Coupling cellular phenotype and mechanics to understand extracellular matrix formation and homeostasis in osteoarthritis*

Osteoarthritis of the knee is a common degenerative disease during aging. It is typically caused by articular cartilage degeneration. Cartilage, which is located between bone surfaces, is a viscoelastic material aiming to absorb, redirect and transmit mechanical forces during movement. Without the cartilages' buffering capacity, bones come into direct contact inducing severe pain up to the stage where affected individuals loose mobility. The mechanisms of cartilage remodeling are poorly understood, and there is currently no effective method to reconstitute damaged cartilage. Cartilage consists of extracellular matrix (ECM) and a low density of cells (chondrocytes), which generate matrix proteins. The composition of the matrix gives the cartilage specific viscoelastic properties, which are sensed by chondrocytes feeding back on ECM remodeling. The aim of this study is to build a mathematical model that couples mechanical ECM properties with chondrocyte phenotype in the upkeep of cartilage homeostasis. We model the viscoelastic properties of the cartilage in terms of a linear Kelvin-Voigt model, where the dampening ratio feeds back on the phenotypic switching behaviour in chondrocytes. The chondrocytes, depending on their phenotypic state, may either produce proteoglycans or collagens or both, which alters the viscoelastic properties of the cartilage. We formulate a coupled system of equations integrating mechano-sensitive phenotypic switching behaviour of chondrocytes with respect to ECM remodelling. We define cartilage homeostasis as the fixed point of the derived systems of equations. Using this framework we can reproduce the long term changes in cartilage composition during aging.