Both development and progression of knee osteoarthritis have been associated with the loading of the knee joint during walking. We are, therefore, interested in developing strategies for changing walking biomechanics to offload the knee joint without resorting to surgery. In this study, simulations of human walking were performed using a 2D bipedal forward dynamics model. A simulation generated by minimizing the metabolic cost of transport (CoT) resembled data measured from normal human walking. Three simulations targeted at minimizing the peak axial knee joint contact force instead of the CoT reduced the peak force by 12–25% and increased the CoT by 11–14%. The strategies used by the simulations were (1) reduction in gastrocnemius muscle force, (2) avoidance of knee flexion during stance, and (3) reduced stride length. Reduced gastrocnemius force resulted from a combination of changes in activation and changes in the gastrocnemius contractile component kinematics. The simulations that reduced the peak contact force avoided flexing the knee during stance when knee motion was unrestricted and adopted a shorter stride length when the simulated knee motion was penalized if it deviated from the measured human knee motion. A higher metabolic cost in an offloading gait would be detrimental for covering a long distance without fatigue but beneficial for exercise and weight loss. The predicted changes in the peak axial knee joint contact force from the simulations were consistent with estimates of the joint contact force in a human subject who emulated the predicted kinematics. The results demonstrate the potential of using muscle-actuated forward dynamics simulations to predict novel joint offloading interventions.

References

1.
D'Ambrosia
,
R. D.
,
2005
, “
Epidemiology of Osteoarthritis
,”
Orthopedics
,
28
(
S2
), pp.
s201
s205
.
2.
Sharma
,
L.
,
Hurwitz
,
D. E.
,
Thonar
,
E. J.
,
Sum
,
J. A.
,
Lenz
,
M. E.
,
Dunlop
,
D. D.
,
Schnitzer
,
T. J.
,
Kirwan-Mellis
,
G.
, and
Andriacchi
,
T. P.
,
1998
, “
Knee Adduction Moment, Serum Hyaluronan Level, and Disease Severity in Medial Tibiofemoral Osteoarthritis
,”
Arthritis Rheum.
,
41
(
7
), pp.
1233
1240
.10.1002/1529-0131(199807)41:7<1233::AID-ART14>3.0.CO;2-L
3.
Miyazaki
,
T.
,
Wada
,
M.
,
Kawahara
,
H.
,
Sato
,
M.
,
Baba
,
H.
, and
Shimada
,
S.
,
2002
, “
Dynamic Load at Baseline Can Predict Radiographic Disease Progression in Medial Compartment Knee Osteoarthritis
,”
Ann. Rheum. Dis.
,
61
(
7
), pp.
617
622
.10.1136/ard.61.7.617
4.
Thorp
,
L. E.
,
Sumner
,
D. R.
,
Block
,
J. A.
,
Moisio
,
K. C.
,
Shott.
S.
, and
Wimmer
,
M. A.
,
2006
, “
Knee Joint Loading Differs in Individuals With Mild Compared to Moderate Medial Knee Osteoarthritis
,”
Arthritis Rheum.
,
54
(
12
), pp.
3842
3849
.10.1002/art.22247
5.
Astephen
,
J. L.
,
Deluzio
,
K. J.
,
Caldwell
,
G. E.
,
Dunbar
,
M. J.
, and
Hubley-Kozey
,
C. L.
,
2008
, “
Gait and Neuromuscular Pattern Changes are Associated With Differences in Knee Osteoarthritis Severity Levels
,”
J. Biomech.
,
41
(
4
), pp.
868
876
.10.1016/j.jbiomech.2007.10.016
6.
Lafeber
,
F. P.
,
Intema
,
F.
,
Van Roermund
,
P. M.
, and
Marijnissen
,
A. C.
,
2006
, “
Unloading Joints to Treat Osteoarthritis, Including Joint Distraction
,”
Curr. Opin. Rheumatol.
,
18
(
5
), pp.
519
525
.10.1097/01.bor.0000240366.54960.a1
7.
Englund
,
M.
,
2010
, “
The Role of Biomechanics in the Initiation and Progression of OA of the Knee
,”
Best Pract. Res. Clin. Rheumatol.
,
24
(
1
), pp.
39
46
.10.1016/j.berh.2009.08.008
8.
Waller
,
C.
,
Hayes
,
D.
,
Block
,
J. E.
, and
London
,
N. J.
,
2011
, “
Unload it: The Key to the Treatment of Knee Osteoarthritis
,”
Knee Surg. Sports Traumatol. Arthrosc.
,
19
(
11
), pp.
1823
1829
.10.1007/s00167-011-1403-6
9.
Deie
,
M.
,
Ochi
,
M.
,
Adachi
,
N.
,
Kajiwara
,
R.
, and
Kanaya
,
A.
,
2007
, “
A New Articulated Distraction Arthroplasty Device for Treatment of the Osteoarthritic Knee Joint: A Preliminary Report
,”
Arthroscopy
,
23
(
8
), pp.
833
838
.10.1016/j.arthro.2007.02.014
10.
Intema
,
F.
,
Van Roermund
,
P. M.
,
Marijnissen
,
A. C.
,
Cotofana
,
S.
,
Eckstein
,
F.
,
Castelein
,
R. M.
,
Bijlsma
,
J. W.
,
Mastberg
,
S. C.
, and
Lafeber
,
F. P.
,
2011
, “
Tissue Structure Modification in Knee Osteoarthritis by Use of Joint Distraction: An Open 1-Year Pilot Study
,”
Ann. Rheum. Dis.
,
70
(
8
), pp.
1441
1446
.10.1136/ard.2010.142364
11.
Cole
,
B. J.
, and
Harner
,
C. D.
,
1999
, “
Degenerative Arthritis of the Knee in Active Patients: Evaluation and Management
,”
J. Am. Acad. Orthop. Surg.
,
7
(
6
), pp.
389
402
.
12.
Lützner
,
J.
,
Kasten
,
P.
,
Günther
,
K. P.
, and
Kirschner
,
S.
,
2009
, “
Surgical Options for Patients With Osteoarthritis of the Knee
,”
Nat. Rev. Rheumatol.
,
5
(
6
), pp.
309
316
.10.1038/nrrheum.2009.88
13.
Feeley
,
B. T.
,
Gallo
,
R. A.
,
Sherman
,
S.
, and
Williams
,
R. J.
,
2010
, “
Management of Osteoarthritis of the Knee in the Active Patient
,”
J. Am. Acad. Orthop. Surg.
,
18
(
7
), pp.
406
416
.
14.
Komi
,
P. V.
,
1990
, “
Relevance of In Vivo Force Measurements to Human Biomechanics
,”
J. Biomech.
,
23
(S
1
), pp.
23
34
.10.1016/0021-9290(90)90038-5
15.
Kutzner
,
I.
,
Heinlein
,
B.
,
Graichen
,
F.
,
Bender
,
A.
,
Rohlmann
,
A.
,
Halder
,
A.
,
Beier
,
A.
, and
Bergmann
,
G.
,
2010
, “
Loading of the Knee Joint During Activities of Daily Living Measured In Vivo in Five Subjects
,”
J. Biomech.
,
43
(
11
), pp.
2164
2173
.10.1016/j.jbiomech.2010.03.046
16.
Neptune
,
R. R.
,
2000
, “
Computer Modeling and Simulation of Human Movement: Applications in Sport and Rehabilitation
,”
Phys. Med. Rehabil. Clin. N. Am.
,
11
(
2
), pp.
417
434
.
17.
Fregly
,
B. J.
,
Reinbolt
,
J. A.
, and
Chmielewski
,
T. L.
,
2008
, “
Evaluation of a Patient-Specific Cost Function to Predict the Influence of Foot Path on the Knee Adduction Torque During Gait
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
1
), pp.
63
71
.10.1080/10255840701552036
18.
Seireg
,
A.
, and
Arvikar
,
R. J.
,
1975
, “
The Prediction of Muscular Load Sharing and Joint Forces in the Lower Extremities During Walking
,”
J. Biomech.
,
8
(
2
), pp.
89
102
.10.1016/0021-9290(75)90089-5
19.
Hatze
,
H.
,
1984
, “
Quantitative Analysis, Synthesis and Optimization of Human Motion
,”
Hum. Mov. Sci.
,
3
(
1
), pp.
5
25
.10.1016/0167-9457(84)90003-4
20.
Miller
,
R. H.
,
Umberger
,
B. R.
, and
Caldwell
,
G. E.
,
2012
, “
Limitations to Maximum Sprinting Speed Imposed by Muscle Mechanical Properties
,”
J. Biomech.
,
45
(
6
), pp.
1092
1097
.10.1016/j.jbiomech.2011.04.040
21.
Miller
,
R. H.
,
Umberger
,
B. R.
,
Hamill
,
J.
, and
Caldwell
,
G. E.
,
2012
, “
Evaluation of the Minimum Energy Hypothesis and Other Potential Optimality Criteria for Human Running
,”
Proc. R. Soc. London, Ser. B
,
279
(
1733
), pp.
1498
1505
.10.1098/rspb.2011.2015
22.
Waters
,
R. L.
, and
Mulroy
,
S.
,
1999
, “
The Energy Expenditure of Normal and Pathologic Gait
,”
Gait and Posture
,
9
(
3
), pp.
207
231
.10.1016/S0966-6362(99)00009-0
23.
Umberger
,
B. R.
,
Gerritsen
,
K. G. M.
, and
Martin
,
P. E.
,
2003
, “
A Model of Human Muscle Energy Expenditure
,”
Comput. Methods Biomech. Biomed. Eng.
,
6
(
2
), pp.
99
111
.10.1080/1025584031000091678
24.
Umberger
,
B. R.
,
2010
, “
Stance and Swing Phase Costs in Human Walking
,”
J. R. Soc., Interface
,
7
(
50
), pp.
1329
1340
.10.1098/rsif.2010.0084
25.
Umberger
,
B. R.
,
Gerritsen
,
K. G. M.
, and
Martin
,
P. E.
,
2006
, “
Muscle Fiber Type Effects on Energetically Optimal Cadences in Cycling
,”
J. Biomech.
,
39
(
8
), pp.
1472
1479
.10.1016/j.jbiomech.2005.03.025
26.
Winter
,
D. A.
,
1983
, “
Biomechanical Motor Patterns in Normal Walking
,”
J. Motor Behav.
,
15
(
4
), pp.
302
330
.
27.
Knutson
,
L. M.
, and
Soderberg
,
G. L.
,
1995
, “
EMG: Use and Interpretation in Gait
,”
Gait Analysis: Theory and Application
,
R. L.
Craik
, and
C. A.
Oatis
, eds.,
Mosby
,
St. Louis, MO
, pp.
307
327
.
28.
Cappellini
,
G.
,
Ivanenko
,
Y. P.
,
Poppele
,
R. E.
, and
Lacquaniti
,
F.
,
2006
, “
Motor Patterns in Human Walking and Running
,”
J. Neurophysiol.
,
95
(
6
), pp.
3426
3437
.10.1152/jn.00081.2006
29.
Aerts
,
P.
, and
De Clercq
,
D.
,
1993
, “
Deformation Characteristics of the Heel Region of the Shod Foot During a Simulated Heel Strike: The Effect of Varying Midsole Hardness
,”
J. Sports Sci.
,
11
(
5
), pp.
449
461
.10.1080/02640419308730011
30.
Cobb
,
F.
,
2008
,
Structural Engineer's Pocket Book
,
Butterworth-Heinemann
,
London
.
31.
Song
,
P.
,
Kraus
,
P.
,
Kumar
,
V.
, and
Dupont
,
P.
,
2001
, “
Analysis of Rigid Body Dynamic Models for Simulation of Systems With Frictional Contacts
,”
J. Appl. Mech.
,
68
(
1
), pp.
118
128
.10.1115/1.1331060
32.
Yamaguchi
,
G. T.
, and
Zajac
,
F. E.
,
1989
, “
A Planar Model of the Knee Joint to Characterize the Knee Extensor Mechanism
,”
J. Biomech.
,
22
(
1
), pp.
1
10
.10.1016/0021-9290(89)90179-6
33.
Winter
,
D. A.
,
2009
,
Biomechanics and Motor Control of Human Movement
,
Wiley
,
New York
.
34.
Crowninshield
,
R. D.
, and
Brand
,
R. A.
,
1981
, “
The Prediction of Forces in Joint Structures: Distribution of Intersegmental Resultants
,”
Exercise Sport Sci. Rev.
,
9
, pp.
159
181
.10.1249/00003677-198101000-00004
35.
Herzog
,
W.
, and
Read
,
L. J.
,
1993
, “
Lines of Action and Moment Arms of the Major Force-Carrying Structures Crossing the Human Knee Joint
,”
J. Anat.
,
182
(
2
), pp.
213
230
.
36.
Thelen
,
D. G.
,
2003
, “
Adjustments of Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older Adults
,”
J. Biomech. Eng.
,
125
(
1
), pp.
70
77
.10.1115/1.1531112
37.
Riener
,
R.
, and
Edrich
,
T.
,
1999
, “
Identification of Passive Elastic Joint Moments in the Lower Extremities
,”
J. Biomech.
,
32
(
5
), pp.
539
544
.10.1016/S0021-9290(99)00009-3
38.
Brandon
,
S. C. E.
, and
Deluzio
,
K. J.
,
2011
, “
Robust Features of Knee Osteoarthritis in Joint Moments are Independent of Reference Frame Selection
,”
Clin. Biomech. (Bristol, Avon)
,
26
(
1
), pp.
65
70
.10.1016/j.clinbiomech.2010.08.010
39.
Umberger
,
B. R.
,
2008
, “
Effects of Suppressing Arm Swing on Kinematics, Kinetics, and Energetics of Human Walking
,”
J. Biomech.
,
41
(
11
), pp.
2575
2580
.10.1016/j.jbiomech.2008.05.024
40.
Lundberg
,
H. J.
,
Foucher
,
K. C.
,
Andriacchi
,
T. P.
, and
Wimmer
,
M. A.
,
2012
, “
Direct Comparison of Measured and Calculated Total Knee Replacement Force Envelopes During Walking in the Presence of Normal and Abnormal Gait Patterns
,”
J. Biomech.
,
45
(
6
), pp.
990
996
.10.1016/j.jbiomech.2012.01.015
41.
Neptune
,
R. R.
,
Kautz
,
S. A.
, and
Zajac
,
F. E.
,
2001
, “
Contributions of the Individual Ankle Plantar Flexors to Support, Forward Progression and Swing Initiation During Walking
,”
J. Biomech.
,
34
(
11
), pp.
1387
1398
.10.1016/S0021-9290(01)00105-1
42.
Anderson
,
F. C.
, and
Pandy
,
M. G.
,
2001
, “
Dynamic Optimization of Human Walking
,”
J. Biomech. Eng.
,
123
(
5
), pp.
381
390
.10.1115/1.1392310
43.
Higginson
,
J. S.
,
Neptune
,
R. R.
, and
Anderson
,
F. C.
,
2005
, “
Simulated Parallel Annealing Within a Neighborhood for Optimization of Biomechanical Systems
,”
J. Biomech.
,
38
(
9
), pp.
1938
1942
.10.1016/j.jbiomech.2004.08.010
44.
Goffe
,
W. L.
,
Ferrier
,
G. D.
, and
Rogers
,
J.
,
1994
, “
Global Optimization of Statistical Functions With Simulated Annealing
,”
J. Econometr.
,
60
(
1
), pp.
65
99
.10.1016/0304-4076(94)90038-8
45.
Sparrow
,
W. A.
, and
Newell
,
K. M.
,
1998
, “
Metabolic Energy and the Regulation of Movement Economy
,”
Psychon. Bull. Rev.
,
5
(
2
), pp.
173
196
.10.3758/BF03212943
46.
Hamill
,
J.
,
Russell
,
E. M.
,
Gruber
,
A. H.
,
Miller
,
R. H.
, and
O'Connor
,
K. M.
,
2009
, “
Extrinsic Foot Muscle Forces When Running in Varus, Valgus and Neutral Wedged Shoes
,”
Footwear Sci.
,
1
(
3
), pp.
153
161
.10.1080/19424280903535462
47.
Winby
,
C. R.
,
Lloyd
,
D. G.
,
Besier
,
T. F.
, and
Kirk
,
T. B.
,
2009
, “
Muscle and External Load Contribution to Knee Joint Contact Loads During Normal Gait
,”
J. Biomech.
,
42
(
14
), pp.
2294
2300
.10.1016/j.jbiomech.2009.06.019
48.
Cohen
,
J.
,
1988
,
Statistical Power Analysis for the Behavioral Sciences
,
Rutledge
,
New York
.
49.
Morrison
,
J. B.
,
1970
, “
The Mechanics of the Knee Joint in Relation to Normal Walking
,”
J. Biomech.
,
3
(
1
), pp.
51
61
.10.1016/0021-9290(70)90050-3
50.
Schipplein
,
O. D.
, and
Andriacchi
,
T. P.
,
1991
, “
Interaction Between Active and Passive Knee Stabilizers During Level Walking
,”
J. Orthop. Res.
,
9
(
1
), pp.
113
119
.10.1002/jor.1100090114
51.
Taylor
,
W. R.
,
Heller
,
M. O.
,
Bermann
,
G.
, and
Duda
,
G. N.
,
2004
, “
Tibio-Femoral Loading During Human Gait and Stair Climbing
,”
J. Orthop. Res.
,
22
(
3
), pp.
625
632
.10.1016/j.orthres.2003.09.003
52.
Shelburne
,
K. B.
,
Torry
,
M. R.
, and
Pandy
,
M. G.
,
2006
, “
Contributions of Muscles, Ligaments, and the Ground-Reaction Force to Tibiofemoral Joint Loading During Normal Gait
,”
J. Orthop. Res.
,
24
(
10
), pp.
1983
1990
.10.1002/jor.20255
53.
Richards
,
C.
, and
Higginson
,
J. S.
,
2010
, “
Knee Contact Force in Subjects With Symmetrical OA Grades: Differences Between OA Severities
,”
J. Biomech.
,
43
(
13
), pp.
2595
2600
.10.1016/j.jbiomech.2010.05.006
54.
Sasaki
,
K.
, and
Neptune
,
R. R.
,
2010
, “
Individual Muscle Contributions to the Axial Knee Joint Contact Force During Normal Walking
,”
J. Biomech.
,
43
(
14
), pp.
2780
2784
.10.1016/j.jbiomech.2010.06.011
55.
Kumar
,
D.
,
Rudolph
,
K. S.
, and
Manal
,
K. T.
,
2012
, “
EMG-Driven Modeling Approach to Muscle Force and Joint Load Estimations: Case Study in Knee Osteoarthritis
,”
J. Orthop. Res.
,
30
(
3
), pp.
377
383
.10.1002/jor.21544
56.
Ackermann
,
M.
, and
van den Bogert
,
A. J.
,
2010
, “
Optimality Principles for Model-Based Prediction of Human Gait
,”
J. Biomech.
,
43
(
6
), pp.
1055
1060
.10.1016/j.jbiomech.2009.12.012
57.
Camilleri
,
M. J.
,
Hull
,
M. L.
, and
Hakansson
,
N.
,
2007
, “
Sloped Excitation Waveforms Improve the Accuracy of Forward Dynamic Simulations
,”
J. Biomech.
,
40
(
7
), pp.
1423
1432
.10.1016/j.jbiomech.2006.06.009
58.
Fregly
,
B. J.
,
Reinbolt
,
J. A.
,
Rooney
,
K. L.
,
Mitchell
,
K. H.
, and
Chmielewski
,
T. L.
,
2007
, “
Design of Patient-Specific Gait Modifications for Knee Osteoarthritis Rehabilitation
,”
IEEE Trans. Biomed. Eng.
,
54
(
9
), pp.
1687
1695
.10.1109/TBME.2007.891934
59.
Walter
,
J. P.
,
D'Lima
,
D. D.
,
Colwell
,
C. W.
, and
Fregly
,
B. J.
,
2010
, “
Decreased Knee Adduction Moment Does Not Guarantee Decreased Medial Contact Force During Gait
,”
J. Orthop. Res.
,
28
(
10
), pp.
1348
1354
.10.1002/jor.21142
60.
Felson
,
D. T.
,
Anderson
,
J. J.
,
Naimark
,
A.
,
Walker
,
A. M.
, and
Meenan
,
R. F.
,
1988
, “
Obesity and Knee Osteoarthritis: The Framingham Study
,”
Ann. Intern. Med.
,
109
(
1
), pp.
18
24
.
61.
Zhang
,
Y.
, and
Jordan
,
A. M.
,
2010
, “
Epidemiology of Osteoarthritis
,”
Clin. Geriatr. Med.
,
26
(
3
), pp.
355
369
.10.1016/j.cger.2010.03.001
62.
Messier
,
S. P.
,
Gutekunst
,
D. J.
,
Davis
,
C.
, and
DeVita
,
P.
,
2005
, “
Weight Loss Reduces Knee-Joint Loads in Overweight and Obese Older Adults With Knee Osteoarthritis
,”
Arthritis Rheum.
,
52
(
7
), pp.
2026
2032
.10.1002/art.21139
63.
Messier
,
S. P.
,
Legault
,
C.
,
Loeser
,
R. F.
,
Van Arsdale
,
S. J.
,
Davis
,
C.
,
Ettinger
,
W. H.
, and
DeVita
,
P.
,
2011
, “
Does High Weight Loss in Older Adults With Knee Osteoarthritis Affect Bone-On-Bone Joint Loads and Muscle Forces During Walking?
,”
Osteoarthritis Cartilage
,
19
(
3
), pp.
272
280
.10.1016/j.joca.2010.11.010
64.
Bliddal
,
H.
,
Leeds
,
A. R.
,
Stigsgaard
,
L.
,
Astrup
,
A.
, and
Christensen
,
R.
,
2011
, “
Weight Loss as Treatment for Knee Osteoarthritis Symptoms in Obese Patients: 1-Year Results From a Randomized Controlled Trial
,”
Ann. Rheum. Dis.
,
70
(
10
), pp.
1798
1803
.10.1136/ard.2010.142018
65.
Christensen
,
R.
,
Astrup
,
A.
, and
Bliddal
,
H.
,
2005
, “
Weight Loss: The Treatment of Choice for Knee Osteoarthritis? A Randomized Trial
,”
Osteoarthritis Cartilage
,
13
(
1
), pp.
20
27
.10.1016/j.joca.2004.10.008
66.
Gök
,
H.
,
Ergin
,
S.
, and
Yavuzer
,
G.
,
2002
, “
Kinetic and Kinematic Characteristics of Gait in Patients With Medial Knee Arthrosis
,”
Acta Orthop. Scand.
,
73
(
6
), pp.
647
652
.10.1080/00016470308540855
67.
Deluzio
,
K. J.
, and
Astephen
,
J. L.
,
2007
, “
Biomechanical Features of Gait Waveform Data Associated With Knee Osteoarthritis: An Application of Principal Component Analysis
,”
Gait and Posture
,
25
(
1
), pp.
86
93
.10.1016/j.gaitpost.2006.01.007
68.
Zeni
,
J. A.
, and
Higginson
,
J. S.
,
2011
, “
Knee Osteoarthritis Affects the Distribution of Joint Moments During Gait
,”
Knee
,
18
(
3
), pp.
156
159
.10.1016/j.knee.2010.04.003
69.
Kaufman
,
K. R.
,
Hughes
,
C.
,
Morrey
,
B. F.
,
Morrey
,
M.
, and
An
,
K. N.
,
2001
, “
Gait Characteristics of Patients With Knee Osteoarthritis
,”
J. Biomech.
,
34
(
7
), pp.
907
915
.10.1016/S0021-9290(01)00036-7
70.
Baliunas
,
A. J.
,
Hurwitz
,
D. E.
,
Ryals
,
A. B.
,
Karrar
,
A.
,
Case
,
J. P.
,
Block
,
J. A.
, and
Andriacchi
,
T. P.
,
2002
, “
Increased Knee Joint Loads During Walking are Present in Subjects With Knee Osteoarthritis
,”
Osteoarthritis Cartilage
,
10
(
7
), pp.
573
579
.10.1053/joca.2002.0797
71.
Childs
,
J. D.
,
Sparto
,
P. J.
,
Fitzgerald
,
G. K.
,
Bizzini
,
M.
, and
Irrgang
,
J. J.
,
2004
, “
Alterations in Lower Extremity Movement and Muscle Activation Patterns in Individuals With Knee Osteoarthritis
,”
Clin. Biomech. (Bristol, Avon)
,
19
(
1
), pp.
44
49
.10.1016/j.clinbiomech.2003.08.007
72.
Gregor
,
R. J.
,
Komi
,
P. V.
,
Browning
,
R. C.
, and
Järvinen
,
M.
,
1991
, “
A Comparison of the Triceps Surae and Residual Muscle Moments at the Ankle During Cycling
,”
J. Biomech.
,
24
(
5
), pp.
287
297
.10.1016/0021-9290(91)90347-P
73.
Hof
,
A. L.
,
1997
, “
The Relationship Between Electromyogram and Muscle Force
,”
Sportverletz. Sportschaden
,
11
(
3
), pp.
79
86
.10.1055/s-2007-993372
74.
Ritchie
,
J. M.
, and
Wilkie
,
D. R.
,
1958
, “
The Dynamics of Muscular Contraction
,”
J. Physiol.
,
143
(
1
), pp.
104
113
.
75.
Chleboun
,
G. S.
,
Busic
,
A. B.
,
Graham
,
K. K.
, and
Stuckey
,
H. A.
,
2007
, “
Fascicle Length Change of the Human Tibialis Anterior and Vastus Lateralis During Walking
,”
J. Orthop. Sports Phys. Ther.
,
37
(
7
), pp.
372
379
.10.2519/jospt.2007.2440
76.
Zarrugh
,
M. Y.
, and
Radcliffe
,
C. W.
,
1978
, “
Predicting Metabolic Cost of Level Walking
,”
Eur. J. Appl. Physiol.
,
38
(
3
), pp.
215
223
.10.1007/BF00430080
77.
Martin
,
P. E.
, and
Marsh
,
A. P.
,
1992
, “
Step Length and Frequency Effects on Ground Reaction Forces During Walking
,”
J. Biomech.
,
25
(
10
), pp.
1237
1239
.10.1016/0021-9290(92)90081-B
78.
Holt
,
K. J.
,
Jeng
,
S. F.
,
Rr
,
R. R.
, and
Hamill
,
J.
,
1995
, “
Energetic Cost and Stability During Human Walking at the Preferred Stride Velocity
,”
J. Motor Behav.
,
27
(
2
), pp.
164
178
.10.1080/00222895.1995.9941708
79.
Bertram
,
J. E. A.
,
2005
, “
Constrained Optimization in Human Walking: Cost Minimization and Gait Plasticity
,”
J. Exp. Biol.
,
208
(
6
), pp.
979
991
.10.1242/jeb.01498
80.
Russell
,
E. M.
,
Braun
,
B.
, and
Hamill
,
J.
,
2010
, “
Does Stride Length Influence Metabolic Cost and Biomechanical Risk Factors for Knee Osteoarthritis in Obese Women?
,”
Clin. Biomech.(Bristol, Avon)
,
25
(
5
), pp.
438
443
.10.1016/j.clinbiomech.2010.01.016
81.
Edwards
,
W. B.
,
Taylor
,
D.
,
Rudolphi
,
T. J.
,
Gillette
,
J. C.
, and
Derrick
,
T. R.
,
2009
, “
Effects of Stride Length and Running Mileage on a Probabilistic Stress Fracture Model
,”
Med. Sci. Sports Exercise
,
41
(
12
), pp.
2177
2184
.10.1249/MSS.0b013e3181a984c4
82.
Chow
,
C. K.
, and
Jacobson
,
D. H.
,
1971
, “
Studies of Human Locomotion via Optimal Programming
,”
Math. Biosci.
,
10
(
3–4
), pp.
239
306
.10.1016/0025-5564(71)90062-9
83.
Simic
,
M.
,
Hinman
,
R. S.
,
Wrigley
,
T. V.
,
Bennell
,
K. L.
, and
Hunt
,
M. A.
,
2011
, “
Gait Modification Strategies for Altering Medial Knee Joint Load: A Systematic Review
,”
Arthritis Care Res.
,
63
(
3
), pp.
405
426
.10.1002/acr.20380
84.
Van den Bogert
,
A. J.
,
Blana
,
D.
,
Heinrich
,
D.
,
2011
, “
Implicit Methods for Efficient Musculoskeletal Simulation and Optimal Control
,”
Procedia IUTAM
,
2
, pp.
297
316
.10.1016/j.piutam.2011.04.027
85.
Young
,
A.
,
Getty
,
J.
,
Jackson
,
A.
,
Kirwan
,
E.
,
Sullivan
,
M.
, and
Parry
,
C. W.
,
1983
, “
Variations in the Pattern of Muscle Innervation by the L5 and S1 Nerve Toots
,”
Spine
,
8
(
6
), pp.
616
624
.10.1097/00007632-198309000-00007
You do not currently have access to this content.