Frequency dependence of speckle in continuous-wave ultrasound with implications for blood perfusion measurements

Speckle in continuous wave (CW) Doppler has previously been found to cause large variations in detected Doppler power in blood perfusion measurements, where a large number of blood vessels are present in the sample volume. This artifact can be suppressed by using a number of simultaneously transmitted frequencies and averaging the detected signals. To optimize the strategy, statistical properties of speckle in CW ultrasound need to be known. This paper presents analysis of the frequency separation necessary to obtain independent values of the received power for CW ultrasound using a simplified mathematical model for insonation of a static, lossless, statistically homogeneous, weakly scattering medium. Specifically, the autocovariance function for received power is derived, which functionally is the square of the (deterministic) autocorrelation function of the effective sample volumes produced by the transducer pair for varying frequencies, at least if a delta correlated medium is assumed. A marginal broadening of the modeled autocovariance functions is expected for insonation of blood. The theory is applicable to any transducer aperture, but has been experimentally verified here with 5-MHz, 6.35-mm circular transducers using an agar phantom containing small, randomly dispersed glass particles. A similar experimental verification of a transducer used in multiple-frequency blood perfusion measurements shows that the model proposed in this paper is plausible for explaining the decorrelation between different channels in such a measurement.