Multiscale modeling of hemolysis during microfiltration

Abstract

In this paper, we propose a multiscale numerical algorithm to simulate the hemolytic release of hemoglobin (Hb) from red blood cells (RBCs) flowing through sieves containing micropores with mean diameters smaller than RBCs. Analyzing the RBC damage in microfiltration is important in the sense that it can quantify the sensitivity of human erythrocytes to mechanical hemolysis while they undergo high shear rate and high deformation. Here, the numerical simulations are carried out via lattice Boltzmann method and spring connected network (SN) coupled by an immersed boundary method. To predict the RBC sublytic damage, a sub-cellular damage model derived from molecular dynamic simulations is incorporated in the cellular solver. In the proposed algorithm, the local RBC strain distribution calculated by the cellular solver is used to obtain the pore radius on the RBC membrane. Index of hemolysis (IH) is calculated by resorting to the resulting pore radius and solving a diffusion equation considering the effects of steric hinderance and increased hydrodynamic drag due to the size of the hemoglobin molecule. It should be mentioned that current computational hemolysis models usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged RBCs. These empirical correlations contain ad hoc parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis under different conditions. In contrast to the available hemolysis model, the proposed algorithm does not have any empirical parameters. Therefore, it can predict the IH in microfilter with different sieve pore sizes and filtration pressures. Also, in contrast to empirical correlations in which the Hb release is related to shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and hemoglobin release. In this paper, the cellular solver is validated by simulating optical tweezers experiment, shear flow experiment as well as an experiment to measure RBC deformability in a very narrow microchannel. Moreover, the shape of a single RBC at the rupture moment is compared with corresponding experimental data. Finally, to validate the damage model, the results obtained from our parametric study on the role of filtration pressure and sieve pore size in Hb release are compared with experimental data. Numerical results are in good agreement with experimental data. Similar to the corresponding experiment, the numerical results confirm that hemolysis increases with increasing the filtration pressure and reduction in pore size on the sieve. While in experiment, the RBC pore size cannot be measured, the numerical results can quantify the RBC pore size. The numerical results show that at the sieve pore size of 2.2 μm above 25 cm Hg, RBC pore size is above 75 nm and RBCs experience rupture. More importantly, the results demonstrate that the proposed approach is independent from the operating conditions and it can estimate the hemolysis in a wide range of filtration pressure and sieve pore size with reasonable accuracy.

Keywords: Hemolysis; High deformation; High shear rate; Microfiltration; Multiscale modeling; Red blood cell.

Fig. 1

Numerical algorithm flowchart

Fig. 2

The summary of multiscale cell damage model: a RBC deformation in a micro-channel; b local strain distribution and nano-pore formation on the RBC membrane; c Hb diffusion out of porated regions on the high-strained triangulated meshes

Fig. 3

a computational grid and sample local normal vectors for triangular patches, b 2D illustration of kinematics for stretching and bending in spring connected network

Fig. 4

Schematic view of the optical tweezers experiment

Fig. 5

Comparison between axial and transverse RBC diameters obtained from numerical simulation and experimental data by Mills et al. (2004)

Fig. 6

Schematic view of the shear flow experiment

Fig. 7

Comparison between deformation index obtained from numerical simulation and experimental data by Yao et al. (2001)

Fig. 8

Computational domain together with the boundary conditions for an RBC squeezing through a micro-channel

Fig. 9

Schematic representation of a RBC traversing across a microfluidic channel, with a constriction 30 μm long, 4 μm wide and 2.7 μm high: a numerical simulation, b experimental study (Quinn 2011)

Fig. 10

Simulated RBC lengths along with experimental ones (Quinn 2011) at the center of the microfluidic channel with different channel widths

Fig. 11

Inflated RBC shape at the lysis moment in a 60 μm long and 5 μm wide microchannel: a numerical simulation, b experimental results (Abkarian et al. 2008)

Fig. 12

Front view of the strain distribution on the RBC at the rupture moment

Fig. 13

Modeling microfilteration at cellular scale

Fig. 14

RBC deformation during squeezing through one pore of the microfilter at three different instances for Δp = 50 cm Hg

Fig. 15

Effect of filtration pressure and sieve pore size on hemolysis index