Quantifying cellular (re)-organization in 3-D cancer models using persistent homology

Automated analysis of high-throughput, time-lapse microscopy data is essential for the development of multi-scale, patient-specific models that accurately mimic the complex behavior of cells observed in vivo. Many state-of-the-art methods for processing 3-D microscopy datasets rely on supervised machine learning methods for image segmentation, cell tracking and cell shape classification. These methods are computationally expensive, requiring difficult-to-obtain training data and parameter tuning. We propose an alternative approach, based on topological data analysis, to quantify changes in tumor architecture by analyzing point clouds obtained from cell nuclei positions. Using persistent homology, a topological barcode is extracted from each point cloud, which corresponds to the presence of topological features (clusters, acini and lumens) at multiple spatial scales. The barcode provides a unique insight into the spatial organization of data, which is often missing from typical analyses based on machine learning and statistics. By linking topological barcodes across time, the temporal persistence of topological features can be measured. The proposed methodology is able to identify nuclei associated with distinct clusters, acini and lumens in an unsupervised manner. Using this information, we ascertain the movement of cells between topological features. Furthermore, we classify qualitatively distinct organizational structures by clustering based on pairwise Wasserstein distances between topological barcodes. In this talk, I will introduce our methodology and demonstrate its potential for investigating tissue reorganization during tumorigenesis and metastasis.