Abstract

Passive energy storage and return (ESR) feet are current performance standard in lower limb prostheses. A recently developed semi-active variable-stiffness foot (VSF) prosthesis balances the simplicity of a passive ESR device with the adaptability of a powered design. The purpose of this study was to model and simulate the ESR properties of the VSF prosthesis. The ESR properties of the VSF were modeled as a lumped parameter overhung beam. The overhung length is variable, allowing the model to exhibit variable ESR stiffness. Foot-ground contact was modeled using sphere-to-plane contact models. Contact parameters were optimized to represent the geometry and dynamics of the VSF and its foam base. Static compression tests and gait were simulated. Simulation outcomes were compared to corresponding experimental data. Stiffness of the model matched that of the physical VSF (R2: 0.98, root-mean-squared error (RMSE): 1.37 N/mm). Model-predicted resultant ground reaction force (GRFR) matched well under optimized parameter conditions (R2: 0.98, RMSE: 5.3% body weight,) and unoptimized parameter conditions (R2: 0.90, mean RMSE: 13% body weight). Anterior–posterior center of pressure matched well with R2 > 0.94 and RMSE < 9.5% foot length in all conditions. The ESR properties of the VSF were accurately simulated under benchtop testing and dynamic gait conditions. These methods may be useful for predicting GRFR arising from gait with novel prostheses. Such data are useful to optimize prosthesis design parameters on a user-specific basis.

References

1.
Schaarschmidt
,
M.
,
Lipfert
,
S. W.
,
Meier-Gratz
,
C.
,
Scholle
,
H. C.
, and
Seyfarth
,
A.
,
2012
, “
Functional Gait Asymmetry of Unilateral Transfemoral Amputees
,”
Hum. Mov. Sci.
,
31
(
4
), pp.
907
917
.10.1016/j.humov.2011.09.004
2.
Sanderson
,
D. J.
, and
Martin
,
P. E.
,
1997
, “
Lower Extremity Kinematic and Kinetic Adaptations in Unilateral Below-Knee Amputees During Walking
,”
Gait Posture
,
6
(
2
), pp.
126
136
.10.1016/S0966-6362(97)01112-0
3.
van Schaik
,
L.
,
Geertzen
,
J. H.
,
Dijkstra
,
P. U.
, and
Dekker
,
R.
,
2019
, “
Metabolic Costs of Activities of Daily Living in Subjects With Lower Limb Amputation: A Systematic Review and Meta-Analysis. Article Submitted for Publication
,”
PLoS One
,
14
(
3
), p.
e0213256
.10.1371/journal.pone.0213256
4.
Mckechnie
,
P. S.
, and
John
,
A.
,
2014
, “
Anxiety and Depression Following Traumatic Limb Amputation: A Systematic Review
,”
Injury
,
45
(
12
), pp.
1859
66
.10.1016/j.injury.2014.09.015
5.
Gailey
,
R.
,
Allen
,
K.
,
Castles
,
J.
,
Kucharik
,
J.
, and
Roeder
,
M.
,
2008
, “
Review of Secondary Physical Conditions Associated With Lower-Limb Amputation and Long-Term Prosthesis Use
,”
JRRD
,
45
(
1
), pp.
15
30
.10.1682/JRRD.2006.11.0147
6.
Casillas
,
J. M.
,
Dulieu
,
V.
,
Cohen
,
M.
,
Marcer
,
I.
, and
Didier
,
J. P.
,
1995
, “
Bioenergetic Comparison of a New Energy-Storing Foot and SACH Foot in Traumatic Below-Knee Vascular Amputations
,”
Arch. Phys. Med. Rehabil.
,
76
(
1
), pp.
39
44
.10.1016/S0003-9993(95)80040-9
7.
Postema
,
K.
,
Hermens
,
H. J.
,
De Vries
,
J.
,
Koopman
,
H. F. J. M.
, and
Eisma
,
W. H.
,
1997
, “
Energy Storage and Release of Prosthetic Feet Part 1: Biomechanical Analysis Related to User Benefits
,”
Prosthet. Orthot. Int.
,
21
(
1
), pp.
17
27
.10.3109/03093649709164526
8.
Farris
,
D. J.
, and
Sawicki
,
G. S.
,
2012
, “
The Mechanics and Energetics of Human Walking and Running: A Joint Level Perspective
,”
J. R. Soc. Interface
,
9
(
66
), pp.
110
18
.10.1098/rsif.2011.0182
9.
Winter
,
D. A.
,
1983
, “
Energy Generation and Absorption at the Ankle and Knee During Fast, Natural, and Slow Cadences
,”
Clin. Orthop. Relat. Res.
,
175
, pp.
147
154
.https://pubmed.ncbi.nlm.nih.gov/6839580/
10.
Glanzer
,
E. M.
, and
Adamczyk
,
P. G.
,
2018
, “
Design and Validation of a Semi-Active Variable Stiffness Foot Prosthesis
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
26
(
12
), pp.
2351
2359
.10.1109/TNSRE.2018.2877962
11.
Fey
,
N. P.
,
Klute
,
G. K.
, and
Neptune
,
R. R.
,
2013
, “
Altering Prosthetic Foot Stiffness Influences Foot and Muscle Function During Below-Knee Amputee Walking: A Modeling and Simulation Analysis
,”
J. Biomech.
,
46
(
4
), pp.
637
644
.10.1016/j.jbiomech.2012.11.051
12.
Strbac
,
M.
, and
Popovic
,
D.
,
2012
, “
Software Tool for the Prosthetic Foot Modeling and Stiffness Optimization
,”
Comput. Math. Methods Med.
, 2012, pp.
1
8
.10.1155/2012/421796
13.
Tryggvason
,
H.
,
Starker
,
F.
,
Lecomte
,
C.
, and
Jonsdottir
,
F.
,
2020
, “
Use of Dynamic FEA for Design Modification and Energy Analysis of a Variable Stiffness Prosthetic Foot
,”
Appl. Sci.
,
10
(
2
), p.
650
.10.3390/app10020650
14.
Laprè
,
A. K.
,
Umberger
,
B. R.
, and
Sup
,
F.
,
2014
, “
Simulation of a Powered Ankle Prosthesis With Dynamic Joint Alignment
,”
36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
, EMBC 2014, Chicago, IL, Aug. 26–30, pp.
1618
1621
.10.1109/EMBC.2014.6943914
15.
Willson
,
A. M.
,
Richburg
,
C. A.
,
Czerniecki
,
J.
,
Steele
,
K. M.
, and
Aubin
,
P. M.
,
2020
, “
Design and Development of a Quasi-Passive Transtibial Biarticular Prosthesis to Replicate Gastrocnemius Function in Walking
,”
ASME J. Med. Devices
,
14
(
2
), p.
025001
.10.1115/1.4045879
16.
Fey
,
N. P.
,
Klute
,
G. K.
, and
Neptune
,
R. R.
,
2012
, “
Optimization of Prosthetic Foot Stiffness to Reduce Metabolic Cost and Intact Knee Loading During Below-Knee Amputee Walking: A Theoretical Study
,”
ASME J. Biomech. Eng.
,
134
(
11
), p.
111005
.10.1115/1.4007824
17.
Russel
,
E. E.
, and
Miller
,
R. H.
,
2018
, “
Maintenance of Muscle Strength Retains a Normal Metabolic Cost in Simulated Walking After Transtibial Limb Loss
,”
PLoS One
,
13
(
1
), p.
e0191310
.10.1371/journal.pone.0191310
18.
Miller
,
S.
,
2020
, “
Simscape Multibody Contact Forces Library
,” MathWorks, Natick, MA, accessed Mar. 25, 2021, https://www.mathworks.com/matlabcentral/fileexchange/47417-simscape-multibody-contact-forces-library
19.
LaPrè
,
A. K.
,
Price
,
M. A.
,
Wedge
,
R. D.
,
Umberger
,
B. R.
, and
Sup
,
F. C.
,
2018
, “
Approach for Gait Analysis in Persons With Limb Loss Including Residuum and Prosthesis Socket Dynamics
,”
Int. J. Numer. Method. Biomed. Eng.
,
34
(
4
), p.
e2936
.10.1002/cnm.2936
20.
Jia
,
X.
,
Zhang
,
M.
, and
Lee
,
W. C. C.
,
2004
, “
Load Transfer Mechanics Between Trans-Tibial Prosthetic Socket and Residual Limb—Dynamic Effects
,”
J. Biomech.
,
37
(
9
), pp.
1371
77
.10.1016/j.jbiomech.2003.12.024
21.
De Leva
,
P.
,
1996
, “
Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters
,”
J. Biomech.
,
29
(
9
), pp.
1223
1230
.10.1016/0021-9290(95)00178-6
22.
Wu
,
G.
,
Siegler
,
S.
,
Allard
,
P.
,
Kirtley
,
C.
,
Leardini
,
A.
,
Rosenbaum
,
D.
,
Whittle
,
M.
,
D'Lima
,
D. D.
,
Cristofolini
,
L.
,
Witte
,
H.
,
Schmid
,
O.
, and
Stokes
,
I.
,
2002
, “
ISB Recommendation on Definitions of Joint Coordinate System of Various Joints for the Reporting of Human Joint Motion - Part I: Ankle, Hip, and Spine
,”
J. Biomech.
,
35
(
4
), pp.
543
548
.10.1016/S0021-9290(01)00222-6
23.
Grood
,
E. S.
, and
Suntay
,
W. J.
,
1983
, “
A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee
,”
ASME J. Biomech. Eng.
,
105
(
2
), pp.
136
144
.10.1115/1.3138397
24.
Thakallapelli
,
A.
,
Ghosh
,
S.
, and
Kamalasadan
,
S.
,
2016
, “
Real-Time Frequency Based Reduced Order Modeling of Large Power Grid
,”
IEEE Power and Energy Society General Meeting
, IEEE Computer Society, Boston, MA, July 17–21, pp.
1
5
.10.1109/PESGM.2016.7741877
25.
Kikuchi
,
R.
,
Misaka
,
T.
, and
Obayashi
,
S.
,
2016
, “
International Journal of Computational Fluid Dynamics Real-Time Prediction of Unsteady Flow Based on POD Reduced-Order Model and Particle Filter
,”
Int. J. Comut. Fluid Dyn.
,
30
(
4
), pp.
285
306
.10.1080/10618562.2016.1198782
26.
Fey
,
N. P.
,
Klute
,
G. K.
, and
Neptune
,
R. R.
,
2011
, “
The Influence of Energy Storage and Return Foot Stiffness on Walking Mechanics and Muscle Activity in Below-Knee Amputees
,”
Clin. Biomech.
,
26
(
10
), pp.
1025
1032
.10.1016/j.clinbiomech.2011.06.007
27.
Zelik
,
K. E.
,
Collins
,
S. H.
,
Adamczyk
,
P. G.
,
Segal
,
A. D.
,
Klute
,
G. K.
,
Morgenroth
,
D. C.
,
Hahn
,
M. E.
,
Orendurff
,
M. S.
,
Czerniecki
,
J. M.
, and
Kuo
,
A. D.
,
2011
, “
Systematic Variation of Prosthetic Foot Spring Affects Center-of-Mass Mechanics and Metabolic Cost During Walking
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
19
(
4
), pp.
411
419
.10.1109/TNSRE.2011.2159018
28.
Jin
,
L.
,
Roland
,
M.
,
Hahn
,
M. E.
, and
Adamczyk
,
P. G.
,
2016
, “
The Effect of High-and Low-Damping Prosthetic Foot Structures on Knee Loading in the Uninvolved Limb Across Different Walking Speeds
,”
J. Appl. Biomech.
,
32
(
3
), pp.
233
240
.10.1123/jab.2015-0143
29.
Webber
,
C. M.
, and
Kaufman
,
K.
,
2017
, “
Instantaneous Stiffness and Hysteresis of Dynamic Elastic Response Prosthetic Feet
,”
Prosthet. Orthot. Int.
,
41
(
5
), pp.
463
468
.10.1177/0309364616683980
30.
Womac
,
N. D.
,
Neptune
,
R. R.
, and
Klute
,
G. K.
,
2019
, “
Stiffness and Energy Storage Characteristics of Energy Storage and Return Prosthetic Feet
,”
Prosthet. Orthot. Int.
, 43(3), pp.
266
275
.10.1177/0309364618823127
31.
Van Hulle
,
R.
,
Schwartz
,
C.
,
Denoël
,
V.
,
Croisier
,
J.-L.
,
Forthomme
,
B.
, and
Brüls
,
O.
,
2020
, “
A Foot/Ground Contact Model for Biomechanical Inverse Dynamics Analysis
,”
J. Biomech.
,
100
(
2020
).
32.
Lopes
,
D. S.
,
Neptune
,
R. R.
,
Ambrósio
,
J. A.
, and
Silva
,
M. T.
,
2015
, “
A Superellipsoid-Plane Model for Simulating Foot-Ground Contact During Human Gait
,”
Comput. Methods Biomech. Biomed. Eng.
, 19(9), pp.
954
963
.10.1080/10255842.2015.1081181
33.
Brown
,
P.
, and
McPhee
,
J.
,
2018
, “
A 3D Ellipsoidal Volumetric Foot–Ground Contact Model for Forward Dynamics
,”
Multibody Syst. Dyn.
,
42
(
4
), pp.
447
467
.10.1007/s11044-017-9605-4
34.
Jackson
,
J. N.
,
Hass
,
C. J.
, and
Fregly
,
B. J.
,
2016
, “
Development of a Subject-Specific Foot-Ground Contact Model for Walking
,”
ASME J. Biomech. Eng.
,
138
(
9
), p.
091002
.10.1115/1.4034060
35.
Winter
,
D. A.
, and
Sienko
,
S. E.
,
1988
, “
Biomechanics of Below-Knee Amputee Gait
,”
J. Biomech.
,
21
(
5
), pp.
361
367
.10.1016/0021-9290(88)90142-X
36.
Su
,
P.-F.
,
Gard
,
S. A.
,
Lipschutz
,
R. D.
, and
Kuiken
,
T. A.
,
2008
, “
Differences in Gait Characteristics Between Persons With Bilateral Transtibial Amputations, Due to Peripheral Vascular Disease and Trauma, and Able-Bodied Ambulators
,”
Arch. Phy.s Med. Rehabil.
,
89
(
7
), pp.
1386
1394
.10.1016/j.apmr.2007.10.050
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