Order and chaos in the flow of red blood cells

众所周知，在小的管子和毛细血管中，红细胞以一种非常规则的排列柱状流动，粘性应力使它们变形成子弹状。在较大的血管或管中，这种规律就失效了，在那里，细胞呈现出各种复杂的形状，并以不规则的、明显混乱的相互作用流动。这项工作将研究这种明显的分岔，导致不稳定和混沌运动的开始。它既是一种重要的流体力学不稳定性，具有生物物理意义，也是处理血细胞的微流体装置设计中的一个重要考虑因素。在这样的装置中形成和保持均匀的细胞行，将有助于在逐个细胞的基础上处理它们，用于诊断或过滤目的。智力优势：虽然流动红细胞在低雷诺数时的流体动力相互作用是线性的，但整个系统明显是非线性的。几何非线性与细胞的位置和他们的变形形状提出了分析的挑战。提出了一种系统的方法来开发一种描述，具有预测能力，特别关注导致流动红细胞柱不稳定的因素。一个高度精确的模拟工具将用于在复杂几何形状的管或血管中流动的相互作用和实际灵活的血细胞的集体运动。它是一种光谱边界积分解算器，已在最近的几项研究中使用，包括对小管中血流的基本分析，磁性纳米颗粒的靶向药物输送，以及作为炎症反应一部分的红细胞对白细胞的生物医学重要力量和运输效应。初步的模拟结果表明，排列流和明显的混沌流之间存在着分岔，这取决于血管直径和细胞体积分数。将进行分析工作来描述这种分歧。模拟将用于计算所有摄动自由度的线性相互作用，从而提供一个完整的线性动力学模型。这个线性系统将用标准的方法进行分析，如果必要的话，还可以用瞬态代数增长方法来描述小扰动的行为。一个刚性球体模拟更容易处理，并为所建议的工作提供了一个起点。本文还给出了一个初步结果。目标是在数学描述中推进理解，从而使简化的动力学描述可以用于预测生物和微流体工程重要性的现象。更广泛的影响：在流体力学、高级模拟、应用数学和生物物理学的交叉点上，这样的研究基本上是跨学科的，因此从教育的角度来看具有很高的价值。在这种特殊情况下，分析工具将转化为一种简化的描述，既可以阐明生物物理现象，又可以为微流体装置的分析和设计提供指导。PI将通过开发和分发用户友好的简化细胞相互作用模型来扩大这项工作对STEM的影响。这将与本科生研究助理合作完成，目标是实现基于模拟的生物微流体设计项目，以简化血细胞处理设备。

PI: Freund, Jonathan Proposal Number: 1336972 It is well-known that in small tubes and capillary vessels, red blood cells flow in a strikingly regular lined-up column, with viscous stresses deforming them into bullet-like shapes. This regularity fails in larger vessels or tubes, where the cells take on varied and intricate shapes and flow with irregular and apparently chaotic interactions. This work will investigate this apparent bifurcation, leading to the onset of instability and chaotic motion. It is both an important fluid mechanical instability, with biophysical implications, and an important consideration in the design of microfluidic devices that process blood cells. Forming and maintaining uniform rows of cells in such a device will facilitate processing them on a cell-by-cell basis for diagnostic or filtering purposes.Intellectual Merit :Although hydrodynamic interactions at the low Reynolds numbers of flowing red blood cells are linear, the overall system is significantly nonlinear. Geometric nonlinearities associated with the cell positions and their deformable shapes present analytical challenges. A systematic approach is proposed to develop a description, with predictive capability, focusing in particular on the factors leading to the destabilitization of flowing red blood cell columns. A highly accurate simulation tool will be used for the collective motion of interacting and realistically flexible blood cells flowing within complex-geometry tubes or vessels. It is a spectral boundary integral solver, which has been used in several recent studies, including the fundamental analysis of blood flow in small tubes, the transport of magnetic nanoparticles for targeted drug delivery, and the biomedically important forces and transport effects of red blood cells on white blood cells as part of the inflammation response. Preliminary simulation results suggest the existence of a bifurcation between the lined-up flow and the apparently chaotic flow, which depends upon vessel diameter and cell volume fraction. Analytical work to describe the bifurcation will be pursued. The simulation will be used to calculate the linear interaction of all perturbation degrees of freedom and thereby will provide a complete linear dynamic model. This linear system will be analyzed with standard and, if necessary, transient algebraic growth methods to describe the behavior of small perturbations. A rigid-sphere analog is much more tractable and provides a starting-point for the proposed effort. An initial result for this is also presented. A goal is to advance understanding within a mathematical description to the point that a reduced dynamical description can then be used to predict phenomena of biological and microfluidic engineering importance.Broader Impacts :Studies such as this at the juncture of fluid mechanics, advanced simulation, applied mathematics, and biophysics are fundamentally interdisciplinary and therefore of high value from an educational perspective. In this particular case the analytical tools will translate into a reduced description that can both illuminate biophysical phenomena and provide guidance for the analysis and design of microfluidic devices. The PI will broaden the STEM impact of this work via the development and distribution of a user-friendly reduced model of cell interactions. This will be done in collaboration with undergraduate research assistants, and with the goal to enable simulation-based bio-microfluidic design projects for simplified blood-cell-handling devices.