Effects of osmotic pressure in the extracellular matrix on tissue deformation

In soft tissues, large molecules such as proteoglycans trapped in the extracellular matrix (ECM) generate high levels of osmotic pressure to counter-balance external pressures. The semi-permeable matrix and fixed negative charges on these molecules serve to promote the swelling of tissues when there is an imbalance of molecular concentrations. Structural molecules, such as collagen fibres, form a network of stretch-resistant matrix, which prevents tissue from over-swelling and keeps tissue integrity. However, collagen makes little contribution to load bearing; the osmotic pressure in the ECM is the main contributor balancing external pressures. Although there have been a number of studies on tissue deformation, there is no rigorous analysis focusing on the contribution of the osmotic pressure in the ECM on the viscoelastic behaviour of soft tissues. Furthermore, most previous works were carried out based on the assumption of infinitesimal deformation, whereas tissue deformation is finite under physiological conditions. In the current study, a simplified mathematical model is proposed. Analytic solutions for solute distribution in the ECM and the free-moving boundary were derived by solving integro-differential equations under constant and dynamic loading conditions. Osmotic pressure in the ECM is found to contribute significantly to the viscoelastic characteristics of soft tissues during their deformation.