Cal Poly Cartilage Biomechanics Group

P.I. Stephen M. Klisch, Ph.D.

Modeling AC growth with a cartilage growth finite element model

The objective of this work is to develop a CGFEM to solve non-homogeneous and time-dependent growth boundary value problems. Due to the different time scales of growth and applied mechanical loading, the computational approach separates the solution of the growth boundary-value problem into two parts: one that describes the actual mechanical loading with a time scale on the order of seconds, and another that describes the resulting growth of the tissue with a time scale (i.e. increment) of 1 day. A commercial finite element code (ABAQUS) is combined with an external program (MATLAB) to solve the non-homogeneous time-dependent growth boundary value problem in an incremental fashion.

For the first time increment, poroelastic FEA (ABAQUS) determines time-averaged values of mechanical variables (e.g. relative fluid velocity or matrix shear stress) used to determine incremental growth tensors from growth laws. Then, the incremental growth boundary-value problem is solved using an “elemental growth routine” (MATLAB) to determine new values of element geometry, composition, and GAG-COL pre-stresses. A new specimen global reference configuration is obtained using FEA (ABAQUS) to find equilibrium upon updating the solid matrix constitutive equations and stress for each element. Then, poroelastic FEA determines the mechanical variables during the second time increment, the elemental growth routine is called, and this iterative procedure is followed through the entire growth process.

The CGFEM has been used to simulate in vitro growth of AC explants subjected to dynamic CC and UCC loading protocols. Most recently, the CGFEM simulated in vitro growth of AC explants in a steady-state permeation bioreactor utilizing two competing hypotheses for the growth laws: one that is triggered by fluid permeation velocity and one by maximum shear stress. The results provided predictions for geometric, biomechanical, and biochemical parameters of grown tissue specimens that may be experimentally measured and, consequently, suggest key biomechanical measures to analyze as pilot experiments are performed. The results illustrate that the CGFEM can be used to predict the evolution of non-uniform tissue composition, residual stress, and mechanical properties due to differential and non-uniform growth.

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© 2008 Stephen M. Klisch | Mechanical Engineering

College of Engineering | Cal Poly San Luis Obispo