A new maximum likelihood blood velocity estimator incorporating spatial and temporal correlation

The blood flow in the human cardiovascular system obeys the laws of fluid mechanics. Investigation of the flow properties reveals that a correlation exists between the velocity in time and space. The possible changes in velocity are limited, since the blood velocity has a continuous profile in time and space. This paper presents a new estimator (STC-MLE), which incorporates the correlation property. It is an expansion of the maximum likelihood estimator (MLE) developed by Ferrara et al. With the MLE a cross-correlation analysis between consecutive RF-lines on complex form is carried out for a range of possible velocities. In the new estimator an additional similarity investigation for each evaluated velocity and the available velocity estimates in a temporal (between frames) and spatial (within frames) neighborhood is performed. An a priori probability density term in the distribution of the observations gives a probability measure of the correlation between the velocities. Both the MLE and the STC-MLE have been evaluated on simulated and in-vivo RF-data obtained from the carotid artery. Using the MLE 4.1% of the estimates deviate significantly from the true velocities, when the performance is evaluated on the simulated data. These deviating estimates arise, as the search range in the correlation analysis exceeds one wavelength. By performing a similar investigation with the STC-MLE, no highly deviating estimates occur. The allowed search range is therefore larger with the STC-MLE. The performance evaluation on in-vivo data further reveals that the number of highly deviating velocity estimates in the tissue parts of the RF-signals are reduced with the STC-MLE. In general the resulting profiles are continuous and more consistent with the true velocity profile, and the introduction of the correlation property has improved the estimates.