On the variance of mean integrated backscatter from moving blood

This work evaluates the variance of the integrated backscatter. (IBS) of the received ultrasound signal from moving blood, as a measure of the quality of the mean IBS estimate. The paper formulates how the measurement parameters should be specified so that an appropriately low variance is ensured for the IBS estimate. We provide first an analytic formulation of the statistics of the IBS, based on a sequence of sampled backscattered signals from moving blood. The analysis incorporates the degree of correlation among the samples of the RF signal and among the IBS of individual backscattered signals, based on which the number of measurements required to obtain an IBS estimate with a specified variance is readily calculated. The analytical model is then evaluated on a sequence of synthetically generated backscatter echoes as well as on a sequence of experimentally acquired echoes from circulating blood-mimicking fluid. For both sequences, the actual variance of the mean IBS estimate for the echoes was found to be in a good agreement with the variance determined from the analytic model.