Approximation of the actual spatial distribution of the b-matrix in diffusion tensor imaging with bivariate polynomials

The aim of this work was to find an analytical expression describing the b-matrix spatial distribution (BSD) in diffusion tensor imaging, obtained by means of simple calibration to a water isotropic phantom. The bivariate second degree polynomial function was fitted for the complete set of spatially distributed b-matrix elements derived through measurements on a 3 Tesla clinical scanner. Smooth, noise free b-matrices were obtained with clear patterns of systematic errors. Diffusion tensor eigenvalues were derived with much better accuracy than for previous BSD calibration. The proposed approach does not require many averages during the acquisition of the phantom and thus can shorten the BSD calibration.