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Three‐dimensional analysis of the geometry of individual multiple sclerosis lesions: Detection of shape changes over time using spherical harmonics
Author(s) -
GoldbergZimring Daniel,
Achiron Anat,
Guttmann Charles R.G.,
Azhari Haim
Publication year - 2003
Publication title -
journal of magnetic resonance imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.563
H-Index - 160
eISSN - 1522-2586
pISSN - 1053-1807
DOI - 10.1002/jmri.10365
Subject(s) - lesion , spherical harmonics , multiple sclerosis , geometry , spherical geometry , magnetic resonance imaging , shape analysis (program analysis) , volume (thermodynamics) , in vivo , medicine , mathematics , pathology , radiology , physics , mathematical analysis , computer science , biology , static analysis , quantum mechanics , psychiatry , programming language , microbiology and biotechnology
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. J. Magn. Reson. Imaging 2003;18:291–301. © 2003 Wiley‐Liss, Inc.