Non‐monotonic time‐ and frequency‐dependent diffusion kurtosis in the human brain revealed by pulsed and oscillating gradient experiments

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Abstract
Purpose: To investigate the time and frequency dependence of diffusion kurtosis in the in vivo human brain with pulsed (PGSE) and oscillating gradient spin‐echo (OGSE) experiments over a range of diffusion times and frequencies using high‐performance gradients.Methods: Four OGSE waveforms probing centroid frequencies of 11, 20, 34, and 51 Hz, corresponding to equivalent effective diffusion times of 22.7, 12.5, 7.4, and 4.9 ms; and three PGSE waveforms probing effective diffusion times of 50, 22.7, and 12.5 ms were designed for experimentation. Seven healthy volunteers were scanned using said waveforms at b‐values of 500, 1000, and 2000 s/mm2. Kurtosis metrics were computed and evaluated in various white and gray matter regions of interest. Complementary Monte‐Carlo simulations were performed using a simple substrate with varying permeabilities and the same gradient waveforms as used for in vivo imaging.Results: Non‐monotonic, biphasic kurtosis time‐ and frequency‐dependences were observed in different white and gray matter regions. This behavior supports the notion that kurtosis is influenced by the combined effects of water‐restriction interactions, inter‐compartmental water exchange, and tissue heterogeneity. Kurtosis values measured using OGSE and PGSE waveforms at the same effective diffusion times showed significant discrepancies, with consistently higher values from PGSE than OGSE. These discrepancies are mainly attributed to differences in exchange sensitivities among gradient waveforms based on analogous findings from Monte‐Carlo simulations.Conclusion: Kurtosis was found to exhibit biphasic time‐ and frequency‐dependence in the human brain. When interpreting kurtosis measurements, the influence of exchange sensitivities of employed gradient waveforms should be considered.

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