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TECHNICAL PAPERS: Soft Tissue

# Stresses and Strains in the Medial Meniscus of an ACL Deficient Knee under Anterior Loading: A Finite Element Analysis with Image-Based Experimental Validation

[+] Author and Article Information
Jiang Yao

Department of Mechanical Engineering,  University of Rochester, Rochester, New York 14627

Jason Snibbe

Beverly Hills Orthopedic Group, Beverly Hills, California

Michael Maloney

Department of Orthopaedics,  University of Rochester Medical Center, Rochester, New York 14627

Amy L. Lerner1

Department of Biomedical Engineering,  University of Rochester, Rochester, New York 14627

1

Corresponding author; Tel: 585-275-7847; Fax: 585-276-1999; e-mail: amy.lerner@rochester.edu.

J Biomech Eng 128(1), 135-141 (Sep 14, 2005) (7 pages) doi:10.1115/1.2132373 History: Received February 11, 2005; Revised September 14, 2005

## Abstract

The menisci are believed to play a stabilizing role in the ACL-deficient knee, and are known to be at risk for degradation in the chronically unstable knee. Much of our understanding of this behavior is based on ex vivo experiments or clinical studies in which we must infer the function of the menisci from external measures of knee motion. More recently, studies using magnetic resonance (MR) imaging have provided more clear visualization of the motion and deformation of the menisci within the tibio-femoral articulation. In this study, we used such images to generate a finite element model of the medial compartment of an ACL-deficient knee to reproduce the meniscal position under anterior loads of 45, 76, and $107N$. Comparisons of the model predictions to boundaries digitized from images acquired in the loaded states demonstrated general agreement, with errors localized to the anterior and posterior regions of the meniscus, areas in which large shear stresses were present. Our model results suggest that further attention is needed to characterize material properties of the peripheral and horn attachments. Although overall translation of the meniscus was predicted well, the changes in curvature and distortion of the meniscus in the posterior region were not captured by the model, suggesting the need for refinement of meniscal tissue properties.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

MR compatible device to apply anterior loads to cadaveric knee during imaging. The femur and tibia bones were potted in PVC pipes which were mounted in the femoral and tibial holding device. The flexion angle can be adjusted by sliding the femoral holding device along the grooves in the side plates. Because the knee was positioned in prone position in the device, a counterweight was applied to balance the weight of the tibia. Anterior load was applied by pulling the tibial holding device downwards via two Teflon bushings sliding on the brass rods on both sides of the tibial holding device.

Figure 2

Finite element model of femur∕tibia cartilage, medial meniscus and its attachments. (a) Top lateral view. (b) Top medial view without femur cartilage. The meniscal peripheral attachments were modeled as spring elements connecting the inferior peripheral edges of the meniscus and the tibia cartilage. (L=lateral, A=anterior, S=superior.)

Figure 3

(Left) Overlay of the medial meniscus digitization at initial unloaded position (cyan) and at anterior loaded positions (red), i.e. 45N (a), 76N (c), and 107N (e). (Right) Overlay of the medial meniscus digitization (red) and finite element model prediction (blue) at 45N (b), 76N (d), 107N (f). The volume errors were 13.3%, 18.5%, and 14.6% at these three loaded positions. (M=medial, L=lateral, A=anterior, P=posterior, I=inferior, S=superior, unit=mm.)

Figure 4

The minimum curvature contour plot for the posterior one third of the meniscal inferior surface from smoothed digitization (a,c,e) and FE model prediction (b,d,f) at 45N(a–b), 76N(c–d), and 107N(e–f). Negative (blue) regions indicate concave curvature of the meniscal surface as it wraps over the tibial surface. (M=medial, L=lateral, A=anterior, P=posterior, I=inferior, S=superior.)

Figure 5

Comparison of the meniscal position predicted from FE model (blue solid line) to those digitized from MRI (red dashed line) at 45N (a), 76N (b), and 107N (c). Images indicated that the meniscus both translated posteriorly relative to the tibia, and wrapped over the posterior tibial boundary. Although translation was reasonably predicted, the distortion was not as dramatic in the FE model prediction. Note: images were digitally retouched for clarity to remove an air bubble present in the joint space.

Figure 6

(a) Inferior view of the hydrostatic pressure contour of the medial meniscus under anterior load of 107N. (b) Hydrostatic pressure contour plot within sagittal plane passing through the most curved point on the meniscal inferior surface, as indicated by the line on the left figure.

Figure 7

(a) Top view of the total strain energy density (strain energy per unit volume) contour of the medial meniscus under anterior load of 107N. (b) Total strain energy density contour plot within sagittal plane passing through the most curved point on the meniscal inferior surface, as indicated by the line on the left figure.

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