A theoretical description of blood flow through the mitral orifice

A nonlinear differential equation describing the Doppler velocity profile for blood flow through the mitral valve has been derived. This equation is based on fluid dynamics and a simple, but comprehensive model of atrial and ventricular mechanics. A numerical solution to the equation is described and provides excellent agreement with Doppler velocity curves obtained clinically. One important result of the theory is that in patients with mitral stenosis, the slope of the clinically observed straight-line descent of the velocity profile is proportional to the mitral orifice area and inversely proportional to the atrioventricular compliance.