AUTHOR=Rotkopf Lukas T. , Wehrse Eckhard , Schlemmer Heinz-Peter , Ziener Christian H. TITLE=Gaussian Local Phase Approximation in a Cylindrical Tissue Model JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.662088 DOI=10.3389/fphy.2021.662088 ISSN=2296-424X ABSTRACT=

In NMR or MRI, the measured signal is a function of the accumulated magnetization phase inside the measurement voxel, which itself depends on microstructural tissue parameters. Usually the phase distribution is assumed to be Gaussian and higher-order moments are neglected. Under this assumption, only the x-component of the total magnetization can be described correctly, and information about the local magnetization and the y-component of the total magnetization is lost. The Gaussian Local Phase (GLP) approximation overcomes these limitations by considering the distribution of the local phase in terms of a cumulant expansion. We derive the cumulants for a cylindrical muscle tissue model and show that an efficient numerical implementation of these terms is possible by writing their definitions as matrix differential equations. We demonstrate that the GLP approximation with two cumulants included has a better fit to the true magnetization than all the other options considered. It is able to capture both oscillatory and dampening behavior for different diffusion strengths. In addition, the introduced method can possibly be extended for models for which no explicit analytical solution for the magnetization behavior exists, such as spherical magnetic perturbers.