Computational methods for the suspensions of deformable and rigid particles and their applications to modelling of blood flows

该项目的重点是开发用于模拟可变形和刚性颗粒悬浮液的计算方法及其在微通道流动中的血流微循环和细胞分离建模中的应用。直接模拟红细胞在流体中的三维运动和动力学是一个计算上的挑战。我们将使用弹簧网络模型及其相关的能量势来模拟红细胞的膜。我们建议将弹簧网络模型与浸入边界方法、有限元方法和算子分裂技术相结合，以模拟三维的细胞-流体和细胞-细胞相互作用。我们还希望将上述方法与分布式拉格朗日乘子/虚拟域方法相结合，这些方法与浸没边界方法密切相关，以模拟细胞和固体颗粒的悬浮液。通过PI提出的计算方法，将对微血管中的红细胞进行有效的三维模拟，以研究微循环中红细胞的流变学，微血管中固体颗粒的边缘动力学和微通道中的细胞分离。微循环发生在最小的血管中（即，小动脉、毛细血管和小静脉）负责调节各个器官中的血流以及血液和组织之间的交换。由于血液中含有约40-45%的红细胞，以及血小板和白细胞，这些有形成分的相互作用在确定血液特性中起着至关重要的作用。由于其大的体积分数和它们的聚集能力，红细胞是血流特性的最重要的决定因素。虽然悬浮液流变学的理论通常集中在无限域中的均匀流动，但微循环中血液流动的重要现象取决于血管几何形状、细胞变形性、壁顺应性、流动剪切速率以及许多微尺度化学、生理和生物因素的综合影响。我们专注于流变学方面的微循环涉及可变形细胞，细胞-细胞相互作用和血管的几何形状，这是特别具有挑战性的理论和计算。第一个主要应用是研究微血管中固体颗粒的边集动力学。用于生物医学成像和治疗的刚性颗粒的血管内递送被认为是心血管和肿瘤应用中的强大且有前途的工具。这些颗粒可以装载药物分子和造影剂，并通过血液流动通过循环系统运输。它们通常用配体分子修饰，所述配体分子能够与在病变细胞（或靶细胞）上表达的抗原特异性相互作用。需要分析颗粒形状、尺寸和密度对边集倾向的影响，以找到最佳设计。第二个主要应用是研究微通道流动中的细胞分离。主要的重点是在微流体生物芯片平台上获得健康和患病红细胞的分离，因为它们的变形性和大小。软物体的分离在医学和生物学应用中具有巨大的相关性，因为变形能力的丧失通常沿着着疾病，例如疟疾、糖尿病或癌症，仅举几例。因此，用于分选或分离细胞的微流体系统对于诊断和透析应用都将是非常重要的。

This project focuses on developing computational methods for simulating the suspensions of deformable and rigid particles and their applications to modeling the microcirculation of blood flow and cell separation in microchannel flow. It is computationally challenging to simulate directly the three-dimensional motion and dynamics of hydrodynamically interacting red blood cells in a fluid. We will use a spring network model with its associated energy potential to model the membrane of the red blood cell. We propose to combine the spring network model with the immersed boundary methods, finite element methods and operator splitting techniques to simulate the cell-fluid and cell-cell interactions in three dimensions. We also want to combine the above proposed methodology with the distributed Lagrange multiplier/fictitious domain methods, which are closed related to the immersed boundary methods, to simulate the suspensions of cells and solid particles. Through the computational methodologies proposed by the PIs, efficient three-dimensional simulations of the red blood cells in microvessels will be performed to study the rheology of red blood cells in microcirculation, the margination dynamics of solid particles in microvessels and the cell separation in microchannels.The microcirculation, which takes place in the smallest blood vessels (i.e., arterioles, capillaries, and venules), is responsible for regulating blood flow in individual organs and for exchange between blood and tissue. Since blood contains about 40-45% red blood cells by volume, as well as platelets and leukocytes, the interactions of these formed elements play a crucial role in determining blood characteristics. Because of their large volume fraction and their aggregation capacity, red blood cells are the most important determinant of blood flow characteristics. While theories of suspension rheology generally focus on homogeneous flows in infinite domains, the important phenomena of blood flows in microcirculation depend on the combined effects of vessel geometries, cell deformabilities, wall compliance, flow shear rates, and many micro-scale chemical, physiological, and biological factors. We concentrate on the rheological aspects of flow in microcirculation involving deformable cells, cell-cell interactions and vessel geometry, which is particularly challenging theoretically and computationally. The first main application is to study the margination dynamics of solid particles in microvessels. The intravascular delivery of rigid particles for biomedical imaging and therapy is being recognized as a powerful and promising tool in cardiovarscular and oncological applications. These particles can be loaded with drug molecules and contrast agents and transported by the blood flow through the circulatory system. They are generally decorated with ligand molecules which are able to interact specifically with antigens expressed over diseased cells (or target cells). The effect of particle shape, size and density on margination propensity is needed to be analyzed in order to find the optimal design. The second main application is to study cell separation in microchannel flow. The main focus is to gain inside in the separation of healthy and sick red blood cells due to their deformability and size on a microfluidic biochip platform. Separation of soft objects is of enormous relevance in medical and biological applications, since very often a loss in deformability comes along with diseases such as malaria, diabetes mellitus or cancer, just to name a few. Hence, a microfluidic system to sort or separate cells would be of tremendous importance for both diagnostic and dialysis applications.