Statistical bias and variance in blood flow estimation by spectral analysis of Doppler signals

The stochastic nature of the Doppler signal is discussed as a source of variability and bias in estimation of mean blood velocity and flow performed using the Discrete or Fast-Fourier Transform. The estimators studied are those appropriate when the ultrasound beam is assumed to be wide enough to insonate the cross-section of the vessel uniformly, and assumed to be narrow enough to insonate only a diameter. Approximate expressions are derived theoretically for the biases and variances of these statistics when the Doppler power spectrum is uniform. For more complex spectra numerical evaluation is carried out by computer. Results for the double-sided spectra obtained from mixed flow are inferred from the single-sided cases. Typically, an estimate of instantaneous mean velocity has very little bias added (< 1%) but might have a standard error of approximately 10% of its mean value, and an estimate of flow in one cardiac cycle a standard error of approximately 1% of its mean value.