Generalized analytic expressions for the b matrix of twice-refocused spin echo pulse sequence

Abstract

ABSTRACT Diffusion weighted imaging (DWI) technique has been used to help understand the human brain white matter Þberstructures in vivo . Currently used standard diffusion tensor magnetic resonance imaging (DTI) tractography based on thesecond order diffusion tensor model has limitations in its ability to resolve complex Þber tracts. The generalized diffusiontensor (GDT) imaging technique has been proposed to overcome these limitations associated with the standard secondorder tensor model. Based on the GDT model, a generalized partial differential equation (PDE) governing the anisotropicdiffusion process can be derived. For the purpose of solving the PDE and computing the generalized diffusion tensor, wederive a generalized analytic expression for the high order b matrix in the case of twice-refocused spin echo (TRSE) pulsesequence which is used in the DWI data acquisition. The TRSE pulse sequence is considered because of its ability to nullthe eddy current effect generated during the scanning. The b matrix was computed by integrating the transverse precessingmagnetizationbetweentheexcitationtimeandtheechotime(TE).Inourexperiments,weshowsomecomputationalresultsofthegeneralized b matrixbasedonthenewanalyticexpression. Inaddition,comparisonsbetweenthegeneralized b matrixcomputed using our formula and the second order b matrix given by the MRI machine are presented. The characteristicsof the fomula and the data are discussed at last.Keywords: Diffusion tensor imaging; Generalized diffusion tensor; b Matrix; Twice-refocused spin echo