Fractal dimension and white matter changes in multiple sclerosis

The brain white matter (WM) in multiple sclerosis (MS) suffers visible and non-visible (normal-appearing WM (NAWM)) changes in conventional magnetic resonance (MR) images. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of a complex object. Our aim was to assess the usefulness of FD analysis in the measurement of WM abnormalities in conventional MR images in patients with MS, particularly to detect NAWM changes. First, we took on a voxel-based morphometry approach optimized for MS to obtain the segmented brain. Then, the FD of the whole grey-white matter interface (WM border) and skeletonized WM was calculated in patients with MS and healthy controls. To assess the FD of the NAWM, we focused our analysis on single sections without lesions at the centrum semiovale level. We found that patients with MS had a significant decrease in the FD of the entire brain WM compared with healthy controls. Such a decrease of the FD was detected not only on MR image sections with MS lesions but also on single sections with NAWM. Taken together, the results showed that FD identifies changes in the brain of patients with MS, including in NAWM, even at an early phase of the disease. Thus, FD might become a useful marker of diffuse damage of the central nervous system in MS.