An analytical model of the Doppler spectrum for peak blood velocity detection

Ultrasound echo-Doppler techniques play a major role in the diagnostics of the human circulatory system. In an echo-Doppler exam the scatterers´ velocity distribution is assessed by insonating the blood particles with ultrasound bursts and by evaluating the Doppler shift from the spectrum of the backscattered signal. In particular, the maximum blood velocity is a parameter of high medical interest, and several methods have been proposed so far for its measurement from the Doppler spectrum. Unfortunately, they are approximate and based on heuristic power thresholds that are inaccurate and strongly affected by noise. Recently a mathematical model of the Doppler spectrum has been proposed which represents a solid base to calculate the threshold to be applied for accurate maximum velocity detection. This model is based on the summation of the pulses produced by quantized “shells” of flow where the velocity is considered constant. In this work we extend this model by using a continuous approach that allows obtaining an analytical expression for such a threshold. The proposed model confirms and reinforces the results produced by the original approach, and can be exploited for an accurate detection of the maximum blood velocity.