Mathematical characterization of the nonlinear thermorheological behavior of the vascular tissue

A characterization of the passive nonlinear thermorheological response of incompressible, curvilinearly orthotropic arterial tissue is presented in the framework of modern continuum thermodynamics. The stress tensor, the specific entropy, the specific internal energy and the heat flux vector and expressed as functionals of the histories of local deformation, temperature and the temperature gradient. These functionals are systematically reduced by subjecting them to the requirements of Clausius-Duhem inequality and material frame indifference. The reduced functionals are then specialized to reflect the material frame indifference. The reduced functionals are then specialized to reflect the material symmetry characterizing the tissue by using the histories of the joint invariants of the Green-St. Venant strain tensor and temperature as the independent argument functions. The functionals are expressed in terms of series of multiple integrals and terms upto and including second order integrals are retained. An approach toward experimental determination of the 14 constitutive functions to describe two stress differences is outlined. It is believed that the characterization presented here will provide a rational basis for simpler thermorheological descriptions and experimental programs to include important thermorheologic considerations.