title: Three-dimensional analysis of the geometry of individual multiple sclerosis lesions: detection of shape changes over time using spherical harmonics.
abstract: OBJECTIVE
  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.
  
  
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa, Israel.
authors.forename: Daniel
authors.initials: D
authors.lastname: Goldberg-Zimring
authors.forename: Anat
authors.initials: A
authors.lastname: Achiron
authors.forename: Charles R G
authors.initials: CR
authors.lastname: Guttmann
authors.forename: Haim
authors.initials: H
authors.lastname: Azhari
mesh_terms: D000328:Adult; D005500:Follow-Up Studies; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D009103:Multiple Sclerosis / Q000473:pathology*