MS8: Modeling Tumor-Immune Dynamics, Disease Progression, and Treatment

Monday, July 17, 3:00-5:30, Ballroom East


Lisette de Pillis (Mathematics,(Mathematics, Harvey Mudd College, Claremont, CA, USA),
Amina Eladdadi (Mathematics, The College of Saint Rose, Albany NY, USA),

The immune system has been documented to play a role in tumour control for more than a century and resulted in the development of immune therapies to combat cancer. Some types of immune therapies have shown success but many anti-tumour immune therapies do not show the expected results. The immune-editing hypothesis emphasizes the dual role of macrophages in the immune response with M1 macrophages tumour-promoting and M2 macrophages tumour-suppressing. However, experimental studies have shown contradicting results. Understanding of the biological mechanisms governing the immune tumour interactions is far from complete but known to be complex, involving many non-linear interactions. Mathematical biology and the tools in this field are ideally suited to complement experimental studies and analyse the complex non-linear interactions. We developed an ODE model to analyse the role of macrophages in the tumour immune interactions.

Therapeutic cancer vaccines treat cancers that have already developed by stimulating special cancer killing cells known as cytotoxic T cells. Despite showing promise, positive clinical outcomes have yet to be realized and a possible reason is due to the functional avidity of the T cell response. Vaccines elicit a low-avidity (i.e., weakly tumor-killing) T cell response, and the mere presence of low-avidity T cells can inhibit cancer killing by high-avidity T cells. By considering this “high-low interference” explicitly, we use a probabilistic agent- based model to explore what the optimal vaccination strategy is.

The advent of immunotherapy has brought about a new era of cancer treatment, one that promises great potential for tumor eradication. In order to reap the full benefits of such therapies, it is necessary to understand how they function in each patient and optimize how the therapies can be administered for the greatest responses. With this goal, we have developed a mathematical multiscale systems pharmacology model that would allow us to explicate in silico potential biomarkers for the identification of patients who would benefit most from particular types of immunotherapies, and optimally predict therapeutic regimens for those patients.

The model focuses on the molecular, cellular and tissue level changes that would occur during an immune response against a tumor, with a particular focus on the activities of immune checkpoint inhibitors against PD-1, PD-L1 and CTLA-4, administered as mono- or combination therapies. The model incorporates experimentally determined receptor binding constants, and cellular and molecular dynamics, as well as various cell types and states, including a heterogeneous tumor representation (for checkpoint receptor expression). In total, the model comprises of approximately 400 molecular and cellular species, and a mix of about 200 algebraic equations, 300 ODEs, and several discontinuous equation sets. Parameters were chosen to simulate the treatment of NSCLC and melanoma; although the framework is flexible enough to model other types of cancers, given their respective parameters. While the model is large, it has ample literature support quantitatively and qualitatively, with parameters mostly reflecting experimental and clinical values.

Qualitatively, the model identifies the pharmacokinetics of the immune checkpoint inhibitors in a manner consistent with previous studies, and additionally predicts the effects of those therapies on tumor response with results mirroring those reported from several published clinical trials. This includes the dose responses of the therapies in relation to their pharmacodynamic effects. In a quantitative manner, cellular densities, molecular expression levels, and T cell clonality levels differentiating therapy responders from non-responders are very similar to those reported in the literature. Future studies will allow statistical analyses of virtual population cohorts for further qualitative and quantitative confirmation of the generated results, and more refined predictions. Supported by grants from MedImmune and NIH R01CA138264.

One of the biggest barriers in treating solid tumours is the inability of the therapeutic vectors to propagate throughout the tumour mass due to the high density of the tumour and tumour stroma. The dense nature of many solid tumours can be attributed to a gel-like substance known as the extracellular matrix (ECM). This thick and compact structure acts as a physical barrier by shielding the malignant cells and reducing drug penetration and efficacy. One method to tackle the over-expression of ECM in solid tumours, is by using a relaxin-expressing adenovirus designed to degrade the ECM within the tumour, thereby increasing the effectiveness of the oncolytic virus. In this presentation, we explore this problem by introducing a system of reaction-diffusion PDEs, including tumour cells and anti-tumour viruses. Mimicking the heterogeneous environment observed in solid tumours, we aim to model the dynamics of ECM degradation and the subsequent effect on the malignant cells due to changes in drug penetration and diffusion.

In this presentation we develop and analyse a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood, alongside the cancer stem cell population. The proposed model consists of a system of five differential equations with two delays. Model analyses and simulations suggest that the emergence of the cancer stem cell population provides an aberrant environment in which the malignant population in the bone marrow could keep expanding even at equilibrium. Most notably, the stability analysis reveals that the mere existence of the cancer stem cell population tends to enhance and stimulate the expansion of non-stem malignant clones not only temporally but also at equilibrium and the converse also happens. This suggests that the cancer stem cell population is very crucial and critical in propagating malignancy.