The two-dimensional model, in fact, led to a patent on such a valve. It was the advent of the NSF supercomputer centers, Peskin says, that permitted his group to extend their computations from two to three dimensions. The calculation and examination of a single heartbeat in the present 3D model has taken approximately one week of CPU time on a single PSC C90 processor. When the code was parallelized recently to use all 16 processors, Peskin and McQueen obtained a speedup of a factor of 10. The group is currently reorganizing the code to take advantage of domain decomposition methods and to make use of the powerful IBM SP-2, Cray T3D, and similar machines.
Clot formation is, in fact, the chief risk associated with artificial heart valves.
High resolution, made possible by supercomputers, is important to this work on the heart, Peskin points out. Even so, this grid is barely adequate. Fortunately, the flow pattern of blood in the heart is not very sensitive to the Reynolds number, and improvements in numerical methodology, such as local mesh refinement near boundaries or the use of entirely grid-free methods, may make it possible to avoid the extreme computational requirements implied by such a refinement of a uniform grid. Increased computer power is needed not only to do the current computation more correctly, but also to bring in additional phenomena that are highly relevant to blood flow in the heart. Two examples of such phenomena are the electrical activity that coordinates and controls the heartbeat and the dynamics of the blood clotting process, which is important in evaluating the function of prosthetic cardiac valves.