Graph-theoretic characterization of nuclear spatial organization in renal cell carcinoma images

Renal cell carcinoma (RCC) is a highly prevalent and aggressive kidney malignancy that necessitates accurate histopathological evaluation for effective diagnosis and treatment planning. While traditional diagnostic approaches primarily rely on nuclear morphology, emerging computational techniques offer alternative strategies to quantify nuclear spatial organization. This study leverages topological data analysis and graph theory to characterize nuclear aggregation patterns in RCC histopathological images.

Graph-based features, including Betti numbers (β₀ and β₁) and clustering coefficients, were extracted to quantify nuclear connectivity and structural organization. Nuclear segmentation was performed across multiple intensity thresholds to assess the impact of threshold variation on feature extraction. The elbow method was used to determine the optimal threshold, balancing connectivity, and structural stability. Statistical significance between tumor and normal tissues was evaluated using the Mann-Whitney U test.

Betti numbers (β₀ and β₁) and clustering coefficients exhibited distinct trends across different threshold values, effectively differentiating RCC from normal renal tissue. Tumor tissues demonstrated higher β₁ and clustering coefficient values, indicating increased nuclear aggregation and irregular connectivity, while normal tissues exhibited higher β₀ values, suggesting a more fragmented nuclear distribution. The elbow method identified 100 pixels as the optimal threshold for feature extraction, and statistical analysis confirmed significant differences (p < 0.05) between tumor and normal tissues.

The results validate the effectiveness of topological and graph-based descriptors in capturing tumor-associated structural variations. By systematically evaluating intensity thresholds and selecting the optimal one, this study enhances the reliability of nuclear aggregation-based differentiation. The proposed computational framework supports automated RCC diagnosis and improves histopathological assessment, demonstrating the potential of topological data analysis and graph theory in medical imaging.