Accurate prediction of plantar shear stress and internal stress in the soft tissue layers of the foot using finite element models would provide valuable insight into the mechanical etiology of neuropathic foot ulcers. Accurate prediction of the internal stress distribution using finite element models requires that realistic descriptions of the material properties of the soft tissues are incorporated into the model. Our investigation focused on the creation of a novel three-dimensional (3D) finite element model of the forefoot with multiple soft tissue layers (skin, fat pad, and muscle) and the development of an inverse finite element procedure that would allow for the optimization of the nonlinear elastic coefficients used to define the material properties of the skin muscle and fat pad tissue layers of the forefoot based on a Ogden hyperelastic constitutive model. Optimization was achieved by comparing deformations predicted by finite element models to those measured during an experiment in which magnetic resonance imaging (MRI) images were acquired while the plantar surface forefoot was compressed. The optimization procedure was performed for both a model incorporating all three soft tissue layers and one in which all soft tissue layers were modeled as a single layer. The results indicated that the inclusion of multiple tissue layers affected the deformation and stresses predicted by the model. Sensitivity analysis performed on the optimized coefficients indicated that small changes in the coefficient values (±10%) can have rather large impacts on the predicted nominal strain (differences up to 14%) in a given tissue layer.

References

References
1.
Budhabhatti
,
S. P.
,
Erdemir
,
A.
,
Petre
,
M.
,
Sferra
,
J.
,
Donley
,
B.
, and
Cavanagh
,
P. R.
,
2007
, “
Finite Element Modeling of the First Ray of the Foot: A Tool for the Design of Interventions
,”
ASME, J. Biomech. Eng.
,
129
(
5
), pp.
750
756
.10.1115/1.2768108
2.
Cheung
,
J. T.
,
An
,
K. N.
, and
Zhang
,
M.
,
2007
, “
Consequences of Partial and Total Plantar Fascia Release: A Finite Element Study
,”
Foot Ankle Int.
,
27
(
2
), pp.
125
132
. Available at: http://fai.sagepub.com/content/27/2/125.full.pdf
3.
Goske
,
S.
,
Erdemir
,
A.
,
Petre
,
M.
,
Budhabhatti
,
S.
, and
Cavanagh
,
P. R.
,
2006
, “
Reduction of Plantar Heel Pressures: Insole Design Using Finite Element Analysis
,”
J. Biomech.
,
39
(
13
), pp.
2363
2370
.10.1016/j.jbiomech.2005.08.006
4.
Erdemir
,
A.
,
Saucerman
,
J. J.
,
Lemmon
,
D.
,
Loppnow
,
B.
,
Turso
,
B.
,
Ulbrecht
,
J. S.
, and
Cavanagh
,
P. R.
,
2005
, “
Local Plantar Pressure Relief in Therapeutic Footwear: Design Guidelines From Finite Element Models
,”
J. Biomech.
,
38
(
9
), pp.
1798
1806
.10.1016/j.jbiomech.2004.09.009
5.
Mackey
,
J. R.
, and
Davis
,
B. L.
,
2006
, “
Simultaneous Shear and Pressure Sensor Array for Assessing Pressure and Shear at Foot/Ground Interface
,”
J. Biomech.
,
39
(
15
), pp.
2893
2897
.10.1016/j.jbiomech.2005.10.001
6.
Yavuz
,
M.
,
Erdemir
,
A.
,
Botek
,
G.
,
Hirschman
,
G. B.
,
Bardsley
,
L.
, and
Davis
,
B. L.
,
2007
, “
Peak Plantar Pressure and Shear Locations: Relevance to Diabetic Patients
,”
Diabetes Care
,
30
(
10
), pp.
2643
2645
.10.2337/dc07-0862
7.
Yavuz
,
M.
,
Botek
,
G.
, and
Davis
,
B. L.
,
2007
, “
Plantar Shear Stress Distributions: Comparing Actual and Predicted Frictional Forces at the Foot-Ground Interface
,”
J. Biomech.
,
40
(
13
), pp.
3045
3049
.10.1016/j.jbiomech.2007.02.006
8.
Reiber
,
G. E.
,
2001
, “
Epidemiology of Foot Ulcers and Amputations in the Diabetic Foot
,”
In The Diabetic Foot
,
Mosby
,
St. Louis, MO
, pp.
13
22
.
9.
Lemmon
,
D.
,
Shiang
,
T. Y.
,
Hashmi
,
A.
,
Ulbrecht
,
J. S.
, and
Cavanagh
,
P. R.
,
1997
, “
The Effect of Insoles in Therapeutic Footwear—A Finite Element Approach
,”
J. Biomech.
,
30
(
6
), pp.
615
620
.10.1016/S0021-9290(97)00006-7
10.
Chen
,
W. P.
,
Ju
,
C. W.
, and
Tang
,
F. T.
,
2003
, “
Effects of Total Contact Insoles on the Plantar Stress Redistribution: A Finite Element Analysis
,”
Clin. Biomech. Bristol
,
18
(
6
), pp.
S17
S24
.10.1016/S0268-0033(03)00080-9
11.
Cheung
,
J. T. M.
, and
Zhang
,
M.
,
2005
, “
A 3-Dimensional Finite Element Model of the Human Foot and Ankle for Insole Design
,”
Arch. Phys. Med. Rehabil.
,
86
(
2
), pp.
353
358
.10.1016/j.apmr.2004.03.031
12.
Jacob
,
S.
, and
Patil
,
M. K.
,
1999
, “
Stress Analysis in Three-Dimensional Foot Models of Normal and Diabetic Neuropathy
,”
Front Med. Biol. Eng.
,
9
(
3
), pp.
211
227
.
13.
Spears
, I
. R.
,
Miller-Young
,
J. E.
,
Sharma
,
J.
,
Ker
,
R. F.
, and
Smith
,
F. W.
,
2007
, “
The Potential Influence of the Heel Counter on Internal Stress During Static Standing: A Combined Finite Element and Positional MRI Investigation
,”
J. Biomech.
,
40
(
12
), pp.
2774
2780
.10.1016/j.jbiomech.2007.01.004
14.
Actis
,
R. L.
,
Ventura
,
L. B.
,
Smith
,
K. E.
,
Commean
,
P. K.
,
Lott
,
D. J.
,
Pilgram
,
T. K.
, and
Mueller
,
M. J.
,
2006
, “
Numerical Simulation of the Plantar Pressure Distribution in the Diabetic Foot During the Push-Off Stance
,”
Med. Biol. Eng. Comput.
,
44
(
8
), pp.
653
663
.10.1007/s11517-006-0078-5
15.
Gefen
,
A
.,
2003
, “
Plantar Soft Tissue Loading Under the Medial Metatarsals in the Standing Diabetic Foot
,”
Med. Eng. Phys.
,
25
(
6
), pp.
491
499
.10.1016/S1350-4533(03)00029-8
16.
Ledoux
,
W. R.
, and
Blevins
,
J. J.
,
2007
, “
The Compressive Material Properties of the Plantar Soft Tissue
,”
J. Biomech.
,
40
(
13
), pp.
2975
2981
.10.1016/j.jbiomech.2007.02.009
17.
Miller-Young
,
J. E.
,
Duncan
,
N. A.
, and
Baroud
,
G.
,
2002
, “
Material Properties of the Human Calcaneal Fat Pad in Compression: Experiment and Theory
,”
J. Biomech.
,
35
(
12
), pp.
1523
1531
.10.1016/S0021-9290(02)00090-8
18.
Bosboom
,
E. M.
,
Hesselink
,
M. K.
,
Oomens
,
C. W.
,
Bouten
,
C. V.
,
Drost
,
M. R.
, and
Baaijens
,
F. P.
,
2001
, “
Passive Transverse Mechanical Properties of Skeletal Muscle Under In Vivo Compression
,”
J. Biomech.
,
34
(
10
), pp.
1365
1368
.10.1016/S0021-9290(01)00083-5
19.
Oomens
,
C. W.
,
Bressers
,
O. F.
,
Bosboom
,
E. M.
,
Bouten
,
C. V.
, and
Blader
,
D. L.
,
2003
, “
Can Loaded Interface Characteristics Influence Strain Distributions in Muscle Adjacent to Bony Prominences
,”
Comput. Methods Biomech. Biomed. Eng.
,
6
(
3
), pp.
171
180
.10.1080/1025584031000121034
20.
Zobitz
,
M. E.
,
Luo
,
Z. P.
, and
An
,
K. N.
,
2001
, “
Determination of the Compressive Material Properties of the Suprasinatus Tendon
,”
ASME, J. Biomech. Eng.
,
123
(
1
), pp.
47
51
.10.1115/1.1339816
21.
Petre
,
M.
,
Erdemir
,
A.
, and
Cavanagh
,
P. R.
,
2008
, “
An MRI-Compatible Foot-Loading Device for Assessment of Internal Tissue Deformation
,”
J. Biomech.
,
41
(
2
), pp.
470
474
.10.1016/j.jbiomech.2007.09.018
22.
Smith
,
K. E.
,
Commean
,
P. K.
,
Mueller
,
M. J.
,
Roberston
,
D. D.
,
Pilgram
,
T.
, and
Johnson
,
J.
,
2000
, “
Assessment of the Diabetic Foot Using Spiral Computed Tomography Imaging and Plantar Pressure Measurements; A Technical Report
,”
J. Rehabil. Res. Dev.
,
37
(
1
), pp.
31
40
.
23.
Cavanagh
,
P. R.
,
1999
, “
Plantar Soft Tissue Thickness During Ground Contact in Walking
,”
J. Biomech.
,
32
(
6
), pp.
623
628
.10.1016/S0021-9290(99)00028-7
24.
Gefen
,
A.
,
Megido-Ravid
,
M.
,
Azariah
,
M.
,
Itzchak
,
Y.
, and
Arcan
,
M.
,
2001
, “
Integration of Plantar Soft Tissue Stiffness Measurements in Routine MRI of the Diabetic Foot
,”
Clin. Biomech. Bristol
,
16
(
10
), pp.
921
925
.10.1016/S0268-0033(01)00074-2
25.
Cheung
,
Y. Y.
,
Doyley
,
M.
,
Miller
,
T. B.
,
Kennedy
,
F.
,
Lynch
,
F.
,
Wrobel
,
J. S.
,
Paulson
,
K.
, and
Weaver
,
J.
,
2006
, “
Magnetic Resonance Elastography of the Plantar Fat Pads: Preliminary Study in Diabetic Patients and Asymptomatic Volunteers
,”
J. Comput. Assist Tomogr.
,
30
(
2
), pp.
321
326
.10.1097/00004728-200603000-00031
26.
Weaver
,
J. B.
,
Doyley
,
M.
,
Cheung
,
Y.
,
Kennedy
,
F.
,
Madsen
,
E. L.
,
Van Houten
,
E. E.
, and
Paulsen
,
K.
,
2005
, “
Imaging the Shear Modulus of the Heel Fat Pads
,”
Clin. Biomech. Bristol
,
20
(
3
), pp.
312
319
.10.1016/j.clinbiomech.2004.11.010
27.
Bus
,
S. A.
,
Maas
,
M.
,
Cavanagh
,
P. R.
,
Michels
,
R. P. J.
, and
Levi
,
M.
,
2004
, “
Plantar Fat-Pad Displacement in Neuropathic Diabetic Patients With Toe Deformity: A Magnetic Resonance Imaging Study
,”
Diabetes Care
,
27
(
10
), pp.
2376
2381
.10.2337/diacare.27.10.2376
28.
Erdemir
,
A.
,
Viveiros
,
M. L.
,
Ulbrecht
,
J. S.
, and
Cavanagh
,
P. R.
,
2006
, “
An Inverse Finite-Element Model of Heel-Pad Indentation
,”
J. Biomech.
,
39
(
7
), pp.
1279
1286
.10.1016/j.jbiomech.2005.03.007
29.
Abaqus 6.10 User Manual http://simulia.com.
30.
Petre
,
M.
,
Wyllie
,
J.
,
Sferra
,
J.
,
Donley
,
B.
,
Erdemir
,
A.
,
Doehring
,
T.
,
Considine
,
J.
,
Thangudu
,
P.
, and
Cavangh
,
P. R.
,
2006
, “
Normal Sesamoid Motion During First MTPH Dorisiflexion
,”
American Academy of Orthopaedic Surgeons Annual Meeting
,
Chicago, IL
.
31.
Ogden
,
R. W.
,
Non-Linear Elastic Deformations
,
Ellis Horwood
,
Chinchester
.
32.
Criscione
,
J. C.
,
2003
, “
Rivlin's Representation Formula Is Ill-Conceived for the Determination of Response Functions Via Biaxial Testing
,”
J. Elasticity
,
70
, pp.
129
147
.10.1023/B:ELAS.0000005586.01024.95
33.
Belegundu
,
A. D.
, and
Chandrupatla
,
T. R.
,
1999
,
Optimization Concepts and Applications in Engineering
,
Prentice Hall
,
Upper Saddle River, NJ
.
34.
Budhabhatti
,
S. P.
,
Erdemir
,
A.
, and
Cavangh
,
P. R.
,
2005
, “
Influence of Foot Orientation and Bone Structure on Plantar Pressure Distribution
,”
XXth Congress of the International Society of Biomechanics/29th Annual Meeting of the American Society of Biomechanics
,
Cleveland, OH
.
35.
Wu
,
J. Z.
,
Dong
,
R. G.
,
Smutz
,
W. P.
, and
Schopper
,
A. W.
,
2003
, “
Nonlinear and Viscoelastic Characteristics of Skin Under Compression; Experiment and Analysis
,”
Biomed. Mater. Eng.
,
13
(
4
), pp.
373
385
.
36.
Natali
,
A. N.
,
Fontanella
,
C. G.
, and
Carniel
,
E. L.
,
2012
, “
A Numerical Model for Investigating the Mechanics of Calcaneal Fat Pad Region
,”
J. Mech. Behavior Biomed. Mater.
,
5
, pp.
216
223
.10.1016/j.jmbbm.2011.08.025
37.
Sharafi
,
B.
and
Blemker
,
S. S.
,
2010
, “
A Micromechanical Model of Skeletal Muscle to Explore the Effects of Fiber and Fascicile Geometry
,”
J. Biomech.
,
43
, pp.
3207
3213
.10.1016/j.jbiomech.2010.07.020
38.
Chokhandre
,
S.
,
Halloran
,
J. P.
,
van den
Bogert
,
A. J.
, and
Erdemir
,
A.
,
2012
, “
A Three-Dimensional Inverse Finite Element Analysis of the Heel Pad
,”
J. Biomech. Eng.
,
134
, pp.
1
9
.10.1115/1.4005692
39.
Veress
,
A.
I
.
,
Gullberg
,
G. T.
, and
Weiss
,
J. A.
,
2005
, “
Measurement of Strain in the Left Ventricle During Diastole With Cine-MRI and Deformable Image Registration
,”
ASME, J. Biomech. Eng.
,
127
(
7
), pp.
1195
1207
.10.1115/1.2073677
40.
Petre
,
M. T.
,
Erdemir
,
A.
, and
Cavanagh
,
P. R.
,
2006
, “
Determination of Elastomeric Foam Parameters for Simulations of Complex Loading
,”
Comput. Methods Biomech. Biomed. Eng.
,
9
(
4
), pp.
231
242
.10.1080/10255840600747620
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