A three-dimensional computer model of the human heart for studying cardiac fluid dynamics

In all areas of computational fluid dynamics (CFD), proper treatment of the boundary conditions is essential to computing fluid behavior correctly. In many engineering problems, CFD is simplified by a priori knowledge of the motion of the boundary. The well-known parabolic velocity profile in fully-developed flow of an incompressible Newtonian fluid in a pipe of circular cross-section is easily computed because the boundary (the pipe wall) is known to be in a fixed location. Even in more complex settings, such as flow around a ship's propeller, the motion of the boundary (the propeller) can be specified in advance. By contrast, in most biological fluid dynamics problems the boundaries are not rigid and their motions are the result of forces imposed on them by the motion of the surrounding fluid. The motion of the fluid, of course, cannot be known without knowledge of the boundary motion. The motion of the boundary and the motion of the fluid form a coupled system; both motions must be computed simultaneously, which makes biological CFD difficult. A particular problem of interest is the flow of blood in the chambers of the human heart. The heart is an organ whose muscular contractions pump blood around the body. Simplifying somewhat, the heart consists of two main pumping chambers that contract simultaneously. One chamber, the left ventricle, accepts oxygen-enriched blood from the lungs and pumps it to the body. The other chamber, the right ventricle, accepts oxygen-depleted blood from the body and pumps it to the lungs. The inlet and outlet of each ventricle are guarded by valves whose opening and closing guarantee one-directional flow around the circulatory system. There are a total of four valves. The valves generally consist of two or three leaflets - membranes made of very flexible but inextensible material. Familiar examples of materials with this property would be paper or fabric which can be easily bent or twisted but which are not easily stretched. One edge of each valve leaflet is securely attached to the wall of the heart, but the other edge is free of attachment and can move with the flow. Structures analogous to a valve leaflet are a shirt pocket, with one edge (three sides of a rectangular patch pocket) securely stitched to the shirt and one edge free of attachment, or a flag, one edge attached to the flag pole, the other edge free to wave in the wind. When flow is passing through the valve in the forward direction, the valve's leaflets are po