Experimental Assessment of the b-Matrix using a Reference Phantom in Diffusion Tensor Imaging

Purpose: Diffusion tensor imaging (DTI) has opened new possibilities to investigate the brain. It is, however, very important to know the exact diffusion weighting (spatial orientations and strengths) which is summarized in the so-called b-matrix. The coefficients of the b-matrix are usually calculated by using a simple equation which only takes into account the diffusion gradients and their spatial orientation. In this study we have determined the b-matrix analytically taking into account all gradients (including the imaging gradients). This leads to a system of equations with three unknown parameters (mean diffusion weighting strength, cross-term contribution of the gradients oriented in readout and slice selection direction, respectively) which requires at least three measurements in different directions to determine these unknowns. Since DTI is always acquired with at least six diffusion-weighted measurements in different directions, one is able to asses the full b-matrix experimentally, provided that the gradient scheme of the sequence and the diffusion coefficient of an isotropic phantom (e.g., water) is known. Materials: All measurements were performed using a 1.5 T whole-body MR-Scanner (Siemens Vision, Erlangen, Germany). The diffusion coefficient of the phantom was determined by using a cross-term free diffusion acquisition method. To determine the full b-matrix we acquired a full diffusion tensor scan (six different diffusion-weighted directions) and derived the correction factors and the mean diffusion strength by solving the corresponding system of equations. Results: As expected the individual elements of the experimentally determined b-matrix were different from the elements obtained by using the simplified b-value calculation Depending on the actual b-value (100–1000s/mm²) deviations of up to 30% (for low b-values) were observed for some of the elements. The experimentally determined b-matrix was in very good agreement with the fully analytically calculated b-matrix. Discussion: The presented experimental approach provides a simple way to assess the b-matrix in very good correlation to the analytically calculated b-matrix. For this approach only knowledge of the gradient scheme, the protocol parameter (field of view, matrix size and slice thickness) and the diffusion coefficient of the phantom is required. However, the accuracy of this method critically depends on the accuracy of the numerical value of the diffusion coefficient.