Three-dimensional analysis of the geometry of individual multiple sclerosis lesions: Detection of shape changes over time using spherical harmonics

Purpose: To suggest a quantitative method for assessing the temporal changes in the geometry of individual multiple sclerosis (MS) lesions in follow-up studies of MS patients. Materials and Methods: Computer simulated and in vivo magnetic resonance (MR) imaged MS lesions were studied. Ten in vivo MS lesions were identified from sets of axial MR images acquired from a patient scanned consecutively for 24 times during a one-year period. Each of the lesions was segmented and its three-dimensional surface approximated using spherical harmonics (SH). From the obtained SH polynomial coefficients, indices of shape were defined, and analysis of the temporal changes in each lesion's geometry throughout the year was performed by determining the mean discrete total variation of the shape indices. Results: The results demonstrate that most of the studied lesions undergo notable geometrical changes with time. These changes are not necessarily associated with similar changes in size/volume. Furthermore, it was found that indices corresponding to changes in lesion shape could be 1.4 to 8.0 times higher than those corresponding to changes in the lesion size/volume. Conclusion: Quantitative three-dimensional shape analysis can serve as a new tool for monitoring MS lesion activity and study patterns of MS lesion evolution over time.