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

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.