Blood flows in capillary networks*

Modeling blood flows at the microscale is essential to improve the understanding of physiological processes occurring in capillary networks, such as vascular resistance. Progress has been made regarding 1D modeling (based on empirical correlations) or experimental techniques. Recent work (Balogh and Bagchi JCP 2017) showed results of microscale simulations of blood flows involving deformable red blood cells (RBCs) through networks of capillaries. 

We develop a numerical approach relying on a direction splitting method to solve Navier-Stokes equations coupled with an Immersed Boundary Method for the representation of vascular walls described by the means of triangulated surfaces. The deformation of RBCs is handled by a membrane model (Fedosov et al Biophy. J. 2010). The membrane forces are coupled to the fluid using a 3D Dirac delta function. 

We present results of blood flow simulations involving RBCs in complex geometries built with CAD tools. The geometries considered present the characteristics of the complex structure of microvascular networks, such as multiple merging, bifurcating and winding vessels. We compare time-averaged quantities with in-vivo data.