Modeling Anisotropic Electrical Conductivity of Blood: Translating Microscale Effects of Red Blood Cell Motion into a Macroscale Property of Blood.

Cardiovascular diseases are a leading global cause of mortality. The current standard diagnostic methods, such as imaging and invasive procedures, are relatively expensive and partly connected with risks to the patient. Bioimpedance measurements hold the promise to offer rapid, safe, and low-cost alternative diagnostic methods. In the realm of cardiovascular diseases, bioimpedance methods rely on the changing electrical conductivity of blood, which depends on the local hemodynamics. However, the exact dependence of blood conductivity on the hemodynamic parameters is not yet fully understood, and the existing models for this dependence are limited to rather academic flow fields in straight pipes or channels. In this work, we suggest two closely connected anisotropic electrical conductivity models for blood in general three-dimensional flows, which consider the orientation and alignment of red blood cells (RBCs) in shear flows. In shear flows, RBCs adopt preferred orientations through a rotation of their membrane known as tank-treading motion. The two models are built on two different assumptions as to which hemodynamic characteristic determines the preferred orientation. The models are evaluated in two example simulations of blood flow. In a straight rigid vessel, the models coincide and are in accordance with experimental observations. In a simplified aorta geometry, the models yield different results. These differences are analyzed quantitatively, but a validation of the models with experiments is yet outstanding.