A mathematical basis for the application of the modified geometric method to maximum frequency estimation

The application of ultrasound in assessing the fetal cardiovascular system often requires the accurate estimation of maximum blood flow velocity waveforms using Doppler measurements. The modified geometric method estimates the maximum Doppler frequency as the frequency at which the vertical distance between the integrated spectrum and the reference line that connects the origin to the maximum value of the integrated spectrum is the largest. This paper presents a mathematical formulation for a class of maximum blood flow velocity estimation algorithms that includes the modified geometric method. The analysis provides a rationale for the continued use of the modified geometric method for estimating the maximum frequency envelopes of Doppler signals. This paper also contains experimental results demonstrating the superiority of the modified geometric method over a commonly used threshold crossing method.