Conformal mapping of nuclei in 3D tomographic cell images to assess shape heterogeneity

Nuclear shape and its heterogeneity are diagnostically important criteria used by pathologists in cancer diagnosis. Pathology assessment is currently qualitative and is based on 2D brightfield microscopy images. We propose an imaging informatics framework to quantify nuclear pleomorphism by statistical characterization of 3D nuclear shape. We applied optical projection tomographic microscopy (OPTM) to image individual hematoxylin and eosin-stained cells with isotropic, sub-micron spatial resolution. We used adaptive thresholding schemes to segment cells and nuclei, and applied spherical conformal mapping methods on the 3D nuclear masks to compute 256 rotation invariant coefficients as shape descriptors for each nucleus. As a first application, we tested our methods on normal and cancerous epithelial cell lines derived from human esophagus and breast, analyzing 10 cell images per class. We applied ANOVA techniques to assess variations in nuclear shape within each cell type and among the four cell types. The automated segmentation was 96% accurate compared to manual tracing of the volumes of interest. Statistical analysis of shape coefficients revealed that cancer cell nuclei from both organs exhibited considerably larger variance in their coefficients relative to the corresponding normal cell nuclei. Our results demonstrate the promise of our methodology for the development of quantitative pathological assessments.