Estimation of the Doppler ultrasound maximal umbilical waveform envelope: I. Estimation method

We developed a parametric method of estimating the Doppler ultrasound (US) umbilical maximal flow waveform envelope that is robust to varying levels of signal-to-noise ratio (SNR). The method differs from previously proposed estimation algorithms in that it does not incorporate preliminary removal or reduction of noise; thus, avoiding potential resulting biases. Instead, we relied on a multiple time series interpretation that facilitates a regression approach. The maximal waveform shape was assumed to take the form of a periodic series of gamma functions with a hidden baseline that is typically not reached on the downward diastolic phase before the flow increases to the systolic peak. The waveform shape is fitted via optimisation of the cross correlation of the Doppler signal and a periodic reference function locating the cardiac cycles within the blood flow image. Starting values for the iterative optimisation process were obtained using nonstandard least squares regression. Assessments of the fit of the model to waveform data were carried out through visual inspection. In 7 of 327 images analysed (2.1%), there appeared to be some discrepancy between the waveform shape and the gamma waveform envelope, such as variations in systolic or diastolic flows. Modification of the estimation procedure to incorporate blood flow cycles of slightly different lengths and use of other functional forms may improve the fit for waveforms for which the gamma fit is poor. The method has been developed with special reference to umbilical blood flow images, but it can be used directly to model blood flow in other low-resistance vessels or adapted for other vessels with different shape characteristics.