1D Models for Blood Flow in Small Vessels Using the Cosserat Theory

Abstract

This paper is motivated by the study of 1D fluid models for blood flow in the vascular system. In our work, we consider blood modeled as an incompressible shear-thinning generalized Newtonian fluid in a straight rigid and impermeable vessel with circular cross-section of constant radius. To study this problem, we use an approach based on the Cosserat theory (also called director theory) related to fluid dynamics which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this new system we obtain the unsteady relationship between mean pressure gradient and volume flow rate over a finite section of the tube for the specific cases of power law and Carreau-Yasuda viscosity functions, and also the correspondent equations for the wall shear stress which enters directly in the formulation as a dependent variable.