Continuous Tensor Field Approximation of Diffusion Tensor MRI data

Diffusion Tensor MRI (DT-MRI) measurements are a discrete noisy sample of an underlying macroscopic effective diffusion tensor field, D(x), of water. This field is presumed to be piecewise continuous/smooth at a gross anatomical length scale. Here we describe a mathematical framework for obtaining an estimate of this tensor field from the measured DT-MRI data using a spline-based continuous approximation. This methodology facilitates calculation of new structural quantities and provides a framework for applying differential geometric methods to DT-MRI data. A B-spline approximation has already been used to improve robustness of DT-MRI fiber tractography. Here we propose a piecewise continuous approximation based on Non-Uniform Rational B-Splines (NURBS), which addresses some of the shortcomings of the previous implementation.