A detailed 3D anatomical model of the patellofemoral joint was developed to study the tracking, force, contact and stability characteristics of the joint. The quadriceps was considered to include six components represented by 15 force vectors. The patellar tendon was modeled using four bundles of viscoelastic tensile elements. Each of the lateral and medial retinaculum was modeled by a three-bundle nonlinear spring. The femur and patella were considered as rigid bodies with their articular cartilage layers represented by an isotropic viscoelastic material. The geometrical and tracking data needed for model simulation, as well as validation of its results, were obtained from an in vivo experiment, involving MR imaging of a normal knee while performing isometric leg press against a constant 140 N force. The model was formulated within the framework of a rigid body spring model and solved using forth-order Runge-Kutta, for knee flexion angles between zero and 50 degrees. Results indicated a good agreement between the model predictions for patellar tracking and the experimental results with RMS deviations of about 2 mm for translations (less than 0.7 mm for patellar mediolateral shift), and 4 degrees for rotations (less than 3 degrees for patellar tilt). The contact pattern predicted by the model was also consistent with the results of the experiment and the literature. The joint contact force increased linearly with progressive knee flexion from 80 N to 210 N. The medial retinaculum experienced a peak force of 18 N at full extension that decreased with knee flexion and disappeared entirely at 20 degrees flexion. Analysis of the patellar time response to the quadriceps contraction suggested that the muscle activation most affected the patellar shift and tilt. These results are consistent with the recent observations in the literature concerning the significance of retinaculum and quadriceps in the patellar stability.

References

References
1.
Fulkerson
,
J. P.
, 2002, “
Diagnosis and Treatment of Patients with Patellofemoral Pain
,”
The American Journal of Sports Medicine
,
30
(
3
), pp.
447
456
.
2.
Essinger
,
J. R.
,
Leyvraz
,
P. F.
,
Heegard
,
J. H.
, and
Robertson
,
D. D.
, 1989, “
A Mathematical Model for the Evaluation of the Behaviour During Flexion of Condylar-type Knee Prostheses
,”
J. Biomech.
,
22
(
11-12
), pp.
1229
1241
.
3.
Hefzy
,
M. S.
, and
Yang
,
H.
, 1993, “
A Three-dimensional Anatomical Model of the Human Patello-Femoral Joint, for the Determination of Patello-femoral Motions and Contact Characteristics
,”
J. Biomed. Eng.
,
15
(
4
), pp.
289
302
.
4.
Hirokawa
,
S.
, 1991, “
Three-dimensional Mathematical Model Analysis of the Patellofemoral Joint
,”
J. Biomech.
,
24
(
8
), pp.
659
671
.
5.
Hirokawa
,
S.
, 1992, “
Effects of Variation on Extensor Elements and Operative Procedures in Patellofemoral Disorders
,”
J. Biomech.
,
25
(
12
), pp.
1393
1401
.
6.
Amis
,
A. A.
, and
Farahmand
,
F.
, 1996, “
Extensor Mechanism of the Knee
,”
Current Orthopaedics
,
10
(
2
), pp.
102
109
.
7.
Shih
,
Y. F. B. A.
, and
Amis
,
A. A.
, 2004, “
The Cartilaginous and Osseous Geometry of the Femoral Trochlear Groove
,”
Knee Surg. Sports Traumatol. Arthrosc.
,
12
(
4
), pp.
300
306
.
8.
Heegaard
,
J.
,
Leyvraz
,
P. F.
,
Curnier
,
A.
,
Rakotomanana
,
L.
, and
Huiskes
,
R.
, 1995, “
The Biomechanics of the Human Patella During Passive Knee Flexion
,”
J. Biomech.
,
28
(
11
), pp.
1265
1279
.
9.
Elias
,
J. J.
,
Bratton
,
D. R.
,
Weinstein
,
D. M.
, and
Cosgarea
,
A. J.
, 2006, “
Comparing Two Estimations of the Quadriceps Force Distribution for use During Patellofemoral Simulation
,”
J. Biomech.
,
39
(
5
), pp.
865
872
.
10.
Elias
,
J. J.
,
Wilson
,
D. R.
,
Adamson
,
R.
, and
Cosgarea
,
A. J.
, 2004, “
Evaluation of a Computational Model Used to Predict the Patellofemoral Contact Pressure Distribution
,”
J. Biomech.
,
37
(
3
), pp.
295
302
.
11.
Mesfar
,
W.
, and
Shirazi-Adl
,
A.
, 2005, “
Biomechanics of the Knee Joint in Flexion Under Various Quadriceps Forces
,”
The Knee
,
12
(
6
), pp.
424
434
.
12.
Jafari
,
A.
,
Farahmand
,
F.
, and
Meghdari
,
A.
, 2008, “
The Effects of Trochlear Groove Geometry on Patellofemoral Joint Stability -- A Computer Model Study
,”
Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
,
222
(
1
), pp.
75
88
.
13.
Ahmed
,
A. M.
,
Burke
,
D. L.
, and
Yu
,
A.
, 1983, “
In-vitro Measurement of Static Pressure Distribution in Synovial Joints - Part II: Retropatellar Surface
,”
J. Biomech. Eng.
,
105
(
3
), pp.
226
236
.
14.
Ahmed
,
A. M.
,
Shi
,
S.
,
Hyder
,
A.
, and
Chan
,
K. H.
, 1988, “
The Effect of Quadriceps Tension Characteristics on the Patellar Tracking Pattern
,”
Trans. Orthop. Res. Soc.
,
13
, pp.
280
285
.
15.
Farahmand
,
F.
,
Tahmasbi
,
M. N.
, and
Amis
,
A.
, 2004, “
The Contribution of the Medial Retinaculum and Quadriceps Muscles to Patellar Lateral Stability – An In-vitro Study
,”
Knee
,
11
(
2
), pp.
89
94
.
16.
Goh
,
J. C. H.
,
Lee
,
P. Y. C.
, and
Bose
,
K.
, 1995, “
A Cadaver Study of the Function of the Oblique Part of Vastus Medialis
,”
J. Bone Joint Surg. Br.
,
77
(
2
), pp.
225
231
.
17.
Heegaard
,
J.
,
Leyvraz
,
P. F.
,
Van Kampen
,
A.
,
Rakotomanana
,
L.
,
Rubin
,
P. J.
, and
Blankevoort
,
L.
, 1994, “
Influence of Soft Structures on Patellar Three-dimensional Tracking
,”
Clinical Orthop. Relat. Res.
299
, pp.
235
243
.
18.
Hille
,
E.
,
Schulitz
,
K. P.
,
Henrichs
,
C.
, and
Schneider
,
T.
, 1985, “
Pressure and Contact-Surface Measurements within the Femoropatellar Joint and Their Variations Following Lateral Release
,”
Arch. Orthop. Trauma Surg.
,
104
(
5
), pp.
275
282
.
19.
Philippot
,
R.
,
Boyer
,
B.
,
Testa
,
R.
,
Farizon
,
F.
, and
Moyen
,
B.
, 2011, “
The Role of the Medial Ligamentous Structures on Patellar Tracking During Knee Flexion
,”
Knee Surg. Sports Traumatol. Arthrosc.
,
20
(
2
), pp.
331
336
.
20.
Senavongse
,
W.
, and
Amis
,
A. A.
, 2005, “
The Effects of Articular, Retinacular, or Muscular Deficiencies on Patellofemoral Joint Stabilitiy
,”
J. Bone Joint Surg. Br.
,
87
(
4
), pp.
577
582
.
21.
Tahmasbi
,
M. N.
, ,
Farahmand.
F.
,
Amis
,
A. A.
, 1999, “
A Biomechanical Study of Lateral Release and Elmslie-Trillat Procedures to Restabilise the Maltracking Patella
,”
Acta Medica Iranica
,
37
, pp.
227
231
.
22.
Harvinder Bedi
,
J. M.
, 2010, “
The Biomechanics of Medial Patellofemoral Ligament Repair Followed by Lateral Retinacular Release
,”
Am. J. Sports Med.
,
38
(
7
), pp.
1462
1467
.
23.
Powers
,
C. M. W. S.
,
Fredericson
,
M.
,
Guillet
,
M.
,
Shellock
,
F. G.
, 2003, “
Patellofemoral Kinematics During Weight-bearing and Non-weight-bearing Knee Extension in Persons with Lateral Subluxation of the Patella: A Preliminary Study
,”
J. Orthop. Sports Phys. Ther.
,
33
(
11
), pp.
677
685
.
24.
Caruntu
,
D. I.
, and
Hefzy
,
M. S.
, 2004, “
3-D Anatomically Based Dynamic Modeling of the Human Knee to Include Tibio-femoral and Patello-femoral Joints
,”
J. Biomech. Eng.
,
126
(
1
), pp.
44
53
.
25.
Kwak
,
S. D.
,
Blankevoort
,
L.
,
Ahmad
,
C. S.
,
Gardner
,
T. R.
,
Grelsamer
,
R. P.
,
Henry
,
J. H.
,
Ateshian
,
G. A.
, and
Mow
,
V. C.
, 1995, “
An Anatomically Based 3-D Coordinate System for the Knee Joint
,”
Adv. Bioeng.
BED-31
, pp.
309
310
.
26.
Modersitzki
,
J.
,
Numerical Methods for Image Registration
(
Oxford University
,
New York
, 2004).
27.
Guoan
,
L.
,
Sakamoto
,
M.
, and
Chao
,
E. Y. S.
, 1997, “
A Comparison of Different Methods in Predicting Static Pressure Distribution in Articulating Joints
,”
J. Biomech.
,
30
(
6
), pp.
635
638
.
28.
Blankevoort
,
L.
,
Kuiper
,
J. H.
,
Huiskes
,
R.
, and
Grootenboer
,
H. J.
, 1991, “
Articular Contact in a Three-dimensional Model of the Knee
,”
J. Biomech.
,
24
(
11
), pp.
1019
1031
.
29.
Mow
,
V. C.
,
Lai
,
W. M.
, and
Holmes
,
M. H.
, 1982, “
Advanced Theoretical and Experimental Techniques in Cartilage Research
,”
J. Biomech.
,
15
(
10
), pp.
795
795
.
30.
Blankevoort
,
L.
, and
Huiskes
,
R.
, 1996, “
Validation of a Three-dimensional Model of the Knee
,”
J. Biomech.
,
29
(
7
), pp.
955
961
.
31.
Merican
,
A. M.
,
Sanghavi
,
S.
,
Iranpour
,
F.
, and
Amis
,
A. A.
, 2009, “
The Structural Properties of the Lateral Retinaculum and Capsular Complex of the Knee
,”
J. Biomech.
,
42
(
14
), pp.
2323
2329
.
32.
Kang
,
H. J.
,
Wang
,
F.
,
Chen
,
B. C.
,
Su
,
Y. L.
,
Zhang
,
Z. C.
, and
Yan
,
C. B.
, 2010, “
Functional Bundles of the Medial Patellofemoral Ligament
,”
Knee Surg. Sports Trauma. Arthrosc.
,
18
(
11
), pp.
1511
1516
.
33.
Nomura
,
E.
,
Inoue
,
M.
, and
Osada
,
N.
, 2005, “
Anatomical Analysis of the Medial Patellofemoral Ligament of the Knee, Especially the Femoral Attachment
,”
Knee Surg. Sports Trauma. Arthrosc.
,
13
(
7
), pp.
510
515
.
34.
Farahmand
,
F.
,
Senavongse
,
W.
, and
Amis
,
A. A.
, 1998, “
Quantitative Study of the Quadriceps Muscles and Trochlear Groove Geometry Related to Instability of the Patellofemoral Joint
,”
J. Ortho. Res.
,
16
(
1
), pp.
136
143
.
35.
Senavongse
,
W.
,
Farahmand
,
F.
,
Jones
,
J.
,
Andersen
,
H.
,
Bull
,
A. M. J.
, and
Amis
,
A. A.
, 2003, “
Quantitative Measurement of Patellofemoral Joint Stability: Force-displacement Behavior of the Human Patella in vitro
,”
J. Ortho. Res.
,
21
(
5
), pp.
780
786
.
36.
Kellis
,
E.
, and
Baltzopoulos
,
V.
, 1999, “
in vivo Determination of the Patella Tendon and Hamstrings Moment Arms in Adult Males Using Videofluoroscopy During Submaximal Knee Extension and Flexion
,”
Clin. Biomech.
,
14
(
2
), pp.
118
124
.
37.
Elliott
,
D. M.
,
Narmoneva
,
D. A.
, and
Setton
,
L. A.
, 2002, “
Direct Measurement of the Poisson’s Ratio of Human Patella Cartilage in Tension
,”
J. Biomech. Eng.
,
124
(
2
), pp.
223
228
.
38.
Hewitt
,
J.
,
Guilak
,
F.
,
Glisson
,
R.
, and
Parker Vail
,
T.
, 2001, “
Regional Material Properties of the Human Hip Joint Capsule Ligaments
,”
J. Ortho. Res.
,
19
(
3
), pp.
359
364
.
39.
Woo
,
S. L. Y.
,
Johnson
,
G. A.
, and
Smith
,
B. A.
, 1993, “
Mathematical Modeling of Ligaments and Tendons
,”
J. Biomech. Eng.
,
115
(
4 B
), pp.
468
473
.
40.
Cowin
,
S. C.
, and
Doty
,
Stephen B.
,
Tissue Mechanics
(
Springer
,
New York
, 2007).
41.
Johnson
,
G. A.
,
Tramaglini
,
D. M.
,
Levine
,
R. E.
,
Ohno
,
K.
,
Choi
,
N. Y.
, and
Woo
,
S. L. Y.
, 1994, “
Tensile and Viscoelastic Properties of Human Patellar Tendon
,”
J. Ortho. Res.
,
12
(
6
), pp.
796
803
.
42.
Mow
,
V. C.
,
Ateshian
,
G. A.
, and
Spiiker
,
R. L.
, 1993, “
Biomechanics of Diarthrodial Joints: A Review of Twenty Years of Progress
,”
J. Biomech. Eng.
,
115
(
4 B
), pp.
460
467
.
43.
Amis
,
A. A.
,
Firer
,
P.
,
Mountney
,
J.
,
Senavongse
,
W.
, and
Thomas
,
N. P.
, 2003, “
Anatomy and Biomechanics of the Medial Patellofemoral Ligament
,”
Knee
,
10
(
3
), pp.
215
220
.
44.
Ghosh
,
K. M.
,
Merican
,
A. M.
,
Iranpour-Boroujeni
,
F.
,
Deehan
,
D. J.
, and
Amis
,
A. A.
, 2009, “
Length Change Patterns of the Extensor Retinaculum and the Effect of Total Knee Replacement
,”
J. Ortho. Res.
,
27
(
7
), pp.
865
870
.
45.
Garcia
,
J. J.
, and
Cortes
,
D. H.
, 2006, “
A Nonlinear Biphasic Viscohyperelastic Model for Articular Cartilage
,”
J. Biomech.
,
39
(
16
), pp.
2991
2998
.
46.
Mow
,
V. C.
,
Holmes
,
M. H.
, and
Lai
,
W. M.
, 1984, “
Fluid Transport and Mechanical Properties of Articular Cartilage: A Review
,”
J. Biomech.
,
17
(
5
), pp.
377
394
.
47.
Winter
,
D. A.
,
Biomechanics and Motor Control of Human Movement
(
Wiley
,
New York
, 2009).
48.
Esfandiarpour
,
F.
,
Shakourirad
,
A.
,
Talebian Moghaddam
,
S.
,
Olyaei
,
G. R.
,
Eslami
,
A.
, and
Farahmand
,
F.
, 2011, “
Comparison of Kinematics of Healthy and ACL-Deficient Knees during Passive Flexion and Active Leg Press
,” Knee (to be published).
49.
Koh
,
T. J.
,
Grabiner
,
M. D.
, and
De Swart
,
R. J.
, 1992, “
in vivo Tracking of the Human Patella
,”
J. Biomech.
,
25
(
6
), pp.
637
643
.
50.
Kujala
,
U. M.
,
Osterman
,
K.
,
Kormano
,
M.
,
Komu
,
M.
, and
Schlenzka
,
D.
, 1989, “
Patellar Motion Analyzed by Magnetic Resonance Imaging
,”
Acta Orthop. Scand.
,
60
(
1
), pp.
13
16
.
51.
Sheehan
,
F. T.
,
Zajac
,
F. E.
, and
Drace
,
J. E.
, 1999, “
in vivo Tracking of the Human Patella Using Cine Phase Contrast Magnetic Resonance Imaging
,”
J. Biomech. Eng.
,
121
(
6
), pp.
650
656
.
52.
Tang
,
T. S. Y.
,
MacIntyre
,
N. J.
,
Gill
,
H. S.
,
Fellows
,
R. A.
,
Hill
,
N. A.
,
Wilson
,
D. R.
, and
Ellis
,
R. E.
, 2004, “
Accurate Assessment of Patellar Tracking Using Fiducial and Intensity-Based Fluoroscopic Techniques
,”
Med. Image Anal.
,
8
(
3
), pp.
343
351
.
53.
Eslami
,
A.
,
Esfandiarpour
,
F.
,
Shakourirad
,
A.
, and
Farahmand
,
F
., 2011, “
A Multiscale Phase Field Method for Joint Segmentation-Rigid Registration – Application to Motion Estimation of Human Knee Joint
,”
Biomed. Eng. Appl. Basis Commun.
23
(
6
), pp.
445
456
.
54.
Hehne
,
H. J.
, 1990, “
Biomechanics of the Patellofemoral Joint and its Clinical Relevance
,”
Clin. Ortho. Relat. Res.
,
258
, pp.
73
85
.
55.
Li
,
G.
,
DeFrate
,
L. E.
,
Zayontz
,
S.
,
Park
,
S. E.
, and
Gill
,
T. J.
, 2004, “
The Effect of Tibiofemoral Joint Kinematics on Patellofemoral Contact Pressures Under Simulated Muscle Loads
,”
J. Ortho. Res.
,
22
(
4
), pp.
801
806
.
56.
Buff
,
H.-U.
,
Jones
,
L. C.
, and
Hungerford
,
D. S.
, 1988, “
Experimental Determination of Forces Transmitted through the Patello-femoral Joint
,”
J. Biomech.
,
21
(
1
), pp.
17
23
.
57.
Mountney
,
J.
,
Senavongse
,
W.
,
Amis
,
A. A.
, and
Thomas
,
N. P.
, 2005, “
Tensile Strength of the Medial Patellofemoral Ligament Before and After Repair or Reconstruction
,”
J. Bone Joint Surg. Br
,
87-B
(
1
), pp.
36
40
.
58.
Buckens
,
C. F. M.
, and
Saris
,
D. B. F.
, 2010, “
Reconstruction of the Medial Patellofemoral Ligament for Treatment of Patellofemoral Instability: A Systematic Review
,”
Am. J. Sports Med.
,
38
(
1
), pp.
181
188
.
59.
Fisher
,
B.
,
Nyland
,
J.
,
Brand
,
E.
, and
Curtin
,
B.
, “
Medial Patellofemoral Ligament Reconstruction for Recurrent Patellar Dislocation: A Systematic Review Including Rehabilitation and Return-to-Sports Efficacy
,”
Arthroscopy: J. Relat. Surg.
,
26
(
10
), pp.
1384
1394
.
60.
Farahmand
,
F.
,
Tahmasbi
,
M. N.
, and
Amis
,
A. A.
, 1998, “
Lateral Force-displacement Behaviour of the Human Patella and its Variation with Knee Flexion – A Biomechanical Study in vitro
,”
J. Biomech.
,
31
(
12
), pp.
1147
1152
.
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