FRG:Collaborative Research: Chemically-active Viscoelastic Mixture Models in Physiology: Formulation, Analysis, and Computation

这个项目涉及几个复杂生物过程的数学模型的开发和分析，每个过程都对基础和健康科学具有重要意义：细胞起泡及其通过细胞外基质在细胞运动中的作用，动脉血凝血中的血小板沉积和纤维蛋白凝胶，粘蛋白分泌及其在胃中酸运输中的作用，蛋白质的分类和高尔基体的运输。尽管这些过程的生物学细节截然不同，但一个共同的主题是，每个过程都涉及一种复杂的粘弹性材料混合物，其行为由力学、流动、物理结构和化学的动态相互作用决定。这些过程的数学描述需要描述多相流、成分、结构和化学的演变以及应力和成分/结构之间的关系的方程。结合这些因素的复杂模型的求解和分析将带来巨大的数学和计算挑战。为了应对这些挑战，研究人员将开发和应用先进的数值算法，以获得对这些重要生理过程的作用机制的基本见解。这项工作将导致在理解复杂材料的力学和动力学在生物系统功能中的基本作用方面取得新的和重要的进展。反过来，这将支持改进一系列严重医疗疾病的诊断和治疗，包括冠状动脉疾病、癌症和代谢性疾病。这项工作还将使人们更好地了解复杂材料，并有助于设计新的新材料，以应对紧迫的技术挑战。此外，新计算算法的设计将导致在科学和工程中使用高性能计算的新能力。该项目的高度跨学科性质将为培训年轻科学家掌握新的多学科科学方法提供许多机会。许多重要的生理过程涉及不同类型的材料之间的相互作用(例如，水与细胞或水与聚合物凝胶)，这些材料彼此相对运动。材料之间的物理相互作用会受到化学反应的强烈影响，而化学反应又会受到材料运动和其他相互作用的影响。更好地了解这种复杂的系统是如何工作和受到监管的，对于理解这些重要的过程以及如何操纵它们以改善人类健康至关重要。因为这些过程受物理和化学原理和性质的支配，而且这些原理和性质可以用数学来表示，所以可以用数学工具来处理这些问题。通过数学分析和计算模拟，可以发展对材料行为的新见解，并可以获得丰富的数据，补充从传统实验室实验获得的数据。因此，数学和实验研究人员在这个项目中的结合有望在重要的生理和病理情况下带来重要的新见解，包括血液凝结、新陈代谢和癌症转移。此外，该项目开发的数学和计算工具将影响非生物复合材料的发展，以应对紧迫的技术挑战。

This project concerns development and analysis of mathematical models of several complex biological processes, each with major importance to the fundamental and health sciences: cellular blebbing and its role in cellular locomotion through extracellular matrix, platelet deposition and fibrin gelation in arterial blood clotting, mucin secretion and its role in acid transport in the stomach, protein sorting and trafficking by the Golgi apparatus. Although the details of the biology of these processes are vastly different, a common theme is that each involves a complex viscoelastic material mixture whose behavior is determined by the dynamic interplay of mechanics, flow, physical structure, and chemistry. The mathematical description of these processes requires equations describing multiphase flow, the evolution of composition, structure and chemistry, and the relationship between stresses and composition/structure. The solution and analysis of sophisticated models that combine these elements will pose substantial mathematical and computational challenges. To meet these challenges, the investigators will develop and apply advanced numerical algorithms to gain fundamental insights into the mechanisms of function of these important physiological processes. This work will lead to novel and important advances in understanding the essential role of the mechanics and dynamics of complex materials in the function of biological systems. This, in turn, will support improved diagnosis and treatment of a range of serious medical disorders including coronary artery disease, cancer, and metabolic disease. The work will also lead to better understanding of complex materials in general and contribute to the design of novel new materials for meeting pressing technological challenges. Furthermore, the design of new computational algorithms will lead to new capabilities in the use of high-performance computing in science and engineering. The highly interdisciplinary nature of the project will provide many opportunities for training young scientists in the new multi-disciplinary approach to science.Many important physiological processes involve interactions between materials of different types (for example, water and cells or water and polymer gels) and which move relative to one another. The physical interactions between the materials can be strongly influenced by chemical reactions, and the chemical reactions in turn are influenced by the materials' motion and other interactions. Better insight into how such complex systems work and are regulated is critical to understanding these important processes and how they can be manipulated to improve human health. Because these processes are governed by physical and chemical principles and properties, and because these principles and properties can be expressed mathematically, mathematical tools can be brought to bear on these problems. Through mathematical analysis and computational simulations, new insights into the materials' behavior can be developed and a wealth of data can be obtained that complements the data obtainable from traditional laboratory experiments. Hence the combination of mathematical and experimental investigators brought together in this project is expected to lead to significant new insights in important physiological and pathological situations including blood clotting, metabolism, and cancer metastasis. Further the mathematics and computational tools developed in the project will impact the development of non-biological complex materials to meet pressing technological challenges.