energy storage and return prostheses: developing a biomechanical model of amputee sprinting

NeverStandS+ll FacultyofEngineering GraduateSchoolofBiomedicalEngineering

Energy Storage and Return Prostheses: Developing a Biomechanical Model of Amputee Sprinting

Presenter: StaceyRigneySupervisors: Prof.AnneSimmons,Dr.LaurenKark

Graduate School of Biomedical Engineering Graduate School of Biomedical Engineering

Background

Photo: Courtesy of WBGH ‘Medal Quest’ <http://www.pbs.org/newshour/multimedia/paralympics/5.html>

•  Human gait cycle

•  Anatomical vs prosthetic lower-limbs

2


Human Gait Cycle

IC# LR# MS# TS# PS# IS# MS# TS#

St+A##

St+G##

Sw+G##

Sw+R##

Sw+A##

IC# LR# MS# TS# PS# IS# MS# TS#

St+A##

St+G##

Sw+G##

Sw+R##

Sw+A##

Walking

Running

Figures:S.M.Rigney,A.SimmonsandL.Kark,“AmputeeGait:AReviewofBiomechanicalModels,”IEEEReviewsinBiomedicalEngineering,underreview.3


Human Gait Cycle Walking

Running

Images:hMp://www.dingosbreakfastclub.net/DingosBreakfastClub/BioMech/BioMechLightness.html

InvertedPendulum

Spring-loadedmass

4


Background

Photo: Courtesy of WBGH ‘Medal Quest’ <http://www.pbs.org/newshour/multimedia/paralympics/5.html>

•  Human gait cycle

•  Anatomical vs prosthetic lower-limbs

5


Anatomical Lower-limb

•  Ankle joint + calf muscles and tendons =

‘bouncy ball’

•  Muscles act as struts maintaining tension

–  active element

•  Tendons act as elastic springs

–  passive element

•  Anatomical limb is 241% efficient

6


Prosthetic Lower-limb

•  No ankle joint or muscles

•  ‘Springiness’ achieved via compression

•  Passive element only

•  Maximum 100% efficiency

7


Running-Specific Prostheses (RSP)

Flex-Run Flex-Sprint Cheetah Xtend

Cheetah Xtreme Sprinter 1E90 C-Sprint 1C2

Össur Ottobock

8


Disabled or Super-abled?

Video: https://www.youtube.com/watch?v=HNtZ_lbhafE 9


How Do We Decide?

10


How Do We Decide?

•  Assess prosthesis alone: in vitro

10


How Do We Decide?


–  Mechanical testing

10


How Do We Decide?



•  Assess prosthesis during gait: in vivo

Photo: http://www.ibtimes.co.uk/otto-bock-sports-prosthesis-amateur-everyday-athletes-377186 10


How Do We Decide?




–  Indirectly: measure speed, VO2, personal preference

–  Directly: gait analysis



Mechanical Testing

Support block (‘socket’) Fixed base

Prosthesis

y

x •  Compress prosthesis in a Material

Testing System (INSTRON)

•  Measure Force-Displacement

•  Compare results for different

prostheses under same load

Load cell

Figure: S. M. Rigney, A. Simmons and L. Kark, “Stance phase mechanical characterisation of a running-specific lower-limb prosthesis,” in Proc. 2014 Aus. Biomed. Eng. Conf., Canberra, A.C.T., Australia, 2014. 11


Mechanical Testing

Support block (‘socket’) Fixed base

Prosthesis

y

x •  Compress prosthesis in a Material

Testing System (INSTRON)

•  Measure Force-Displacement

•  Compare results for different

prostheses under same load

Figure: S. M. Rigney, A. Simmons and L. Kark, “Stance phase mechanical characterisation of a running-specific lower-limb prosthesis,” in Proc. 2014 Aus. Biomed. Eng. Conf., Canberra, A.C.T., Australia, 2014. 11


How Do We Decide?




–  Indirectly: measure speed, VO2, personal preference

–  Directly: gait analysis



Gait Analysis

•  Infrared motion-capture cameras

•  Passive-reflective markers

•  Displacement of markers tracked

over time

•  Force plates embedded in

ground

Photo: http://mocap.cs.cmu.edu/info.php 13


Gait Analysis

Raw data

14


Gait Analysis


15


Gait Analysis


•  Label markers using VICON Nexus software

15


Gait Analysis



•  Construct link-segment model of skeleton and prosthesis

15


Lower-limb Models

Anatomical lower-limb

•  Rigid shank and foot •  Articulating ankle joint

Prosthetic lower-limb

•  Continuous and elastic •  ‘Springiness’ achieved by

compression

16


Continuum Mechanics

•  Change shape under load

•  Undergo displacement

•  Undergo deformation

M$

M$

N$

R$

R$

M$

DISPLACE&

DEFORM$

O$

M$N$

O’’$

M$

N$

R$

O’$

DEFORM$

R$

N$ M$

O’’’$

DISPLACE&



Rigid Body Mechanics

•  Maintain shape under load

•  Undergo displacement

•  Undergo deformation

M$

M$

N$

R$

R$

M$

DISPLACE&

DEFORM$

O$

M$N$

O’’$

M$

N$

R$

O’$

DEFORM$

R$

N$ M$

O’’’$

DISPLACE&



Lower-limb Models

Two-linksegment

Exis+ng

19


Lower-limb Models

Two-linksegment

Exis+ng

Mul+ple-linksegment

New

20

FiniteElementAnalysis


Mul+ple-linksegment

Lower-limb Models

21

FiniteElementAnalysisTwo-linksegment

Exis+ng New


Mul,ple-linksegment

Lower-limb Models

21


Exis+ng New


Two-link Segment Model

•  Shank and foot connected via an

articulating ‘ankle’ joint

22


Multiple-link Segment Model

•  No distinct shank and foot segments

•  Entire prosthesis modeled as

multiple segments connected via

articulating joints

•  1DoF sagittal plane joints

23


Multiple-link Segment Model: Inverse Dynamics

•  Similar process to two-link

segment model

•  Calculate joint reaction forces

and moments for additional

segments

24Figure:Rigney,S.M.,A.Simmons,andL.Kark,“Lower-limbkinema+csandkine+csduringamputeerunning:anewapproach”,

25thCongressoftheInterna+onalSocietyofBiomechanics,Glasgow,UK,2015.

RPL1

RPL2

RPL3

RTIB

RPL4 RPL5

RPL6 RPL7

RANK

RTOE RHEE

RPB1 RPB2

RPB3

k3, b3

Fx

M

m6, I6

GRFy

GRFx

GRFM

Fy

m5, I5

m4, I4

m3, I3

m2, I2

m1, I1

k5, b5 k4, b4

k2, b2

k1, b1

y

x


OpenSim Inverse Kinematics and Dynamics

24


Design of Experiments for MLS model

•  Half factorial DoE, 95% CI

•  Factors/variables tested:

–  Joints 1-5, fixed or free

–  2nd degree interactions

–  16 configurations in total

•  Results of interest:

–  Hip flexion and moment

–  Knee flexion and moment

J5J4

J3

J2J1

25Figure:Rigney,S.M.,A.Simmons,andL.Kark,“Lower-limbkinema+csandkine+csduringamputeerunning:anewapproach”,

25thCongressoftheInterna:onalSocietyofBiomechanics,Glasgow,UK,2015.


Results - Moments

26

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

0 20 40 60 80 100-300

-200

-100

0

100

200

300Affected

Hip

Mom

ent (

Nm

)

0 20 40 60 80 100-300

-200

-100

0

100

200

300Unaffected

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

Kne

e M

omen

t (N

m)

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

0 20 40 60 80 100-300

-200

-100

0

100

200

300Affected

Hip

Mom

ent (

Nm

)

0 20 40 60 80 100-300

-200

-100

0

100

200

300Unaffected

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

Kne

e M

omen

t (N

m)

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40


Results - Angles

26

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

0 20 40 60 80 100-300

-200

-100

0

100

200

300Affected

Hip

Mom

ent (

Nm

)

0 20 40 60 80 100-300

-200

-100

0

100

200

300Unaffected

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

Kne

e M

omen

t (N

m)

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

0 20 40 60 80 100-300

-200

-100

0

100

200

300Affected

Hip

Mom

ent (

Nm

)

0 20 40 60 80 100-300

-200

-100

0

100

200

300Unaffected

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

0 20 40 60 80 100% Stance Phase

-200

-100

0

100

200

300

Kne

e M

omen

t (N

m)

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

0 20 40 60 80 100-60

-40

-20

0

20

40

Hip

Fle

xion

(deg

)

0 20 40 60 80 100-60

-40

-20

0

20

40

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40

Kne

e Fl

exio

n (d

eg)

PiG Hybrid MLS

0 20 40 60 80 100% Stance Phase

-60

-40

-20

0

20

40


Mul+ple-linksegment

Lower-limb Models

27


Exis+ng New

✓ ✓


Gait Analysis




28


Gait Analysis




Finite Element

28


Overview of Methodology

1.  Experimental gait analysis

=  spatial boundary conditions

2.  Inverse FEA

=  material properties

3.  Dynamic FEA

=  elastic strain energy

29Figure:Rigney,S.M.,A.Simmons,andL.Kark,”Finiteelementanalysisofalower-limbrunning-specificprosthesis”inThe8thAustralasian

CongressonAppliedMechanics2014.Barton,A.C.T,Australia:EngineersAustralia.


Passive-reflective Markers

•  Custom marker set

•  Coordinates recorded at 250Hz

•  Allows fully prescribed movement of the femur, tibia, socket and prosthesis

30

RTHI

RKNE

RSOT

RSOB

RPL1-3RPB1RPB2RPB3

RTIBRPL4RPL5

RPL6 RPL7 RANK

RHEE RTOE

Figure:Rigney,S.M.,A.Simmons,andL.Kark,“ConcurrentMul+bodyandFiniteElementAnalysisoftheLower-limbDuringAmputeeRunning”,in37thAnnualInterna:onalConferenceoftheIEEEEngineeringinMedicineandBiologySociety,Milano,Italy,2015.


Finite Element Analysis (FEA)

•  Quasi-static parametric solver

•  Prescribed displacement

–  1DOF rotation of femur @ RTHI

–  3DOF translation of socket + prosthesis @ RPL1

–  3DOF translation of shoe @ RTOE

•  1DOF hinge knee joint

MPa MPa

RTHI (θx)

RPL1 (x,y,z)

RTOE (x,y,z)

31Figure:Rigney,S.M.,A.Simmons,andL.Kark,“ConcurrentMul+bodyandFiniteElementAnalysisoftheLower-limbDuringAmputee

Running”,in37thAnnualInterna:onalConferenceoftheIEEEEngineeringinMedicineandBiologySociety,Milano,Italy,2015.


Finite Element Analysis (FEA)

MPa

31

•  Quasi-static parametric solver

•  Prescribed displacement

–  1DOF rotation of femur @ RTHI

–  3DOF translation of socket + prosthesis @ RPL1

–  3DOF translation of shoe @ RTOE

•  1DOF hinge knee joint



Simulated vs Actual Marker Displacement

preliminary quasi-static study demonstrates the potential of subject-specific multibody models for amputee gait analysis.

A number of areas have been identified where the model could be further refined. The simulated reaction force did not exhibit the oscillations of the experiments due to the quasi-static nature of the simulation. The use of a time-dependent solver that includes inertial effects may improve the accuracy of the oscillatory phenomena at initial contact. The model utilized a 1DOF prescribed displacement of the femur and 1DOF hinge joint at the knee; this simplification considerably reduced computational effort, however this affected the accuracy of the simulated prosthesis motion in the lateral direction (x-axis). The reaction force and moment in this plane of movement is very low, therefore it is unlikely to be of great consequence when calculating joint torque and power in future time-dependent studies. The shape of the longitudinal (y-axis) reaction force was offset from the experimental results in the time domain, which is likely to be improved by refining the shoe geometry. Finally, improved accuracy could be obtained by modeling the carbon fiber as a heterogeneous orthotropic material, as its very nature as a composite is to have varying stiffness depending on thickness, composition and layering.

Extension of this project will include the addition of viscoelastic damping parameters to enable a time-dependent simulation, which will result in the ability to calculate: joint torque and power; energy absorbed, dissipated and returned by the prosthesis; prosthesis work and efficiency; and the comparison of these values with results obtained through conventional link-segment rigid-body mechanics models. Seamless integration with motion capture software, such as Vicon Nexus, will facilitate the integration of FE analysis with existing clinical practices. Additionally, the presented skeletal and prosthesis model can be combined with other clinical measures, such as MRI, to enable patient-specific hard and soft tissue modeling, such as the menisci of the knee and/or residual limb tissue mechanics. Concurrent multibody and FE models present an exciting new avenue for patient-specific modeling.

REFERENCES [1] L. G. Stansbury, S. J. Lalliess, J. G. Branstetter, M. R. Bagg and J. B.

Holcomb, “Amputations in US military personnel in the current conflicts in Afghanistan and Iraq,” J. Orthop. Trauma, vol. 22, no. 1, pp. 43-46, 2008.

[2] G. P. Bruggeman, A. Arampatzis, F. Emrich and W. Potthast, “Biomechanics of double transtibial amputee sprinting using dedicated sprint prostheses,” Sports Technol., vol. 4-5, no. 1, pp. 220-227, 2008.

[3] A.B. Sawers and M.E. Hahn, “The potential for error with use of inverse dynamic calculations in gait analysis of individuals with lower limb loss: A review of model selection and assumptions,” J. Prosthet. Orthot., vol. 22, no. 1, pp. 56-61, 2010.

[4] D.A. Winter, Biomechanics and motor control of human movement. Hoboken, New Jersey: John Wiley & Sons, Inc., 2009.

[5] M. D. Geil, M. Parnianpour, P. Quesada, N. Berme and S. Simon, “Comparison of methods for the calculation of energy storage and return in a dynamic elastic response prosthesis,” J. Biomech., vol. 33, no. 12, pp. 1745-1750, 2000.

[6] C. A. Truesdell, Essays in the history of mechanics. New York: Springer, 1968.

[7] S. M. Rigney, A. Simmons and L. Kark, “Finite element analysis of a lower-limb running-specific prosthesis,” in 8th Aust. Cong. App. Mech., Barton, A.C.T, Australia, 2014, pp. 297-305.

[8] M.P. Kadaba, H. Ramakrishnan and M. Wootten, “Measurement of lower extremity kinematics during level walking,” J. Orthop. Res., vol. 8, no. 3, pp. 383-392, 1990.

[9] S. M. Rigney, A. Simmons and L. Kark, “Stance phase mechanical characterisation of a running-specific lower-limb prosthesis,” in Proc. 2014 Aust. Biomed. Eng. Conf., Canberra, A.C.T., Australia, 2014, to be published.

[10] S. M. Rigney, A. Simmons and L. Kark, “Mechanical Efficiency of a Running-Specific Energy Storage and Return Prosthesis,” in Bk Abstracts 9th Aust. Biomech. Conf., Wollongong, NSW, Australia, 2014, pp. 43.

[11] S. L. Delp, F. C. Anderson, A. S. Arnold, J. P. Loan, A. Habib, C. T. John, E. Guendelman and D. G. Thelen, “OpenSim: open-source software to create and analyze dynamic simulations of movement,” IEEE Trans. Biomed. Eng., vol. 54. No. 11, pp. 1940-1950, 2007.

[12] S. L. Delp, J. P. Loan, M. G. Hoy, F. E. Zajac, E. L. Topp and J. M. Rosen, “An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures,” IEEE Trans. Biomed. Eng., vol. 37, no. 8, pp. 757-767, 1990.

[13] F. C. Anderson and M.G. Pandy, “A dynamic optimization solution for vertical jumping in three dimensions,” Comput. Meth. Biomech. Biomed. Eng., vol. 2, no. 3, pp. 201-231, 1999.

[14] F. C. Anderson and M.G. Pandy, “Dynamic optimization of human walking,” J. Biomech. Eng., vol. 123, no. 5, pp. 381-390, 2001.

[15] G.T. Yamaguchi and F.E. Zajac, “A planar model of the knee joint to characterize the knee extensor mechanism,” J. Biomech., vol. 22, no. 1, pp. 1-10, 1989.

[16] X. Bonnet, H. Pillet, P. Fodé, F. Lavaste and W. Skalli, “Finite element modelling of an energy-storing prosthetic foot during the stance phase of transtibial amputee gait,” Proc. Inst. Mech. Eng. Part H: J. Eng. Med., vol. 226, no. 1, pp. 70-75, 2012.

[17] M. Omasta, D. Paloušek, T. Návrat and J. Rosický, “Finite element analysis for the evaluation of the structural behaviour of a prosthesis for trans-tibial amputees,” Med. Eng. Phys., vol. 34, no. 1, pp. 38-45, 2012.

(a) (b) (c)

Figure 5. Experimental and simulated marker displacement in the laboratory (a) lateral or x-axis, (b) longitudinal or y-axis, and (c) vertical or z-axis.

32

-100

0

100

200

300

400

500

0 20 40 60 80 100

MarkerD

isplacem

ent(mm)

StancePhase(%)

0 20 40 60 80 100

StancePhase(%)0 20 40 60 80 100

StancePhase(%)



Results

33

-30

0

30

60

90

-600 -300

0 300 600 900

1200 1500 1800

0 20 40 60 80 100

Ela

stic

Str

ain

Ene

rgy

(J)

Gro

und

Rea

ctio

n Fo

rce

(N)

Stance Phase (%) Exp RFx Exp RFy Exp RFz FEA RFx FEA RFy FEA RFz FEA Energy



Benefits of FEA

34

•  Replicates prosthesis

compression

•  Elastic strain energy cannot be

calculated via other methods

•  Seamlessly integrates prosthesis

and skeletal models

•  Viable alternative to the existing

2-link segment model



Mul+ple-linksegment

Lower-limb Models

35


Exis+ng New

✓ ✓ ✓


Cost-benefit analysis

•  High-accuracy models require

additional:

–  computer power

–  solution time

–  operator expertise

•  Clinical effect of new models

currently unknown Accuracy

Compu

ta+o

nalCost

Two-linksegment

Mul+ple-linksegment

FEA

36


Conclusions

•  Able-bodied gait analysis techniques usually directly applied to

amputee gait

37


Conclusions


amputee gait

•  Prosthetic lower-limb ≠ anatomical lower-limb

37


Conclusions


amputee gait


•  Two new in vivo gait analysis models

37


Conclusions


amputee gait



•  Multiple-link segment model produces significantly different results

compared to conventional methods

37


Conclusions


amputee gait



•  Multiple-link segment model produces significantly different results

compared to conventional methods

•  FEA model gives results not available through conventional methods

37


Questions?

Contact: [email protected]

38


Rigid Body Mechanics: Assumptions

1.  Point mass m

m



1.  Point mass m

2.  Location of m is constant

m



1.  Point mass m


3.  Mass moment of inertia I remains constant

m, I



1.  Point mass m



4.  Segment lengths remain constant



1.  Point mass m



4.  Segment lengths remain constant

5.  Segments connected by frictionless joints


Two-link Segment Model: Inverse Dynamics

•  Find m and I

–  Measure subject

–  Calculate using anthropometry data

•  Measure GRFx, GRFy and GRFM

using force plates

•  Calculate Fx, Fy, and M

Figure:Rigney,S.M.,A.Simmons,andL.Kark,Lower-limbkinema:csandkine:csduringamputeerunning:anewapproach.2015,tobepublished.


Lumped-parameter Model

(Klute and Berge 2004)

Springelement

Damperelement

Viscoelas+cmechanicalsystem


Springelement

Damperelement

Viscoleas+cmechanicalsystem


(Klute and Berge 2004)



•  Non-linear spring and damper

–  modified Voigt model

•  Models overall behaviour

•  Also known as ‘phenomenological model’

–  describes observed phenomena

–  not developed from theoretical principles



F F F F

F

F

F

F

F FG

•  Strain-hardening spring

–  Proportionality constant a

–  Position exponential constant b

•  Position-dependent damper

–  Proportionality constant c

–  Position exponential constant d

–  Velocity exponential constant e



•  Advantages



•  Advantages

–  Allows for viscoelastic behaviour of the prosthesis



•  Advantages


–  Computationally efficient



•  Advantages



•  Disadvantages



•  Advantages




–  Requires mechanical testing to determine parameters



•  Advantages




–  Requires mechanical testing to determine parameters

–  Currently not integrated with motion-capture software