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Research Papers

A Detailed and Validated Three Dimensional Dynamic Model of the Patellofemoral Joint

[+] Author and Article Information
Mohammad Akbar

 School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 11155, Iranma_12465@yahoo.com

Farzam Farahmand1

 School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 11155, Iran; RCSTIM, Tehran University of Medical Sciences, Tehran 14185, Iranfarahmand@sharif.edu

Ali Jafari

 RCSTIM, Tehran University of Medical Sciences, Tehran 14185, Iranaliejafari@yahoo.com

Mahmoud Saadat Foumani

 School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 11155, Iranm_saadat@sharif.edu

1

Corresponding author.

J Biomech Eng 134(4), 041005 (Apr 26, 2012) (13 pages) doi:10.1115/1.4006403 History: Received September 07, 2011; Revised March 05, 2012; Posted March 21, 2012; Published April 26, 2012; Online April 26, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 10

The predictions of the quasi static and dynamic analyses of the model for the tensile forces of the medial (MR) and lateral (LR) retinaculum during the simulated leg press activity, with a constant 140 N pressing force

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Figure 11

The patellar dynamic response to the quadriceps muscles contraction, from initial resting position, while the knee flexion angle was kept fixed to zero, 20 and 40 degrees, respectively

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Figure 12

The predictions of the quasi static and dynamic analyses of the model for the ratio of the patellofemoral contact force to the quadriceps force as a function of progressive knee flexion. The experimental results of the literature have been also shown for comparison [14,56].

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Figure 1

The subject’s knee in the MRI compatible testing apparatus, equipped with a pneumatic force transducer to be used during the isometric leg-press experiment

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Figure 2

The MR image data was segmented to obtain the 3D geometries of the cartilaginous layers and the articulating surfaces of the distal femur, proximal tibia and patella, as point clouds

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Figure 3

The local anatomical coordinate systems of femur, tibia and patella

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Figure 4

Landmark registration of the femur, patella and tibia at 40 degrees knee flexion to the reference models of knee full extension

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Figure 5

The 3D model of the patellofemoral joint including the femoral and patellar articulating surfaces and their articular cartilage layers, the medial and lateral retinaculum (MR and LR, respectively), the patellar tendon (PT) and the quadriceps muscles components, i.e., the rectus femoris (RF), the vastus intermedius (VI), the vastus medialis longus (VML) and obliquus (VMO), and the vastus lateralis longus (VLL) and obliquus (VLO)

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Figure 6

(a) The bone and cartilagous surfaces of the patella and femur subjected to virtual penetration at point pi,j. (b) the mechanical model of patellofemoral contact considering pi,j. and Fn,m as the contact points on the patella and femur, respectively

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Figure 7

The tracking results of the patellofemoral joint during the leg press as a function of progressive knee flexion. The predictions of the quasi static and dynamic analysis are compared with the experimental results of the same knee.

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Figure 8

The predictions of the quasi static analysis of the model for the patellofemoral joint contact area and pressure during the simulated leg press activity, with a constant 140 N pressing force. The results are shown at the anterior and posterior views of the femoral and patellar articulating surfaces, respectively, for different knee flexion angles examined. The experimental contact zones, estimated using the MRI data, have been also shown (dash lines) for comparison.

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Figure 9

The predictions of the quasi static and dynamic analyses of the model for the patellofemoral joint contact force during the simulated leg press activity, with a constant 140 N pressing force

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