Doppler power spectrum from a Gaussian sample volume

A closed-form expression for the Doppler power spectrum due solely to the r ange of blood velocities passing through a Gaussian sample volume placed an ywhere in a vessel under conditions of axisymmetric flow, uniform backscatt er and negligible intrinsic spectral broadening has been derived. The formu lation presented here allows the independent specification of the sample vo lume position and width, in the three dimensions, and enables simple estima tions of spectral shape for pulsed wave Doppler systems. Simpler expression s were derived for the cases of symmetric sample volume projections onto th e vessel cross-section and/or sample volumes centred in the vessel. Closed form expressions were derived for mean frequency and spectral width in the case of a symmetric sample volume projection centred in the vessel. The eff ects of sample volume size and position on the Doppler spectral width and m ean frequency are shown for a range of velocity profiles. (C) 2000 Elsevier Science B.V. All rights reserved.