Assessment of multiple sclerosis lesions with spherical harmonics: comparison of MR imaging and pathologic findings

Spherical harmonics (SH) were used to approximate the volume and three-dimensional geometry of multiple sclerosis (MS) lesions in deceased patients. The institutional ethical committee does not require its approval for studies involving pathologic specimens. Pathologic findings were used as the reference standard. In addition, lesion volume was measured with cylindrical approximation (CA). Volumetric comparisons of biases were based on summary statistics, Spearman correlation, Wilcoxon test, and two-way analysis of variance. Shape comparison metrics included mean distance and Dice similarity coefficient (DSC). Eight of 11 lesions had smaller biases with SH method (P < .001). Median biases with SH and CA did not differ significantly, as compared with pathologic findings (r = 1.00 vs 0.99, respectively). Variances of the biases were significantly smaller for SH (P = .04). Ranges of normalized distance and DSC were 0.1%-2.5% and 75%-96%, respectively. Mean DSC was significantly higher than 70% (P < .001). SH method provided unbiased lesion volume and added geometric information that may enable a better understanding of the pathogenesis and lesion evolution over time.