Non‐parametric graphnet‐regularized representation of dMRI in space and time

Highlightsq&tgr;‐dMRI signal representation without making biophysical assumptions.Non‐parametric, time‐dependent reconstruction of the diffusion signal and EAP.Effective GraphNet regularization to reduce q&tgr;‐DWI sampling requirements.Analytic estimation of time‐dependent q‐space index functions (q&tgr;‐indices).Good test‐retest reproducibility of q&tgr;‐index trends in two wild‐type mice. Graphical abstract Figure. No Caption available. Abstract Effective representation of the four‐dimensional diffusion MRI signal – varying over three‐dimensional q‐space and diffusion time &tgr; – is a sought‐after and still unsolved challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this q&tgr;‐space. Following recent terminology, we refer to our q&tgr;‐functional basis as “q&tgr;‐dMRI”. q&tgr;‐dMRI can be seen as a time‐dependent realization of q‐space imaging by Paul Callaghan and colleagues. We use GraphNet regularization – imposing both signal smoothness and sparsity – to drastically reduce the number of diffusion‐weighted images (DWIs) that is needed to represent the dMRI signal in the q&tgr;‐space. As the main contribution, q&tgr;‐dMRI provides the framework to – without making biophysical assumptions – represent the q&tgr;‐space signal and estimate time‐dependent q‐space indices (q&tgr;‐indices), providing a new means for studying diffusion in nervous tissue. We validate our method on both in‐silico generated data using Monte–Carlo simulations and an in‐vivo test‐retest study of two C57Bl6 wild‐type mice, where we found good reproducibility of estimated q&tgr;‐index values and trends. In the hopes of opening up new &tgr;‐dependent venues of studying nervous tissues, q&tgr;‐dMRI is the first of its kind in being specifically designed to provide open interpretation of the q&tgr;‐diffusion signal.

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