Mathematical modeling of flow-generated forces in an in vitro system of cardiac valve development

Heart valve defects are the most common cardiac defects. Therefore, defining the mechanisms of cardiac valve development is critical to our understanding and treatment of these disorders. At early stages of embryonic cardiac development, the heart begins as a simple tube that then becomes constricted into separate atrial and ventricular regions by the formation of small, mound-like structures, called atrioventricular (AV) cushions. As valve development continues, these mounds fuse and then elongate into valve leaflets. A longstanding hypothesis proposes that blood flow-generated shear stress and pressure are critical in shaping the cushions into leaflets. Here we show results from a two-dimensional mathematical model that simulates the forces created by blood flow present in a developing chick heart and in our in vitro, tubular model system. The model was then used to predict flow patterns and the resulting forces in the in vitro system. The model indicated that forces associated with shear stress and pressure have comparable orders of magnitude and collectively produce a rotational profile around the cushion in the direction of flow and leaflet growth. Further, it was concluded that the replication of these forces on a cushion implanted in our tubular in vitro system is possible. Overall, the two-dimensional, mathematical model provides insight into the forces that occur during early cardiac valve elongation.