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

Diffusion weighted imaging (DWI) technique has been used to help understand the human brain white matter fiber structures in vivo. Currently used standard diffusion tensor magnetic resonance imaging (DTI) tractography based on the second order diffusion tensor model has limitations in its ability to resolve complex fiber tracts. The generalized diffusion tensor (GDT) imaging technique has been proposed to overcome these limitations associated with the standard second order tensor model. Based on the GDT model, a generalized partial differential equation (PDE) governing the anisotropic diffusion process can be derived. For the purpose of solving the PDE and computing the generalized diffusion tensor, we derive a generalized analytic expression for the high order b matrix in the case of twice-refocused spin echo (TRSE) pulse sequence which is used in the DWI data acquisition. The TRSE pulse sequence is considered because of its ability to null the eddy current effect generated during the scanning. The b matrix was computed by integrating the transverse precessing magnetization between the excitation time and the echo time (TE). In our experiments, we show some computational results of the generalized b matrix based on the new analytic expression. In addition, comparisons between the generalized b matrix computed using our formula and the second order b matrix given by the MRI machine are presented. The characteristics of the fomula and the data are discussed at last.