Microscopic imaging techniques have given us access to high fidelity measurements of subcellular molecule and protein mass distributions. Quantitative analysis of these has the potential to elucidate biological mechanisms as well help perform diagnosis and clinical outcome predictions in cancer and other pathologies. By using the mathematics of optimal transport, we can quantitatively compare distributions of mass in different cells and in different populations. We show how this concept can be used to create mathematical models that can elucidate information about mass and protein distributions in different cells as well as inform clinical decision making. In particular, we use this emerging mathematical modeling framework to determine shared nuclear chromatin distribution features that predict malignancy across multiple cancers, among other applications.