Estimation of the blood velocity spectrum using a recursive lattice filter

In medical ultrasound the blood velocity distribution in a vessel can be found by emitting a pulsed field into the patient. The field is then scattered by the tissues and the red blood cells, and a single complex sample set is acquired at the depth of interest for each pulse emitted. The signals acquired for showing the blood velocity distribution are inherently non-stationary, due to the pulsatility of the flow. All current signal processing schemes assume that the signal is stationary within the window of analysis, although this is an approximation. In this paper a recursive least-squares lattice filter is used for finding a parametric model for the velocity distribution. A new set of complex coefficients is calculated for each point in time, and it is thus possible to track the non-stationary properties of the stochastic velocity signal. The dynamic characteristics of the non-stationarity are incorporated through an exponential decay factor, that sets the exponential horizon of the filter. A factor close to 1 gives a long horizon with low variance estimates, but can not track a highly non-stationary flow. Setting the factor is therefore a compromise between estimate variance and the filter's dynamic adaptation. Using a lattice filter gives a structure that is easy and robust, when implemented with fixed point arithmetic. The procedure has been tested on both simulated and in-vivo data, and gives spectral estimates quite different from the normal FFT approach. Synthetic data were generated based on the measured time evolution of the spatial mean velocity in the femoral artery. The smooth theoretical velocity distribution is then known and can be compared to the estimated distribution. Using 8 parameters a very smooth estimate of the velocity distribution is seen, more in line with the actual distributions that always will be smooth. Setting the exponential decay factor to 0.99 gives satisfactory results for in-vivo data from the carotid artery. The filter can easily be implemented using a standard fixed-point signal processing chip for real-time processing