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TECHNICAL PAPERS: Joint/Whole Body

# Sensitivities of Medial Meniscal Motion and Deformation to Material Properties of Articular Cartilage, Meniscus and Meniscal Attachments Using Design of Experiments Methods

[+] Author and Article Information
Jiang Yao, Paul D. Funkenbusch

Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627

Jason Snibbe

Beverly Hills Orthopedic Group, Beverly Hills, CA

Mike Maloney

Department of Orthopaedics, University of Rochester Medical Center, Rochester, NY 14627

Amy L. Lerner

Department of Biomedical Engineering, University of Rochester, Rochester, NY 14627-0168amy.lerner@rochester.edu

J Biomech Eng 128(3), 399-408 (Dec 27, 2005) (10 pages) doi:10.1115/1.2191077 History: Received June 30, 2005; Revised December 27, 2005

## Abstract

This study investigated the role of the material properties assumed for articular cartilage, meniscus and meniscal attachments on the fit of a finite element model (FEM) to experimental data for meniscal motion and deformation due to an anterior tibial loading of $45N$ in the anterior cruciate ligament-deficient knee. Taguchi style L18 orthogonal arrays were used to identify the most significant factors for further examination. A central composite design was then employed to develop a mathematical model for predicting the fit of the FEM to the experimental data as a function of the material properties and to identify the material property selections that optimize the fit. The cartilage was modeled as isotropic elastic material, the meniscus was modeled as transversely isotropic elastic material, and meniscal horn and the peripheral attachments were modeled as noncompressive and nonlinear in tension spring elements. The ability of the FEM to reproduce the experimentally measured meniscal motion and deformation was most strongly dependent on the initial strain of the meniscal horn attachments $(ε1H)$, the linear modulus of the meniscal peripheral attachments $(EP)$ and the ratio of meniscal moduli in the circumferential and transverse directions $(Eθ∕ER)$. Our study also successfully identified values for these critical material properties ($ε1H=−5%$, $EP=5.6MPa$, $Eθ∕ER=20$) to minimize the error in the FEM analysis of experimental results. This study illustrates the most important material properties for future experimental studies, and suggests that modeling work of meniscus, while retaining transverse isotropy, should also focus on the potential influence of nonlinear properties and inhomogeneity.

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## Figures

Figure 1

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 2

Schematics comparing how volume error (a), volume error due to deformation (b), and volume error due to translation (c) were established. Circle represents the MR digitization of the meniscus, square represents the FE prediction of the meniscus.

Figure 3

Contour plots of volume error (predicted by CCD model) with respect to: (a) ratio of meniscal moduli in the circumferential and transverse directions (Eθ∕ER) and initial strain of meniscal horn attachments (ε1H), (b) Eθ∕ER and linear modulus of meniscal peripheral attachments (EP).

Figure 4

The effect of linear modulus of meniscal horn attachment (EP) on meniscal translation. Medial meniscus digitization at 45N anterior loaded position was rendered in red, two FEM predictions of meniscal positions were in blue. (1) EP=1MPa, (2) EP=5.5MPa. For both models, other material properties were the same (Ec=5MPa, vC=0.49, Eθ=200MPa, ER=10MPa, vθR=0.55, vRZ=0.55, GθR=19MPa, ε1H=0.025, ε2H=0, EH=600MPa, ε1P=0.05, ε2P=0.05, EP=5.5MPa). The resulted volume errors were 18.5 and 12.8%. Red dots show the position of the centroid for the digitization, blue dots were the positions of the centroids for both model predictions.

Figure 5

Comparison of the meniscal position predicted from finite element models (blue solid line) to those digitized from MRI (red dash line) at three sagittal cutting planes. Two model predictions were studied with different values for the linear modulus of the peripheral attachment (EP). (a.1-3) EP=1MPa, (b.1-3) EP=5.5MPa. For both models, other material properties were the same (Ec=5MPa, vC=0.49, Eθ=200MPa, ER=10MPa, vθR=0.55, vRZ=0.55, GθR=19MPa, ε1H=0.025, ε2H=0, EH=600MPa, ε1P=0.05, ε2P=0.05, EP=5.5MPa). Note: images were digitally retouched for clarity to remove an air bubble present in the joint space.

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