3‐D surface reconstruction of multiple sclerosis lesions using spherical harmonics

A new approach to approximate the 3-D shape of multiple sclerosis (MS) lesions and to calculate their volumes is presented. The suggested method utilizes sets of MS lesion contours taken from segmented MR images and approximates their 3-D surfaces by spherical harmonics. This method was applied to obtain 3-D reconstructions of in vivo and simulated MS lesions and to calculate their volumes. The results show good geometrical approximations of the original MS lesions' 3-D shapes and good consistency in volume estimation independent of the size of the lesions. The average volume estimation error was smaller than the commonly used technique of slice stacking (15.5 +/- 13.4% and 13.1 +/- 10.1% vs. 25.0 +/- 17.0%). The method presented here offers a tool for analyzing the geometrical characteristics of MS lesions in 3-D as well as their volumes. The geometrical information may potentially serve as an additional clinical index for monitoring the disease.