A theoretical model for the noninvasive assessment of the transmitral pressure-flow relation

The purpose of this paper is to formulate from the equations of fluid mechanics an equation which describes the transmitral pressure-flow relationship. According to the linear momentum equation applied to the atrioventricular coupling, the left-atrium-left-ventricle pressure difference (Pa-Pv) can be written as Pa-P v = A delta v/delta t + B v 2 + C v, where v is the transmitral blood velocity and A, B, and C are variables related to the geometry of the atrium, ventricle and mitral orifice, respectively. Based on this theory, Pa-Pv is calculated noninvasively in a patient with a nonobstructive mitral valve. Mitral flow and cardiac dimensions recorded by Doppler echocardiography are digitized and analyzed. Calculation shows that Pa-Pv reaches its peak value at the time of flow peak acceleration and has already considerably decreased at the time of peak velocity. The time course of calculated Pa-Pv is in close agreement with the published experimental catherization data. Numerical computation of early diastolic left atrium and left ventricle pressure curves based on the experimental data of others for the time constant of left ventricular relaxation, left atrial and ventricular chambers stiffness constants, combined with sine-waveform-simulated mitral flow, verifies the time course and the magnitude of Pa-Pv as predicted from flow equations. This paper provides a theoretical method for the noninvasive assessment of the transmitral pressure-flow relationship using ultrasound technique and might help to achieve a better understanding of the diastolic function as assessed by Doppler echocardiography.