A monolithic fluid‐structure interaction framework applied to red blood cells

Abstract

A parallel fully coupled (monolithic) fluid-structure interaction (FSI) algorithm has been applied to the deformation of red blood cells (RBCs) in capillaries, where cell deformability has significant effects on blood rheology. In the present FSI algorithm, fluid domain is discretized using the side-centered unstructured finite volume method based on the Arbitrary Lagrangian-Eulerian (ALE) formulation; meanwhile, solid domain is discretized with the classical Galerkin finite element formulation for the Saint Venant-Kirchhoff material in a Lagrangian frame. In addition, the compatible kinematic boundary condition is enforced at the fluid-solid interface in order to conserve the mass of cytoplasmic fluid within the red cell at machine precision. In order to solve the resulting large-scale algebraic linear systems in a fully coupled manner, a new matrix factorization is introduced similar to that of the projection method, and the parallel algebraic multigrid solver BoomerAMG is used for the scaled discrete Laplacian provided by the HYPRE library, which we access through the PETSc library. Three important physical parameters for the blood flow are simulated and analyzed: (1) the effect of capillary diameter, (2) the effect of red cell membrane thickness, and(3) the effect of red cell spacing (hematocrit). The numerical calculations initially indicate a shape deformation in which biconcave discoid shape changes to a parachute-like shape. Furthermore, the parachute-like cell shape in small capillaries undergoes a cupcake-shaped buckling instability, which has not been observed in the literature. The instability forms thin riblike features, and the red cell deformation is not axisymmetric but three-dimensional. KEYWORDS buckling instability, compatible interface condition, fluid-structure interaction, monolithic approach, red blood cell deformation Int J Numer Meth Biomed Engng. 2019;35:e3171.wileyonlinelibrary.com/journal/cnm

Valid Presumption of Shiga Toxin-Mediated Damage of Developing Erythrocytes in EHEC-Associated Hemolytic Uremic Syndrome

“…Erythrocytes can readily change their shape when exposed to mechanical forces in the bloodstream and can flow smoothly without any damage when passing narrow capillaries, which is a feature that can be significantly altered under pathological conditions. Narrow capillaries determine the erythrocytes’ flow-induced morphological alterations including the change of the biconcave discoid shape to parachute and slipper shapes observed in microchannels, which serve as idealized microvessels [ 437 , 438 , 439 , 440 , 441 ]. Improvements in experimental technologies using microfluidic models allows for the exact determination of applied shear stress and associated forces toward RBCs, their microcirculatory dynamics, mechanical stability and deformability, heterogeneity in rheological properties, the deformation of molecular architecture as well as hydrodynamic and macromolecule-induced interaction [ 436 , 442 , 443 , 444 , 445 , 446 , 447 , 448 ].…”

Numerical investigation on red blood cell flow based on unstructured grid

“…In the RBCs flow for a vessel diameter of 9.02 μm, the shape of an RBC changes from biconcave to parachute shape. As the result of Cetin and Sahin, 50 the buckling instability is observed to happen when the flow rate is low. And as the flow rate increases, there is no buckling instability.…”

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.…”