SWAMBA Workshop on Mathematical Oncology

Alexander Anderson, Moffitt Cancer Centre, USA

Title: Evolutionary Therapy

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.

Sarah Brüningk, ETH Zurich, Switzerland

Title: Prediction and modelling of radiotherapy response in hard-to-treat brain tumours – a combination of machine learning and mechanistic modelling

Given their delicate anatomical location and biological nature as infiltrating diseases, malignancies of the brain remain hard to treat and patients are faced with poor prognosis. Radiotherapy (RT) remains one of the key-life prolonging and palliative treatment options for these patients. Adaptation of the delivered dosing and fractionation, such as hypofractionation or intermittent delivery, could improve the efficacy of this treatment.  We explore the potential of RT personalization through mechanistic modelling based on personalized estimates of RT sensitivity. Previously, the radiosensitivity index (RSI) has been suggested to stratify patients based on their RT response. This index is based on genetic tumour information, which may, however, not always be readily available. We investigate the use of machine learning to estimate biomarkers of RT response from non-invasive magnetic resonance imaging that could in turn be used as model parameters to simulate alternative treatment scenarios. The aim of this presentation will be to provide an insight into the complementary potential of machine learning and mechanistic modelling with application examples to optimize the RT treatment of malignant brain tumours such as recurrent high-grade glioma or paediatric diffuse midline glioma.

Joshua Bull, University of Oxford, UK

Title: Mathematical methods for mapping multiplex models of macrophages

Mark Chaplain, University of St.Andrews, UK

Title: Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Rheumatoid arthritis (RA) is a chronic inflammatory disorder that causes pain, swelling and stiffness in the joints, and negatively impacts the life of affected patients. The disease does not have a cure yet, as there are still many aspects of this complex disorder that are not fully understood. While mathematical models can shed light on some of these aspects, to date there are few such models that can be used to better understand the disease. As a first step in the mechanistic understanding of RA, in this study we introduce a new hybrid mathematical modelling framework that describes pannus formation in a small proximal interphalangeal (PIP) joint. We perform numerical simulations with this new model, to investigate the impact of different levels of immune cells (macrophages and fibroblasts) on the degradation of bone and cartilage. Since many model parameters are unknown and cannot be estimated due to a lack of experiments, we also perform a sensitivity analysis of model outputs to various model parameters (single parameters or combinations of parameters). Finally, we discuss how our model could be applied to investigate current treatments for RA, for example, methotrexate, TNF-inhibitors or tocilizumab, which can impact different model parameters.

[Joint work with F Macfarlane, R Eftimie] 

Heiko Enderling, Moffitt Cancer Centre, USA

Title: Personalizing radiation oncology with mathematical modeling

Abstract: TBA

Sara Hamis, Tampere University, Finland

Title: Analysing cancer cell populations with spatio-temporal cumulant models

Spatio-temporal cumulant models (STCMs), which have arisen from recent advances in theoretical ecology, can be used to describe population dynamics generated by a specific family of individual-based models, namely stochastic point processes (SPPs). STCMs are spatially resolved population models formulated by a system of ordinary differential equations that approximate the dynamics of two SPP-generated summary statistics: first-order Spatio-temporal cumulants (densities), and second-order Spatio-temporal cumulants (spatial covariances).

In this talk, we exemplify how STCMs can be used in mathematical oncology by modelling a theoretical cancer cell population comprising interacting growth factor producing and non-producing cells. Our results demonstrate that STCMs can capture SPP-generated population density dynamics, even when mean-field population models (MFPMs) fail to do so. From both MFPM and STCM equations, we derive treatment-induced cell death rates required to achieve non-growing cell populations. When testing these treatment strategies in SPP-generated cell populations, our results demonstrate that STCM-informed strategies match or outperform MFPM-informed strategies in terms of inhibiting population growth. We argue that STCMs provide a new framework in which to study cell-cell interactions and can be used to deepen the mathematical analysis of IBMs and thereby increase IBMs’ applicability in cancer research.

Mohit Kumar Jolly, IISc Bangalore, India

Title: Design principles of cell-state switching networks in cancers

Reversible switching among multiple cell-states (phenotypes) is a hallmark of cancer metastasis and therapy resistance – the two major unsolved clinical challenges in cancer. These switches are often orchestrated by underlying regulatory networks. While we understand the dynamics of simple network motifs, how do large networks lead to a limited number of cell-states, despite their complexity, remains largely elusive. Here, we investigate multiple different networks governing cell-state switching across cancer types and identified a latent design principles in their topology that limits their phenotypic repertoire – the presence of two “teams” of nodes engaging in a mutually inhibitory feedback loop, forming a toggle switch. These teams are specific to these networks and directly shape the phenotypic landscape and consequently the frequency and stability of terminal phenotypes vs. the intermediary ones. Our analysis reveals that network topology alone can contain information about phenotypic distributions it can lead to, thus obviating the need to simulate them. We unravel topological signatures that can drive canalization of cell-states in cancers.

Peter Kim, University of Sydney, Australia

Tommaso Lorenzi, Politecnico di Torino, Italy

Title: Dissecting the impact of phenotypic heterogeneity on the growth of cell populations: a partial differential equation approach

In this talk, partial differential equation models for the growth of phenotypically heterogeneous cell populations will be considered. In these models, the phenotypic state of each cell is described by a structuring variable that captures intercellular variability in cell proliferation and migration rates. A formal derivation of such continuum models from corresponding individual-based models will be carried out, analytical and numerical results summarising the behaviour of the solutions to the model equations will be presented, and the insights generated by these results into the way proliferation-migration tradeoffs shape the phenotypic structuring of tumours will be discussed.

Angélique Stéphanou, University of Grenoble-Alps, France

Title: Investigation of the metabolic heterogeneity in tumour spheroids with a hybrid multi-scale model

We developed a hybrid multi-scale model to describe the growth of tumour spheroids as observed in vitro. The model specifically focuses on the description of the cell energy metabolism that involves the cooperative effects of oxidative phosphorylation and glycolysis. To that end, we used coupled ordinary differential equations for the cell metabolism that are solved for each cell of an agent based model. The diffusion of the two main nutrients, oxygen and glucose, are described with partial differential equations. The consumption rates of these substrates are modulated by the extracellular acidity in agreement with recent experimental observations. Our simulation results show that the cell metabolism is spatially and temporally heterogeneous in the growing spheroids. A whole landscape of metabolic attractors can be described where the Warburg effect, often described as a hallmark of cancer, appears as a transient state.