Gaussian local phase approximation in a cylindrical tissue model

• Verfasst von: Rotkopf, Lukas Thomas [VerfasserIn]
• Verfasst von: Wehrse, Eckhard [VerfasserIn]
• Verfasst von: Schlemmer, Heinz-Peter [VerfasserIn]
• Verfasst von: Ziener, Christian H. [VerfasserIn]
• Titel: Gaussian local phase approximation in a cylindrical tissue model
• Verf.angabe: Lukas T. Rotkopf, Eckhard Wehrse, Heinz-Peter Schlemmer and Christian H. Ziener
• E-Jahr: 2021
• Jahr: 20 May 2021
• Umfang: 13 S.
• Fussnoten: Gesehen am 02.03.2022
• Titel Quelle: Enthalten in: Frontiers in physics
• Ort Quelle: Lausanne : Frontiers Media, 2013
• Jahr Quelle: 2021
• Band/Heft Quelle: 9(2021) vom: 20. Mai, Artikel-ID 662088, Seite 1-13
• ISSN Quelle: 2296-424X
• DOI: doi:10.3389/fphy.2021.662088
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1794382607

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.