Microrheology and constitutive equation of soft tissue

The connection between microrheology and the constitutive equation of soft tissue is illustrated by an example of the incremental bulk modulus of the lung. It is shown that the following pieces of information are needed in order to make the connection: The detailed structure of the tissue embodied in a mathematical model, the morphometric data on the structural elements, the rheologic data of the materials, and the configuration at zero-stress state, or equivalently, the stress and strain at a homeostatic state. In the case of the lung, we have information on the first three items, but not the last one. Hence hypotheses have to be introduced concerning the homeostatic condition, the most important of which are the uniform fiber stress and the "optimal design" assumptions. We have shown that these data and hypotheses lead to theoretical results that are in good agreement with experimental observations.