Machine Learning Techniques and Stochastic Modeling in Mathematical Oncology

Abstract

The cancer stem cell hypothesis claims that tumor growth and progression are driven by a (typically) small niche of the total cancer cell population called cancer stem cells (CSCs). These CSCs can go through symmetric or asymmetric divisions to differentiate into specialised, progenitor cells or reproduce new CSCs. While it was once held that this differentiation pathway was unidirectional, recent research has demonstrated that differenti- ated cells are more plastic than initially considered. In particular, differentiated cells can de-differentiate and recover their stem-like capacity. Two recent papers have considered how this rate of plasticity affects the evolutionary dynamic of an invasive, malignant population of stem cells and differentiated cells into existing tissue [64, 109]. These papers arrive at seemingly opposing conclusions, one claiming that increased plasticity results in increased invasive potential, and the other that increased plasticity decreases invasive potential. Here, we show that what is most important, when determining the effect on invasive potential, is how one distributes this increased plasticity between the compartments of resident and mutant-type cells. We also demonstrate how these results vary, producing non-monotone fixation probability curves, as inter-compartmental plasticity changes when differentiated cell compartments are allowed to continue proliferating, highlighting a fundamental dif- ference between the two models. We conclude by demonstrating the stability of these qualitative results over various parameter ranges. Imaging flow cytometry is a tool that uses the high-throughput capabilities of conven- tional flow cytometry for the purposes of producing single cell images. We demonstrate the label free prediction of mitotic cell cycle phases in Jurkat cells by utilizing brightfield and darkfield images from an imaging flow cytometer. The method is a non destructive method that relies upon images only and does not introduce (potentially confounding) dies or biomarkers to the cell cycles. By utilizing deep convolutional neural networks regularized by generated, synthetic images in the presence of severe class imbalance we are able to produce an estimator that outperforms the previous state of the art on the dataset by 10-15%. The in-silico development of a chemotherapeutic dosing schedule for treating cancer relies upon a parameterization of a particular tumour growth model to describe the dynamics of the cancer in response to the dose of the drug. In practice, it is often prohibitively difficult to ensure the validity of patient-specific parameterizations of these models for any particular patient. As a result, sensitivities to these particular parameters can result in therapeutic dosing schedules that are optimal in principle not performing well on particular patients. In this study, we demonstrate that chemotherapeutic dosing strategies learned via reinforcement learning methods are more robust to perturbations in patient-specific parameter values than those learned via classical optimal control methods. By training a reinforcement learning agent on mean-value parameters and allowing the agent periodic access to a more easily measurable metric, relative bone marrow density, for the purpose of optimizing dose schedule while reducing drug toxicity, we are able to develop drug dosing schedules that outperform schedules learned via classical optimal control methods, even when such methods are allowed to leverage the same bone marrow measurements.