RECONSTRUCTION OF BONE GEOMETRY FOR THE

MANUFACTURE OF CUSTOMiZED RADIAL FIEAD IMPLANTS

Rasha Al-Naji

Faculty of Engineering Science

Department of Mechanical & Materials Engineering

/

Submitted in partial fulfihent

of the requirements for the degree of

Master of Engineering Science

Faculty of Graduate Studies

The University of Western Ontario

London, Ontario

May, 1 998

O Rasha Al-Naji 1998

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ABSTRACT

Cornmercially available orthopedic radial head implants are traditionally produced in

quantities of standard shapes and sizes which do not fully match the ïrregular shape of the

bone articulations. From the viewpoint of implant kinematics, Wear, and fmation. an

implant which more closely approximates the normal anatomy of the radial head is likely

to be superior to the standard implants. This work provides a description of how reverse

engineering technology cm be used to replicate the geometry of the radiai head and

manufacture a customized implant. Reverse engineering is the process of generating

accurate three-dimensional computer aided design models of fiee-form surfaces from

rneasured coordinate data. The measured data is a sequence of 2D cross-sections of the

bone acquired by computer tornography imagery. The surface model is generated by

fitting closed contours to the edge points extracted from the individual cross-sections, and

then lofting these contours. The closed contours are fitted using a Bernstein Basis

Function network. It is an adaptive approach to detennining a small number of control

points that enables a closed Bezier curve to be reconstructed from rneasured points. Once

the leaming phase is complete, the weights of the network represent the control points of

the defining polygon net used to generate the closed Bezier curves. The location of the

weights are deterrnined by a least-mean square learning algorithm. M e r the solid model

is produced. it is used to generate a tool path for machining the implant using a

computerized numerical control milling machine. The rnachined prototype is then

inspected using a coordinate measuring machine to venh its geornetry. Experiments are

presented in this work in order to confïrm the effectiveness of this technique for reverse

engineering and rnanufacturing radiai head replacements.

... I l l

I would like to express rny sincere thanks to my advisors Dr. George Knopf, Dr.

J i m Johnson. and Dr. Graham King for their valuable guidance, encouragement, and

assistance.

I would aiso like to acknowledge the support of the staff at St. Joseph's Heaith

Centre. My special appreciation goes to Dr. Ting-Yim Lee and Mr. Aleksa Cenic for

providing the CT image data, Mr. Jay Davis for providing the Xstatpak software, and Dr.

John Bennett for assisting me in resolving a major obstacle in my work.

My sincere appreciation also goes to Mr. Marion Jaworski, and to the staff at the

UWO machine shop for their support and recommendations during my experimental

work.

Thanks are also due to my fellow graduate students who provided me with

vaiuable assistance and suggestions.

1 would also like to thank my sister, Huda Al-Naji, for her artistic creations of

some figures presented in this work. And last but not least, I would like to thank my

parents, Hassan Al-Naji and Sameeha Sweedan, for their endless support throughout my

student career.

TABLE OF CONTENTS

CERTIFICATE OF EXAMINATION

ABSTRACT

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

CHAPTER I INTRODUCTION .......................................................... 1

....................................................................... 1 . 1 Introduction 1

............................. 1.2 Roblem Statement : Radial Head Replacement 2

................................................................ 1.3 Literature Review 5

.................................................................. 1.4 Thesis Overview 7

.... CHAPTER 2 STEPS IN REVERSE ENGINEERING BONE STRUCTURE

2.1 Introduction ....................................................................... 2.2 Data Acquisition ................................................................. 2.3 Data Translation into a CAD Package ........................................

..... 2.4 Solid Mode1 Creation . Contour Fitting And Surface Reconstruction

.......................................................... 2.5 Prototype Manufacture

2.6 Evaluation of Reverse Engineering Process ..................................

2.6.1 Visual inspection of prototype ....................................... ............................................................. 2.6.2 Discussion

2.7 Concluding Remarks ............................................................

CHAPTER 3 CURVE APPROXIMATION USNG A BERNSTEIN BASIS

FVNCTION (BBF) NETWORK ........................................ Introduction ....................................................................... Contour Approximation Using Bezier Curves ............................... Basis Function Neural Networks .............................................. Closed Contour Approximation Using Bernstein Basis Function

Network (BBF) ................................................................... Concluding Remarks ............................................................

CHAPTER 4 RECONSTRUCTING SURFACES IFROM SEIUAL CROSS-

......................... SECTIONS USING THJ3 BBF NETWORK

4.1 Introduction ....................................................................... 4.2 Image Segmentation .............................................................

4.2.1 Morphological operations ........................................... 4.2.2 Edge detection algorithm ............................................

4.3 Boundary Tracking .............................................................. 4.4 Parame terization ................................................................. 4.5 Contour Fitting ................................................................... 4.6 Weight Adaptation Using BBF Networks ....................................

4.6.1 Weight adaptation algorithm ........................................ 4.6.2 Weight update .........................................................

4.7 Lofting ............................................................................. 4.8 Concluding Remarks ............................................................

................... CHAPTER 5 RECONSTRUCTION OF THE RADIAL HEAD 46

5.1 Introduction ....................................................................... 46

5.2 Results Of Surface Reconstruction Of Radial Head Geometry ............ 47

5.2.1 Results of the extemal prograrn .................................... 47

5.2.2 Results of the internai program ..................................... 50

5.3 Generation Of Radial Head Implant ........................................... 52

5.3.1 Generation of implant head ......................................... 53

5.3.2 Generation of implant insert .................... ..... ............ 53

5.4 Concluding Remarks ............................................................ 53

CHAPTER 6 PROTOTYPE MANUFACTURE AND VERIFICATION ........ 6.1 Introduction ....................................................................... 6.2 Prototype Manufacture ..........................................................

6.2.1 Part set-up .............................................................. 6.2.2 Machine code generation ............................................ 6.2.3 Machining problems ..................................................

6.3 Verification Of Prototype ....................................................... 6.4 Prototype Verification Using The CMM .....................................

6.4.1 Inspection method .................................................... 6.4.2 Results ................................................................. 6.4.3 Discussion .............................................................

6.5 Concluding Remarks ............................................................

....................... CHAPTER 7 CONCLUSIONS AND FUTURE WORK ...... 69

APPENDIX 1 ................................................................................... 72

APPENDIX2 ................................................................................... 81

REFERENCES ........................ ,. ..................................................... 84

VITA ............................................................................................. 88

LIST OF FIGURES

1.1 The anatorny of the radius and its location in the upper limb ....................... ............................................... 1.2 Articulating surfaces in the elbow joint

............................................................. 2.1 Steps in reverse engineering

................................................. 2.2 CT machine used to scan cadaver arm

....................................... 2.3 A CT image of the radius near the elbow joint

................................... 2.4 The generation of contours from image edge data

.................... 2.5 The lofting of contours which defme the radial head geometry

2.6 Visual inspection of the implant prototype compared to the original radial head

2.7 Initial inspection of prototype's geometrical fit with the original cadaver arm

3.1 An example of a Bezier curve defined by five control points and a parameter

....................................................................................... value u

....................................................... 3.2 Schematic of a biological neuron

............................................................. 3.3 An artificial neural network

....................................................... 3.4 Block diagram of a BBF network

......... 4.1 Pnmary steps in the process of reconstructing the radial head geometry

............... 4.2 A typical CI' slice edge data as produced by the Xstatpak software

.................................................... 4.3 An example of dilation of an image

.................................................... 4.4 An example of erosion of an image

4.5 The effect of dilation and erosion operations on slice 15 using a 5x5 structuring

................................................... ............................... element .. .................................. 4.6 The result of edge detection algorithm for slice 15

................................................................ 4.7 Training data for slice 15

The resultant Bezier c w e for stice 15. and the training data used for the

weight adaptation algorithm .............................................................

Closed contours outlining the geometry of the radius bone for senes D .......... Closed contours of the inside of the radius bone for series D ...................... Surface mode1 of implant D .............................................................

................................................................. Bone mode1 for series C

Machining of radial head prototype using the Fadal 5-axis CNC machine ....... Problem area for machining the bone mode1 of series C ............................ Cornparison between the CT data of slices 8 and 9 from senes C and the

............................................................... approximated Bezier curves

Results of cornparison for series C between CT edge slice information and its

corresponding approximated contour .................................................... ..................................................... Measurement of part by the CMM

Results of CMM inspection for series B .............................................. A bar chart of the mean and standard deviation of average error values from

~rototwes and standard im~lants com~ared to radius s~ecirnens ...................

LIST OF TABLES

5.1 Results of the extemal program using CT information of senes 13 ................ 49

................. 5.2 Results of the intemal program using CT information of senes 13 51

............................................ 6.1 Tool and program information parameters 58

6.2 Surnmary of CMM inspection results for the 5 radial head specimens ............ 66

CHAPTER 1

INTRODUCTION

1.1 Introduction

Orthopedic prostheses are traditionally produced in large quantities of standard

shapes and sizes and used to replace human bones and joints. These implants are created

fiom geometric shapes such as spheres, cones, and cylinders. The axisymmetrical shapes

do not generally match the irregular bone articulation of the human anatomy. Although

the actual geometric shape of any human bone structure varies greatly arnongst different

individuals. the same standard implants are used widely in this expensive application.

Over 220,000 total hip replacements are performed each year in the US at a cost of

greater than J 10,000 per surgery [ 1 1.

Replacements for human joints and bones are manufactured in large quantities in

order to reduce costs. Some replacement implants are available in a greater nurnber of

sizes. For example, a total hip joint replacement series has four interconnecting

components, each available in up to 30 sizes in 1 mm increments [2]. The most suitable

combination is usually selected for a certain individual. Some implant manufactures

offer in excess of 100 hip size configurations, and the numbers may be doubled as

research and technology advance each year. However, these implants do not offer

identicai replacements for the damaged joints or bones.

Custornized implants are potentially a significant improvement over the standard

off-the-shelf implants. They have the potential to provide optimal fit and superior

articulation with the surrounding skeletal structure. They also minimize the removd of

skeletal mass during surgery, which is often done to fit the standard implants. But

customized implants are usually produced manually and cm cost up to 4 times that of

standardized implants. A standard femoral hip implant cost approximately $2.000 while

a customized prosthesis cost from $5.000 to more than $10,000 for more complex

structures [3]. A rapidly manufactured surgical implant that reproduces the matornical

structure of the replaced bone matenal would, in al1 likelihood, be an improvement over

both the standard prosthesis and a custornized one produced manually [4].

1.2 Problern Statement : Radial Head Replacement

The radius is the long bone on the laterai thumb side of the forearm that extends

from the wrist to the elbow. Figure 1.1 illustrates the anatomy of the upper limb and the

radius. The radial head is located at the upper end of the radius and foms part of the

elbow joint [5 ] .

humerus

capitellum

radius

radial neck

ulna

radial head

tuberosi ty

(a) The anatomy of the upper limb. (b) The bone structure of the radius.

Figure 1.1 The anatomy of the radius and its location in the upper limb.

radio-capitellum articulation

/

radius

uina

Figure 1.2 Articulating surfaces in the elbow joint.

In general, joint articulating surfaces play an important role in providing joint

constra.int or stability [6]. The elbow joint is inherently stable because of the highly

congrnous articula. surfaces. The elbow joint has three articulations which provide two

types of motion. These articulations are illustrated in Figure 1.2. The ulno-trochlea and

radio-capitellum articulation allow flexion and extension of the elbow resembling a hinge

joint [7]. The other articulation is the proximal radio-ulnar joint in which the radial head

rolls and slides in the lesser sigmoid notch of the ulna during rotation of the foreann [7].

The axial force component acts on the radio-humeral joint, while the tangential

component of eIbow joint forces is transferred to the ulna via the radio-ulnar joint, which

ailows axial rotation or a pivoting type of motion [7-91.

The radial head is considered a secondary stabilizer of the elbow joint and

provides an important contribution of stress transmission across the joint [6,7,10,11].

Studies have s h o w that 30% of resistance to valgus stress affecting the elbow joint is

contributed by the radial head [7]. Approximately 40% of the axial loads are transmitted

across the radio-capitellum articulation and 60% across the uino-humeral joint [6]. The

absolute force through a radial head with certain activities is estimated to exceed severd

times body weight [6,8]. These fmdings lead to the conclusion that if the radiai head is

damaged or removed, the elbow may be rendered unstable.

Kuiematics is an important factor in the design of joint replacement implants. The

prosthesis must provide adequate range of motion. restore normal biomechanical function

to the active patient, relieve pain, and duplicate size and geometric configuration of the

joint [7]. Elbow stability requires articular integrity. A prosthesis designed to replicate

normal radio-humeral and radio-ulnar articulations can distribute loads more uniformly

and provide better strength and stability [8].

Total elbow joint arthroplasty is required in comrnon joint disorders such as

rheumatoid. and post-traumatic arthritis. For total joint replacement. the joint articulating

surfaces are replicated by standard implant configurations. This approach has proved to

adequately restore the stability of the joint as well as replicate the axis of rotation and

flexion- extension motion 161.

In many cases, oniy partial replacement of the joint is required (hemiarthroplasty).

The most frequently used partial replacement of the elbow joint is the radial head.

Replacements are required for severe fractures of the radial head which c m not be

surgically repaired [7]. Radial head fractures represent 1.7 -5.4 % of al1 fractures [7].

They occur in 17- 19% of al1 cases of elbow trauma and account for 33% of elbow

fractures. Replacing the radial head restores stability required by active people, ailows

greater motion, and less elbow pain compared to fractures treated by excision alone [7].

Standard radial head implants work well when both sides of the elbow joint are

being replaced; such as in total joint arthroplasty. However, complications occur when

only the radial head is replaced with a standard implant. Current radial head prosthesis

designs result in dislocation, fatigue failure. implant loosening. and fractures [7,8]. A

major cause of these complications is extensive Wear of the articulating surfaces which

may be attributed to irregular loading of the prosthetic-bone interface, due to inaccurate

duplication of the original size and anatomic shape [12].

There are no reported studies using the normal anatomic radiai head geometry as a

baseline for prosthetic design [12.13]. The geomenic shape of the radial head is highly

non-syrnmetric and can not be replicated by a symrneaical implant [12]. It is posnilated

that standard radial head implants lack the ability to restore joint congruency and

kinematics to a natural state [12]. As a consequence, conventional radial head implants

often fit poorly and lead to premature cartilage Wear on the capitellum articular surface.

Furthemore, the articulating surface of the radial head is eccentric to the central axis of

the radius neck; although most implants have the stem located in the centre of the head

[6,12]. This may effect the normal axial load-bearing function of the radial head. The

most cornmonly used radiai head prosthesis is made of silicone [6]; however, serious

mechanical and biological disadvantages have been common complications [13,14].

1.3 Literature Review

Manual construction of customized orthopaedic prostheses is a time consurning

process which results in high costs. The most cornmon solution for efficient production

of custornized prosthesis, reached by most research groups. was implcmentation of

CAD/CAM technology (Cornputer Aided DesignKomputer Aided Manufacturing).

CADKAM systems can aid in translating anatomical data into a cornputer mode1 of the

examined bone[l5]. CAD models facilitate improved implant-bone fit, stability, and

ensure biomechanically comect geometry. Computerized Tornography (CT) imagery

seems to be the most cornmon means to acquire information needed to generate 3D

skeietai models [2,3.16,17]. Ultrasound technology has also been used for creating

information in order to fabncate prosthetic devices [ 1 8,191. The reconstructed 3D

geometry data is combined with design features to provide the optimal implant-bone

mechanics and minimize, or elirninate, the use of bone cernent needed to fi the implant

to the bone. Another possible application is that surgeons can actually plan and practice

delicate operating procedures pnor to surgery by utilizing precise models of implant and

bone geornetry. Creating CAD models allows for fmite element analyses of the implant

and bone structure which allow for implant modification. This would lead to predictions

regarding the success of the implant and its usefül life.

Cumently available CAD programs, however, are designed to serve mechanical

engineering applications such as the automobile industry. The most popular schemes in

commercial solid modelling packages are Boundary Representation (B-rep) and

Constructive Solid Geometry (CSG) [20]. B-rep is based on creating a solid model from

faces, edges. and vertices which are linked together in a way that ensures the topological

consistency of the rnodel. CSG is based on the generalization that most solid models can

be made from primitives such as blocks. spheres, and cylinders. The basic geometric

shapes are combined with a set of Boolean operations to create the desired model. These

mathematically based applications are unsuitable to produce the free form shapes of the

human body.

In order to create a successful prosthesis production system, a collaboration of

institutions is needed to combine expertise and resources in orthopedic surgery, image

scanning technology, and engineering. An example of a system that was created by a

number of diverse research groups is an interactive software program that has been

developed in order to create an optimal-fit hip stem, based on 3D bone geornetry data

obtained from CT scans [16]. The interactive process pemüts the redefmition of the

prepared 3D data. Four modules constituted the system: geometry, preprocessing, stem

design, and post processing. The software also allowed surgical procedures to be

simulated pnor to surgery in order to guarantee a successful insertion. It also allowed for

further studies of axial loading and bending moments. This software was used to create

implants using individual models, and the resultant designs were scaled to standard sizes

with averaged geometry. The result was an improvement over the standard syrnmetrically

shaped prostheses [ 1 61.

Another research group has developed a software program that converts CT

information into a closed contour representation [3,4]. The bone edges are Iocated by

utilizing CT attenuation values which enable the isolation of bone information from the

soft tissue. These values are input into a series of algorithms that output closed contours

outlining the shape, and generate instructions for rnilling machines. The software also

d o w s manual interaction at the CAD/CAM station for design modifications.

Rapid prototyping systems are used by most prosthesis designers to manufacture

prototypes of the implants. Such systems can speed prosthesis design and improve fit and

quality; and they can also aid in planning for surgery by making models that dispiay

locations of critical tissues and structures [17]. The most common rapid prototyping

technique is computerized numerical control machining (CNC). This technique is used to

machine the actual implant, came a positive mold pattern for vacuum forming processes.

or machine dies for forging. Parts are usually fabricated using CNC machines, either in-

house or at a machine shop facility. The geometry information is provided in the form of

IGES files, CAD drawings or blueprints. The design of an implant is usually modified

for manufacturability and ease of insertion.

1.4 Thesis Overview

The focus of this thesis work is the application of reverse engineering technology

in the field of upper limb surgery. More specifically, in the production of a customized

prosthesis for the head of the radius bone of the elbow joint.

The steps involved in the process of reverse engineering the radial head from CT

imagery and manufacturing a custom orthopaedic implant are described in the foilowing

chapters. An overview of the steps involved in reverse engineering bone geometry is

presented in Chapter 2. This chapter will also summa.rize the procedures and results of an

initial experiment to reverse engineer a radial head. Chapter 3 proposes a method for

adaptively reconstructing contours from a sequence of cross-sectional irnagery. A two-

layer neural network, called the Bernstein Basis Function (BBF) network, is used to

determine the control points of a closed Bezier curve that best approximates the data

dong the boundary of a segrnented bone region.

Chapter 4 describes the steps involved in reconsmicting closed contours and

approximating surfaces from senal Cï imagery. It also presents the adaptive algonthm

that computes Bezier control points from the edge data extracted from each cross-

sectional slice. Chapter 5 presents the application of this algorithm for the purpose of

reverse engineering the bone surface geometry of the radial head. It will also include the

results of a number of implant manufactunng experiments. The validation results of the

bone geometry using the Coordinate ~Measuring Machine (CMM) are also included in

Chapter 5. Concluding remarks and recommendations are given in Chapter 6.

CHAPTER 2

STEPS IN REVERSE ENGINEERING B O N . STRUCTURE

2.1 Introduction

This chapter introduces the process of reverse engineering. This process was used

to make the goal of producing customized prosthesis attainable in the most efficient and

cost effective way [21]. Reverse engineering is the process of generating a three-

dimensionai model of an existing object. The CO-ordinate data describing the geometry of

the object is usually extracted by a data acquisition system, such as a CO-ordinate

measuruig machine (CMM), ultrasound. laser scanning, magnetic resonance, or computer

tomography (CT) imaging systems.

The scanned information is then processed in order to be translated into a

Cornputer Aided Design (CAD) package for mode1 visualisation and further design

modifications. The data processing involves filtering the data to eliminate any corrupted

data or noise, translating the data into an acceptable format for the CAD package. and

finaily fitting the data with paramevic curves or surfaces in order to produce the final

solid model.

Once the solid mode1 is reconstructed, it c m be manufactured using a number of

rapid prototyping techniques such as stereolithography, selective laser sintering, and

larninated object manufacturing [17,22,28-301. For these techniques the 3D CAD model

is required to be translated into a standard format (STL) in order to be fed electronically

into the rapid prototyping machine. Another rapid prototyping technique is computerized

numerical control (CNC) machining, which is generating a machine tool path from the

solid model and using it to manufacture the part using a CNC machine [2,16,3 11. CNC

aliows for a larger variety of materials to be used in prototype manufacturing.

The final step in a reverse engineering process is inspecting the manufactured

prototype to ensure that the surface geometry does not deviate by more than a given

tolerance from the original measured data. Besides the usual visual inspection of the part,

a more accurate evaluation can be achieved with the use of a CMM. The general steps

outlined above for reverse engineering are summarized in Figure 2.1.

i Data Acquisition 1

1 Data Translation into CAD Package 1

I + Solid Mode1 Creation

Prototype Manufacture m 1 +

Prototype Inspection and Testing

Figure 2.1 Steps in reverse engineering.

Reverse engineering methods are potentially of great benefit in the prosthetic

manufacturing field. The steps introduced above c m be applied to produce custornized

implants. One cornrnon method of acquiring anatomy information is computer

tomography (CT) [3,23]. CT provides cross-sectionai image data of a scanned body.

Each CT image represents a single cross-section of the bone anatomy. CT X-ray

attenuation values are used to locate bone edge data. This data is filtered, translated into

real CO-ordinates, and transferred into a CAD system in order to create a solid mode1 of

the entire part. Once the solid mode1 is created, it can be manufactured using machining

or rapid prototyping techniques.

Efforts to automate this process have been made by a number of research groups

in an attempt to reduce the cost and tirne required to produce custom prostheses [3,16,17].

A common outcome of most of these efforts was the dependency of the process on

available facilities and machine specific proprietary cornputer programs. However.

several implants were successfully produced. such as facial bone. hip, knee. and pelvic

components [2,3,15,16].

The following is a description of an initial pilot investigation of reverse

engineering a radial head using the steps introduced above. A prototype of the implant

was developed using the facilities and resources available at The Hand and Upper Limb

Centre at St. Joseph's Health Centre, and The University of Western Ontario Faculty of

Engineering Science. The majority of the development process was done manually in

order to understand the basics of the reverse engineering process and use the results in the

design of a more efficient process.

2.2 Data Acquisition

CT images of a cadaver arm were acquired at St. Joseph's Health Centre using a

General Electnc Highspeed Advantage Rapid Processing CT Scanner, which is illustrated

in Figure 2.2. Scanning started at 40 mm below the elbow joint and moved towards the

elbow at 1 mm increments to create a total of 40 CT image slices. Out of these 40 image

slices. slices I through 30 included the required information to recreate a solid mode1 of

the radius bone (slice 1 is the fxst CT scan taken at 40 mm below the elbow joint).

Figure 2.2 CT machine used to scan cadaver m.

The format of the CT image data was converted using a machine specific

propnetary cornputer program. The data conversion was necessary in order to allow the

analysis of each image slice using the in-house ~ s t a t ~ a k ' , a CT imaging software.

Xstatpak allowed the user to highlight the radius bone cross-section in each slice as the

region of interest (ROI). This was done by varying the lower limit of the CT number

Alter in order to allow only the bone region to be selected [23]. The outline of each bone

slice was defmed using the edge detection algorithm available in the Xstatpak software.

Figure 2.3 is an example of a CT image of the radius as viewed using Xstatpak.

xstatpaks is a multipurpose image quantification utility for use by resûuchers in medical imaging. It was created by Jay Davis at St. Joseph's Health Center.

Radiu cross-

Figure 2.3 A CT image of the radius near the eibow joint.

2.3 Data Translation into a CAD Package

The CO-ordinates of each bone slice outiine were expressed in x and y pixel

numbers, with the ongin at the top left corner of the slice. The CAD software used in this

process was 1-DEAS Master Series V3.0. The format of the output of the Xstatpak

package was not acceptable as an input to the 1-DEAS software package. A C program

was written in order to transfonn each slice information into an 1-DEAS program file. It

also ~anslated the pixel numbers into real CO-ordinate points of x and y values. The

resolution of the images was at 1 5 c d 5 12 pixels, dictating a conversion factor of 1 mm =

3.41333 pixels to be used in the program. The program created points rather than splines

in order to avoid distorted contour shapes due to image noise. Each 1-DEAS prograrn file

was run separately at lrnm spacing between each slice.

2.4 Solid Mode1 Creation - Contour Fitting And Surface Reconstruction

At this point, prosthesis design considerations dictated the manual manipulation

of points of each slice. The radial head prosthesis consists of two parts: the head and the

stem. Clear information of the inside bone edge was available from slices 1 through 18

of the particular series of slice data. These slices provided the outside geometry of the

stem. The stem was scaled down by a factor of 0.73 to ensure a smooth fit into the

medullary canal of the radial neck. Slices 19 through 30 provided the geometry for the

prosthesis head by creating splines from the points defming the circumference of the

radial head. Figure 2.4 presents an example of a radial head contour created from a

translated CT image slice. Each contour was created using the 3D spline feature in 1-

DEAS 1241. This subroutine fits a Non Uniform Rational B-spline curve (NU=) to the

selected data points. If a large number of data points is selected a high order NURB may

cause oscillation between points. The points defuiing the splines were selected manually

in order to ensure smooth contours and to avoid image noise distortions.

(a) image data point. (b) contour created from data points.

Figure 2.4 The generation of contours from image edge data.

The solid mode1 was created using the lofting feanire in the 1-DEAS Surfacing

application. The lofting command was used twice: to loft the contours defining the radial

head and to loft the contours defïning the insert. Figure 2.5 illustrates the lofting of the

contours that defmed the outside geometry of the radial head. Once lofted, the radial

head was joined to the insert using the join cornrnand in the 1-DEAS Master Modeler

task.

Figure 2.5 The lofting of contours which defmed the radial head geometry.

2.5 Prototype Manufacture

The fmalized solid model was then used to generate the tool-path for machining a

prototype of the implant. This was done by using the IDEAS Manufacturing application

and its Generative Machining task. The part was manufactured using a five-axis CNC

vertical milling machine (Fada1 VMC 4020). The solid model was centered inside a 40

mm x 40 mm x 50.8 mm stock piece. The z=O plane was placed on the centreline of the

biock and the part. The fint machining operation created was a volume clear using a 114

inch (6.35 mm) end mill. The second operation was a copy mil1 which used a 1/ 16 inch

(1.5875 mm) bal1 rnill. Both operations stopped at the centreline of the stock and the

model. Both parts had to be rotated 180 degrees in order to create the same operations for

the second half of the part, with a separate program written for each side. Prototypes of

the part were made of delrin. An alternative method was developed to machine a more

accurate prototype by utilising the rotating axis on the CNC in order to reduce the set-up

time and machine the part using a single program. This method is presented in Chapter 5.

2.6 Evaluation of Reverse Engineering Process

2.6.1 Visual inspection of prototype

The manufactured prototype was cornpared to the original radial head. The

specimen origindly scanned was renieved from storage and dissected. The original radiai

head was removed from the arm for a close visual cornparison with the prototype as

shown in Figure 2.6. The manufactured radial head implant was then inserted into the

cadaver arm to examine the fit and the articulation of the implant with the humerus and

the ulna; this is s h o w in Figure 2.7. Qualitatively, the results of both initial inspections

were satisfactory and very promising.

The surface information of radio-capitellum articulation could not be generated by

the Ci' scans, because the scans only provided 2D planar images without any depth

information. Thus the machined prototype lacked that dish surface information.

However. it was approximated by modimng the CAD mode1 on 1-DEAS. It was created

by a surface operation of a sphere cut out of the top surface of the radial head.

Figure 2.6 Visual inspection of the implant prototype compared to the original radial

head.

Figure 2.7 Lnitial inspection of the prototype's geometrical fit with the original cadaver

arrn.

2.6.2 Discussion

The manual process of pmducing the custom prosthesis was lengthy, with a few

challenging obstacles. The rnost important one was the Iack of a standard format to

transfer information directly from one machine to the other. A proprietary program was

needed to convert the raw CT image files into a format suitable for the Xstatpak software.

As well, a computer program was written to translate the edge detection information into

a program file specifically for the 1-DEAS Package. The program processed one file at a

time and was only useful for the 1-DEAS software package. The work environment and

technologies used for this production process were limited to the specific machines with

the specific programs available.

Another major dBiculty was creating the contours from the data points. The

manual process was very time consuming and involved some estimation of the

appropriate points to be chosen. Inaccurate data due to noise was a reoccurring problem

during contour creations. A visual inspection of al1 the created contours was essential to

ensure that once they were put together they resembled the original bone geometry.

Furthemore, the manufacturhg process had sorne initiai problems of tool and

part collisions as well as tool and machine coIlisions. Most problems were primarily

caused by the G-Code post processor which translated the tool path information from the

software package into the G code for the CNC. These problems were solved by verifying

the validity of the tool path using the animation feature on 1-DEAS and by visually

inspecting the G code.

2.7 Concluding Rernarks

The pilot reverse engineering experiment described above was the first milestone

in the overall goal of autornating the production of custornised radial head prosthesis. As

the experiment evaluation indicated. the manual creation of the cross-sectional contours

proved to be the most time consuming step in the overall process. Therefore, the next

step in this work was to improve the efficiency of the contours reconsûuction process.

Several research groups have developed surface fitting techniques for the purpose

of reverse engineering a 3D object [25-271. However. a different approach will be taken

in this case. The goal is to apply curve fitting techniques to the measurement data in

order to automate the generation of the cross-sectional contours. This approach will

allow the prosthesis design specialist to manipulate the resuitant contours manually

before producing the solid mode1 by lofting. This approach relies on the fact that the

lofting feature of the 1-DEAS Surfacing application proved to be satisfactory and very

time efficient.

CHAfTER 3

CURVE APPROXIMATION USING A BERNSTEIN BASIS

FUNCTION (BBF) NETWORK

3.1 Introduction

The overall objective of this work is to create an accurate solid model of the radial

head geometry for the purpose of producing a customized implant. This solid model will

be created from the cross-sectional CT image data of the bone. The approach taken here

is to focus on generating accurate closed contours that approximate the outline of each

bone cross-section, using appropriate curve approximation techniques. These contours

can then be translated into a CAD package and used to design a solid model of the radial

head implant.

There are two methods of obtaining curves fiom measured data, curve fining

techniques and curve approximation techniques [32]. Curve fitting requires the curve to

pass through al1 the measured data. Exarnples of curve fitting are cubic splines and

parabolically blended curves. For curve approximation techniques, the resulting curve

passes through a few (if any) of the measured points. Control points are used to define

the desired curve. Examples of curve approximation techniques are Bezier curves and B-

spline curves.

The initial measured data in this case is the slice outline that was produced using

the Xstatpak software described in Section 2.2. As indicated in Figure 2.4, a typical slice

includes noise that makes curve fitting (connecting dl data points) an impractical method.

Due to the nature of the measured data, curve approximation techniques are used to

obtain the closed contours from the bone outline information.

These techniques are used to develop an adaptive algonthm to reconstruct the

closed contours from the serial CT imagery of the radial head. A two-layered Bemstein

Basis Function Neural Network is used to apply the algorithm to reconstmct the bone

geometry and translate the results to a CAD package. The following sections include a

description of the contour approximation method used, a bnef introduction to neural

networks, and the application of Bernstein Basis Function networks in closed contour

approximation of the radial head geomeq.

3.2 Contour Approximation Using Bezier Curves

The approximation technique used to fit curves to the bone cross-sectional data

utilises Bezier curves. A Bezier c w e is defmed by a set of control points that form a

polygon [32]. The shape of the curve follows that of the polygon. The end points of the

curve and the polygon are coincident. The tangent vectors at both ends of the curve have

the same direction as the corresponding fust and Iast polygon spans. Furthermore, the

curve lies within the convex hull of the d e f ~ g polygon. The convex hull is the largest

convex defined by the polygon points. The degree of the resultant curve, n. is one less

than the number of control points, n + l . A Bezier curve is also defmed by a parameter

value u, O I u I 1. This value is the relative distance of a point moving dong the curve.

An example of a Bezier curve is given in Figure 3.1 to illustrate its main properties.

P3

Figure 3.1 An example of a Bezier curve defined by five control points and a parameter

value u.

The mathematicai representation of a Bezier curve defmes a point s(u) on the

curve at some parametric distance u by:

where wi is the i" control point, and @Ju) is the Bernstein polynomiai. A Bernstein

polynornial of degree n is defined by:

Closed Bezier curves are used to approxirnate the cross-sectional data of the radial

head. One major advantage of closed Bezier curves is that they require only a small

number of control points in order to define the bone geometry. Assuming that the edge

data of a CT image is pre-ordered and stored in array [P.] = [PdTx2, where pu is the fh J

.th edge data point in the J image slice, and pQ = [xG , yJ. The u value is assigned to each

data point by using the centripetai parameterization technique, which will be discussed in

the following chapter. The bone circumference is then represented by coordinate array

[PjlTx2 and parameter array [Uj lTxl After parameterization, a curve approximation

technique is used to determine the control points that best approximate the bone cross

section. Equation 3.1 is slightly modified to account for a different set of control points

for each CT slice information:

sj (u) - i=O

where sj (u), and u are as defined above, and wij = [wXii, w ] is the i' control point

vector in the cross-section j. The system of equations can be written as

For a curve approximation application, the measured data points are assumed to

equal the Bezier curve points at the sarne u value: i.e. [SJ=[P$ Therefore equation 3.4

becomes:

solving for the control points array, equation 3.5 is rewritten as:

Since the number of conbol points are less than the data points the system of

equations can only be solved using a least squares fitting procedure L26.321, which is

defmed as:

where T is the matrix transpose.

The curve fitting procedure described above does not guarantee that a closed

curve will be generated for the points extracted from the bone outline. Minimal

requirernents for a srnooth closed curve are positional (CO) continuity, and tangentid (C ')

continuity. The resulting Bezier cuwe is only CO continuous if the fust and 1 s t control

points of a polygon net are the sarne, i.e. coincident. Furthemore, the Bezier curve is CI

continuous only if the fust and last segments of the control polygon have the sarne slope;

i.e. collinear. Additional constraints must, therefore, be placed on the selection of

acceptable control points.

The necessary constraints can be developed from the basic properties of the

Bernstein polynornials. The Bezier curve interpolates the fmt and 1 s t control points;

that is. it passes through wOj and w for u = O and 1 in Equation 3.3. Furthemore, the n~ i

curve is tangent to the first and last segments of the charactenstic polygon.

To ensure CO continuity. a closed Bezier curve can be generated by closing its

characteristic polygon by choosing w and w to be coincident. First-order ci OJ n~

continuity cm be achieved by ensuring that the slope of the fmt polygon segment equals

the siope of the last polygon segment; that is

3.3 Basis Function Neural Networks

A neural network is a computing architecture that was inspired by the biological

neural system [34,35]. In the biological system, information is processed at simple

elements called neurons. The main components of a neuron are the soma, dendrites, and

axon. Signals are transmitted from the axon branches of one neuron to the dendrites of

another through a synaptic gap. or a comection link. by means of a chemical process.

The chemical transmitter at each comection link scales the frequency of the signals by an

associated factor or weight. The soma sums dl the incorning signals by applying an

activation function in order to determine one output signal which is then transrnitted to

other neurons. Figure 3.2 describes the main components of a biological neuron.

Figure 3.2 Schematic of a biological neuron.

An artificial neural network resembles the biological neural system in its

components and their hnctions. The neural network also consists of neurons and

connection links. The neurons process information and send it to other neurons through

the connection links. At these Iinks the information is modified by a certain weight

before it is received by the next neuron. The receiving neuron sums al1 the weighted

input information and transrnits a single output to other neurons. Figure 3.3 descnbes a

simple artificial neural network mode1 used in computing applications.

Figure 3.3 An artificial neural network.

The building blocks of a neural network are the computing architecture and the

method of training [35,37.38]. A neural network is usually organized in the form of

layers. The simple network shown in Figure 3.3 is referred to as a single-Iayer network

due to its one computing output layer. The input layer is not counted since it is only an

input source with no computations. A multi- layered network consists of an input layer,

hidden layers where computations occur and fmally an output layer. The key

characteristic of neural networks is their ability to learn and adapt. The input vectors

represent the new neural information or training data, whiie the weight vectors represent

the knowledge base. The applications of neural networks include sorting and recalling

pattems, grouping similar patterns, speech recognition, and machine-vision systems.

A neural network cm be used to solve a curve or surface approximation problem,

where learning is equivalent to finding a curve or surface that fits the training data (i.e.

measurement points) with the desired accuracy [25,39]. One type of such neural network

is a basis function network. It is a two-layer computing structure where the outputs are

the linear combination of weighted basis functions. The hidden layer neurons compute

these basis functions based on the input received from the input layer. An exarnple of

this type of network is Radial Basis Function (RBF) networks, which use Gaussian ba i s

functions in the hidden layer computations [35,36]. Similarly, the Bemstein Basis

Function Network (BBF) cornputes Bernstein functions used in the construction of a

Bezier curve (Equation 3.2). The next section introduces the application of the BBF

network in reconstructing the radial head geometry.

3.4 Closed Contour Approximation Using Bernstein Basis Function Network (BBF)

The BBF network is an adaptive approach to determine a small number of control

points that will approximate a Bezier curve from measured data [25,40]. This approach is

used in the application of reconstructing the radial head geometry by approximating a

closed contour for each individual cross-section using the curve approximation technique

described in Section 3.2. Figure 3.4 is a block diagram of the BBF network. Initially, the

measured coordinates (x . y .) are translated into parametric u values. These values Y tJ ti

constitue the input layer. The neurons in the hidden layer cornpute the Bernstein basis

fbnctions. The neurons in the second layer perform a linear sumrnation of weighted bais

function outputs to produce the reconstructed coordinates (x(u +), y(u .)). The weights in rl rl

the BBF network represent the control points required to reconstmct a Bezier curve.

These weights are updated using a learning algorithm that will be discussed in Chapter 4.

The network continues the weight adaptation process until an assigned nurnber of

iterations is reached or a desired accuracy is achieved. The resultant control points are

then used to create a closed Bezier contour that approximates the outline of the bone

slice .

- - - - - - - - - - - - 1 I reconstnicted 1

input coordinates

1 L - , , - - , , , , , error

e, = prj - SL+f, 1

Least- Mean-Squares Leaming Algorithm

Figure 3.4 Block diagram of a BBF network.

3.5 Conclucihg Remarks

This chapter described the basic principles of curve approximation techniques

using Bezier curves. Furthemore, the BBF network was introduced to describe the

computing mode1 used to implement the curve approximation technique. The theory

presented in this chapter represents the building blocks of programniing algorithms that

are combined into one computer program. This computer program requires the

segmented CT information as input and provides a series of closed contours of the radial

head cross-sections, with the desired accuracy, as outputs. The algorithms are explained

in detail in the next chapter.

CHlAPTER 4

RECONSTRUCTING SURFACES FROM SERIAL CROSS-

SECTIONS USING THE BBF NETWORK

4.1 Introduction

The current chapter describes in detail the main steps taken to reconstruct the

solid mode1 of the radial head from the serial cross-sections. The basic principles of

Bezier curve approximating techniques and the BBF network that were discussed in

Chapter 3 are applied. Most of the steps are compiled into a single computer program

which uses the processed (3T image data to produce a series of closed contours that

correspond to each CT slice image, and define the geometry of the reverse engineered

radial head.

The main steps that define the reconstruction process are image segmentation.

boundary tracking, parameterization, contour fitting, and lofting of the fitted contours

[26,27]. These steps are discussed in the following sections. Figure 4.1 represents a

simplified flowchart of the main blocks of algonthrns used in the computer program.

/ f Input

degree n number of iterations

number of cross-sections Xstatpak image data /

1 h a g e segmentation I

B oundary trac king i

/ ~ o n û o i points

/ and Closed contours of

cross-sections

of radial head

i End

Figure 4.1 Prirnary steps in the process of reconstmcting the radial head geometry.

4.2 Image Segmentation

Image segmentation is the f m t step in the reconstruction process following the

data acquisition phase using the CT imaging equipment. A CT image usually consists of

a large number of pixel data. It includes die scan data of the target bone dong with the

surrounding tissue and adjacent bone ji.e. the ulna and humerus). The region of interest

(ROI) rnust be identified and extracted fiom each cross-sectional image. Segmentation of

the CT images, required to eliminate unnecessary information, involves the extraction of

boundary points around the ROI to reduce the number of data points for ease of data

handling and manipulation.

The series of CT images of the radial head were acquired at St. Joseph's Health

Centre using a General Electnc Highspeed Advantage Rapid Processing CT Scanner.

Scanning starts at some distance above the elbow joint and moves towards the hand at 1

mm increments. The raw CT data needed to be converted into a format that would allow

it to be analyzed and processed. The conversion is done using a proprietary cornputer

prograrn created for the specific General Electric CT Scanner. The f i t CT image

segmentation operation was done using Xstatpak imaging software. which was introduced

in Chapter 2. It allowed the user to create an ROI around the radius. Once the data

analysis is restricted to the desired region. the user is able to Vary the lower limit of the

CT number filter in order to highlight the image pixels that constinite the bone image

information (bone pixel intensity is greater than that of the surrounding soft tissue). The

outline of the image is then estimated using a propnetary edge detection algorithm

available in the software. The principle of this algorithm is to undergo a scan of the

image and record the fmt and last highlighted pixels in the same continuous line of pixels

in the ROI.

If gaps exist within the bone region, one line across the image would have a

number of edge pixels rather than the ideal number of two edge pixels for each line. For

this reason further segmentation of the image is required in order to elirninate irrelevant

edge data from the segmented bone information that was exrracted using Xstatpak.

Figure 4.2 illustrates the noise included in a typical edge pixel image. The slice presented

is slice number 15 from specimen series E. The same slice will be used in figures

throughout this chapter to illustrate the effects of the different steps of the surface

reconstruction process.

+-

f i t , Ti

Figure 4.2 A typical CT slice edge data as produced by the Xstatpak software.

(series E, slice 15).

4.2.1 Morphological operations

Morphological operations are used to further simpliQ and defme the segmented

region boundaries. Mathematical morphology is a term adopted from the original

morphology meanhg that refers to the study of form and structure in scientific fields such

as biology and geography. Morphological operations in general are tools for extracting

the digitized image components that are needed for image description and analysis such

as boundaries, skeletons, and convex hulls. Mathematical morphology is also used to

preprocess images for the purpose of filtering or thinning [41].

The language of binary mathematical morphology is set theory. Morphological

transformations involve the manipulation of two sets [41-431. The set of points being

morphologically transfomed are referred to as the selected set. The set of points that acts

on the selected set is referred to as the structuring element. The geometric characteristics

of this senicturing element reflects the shape of interest to be observed in the selected set.

In the binary image case the selected set is the foreground and the complement set is the

background. The shape of a binary image is represented by a set of al1 black pixels in a

black and white image. Therefore. the selected set is actuaily the set of points that

completely describes the image. In binary images the sets are members of a 2-D integer

space.

Most morphological operations used in image analysis are based on erosion and

dilation. Dilation is a morphologicai transformation that combines the image set and the

structuring element set by using vector addition of the set elements [42,43]. It is an

operation that can be described as filling, expanding or growing of the original image. If

a senicturing element B is swept over the image A, each time the ongin of B touches a

black pixel (a binary l ) , the entire translated shape of 6 is added to the output image by

an OR operation where initiaily the output image had only white pixels (binary O). Figure

4.3 demonstrates a simple example of the dilation operation.

Original image Structuring element Dilated image

Figure 4.3 An example of dilation of an image.

Erosion is a morphological transformation that combines two sets by vector

subtraction of set elements and uses containment as its basis set [42,43]. Erosion is

referred to as a shrinking or reducing operation of the original image. The smicturing

element B can be viewed as a probe that slides across the image A testing the composition

of A. The origin of B is translated at a point x, if 8 is contained in A then x belongs to the

eroded image using an AND operation. Figure 4.4 is a simple example that demonstrates

the erosion operation.

Origind image Structuring element Eroded image

Figure 4.4 An example of erosion of an image.

In the particular application of reconstnicting the radiai head bone, the edge image

was fmt modified by filling the spaces between edge pixels as shown in Figure 4.5a. A

dilation operation was then perfomed on the segrnented bone data followed by an erosion

operation. A 5 x 5 smicnuing element of pixels was used in both operations. These

morphological transformations are intended to eliminate the noise in the segmented data

in order to allow for an optimal reconstruction of the bone outline. The slice presented in

Figure 4.5a was processed using these morphological transformations; the result is

presented in Figure 4.5b.

Original image Processed image

Figure 4.5 The effect of dilation and erosion operations on slice 15 using a 5x5

structuring element.

4.2.2 Edge detection dgonthm

After the morphological operations an edge detection algorithm is applied in order

to isolate the set of pixels that are needed for the curve fitting technique. The aigorithm

involves scanning the segmented region from left to right fmt, and then from top to

bottom in order to get al1 the pixels that define the binary image outline. These pixels are

located by detecting a difference in the binary pixel values. An edge pixel is the f i t

black pixel between the black image and the white background. A difference in value of

absolute 1 between two adjacent pixels yields a location of an edge point. The edge

points of slice 15 are presented below in Figure 4.6 .

Figure 4.6 The result of the edge detection algorithm for slice 15.

4.3 Boundary Tracking

Once the image data is reduced to pixels that lie along the outer circurnference of

the segmented bone region, a tracking algorithm is applied to link these edge points into

an appropriate sequence. Grouping the edge pixels into a sequence is necessary for the

curve approximation process. The tracking starts by scanning across the image until an

edge pixel is found. That edge pixel is labeled as a starting point for the tracking process.

A spiral clockwise search is then started around that fmt pixel. The clockwise search is

based on examining the neighboring pixels of the current edge point in order to find the

next nearest edge pixel.

The ordered edge pixels are converted into real coordinate values expressed in

metric units, and are stored in array [P.] - [ p d T f l , where pQ = [ x ~ , y+ represents the J

coordinate locations of edge pixel t, T is the total number of edge pixels in the bone

region circumference, and j identifies the individual cross-section image. A restriction on

the tracking algorithm was added in order to ensure that the reconstnicted Bezier curve is

closed and, thereby, CO continuity is obtained. This restriction dictates that the first, plJ7

and last pTj coordinate in array [PJ must be identical. This is achieved by making the

boundary tracking process follow along the edge until the f i t point is reached again,

which ensures a closed contour. Once the tracking operation is complete, the ordered

edge coordinates are used as the training data in the curve approximation procedure. The

data is also stored in a file in order to venQ the segmentation and edge detection

methods. Figure 4.7 presents the training data for the outer edge of stice 15.

Figure 4.7 Training data for slice 15.

4.4 Parameterization

The image segmentation and boundary tracking processes descnbed above are the

initial steps required to convert the bone CI' images into a format that c m be used for the

curve approximation technique. The image is now simplified h to sequenced data that

outline the border of the bone cross-sections. The next step in the curve approximation

process is pararneterization. As mentioned in Chapter 3, Bezier curve approximation

techniques are used to fit a closed contour to the data outlining the bone region. A Bezier

curve is defimed by a parameter value u. O I u I 1. which is the relative distance of a point

moving dong the curve (illustrated in Figure 3.1). Parametenzation is the process of

assigning a parameter value u to each of the edge data points.

The choice of parameters influences the shape of the curve. The main concem in

such reverse engineering applications is to obtain a "fairly smooth" or 'pleasing" curve

through the rneasurement data. The pararneters must be chosen with this concem in

rnind. The term "pleasing" is difficult to quantifi; therefore, it is difficult to distinguish a

good set of pararneters. A satisfjmg proof would be creating a c u v e that suitably

conforms in shape to the polygonal curve defmed by comecting the initial points (i.e.

training data as presented in Figure 4.7).

There are three cornmon pararneterization techniques: uniform, chord length. and

centripetal parameterization. A generalization of the three methods can be presented in

the exponential mode1 [44,45],

where ul -0.0, uT = 1.1 1 1 1 is distance metric, T is the nurnber of data point vecton, and

This mode1 reduces to the uniform parameterization when e = 0, and to the chord

length parameterization when e 4. Uniform pararneterization is a simple technique

which does not take into account the distribution of the data points [44,45]. A better

choice of pararneters is determined using cumulative chord length parameterization.

[44,45]. If the data is evenly spaced the technique is approximately the same as uniform

pararneterization. Therefore, this method is most advantageous when the points are

unevenly spaced. hevious research concluded that reducing the value of e causes the

resulting shape of the fitted cuve to move towards the shape that results from uniform

parameterization, while an increase in e will move the curve to one that tends toward the

chord length rnethod [45]

Another pararneterization method is the centripetal model. It is as

computationalIy simple as chord length parameterization but proved to work better [45].

The centripetal model is a method between the uniform and chord length with e - 0.5 in

Equation 4.1. It achieves a good balance of the other two methods and it tends to observe

the changing nature of the curvature for curve fitting. The resulting curve proved to

conform well to the data polygon.

For the current application of approximating curves to serial cross-sections, the

centripetal parameterization model was used. After the CT edge data of each slice, j, is

ordered and stored in array [PJ, a u value is assigned to each data by using the centripetal

model. Equation 4.1 is rewritten to accommodate for the multiple number of data sets.

The parameter value uG assigned to the th data point in slice j is given by:

th where u = O, urj = 1. II II is the distance metric, and p - is the t vector in array [P$ Z J r J

The bone circumference is now represented by coordinate array [P.] and parameter J Tx2

maY wj lTxi

4.5 Contour Fitting

After pararnetenzation, a curve fitting technique must be used to determine the

control points of the defining Bezier control polygon net that will be used to generate a

curve that best approximates the data outlining the segmented bone region [NI. As

descnbed in Chapter 3, the least squares LSQ fitting approach was applied to generate the

unknown control points which were defined by Equation 3.7.

In addition to Equation 3.7, more constraints are necessary to yield an accurate

curve. One constraint is to repeat the fmt and last polygon vertex, in order to have a 1

closed curve. Secondly, the curve must be constrained to be C continuous, Le. the f i t

and last segments of the control polygon must have the same slope. These constraints are

discussed in detail in the previous chapter.

The least mean squares, LMS, approach is used to minirnize the error of the curve

defined by the sum of the squares of the error vector magnitudes. The error vector

magnitude 1 py - S ( U ~ 1 denotes the error of the measurement point p The error of the r ~ -

curve is reduced by updating the control points (weights). The final control points are

found by repeating the LSQ fitting and weight correction until reaching a convergence

condition. The convergence condition is met when the average error vector magnitude of

al1 the points is smaller than a given accuracy, or when the number of iterations exceeds a

specified bound.

4.6 Weight Adaptation Using BBF Networks

The small number of control points that are required to generate a closed Bezier

curve is detemiined using the two-layered Bernstein Basis Function (BBF) network

discussed in Chapter 3. The weight vectors for the neurons in the output layer are trained

using the LMS algorithm. The network weights , w i j are rnodified to minimize the mean

squared error between the desired and the actual outputs of the network.

4.6.1 Weight adaptation algorithm

The training set for adapting the weights consists of the input-output pairs

( u r j , pl>. The weight adaptation algorithm used by the BBF network is given by the

following steps:

Step O. Set the parameter values required for the desired output as follows:

Set the initial desired degree of curve n, (where number of control points is n+l)

Set the average error to a desired accuracy, emU.

Set the maximum number of cycles through the training to equal kW

Step 1. Assign a parametnc value u to each edge data point, p using the centripetal r~ f J'

parameterization algorithm (Equation 4.2).

Step 2. For the fmt cross-section, initialize the weights, wiVl, to small random values

taken around the centroid of the data set [Pl 1. For al1 other cross-sections,

j > 1, initialize the weights to the converged weight values obtained from the

previous cross-sectionai plane, wi j-r*

Step 3. To ensure CO continuity for the closed Bezier curve, set the weight values

w o j = p l j and wnj=pTj .

Step 4. While the stopping condition is false, do Steps 5- 10.

Step 5. Randomly select a &hg pair (u , p, ) from arrays [Uj JTxi and r j

Step 6. Determine the output of the basis function neurons in layer 1, by

c o m p u ~ g the Benstein basis functions at ut using

n! t n-i @j,n('tj ) = i ( - U t , j ( 1- U i )

Sfep 7. Determine the response of the neurons in the output layer by

calculating the Bezier cuve coordinate values at utj using

Step 8. Calculate the error for each output neuron in layer 2 by

where the error vector is given by et = [ex[ , eyt ] .

Step 9. Update the weights for i = 1,2. ... n - 1 according to

W . . (k+l ) = W. .(k) + a. (e, @i,n(u,) + A wjJ (k) ) LJ 1J

where a = 0.25, and the momentum terrn is

A W . . (k) = wij (k) - wij (k-1). (4.6b) 'J

Step 10. While considering 1 '' order continuity, update both second and

second to last weights, i = 1 and n - 1, according to

where f! = 0.01. and the slope at the polygon end-points is given by

Step I I . Calculate the mean-squared error by

where T is the total nurnber of data points, and T is the vector transpose.

Step 12. Test for stopping conditions:

If MSEj 5 e,, then STOP

If MSE. > em, and k c kmar then go to Step 4 J

If MSE . > e,, and k = kmar , then: J

add a desired number of control points to the total number of control

points used in order to improve the curve fit accuracy (an increment of 5

control points was used during prograrnming)

reset the number of iterations to k - 1

if the number of control points is greater than maximum number allowed

for computations then STOP, othenvise go to Step 2

After convergence of the algorith, the weights of the neural network correspond

to the control points that will generate a closed Bezier cuve which approximates the

boundary for the segmented bone region in one particular slice. Furthexmore, the

resulting control polygons over the entire measured bone structure will be approximately

aligned because of the small separation between adjacent slices and initial conditions

based on the control points extracted from the previous slice

A successfully fitted cume might be defmed as one within the given tolerance. In

other words, the average error of the closed contour is smaller than the specified

tolerance. For unsuccessfbl curves, increasing the number of control points or increasing

the number of iterations is required. However, an optimal successful curve is created in

the les t possible number of control points, and there is always a Iimit to how useful is

increasing the number of iterations. The weight adaptation algorithm increases the

number of control points incrementally as required for each individual slice up tg 35

control points. It was also found that the benefit of increasing the number of iterations is

limited to approximately 2000 iterations. Figure 4.8 illustrates a Bezier curve generated

from the training data of Figure 4.7 which is superimposed on the same figure.

Figure 4.8 The resultant BeUer curve for slice 15 ( solid curve), and the training data

used for the weight adaptation algorithm.

4.6.2 Weight update

The BBF network weights were continuousiy updated within an epoch (a cycle

through the data set). The control points were updated based on the computation results

of each input-output pair ( u t j . p,.) The changes were proportional to the LMS error as

presented in Equation 4.6a. The error calculated from each pair was used to update the

control points used for the next pair. The magnitude of the change depends on the choice

of leaming rate a. A value between 0.1 and 0.9 have been used in many applications

[46]. A constant value of 0.25 was proven effective in the current application of curve

fitting. A momentum terni, defined in Equation 4.6b, was used in order to accelerate the

correction process.

Further weight updates were required for the second and second to last weights,

'VI j a'd Wn-rS to account for C' continuity. In this case, the weight vector changes were

proportional to the difference in the slopes of the fmt and last segments of the control

polygon as illustrated in Equation 4.7a. A small learning rate value of B = 0.01 proved to

be suitable for this specific application.

The final step in the solid mode1 reconstruction process was lofting the seriai

cross-sections. Lofting is a surface construction technique that involves joining a series

of two-dimensional closed sections. It forms a smooth surface by interpolating between

these sections. The success of the smooth surface reconstruction technique is dependent

upon the proper alignment of the contours [47]. Proper alignment of the cross-sections

starts at the data acquisition stage, since the CT machine scans the bone dong one axis at

equal increments. Further alignment of the reconstructed closed contours is obtained by

using the weights of the previous cross-sections as initial conditions for determining

weights of the section in the curve fitting process.

The output of the computer prograrn described in this Chapter was a senes of

closed contours that defined the outline of each bone slice. The output file that contained

the contour information was specificdy formatted for the 1-DEAS software package.

Once the contours were transferred into the CADICAM software, the lofting command

was applied. Tramferring the bone geometry as closed contours rather than one complete

surface enables the user to manipulate the geometry easily. The customized implant

production process should not be completely automated, because the bone mode1 has to

be modified and redesigned for optimal fit and functioning of the implant. The lofting

process using the 1-DEAS software was very user-friendly and time efficient.

The steps involved in the reconstruction of cross-sectional contours from CT

images of the radial head are image segmentation, boundary tracking. parameterization,

contour fitting, and lofting. Algorithrns for these steps were combined into one computer

prograrn. The program input was image edge data acquired from the Xstatpak software.

The main output of the program was a series of closed contours, one for each slice

information, in the 1-DEAS software program file format. These contours were then

uansformed into the CADICAM package for implant design and surface construction.

using the lofting cornmand available in the software. Chapter 5 presents the results of the

computer program.

CHAPTER 5

RECONSTRUCTION OF THl3 RADIAL HEAD

S. 1 Introduction

CT scanning of five denuded and embalrned cadaveric radial head specimens has

been done at St. Joseph's Health Center. CT scanning started at a few millimeters above

the elbow joint and moved down towards the radial head at 1 mm incrernents.

Approximately 45 scans were taken for each specimen. The scanned images of each

specimen were reduced to the number of images containing the required information.

These images were processed using the Xstatpak software package as described in

Chapter 2.

The cornputer algorithm described in Chapter 4 was used to reconstruct the

geometry of the five radial heads. Two versions of the program were created. One

version, referred to as the external program, was wntten to reconsmct ciosed contours

that defined the outer geometry of the radius bone specimen. The second version.

referred to as the intemal program, created closed contours of the inside edges of the

bone. The output of the intemal program was required for implant design considerations.

The difference between the two programs was mainly in the boundary tracking aigorithm.

The extemai program generates the training data from the outside contour in the edge

image presented in Figure 4.6, while the intemal program tracks the inside contour.

Once the resultant contours were transferred into the 1-DEAS software package

they were used to reconstruct the surface geometry of the radial head and redesign it for

the purpose of creating a soiid mode1 of a radial head prosthesis. The five sets of radial

head image scans were labeled A through E. The radial head specimens were reserved

until the prototypes were manufactured and ready for the verification procedures. Series

D will be referred to, as an example, throughout this Chapter in order to clariQ the

description of procedures and results. The results for the other series are presented in

Appendix 1.

5.2 Results Of Surface Reconstruction Of Radiai Head Geometry

For both extemal and intemal computer prograrns. the BBF network was trained

to fit a closed Bezier curve to the properly segmented bone information. Initially, ten

basis function neurons were used in layer 1 in order to generate a 9& degree Bezier curve

for each slice. However, in certain circumstances, that number had to increase in order to

meet the convergence requirements. The weights were adapted one slice at a time. The

maximum number of cycles through the training data for each slice was set to km, =

2000 and the maximum error was set to e,, = 0.1. If the algorithm did not converge

after 2000 cycles through the training data (i.e. LMSj > 0.1) the number of weights was

increased by 5 and the computing cycle started again at k - 1. Once the network

converged the weights were stored in the control point array [W .]. The process was then J

repeated for the parametenzed boundary data extracted from the next slice, and weights

from the previous slice were used as initial conditions.

5.2.1 Results of the external prograrn

Figure 5.1 illustrates the resultant closed contours for senes D after importing

them into the 1-DEAS software. The centroid points of each slice were also determined

by the prograrn and imported to 1-DEAS. These points were produced for design and

rnachining purposes.

Table 5.1 surnrnarizes some parameter value results of the extemal program for

series D. For this particular senes, the BBF network was able to converge by meeting the

required accuracy condition rather than meeting the conditions of maximum number of

control points or iterations. Most contours required only 11 control points in order to

meet the maximum error requirements. The most consistent exceptions were the fmt or

second slice of each series, as well as the slices that represent tuberosity cross-sections

(the radius tuberosity is illustrated in Figure 1.1). For senes D, the closed contours start

with an irregular shape which represents a slice of the image at the start of the radiai head.

Other series had one or two slices which resembled a "crescent moon" shape. This type

of cross-section usually required the highest number of control points and largest

computation time, relative to the rest of the slices in the series. The slices which defie

the radial head geornetry had a smooth elliptical shape with far fewer contro! points. As

the contours approach the tuberosity region, they become relatively irregular in shape and

somehmes require more control points to approximate their shapes.

Figure 5.1 Closed contours outlining the geornetry of the radius bone for senes D.

Table 5.1 Results of the extemal program using CT information of series D.

-

No. of No. of cycles

control points through

training data

5.2.2 Results of the internai program

Figure 5.2 illustrates the resultant intemal contours for series D and their

centroids. In this case, it is clear that not ail contours define the inside edges of the radius

bone. For example the fmt 3 contours were created fiom cross-sections at the middle of

the radial head. These cross-sections should not have inside contours, therefore, the

resultant contours are small which simply indicate some noise data within the image.

Table 5.2 shows the results of the BBF neural network of the internai program for

senes D. The symbol '-' is used for slices which did not have inside contours. The

results show about 12 contours (for slices 19-30) which approximate the inside edges of

the radius. The highly inegular shapes of slices 31-40 did not dlow the network to

converge to the appropriate accuracy. However, these slices were cross-sections of the

tuberosity which were not required for implant design.

Figure 5.2 Closed contours of the inside of the radius bone for series D.

Table 5.2 Results of the intemal program using CT information of senes D.

I Slice no. l MSE No. of No. of cycles

control points through

training data

53 Generation Of Radial Head Implant

The radial head implant consists of two parts: the radial head and insert. The

insert is the part of the prosthesis that is inserted into the hollow cavity of the radius bone

in order to fix it f d y in place. After the approximated closed Bezier curves of both

prograrns are transfemed into the 1-DEAS software package. the user is able to snidy the

resultant contours and determine the contours required for designing a proper radial head

and insert for the prosthesis. After the design phase and surface reconstruction phase of

each part were complete, the two parts were joined using a join command available in the

1-DEAS software. Figure 5.3 represents the surface mode1 of implant D.

Figure 5.3 Surface mode1 of implant D.

5.3.1 Generation of implant head

The solid model of the radial head was created by lofting the appropriate

contours that defme its geometry. The number of contours required to defme the

radial head was determined by observing interna1 contour representation. For series D,

slices 7 through 19 were used. This choice of contours was based on the fact that the

intemal contours started at slice 19 which meant that at this particular slice, the radial

head ends and the radius neck must start. This observation was based on the contour

representations and the tabulated results of the programs. The 13 closed contours were

lofted using the lofting cornrnand available in the 1-DEAS Master Surfacing Task.

5.3.2 Generation of implant insert

The shape of the insert was created by selecting the appropriate internai contours.

The intemal contours were used to ensure accurate positioning of the insert relative to the

radial head. As mentioned in Chapter 1, the radial head is offset from the neck of the

radius [12]; therefore, the insert should not be located in the centre of the head as most

currently available prosthesis are designed. For series D, contours 9 through 27 were

selected and scaied down to allow insertion into the bone. They were then lofted and

joined to the radial head solid model as shown in Figure 5.3.

5.4 Concluding Remarks

This Chapter presented the results of the BBF network algorithm. The low MSE

values presented in Tables 5.1 and 5.2 indicate that the curve fitting and weight

adaptation dgorithms were satisfactory and very promising. The output contours were

used to design a radial head prosthesis that best mimics the normal anatomy. The solid

model of the implant was then used to generate a machining code and was manufactured

using the Fada1 5-axis CNC machine. This step in the reverse engineering process is

discussed in the next chapter.

CHAPTER 6

PROTOTYPE MANüFACTURE AND VERIF'ICATION

6.1 Introduction

The next step in the reverse engineering process that followed the solid model

creation was prototype manufacture and verifications. The Fadal 5-axis CNC machine

was used to manufacture the prototypes, and the machine tool path was generated using

the SURFCAM V6.1 CAM package.

The prototype venfication methods used include inspection of the series of closed

contours produced by the BBF network, as well as inspection of the radial head geometry.

Accurate inspection of the radial head geometry was done using the DEA Swift tactile

probe coordinate measuring machine (CMM), which had an accuracy of I ,005 mm. The

CMM inspection established a cornparison between the geometry of the radial head

specimen, the machined prototype. and standard implants. In order to align the parts

accurately a prototype of the radius specimen, rather than the implant was required.

Therefore, a radius bone model was made from the external contours of each of the five

specimens. The bone model included the niberosity of the radial head which played a

major roie in the proper alignment of both sarnples for CMM inspection. Figure 6.1

illustrates the bone mode1 for series C.

Radius tu berosity

Figure 6.1 Bone model for series C.

6.2 Prototype Manufacture

Based on the results from the fmt reverse engineering experirnent descnbed in

Chapter 2, Caxis machining was proved to be superior to 3-axis for the application of

radius prototype manufacture. The most significant advantages of Caxis over 3-axis

machining were the seamless and smoother machined surfaces as well as shorter set-up

times. The one main drawback was that the time to machine a surface using Caxis was

significantly greater than the time required to machine it using 3-mis programming.

The 1-DEAS Generative Machining Task was not capable of generating machine

code for Caxis rnilling. However, SURCAM version 6.1, also available at UWO, had

that capability as well as a post-processor which translated rnachining code to the Fada1

CNC machine. The geometric data of the solid model was transferred from the 1-DEAS

software to SURFCAM via IGES translators (Initial Graphics Exchange Specification).

Problems associated with product model data exchange included the fact that the

translated geometry was not identical to the original representation. This caused major

difficulties in machine code generation. For exampie, a surface created by the 1-DEAS

lofting cornmand may be constnicted fiom a number of surface patches, but it was still

considered as one surface for machining purposes. SURFCAM on the other hand,

considered every surface patch a separate surface. During the Caxis machine code

generation SURFCAM only allowed the generation of code for one surface at a time with

no considerations given to the adjacent patches, which caused gouging in the surfaces.

Another transfer problem was that some surface models did not comply with the

original shape. They either had extra boundary curves or untrimmed planes. A number

of surface manipulation techniques were attempted within SURFCAM, but the results

seemed unsatisfactory and did not resolve most of the machining problems. Other

solution attempts focused on exploring different methods of machining the surface. but

these attempts failed as well. The final solution was to create the surfaces using

SURFCAM's lofting procedure which proved to be a time efficient process.

6.2.1 Part set-up

The radius bone prototype was machined from a cylindncal stock of delrin. The

stock was placed inside the rotary table of the CNC machine. The table rotates about the

x-ais. The solid model was carefully placed in the same orientation using the sarne

reference system on the cornputer software. Figure 6.2 illustrates the set-up for prototype

machining.

The dish of the radial head was machined manually using a 3 1.75 mm (1 !A inch)

bal1 mill. The part was rotated 90" from its original orientation, and the spherical surface

was then dnlled into the part at a depth of approximately 2.4 mm. The dish was centered

at the centroid of the radial head which was calculated by the extemal prograrn. The

parameters used for the dish were chosen based on a study of the radius anatomy [12].

Figure 6.2 Machining of radial head prototype using the Fada1 5-axis CNC machine.

6.2.2 Machine code generation

The prototype was machined using two separate machining operations. The f î t

operation was a volume clear which was a quick way to reduce the stock size to the

approximate size of the final part. The second operation was the finishing cut that

produced the final part. A number of initial test prototypes were machined using different

machining parameters such as tool size and cutting increments. The final prototypes were

machined using the parameters summarized in Table 6.1.

Table 6.1 Tool and program information parame ters.

Volume Clear ûperation Finishing Cut

(Copy Mill Operation)

I - - -- --

Stock to leave 3 mm O I

Tool type and diarne ter

hcrement size I 1 mm I 0.25 mm I surface tolerance 1 0.5 mm l 0.10 mm I

bal1 rnill, 3.175 mm

(1/8 inch)

relative plane clearance I 5 mm I 5 mm I

bal1 mill, 1 S875mm

(111 6 inch)

Spindle Speed 1 2500 rpm l 2500 rpm I Feed rate 1 500 mrn/revolution 1 500 mm/revolution I

6.2.3 Machining problems

Plunge rate

The number of problems encountered dunng the machining phase were mainly

contributed to software limitations. The one main cause of the problems was the nature

of the bone mode1 geometry. This problem existed for senes A. B. and C; but not series

D and E. More specifically, the problem was machining the articulating surface defmed

by the fmt 2 slices of the series of contours. The rest of the surface beyond these two

contours was easily machined. The "crescent-rnoon" shape of the fmt 2 slices of the

problem series created a machining difficulty, when they were lofted with the rest of the

contours. This difficulty was not encountered with senes D and E because they only had

one such contour. Since the cutter tool cm ody approach the part vertically as it rotates.

the tool gouged into the part as it attempted to machine the irregular surface, which often

caused the tool to break. Figure 6.3 illustrates the geornetry of the problem segment of

senes C.

300 mm/revolu tion I 300 mm/revolution

Figure 6.3 Problem area for machining the bone mode1 of series C.

Since the time to machine the f i t segment of the bone took almost two houn, it

became necessary to veriQ the code before machining during the different attempts of

solving the problem. Some verification was done by inspecting the machine code

visually to look for values approaching the centre of the stock as it rotated. Another

verification method was to observe a simulation of the machining operation using the

SURCAM Verify module. and try to predict gouging or other cutting problems. Finally

the most effective verification method was to machine a test prototype using softer

materid at a high feed rate.

A number of attempts were made to eliminate the problem with rnachining series

A through C. One attempt was to limit the depth of cut to avoid tool damage by gouging

deeply into the part. This approach did not produce an acceptable f i i sh for the fmt 2

mm of the part.

Another attempt was to machine the part starting from the 3rd slice. then rotating

the part 90° to machine a lofted surface of the first two slices using 3-axis machining. in

order for this method to succeed, the orientation of the part in the CNC machine had to be

identical to the one in the SURFCAM software. Unfortunately, this was not the case.

Due to the way SURFCAM machined surfaces, the segment machined had a rotational

displacement and did not fit with the rest of the part.

A trial was made to machine the prototype using the SURFCAM 3-axis capability.

One side was to be machined and then rotated by the CNC machine rotary table exactly

180' to machine the other side. This attempt was unsuccessful because SURFCAM

generated the code so that it cut right through the part to go to the next cutting path. This

was caused by the fact that the part still continued below the lirnited depth. if the part

was hdved, this method is believed to be successful. However, SURFCAM was not

equipped to accomplish this surface editing procedure efficiently.

On the other hand, 1-DEAS software did not have the SURFCAM limitations

mentioned above. Therefore, machining the part using 1-DEAS 3-axis capabilities was

the next attempt. This procedure was identical to the one successfully implemented for

the f i t reverse engineering experiment described in Chapter 2. Unfortunately, the I-

DEAS software was updated since then to a newer version which failed to even generate

machine code for the part. This was an example of the cornmon problems related to

software updates.

The fuial solution was inspired by the fact that series D and E did not have this

problem because they had only one irregular contour. The fact that the othen had two

was the cause of the machining problems. Therefore, the final atternpt compromised one

of the contours in order to produce a machinable part using the available software. The

bone models were constructed using SURFCAM and machine code was created using its

4-axis machining procedure as described in the previous section.

6.3 Verification Of Prototype

Initial investigation of the accuracy of the solid mode1 started at the programming

output stage. The average MSE values for each contour were recorded in order to

indicate a measure of success for the curve fitting process. As the results in Appendices

A through D indicated, the average MSE values for d l contours defining the radial head

geornetry were less than 0-Imm. The exceptions were the f i t two slices due to a limited

number of control points that can be used in the computations to approximate their

compiex shape. However, when fitted contours of these slices were compared to the

original data they appeared to conform well with the general shape. Figure 6.4 illustrates

the results of that comparison. Slice 8 is the first slice of the senes.

Slice 8 Slice 9

Figure 6.4 Cornparison between the CT data of slices 8 and 9 from senes C and the

approximated Bezier curves.

The visual comparison of each fitted contour to its original CT scan data was

another method of qualitatively validating the results of the BBF network. This was

accomplished by importing the Cï edge slice information into 1-DEAS as points, and

comparing each slice of each series with its corresponding approximated contour. This

inspection concluded that the contours closely approximated the slice information. In

addition to the results presented in Figure 6.4, other examples are presented in Figure 6.5.

Slice 15 Slice 19

Slice 25 Slice 38

Figure 6.5 Results of cornparison for senes C between CT edge slice information and its

corresponding approximated contour.

The initial inspection of the manufactured prototype was to visually compare its

geometry to the original bone. The scanned cadaver arms were retrieved from storage

and dissected. The visual comparison of the original radius specimens with the

prototypes was also satisfactory.

6.4 Prototype Verification Using The CMM

The radius was cleaned of sofi tissue and resected approximately 40 mm distal to

the radial head. The size of the extracted bone specimen was chosen to approximate the

size of the manufactured prototypes. This allowed the alignment of both parts to be as

accurate as possible. Measurements of each radial head specimen and its machined

prototype were taken using a CMM. The most cntical factor in this procedure was to

align borh parts in the same orientation for optimal comparison results. Five standard

radial head implants were measured in order to establish a comparison between the

available off-the-shelf implants and the machined prototypes.

6.4.1 Inspection method

The part to be inspected was placed into an indexing table as shown in Figure 6.6.

Two sets of profile measurement were taken across the bone. One set , Profile 1, was

taken at angle zero on the indexing table and passed through the middle of the tuberosity,

and the second set, Profile II, was taken after rotating the part 90°. For each profile

measurement, centroid values of each part were approximated using a routine available in

the TUTOR software, which provides controls for the CMM machine. The profile

measurements were then taken across the centroids. This technique was developed to

ensure optimal accuracy of profile comparison between the inspected parts.

A star probe was used to take point measurements across the parts as s h o w in

Figure 6.6. The x and y ongins were placed at the centre of the rotary table. The

reference system used and origin were consistent during the entire inspection process.

Figure 6.6 Measurement of part by the C M . .

The results of the CMM inspection were imported as points into 1-DEAS in order

to visually compare the profile of the radius specimen with its corresponding rnachined

prototype and standard implant. The results seemed to have a slight shift. This shift was

reduced by mapping the centroids of the prototype and standard implant ont0 the

specimen's centroid as illustrated in Figure 6.7.

Profile 1 - original Profile 1 - translated

Profile II - original Profile II - trantslated

Figure 6.7 Results of CMM inspection for series B.

The CMM measurement results were imported into Microsoft Exce1 in order to

quant@ the comparison analysis. The measurement values were fmt modified according

to the centroid mapping in order to produce the aanslated measurement sets. The results

were then used to calculate the erron of the prototype and the standard implants with

respect to the original bone. The mean and maximum error of each set of measurements

were calculated. Table 6.2 includes a summary of the results for the five series. The

mean and standard deviation of the five average error values for each part were calculated

in order to further define the conclusion of the cornparison analysis. The results are

illustrated in the bar chart in Figure 6.8.

Table 6.2 Summary of CMM inspection results.

1 Prototv~e 1 Standard Im~lant

Standard Deviation

Radius Specimen

A 8 C D

H Standard deviation

Prototypes Standard

Figure 6.8 A bar chart of the mean and standard deviation of average error values from

Average Error (mm) 0.75 0.34 0.58 0.43

prototypes and standard implants compared to radius specimens.

Maximum Error (mm)

2.89 1.65 1.63 1.48

Average Error (mm) 2.96 2.3 1 2.03 1 -20

Maximum Error (mm)

7.40 4.00 3.65 4.74

6.43 Discussion

An investigation of all the graphical results, similar to Figure 6.7. are included in

Appendix 2, for the five senes funher indicate the advantages of the customized implant.

The largest standard implant available was smailer than three of the five bone specimens,

and the smailest implant was larger than one specimen. The maximum errors of the

standard implants were found at regions with a large change in radial head diameters as

illustrated in Figure 6.7. The standard implants had the geometrical shape of a cone with

a small difference in their minimum and maximum diameters. The symrnetrical shape is

no match for the highly imegular geometry of the radial head.

As indicated in Table 6.2, the average error of the standard implant rneasurements

is over three times that of the prototype and has a variance value that is approximately

three times greater. An interesthg observation is that the average error of the standard

implant is greater than the maximum error of the rnachined prototype. This observation

highlights the advantages of the customized implant over the standard one.

The accuracy of the rneasurement of the bone specimens and the prototype is

dependent on the accuracy of the alignment. Although the mapping of centroids

technique produced satisfactory results, some error rnight exist in the centroid

approximation procedure itself. The irregular geometry of the two inspected parts posed

a difficulty in determinhg a measure of rotational displacements or errors.

6.5 Concluding Remarks

The prototype manufacture and CMM inspection processes were important steps

of the reverse engineering process of the radial head. They allowed physicai comparison

between the reconstructed solid mode1 and the original specimen. The problems

encountered during the manufacturing phase were specifîc to the CAM software used to

generate the tool path code. However, the irregular geometry of the mode1 was prone to

machining difficulties regardless of the software or CNC machine used

Verification of the curve fitting process was accomplished by observing the MSE

values of the output contours and visual cornparison between the original CT scan data

and the output. The visual inspection of the machined part conaibuted to the validation

of the general geometry and machining process. However, the CMM inspection process

was a method of evaluating the entire reverse en,~eering process, from the data

acquisition stage to prototype manufacture.

CHAPTER 7

CONCLUSION AND FUTURE WORK

The objective of this work was the application of reverse engineering technology

in the production of a custornized prosthesis for the head of the radius of the elbow joint.

There are no reported studies using the normal anatornic radial head geometry as a

baseline for prosthetic design. The geometric shape of the radial head is highly non-

symmetric and can not be easily replicated by a symmetrical implant.

This work outlined the main steps to reverse engineer the radial head geometry.

The surface mode1 of the radial head was generated by fitting closed contours to cross-

sectional CT image data of the bone. The contours were fitted using a BBF network

which is an adaptive approach to determine a small number of control points in order to

reconstnict a closed Bezier curve from measured points. Prototypes of five radius bone

specirnens were manufactured.

A comparative study of the geometry of the original radius specimens, machined

prototypes, and standard implants was conducted by CMM inspection. The snidy

confmed the potential advantages of a customized implant over the standard off-the

shelf-implant.

The results of the CMM measurement study provided a measure of an

accumulated error for the entire reverse engineering process. The most dominant error

source is the data acquisition technique. The noise found in the CT images is the most

important cause of inaccuracies in the reconsmicted geometry. The curve approximation

techniques can only be as good as the data. The technique contributed a slight error due

to the approximating nature of Bezier curves. However, the resultant closed contours

were proven to closely f i t the original CT image data.

The second most important source of error is the transfer of surface geornetry

using IGES. The inaccuracies in the CAD fdes transfer between software packages

resulted in some irregular geometry of machining modeis and difficulties in the

machining process.

A series of minor error sources rnay also be found in the machining process.

These sources may included part set-up, tool length and fixture offset, machine accuracy,

and tool path approximations of the curved surface using lines and arcs. The CMM

inspection process may also have sources of error. Although the parts were carefully

aligned, some rotational offsets may have occurred due to the difficulty in verifying the

alignment accuracy .

Recommendations for further work to improve the proposed reverse engineering

process include the evaluation of each major source of error in order to minirnize its

effects. The most prominent area of improvement is the data acquisition technique. An

investigation of noise reduction in Ci' irnagery is required. This investigation should

consider improving the Ci' image quality without jeopardizing the patient's safety.

Alternative data acquisition techniques, such as ultrasound imaging, should also be

considered and compared to CT imagery in order to be able to implement the most

appropriate technique for the surface reconstruction application.

To eliminate the file transfer problems, a single CAD software should be csed for

the generation of the surface mode1 and the machining code. Alternative rapid

prototyping techniques such as stereolithography should also be considered because of

their capability of producing higNy complex shapes. Although such techniques have

lirnited selection of materiais, they are still more suitable for prototype manufacturing.

The desired degree of accuracy and material selection of a custornized implant will be the

two factors that detennine the manufacniring technique.

The process outlined in this work can be repeated using a calibration object. A

simple object composed from geomeaic primitives can be easily machined and accurately

aligned for CMM measurements Therefore. it would clearly defme the magnitude and

sources of error for the proposed reverse engineering process.

Fmally, in order to replace a damaged radial head, the proposed surface

reconstruction process will have to be applied to the undamaged radial head in the

opposite elbow joint. The solid mode1 can then be modified in order to accurately replace

the darnaged bone. Extensive work in this area is recornrnended in order to identiQ,

implement, and test the required modifications (such as mirroring of the image). This

step is required before the process can be hl ly implemented in clinical applications.

APPENDIX 1

RESULTS OF CONTOUR APPROXIMATION TECHNIQUE

This appendix includes the results of the external program used to generate closed

contours from the seriai CT data of series A, B, C, and E. Results for senes D are

included in Chapter 5. The results are presented in tables that sumrnarize parameter

values of the extemal program output, and figures that show the closed contours outlining

the geometry of the radius bone.

Results of the extemai prograrn using CT information of series A.

No. of cycles

through training data

2000 2000 285 286 1747 156 584 192 134

Slice no.

5 6 7 8 9 I O 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

MSE

O, 149 .197

0.099 0.099 0.099 0.099 0.099 0.099 0.099

No. of control

points

31 31 16 16 11 11 11 16 16

0.099 0.099 0.099 0.085 0.066 0.059 0.072 0.096 0.097 0.076 0.079 0.099 0.099 0.086 0.099 0.099 0.099 0.099 0.099 0.099 0.099 0.099 0.099 0.099 0.099 0.099

16 16 11 11 11 11 11 11 11 11 11 11 11 11 11 21 16 21 16 16 16 16 16 16 11 11

378 243 1453

2 2 2 1 1 2 2 2 3

20 2

23 1629 832 330 1350 208 368 45 1 35 1 1 49 1178 689

Closed contours outlining the geornetry of the radius bone for series A.

Results of the external prograrn using CT information of series B.

Slice no. MSE No. of control

points

No. of cycles

through training data

Closed contours outlining the geometry of the radius bone for senes B.

Results of the external program using CT information of series C.

I I 1 points 1 through training data

No. of cycles No. of controi Slice no. MSE

Closed contours outlining the geometry of the radius bone for series C.

Results of the external program using CT information of series E.

I I 1 points 1 through training data

Slice no. MSE No. of control No. of cycles

Closed contours outlining the geomeuy of the radius bone for senes E.

APPENDIX 2

RESULTS OF CMM INSPECTION

This appendix is a collection of the CMM inspection results as figures of radial

head profile rneasurements. The profiles of the radial head specimen are presented dong

with the profiles of the measured machined protorypes and standard impiants The

original specimen is presented by dark points. the prototype in a lighter shade, and the

standard is the solid line. Senes A, C, D, and E are presented in this appendix. Results

of series B are included in Chapter 6.

Profile 1 for series A

Profile 1 for series C

Profile II for series A

Rofile II for series C

Profile 1 for senes D Profile II for series D

Profile 1 for series E Profile II for series E

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