Extracting ventricular and atrial compliance and mitral impedance from Doppler inflow velocity and chamber pressures: inversion of a mitral flow model

A lumped parameter mathematical model of left ventricular filling applicable to analysis of Doppler mitral velocity inflow patterns has been developed. As originally formulated, the model utilizes user-provided chamber compliance and mitral impedance parameters and returns the time course of chamber pressure and mitral velocity and flow. The authors describe their initial experience with an algorithm to invert the model, i.e. to analyze observed pressure and flow data and extract the compliance and impedance parameters underlying the observed curves. This algorithm repeatedly solves the forward model, adjusting the physiologic parameters using the Marquardt method until the fit to the observed pressure and flow data is optimized. This algorithm was tested against computer-generated data with up to 10% Gaussian noise. It has also been validated with data from an in vitro analog of the left heart and from a canine model of mitral stenosis. Other possible inversion schemes, such as those which utilize only noninvasive data, are also discussed