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.

在本文中，我们提出了一种多尺度数值算法，以模拟流经筛孔且平均直径小于RBC的筛孔的红细胞（RBC）溶血释放血红蛋白（Hb）。在微滤中分析RBC损伤很重要，因为它可以量化人红细胞在经历高剪切速率和高变形时对机械溶血的敏感性。在这里，数值模拟是通过晶格玻尔兹曼方法和通过沉浸边界方法耦合的弹簧连接网络（SN）进行的。为了预测RBC的细胞分解损伤，将源自分子动力学模拟的亚细胞损伤模型纳入细胞求解器。在提出的算法中，由细胞求解器计算的局部RBC应变分布用于获得RBC膜上的孔半径。溶血指数（IH）通过求出最终的孔半径并考虑空间位阻和因血红蛋白分子大小而增加的流体动力阻力的影响来求解扩散方程。应当提到的是，当前的计算溶血模型通常利用对受损RBC血浆中释放的游离血红蛋白（Hb）的经验拟合。这些经验相关性包含取决于特定设备和操作条件的临时参数，因此不能用于预测不同条件下的溶血。与可用的溶血模型相反，所提出的算法没有任何经验参数。因此，它可以预测具有不同筛孔大小和过滤压力的微滤器中的IH。此外，与经验相关性相反，在经验相关性中，Hb释放与剪切应力和暴露时间有关，而没有考虑物理过程，所提出的模型将RBC膜的流致变形与膜通透性和血红蛋白释放联系起来。本文通过模拟光镊实验，剪切流实验以及在非常狭窄的微通道中测量RBC变形能力的实验对蜂窝求解器进行了验证。此外，将单个红细胞在破裂时刻的形状与相应的实验数据进行了比较。最后，要验证损害模型，从我们关于过滤压力和筛孔大小在Hb释放中的作用的参数研究中获得的结果与实验数据进行了比较。数值结果与实验数据吻合良好。类似于相应的实验，数值结果证实溶血随着过滤压力的增加和筛孔尺寸的减小而增加。虽然在实验中无法测量RBC孔径，但数值结果可以量化RBC孔径。数值结果表明，在25 cm Hg以上的筛孔孔径为2.2 µm时，RBC孔径大于75 nm，RBC会破裂。更重要的是，