Persistent homology for the quantification of prostate cancer morphology in two and three-dimensional histology
The current system for evaluating prostate cancer architecture is the Gleason Grade system, which divides the morphology of cancer into five distinct architectural patterns, labeled numerically in increasing levels of cancer aggressiveness and generates a score by summing the labels of the two most dominant patterns. The Gleason score is currently the most powerful prognostic predictor of patient outcomes; however, it suffers from problems in reproducibility and consistency due to the high intra-observer and inter-observer variability among pathologists. In addition, the Gleason system lacks the granularity to address potentially prognostic architectural features beyond Gleason patterns. We look towards persistent homology, a tool from topological data analysis, to provide a means of evaluating prostate cancer glandular architecture. The objective of this work is to demonstrate the capacity of persistent homology to capture architectural features independently of Gleason patterns in a representation suitable for unsupervised and supervised machine learning. Specifically, using persistent homology, we compute topological representations of purely graded prostate cancer histopathology images of Gleason patterns and show that persistent homology is capable of clustering prostate cancer histology into architectural groups through discrete representations of persistent homology in both two-dimensional and three-dimensional histopathology. We then demonstrate the performance of persistent homology based features in common machine learning classifiers, indicating that persistent homology can both separate unique architectures in prostate cancer, but is also predictive of prostate cancer aggressiveness. Our results indicate the ability of persistent homology to cluster into unique groups with dominant architectural patterns consistent with the continuum of Gleason patterns. In addition, of particular interest, is the sensitivity of persistent homology to identify specific sub-architectural groups within single Gleason patterns, suggesting that persistent homology could represent a robust quantification method for prostate cancer architecture with higher granularity than the existing semi-quantitative measures. This work develops a framework for segregating prostate cancer aggressiveness by architectural subtype using topological representations, in a supervised machine learning setting, and lays the groundwork for augmenting traditional approaches with topological features for improved diagnosis and prognosis.