Cellular Level In-silico Modeling of Blood Rheology with An Improved Material Model for Red Blood Cells

Abstract

Many of the intriguing properties of blood originate from its cellular nature. Therefore, accurate modeling of blood flow related phenomena requires a description of the dynamics at the level of individual cells. This, however, presents several computational challenges that can only be addressed by high performance computing. We present Hemocell, a parallel computing framework which implements validated mechanical models for red blood cells and is capable of reproducing the emergent transport characteristics of such a complex cellular system. It is computationally capable of handling large domain sizes, thus it is able to bridge the cell-based micro-scale and macroscopic domains. We introduce a new material model for resolving the mechanical responses of red blood cell membranes under various flow conditions and compare it with a well established model. Our new constitutive model has similar accuracy under relaxed flow conditions, however, it performs better for shear rates over 1,500 s−1. We also introduce a new method to generate randomized initial conditions for dense mixtures of different cell types free of initial positioning artifacts.

Bridging the computational gap between mesoscopic and continuum modeling of red blood cells for fully resolved blood flow

“…This approach is proven to have equivalent rheological behavior with the generalized Maxwell model as proposed by Semblat 1997 [42]. Similar approach is followed by Fedosov et al 2010 [19] & Hemocell [21].…”

“…It is obvious that our solver is characterized by strong mesh independence which is a direct consequence of the proper discretization of the continuous energies (a general advantage of FEM-based solvers). Currently, all the state-of-the-art solvers [19,21] are based on coarse-grained spectrin-link models which are essentially mass-viscoelastic spring systems. Their calibration is based on a method first introduced by Dao et al 2006 [15] and later extended by Fedosov et al 2010 [19], which relies on a regular two-dimensional sheet of springs, i.e., equilateral triangular elements.…”

“…In the mass-spring solvers [19,21], the viscosity of the RBC membrane is tackled through the addition of a dissipative force F D i j = −ηv i j , where η is the membrane viscosity and v i j is the relative velocity of the spring ends. However, this forcing term has the same disadvantage as the Rayleigh damping, i.e., it damps rigid body motions instead of only the relative ones.…”

“…For this reason, the coarse-grained models of Dupin et al 2007 [18], Pivkin and Karniadakis 2008 [17], Fedosov et al 2010 [19], and Reasor et al 2011 [20] have gained substantial attention during the last years, where the surface discretization demands about 500 vertices. Currently, state-of-the-art solvers like Hemocell [21,22] and the solver of Fedosov [19] are based on this modeling approach. These coarse-grained methods outperform all the others in terms of computational time.…”

Detection of arterial wall abnormalities via Bayesian model selection

“…Mathematical models for hemodynamics trace back to the work of Euler, who described a onedimensional treatment of blood flow through an arterial network with rigid tubes [11,33]; more sophisticated one-dimensional models are still used to study a variety of physio-pathological phenomena [1,2,13,21,23,29,30,37]. Computational advances have also allowed for the development of computationally intensive three-dimensional models [12,14,32,34,39,40], which have been used to accurately simulate specific human arteries (e.g., the carotid arteries [18]) and model their material properties (e.g., of cerebral arterial walls [38]). There also exist multicomponent models [10], which are amenable to applications such as modeling oxygen transport to solid tumors [6] and surgical tissue flaps [24,25].…”