Abstract
SummaryThe lattice Boltzmann method (LBM) combined with the immersed boundary method is a common tool to simulate the movement of red blood cel ls (RBCs) through blood vessels. With very few exceptions, such simulations neglect the difference in viscosities between the hemoglobin solution inside the cells and the blood plasma outside, although it is well known that this viscosity contrast can severely affect cell deformation. While it is easy to change the local viscosity in LBM, the challenge is to distinguish whether a given lattice point is inside or outside the RBC at each time step. Here, we present a fast algorithm to solve this issue by tracking the membrane motion and computing the scalar product between the local surface normal and the distance vector between the closest LBM lattice point and the surface. This approach is much faster than, for example, the ray‐casting method. With the domain tracking applied, we investigate the shape transition of a RBC in a microchannel for different viscosity contrast and validate our method by comparing with boundary‐integral simulations.
Highlights
Red blood cells (RBCs) flowing through small blood vessels or microchannels show a fascinating wealth of flow states including steady shapes, dynamic states where the membrane periodically rotates around the cell interior, or tumbling motions.[1,2,3,4,5,6,7,8,9,10,11,12]
We presented an efficient tracking algorithm to distinguish the interior fluid of a dynamically deforming RBC from the outside fluid during a lattice-Boltzmann-immersed-boundary simulation
As our algorithm treats only those lattice Boltzmann method (LBM) lattice points which are in immediate vicinity to the RBC membrane, it is capable of very accurate discrete volume tracking without significantly impacting simulation performance
Summary
Red blood cells (RBCs) flowing through small blood vessels or microchannels show a fascinating wealth of flow states including steady shapes, dynamic states where the membrane periodically rotates around the cell interior, or tumbling motions.[1,2,3,4,5,6,7,8,9,10,11,12] Experimental techniques to visualize these flow states are still mostly limited to two-dimensional (2D) video microscopy,[13,14,15,16] progress toward three-dimensional (3D) imaging techniques has recently been made.[17]. A RBC consists of a thin elastic membrane surrounding the interior hemoglobin solution which to a good approximation can be viewed as a Newtonian liquid with a viscosity about five times larger than the surrounding blood plasma.[10,18] This viscosity contrast λ is essential for the RBC dynamics.[19,20,21,22,23,24,25,26] Depending on the numerical technique, it can be more or less tedious to include the parameter λ into numerical simulations. In boundary-integral methods (BIM), the consideration of a viscosity contrast is conceptually straightforward, computationally costly.[27,28,29,30] Particle methods such as smoothed dissipative particle dynamics (SDPD) are able to include viscosity contrast,[7] this is not always done.[5,31]
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