Spatio-temporal mapping of intracardiac pressure gradients. A solution to Euler's equation from digital postprocessing of color Doppler M-mode echocardiograms

Doppler assessment of intracardiac pressure gradients using the simplified Bernoulli equation is inaccurate in the absence of a restricted orifice. The purpose of this study is to develop a new general method to map instantaneous pressure gradients inside the heart using Doppler echocardiography. Color Doppler M-mode recordings are digitally postprocessed with a software algorithm that decodes flow velocity and fits a bivariate spatio-temporal tensor-product smoothing spline. Temporal and spatial accelerations are then calculated by analytical derivation of the fitted velocity data, allowing solution of both inertial and convective terms of Euler's equation. A database of 39 transmitral inflow and transaortic outflow color Doppler M-mode recordings from 20 patients with a number of cardiac conditions was analysed, along with matched pulsed-wave spectral recordings. A close agreement was observed between the spectral and postprocessed color Doppler velocity values (error = 0.8 +/- 11.7 cm/s), validating the data decoding and fitting process. Spatio-temporal pressure-gradient maps were obtained from all studies, allowing visualisation of instantaneous pressure gradients from the atrium to the apex during left ventricular filling, and from the apex to the outflow tract during ejection. Instantaneous pressure differences between localised intracardiac sample points closely matched previously published catheterization findings, both in magnitude and waveform shape. Our method shows that intracardiac instantaneous pressure gradients can be analysed noninvasively using color Doppler M-mode echocardiography combined with image postprocessing methods.