A quantitative measurement method for nuclear-pleomorphism scoring in breast cancer

Background/Objectives: Nuclear pleomorphism, a crucial determinant of breast cancer grading under the Nottingham Histopathology Grading (NHG) system, remains inadequately quantified in the existing literature. Motivated by this gap, our study seeks to investigate and establish correlations among morphological features across various scores of nuclear pleomorphism, as per the NHG system. We aim to quantify nuclear pleomorphism across these scores and validate our proposed measurement method against ground-truth data. Methods: Initially, we deconstruct the descriptions of nuclear pleomorphism into three core elements: size, shape, and appearance. These elements are subsequently mathematically modeled into equations, termed (Formula presented.), (Formula presented.), and (Formula presented.). These equations are then integrated into a unified model termed Harmonic Mean (HM). The HM equation yields a value approaching 1 for nuclei demonstrating characteristics of score-3 nuclear pleomorphism and near 0 for those exhibiting features of score-1 nuclear pleomorphism. Results: The proposed HM model demonstrates promising performance metrics, including Accuracy, Recall, Specificity, Precision, and F1-score, with values of 0.97, 0.96, 0.97, 0.94, and 0.95, respectively. Conclusions: In summary, this study proposes the HM equation as a novel feature for the precise quantification of nuclear pleomorphism in breast cancer.