Quantification of intravoxel velocity standard deviation and turbulence intensity by generalizing phase-contrast MRI

Turbulent flow, characterized by velocity fluctuations, is a contributing factor to the pathogenesis of several cardiovascular diseases. A clinical noninvasive tool for assessing turbulence is lacking, however. It is well known that the occurrence of multiple spin velocities within a voxel during the influence of a magnetic gradient moment causes signal loss in phase-contrast magnetic resonance imaging (PC-MRI). In this paper a mathematical derivation of an expression for computing the standard deviation (SD) of the blood flow velocity distribution within a voxel is presented. The SD is obtained from the magnitude of PC-MRI signals acquired with different first gradient moments. By exploiting the relation between the SD and turbulence intensity (TI), this method allows for quantitative studies of turbulence. For validation, the TI in an in vitro flow phantom was quantified, and the results compared favorably with previously published laser Doppler anemometry (LDA) results. This method has the potential to become an important tool for the noninvasive assessment of turbulence in the arterial tree.