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A unique analytical solution of the white matter standard model using linear and planar encodings
Author(s) -
Reisert Marco,
Kiselev Valerij G.,
Dhital Bibek
Publication year - 2019
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.27685
Subject(s) - mesoscopic physics , nonlinear system , diffusion , planar , degeneracy (biology) , mathematics , statistical physics , physics , computer science , algorithm , quantum mechanics , bioinformatics , computer graphics (images) , biology
Purpose It is known that white matter modeling based on commonly used linear diffusion encoding is an ill‐posed problem. We analyze the additional information gained from a double pulsed diffusion encoding. Methods Zeroth (spherical means) and second‐order (harmonic powers) rotation invariant signal features are used to factor micro‐ and mesoscopic contributions. The b‐value dependency up to second‐order of the features form 6 nonlinear equations, which are analyzed. Results The 6 derived equations can be uniquely solved for all relevant biophysical parameters. No assumptions about the form of the mesoscopic contribution (fiber dispersion) is necessary. Under certain conditions the solution still shows a certain degeneracy which is inherent to model. It is further shown that a combination of second‐order information from single and spherical diffusion encoding is not enough to solve the problem. Conclusions A combination of single and double pulsed diffusion encodings is sufficient to solve the full 3 compartment white matter model uniquely.