Some theoretical aspects of quantification of mitral valve regurgitation by the indicator-dilution method; sufficient and insufficient experiments.

Abstract

A theoretical analysis of indicator-dilution curves produced by a pulsatile, two-chamber mathematical model simulating a normal in vivo heart and one with atrioventricular valve regurgitation is presented. A set of difference equations is developed expressing the concentrations within the chambers at the end of each cycle in terms of the number of cycles or beats. It is shown theoretically that the downstroke slope of the dilution curve is insensitive to the extent of regurgitation. Solution of the difference equations for the parameters of the heart governing the curve (chamber volumes, forward output, and regurgitant flow), when the dilution curve is sampled from the chamber in which the injection is made, is achieved through a system of four equations in four unknowns. Sampling of the concentration curve from the chamber which does not receive the injection produces a theoretical curve giving three equations in four unknowns and results in an indeterminate solution. As a consequence, quantification of atrioventricular valve regurgitation through analysis of a single distal indicator-dilution curve following proximal injection cannot be accomplished.