A unified approach to modeling the backscattered Doppler ultrasound from blood

A unified approach to modeling the backscattered Doppler ultrasound signal from blood is presented. The approach consists of summing the contributions from elemental acoustic voxels, each containing many red blood cells (RBCs). For an insonified region that is large compared to a wavelength, it is shown that the Doppler signal is a Gaussian random process that arises from fluctuation scattering, which implies that the backscattered power is proportional to the variance of local RBC concentrations. As a result, some common misconceptions about the relationship between the backscattering coefficient and hematocrit can be readily resolved. The unified approach was also used to derive a Doppler signal simulation model which shows that, regardless of flow condition, the power in the Doppler frequency spectrum is governed by the exponential distribution. For finite beamwidth and paraxial flow, it is further shown that the digitized Doppler signal can be modeled by a moving average random process whose order is determined by the signal sampling rate as well as the flow velocity profile.