The effects of beam shape on the ability to predict changes in vessel size from Doppler signal power

Theory suggests that, under certain ideal circumstances, the power of a Doppler signal is proportional to the size of the vessel from which it is recorded and can, therefore, be used to assess the scale of any changes in vessel size that occur during clinical recordings of cerebral blood flow. However, the relationship between signal power and vessel size depends on the intensity of the incident beam being uniform across the vessel. This is unlikely to be the case for cerebral vessels insonated by commercial transducers. A model was used to estimate the signal power received from vessels insonated by a beam passing through a homogeneous medium, and also by beams passing through each of five samples of temporal bone. In each case, the effects of initial vessel size and various changes in cross-sectional area were investigated for different vessel positions in the beam. The results for the beam paths through bone predict that the power change arising from a change in vessel cross-sectional area is between 5% and 75% smaller than that occurring in a uniform beam. If these results are representative of those arising for an in vivo change in middle cerebral artery size, then the potential magnitude of the error illustrates the caution that may need to be applied when interpreting changes in Doppler signal power.