A three-dimensional, dynamic model of the tibiofemoral and patellofemoral articulations was developed to predict the motions of knee implants during a step-up activity. Patterns of muscle activity, initial joint angles and velocities, and kinematics of the hip and ankle were measured experimentally and used as inputs to the simulation. Prosthetic knee kinematics were determined by integration of dynamic equations of motion subject to forces generated by muscles, ligaments, and contact at both the tibiofemoral and patellofemoral articulations. The modeling of contacts between implants did not rely upon explicit constraint equations; thus, changes in the number of contact points were allowed without modification to the model formulation. The simulation reproduced experimentally measured flexion–extension angle of the knee (within one standard deviation), but translations at the tibiofemoral articulations were larger during the simulated step-up task than those reported for patients with total knee replacements.

1.
Hefzy
,
M. S.
, and
Cooke
,
T. D. V.
,
1996
, “
Review of Knee Models: 1996 Update
,”
Appl. Mech. Rev.
,
49
, pp.
S187–S193
S187–S193
.
2.
Hefzy
,
M. S.
, and
Grood
,
E. S.
,
1988
, “
Review of Knee Models
,”
Appl. Mech. Rev.
,
41
, pp.
1
13
.
3.
Wismans
,
J.
,
Veldpaus
,
F.
,
Janssen
,
J.
,
Huson
,
A.
, and
Struben
,
P.
,
1980
, “
A Three-Dimensional Mathematical Model of the Knee-Joint
,”
J. Biomech.
,
13
, pp.
677
685
.
4.
Yamaguchi
,
G. T.
, and
Zajac
,
F. E.
,
1989
, “
A Planar Model of the Knee Joint to Characterize the Knee Extensor Mechanism
,”
J. Biomech.
,
22
, pp.
1
10
.
5.
Piazza
,
S. J.
, and
Delp
,
S. L.
,
1996
, “
The Influence of Muscles on Knee Flexion During the Swing Phase of Gait
,”
J. Biomech.
,
29
, pp.
723
733
.
6.
Moeinzadeh
,
M. H.
,
Engin
,
A. E.
, and
Akkas
,
N.
,
1983
, “
Two-Dimensional Dynamic Modelling of Human Knee Joint
,”
J. Biomech.
,
16
, pp.
253
264
.
7.
Engin
,
A. E.
, and
Tu¨mer
,
S. T.
,
1993
, “
Improved Dynamic Model of the Human Knee Joint and Its Response to Impact Loading on the Lower Leg
,”
ASME J. Biomech. Eng.
,
115
, pp.
137
143
.
8.
Tu¨mer
,
S. T.
, and
Engin
,
A. E.
,
1993
, “
Three-Body Segment Dynamic Model of the Human Knee
,”
ASME J. Biomech. Eng.
,
115
, pp.
350
356
.
9.
Wongchaisuwat
,
C.
,
Hemami
,
H.
, and
Buchner
,
H. J.
,
1984
, “
Control of Sliding and Rolling at Natural Joints
,”
ASME J. Biomech. Eng.
,
106
, pp.
368
375
.
10.
Abdel-Rahman
,
E.
, and
Hefzy
,
M. S.
,
1993
, “
A Two-Dimensional Dynamic Anatomical Model of the Human Knee Joint
,”
ASME J. Biomech. Eng.
,
115
, pp.
357
365
.
11.
Abdel-Rahman
,
E. M.
, and
Hefzy
,
M. S.
,
1998
, “
Three-Dimensional Dynamic Behaviour of the Human Knee Joint Under Impact Loading
,”
Med. Eng. Phys.
,
20
, pp.
276
290
.
12.
Kim
,
S.
, and
Pandy
,
M. G.
,
1993
, “
A Two-Dimensional Dynamic Model of the Human Knee Joint
,”
Biomed. Sci. Instrum.
,
29
, pp.
33
46
.
13.
Tu¨mer
,
S. T.
,
Wang
,
X.
, and
Akkas
,
N.
,
1995
, “
A Planar Dynamic Anatomical Model of the Human Lower Limb
,”
Biomed. Eng.—Applications, Basis & Communications
,
7
, pp.
365
378
.
14.
Mirtich, B., and Canny, J., 1995, “Impulse-Based Simulation of Rigid Bodies,” Proc. 1995 Symposium on Interactive 3D Graphics, pp. 181–188.
15.
Banks
,
S. A.
,
Markovich
,
G. D.
, and
Hodge
,
W. A.
,
1997
, “
In Vivo Kinematics of Cruciate-Retaining and -Substituting Knee Arthroplasties
,”
J. Arthroplasty
,
12
, pp.
297
304
.
16.
Yamaguchi, G. T., 1989, “Feasibility and Conceptual Design of Functional Neuromuscular Stimulation Systems for the Restoration of Natural Gait to Paraplegics Based on Dynamic Musculoskeletal Models,” Ph.D. Dissertation, Stanford University, Stanford, CA.
17.
Rosenthal
,
D. E.
, and
Sherman
,
M. A.
,
1986
, “
High Performance Multibody Simulations via Symbolic Equation Manipulation and Kane’s Method
,”
J. Astronaut. Sci.
,
34
, pp.
223
239
.
18.
Zajac
,
F. E.
,
1989
, “
Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control
,”
Crit. Rev. Biomed. Eng.
,
17
, pp.
359
411
.
19.
Delp
,
S. L.
,
Loan
,
J. P.
,
Hoy
,
M. G.
,
Zajac
,
F. E.
,
Topp
,
E. L.
, and
Rosen
,
J. M.
,
1990
, “
An Interactive Graphics-Based Model of the Lower Extremity to Study Orthopaedic Surgical Procedures
,”
IEEE Trans. Biomed. Eng.
,
37
, pp.
757
767
.
20.
Schutte
,
L. M.
,
Rodgers
,
M. M.
,
Zajac
,
F. E.
, and
Glaser
,
R. M.
,
1993
, “
Improving the Efficacy of Electrical Stimulation-Induced Leg Cycle Ergometry: An Analysis Based on a Dynamic Musculoskeletal Model
,”
IEEE Trans. Rehabil. Eng.
,
1
, pp.
109
125
.
21.
Delp
,
S. L.
, and
Loan
,
J. P.
,
1995
, “
A Graphics-Based Software System to Develop and Analyze Models of Musculoskeletal Structures
,”
Comput. Biol. Med.
,
25
, pp.
21
34
.
22.
Mommersteeg
,
T. J.
,
Blankevoort
,
L.
,
Huiskes
,
R.
,
Kooloos
,
J. G.
, and
Krauer
,
J. M.
,
1996
, “
Characterization of the Mechanical Behavior of Human Knee Ligaments: A Numerical–Experimental Approach
,”
J. Biomech.
,
29
, pp.
151
160
.
23.
Piazza
,
S. J.
,
Delp
,
S. L.
,
Stulberg
,
S. D.
, and
Stern
,
S. H.
,
1998
, “
Anterior Placement of the Femoral Component in Total Knee Replacement Produces Collateral Ligament Laxity
,”
Trans. 44th Annu. Meet. — Orthop. Res. Soc.
, p.
1028
1028
.
24.
Brantigan
,
O. C.
, and
Voshell
,
A. F.
,
1941
, “
The Mechanics of the Ligaments and Menisci of the Knee Joint
,”
J. Bone Jt. Surg., Am. Vol.
,
23
, pp.
44
66
.
25.
Trent
,
P. S.
,
Walker
,
P. S.
, and
Wolf
,
B.
,
1976
, “
Ligament Length Patterns, Strength, and Rotational Axes of the Knee Joint
,”
Clin. Orthop. Relat. Res.
,
117
,
263
70
.
26.
Haut
,
R. C.
, and
Powlison
,
A. C.
,
1990
, “
The Effects of Test Environment and Cyclic Stretching on the Failure Properties of Human Patellar Tendons
,”
J. Orthop. Res.
,
8
, pp.
532
540
.
27.
Harris
,
N. L.
,
Smith
,
D. A.
,
Lamoreaux
,
L.
, and
Purnell
,
M.
,
1997
, “
Central Quadriceps Tendon for Anterior Cruciate Ligament Reconstruction. Part I: Morphometric and Biomechanical Evaluation
,”
Am. J. Sports Med.
,
25
, pp.
23
28
.
28.
Bechtold
,
J. E.
,
Eastlund
,
D. T.
,
Butts
,
M. K.
,
Lagerborg
,
D. F.
, and
Kyle
,
R. F.
,
1994
, “
The Effects of Freeze-Drying and Ethylene Oxide Sterilization on the Mechanical Properties of Human Patellar Tendon
,”
Am. J. Sports Med.
,
22
, pp.
562
566
.
29.
Gottschalk, S., Lin, M. C., and Manocha, D., 1996, “OBBTree: A Hierarchical Structure for Rapid Interference Detection,” Proc. ACM SIGGRAPH Conference on Computer Graphics, pp. 171–180.
30.
Lo¨tstedt
,
P.
,
1982
, “
Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints
,”
SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
,
42
, pp.
281
296
.
31.
Cottle, R. W., and Dantzig, G. B., 1968, “Complementary Pivot Theory of Mathematical Programming,” Linear Algebra and Its Applications, Vol. 1, pp. 103–125.
32.
Baraff, D., 1994, “Fast Contact Force Computation for Nonpenetrating Rigid Bodies,” Proc. ACM SIGGRAPH Conference on Computer Graphics, pp. 23–34.
33.
Beer, F. P., and Johnston, E. R., 1988, Vector Mechanics for Engineers: Statics and Dynamics, McGraw-Hill, New York.
34.
Baraff, D., 1989, “Analytical Methods for Dynamic Simulation of Non-penetrating Rigid Bodies,” Trans. ACM Siggraph, pp. 223–232.
35.
Piazza, S. J., 1998, “Simulation-Based Design of Total Knee Replacements,” Ph.D. Dissertation, Northwestern University, Evanston, IL.
36.
Banks
,
S. A.
,
Backus
,
S. I.
,
Otis
,
J. C.
,
Haas
,
S. B.
, and
Laskin
,
R. S.
,
2000
, “
Motions and Forces in Total Knee Replacements During Stair Rise
,”
Trans. 46th Annu. Meet. — Orthop. Res. Soc.
, p.
431
431
.
37.
Taylor
,
S. J.
,
Walker
,
P. S.
,
Perry
,
J. S.
,
Cannon
,
S. R.
, and
Woledge
,
R.
,
1998
, “
The Forces in the Distal Femur and the Knee During Walking and Other Activities Measured by Telemetry
,”
J. Arthroplasty
,
13
, pp.
428
437
.
38.
Sathasivam
,
S.
, and
Walker
,
P. S.
,
1997
, “
A Computer Model With Surface Friction for the Prediction of Total Knee Kinematics
,”
J. Biomech.
,
30
, pp.
177
184
.
39.
Mochon
,
S.
, and
McMahon
,
T. A.
,
1980
, “
Ballistic Walking: An Improved Model
,”
Math. Biosci.
,
52
, pp.
241
260
.
40.
Yamaguchi
,
G. T.
, and
Zajac
,
F. E.
,
1990
, “
Restoring Unassisted Natural Gait to Paraplegics via Functional Neuromuscular Stimulation: A Computer Simulation Study
,”
IEEE Trans. Biomed. Eng.
,
37
, pp.
886
902
.
41.
Stauffer
,
R. N.
,
Chao
,
E. Y.
, and
Brewster
,
R. C.
,
1977
, “
Force and Motion Analysis of the Normal, Diseased, and Prosthetic Ankle Joint
,”
Clin. Orthop. Relat. Res.
,
127
, pp.
189
196
.
42.
Cottle
,
R. W.
,
1968
, “
On a Problem in Linear Equalities
,”
J. London Math. Soc.
,
43
, pp.
378
384
.
43.
Neptune
,
R. R.
, and
Hull
,
M. L.
,
1998
, “
Evaluation of Performance Criteria for Simulation of Submaximal Steady-State Cycling Using a Forward Dynamic Model
,”
ASME J. Biomech. Eng.
,
120
, pp.
334
341
.
44.
Winter, D. A., 1979, Biomechanics of Human Movement, Wiley, New York.
45.
Huberti
,
H. H.
,
Hayes
,
W. C.
,
Stone
,
J. L.
, and
Shybut
,
G. T.
,
1984
, “
Force Ratios in the Quadriceps Tendon and Ligamentum Patellae
,”
J. Orthop. Res.
,
2
, pp.
49
54
.
46.
Miller
,
R. K.
,
Murray
,
D. W.
,
Gill
,
H. S.
,
O’Connor
,
J. J.
, and
Goodfellow
,
J. W.
,
1997
, “
In Vitro Patellofemoral Joint Force Determined by a Non-Invasive Technique
,”
Clin. Biomech.
,
12
, pp.
1
7
.
47.
Nisell
,
R.
,
1985
, “
Mechanics of the Knee. A Study of Joint and Muscle Load With Clinical Applications
,”
Acta Orthop. Scand. Suppl.
,
216
, pp.
1
42
.
You do not currently have access to this content.