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Assessment of Multiple Sclerosis Lesions with Spherical Harmonics: Comparison of MR Imaging and Pathologic Findings¹

¹ From the Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa, Israel (D.G.Z., H.A.); Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, 75 Francis St, Boston, MA 02115 (D.G.Z., K.H.Z.); Department of Pathology (B.S., D.N.) and Multiple Sclerosis Center (A.A.), Sheba Medical Center, Tel Hashomer, Israel; Department of Health Care Policy, Harvard Medical School, Boston, Mass (K.H.Z.); and Department of Neurology, Tel Aviv University, Sackler Faculty of Medicine, Tel Aviv, Israel (A.A.). Received December 19, 2003; revision requested February 25, 2004; final revision received August 30; accepted September 17. D.G.Z. supported by the "Sociedad Venezolana Amigos del Technion" and in part by NIH grant R21MH67054 and grant RG3478AZ/Z from the National Multiple Sclerosis Society, U.S. D.G.Z. and K.H.Z. supported in part by NIH grant R01LM007861–01A1. Address correspondence to D.G.Z. (e-mail: daniel@bwh.harvard.edu).

View larger version (149K): [in a new window]   Figure 1. An example of an irregular surface reconstruction with the SH method.

View larger version (160K): [in a new window]   Figure 2a. Photomicrographs show histologic evidence of an MS lesion. (a) Hematoxylin-eosin stain demonstrates hypocellularity with reduction in myelinated fibers and axons (original magnification, x40), (b) which is confirmed with luxol fast blue stain for myelin (original magnification, x40) and (c) Bielschowsky stain for axons (original magnification, x40).

View larger version (166K): [in a new window]   Figure 2b. Photomicrographs show histologic evidence of an MS lesion. (a) Hematoxylin-eosin stain demonstrates hypocellularity with reduction in myelinated fibers and axons (original magnification, x40), (b) which is confirmed with luxol fast blue stain for myelin (original magnification, x40) and (c) Bielschowsky stain for axons (original magnification, x40).

View larger version (172K): [in a new window]   Figure 2c. Photomicrographs show histologic evidence of an MS lesion. (a) Hematoxylin-eosin stain demonstrates hypocellularity with reduction in myelinated fibers and axons (original magnification, x40), (b) which is confirmed with luxol fast blue stain for myelin (original magnification, x40) and (c) Bielschowsky stain for axons (original magnification, x40).

View larger version (34K): [in a new window]   Figure 3. Scatterplot of percentage absolute bias of lesion volume according to SH, against percentage absolute bias of lesion volume according to CA, each standardized according to pathologic volume. Eight (ie, lesions 1, 2, 4, 5, 7, 8, 10, and 11) of the 11 lesions had smaller absolute biases with the SH method than with the CA method, with data points lying under the 45° line.

View larger version (126K): [in a new window]   Figure 4a. Periventricular lesion (arrow) that extended into two coronal MR sections (550/20, field of view of 24 cm, matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of two MR sections, and (c) approximated 3D lesion shape obtained with SH method show that lesion is similar to classical elliptically shaped MS lesion. (d, e) Segmented axial contours (solid line) versus corresponding contours obtained from 3D-reconstructed shape with SH method (dotted line).

View larger version (112K): [in a new window]   Figure 4b. Periventricular lesion (arrow) that extended into two coronal MR sections (550/20, field of view of 24 cm, matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of two MR sections, and (c) approximated 3D lesion shape obtained with SH method show that lesion is similar to classical elliptically shaped MS lesion. (d, e) Segmented axial contours (solid line) versus corresponding contours obtained from 3D-reconstructed shape with SH method (dotted line).

View larger version (112K): [in a new window]   Figure 4c. Periventricular lesion (arrow) that extended into two coronal MR sections (550/20, field of view of 24 cm, matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of two MR sections, and (c) approximated 3D lesion shape obtained with SH method show that lesion is similar to classical elliptically shaped MS lesion. (d, e) Segmented axial contours (solid line) versus corresponding contours obtained from 3D-reconstructed shape with SH method (dotted line).

View larger version (18K): [in a new window]   Figure 4d. Periventricular lesion (arrow) that extended into two coronal MR sections (550/20, field of view of 24 cm, matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of two MR sections, and (c) approximated 3D lesion shape obtained with SH method show that lesion is similar to classical elliptically shaped MS lesion. (d, e) Segmented axial contours (solid line) versus corresponding contours obtained from 3D-reconstructed shape with SH method (dotted line).

View larger version (16K): [in a new window]   Figure 4e. Periventricular lesion (arrow) that extended into two coronal MR sections (550/20, field of view of 24 cm, matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of two MR sections, and (c) approximated 3D lesion shape obtained with SH method show that lesion is similar to classical elliptically shaped MS lesion. (d, e) Segmented axial contours (solid line) versus corresponding contours obtained from 3D-reconstructed shape with SH method (dotted line).

View larger version (130K): [in a new window]   Figure 5a. Periventricular lesion (arrow) that extended into three coronal MR sections (550/20, field of view of 24 cm, and matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of three MR sections, and (c) approximated 3D lesion shape obtained with SH method show pyramidal shape of lesion. (d-f) Segmented axial contours (solid line) versus corresponding contours from 3D-reconstructed shape with SH method (dotted line).

View larger version (103K): [in a new window]   Figure 5b. Periventricular lesion (arrow) that extended into three coronal MR sections (550/20, field of view of 24 cm, and matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of three MR sections, and (c) approximated 3D lesion shape obtained with SH method show pyramidal shape of lesion. (d-f) Segmented axial contours (solid line) versus corresponding contours from 3D-reconstructed shape with SH method (dotted line).

View larger version (83K): [in a new window]   Figure 5c. Periventricular lesion (arrow) that extended into three coronal MR sections (550/20, field of view of 24 cm, and matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of three MR sections, and (c) approximated 3D lesion shape obtained with SH method show pyramidal shape of lesion. (d-f) Segmented axial contours (solid line) versus corresponding contours from 3D-reconstructed shape with SH method (dotted line).

View larger version (17K): [in a new window]   Figure 5d. Periventricular lesion (arrow) that extended into three coronal MR sections (550/20, field of view of 24 cm, and matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of three MR sections, and (c) approximated 3D lesion shape obtained with SH method show pyramidal shape of lesion. (d-f) Segmented axial contours (solid line) versus corresponding contours from 3D-reconstructed shape with SH method (dotted line).

View larger version (17K): [in a new window]   Figure 5e. Periventricular lesion (arrow) that extended into three coronal MR sections (550/20, field of view of 24 cm, and matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of three MR sections, and (c) approximated 3D lesion shape obtained with SH method show pyramidal shape of lesion. (d-f) Segmented axial contours (solid line) versus corresponding contours from 3D-reconstructed shape with SH method (dotted line).

View larger version (14K): [in a new window]   Figure 5f. Periventricular lesion (arrow) that extended into three coronal MR sections (550/20, field of view of 24 cm, and matrix size of 256 x 256 pixels). (a) Pathologic slice, (b) one of three MR sections, and (c) approximated 3D lesion shape obtained with SH method show pyramidal shape of lesion. (d-f) Segmented axial contours (solid line) versus corresponding contours from 3D-reconstructed shape with SH method (dotted line).

View larger version (20K): [in a new window]   Figure 6. Graph shows lesion-specific percentage normalized mean distance, with individual lesions presented in increasing order of pathologic volume. Overall range of the normalized distance was less than 2.5%. Normalized distance tended to be smaller for larger lesions with larger normalizing lesion area. = Maximum of mean distances over all contours per lesion. = Average of mean distances over all contours per lesion. = Minimum of mean distances over all contours per lesion.

View larger version (23K): [in a new window]   Figure 7. Lesion-specific DSC, with individual lesions presented in increasing order of pathologic volume. Mean DSCs are significantly greater than 70% (dotted line). All DSC values were greater than 70%, the threshold found in the literature, suggesting satisfactory spatial overlap. Mean DSC was not correlated with lesion size, suggesting that SH were robust with respect to lesion size. = Maximum of DSCs over all contours per lesion. = Mean of DSCs over all contours per lesion. = Minimum of DSCs over all contours per lesion.