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

Goldberg-Zimring D, Achiron A, Guttmann CRG, Azhari H. Three-dimensional analysis of the geometry of individual multiple sclerosis lesions: detection of shape changes over time using spherical harmonics. J Magn Reson Imaging. 2003;18(3):291–301.

Abstract

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.
Last updated on 02/24/2023