A Stochastic Model of the Backscattered Doppler Ultrasound from Blood

A stochastic model of the continuous wave (CW) Doppler ultrasound signal backscattered from blood is developed. The model incorporates the effects due to the flow-dependent packing and aggregation of red blood cells (RBC´s) at a given hematocrit. The Doppler signal is shown to be a zero-mean, stationary, Gaussian random process which can be completely specified by its autocorrelation function. From the autocorrelation function, explicit closed-form expressions are derived for the power spectral density and the backscattering coefficient. Both expressions are found to be more general than those derived from previous blood models. Further, the values of the statistical parameters in the model are discussed in relation to recently published data on the backscattering coefficient of bovine RBC´s suspended in saline and of bovine whole blood. It is shown that the change in backscatter with flow conditions can be explained by RBC orientation in saline and by RBC aggregation in whole blood.