Axisymmetric nonlinear finite-element analysis was used to simulate force-relaxation and creep data obtained during in vivo indentation of the residual limb soft tissues of six individuals with trans-tibial amputation [1]. The finite-element models facilitated estimation of an appropriate set of nonlinear viscoelastic material coefficients of extended James-Green-Simpson material formulation for bulk soft tissue at discrete, clinically relevant test locations. The results indicate that over 90% of the experimental data can be simulated using the two-term viscoelastic Prony series extension of James-Green-Simpson material formulation. This phenomenological material formulation could not, however, predict the creep response from relaxation experiments, nor the relaxation response from creep experiments [2–5]. The estimated material coefficients varied with test location and subject indicating that these coefficients cannot be readily extrapolated to other sites or individuals.

1.
Silver-Thorn, M. B., Tonuk, E., and Kemp, J., 1999, “In Vivo Indentation of Lower Extremity Limb Soft Tissues,” Proc. 1st BMES EMBS Conference., Atlanta GA, 1, p. 637.
2.
Graf
,
B. K.
,
Vanderby
,
R.
,
Ulm
,
J. M.
,
Rogalski
,
R. P.
, and
Thielke
,
R. J.
,
1994
, “
Effect of Preconditioning on the Viscoelastic Response of Primate Patellar Tendon
,”
Arthroscopy
,
10
, pp.
90
96
.
3.
Thornton
,
G. M.
,
Oliynyk
,
M. A.
,
Frank
,
C. B.
, and
Shrive
,
N. G.
,
1997
, “
Ligament Creep cannot be Predicted from Stress Relaxation at Low Stress: A Biomechanical Study of the Rabbit Medial Collateral Ligament
,”
JBJS
,
15
, pp.
652
656
.
4.
Lakes
,
R. S.
, and
Vanderby
,
R.
,
1999
, “
Interrelation of Creep and Relaxation: A Modeling Approach for Ligaments
,”
J. Biomech. Eng.
,
121
, pp.
612
615
.
5.
Provenzo
,
P.
,
Lakes
,
R.
,
Keenan
,
T.
, and
Vanderby
,
R.
,
2001
, “
Nonlinear Ligament Viscoelasticity
,”
Ann. Biomed. Eng.
,
29
, pp.
908
914
.
6.
Hoaglund
,
F. T.
,
Jergesen
,
H. E.
,
Wilson
,
L.
,
Lamoreux
,
L. W.
, and
Roberts
,
R.
,
1983
, “
Evaluation of the Problems and Needs of Veteran Lower-Limb Amputees in the San Francisco Bay Area during the Period 1977–1980
,”
J. Rehabil. Res. Dev.
,
20
, pp.
57
71
.
7.
Sanders
,
J. E.
,
1995
, “
Interface Mechanics in External Prosthetics: Review of Interface Stress Measurement Techniques
,”
Med. Biol. Eng. Comput.
,
33
, pp.
509
516
.
8.
Silver-Thorn
,
M. B.
,
Steege
,
J. W.
, and
Childress
,
D. S.
,
1996
, “
A Review of Prosthetic Interface Stress Investigations
,”
J. Rehabil. Res. Dev.
,
33
, pp.
253
266
.
9.
Zachariah
,
S. G.
, and
Sanders
,
J. E.
,
1996
, “
Interface Mechanics in Lower-Limb External Prosthetics: a Review of Finite Element Methods
,”
IEEE Trans. Rehabil. Eng.
,
4
, pp.
288
302
.
10.
Zhang
,
M.
,
Mak
,
A. F. T.
, and
Roberts
,
V. C.
,
1998
, “
Finite Element Modelling of a Residual Lower-Limb in a Prosthetic Socket: A Survey on the Development in the First Decade
,”
Med. Eng. Phys.
,
20
, pp.
360
373
.
11.
Steege
,
J. W.
,
Schnur
,
D. S.
, and
Childress
,
D. S.
,
1987
, “
Estimation of Pressure at the Below-Knee Socket by Finite Element Analysis
,”
ASME-BED
,
4
, pp.
39
43
.
12.
Steege, J. W., Schnur, D. S., Van Vorhis, L. R., and Rovick, J. S., 1987, “Finite Element Analysis as a Method of Pressure Estimation at the Below-Knee Socket Interface” Proc. 10th Ann. RESNA Conf., San Jose, CA, pp. 814–816.
13.
Steege, J. W., and Childress, D. S., 1988, “Finite Element Estimation of Pressure at the Below-Knee Socket Interface,” Report of ISPO Workshop on CAD/CAM in Prosthetics and Orthotics, Seattle, WA, pp. 71–82.
14.
Zhang
,
M.
,
Lord
,
M.
,
Turner-Smith
,
A. R.
, and
Robert
,
V. C.
,
1995
, “
Development of a Non-Linear Finite Element Modeling of the Below-Knee Prosthetic Socket Interface
,”
Methods Exp. Phys.
,
17
, pp.
559
566
.
15.
Silver-Thorn
,
M. B.
, and
Childress
,
D. S.
,
1996
, “
Parametric Analysis Using Finite Element Method to Investigate Prosthetic Interface Stresses for Persons with Trans-Tibial Amputation
,”
J. Rehabil. Res. Dev.
,
33
, pp.
227
238
.
16.
Vetrano
,
S. L.
, and
Silver-Thorn
,
M. B.
,
1997
, “
Analysis of Residual Limb Bulk Soft Tissue Behavior Using Nonlinear Finite Element Methods
,”
ASME-BED
,
35
, pp.
201
202
.
17.
Commean
,
P. K.
,
Smith
,
K. E.
,
Vannier
,
M. W.
,
Szabo
,
B. A.
, and
Actis
,
L. R.
,
1997
, “
Finite Element Modeling and Experimental Verification of Lower Extremity Shape Change under Load
,”
J. Biomech.
,
30
, pp.
531
536
.
18.
Houston
,
V. L.
,
Luo
,
G.
,
Mason
,
C. P.
,
Beattie
,
A. C.
,
LaBlanc
,
K. P.
, and
Garbarini
,
M.
,
1997
, “
Tissue Biomechanical Studies for Prosthetic Socket Design
,”
ASME-BED
,
35
, pp.
245
246
.
19.
Fisher
,
C.
,
Simpson
,
G.
, and
Reynolds
,
D.
,
1999
, “
Development of a Finite Element Model of a Transtibial Socket Liner – An Initial Study
,”
Biomed. Sci. Instrum.
,
35
, pp.
39
44
.
20.
Zachariah, S. G., and Sanders, J. E., 1999, “Pre-Stresses due to Trans-Tibial Socket Donning: A Nonlinear Finite Element Analysis with Contact,” Proc. 1st BMES EMBS Conference., Atlanta GA, 1, p. 648.
21.
Seguchi, Y., Tanaka, M., Akazawa, Y., Nakagawa, A., and Kitayama, A., 1989, “Finite Element Analysis and Load Identification of Above-Knee Prosthesis Socket,” 4th Int. ANSYS Conference, Pt. 2, pp. 12.31–12.44.
22.
Brennan
,
J. M.
, and
Childress
,
D. S.
,
1991
, “
Finite Element and Experimental Investigation of Above-Knee Amputee Limb/Prosthesis Systems: A Comparative Study
,”
ASME-BED
,
20
, pp.
547
550
.
23.
Mak, A. F. T., Yu, Y. M., Hong, M. L., and Chan, C., 1992, “Finite Element Models for Analyses of Stresses within Above-Knee Stumps,” Proc. 7th World Congress of ISPO, pp. 147–148.
24.
Zhang
,
M.
, and
Mak
,
A. F. T.
,
1996
, “
Finite Element Analysis of the Load Transfer between an Above-Knee Residual Limb and Its Prosthetic Socket—Roles of Interface Friction and Distal-End Boundary Conditions
,”
IEEE Trans. Rehabil. Eng.
,
4
, pp.
337
346
.
25.
Douglas, T. S., Solomonidis, S. E., Lee, V. S. P., and Spence, W. D., 1997, “Automatic Boundary Extraction from Magnetic Resonance Images of the Residual Limb of a Trans-Femoral Amputee,” Proc. 19th Ann. Conf. EMBS, 2, pp. 577–579.
26.
Tanaka
,
M.
,
Akazawa
,
Y.
,
Nakagawa
,
A.
, and
Kitayama
,
I.
,
1997
, “
Identification of Pressure Distribution at the Socket Interface of an Above-Knee Prosthesis
,”
Adv. Eng. Software
,
28
, pp.
379
384
.
27.
Zhang, M., Mak, A. F. T., and Mak, J., 1998, “Air Cushion Action at the Distal End of Above-Knee Stump with a Prosthetic Socket,” Proc. 20th Ann. Conf. EMBS, 5, pp. 2754–2756.
28.
Vannah
,
W. M.
, and
Childress
,
D. S.
,
1996
, “
Indentor Tests and Finite Element Modeling of Bulk Muscular Tissue In Vivo
,”
J. Rehabil. Res. Dev.
,
33
, pp.
239
252
.
29.
Silver-Thorn
,
M. B.
,
1999
, “
In Vivo Indentation of Lower Extremity Soft Tissues
,”
IEEE Trans. Rehabil. Eng.
,
7
, pp.
268
277
.
30.
Zheng
,
Y. P.
, and
Mak
,
A. F. T.
,
1999
, “
Extraction of Quasi-Linear Viscoelastic Coefficients for Lower Limb Soft Tissues from Manual Indentation Experiment
,”
J. Biomech. Eng.
,
121
, pp.
330
339
.
31.
Fung, Y. C. B., 1972, “Stress-Strain History Relations of Soft Tissues in Simple Elongation,” Biomechanics: Its Foundations and Objectives, Fung, Perrone and Anliker eds., Prentice Hall Inc. Inglewood, NJ, pp. 181–208.
32.
Sauren
,
A. A. H. J.
, and
Rousseau
,
E. P. M.
,
1983
, “
A Concise Sensitivity Analysis of the Quasi-Linear Viscoelastic Model Proposed by Fung
,”
J. Biomech. Eng.
,
105
, pp.
92
95
.
33.
Dortmans
,
L. J. M. G.
,
Sauren
,
A. A. H. J.
, and
Rousseau
,
E. P. M.
,
1984
, “
Coefficient Estimation Using Quasi-Linear Viscoelastic Model Proposed by Fung
,”
J. Biomech. Eng.
,
106
, pp.
198
203
.
34.
Nigul
,
I
, and
Nigul
,
U.
,
1987
, “
On Algorithms of Evaluation of Fung’s Relaxation Function Coefficients
,”
J. Biomech. Eng.
,
20
, pp.
343
352
.
35.
Johnnson
,
G. A.
,
Livesay
,
G. A.
,
Woo
,
S. L. Y.
, and
Rajagopal
,
K. R.
,
1996
, “
A Single Integral Finite Strain Viscoelastic Model of Ligaments and Tendons
,”
J. Biomech. Eng.
,
118
, pp.
221
226
.
36.
Miller
,
K.
, and
Chinzei
,
K.
,
1997
, “
Constitutive Modelling of Brain Tissue: Experiment and Theory
,”
J. Biomech. Eng.
,
30
, pp.
1115
1121
.
37.
Bowen
,
R. M.
,
1980
, “
Incompressible Porous Media Models by the Use of the Theory of Mixtures
,”
Int. J. Eng. Sci.
,
18
, pp.
1129
1148
.
38.
Spilker
,
R. L.
, and
Suh
,
J. K.
,
1990
, “
Formulation and Evaluation of a Finite Element Model for the Biphasic Model of Soft Tissues
,”
Comput. Struct.
,
35
, pp.
425
439
.
39.
Simon
,
B. R.
,
1992
, “
Multiphase Poroelastic Finite Element Models of Soft Tissue Structures
,”
Appl. Mech. Rev.
,
45
, pp.
191
218
.
40.
Liable
,
J. P.
,
Pflaster
,
D.
,
Simon
,
B. R.
,
Krag
,
M. H.
,
Pope
,
M.
, and
Haugh
,
L. D.
,
1994
, “
A Dynamic Coefficient Estimation Procedure for Soft Tissue Using a Poroelastic Finite Element Model
,”
J. Biomech. Eng.
,
116
, pp.
19
29
.
41.
Butler
,
S. L.
,
Kohles
,
S. S.
,
Thielke
,
R. J.
,
Chen
,
C.
, and
Vanderby
, Jr.,
R.
,
1997
, “
Interstitial Fluid Flow in Tendons or Ligaments: A Porous Medium Finite Element Simulation
,”
Med. Biol. Eng. Comput.
,
35
, pp.
742
746
.
42.
Simon
,
B. R.
,
Kaufman
,
M. V.
,
Liu
,
J.
, and
Baldwin
,
A. L.
,
1998
, “
Porohyperelastic-Transport-Swelling Theory Material Properties and Finite Element Models for Large Arteries
,”
Int. J. Solids Struct.
,
35
, pp.
5021
5031
.
43.
Iding
,
R. H.
,
Pister
,
K. S.
, and
Taylor
,
R. L.
,
1974
, “
Identification of Nonlinear Elastic Solids by a Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
,
4
, pp.
121
142
.
44.
Lin
,
H. S.
,
Liu
,
Y. K.
,
Ray
,
G.
, and
Nikravesh
,
P. E.
,
1978
, “
Systems Identification for Material Properties of the Intervertebral Joint
,”
J. Biomech.
,
11
, pp.
1
14
.
45.
Wineman
,
A.
,
Wilson
,
D.
, and
Melvin
,
J. W.
,
1979
, “
Material Identification of Soft Tissue Using Membrane Inflation
,”
J. Biomech.
,
12
, pp.
841
850
.
46.
Ray, G., and Ghista, D. N., 1980, “A Direct Computational Algorithm to Estimate In Vivo Constitutive Properties of Some Cardiovascular Structures,” Finite Elements in Biomechanics, B. R. Simon, ed., Univ. of Arizona, 2, pp. 623–637.
47.
Pao, Y. C., 1982, “Finite Elements in Stress Analysis and Estimation of Mechanical Properties of Working Heart,” Finite Elements in Biomechanics, R. H. Gallagher, B. R. Simon and P. C. Johnson, J. F. Gross, Ed. Wiley, 127-153.
48.
Guccione
,
J. M.
,
McCulloch
,
A. D.
, and
Waldman
,
L. K.
,
1991
, “
Passive Material Properties of Intact Ventricular Myocardium Determined from a Cylindrical Model
,”
J. Biomech. Eng.
,
113
, pp.
42
55
.
49.
Oomenns
,
C. W. J.
,
Ratingen
,
M. R. V.
,
Janssen
,
J. D.
,
Kok
,
J. J.
, and
Hendricks
,
M. A. N.
,
1993
, “
A Numerical-Experimental Method for a Mechanical Characterization of Biological Materials
,”
J. Biomech.
,
26
, pp.
617
621
.
50.
Novak
,
V. P.
,
Yin
,
F. C. P.
, and
Humphrey
,
J. D.
,
1994
, “
Regional Mechanical Properties of Passive Myocardium
,”
J. Biomech.
,
27
, pp.
403
412
.
51.
Vorp
,
D. A.
,
Rajagopal
,
K. R.
,
Smolinski
,
P. J.
, and
Borovetz
,
H. S.
,
1995
, “
Identification of Elastic Properties of Homogenious Orthotropic Vascular Segments in Distension
,”
J. Biomech.
,
28
, pp.
501
512
.
52.
Wang
,
J. L.
,
Parnianpour
,
M.
,
Shirazi-Adl
,
A.
, and
Engin
,
A. E.
,
1996
, “
Development of the Viscoleastic Finite Element Model of Lumbar Motion Segment
,”
ASME PD
,
77
, pp.
51
56
.
53.
Nagaraj
,
A.
,
Ramani
,
K.
,
Kane
,
B. J.
,
Greene
,
R.
,
Dove
,
E. L.
,
Chandran
,
K. B.
, and
McPherson
,
D. D.
,
1997
, “
In-Vivo Regional Assessment of Atherosclerotic Vascular Material Properties Using Three Dimensional Intravascular Ultrasound Reconstruction and Finite Element Analysis
,”
ASME-BED
,
35
, pp.
463
464
.
54.
Flynn
,
D. M.
,
Peura
,
G. D.
,
Grigg
,
P.
, and
Hoffman
,
A. H.
,
1998
, “
A Finite Element Based Method to Determine the Properties of Planar Soft Tissue
,”
J. Biomech. Eng.
,
120
, pp.
202
210
.
55.
Steege
,
J. W.
, and
Childress
,
D. S.
,
1988
, “
Finite Element Modeling of the Below-Knee Socket and Limb: Phase II
,”
Proc. Bioeng. Conf. (ASME-BED)
, pp.
121
129
.
56.
Vannah, W. M., 1990, “Indentor Tests and Finite Element Modeling of Bulk Muscular Soft Tissue In Vivo,” Ph.D. Dissertation, Northwestern University, Evanston, IL.
57.
Vetrano, S. L., and Silver-Thorn, M. B., 1997, “Analysis of Residual Limb Bulk Soft Tissue Behavior Using Nonlinear Finite Element Methods,” Proc. 2nd Ann. Conf. Finite Element Methods Bioeng., MARC Analysis Research Corp., University of Minneapolis, pp. 29–36.
58.
Tonuk
,
E.
, and
Silver-Thorn
,
M. B.
,
2003
, “
Nonlinear Elastic Material Property Estimation of Lower Extremity Residual Limb Tissue
,”
IEEE Trans. Neural Sys. Rehab. Eng.
,
11
(
1
), pp.
43
53
.
59.
Pathak
,
A. P.
,
Silver-Thorn
,
M. B.
,
Thierfelder
,
C. A.
, and
Prieto
,
T. E.
,
1998
, “
A Rate-Controlled Indentor for In Vivo Analysis of Residual Limb Tissues
,”
IEEE Trans. Rehabil. Eng.
,
6
, pp.
12
20
.
60.
Tonuk, E., and Silver-Thorn, M. B., 1999, “Nonlinear Viscoelastic Material Property Estimation for Lower Extremity Residual Limbs,” Proc. 1st BMES EMBS Conference., Atlanta GA, 1, p. 645.
61.
Simo
,
J. C.
,
1987
, “
On a Fully Three-Dimensional Viscoelastic Damage Model: Formulation and Computational Aspects
,”
Comput. Methods Appl. Mech. Eng.
,
60
, pp.
153
173
.
62.
Gerhard
,
A. H.
, and
Simo
,
J. C.
,
1996
, “
A New Viscoelastic Constitutive Model for Continuous Media at Finite Thermomechanical Changes
,”
Int. J. Solids Struct.
,
33
, pp.
3019
3034
.
63.
Sanders
,
J. E.
, and
Daly
,
C. H.
,
1993
, “
Measurement of Stresses in Three Orthogonal Directions at the Residual Limb-Prosthetic Socket Interface
,”
IEEE Trans. Rehabil. Eng.
,
1
, pp.
79
85
.
64.
Silver-Thorn, M. B., 1991, “Prediction and Experimental Verification of Residual Limb/Prosthetic Socket Interface Pressures for Below-Knee Amputees,” Ph.D. Dissertation, Northwestern University, Evanston, IL.
65.
Tonuk, E., and Silver-Thorn, M. B., 1999, “Effect of Curvature on Lower Extremity Residual Limb Models,” Proc. 1st BMES EMBS Conference., Atlanta GA, 1, p. 639.
66.
Malvern, L. E., 1969, “Introduction to the Mechanics of a Continuous Medium,” Prentice-Hall Inc., Englewood Cliffs, New Jersey, pp. 313–319.
67.
Lakes, R. S., 1998, “Viscoelastic Solids,” CRC Press, Washington D. C., pp. 23–30.
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