weight and activity level,

Figure 5-2: Solid model reconstructed from 3D CT data (left) shown as a gold standard alongside

patient-specific fracture from 2D x-ray alignment (right) demonstrating good agreement in fracture

shape. Reconstruction was graciously completed by medical student Marcus Erdman.

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and nonhomogeneous bone material properties that match the patient’s bone mineral density are

examples of how model fidelity can be further enhanced. Second, perhaps the AO/OTA fracture

classification scheme could benefit from further parsing the fracture types. There could be non-

obvious differences in the shape of the patient specific fracture that drive fixation construct

biomechanics, along which a functional classification could be warranted. Further development of

patient specific models, including varying levels of patient specificity, could help identify which

levels of specificity are the most important to model.

Another approach for increasing the patient specificity of a computational model is called

statistical shape modeling.131 In this approach a parametric model of the femur is informed by a

large set of virtually reconstructed patient images such that individual patient demographics can be

used to predict specific femur shapes. A detailed description of this approach as well as a list of

potential applications is described by Heimann and Meinzer in a 2009 review article.174

Unfortunately, statistical shape models estimating fractured femur shapes are not currently

available but may be developed from intact femur statistical shape models.

Custom 3D Printed Implant Design and Modeling for Pediatric Orthopaedic Oncology

The following individuals contributed to work in this section: Scott Tucker, Maryam

Tilton, Ali Elakkari, Alex Preniczky, Guha Manogharan, Edward Fox, Gregory Lewis.

Due to the limitations of available implant hardware, current standards of care for pediatric

orthopaedic oncology reconstruction following bone resection often remove nearby articular joints.

Additive manufacturing, also known as 3D printing, enables rapid, cost-effective production of

custom implants that can be designed with porous features unattainable with traditional

manufacturing methods. Furthermore, personalized 3D printed constructs can improve bone-

implant fixation and be articular-sparing to preserve native, healthy anatomy. In this retrospective

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IRB-approved study, we designed pediatric patient-specific implants based on medical imaging

data for proximal humerus, proximal tibia, midshaft femur, and distal femur osteosarcomas, and

fabricated the implants via electron beam melting additive manufacturing with Ti-6Al-4V powder.

Pediatric oncology patients were identified from our institution. Cases involving proximal

humerus, proximal tibia, midshaft femur, and distal femur were selected and MRI data were

obtained. Bones were reconstructed and rendered as solid models (Mimics software, Materialise).

Virtual resection surgery was performed (SolidWorks software, Dassault Systemes) with guidance

from an orthopaedic musculoskeletal oncology surgeon (Figure 5-3). Implants were designed to fill

post-surgical defects, and lattice structures were designed for each implant (ElementPro software,

nTopology). Specific attention was given to fixation points between implant and bone during the

design for 3D printing workflow using biocompatible titanium alloy. Finite element analysis

(Abaqus software, Dassault Systemes) was used to predict locations and magnitudes of maximum

von mises and principal stress. Loads and boundary conditions were specific to anatomic location

and based on well-established literature.102

90

Novel articular and growth plate-sparing implant designs were designed as alternatives to

joint- sacrificing endoprosthetic reconstruction following tumor resection. The proximal tibia and

distal femur implants shown (Figure 5-4) combine a non-stochastic lattice structure to fill the region

of resected bone, a stem for stabilization and fixation, and a boss for screw fixation to the spared

articular surface. The resulting designs have been 3D printed out of Ti-6Al-4V alloy for future

mechanical testing. Finite element analysis of the proximal tibia implant and lattice structure under

the maximum anticipated loads during gait demonstrated a maximum implant stress of 11.6MPa,

compared to literature-reported fatigue strength values of 200-250MPa at 107 cycles for electron

beam melted Ti-6Al-4V alloy.175

Figure 5-3: Tumor volume visualization for the proximal tibia case with segmented medical image

(left) and resulting 3D reconstruction (right). Tumor is highlighted by the red circle.

91

Thus, four unique custom implants have been designed for different applications in joint-

sparing tumor removal surgery in different anatomical regions. Custom implant design, taking

advantage of unique capabilities of 3D printing, can match defect geometry, improve implant

fixation, and provide porous scaffolds that likely promote bone integration while supporting

physiological loads and restoring function (Figure 5-5). Furthermore, extrapolation of the finite

element analysis stress data can be used to predict the fatigue life of the implant, although this

would likely be affected by any osteointegration that may occur as healing progresses.

Figure 5-4: Workflow for custom implant design for distal femur and proximal tibia osteosarcomas.

Patient imaging data (A, G) is reconstructed into a solid model with virtual tumor removal (B, H)

and an implant is designed to fill the bone defect (C, I). Implant fit is then assessed (D, J). Finite

element simulation stress results of implant mechanical loading from low (blue) to high (red) under

compressive loads (E, K). Additively manufactured Ti-6Al-4V implants (F, L).

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With a well-established workflow, custom 3D printed implants can be designed and

manufactured on a shorter timescale than available through industry, can preserve healthy anatomy,

and can potentially promote osteointegration with porous architecture.

Figure 5-5: Detailed views of the proximal tibia articular-sparing implant design demonstrating

porous architecture and cortical contour.

Chapter 6

Conclusions, Discussion, and Future Work

The FE modeling work presented in this dissertation represents, to my knowledge, the most

comprehensive study of IM femur nail design variables to-date. The results presented have direct

clinical value in both educational and presurgical planning domains. Allegorical clinical data can

be replaced and surpassed by data from computational biomechanics studies such as those in this

work. Specifically, this work suggests in Chapter 3 that larger IM nail diameters reduce the implant

maximum stress and provide more stability over smaller nail diameters. Also shown is that nail

length is a poor independent predictor of shear motion at the fracture site for nearly all simulated

fracture shapes. Furthermore, in the results section of Chapter 4, I demonstrate that some design

variables have synergistic combination effects (the long nail without screws behaves similarly to

the short nail with screws in terms of shear stability). The value of these modeling efforts may

extend beyond surgery as the suggested weightbearing outcomes in Chapter 4 provide rationale for

prescribing postsurgical activity levels based on individual fracture and fixation construct

conditions. I also provide a brief example in Chapter 5 which demonstrates that introducing patient

specificity to generic modeling strategies does impact the results on a clinically relevant scale,

creating a call to action for development of model personalization strategies. Additionally, the near

60% reduction in maximum implant stress between corresponding generic fracture and patient

specific fracture models indicates that perhaps a more robust fracture classification scheme based

on functional biomechanics is needed. In addition to directly answering the research questions

asked in each chapter, this work in sum is aimed at setting a foundation upon which clinical tools

can be developed for both surgical resident education and presurgical planning purposes.

94

One benefit of computational studies is the ability to repeat the simulations under near-

identical conditions and with an alteration in only one design feature. A major advantage of this

capability is that computational models lend themselves well to parametric analyses and fully

exploring a design space. However, this feature of computational models complicates statistical

analysis because the design space is perfectly sampled and there is no variability in simulation

results. Natural variability in data enables most statistical analyses because of the normal

distribution. However, the natural variability in experimental data and the low sample sizes tested

in most mechanical testing experiments makes it difficult to interpret a validation study which

compares noisy experimental data with clean computational data. One often gets the feeling of

chasing one’s own tail when considering the cumulative errors in both mechanical testing and

computational experiments. In fact, computational model repeatability, validation, and verification

were the foci of a 90-minute panel discussion at the 2019 annual meeting of the Orthopaedic

Research Society in Austin, Texas. General consensus was reached that the broad research

community struggles with committing appropriate amounts of time and resources to repeatability,

validation, and verification in our ‘publish or perish’ research environment. However, rigor must

be taken to ensure that the results being reported are the most accurate results available as well as

provide some assessment of systematic errors and how they may influence results.

Initial FE model development for this work presented multiple challenges. Specifically,

due to the complex contact modeled between the fracture fragments, the endosteal canal, the nail,

and the screws, numerical convergence was not often reached. The limits for convergence used in

this work are the ABAQUS default values (5N for force and 10Nm for moment) and were

maintained to ensure accuracy of the Newton Raphson approximation method. However, an

alternative tool called ‘Contact Controls’ in ABAQUS was activated with a coefficient of 0.00001.

Contact controls enables force dampening during conditions when a contact condition opens

(bodies separate from each other) or closes (bodies come into contact with each other). This is

95

useful because the stiffness response of the system to applied load often changes when a contact

condition is altered. Although the analytical load vs displacement curve for that system would have

a sharp vertex when a contact condition changes, the damping enforced by contact controls will

smooth that vertex and help the solver locate an approximation that falls within the aforementioned

equilibrium tolerances (Figure 6-1). Errors introduced by this method can be measured using

energy methods. Specifically, one can compare the dissipated energy (the energy in the system lost

to nonconservative forces such as damping) to the total energy in the system. So long as the energy

dissipated was sufficiently small relative to the total energy (< 2%), errors introduced by damping

were deemed acceptable in this work.

Extensions of this work should expand the simulation library to include more implant

designs such as a retrograde nail and more fracture types such as distal and diaphyseal fractures.

An interesting point of discussion raised in Chapter 3 is whether the stabilizing and stress-reducing

Figure 6-1: Example system load-displacement response shown (green). The piecewise nature of

the green curve demonstrates a change in system stiffness at each of the two vertices, such as what

could happen if bodies came into contact and subsequently separated. The curve drawn in red

indicates the behavior of the simulation when contact controls is engaged. Dampening, which helps

to smooth the load-displacement relationship, introduces error in the approximated solution but

aids numerical convergence.

96

effects of large nail diameter are due to just having a larger diameter or if they are related to the

gap between the implant and the endosteal canal. A study evaluating the same diameter nail in

multiple different reaming scenarios would help identify which feature is driving the trends. In

example, outcome comparisons between simulations using a nail-matched, nail diameter +0.5mm,

and nail diameter +1mm reaming size would indicate if the reaming gap is having an effect. Perhaps

a more exciting extension of this work would focus on introducing varying levels of patient

specificity to the models. A sensitivity analysis on multiple independent and combined patient

specific modeling features could help focus future modeling efforts on the most impactful features.

Additionally, the simulations in this work tend to represent worst-case scenarios because no healing

tissues are accounted for. While this is still relevant as it models the patient immediately

postoperatively, over time we know that fractures undergoing secondary healing experience a

gradual hardening and calcification of tissue within the fracture gap which would provide additional

stability to the fracture and implant. Implant fatigue life predictions could be accurately made if

simulations were developed which could imitate the effects of fracture callus formation and

stiffening.

Appendix A

An Unsupervised Machine Learning Method for Discovering Patient Clusters

Based on Genetic Signatures

Text in this chapter is published in the Journal of Biomedical Informatics176

Authors: Christian Lopez, Scott Tucker, Tarik Salameh, Conrad Tucker

Abstract

Introduction: Many chronic disorders have genomic etiology, disease progression, clinical presentation, and response to

treatment that vary on a patient-to-patient basis. Such variability creates a need to identify characteristics within patient

populations that have clinically relevant predictive value in order to advance personalized medicine. Unsupervised machine

learning methods are suitable to address this type of problem, in which no a priori class label information is available to

guide this search. However, it is challenging for existing methods to identify cluster memberships that are not just a result

of natural sampling variation. Moreover, most of the current methods require researchers to provide specific input

parameters a priori.

Method: This work presents an unsupervised machine learning method to cluster patients based on their genomic makeup

without providing input parameters a priori. The method implements internal validity metrics to algorithmically identify

the number of clusters, as well as statistical analyses to test for the significance of the results. Furthermore, the method

takes advantage of the high degree of linkage disequilibrium between single nucleotide polymorphisms. Finally, a gene

pathway analysis is performed to identify potential relationships between the clusters in the context of known biological

knowledge.

Datasets and Results: The method is tested with a cluster validation and a genomic dataset previously used in the literature.

Benchmark results indicate that the proposed method provides the greatest performance out of the methods tested.

Furthermore, the method is implemented on a sample genome-wide study dataset of 191 multiple sclerosis patients. The

results indicate that the proposed method was able to identify genetically distinct patient clusters without the need to select

parameters a priori. Additionally, variants identified as significantly different between clusters are shown to be enriched

for protein-protein interactions, especially in immune processes and cell adhesion pathways, via Gene Ontology term

analysis.

Conclusion: Once links are drawn between clusters and clinically relevant outcomes, Immunochip data can be used to

classify high-risk and newly diagnosed chronic disease patients into known clusters for predictive value. Further

investigation can extend beyond pathway analysis to evaluate these clusters for clinical significance of genetically related

characteristics such as age of onset, disease course, heritability, and response to treatment.

1. Introduction

With advancements in genome-wide association study (GWAS) techniques and the advent of low cost

genotyping arrays, researchers have developed a significant interest in applying Machine Learning (ML) methods

98

to mine knowledge from patients’ genomic makeup 177,178. This knowledge has allowed researchers to improve

gene annotation and discover relationships between genes and certain biological phenomena 179,180.

The fields of personalized and stratified medicine benefits greatly from ML. For example, many cases in the

field of pharmacogenetics have identified genetic variants with clinically actionable impacts on drug response and

metabolism181,182. Moreover, many chronic disorders (e.g., asthma, diabetes, Crohn’s disease) have genomic

etiology, clinical presentation, and response to treatment that vary on a patient-to-patient basis. Such variability

reveals a need to identify characteristics within patient populations that have clinically relevant insights. For

example, Multiple Sclerosis (MS) is a chronic inflammatory disorder in which progressive autoimmune

demyelination and neuron loss occur in the central nervous system. MS varies from patient-to-patient in genomic

etiology, disease progression, clinical presentation, and response to treatment. Hence, MS patients, like other

chronic autoimmune patients, could benefit from ML methods that advance personalized medicine.

Machine learning methods are commonly classified into supervised and unsupervised methods. Supervised

methods, such as Support Vector Machines 183 and Random Forests 184,185, have been extensively used in the field

of bioinformatics. These methods classify new objects to a determinate set of discrete class labels while minimizing

an empirical loss function (e.g., mean square error). However, supervised methods require the use of a training set

that contains a priori information of several objects’ class labels. In contrast, unsupervised methods do not require

a training set that contains a priori information of objects’ class labels as input. Unsupervised methods are able to

detect potentially interesting and new cluster structures in a dataset. Moreover, they can be implemented when

class label data is unavailable. Hence, if the objective of a study is to discover the class labels that best describe a

set of data, unsupervised machine learning should be implemented in place of supervised methods 178. However, it

is challenging for existing unsupervised ML methods to identify object memberships that are due to the underlying

cluster structures in the dataset rather than the results of natural sampling variation 186. Moreover, most current

methods require researchers to provide certain input parameters a priori (e.g., number of clusters in the dataset),

which can limit their applicability.

In light of the limitations of existing methods and the need to advance personalized medicine, an unsupervised

machine learning method to cluster patients based on their genomic similarity is proposed. The method integrates

statistical analysis that accounts for family-wise-error rate, allowing the method to identify clusters resulting from

the underlying structure of the data and not just due to random chance. Moreover, the method takes advantage of

the high degree of linkage disequilibrium between Single Nucleotide Polymorphisms (SNP) by pruning correlated

nearby SNPs, which helps reduce redundant variants in the dataset. Finally, a gene pathway analysis shows the

potential relationships between the clusters in the context of known biological knowledge. The proposed method

is capable of clustering patients based on their genomic similarity without a priori information. Moreover, it is

capable of identifying the significant variants (i.e., SNPs) between patient sub-groups within a cohort with a

common disorder. Successfully identifying distinct genetic subtypes of patients within genomic datasets

demonstrates the potential of this method to advance personalized medicine of complex diseases with heritable

components, especially autoimmune disorders which have many shared susceptibility loci 187.

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2. Literature review

In the last decade, the field of bioinformatics has seen a significant number of publications implementing

unsupervised machine learning methods, such as clustering algorithms [12-14]. Clustering algorithms partition

data objects (e.g., genes, patients) into groups (i.e., clusters), with the objective of exploring the underlying

structure on a dataset 191. In the medical field, these algorithms have been implemented to identify sets of co-

expressed genes 192, compare patients’ prognostic performance 193, cluster patients based on their medical records

194, and identify subgroups of patients based on their symptoms and other variables 195.

In previous work, genomic stratification of patients (i.e., stratified medicine) has been able to match specific

therapy recommendations to genetic subpopulations by predicting therapeutic response 181,182. However, most of

these studies implemented class label data (i.e., response to treatment) to cluster patients. In clinical datasets, class

label information is not widely available for convenient patient clustering. Unsupervised machine learning methods

can be used in such cases to identify clusters within the dataset. Further investigation of genetic subgroups within

a cohort of patients can offer a better clinical prediction of age of onset, disease course, heritability, and response

to therapy, leading to improved outcomes 196

2.1. Hierarchical clustering algorithms.

Agglomerative hierarchical clustering algorithms are one of the most frequently used algorithms in the

biomedical field 197,198. Researchers have found that hierarchical clustering algorithms tend to perform better than

other algorithms (e.g., k-means, partitioning around Medoids, Markov clustering) when tested in multiple

biomedical datasets 199. The objective of any agglomerative hierarchical clustering algorithm is to cluster a set of

n objects (e.g., patients, genes) based on an n x n similarity matrix. These clustering algorithms have grown in

popularity due to their capability to simultaneously discover several layers of clustering structure, and visualize

these layers via tree diagrams (i.e., dendrogram) 186. Even though these algorithms allow for easy visualization,

they still require preselecting a similarity height cut-off value in order to identify the final number of clusters. In

other words, it still requires researchers to know a priori the number of cluster in the dataset.

Agglomerative hierarchical clustering algorithms can be implemented with different linkage methods. For

example, Ahmad et al. (2016) 193 implemented the Ward’s linkage method to compare patients’ prognostics

performance; while Hamid et al. (2010) 195 implemented the Complete linkage method to identify unknown sub-

group of patients. Unfortunately, depending on the underlying structure of the data, different clustering results can

be obtained by implementing different linkage methods. Ultsch and Lötsch (2017) 200 demonstrated that neither

the Single nor Ward’s linkage methods provided similar clustering results when tested with the Fundamental

Clustering Problem Suite (FCPS) datasets 201. Their results reveal that these linkage methods were able to correctly

cluster all the objects in only a subset of the FCPS datasets. Similarly, Clifford et al. (2011) 202 discovered that

while testing multiple simulated GWAS datasets, the linkage methods of Median and Centroid were the only ones

to consistently be outperformed by the Single, Complete, Average, Ward’s, and McQuitty methods. In light of

these, Ultsch and Lötsch (2017) 200 proposed the use of emergent self-organizing map to visualize clustering of

high-dimensional biomedical data into two-dimensional space. Even though, their method allowed for better

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visualization, it still required preselecting the number of clusters as well as other parameters to perform correctly

(e.g., toroid grid size) 200.

2.2. Parameter selection in clustering algorithms.

In order to avoid preselecting input parameters a priori (e.g., the number of clusters),

researchers have implemented cluster validation metrics. For example, Clifford et al. (2011) 202 proposed a method

that aimed to capture the clustering outcome of multiple combinations of linkage method and similarity metric

based on the Silhouette index 203. The Silhouette index was used to rank the results of the clustering combinations,

and select the best cluster set (i.e., cluster set with largest average Silhouette index). Similarly, Pagnuco et al.

(2017) 192 presented a method that implemented several linkage methods and implemented modified versions of

the Silhouette and Dunn indices 204 to select the final clustering results. Both the Silhouette and Dunn indices

served as internal cluster validation metrics (i.e., no external information needed) to guide the selection of the final

cluster set. However, the Silhouette index has been shown to have a stronger correlation with external cluster

validation metrics, such as the Rand Index, than the Dun index [28,30].

The methods of Clifford et al. (2011) and Pagnuco et al. (2017) did not require selecting the number of clusters

a priori due to the internal cluster validation metrics implemented. These metrics allow for algorithmic selection

of the number of clusters. Nonetheless, the computational complexity of testing all potential clusters increases

linearly with the number of objects in the dataset. Other studies have implemented model-based clustering methods

to overcome these limitations. For example, Sakellariou et al. (2012) 205 implemented an Affinity Propagation 206

algorithm to identify relevant genes in microarray datasets. Shen et al. (2009) 207 implemented an Expectation-

Maximization algorithm 208 to cluster genes based on an integration of multiple genomic profiling datasets.

However, models based methods make underlying assumptions that might not be applicable in certain datasets 209.

Recently, Khakabimamaghani and Ester (2016) 210 presented a Bayesian biclustering method to identify clusters

of patients. They benchmarked their method against the multiplicative Non-negative Matrix Factorization (NMF)

algorithm proposed by Lee and Seung (2001) 211. Their results revealed that their Bayesian biclustering method

was more effective in patient stratification than the NMF. While this Bayesian biclustering method did not require

selecting the number of clusters a priori, it did require selecting parameters for prior probability distributions. The

capability of biclustering algorithms to discover related gene sets under different experimental conditions have

made them popular within the bioinformatics community 212. One of the first works in this area was presented by

Cheng and Church (2000) 213. They proposed an iterative greedy search biclustering algorithm to cluster gene

expression data. Even though their method did not require selecting the number of clusters a priori, it did require

the selection of hyperparameters (e.g., maximum acceptable error).

2.3. Statistical significance of clustering results.

Even though the methods of Clifford et al. (2011) and Pagnuco et al. (2017) aimed to find the optimal clustering

outcome from multiple algorithms, which resembled the consensus clustering approach (i.e., approach in which a

solution is identified by validating multiple outcomes) 214, their methods did not account for possible clustering

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memberships arising due to random variation. Whether identified clusters memberships are due to underlying

cluster structures in the data or are just a result of the natural sampling variation, is a critical and challenging

question that needs to be addressed when clustering high-dimensional data 186. To address this question, Suzuki

and Shimodaira (2013) 215 presented the pvclust R package, which calculates probability values for each cluster

using nonparametric bootstrap resampling techniques. Even though pvclust allows for parallelized computing, it

requires significant time (i.e., 480 mins) when implemented in genomic datasets. This is due to the large number

of resampling iterations (i.e., 10,000) required to reduce the error rate 215. In contrast, Ahmad et al. (2016) 193

applied a non-parametric analysis of variance (ANOVA) Kruskal-Wallis test to compare the clusters within a

hierarchical clustering method. Similarly, Bushel et al. (2002) 216 implemented a single gene parametric ANOVA

test to assess the effects of genes on hierarchical clustering results. Recently, Kimes et al. (2017) 186 proposed a

method based on a Monte Carlo approach to test the statistical significance of hierarchical clustering results while

controlling for family-wise-error rate. However, family-wise-error rate can also be controlled while applying

repetitive statistical tests by implementing a Bonferroni correction 217.

2.4. Integrating domain knowledge into clustering algorithms

Other frequently used clustering algorithms in the bioinformatics field are k-means and fuzzy c-means.

However, these algorithms require initial random assignments of the clusters, which can produce inconsistent

results 202. Hence, they might fail to converge to the same results, even after multiple initiations using the same

dataset 197. In light of these limitations, Tari et al.(2009) 197 proposed the “GO Fuzzy c-means” clustering algorithm.

Their method resembles the fuzzy C-mean algorithms 218 and implements Gene Ontology annotation 219 as

biological domain knowledge to guide the clustering procedure. Even though this method assigned genes to

multiple clusters, which could have improved the biological relevance of the results, it was not capable of

discriminating the cluster memberships that were assigned due to random chance. While the algorithm parameters

selected in this study might have been reasonable for the dataset analyzed, the authors highlighted that future

studies would need to experimentally determine these parameters. Similarly, Khakabimamaghani and Ester (2016)

210 integrated domain knowledge via the selection of parameters for prior probability distributions. However, their

results reveal that the selection of these parameters had a direct impact on their clustering results. When analyzing

the effects of priors, the authors indicate that “final selected priors favor better sample clustering over better gene

clustering” 210. These findings reveal that the parameters need to be carefully selected since they can bias their

method towards better sample clustering rather than better gene clustering results.

Researchers can implicitly integrate domain knowledge to their methods by judiciously selecting the input data

of their algorithms 178. Genomic datasets may include relevant features as well as correlated and non-informative

features. The presence of correlated and non-informative features might obscure relevant patterns and prevent an

algorithm from discovering the underlying cluster structure of a dataset 195. Genomic data is generally high-

dimensional because the number of features is frequently greater than the number of samples. Additionally, genetic

variants are commonly correlated with other variants in close proximity on DNA. Therefore, when clustering

genomic data it is important to prune non-informative and correlated features 178,185.

Highly correlated SNPs are said to be in Linkage Disequilibrium (LD). This characteristic makes it challenging

for unsupervised ML algorithms to discover relevant cluster structures in the dataset. GWA studies present

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significant associations as tag SNPs, implying a true causal SNP can be found within the LD block of a tagged

location 187. LD pruning refers to removing highly correlated SNPs within LD blocks. For example, Yazdani et al.

(2016) 220 identified a subset of informative SNPs based on a correlation coefficient. Similarly, Goldstein et al.

(2010) 185, implemented several correlation coefficient cut-off values (e.g., 0.99, 0.9, 0.8, 0.5) to remove SNPs

with high LD. They achieved this by using the toolsets for Whole-Genome Association and Population-Based

Linkage Analyses (PLINK) 221, resulting in a reduction of up to 76% of the original dataset. This reduction

decreased the computational complexity of their method 185. However, researchers have not agreed yet on a

standard correlation coefficient cut-off value that can be applied to every genomic dataset to reduce complexity

without incurring in significant information loss.

Table 1. Summary of current methods

Papers LD Pruning

Automatic

selection of k *

Statistical tests performed No selection of parameters required ǂ

[9,11,19, 197 X

216 X X

192,202,205,207,210,

211,213

X

186, 193, 215, 222,

X

This work X X X X

*k is the parameter defining the number of cluster in the dataset.

ǂ No parameters or hyperparameters are required to be known or selected a priori by researchers (e.g., prior probability, toroid grid size).

Table 1 shows a summary of the current clustering methods in the field of bioinformatics applied to

genomics data. It can be shown that multiple methods prune the SNPs of their datasets based on the degree of LD

between nearby SNPs. This is done in order to guide their clustering search and remove potentially non-informative

features. However, the vast majority of existing methods still require preselecting the number of clusters and other

parameters a priori (e.g., prior probability distributions, toroid grid size). Moreover, the current methods do not

commonly implement statistical analysis to test for the significance of their results, or to account for possible

family-wise-error rates. In light of this, the authors propose an unsupervised machine learning method to identify

sub-groups within cohorts of patient afflicted with the same disease. This is done by clustering patients based on

their genomic similarity without the need to any a priori information or input parameter. The method presented in

this work takes advantage of LD between SNPs by pruning correlated SNPs. In addition, it automatically selects

the number of clusters by implementing an internal validation metric. The method ensembles the clustering

outcomes of multiple linkage methods via a majority vote approach. Subsequently, it tests for statistical

significance among results while accounting for family-wise-error rate. Finally, a gene pathway analysis is

performed to support the potential medical significance of the results.

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3. Method

An unsupervised machine learning method is presented that does not require selection of input parameters a

priori. The method can help identify patient cluster structures within genomic data and potentially discover

valuable differences between them. This knowledge can be used to advance personalized medicine of complex

diseases with heritable components, especially autoimmune disorders which have many susceptibility loci. Fig. 1

shows an outline of the method presented in this work.

Figure 1. Outline Method

3.1 Linkage Disequilibrium Pruning

Pruning SNPs based on LD serves as a feature reduction step. Thus, in the proposed method, SNPs

that are strongly correlated to other nearby SNPs are pruned, as previously done in the literature. The degree of LD

between SNPs is assessed by calculating the correlation coefficients based on a sliding window method. In this

method, cut-off values of (i) 0.999, (ii) 0.99, (iii) 0.9, (iv) 0.8 and (v) 0.5 are employed. Previous studies have

shown these cut-off values provide a balance between error reduction and information loss 185. Hence, five subsets

of patients’ genomic data containing different sets of SNPs (i.e., features) are generated. The subsets generated

serve as input for the hierarchical clustering step.

3.2 Hierarchical Clustering

The objective of the unsupervised machine learning method proposed in this work is to cluster patients

based on their genomic similarity. Patients’ genomic similarity can be evaluated using a wide range of distance

metrics 202. The selection of the appropriate distance metric is driven by the type of data under analysis (e.g., ratio,

interval, ordinal, nominal or binary scale). For example, the Euclidian distance is appropriated for ratio or interval

scale data, while the Manhattan distance for ordinal scale data 223.

Subsequently, the method proposed in this work employs an agglomerative hierarchical clustering algorithm.

Hierarchical clustering algorithms are frequently used with only one linkage method, which can limit their ability

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to identify underlying cluster structures in certain datasets 200. Hence, in this work, multiple linkage methods are

implemented. The linkage methods used in this work have been shown to consistently outperform other methods

when tested with simulated GWAS datasets 202. The cluster results obtained by implementing different linkage

methods are ensemble in the subsequent steps. This ensemble takes advantage of the performance of multiple

linkage methods. Moreover, it helps identify the underlying structure of the data, since the ensemble approach will

favor cluster structures identified by the majority (i.e., via a majority vote approach) of the linkage methods.

Specifically, the authors propose to implement:

(i) Single Linkage (or Minimum Linkage).

(ii) Complete Linkage (or Maximum Linkage).

(iii) Average Linkage (or Unweighted Pair Group Method with Arithmetic Mean, UPGMA).

(iv) Ward’s Linkage.

(v) McQuitty Linkage (or Weighted Pair Group Method with Arithmetic Mean, WPGMA).

3.3 Parameter Selection

Once the agglomerative hierarchical algorithm is implemented, the Silhouette index is employed as an internal

validity metric. This index has been used in previous studies to rank the results of multiple clustering algorithms

outcomes and guide the selection of final clusters 192,202. Nonetheless, in this method, the index is used to select the

number of clusters for all combinations of LD pruning data subsets (see section 3.1) and linkage methods (see

section 3.2). The number of clusters that provides the largest average Silhouette index value in each of the

combinations is selected.

The computational complexity of testing all possible numbers of clusters increases linearly as the number of

objects in a dataset increases. This can be a challenge in datasets that contain a large number of objects, even with

parallelized computing. In this work, an optimization approach is presented to identify the number of clusters that

maximizes the average Silhouette index. The mathematical formulation of this optimization problem is as follows:

𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑆𝐼 (1)

𝑆𝐼 = 1

𝑘 ∑ [

1

𝜂𝑖 ∑ 𝑆(𝑥)𝑥∈𝑪𝑖

]𝑘𝑖=1 ∀ 𝑖 ∈ 𝑲{1, … , 𝑘} (2)

𝑆(𝑥) = 𝑏(𝑥)−𝑎(𝑥)

max {𝑏(𝑥),𝑎(𝑥)} ∀𝑥 ∈ 𝑪𝑖 (3)

𝑎(𝑥) = 1

𝜂𝑖−1 ∑ 𝑑(𝑥, 𝑦)𝑦∈𝑪𝑖

∀ 𝑥 ≠ 𝑦, 𝑥 and 𝑦 ∈ 𝑪𝑖 (4)

𝑏(𝑖) = 𝑚𝑖𝑛𝑤∈𝑲,𝑤≠𝑖 {1

𝜂𝑤 ∑ 𝑑(𝑥, 𝑔)𝑔∈𝑪𝑤

} ∀ 𝑔 ∈ 𝑪𝑤 , 𝑤 ∈ 𝑲 (5)

1 < 𝑘 ≤ 𝑛 (6)

Where,

𝑆𝐼: is the average Silhouette index of the clusters set K.

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K: is the set of clusters obtained with the hierarchical clustering algorithm for a given number of k

disjoint clusters.

𝜂𝑖: is the number of objects that belongs to cluster 𝐂𝑖 , for 𝑖 ∈ 𝑠et of clusters {𝑲}.

𝑆(𝑥): is the Silhouette of object x, for x ∈ 𝐂𝑖 .

𝑎(𝑥): is the average similarity of object x with all other objects that belong to the same cluster of x

(i.e., 𝐂i).

𝑏(𝑥): is the average similarity of object x with the objects from the nearest clusters 𝐂𝑤, for 𝑤 ∈

𝑠et of cluster {𝑲}, 𝑖 ≠ 𝑤.

Eq. (1) represents the objective function that needs to be maximized (i.e., the average Silhouette index). Eq. (2),

shows the mathematical representation of the average Silhouette index, while Eq. (3) shows the silhouette of a

given object x. Both Eq. (4) and (5) represent the elements that constitute the Silhouette index of a given object x

203. Finally, Eq. (6) constrains the search for the number of clusters to be greater than 1 and less than the total

number of objects n (i.e., the maximum number of clusters). Since the objective function is non-linear with respect

to the parameter k (i.e., number of clusters), this optimization problem needs to be solved with a non-linear

optimization algorithm. In the literature, there are several algorithms suitable to solve this type of optimization

problem 224. Nonetheless, the proposed method is not constrained to any specific optimization algorithm.

Once the number of clusters is identified in all datasets combination, the results are ensemble into a final cluster

set via a majority vote approach. Table 2 shows an example of this consensus clustering approach in which patient

i is assigned to the final cluster 1 since the majority of the cluster results assigned that patient to that given cluster.

Similarly, patient n is assigned to the final cluster 2, since the majority of clusters assigned this patient to this

cluster.

Table 2. Example of consensus clustering

No. LD

Pruning

Linkage

Method

Patient

i cluster

…

Patient

n cluster

1 1 Single 1 2

2 0.99 Single 1 2

3 0.90 Single 1 1

4 0.8 Single 1 2

5 0.5 Single 2 1

… …

24 0.8 McQuitty 2 2

25 0.5 McQuitty 1 2

Final Cluster 1 2

3.4 Statistical Significance

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After the final patient clusters are discovered, a single SNP ANOVA test is performed to reveal the SNPs that

are statistically significantly different between the clusters of patients. This step helps validate that the clusters

generated are different by at least one associated SNP. To account for family-wise-error-rate a Bonferroni

correction is applied by dividing the alpha value by the number of tested SNPs. In the case that no SNPs are found

to be statistically significantly different, it can be concluded that the resulting patients’ clusters might have arisen

due to random chance.

3.5 Gene Pathway Analysis

The set of SNPs significantly associated with differences between patient clusters can be explored via

Gene Ontology (GO) enrichment and mutational burden on molecular pathways. By assigning each SNP to a gene

and performing a gene network analysis, (e.g., via STRING-DB software 225), visualizations of gene networks and

estimations of significant enrichment along GO terms could provide evidence for potential biological significance.

The significance is assessed by comparing the number of evidence-based relationships between selected genes to

the number expected in a set of randomly selected genes. If an enrichment is established, the related genes are

examined by their molecular function, biological relevance, and known associations to the disease from GWA

studies. While pathway analysis does not provide the rigor of direct experiment or clinical trial, it remains valuable

in determining whether selected genes are functionally relevant to the disease studied, as opposed to being a

function of other factors such as ethnicity.

4. Application

The performance of the proposed method is first tested on the datasets presented in the Fundamental

Clustering Problem Suite (FCPS) 201. The FCPS contains 10 different datasets designed to assess the performance

of unsupervised machine learning algorithms on particular clustering challenges (e.g., outliers, undefined cluster

boundaries). The ground truth data of cluster membership are used to test the performance of the proposed method

in identifying clusters resulting from the underlying structures in the data and not just from random variation. To

measure this performance the Rand index 226 validation metric is implemented. Moreover, the performances of

other existing methods in the literature are benchmarked with the same datasets. All the benchmark analyses were

performed on a 12 Core i7 3.4 GHz IntelTM computer with 62.8 GB of RAM and Ubuntu 16.04 LTS. The

benchmark methods were implemented in R v.3.4 227 with the used of the packages mclust v.5.3 228, apcluster

v.1.4.4 229, DatabionicSwarm v.0.9.8 230,231, NNLM v.0.4.1 211, and biclust v.1.2.0 232.

Additionally, the proposed method and the benchmark methods that do not require providing the number of

cluster a priori (i.e., Clifford et al. (2011) 202: hierarchical clustering algorithm with silhouette index, Sakellariou

et al. (2012) 205: Affinity Propagation clustering algorithm, Shen et al. (2009) 207: Expectation Maximization

clustering algorithm, Cheng and Church (2000) 213: Iterative Greedy Search Biclustering algorithm.), are

implemented on two genomic datasets. Frist, the microarray gene expression data of patients with lymphoblastic

and acute myeloid leukemia from Golub et al. (1999) 233 was implemented. The dataset is publically available at

the Broad Institute and has been previously used to test the performance of clustering algorithms 199,234. The dataset

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is composed of microarray gene expression data of 999 genes for 27 patients with acute lymphoblastic leukemia

and 11 patients with acute myeloid leukemia.

Lastly, a dataset of patients diagnosed with MS is employed. DNA samples from 191 Multiple Sclerosis (MS)

patients consented via the Pennsylvania State University PRIDE protocol at Hershey Medical Center were

subjected to the Immunochip assay (Illumina). Allelic variations were measured at previously described

susceptibility loci for multiple immune-mediated disorders 235,236. The Y chromosome data were filtered out of the

dataset to simplify comparisons in a predominantly female cohort. Mitochondrial markers were discarded for

analysis as well. Genotype calling was done with Illumina GenomeStudio v.2011.1 (www.illumina.com), and

genotype markers were excluded if their GenTrain score was less than 0.8, or if their call rate across the cohort

was less than 0.99. Finally, the MS dataset was filtered such that only variants within coding regions (i.e., exons),

were considered. Therefore, the MS dataset was composed of 191 patients and 25,482 SNPs.

With the MS dataset, a 10-fold cross-validation analysis was performed with the objective to test the performance

of the proposed and the benchmark methods, as well as to provide evidence regarding their propensity of overfitting

genomic datasets. In this cross-validation approach, the MS dataset was randomly partitioned into 10 subsets.

Subsequently, the methods were used to cluster the patients within these subsets. The clustering results obtained

from the 10 subsets were compared to those from the complete dataset. The agreement between the clusters

generated with the complete MS dataset and the 10-fold subsets is assessed with the Rand index metric. A match

between the clustering results (e.g., average Rand index of 1) will indicate that the proposed method was not

overfitting the MS dataset, thus, providing arguments of its generalizability. Moreover, it will support that the

method was identifying clusters due to underlying structures in the data and not just due to random variations.

Finally, the groups of SNPs identified by the proposed method to achieve statistical significance between clusters

generated were examined via gene pathway analysis.

4.1 Linkage Disequilibrium Pruning

For the MS dataset, the pruning of SNPs with a high LD was done based on the correlation-coefficient cut-off

values found in the literature, as proposed in section 3.1. LD pruning was performed using the widely used

genotype analysis toolset for Whole-Genome Association and Population-Based Linkage Analyses (i.e., PLINK)

221. This pruning resulted in a reduction of the original dataset as presented in Table 3. These percentages of SNPs

removed are consistent with the results found in previous studies.

Table 3. LD Pruning summary

R2

cut-off value

Number

of SNPs retained

Percentage

of SNPs removed

0.50 5,460 78.57%

0.80 6,849 73.12%

0.90 7,421 70.88%

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0.99 8,666 65.99%

0.999 8,691 65.89%

4.2 Hierarchical Clustering

The FCPS and Golub et al. (1999) 233 datasets contain features that are in ratio scale. Hence, to measure

the similarity between the objects in the datasets the Euclidian distance is implemented. Genotype data can be

ordinal or additive scale, depending on whether heterozygous SNPs are treated as a label or as a half-dosage. While

additive models are more often used for GWA studies, in this work ordinal scale was used to demonstrate flexibility

in the described clustering method. Hence, the genomic similarity of MS patients based on different subsets of

pruned data is evaluated using the Manhattan distance metric. The similarity calculations and the agglomerative

hierarchical algorithm with multiple linkage methods were performed in R v.3.4 227.

4.3 Parameter Selection

The selection of the number of clusters k that maximized the average Silhouette index was performed with a

generalized simulation annealing algorithm. This algorithm was selected due to its underlying theory and proven

performance in problems with non-linear objective functions 237,238. The algorithm was implemented via the R

package GenSA v.1.1.6 239. Nonetheless, other non-linear optimization algorithms or greedy heuristics can also be

implemented. Once the number of clusters in every combination of LD pruned data and linkage method are

selected, the clustering results are ensemble via a majority vote approach (see section 3.3).

4.4. Statistical Significance

After the final clusters have been selected based on the average Silhouette metric and consensus clustering

approach the statistical significance of the results is evaluated. Clusters’ median values for each of the p features

in the MS dataset are evaluated via a single SNP non-parametric ANOVA Kruskal-Wallis test 222. To account for

family-wise-error rate, a Bonferroni correction is applied to the significance alpha level of 0.05 (i.e., Bonferroni

correction= 0.05/p, for p= 25,482).

4.5. Gene Pathway Analysis

Gene variants that show statistical significance are further analyzed via a gene pathway analysis to

explore their potential medical significance. Pathway analysis starts with generating a list of genes determined

from the set of SNPs with strong evidence of significance between patient clusters. Inputting the gene set via the

STRING-DB software algorithms 225 allows for convenient calculation of pathway enrichment hypothesis tests and

visualization of the gene network. STRING-DB determines gene relationships by aggregating several databases

into an evidence score. Experimental evidence comes from the BIND 240, GRID 241, HPRD 242, IntAct 243, MINT

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244, and PID 245 databases. In addition, STRING-DB pulls from the curated databases KEGG 246, Gene Ontology

219, BioCarta 247, and Reactome 248. Interaction frequency is tested for enrichment compared to expectation from a

random sampling of genes, with p-values and false discovery rates reported for enrichment in specific cellular

processes, defined by Gene Ontology references. After statistical testing is done, the gene network is used as a

threshold for high confidence interaction and a k-means clustering algorithm is performed for visualization

purposes (see Fig. 7).

5. Results

5.1. FCPS Benchmark results

The majority of existing methods in the literature require the selection of parameters a priori (e.g., number of

clusters, see Table 1). Hence, to benchmark with multiple methods, the number of clusters provided by the FCPS

was used as input when testing these methods. Figure 2 shows the average Rand index obtained in the FCPS

datasets by the method proposed in this work (i.e., Proposed) and the methods benchmarked. This plot shows that

on average the proposed method outperformed other methods, with an average Rand index of 0.852. The

performance is statistically significantly greater than the results of the methods proposed by Cheng and Church

(2000), Sakellariou et al. (2012), Lee and Seung (2001), Ultsch and Lötsch (2017), and Clifford et al. (2011). Even

though these results indicate that, on average, the proposed method achieved the largest Rand index, there is not

enough evidence to conclude that it was statically significantly greater than the Rand index achieved by the

methods of Shen et al. (2009), Hamid et al. (2010), or Ahmad et al. (2016), at an alpha level of 0.05. This can be

attributed to the relatively small group of validation datasets provided in the FCPS (i.e., 10 datasets).

Note: p-value: <0.001***, <0.01**, <0.05*

Figure 2. Average Rand index for FCPS datasets

110

Note: p-value: <0.001***, <0.01**, <0.05*

Figure 3. The proportion of results with Rand index of 1 for FCPS datasets (i.e., perfect clustering)

Similarly, Figure 3 shows the proportion of the FCPS datasets that achieved a clustering result with a Rand index

of 1 (i.e., perfect clustering) for each of the given methods. The results reveal that the proposed method was able

to obtain a Rand index of 1 in 6 out of the 10 FCPS datasets. The results from the Wilcoxon tests indicate that

these results are statistically significantly greater than the results of the methods proposed by Ultsch and Lötsch

(2017), Cheng and Church (2000), Lee and Seung (2001), and Sakellariou et al. (2012). Even though the results

indicate the proposed method correctly clusters the largest percentages of datasets (i.e., 6/10), there is not enough

evidence to conclude that this proportion is statically significantly greater than the ones from the other methods

benchmarked, at an alpha level of 0.05. Nevertheless, these results provide evidence that the method proposed in

this work is able to identify true clusters in a wider range of datasets with different underlying structures.

5.2. Genomic dataset Benchmark results

Figure 4 presents the Rand index obtained on the Golub et al. (1999) dataset 233 by the method proposed in this

work and the benchmark methods that do not require providing the number of clusters a priori. Fig. 4 indicates

that the proposed method performed better than the methods presented by Clifford et al. (2011), Cheng and Church

(2000), and Sakellariou et al. (2012).

111

Figure 4. Rand index for Leukemia dataset

Figure 5 shows the average Rand index obtained with the MS dataset and the 10-fold cross-validation

approach by the proposed and benchmark methods. The iterative greedy search Biclustering algorithm proposed

by Cheng and Church (2000) was not able to find any cluster structure in the MS dataset; hence it was not included

in this plot. The plot shows that on average the proposed method outperformed the other methods, with an average

Rand index of 0.969. This is statistically significantly greater than the values obtained with the other methods

benchmarked. Moreover, the average Rand index obtained by the proposed method was not significantly different

than an average Rand index of 1 (t-value: -1.963, p-value=0.0812), at an alpha level of 0.05. This reveals that on

average the proposed method found a perfect match between the clusters of patients obtained with the complete

MS dataset and the cross-validation subsets.

\ Note: p-value: <0.001***, <0.01**, <0.05*

Figure 5. Average Rand index for MS dataset

112

Table 4 shows the confusions matrix of the clusters obtained with the proposed method when implementing

the 10-fold cross-validation approach. The table indicates that the proposed method was able to group 96.33% of

the patients’ in the same clusters when both the complete dataset and the different data subsets were used (i.e.,

accuracy of 0.96), which is in line with the average Rand index of 0.969 shown in Fig. 5. The Rand index and

confusion matrix results indicate that the proposed method identified a similar cluster structure even with different

subsets of the MS dataset. This indicates that the proposed method was not overfitting the dataset. Furthermore, it

provides evidence that supports that the method was able to identify clusters due to the underlying structure of the

data and not just due to random change.

Table 4. MS dataset 10-fold cross-validation confusion matrix

Complete Dataset

Cluster

1

Cluster

2

Data

Subsets

Cluster

1 172 0

Cluster

2 7 12

The results from the pathway analysis on the set of statistically significant different SNPs between the

MS patient clusters are shown in Fig. 6. The cluster-defining SNPs show significantly more interactions than

expected among a random sampling of genes. Out of 515 genes, 1,463 interactions were found, with only 942

expected by chance (p-value: 1.04e-10), among a background set of 4,938 genes present on the Immunochip. The

gene interactions in the set shown in Fig. 6 demonstrate a high prevalence of cellular adhesion, cytokine response,

and general immune process pathways.

113

Figure 6. Gene Pathway Analysis results

Table 5 shows relationships between genes based on evidence from literature via STRING-DB 225. The highly

connected pathway depicted contains many genes known to be involved in cell adhesion and leukocyte physiology,

both of which are processes dysregulated in MS 249. Additionally, the genes selected show significant Gene

Ontology term enrichment in these categories, with false discovery rates less than 0.01. Taken together, pathway

analysis reveals that extracting significant features between clusters may be a valid feature reduction technique

for downstream analysis. Genes known to be relevant in MS pathophysiology (e.g., interleukin receptors, STAT

transcription factors, lymphocyte surface proteins from the CCR family) were highlighted despite no use of

supervised methods and label data, implying that the proposed unsupervised method’s value is not just

discovering patient clusters, but reducing the dimensionality by nearly 20-fold with few samples (i.e., from over

25,482 features to around 1,500, using 191 samples).

Pathway ID Pathway

Description

Count

in Gene Set

False

Discovery Rate

GO.0051249 Regulation of

lymphocyte activation

32 0.00641

GO.0002823 Negative

regulation of adaptive

response

9 0.00749

114

GO.0006952 Defense

response

73 0.00749

GO.0002694 Regulation of

leukocyte activation

33 0.00804

GO.0050865 Regulation of

cell activation

35 0.00804

GO.0002376 Immune

system process

93 0.00898

Table 5. Gene Pathway Analysis results

As a secondary observation, an analysis was done on the MS dataset after pruning samples which showed

greater than 0.2 similarity in PLINK’s Identity-By-Descent (IBD) algorithm 250. This was done to remove

potentially related patients from the analysis. IBD identified a total of 11 potentially related patients, from whom

10 were initially assigned to cluster number two. Consequently, after removing these potentially related patients

from the MS dataset and applying the proposed method, the number of patients in the second cluster were reduced

from 12 to 2, and no pathway enrichment was detected. However, the 120 genes detected still included T-cell

relevant proteins such as STAT and JAK, as well as members of the tumor necrosis factor and interleukin families,

supporting the claim that the method identified SNPs relevant to the disease process even if the sample size of the

smaller cluster (n=2) constrains the power of the pathway analysis. Furthermore, the cross-validation results

indicate that the average Rand index achieved after removing potentially related patients (i.e., 0.932) was not

significantly different than the initial cross-validation results (i.e., 0.969, see Fig. 5) (t-value: 1.52, p-value: 0.147).

This reveals that the proposed method was able to identify the same underlying cluster structure in the MS dataset,

and identify patients with similar genomic makeup after the removal of potentially related individuals. These

results provide evidence that supports that the method was able to identify clusters due to the underlying structure

of the data and not just due to random change.

6. Conclusion and future work

Many chronic disorders have genomic etiology, disease progression, clinical presentation, and response to

treatment that vary on a patient-to-patient basis. Such variability creates a need to identify characteristics within

patient populations that have clinically relevant predictive value. Unsupervised machine learning methods are

suitable to address this type of problem, in which no class label information is available to guide this search.

However, it is challenging for existing methods to identify cluster memberships that are due to the underlying

structures in the dataset and not just a result of natural sampling variation. Moreover, most current methods require

researchers to know and provide input parameters a priori. As a result of these limitations and the need to advance

115

personalized medicine, this work proposed an unsupervised machine learning method to identify genomically

distinct patients’ cluster. The proposed method integrates statistical analysis to test for significance of clustering

results and accounts for family-wise-error rate. Moreover, the method is capable of automatically identifying the

number of clusters by implementing an internal validity metric. Similarly, the method takes advantage of the degree

of linkage disequilibrium between SNPs by pruning correlated nearby SNPs, as well as implementing a post-

clustering gene pathways analysis.

The proposed method is tested with clustering validation datasets previously used in the literature. The

benchmark results reveal that proposed method provides, on average, the greatest performance (i.e., average Rand

index 0.852). Moreover, results indicate that it was able to obtain cluster results with a Rand index of 1 (i.e., perfect

clustering) in 6 out of the 10 Fundamental Clustering Problem Suite (FCPS) datasets. Similarly, the method is

applied to a dataset of 38 patients with leukemia, and subsequently to a dataset of 191 Multiple Sclerosis (MS)

patients. The results indicate that the proposed method is able to identify genetically distinct patient clusters without

the need to select the number of clusters or any input parameter a priori. Moreover, the cross-validation results

indicate that the proposed method outperformed the other methods when it comes to data overfitting, since the

average Rand index obtained was significantly greater than the benchmarked methods and not significantly

different than 1. This performance was maintained even after the removal of potentially related patients from the

dataset. This indicates that the method was identifying clusters due to the underlying structure of the data and

avoided overfitting the dataset. The identification of distinct genetic subtypes of patients demonstrates the potential

applicability of this process to advance personalized medicine of complex diseases with heritable components,

especially autoimmune disorders.

When applied to genomic data, the method also shows value as a feature reduction strategy. Out of over

25,482 exonic SNPs and 191 patient samples, the clustering of patients yielded a set of SNPs which significantly

vary between clusters. These variants represent 515 genes, several of which are known to be involved in MS

(CD69, CCRX5, IL-13, STAT3) and cell adhesion (ICAM1, LAMB4). The fact that many highlighted genes are

components of the immune system is not surprising due to the nature of the Immunochip assay, but the enrichment

of leukocyte-specific genes is evidence that the method can result in functionally relevant feature sets, even without

class labels. Notably, 57 genes representing over 10% of the network are involved in cytokine receptor processes.

This is greater than expected from random chance, as cytokine receptors constitute a small percentage of all

Immunochip genes. The evidence presented in this work alone is insufficient to define genetic subtypes of MS, but

the specific SNP set reaching significance may be a valuable resource in experimental studies examining immune

cell dynamics and genetics. For example, the hypothesis that these clusters represent different subtypes of MS can

be tested by evaluating clinical criteria such as image results and disease progression, as well as quantitative

cytokine profiling and gene expression studies for each cluster as a group, compared against random groupings of

patients.

This work demonstrates an iterative unsupervised machine learning method which identifies significant patient

clusters within a genomic dataset. Future research should explore the medical significance of the findings shown

in this work. Similarly, the method from this work should be implemented in studies collecting SNP array and

gene expression microarray data from additional disease cohorts to explore its potential benefits. Further

116

investigation can extend beyond pathway analysis to evaluate these clusters for clinical significance of genetically

related characteristics such as age of onset, disease course, heritability, and response to treatment. Once links are

drawn between clusters and clinically relevant outcomes, the Immunochip can be used to classify high-risk and

newly diagnosed chronic disease patients into clusters with predictive value.

Acknowledgments

The authors acknowledge the NSF I/UCRC Center for Healthcare Organization Transformation (CHOT), NSF

I/UCRC grant #1624727, and the Institute for Personalized Medicine at the Pennsylvania State University.

Additionally, the authors would like to acknowledge Dr. James R. Broach from the Institute for Personalized

Medicine at the Pennsylvania State University, for his valuable contributions. Any opinions, findings, or

conclusions found in this paper are those of the authors and do not necessarily reflect the views of the sponsors.

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Vita - SCOTT M. TUCKER

EDUCATION

Penn State University College of Medicine, Hershey, PA

MD/PhD Student 2013-Present

Penn State University, University Park, PA

PhD, Engineering Science and Mechanics 2015-2019

Cornell University, Ithaca, NY

MEng, Biomedical Engineering 2011

Cornell University, Ithaca, NY

BS, Biological and Environmental Engineering 2010

AWARDS AND HONORS

Penn State Fund for Medical Innovation Grant 2019-2020

I-CORPS Regional Short Course for Medical Innovation Spring 2019

Student Award for Excellence in Innovation 2018

NSF Center for Healthcare Organization Transformation Scholar 2017-2018

International Section for Fracture Repair Poster Award 2018

Daniel A. Notterman Physician Scientist Award 2018

Penn State Pediatric Research Day Young Investigator Award 2018

Penn State Cancer Institute Abstract Top 15 Finalist 2018

Finalist, Herodicus Award for Best Resident Paper (Moira McCarthy, MD) 2012

Cornell Tradition Fellow 2006-2010

Stephen Phillip Memorial Scholar 2006-2010

Northeast Atlantic BioEngineering Conference Student Design Competition 2010

Alpha Zeta Honors Fraternity National Officer of the Year 2008

REPRESENTATIVE PUBLICATIONS

Book Chapter

Tucker SM, Reid, JS, Lewis, GS, Fracture Fixation Biomechanics and Biomaterials,

Springer, 15, 401-26 (2018).

Peer Reviewed Manuscripts

1. Tucker SM, Wee HW, Reid S, Lewis G. Effects of fracture fixation construct and

weightbearing on shear motion in proximal femur fractures. 2019. In preparation

2. Tucker SM, Wee HW, Fox E, Reid S, Lewis G. Parametric finite element analysis of

intramedullary naild fixation of proximal femur fractures. J Orthop Res. 2019. In

review, invited for revisions.

3. Moncal K, Tigli A, Seda R, Abu-laban M, Heo D, Rizk E, Tucker S, Lewis G, Hayes

D, Ozbolat I. miR-148b enriched 3D printed hybrid scaffolds for critical-sized calvarial

bone defect repair. 2019. In review.

4. Smuin D, Tucker SM, Rothermel SD, Lewis G, Mason M. Should we be concerned

about acetabular implant stresses in standard THA and dual mobility constructs with

acetabular bone loss?: A finite element model. 2019. In review.

5. Moncal K, Heo D, Godzik K, Sosnoski D, Mrowczynski O, Rizk E, Ozbolat V, Tucker

SM, Gerhard E, Dey M, Lewis G, Yang J, Ozbolat I. 3D Printing of Poly (ε-

caprolactone)/ Poly (D, L-lactide-co-glycolide)/ Hydroxyapatite composite constructs

for bone tissue engineering. J Mat Res. 2018; 1-15.