Addressing current challenges in cancer immunotherapy with mathematical and computational modeling

The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment, immune-modulating effects of conventional treatments, and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modeling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumor classification, optimal treatment scheduling, and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modelers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumor-immune biology. We conclude the review with recommendations for modelers both with respect to methodology and biological direction that might help keep modelers at the forefront of cancer immunotherapy development.Comment: Accepted for publication in the Journal of the Royal Society Interfac

Stochastic Model for Tumor Control Probability: Effects of Cell Cycle and (A)symmetric Proliferation

Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given dose and schedule of ionizing radiation eradicates all the tumor cells in a given tissue is called the tumor control probability (TCP), and is often used to compare various treatment strategies used in radiation therapy. In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing a stochastic model of a tumor comprised of actively dividing cells and quiescent cells with different radiation sensitivities. We derive an exact phase-diagram for the steady-state TCP of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCP curve. However, for very low doses of radiation, these proportions become significant determinants of the TCP. Moreover, we use a novel numerical approach based on the method of characteristics for partial differential equations, validated by the Gillespie algorithm, to compute the TCP as a function of time. We observe that our results differ from the results in the literature using similar existing models, even though similar parameters values are used, and the reasons for this are discussed.Comment: 12 pages, 5 figure

Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour

Improving treatment of glioblastoma: new insights in targeting cancer stem cells effectively

Glioblastoma is the most common primary malignant brain tumour in the adult population. Despite multimodality treatment with surgery, radiotherapy and chemotherapy, outcomes are very poor, with less than 15% of patients alive after two years. Increasing evidence suggests that glioblastoma stem cells (GSCs) are likely to play an important role in the biology of this disease and are involved in treatment resistance and tumour recurrence following standard therapy. My thesis aims to address two main aspects of this research area: 1) optimization of methods to evaluate treatment responses of GSCs and their differentiated counterparts (non-GSCs), with a particular focus on a tissue culture model that resembles more closely the tumoral niche; 2) characterization of cell division and centrosome cycle of GSCs, investigating possible differences between these cells and non-GSCs, that would allow the identification of targets for new therapeutic strategies against glioblastomas. In the first part of my project, I optimized a clonogenic survival assay, to compare sensitivity of GSCs and non-GSCs to various treatments, and I developed the use of a 3-dimentional tissue culture system, that allows analysis of features and radiation responses of these two subpopulations in the presence of specific microenvironmental factors from the tumoral niche. In the second part, I show that GSCs display mitotic spindle abnormalities more frequently than non-GSCs and that they have distinctive features with regards to the centrosome cycle. I also demonstrate that GSCs are more sensitive than non-GSCs to subtle changes in Aurora kinase A activity, which result in a rapid increase in polyploidy and subsequently in senescence, with a consistent reduction in clonogenic survival. Based on these findings, I propose that kinases involved in the centrosome cycle need to be explored as a novel strategy to target GSCs effectively and improve outcomes of glioblastoma patients

A multiple scale model for tumor growth

We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between cancerous and normal tissue, cell division, apoptosis, vascular endothelial growth factor release, and the coupling between these processes. Simulations of the model are used to investigate the effects of nutrient heterogeneity, growth and invasion of cancerous tissue, and emergent growth laws

Oscillatory dynamics in a model of vascular tumour growth -- implications for chemotherapy

Background\ud \ud Investigations of solid tumours suggest that vessel occlusion may occur when increased pressure from the tumour mass is exerted on the vessel walls. Since immature vessels are frequently found in tumours and may be particularly sensitive, such occlusion may impair tumour blood flow and have a negative impact on therapeutic outcome. In order to study the effects that occlusion may have on tumour growth patterns and therapeutic response, in this paper we develop and investigate a continuum model of vascular tumour growth.\ud Results\ud \ud By analysing a spatially uniform submodel, we identify regions of parameter space in which the combination of tumour cell proliferation and vessel occlusion give rise to sustained temporal oscillations in the tumour cell population and in the vessel density. Alternatively, if the vessels are assumed to be less prone to collapse, stable steady state solutions are observed. When spatial effects are considered, the pattern of tumour invasion depends on the dynamics of the spatially uniform submodel. If the submodel predicts a stable steady state, then steady travelling waves are observed in the full model, and the system evolves to the same stable steady state behind the invading front. When the submodel yields oscillatory behaviour, the full model produces periodic travelling waves. The stability of the waves (which can be predicted by approximating the system as one of λ-ω type) dictates whether the waves develop into regular or irregular spatio-temporal oscillations. Simulations of chemotherapy reveal that treatment outcome depends crucially on the underlying tumour growth dynamics. In particular, if the dynamics are oscillatory, then therapeutic efficacy is difficult to assess since the fluctuations in the size of the tumour cell population are enhanced, compared to untreated controls.\ud Conclusions\ud \ud We have developed a mathematical model of vascular tumour growth formulated as a system of partial differential equations (PDEs). Employing a combination of numerical and analytical techniques, we demonstrate how the spatio-temporal dynamics of the untreated tumour may influence its response to chemotherapy.\ud Reviewers\ud \ud This manuscript was reviewed by Professor Zvia Agur and Professor Marek Kimmel