A unique analytical solution of the white matter standard model using linear and planar encodings

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.