Stable and unbiased flow turbulence estimation from pulse echo ultrasound

A new method for stable and unbiased flow turbulence estimation has been developed for medical ultrasonic color flow imaging. Conventional turbulence estimates from a finite number of transmitted pulses could be biased, unreliable, and erroneous. We found that a conventional method cannot provide quantitative estimates of variance of flow velocity. We propose a new approach for flow turbulence estimation that is based on analysis of the flow velocity vectors. The new method estimates the variance of the flow velocity and provides reliable estimates for flow turbulence. Numerical examples, computer simulations, and experiments using a flow phantom demonstrate that the new method can estimate variance of flow velocity accurately and without bias. This work also reports a complete derivation in the time domain for both unbiased velocity and turbulence estimations. The results include two velocity estimation equations agreeing with the 1-D and 2-D autocorrelation methods derived from the frequency domain. The results indicate that the new method for flow turbulence is particularly useful when the 2-D autocorrelation method is used for color flow imaging. The new method also appears to be able to detect low turbulence; therefore, it may be useful for diagnosing abnormalities such as minor stenoses and valvular jets.