The investigator undertakes modeling and computational simulation of platelet aggregation and coagulation. These are the components of normal blood clotting and of the life-threatening blood clots associated with vascular disease and with the use of cardiovascular prostheses. The investigator and coworkers continue to explore and refine their models of platelet aggregation in small and large diameter vessels; continue development of models of coagulation including the effects of flow, transport, and surface reactions; and integrate the platelet aggregation and coagulation models to form a more comprehensive model of the hemostatic and thrombotic processes. These models use coupled systems of nonlinear partial and ordinary differential equations to describe interactions between the blood's fluid dynamics, the transport of platelets and chemicals in the blood plasma, the mechanics and chemistry of developing aggregates, and the solution-phase and surface-bound biochemistry of the coagulation process. The models present substantial computational challenges that require development and use of state-of-the-art numerical methods for their solution. These include immersed boundary methods for fluid-material interactions, high-resolution finite-difference methods combined with Fourier-collocation spectral methods, immersed-interface methods for handling transport in regions of complex geometry, and parallel computation. This work involves extensive comparisons between computational results and laboratory experiments and is aided by collaboration with leading experts on flow and thrombosis. The proposal is also concerned with developing state-of-the-art parallel computational methods for simulating biofluid dynamic flows like those involved in aggregation and coagulation, and with including these computational tools in a powerful and easy-to-use problem solving environment that facilitates solving a wide range of complex biofluid dynamic problems. Thrombosis, which is the formation of blood clots within vessels of the circulatory system, is the proximal cause of most heart attacks and of other severe cardiovascular problems such as ischemia and angina. It is also a major problem associated with the use of blood-contacting prostheses such as mechanical heart valves. The process by which these blood clots form is very complex and involves many dynamic, sometimes competing, sometimes mutually-reinforcing, biophysical and biochemical processes. A major part of this project involves developing powerful mathematical and computational tools for studying this complex process, and using these tools to probe the factors that effect the location, extent, and speed of formation of thrombi. Computational modeling complements traditional experimental approaches and provides a way to simulate complex dynamic events, like the dynamic interactions among fluid, blood cells, clotting factors, and blood vessel or prosthesis surface that lead to thrombosis, that are beyond the reach of current laboratory techniques. Such simulations can give new insights into the basic mechanisms that control this important biological process, and can ultimately help in the more rational design of therapeutic interventions and prosthetic devices. Many other challenging biological and biomedical flow problems have features in common with that of simulating thrombosis, and so the state-of-the-art parallel computational methods developed for this project potentially have wide-spread application to problems important to basic science, health care, and biotechnology. To help realize this potential the investigators develop and disseminate an easy-to-use software package that facilitates using these computational methods to set up and carry out simulations of important biofluid dynamics problems.
