Determining the turbulent energy spectrum tensor using multidimensional diffusion MRI

Turbulent flows are of interest for various engineering and medical applications. Pulsed field gradient diffusion encoding sequences quantify overall turbulent velocity fluctuations, but do not resolve spectral characteristics of the flow. Modulated gradient sequences have the potential to measure the diffusion spectrum but are limited by unidirectional encoding. In this article, we explore multidimensional diffusion encoding via the double-rotation of the q vector as a tool to study anisotropic turbulent flow. We demonstrate that encoding durations beyond the mean correlation time were required to satisfy the assumption of a Gaussian phase distribution. The diffusion spectrum tensor was reconstructed with reasonable accuracy. However, the assumption of single-peak encoding spectra did not hold. The development of advanced data inversion protocols is required to derive detailed insights into turbulent flow phenomena.