Studies of tumor heterogeneity, tumor microenvironment, and radiotherapy: A mathematical and computational approach

Abstract

Radiotherapy uses high doses of energy to eradicate cancer cells and thus destroy the bulk of tumors. Radiobiologists try to precisely deliver radiation to a targeted area in order to maximize the cancer cell kill rate while trying to minimize damage to normal cells. To achieve this goal, various treatment schedules have been developed, but there still remain significant obstacles to improving the effectiveness of these schedules. It has been observed that various factors play important roles in the effectiveness of treatment. One important factor is tumor heterogeneity, that is, the genetic and epigenetic variations in tumors. This cellular diversity can influence the efficacy of radiotherapy due to the different radiosensitivities among cancer cells. In addition, the interplay between this heterogeneous cellular population and the tumor microenvironment can negatively affect the treatment process. In this thesis, deterministic and stochastic mathematical models are developed to explore the role of heterogeneity and the impact of cellular repair on radiotherapy outcomes. The results suggest that shrinking a tumor is not sufficient to control the disease; the fraction of cells resistant to treatment must also be reduced. In addition, supposedly optimal treatment schedules can lead to markedly different results even in patients with the same type of cancer, due to cellular and microenvironmental differences among tumors. Therefore, based on these variations, it is important to design new therapeutic approaches for each cancer type and even each patient. The modified Gillespie algorithm for discontinuous time changing rates is applied to explore the impact of plasticity, as well as random demographic factors on the tumor control probability. The random modification of tumor microenvironment is shown to influence the efficiency of radiotherapy. Increasing the standard deviation leads to an initial rise in the tumor control probability, which thereafter drops over time if a tumor is not eradicated entirely. The results also confirm that plasticity in a tumor reduces the tumor control probability, especially in highly resistant tumors. In addition, in the presence of plasticity, combining radiotherapy with a targeted therapy increasing the differentiation of CSCs does not increase the probability of CSC and tumor removal greatly. Finally, the impact of regulatory negative feedback on the sphere formation potential of a single CSC is explored. The sphere formation efficiency and average sphere size are shown to escalate when CSC division and dedifferentiation are subject to negative regulatory feedback.