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

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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.