Mathematical models of tumor growth using Voronoi tessellations in pathology slides of kidney cancer.

The impact of patient-specific spatial distribution features of cell nuclei on tumor growth characteristics was analyzed. Tumor tissues from kidney cancer patients were allowed to grow in mice to apply H&E staining and to measure tumor volume during preclinical phase of our study. Imaging the H&E stained slides under a digital light microscope, the morphological characteristics of nuclei positions were determined. Using artificial intelligence based techniques, Voronoi features were derived from diagrams, where cell nuclei were considered as distinct nodes. By identifying the effect of each Voronoi feature, tumor growth was expressed mathematically. Consistency between the computed growth curves and preclinical measurements indicates that the information obtained from the H&E slides can be used as biomarkers to build personalized mathematical models for tumor growth.