Estimation of blood flow using Doppler ultrasound with a narrow beam.

Estimation of mean spatial blood velocity, and hence volumetric flow, using Doppler ultrasound is typically performed under the assumption that the beam samples each part of the cross section of the blood vessel equally. This allows the mean velocity to be regarded as being proportional to the conventional mean Doppler shift frequency. In this work a new frequency estimator of mean velocity is presented for the case where the beam is assumed to be of negligible width compared to the vessel diameter and directed through the vessel axis. This estimator is proportional to the mean velocity if it can be further assumed that the velocity profile is axi-symmetric and is monotonic, or has an idealised bidirectional form. In practice neither the assumption of a uniformly insonating beam nor the assumption of an infinitely narrow beam are valid. Also the Doppler spectrum, as a representation of the velocity distribution of blood cells, is corrupted by spectral broadening, noise, filtering and the stochastic nature of the signal. In addition difficulty exists in the measurement of the representative Doppler angle. The effects on both estimators of these potential sources of error are discussed and compared. The question of volumetric flow measurement at various arterial sites is addressed by modelling the velocity profiles in the vessel throughout the cardiac cycle. Some sources of error affect only the new estimator, so one conclusion drawn is that mean velocity estimation and volumetric flow measurement are better performed using the conventional frequency with a uniformly insonating beam. Nevertheless if the beam is more accurately described as being very narrow and centrally positioned the new estimator performs better than the conventional frequency estimator. This description may well be appropriate if the blood vessels are large and the Doppler beam is transmitted and received using a linear array transducer such as in modern duplex systems.