A comparative mathematical evaluation of contour irregularity using form factor and PERBAS, a new analytical shape factor.

Contour irregularity was mathematically evaluated using two different analytical shape factors: (1) "form factor" (FF), a conventional type of shape analysis formula defined by the formula 4 pi A/P2, and (2) the "PErimeter Ratio Before and After Smoothing" (PERBAS). PERBAS values are obtained by first "smoothing" a contour that contains one or more concavities; surface projections are connected using straight lines and include only tangent lines that do not interest the nucleus, resulting in a convex wrap. Perimeters before and after smoothing were obtained using a MOP-3 computerized image analyzer. Using a series of computer-generated images, it was determined that FF was more sensitive than PERBAS to simple deformations of shape (i.e., having no contour concavities) whereas PERBAS was more specific for surface "roughness" (i.e., contour having at least one concavity). As an application to cancer diagnosis, 6 cases of Burkitt's lymphoma (BL) and 14 cases of Burkitt's-like lymphoma (BLL) were compared for nuclear contour roughness using both shape factors. The BLL group could be distinguished from the BL group on the basis of mean PERBAS values (P = .029), but not on the basis of mean FF values (P = .093). The BL group had a mean PERBAS value of 1.051 +/- 0.023 and a mean FF value of 0.790 +/- 0.068. The BLL group had a mean PERBAS value of 1.093 +/- 0.054 and a mean FF value of 0.723 +/- 0.094. Mean FF and PERBAS values, plotted in a bivariate graphic display, established morphometric shape domains. BL cases occupied a significantly smaller shape domain than did the BLL cases, indicating a greater heterogeneity among nuclear shapes in the latter group. Shape discrimination, in general, was greatly increased when both shape factors were used; this has a great potential for determining cancer diagnosis and patient prognosis.