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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=742867
• 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.

我建议探讨生物流体力学中的问题，其中流体流动与其他生物或物理过程相互作用。我的目标是通过分析和计算方法的结合，对这些复杂的流动有更深入的了解，并发现新的见解。感兴趣的问题分为两个主题：（一）流体-结构相互作用，涉及可变形，弹性结构沉浸在不可压缩流体。其应用包括海洋蠕虫和水母等活跃游泳者的悬浮液;以及充满液体的耳蜗（或内耳）的生物力学。(II)微结构多孔介质中的多相流动与输运。主要重点是研究树木中的液流以及与营养物质运输和其他生物物理过程的耦合，更具体地说，是冻融过程驱动糖槭的汁液渗出。另一个影响更广泛的树种的相关问题是冻结诱导栓塞。这两个主题包含了看似多样化的物理和生物现象，但有一些共同的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;* 解决方案的特点是内部和边界层以及空间尺度的明确分离，这自然得益于多尺度分析和自适应数值方法的应用;和 * 广泛变化的时间尺度，引起数值刚度，这需要使用隐式时间步进算法。我对所有这些问题都采用了类似的解决方法：（1）基于仔细的生物和物理推理推导出详细的数学模型;（2）采用分析技术，如渐近性、线性稳定性和周期均匀化来简化控制方程并获得对解行为的洞察;以及（3）开发精确和有效的数值方案，使得能够进行广泛的参数研究以针对分析解和实验数据来验证模型。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，其中对解决方案的数学结构的洞察被用来对数值方法做出明智的决定。这项工作将产生重大影响，在新的算法来解决复杂的生物流体动力学问题，以及推进多物理和多尺度流动现象的知识。例如，对活性细胞结构和内耳耳蜗液之间相互作用的研究应该有助于提高对哺乳动物听力机制的理解。此外，对枫树液流细胞过程多尺度性质的新见解将导致树木生理学的进步，以及提高枫糖浆行业的树液产量。