Mathematical anatomy, or numerical equations, can explain the collagen fiber architecture of the human heart. This can help understand how the heart functions and in the treatment of disease. In the video below, Charles Peskin of New York University explains the underlying math of the structure and function of the heart. In the aortic and pulmonic valves of the heart, collagen fibers form a branching braided “hammock-like” structure, which exhibits fractal properties. The numerical equations used to define this can help study the architecture and dynamics of the heart and its valves—which in turn aids in understanding and treating diseases.
By formulating partial differential equations for a system of fibers under tension, Peskin’s group explores how these equations can predict the observed fiber architecture of the heart and its valves.
In the IB model heart, all mathematical fibers are immersed or embedded in a fluid. This creates a fiber-reinforced fluid that has mass, volume, and incompressibility. The stress/strain relationship of the muscle fibers is nonlinear and time-dependent—the muscles exhibit much higher stiffness during systole, or the contraction phase of the heart, than in diastole, the relaxation phase. This time dependence drives the model heart through the cardiac cycle, which helps one study heart dynamics
More about Beating in Fluid:
Beating in Fluid: Cilia and Biological Structures
Beating in Fluid: Hearts and Cilia by the Immersed Boundary Method