Modelling and simulation of biofluid mechanics with multiphysics and multiple scales

多物理场、多尺度生物流体力学建模与仿真

• 批准号: RGPIN-2021-04088
• 负责人: Stockie, John
• 金额: $ 4.32万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758585
• 关键词: Modelling; simulation; biofluid; mechanics; multiphysics

I propose to explore problems in biofluid mechanics where the fluid flow interacts with other biological or physical processes. My aim is to develop a deeper understanding of these complex flows and uncover new insights through a combination of analytical and computational methods. The problems of interest fall under two themes: (I) Fluid-structure interaction involving deformable, elastic structures immersed in incompressible fluids. Applications include suspensions of active swimmers such as marine worms and jellyfish; and biomechanics of the fluid-filled cochlea (or inner ear). (II) Multiphase flow and transport in micro-structured porous media. The primary focus is on the study of sap flow in trees and the coupling with nutrient transport and other bio-physical processes, more specifically the freeze-thaw process that drives sap exudation in sugar maple. Another related problem that impacts a much wider range of tree species is freeze-induced embolism.  These two themes comprise a seemingly diverse collection of physical and biological phenomena, but a few common features unify our modelling and computational approaches: * dynamics are governed by nonlinear systems of partial differential equations with strongly-coupled solution components; * solutions are characterized by interior and boundary layers and a clear separation of spatial scales, which naturally benefit from the application of multiscale analysis and adaptive numerical methods; and * widely varying time scales that give rise to numerical stiffness, and which require the use of implicit time-stepping algorithms. I apply a similar solution methodology to all of these problems: (1) deriving a detailed mathematical model based on careful biological and physical reasoning; (2) employing analytical techniques such as asymptotics, linear stability, and periodic homogenization to simplify the governing equations and obtain insight into solution behavior; and (3) developing accurate and efficient numerical schemes that enable extensive parameter studies to validate the model against analytical solutions and experimental data. A defining characteristic of this proposal is the tight interplay between mathematical analysis and algorithm development, where insight into the mathematical structure of solutions is exploited to make informed decisions on numerical methods. This work will have significant impact in terms of novel algorithms for solving complex problems in biofluid dynamics, as well as advancing knowledge of multi-physics and multiscale flow phenomena. For example, studies of interactions between active cell structures and cochlear fluid in the inner ear should lead to improved understanding of mammalian hearing mechanisms. Moreover, new insights into the multiscale nature of cellular processes governing sap flow in maple trees will lead to advances in tree physiology as well as improving sap yields in the maple syrup industry.

我建议探索生物流体力学中流体流动与其他生物或物理过程相互作用的问题，我的目标是深入了解这些复杂的流动，并通过分析和计算方法的结合发现新的见解。分为两个主题：(I) 涉及浸没在不可压缩流体中的流固相互作用可变形弹性结构，应用包括海洋蠕虫和水母等活跃游泳者的悬浮以及生物力学。充满液体的耳蜗（或内耳）。（II）微结构多孔介质中的多相流和传输主要重点是研究树木的液流以及与养分传输和其他生物物理过程的耦合。特别是导致糖枫树液渗出的冻融过程，影响更广泛树种的另一个相关问题是冷冻引起的栓塞，这两个主题包含看似不同的物理和生物现象。但一些共同特征统一了我们的建模和计算方法： * 动力学由具有强耦合解分量的偏微分方程的非线性系统控制 * 解的特征在于内部层和边界层以及空间尺度的清晰分离，这自然有益于来自多尺度分析和自适应数值方法的应用；以及 * 产生数值刚度的广泛变化的时间尺度，并且需要使用隐式时间步进算法来解决所有这些问题： (1) 基于仔细的生物学和物理推理推导详细的数学模型；(2) 采用渐近、线性稳定性和周期性均质化等分析技术来简化控制方程并深入了解解的行为；(3) 开发精确的数学模型。和有效的数值方案，使广泛的参数研究能够根据解析解和实验数据验证模型，该提案的一个定义特征是数学分析和算法开发之间的紧密相互作用，其中利用对解的数学结构的洞察来实现。这项工作将对解决生物流体动力学中的复杂问题的新颖算法以及推进多物理和多尺度流动现象的知识产生重大影响，例如，活性细胞结构之间相互作用的研究。此外，对控制枫树液流的细胞过程的多尺度性质的新见解将促进树木生理学的进步并改善。枫糖浆行业的汁液产量。