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Updated: Aug 18, 2026
Three-Dimensional Shape Modeling and Analysis of Brain Structures
Published on: November 14, 2019
Statistical validation of brain tumor shape approximation via spherical harmonics for image-guided neurosurgery
Daniel Goldberg-Zimring1, Ion-Florin Talos, Jui G Bhagwat
1Department of Radiology, Brigham and Women's Hospital, 75 Francis St, Boston, MA 02115, USA. daniel@bwh.harvard.edu
Rationale And Objectives:
Surgical planning now routinely uses both two-dimensional (2D) and three-dimensional (3D) models that integrate data from multiple imaging modalities, each highlighting one or more aspects of morphology or function. We performed a preliminary evaluation of the use of spherical harmonics (SH) in approximating the 3D shape and estimating the volume of brain tumors of varying characteristics.
Materials And Methods:
Magnetic resonance (MR) images from five patients with brain tumors were selected randomly from our MR-guided neurosurgical practice. Standardized mean square reconstruction errors (SMSRE) by tumor volume were measured. Validation metrics for comparing performances of the SH method against segmented contours (SC) were the dice similarity coefficient (DSC) and standardized Euclidean distance (SED) measure.
Results:
Tumor volume range was 22,413-85,189 mm3, and range of number of vertices in triangulated models was 3674-6544. At SH approximations with degree of at least 30, SMSRE were within 1.66 x 10(-5) mm(-1). Summary measures yielded a DSC range of 0.89-0.99 (pooled median, 0.97 and significantly >0.7; P < .001) and an SED range of 0.0002-0.0028 (pooled median, 0.0005).
Conclusion:
3D shapes of tumors may be approximated by using SH for neurosurgical applications.
