Numerical issues in estimation of integral curves from noisy diffusion tensor data

Abstract: The estimation of a diffusion tensor imaging (DTI) model proposed by involves two steps. The second step requires solving an ordinary differential equation, which in practice is solved by using a numerical approximation. We investigate how to balance the additional numerical error introduced by this approximation with the statistical estimation error using empirical mean integrated squared error for Euler’s and the second order Runge–Kutta approximations. We give practical guideline on how fast should the numerical approximation step grow with respect to the sample size. However, the typical scales of the neural fibers estimated using DTI in brains are much smaller than the maximal allowed numerical approximation step for approximation of any order. It is further observed that a simple Euler’s approximation gives very similar results as obtained by using a more sophisticated numerical approximation of a higher order. In view of the increasing computational costs for numerical approximations of higher orders, the use of Euler’s approximation is well-justified for the DTI. [Copyright &y& Elsevier]