Response of blood flow entering the heart to dissynchronous ventricular recoil

Abstract

To account for mechanical suction at the initiation of the cardiac filling process, we have previously modeled transmitral blood flow driven by synchronous ventricular recoil in terms of a one-dimensional simple harmonic oscillator (SHO) in the Parametrized Diastolic Filling (PDF) formalism. PDF model predictions of blood flow velocity have shown excellent agreement with the diastolic Doppler velocity profile (DVP), the echocardiographically measured blood flow velocity of filling. However, dissynchrony of the cardiac recoil process, defined by the early or late recoil of one region relative to the rest of the ventricle, is known to exist in-vitro and has been observed in-vivo. To model dissynchronous recoil and mathematically explore the range of model predicted blood flow velocity responses, we have developed a new model. Our two-dimensional model utilizes two second order constant coefficient linear differential equations, whose solutions combine to form v( t), the new model's prediction of blood flow velocity. The differential equations are solved as initial value problems with zero initial velocities, unknown initial displacements and unknown damping and spring constants. For a given data set (DVP) we solve the ‘inverse problem’ and determine initial oscillator displacements and parameters iteratively by graphical comparison of v( t) to the DVP contour. We discuss the kinematic features of this refined model, its testable predictions, and provide evidence for its validity by comparison of v( t) to the clinical DVP in a case of known dissynchrony. We comment on the benefits and limitations of this modeling approach.