Fractal dimensions for tumour-related cell types of prostate cancer on histopathology images using multiple-threshold box counting algorithm.

The malignancies of prostate tumour cells are assessed by pathologists as grade groups (GGs) from 1 (least aggressive) to 5 (most aggressive) on histopathology images. GGs are associated with the degree of tumour cell differentiation and may have different self-similarities depending on GG and tumour-related cell types, which are neoplastic epithelial, inflammatory, connective tissue, necrotic, and non-neoplastic epithelial cells. We investigated the associations between GGs and fractal dimensions (FDs) for five types of prostate tumour-related cells using a multiple-threshold box counting algorithm (MTBC). We showed the association of FDs of 9 channel images (eosin, hematoxylin, normalised images for red, green, and blue colour channels) with multiple threshold values on histopathology images (patch images) and the feasibility of FD-threshold images in an artificial intelligence model to classify patients into low (GG≤3) and high (GG≥4) GGs. We constructed FD-threshold images based on MTBC algorithm for characterizing prostate tumour cells. A shallow-convolutional neural network (sCNN) model to classify patients into low and high GGs was trained with input data of the FD-threshold images for all 9 channels and evaluated using the area under receiver operating characteristic curve (AUC). There were statistically significant correlations between the FD of non-neoplastic epithelial cells and GG [Pearson correlation coefficient=-0.849, p=0.001]. Significant correlations also existed for connective tissue and the original images. The AUC for the sCNN classification model into high and low GGs was 0.811. FD can characterise physical properties of prostate tumour-related cells for low and high GGs.