The emergence of drug-resistance is a major challenge in chemotherapy. In this talk we will present our recent mathematical models for describing the dynamics of drug-resistance in solid tumors. Our models follow the dynamics of the tumor, assuming that the cancer cell population depends on a phenotype variable that corresponds to the resistance level to a cytotoxic drug. We incorporate the dynamics of nutrients and two different types of drugs: a cytotoxic drug, which directly impacts the death rate of the cancer cells, and a cytostatic drug that reduces the proliferation rate. Through analysis and simulations, we study the impact of spatial and phenotypic heterogeneity on the tumor growth under chemotherapy. We demonstrate that heterogeneous cancer cells may emerge due to the selection dynamics of the environment. Our models predict that under certain conditions, multiple resistant traits emerge at different locations within the tumor. We show that a higher dosage of the cytotoxic drug may delay a relapse, yet, when this happens, a more resistant trait emerges. Moreover, we estimate the expansion rate of the tumor boundary as well as the time of relapse, in terms of the resistance trait, the level of the nutrient, and the drug concentration. Finally, we propose an efficient drug schedule aiming at minimizing the growth rate of the most resistant trait. By combining the cytotoxic and cytostatic drugs, we demonstrate that the resistant cells can be eliminated.[-]

How combination therapies can reduce the emergence of cancer resistance? Can we exploit intra-tumoral competition to modify the effectiveness of anti-cancer treatments?
Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols for non-small cell lung cancer have been performed.
In silico experiments confirm that the selection of proper infusion schedules plays a key role in the success of anti-cancer therapies. The outcomes of protocols of chemotherapy and immunotherapy (separately and in combination) differing in doses and timing of the treatments are analyzed.
In particular, we highlight how exploiting the competition between cancer populations seems to be an effective recipe to limit the insurgence of resistant populations. In some cases, combination of low doses therapies could yield a substantial control of the total tumor population without imposing a massive selective pressure that would suppress the sensitive clones leaving unchecked the clonal types resistant to therapies.[-]

Cancers are complex evolving systems that adapt to therapeutic intervention through a suite of resistance mechanisms, therefore whilst fixed maximum tolerated dose therapies generally achieve impressive short-term responses, they unfortunately give way to treatment resistance and tumor relapse. Here we discuss evolutionary therapy, a reactive therapeutic approach that changes and evolves with the tumor being treated. Due to the dynamic feedback between changing treatments and the evolving tumor, mathematical models are essential to drive treatment switch points and predict appropriate dosing and drug combinations. Through the integrated application of mathematical and experimental models as well as clinical data we will illustrate that, evolutionary therapy can drive either tumor control or extinction. Our results strongly indicate that the future of precision medicine shouldn't only be in the development of new drugs but rather in the smarter evolutionary, and model informed, application of preexisting ones. [-]

Glioblastoma are notoriously aggressive, malignant primary brain tumors that have variable response to treatment. This presentation will focus on the integrative role of 1) biological sex-differences, 2) heterogeneity in drug-delivery and 3) intra-tumoral molecular diversity (revealed by radiomics) in capturing and predicting this variable response to treatment. Specifically, I will highlight burgeoning insights into sex differences in tumor incidence, outcomes, propensity and response to therapy. I will further, quantify the degree to which heterogeneity in drug delivery, even for drugs that are able to bypass the blood-brain barrier, contributes to differences in treatment response. Lastly, I will propose an integrative role for spatially resolved MRI-based radiomics models to reveal the intra-tumoral biological heterogeneity that can be used to guide treatment targeting and management. [-]