A Growth Mixture Theory for Cartilage

Stephen M. Klisch, University of California - San Diego
Robert L. Sah, University of California - San Diego
Anne Hoger, University of California - San Diego

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NOTE: At the time of publication, the author Stephen Klisch was not yet affiliated with Cal Poly.

Abstract

In this paper we present a model of growth for cartilaginous tissues in which there exists a saturated solid matrix composed of multiple constituents that may grow and remodel independently of each other. Klisch and Hoger recently developed a general theory of volumetric growth for a mixture of ν-1 growing elastic materials and an inviscid fluid, which included a treatment of two special types of internal constraints that are relevant to cartilage. Here, that theory is specialized to construct a cartilage growth model. This theory allows the constituents of the solid matrix to grow independently of each other, and can model the evolution of the constituent pre-stresses and the tissue’s mechanical properties during developmental growth and degeneration. A simple example is presented which illustrates these features of the theory.