A computational approach to modeling cellular-scale blood flow in complex geometry

Abstract

We present a computational methodology for modeling cellular-scale blood flow in arbitrary and highly complex geometry. Our approach is based on immersedboundary methods, which allow modeling flows in arbitrary geometry while resolving the large deformation and dynamics of every blood cell with high fidelity. The present methodology seamlessly integrates different modeling components dealing with stationary rigid boundaries of complex shape, moving rigid bodies, and highly deformable interfaces governed by nonlinear elasticity. Thus it enables us to simulate 'whole' blood suspensions flowing through physiologically realistic microvascular networks that are characterized by multiple bifurcating and merging vessels, as well as geometrically complex lab-on-chip devices. R2C1The focus of the present work is on the development of a versatile numerical technique that is able to consider deformable cells and rigid bodies flowing in three-dimensional arbitrarily complex geometries over a diverse range of scenarios. After describing the methodology, a series of validation studies are presented against analytical theory, experimental data, and previous numerical results. Then, the capability of the methodology is demonstrated by simulating flows of deformable blood cells and heterogeneous cell suspensions in both physiologically realistic microvascular networks and geometrically intricate microfluidic devices.It is shown that the methodology can predict several complex microhemodynamic phenomena observed in vascular networks and microfluidic devices. The present methodology is robust and versatile, and has the potential to scale up to very large microvascular networks at organ levels.

Scalable simulation of realistic volume fraction red blood cell flows through vascular networks

“…For a comprehensive review of general blood flow simulation methods, see [12]. IB methods can produce high-quality simulations of heterogeneous particulate flows in complex blood vessels [3,4,52]. These methods typically require a finite element solve for each RBC to compute membrane tensions and use IB to couple the stresses with the fluid.…”

Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation

“…In the last decades, diverse numerical methods have been developed to discretize the mathematical model proposed by the IB method, such as a hybrid finite difference/finite element discretization [14], a NURBS-based discretization [15], a discretization based on T-splines [16], finite volume discretization for the Navier-Stokes equations [17], and lattice Boltzmann discretization for the Navier-Stokes equations [18,19]. These numerical methods have been applied to a variety of problems, such as heart valve analysis and design [20,21,22,23], cell-scale blood flow [24,25,26], aquatic animal locomotion [27,28], tissue cryofreezing [29], capsule dynamics [30], vesicle dynamics [31], particle laden flows [32], and floating structures [33].…”

A computational modeling of blood flow in asymmetrically bifurcating microvessels and its experimental validation

“…Lee et al simulated drug carrier distribution in a microvessel with individual cells, nanoparticles, and plasma. Balogh and Bagchi performed blood flow simulation in connected microvessels with RBCs. These computational models are helpful in understanding hemodynamics in microvessels.…”