Department of Mathematics, UCI

The evolution and spatial distribution of tissue stresses is of fundamental importance in a number of physiological phenomena. The experimentally-observed collapse of tumor blood vessels, for example, which has been attributed to the elevated tissue stresses resulting from confined proliferation of tumor cells, represents a significant barrier to the delivery of blood-borne therapeutic agents. Such stresses are residual in nature, arising in the tissue in the absence of external loads, and result from the incompatibility of growth strains.

Nevertheless, the underlying phenomenological determinants of residual stresses, as well as their purpose and implications in both normal tissue development and various pathological conditions, are poorly understood since there is currently a paucity of mathematical models to elucidate these phenomena. In this presentation a number new mathematical ideas germane to the study of residual stresses in growing soft tissues will be discussed. Emphasis will be placed on 'solid-multiphase' tissue modeling, which represents a new class of mathematical models in which the concepts of poroelasticity are extended to accommodate continuous volumetric growth.