A Hybrid Continuum-Particle Approach for Fluid-Structure Interaction Simulation of Red Blood Cells in Fluid Flows

Abstract

Transport of cells in fluid flow plays a critical role in many physiological processes of the human body. Recent developments of in vitro techniques have enabled the understanding of cellular dynamics in laboratory conditions. However, it is challenging to obtain precise characteristics of cellular dynamics using experimental method alone, especially under in vivo conditions. This challenge motivates new developments of computational methods to provide complementary data that experimental techniques are not able to provide. Since there exists a large disparity in spatial and temporal scales in this problem, which requires a large number of cells to be simulated, it is highly desirable to develop an efficient numerical method for the interaction of cells and fluid flows. In this work, a new Fluid-Structure Interaction formulation is proposed based on the use of hybrid continuum-particle approach, which can resolve local dynamics of cells while providing large-scale flow patterns in the vascular vessel. Here, the Dissipative Particle Dynamics (DPD) model for the cellular membrane is used in conjunction with the Immersed Boundary Method (IBM) for the fluid plasma. Our results show that the new formulation is highly efficient in computing the deformation of cells within fluid flow while satisfying the incompressibility constraints of the fluid. We demonstrate that it is possible to couple the DPD with the IBM to simulate the complex dynamics of Red Blood Cells (RBC) such as parachuting. Our key observation is that the proposed coupling enables the simulation of RBC dynamics in realistic arterioles while ensuring the incompressibility constraint for fluid plasma. Therefore, the proposed method allows an accurate estimation of fluid shear stresses on the surface of simulated RBC. Our results suggest that this hybrid methodology can be extended for a variety of cells in physiological conditions.

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

“…The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries , and capillaries, where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.…”

Shape transitions of Red Blood Cell under oscillatory flows in microchannels

“…A and V are the instantaneous total area and total volume of the RBC. The detailed procedure to evaluate the values of A and V for individual elements was reported in our previous work (Akerkouch and Le, 2021).…”

“…V in Equations ( 4) -( 8) (Akerkouch and Le, 2021;Fedosov et al, 2010). The internal force F membrane i contribution from i th vertex can be computed by summing all the nodal forces as:…”

“…The CURVIB method used here has been applied and validated in various FSI problems across different biological engineering areas (Le et al, 2010;Le and Sotiropoulos, 2012;Le et al, 2019). In our previous work (Akerkouch and Le, 2021), we utilize the capabilities of the CURVIB method to capture accurately the complex cellular dynamics of the RBC in fluid flows.…”

“…In this work, we utilized our hybrid continuum-particle simulation methodology (Akerkouch and Le, 2021) to study the response of the RBC to time-dependent shear rates. Our paper is organized as follows.…”