Multiscale Biomechanical Models for Biological Soft Tissue

Dr. Eunjung Kim
Department of Mathematics
University of Notre Dame


Articular cartilage is a resilient soft tissue that supports load joints at the knee, shoulder and hip. Cartilage is primarily comprised of interstitial water (roughly 80% by volume) and extracellular matrix (ECM). Cells called chondrocytes are dispersed through ECM and maintain and regenerate the tissue. Chondrocytes are surrounded by a narrow layer called pericellular matrix (PCM), which is believe to be important for modulating the biomechanical environment of chondrocyte. Since cartilage has no nerve endings and no blood vessels, the metabolic activities of chondrocytes are highly dependent on mechanical characteristics of the local extracellular environment. In this study, computational models will be presented to analyze the multiscale micromechanical environment of chondrocytes.

Firstly, we will discuss transient finite element method (FEM) to model linear biphasic mechanics of a single cell within cartilage layer under cyclic loading. The FEM model was employed to analyze the effects of frequency on mechanical variables in cellular environment under macroscopic loading at 1% strain and in the frequency range 0.01 0.1 Hz. In this frequency range, intracellular axial strains exhibited up to a ten-fold increase in magnitude relative to 1% applied strain. The dynamics of strain amplification exhibited a two-scale response that was highly dependent on ratios of typical time scales in the model, such as the loading period, gel diffusion times for the cell, the PCM and the ECM. In conjunction with strain amplification, solid stress in the surrounding ECM was reduced by up to 35%. We propose here that the computational model developed in this study has potential application in correlating mechanical variables in the cellular microenvironment to biosynthetic responses induced by cyclic loading of native cartilage or engineered cell-gel constructs.

Secondly, we will discuss the formulation, implementation and application of multiscale axisymmetric boundary element method (BEM) for simulating in situ deformation of chondrocyte and the PCM in states of mechanical equilibrium. The BEM was employed to conduct a multiscale continuum model to determine linear elastic properties of the PCM in situ. An inverse analysis was performed using previously reported experimental data on the three-dimensional morphological changes of PCM and chondrocytes within a cartilage explant in equilibrium unconfined compression (Choi et al., J. Biomech, 40:2596-603,2007). Depending on the assumed material properties of the ECM and the choice of cost function in the optimization, estimates of the PCM Young's modulus are consistent with previous measurements of PCM properties on extracted PCM and chondrocyte using micropipette aspiration. Taken together with previous experimental and theoretical studies of cell-matrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte.

This is joint work with Mansoor Haider (NCSU), and our experimental colleague, Farshid Guilak (Duke).