MathOnco_Workshop2022

Ahmad Abbas, Swansea University, UK

Title: Multiscale modelling of the dose distribution in cochlea associated with brain radiotherapy

Objective: This research aims to study the microscopic dose distribution in the temporal bone and cochlea associated with modern radiotherapy treatments using data from Micro CT imaging of resected tissue and a Monte Carlo (MC) algorithm.

Method: Open-access DICOM format data of the resected cochlea tissue was used with the FLUKA MC code to mimic potential high-dose scenarios associated with volume modulated arc therapy. Twenty-three photon energy levels were simulated separately to calculate the dose distribution. The results were processed in MATLAB and then used in advanced, multiscale model to relate results to clinically relevant measures. Eleven different scenarios of tumour irradiation were used to implement in the advanced model. Treatment plans were created for each case and compared with the advanced model.

Results: The Micro CT shows three densities levels in the temporal bone and cochlea that cannot be distinguished in clinical CT. In the low energy range 0.055-0.09 MeV, the largest proportion of the dose (48.8%) was deposited within high-density bone, whereas above 0.125 MeV there is a shift to deposition in low density tissue, reaching 53%. The cases show that the treatment planning system (TPS) overestimated the dose in all cases. In some cases, the percentage difference reached 17.4% in Dmin. Furthermore, the Dmax is significantly underestimated in the TPS and reached -10% and mean dose difference of 8%.

Conclusion:Hearing loss is side effects of radiotherapy treatment. Increasing the model accuracy by using micro-CT resolution data and MC computation can help reduce the dose to the cochlea.

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/ Fiona Macfarlane, 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] 

Mark Davies, Swansea Bay University Health Board (NHS), UK

Title: The evolution of cancer treatment

Great progress has been made in the treatment of cancer in recent years. An increase in our understanding of the disease, largely driven by improvements in genomic technology, has led to a shift to more personalized care. However, mathematical models of cancer evolution and ecology, backed by empirical evidence, have suggested ways in which oncology practice could be significantly improved. I will discuss these new potential approaches to the treatment of cancer, highlighting areas where collaboration between oncologists and mathematicians could lead to better clinical outcomes.

Heiko Enderling, Moffitt Cancer Centre, USA

Title: Personalization radiation therapy using differential equations

The standard radiotherapy protocols deliver the same total dose and dose fractionation for all patients. One shortcoming of current clinical practice is that radiation protocols do not consider patient-specific factors that may influence outcome. We present a quantitative framework to estimate a personalized radiation dose for individual patients, based on pre- and early on-treatment tumor volume dynamics. We show that mathematical modeling of tumor growth and radiation response dynamics can fit the clinical data with high accuracy, and demonstrate the feasibility of using tumor volume dynamics to inform dose personalization and stratification for dose escalation and de-escalation.

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

Title: Modelling the effect of T cell heterogeneity on anti-cancer T cell vaccines

Current anti-cancer T cell vaccines often do not substantially reduce tumour burdens despite stimulating large numbers of anti-tumour T cells.  Recent experiments have shown that this failure might result because most vaccine-elicited T cells might have low avidity to tumour cells.  Moreover, these low-avidity T cells, which are abundant, do not effectively kill cancer cells and potentially inhibit the efficacy of nearby high-avidity T cells.

The presence of high and low-avidity anti-cancer T cells could produce a Goldilocks effect, in which stimulating more T cells does not necessarily produce better outcomes.  By modelling T cell selection using a system of ordinary differential equations, we show that modulating vaccine deliveries and dosages to preferentially elicit high-avidity T cells could improve efficacy.  Our model demonstrates a proof-of-concept approach to tuning anti-cancer T cell repertoires to improve T cell vaccination strategies.

Leonardo Lonati, University of Pavia, Italy

Title: Integrating cell cycle data from in vitro and in silico models to target cancer resistance after radiation therapy

Research efforts are being carried out to target Colorectal cancer (CRC) resistance to treatment: the use of in vitro and in silico models can help understand associated mechanisms in controlled conditions. Starting from a pre-clinical in vitro dataset on the radiation-response of the colorectal adenocarcinoma Caco-2 cell line, we developed a compartmental model which follows cell cycle transitions, tumoral growth, and cell death rate after X-ray exposure up to 10 Gy. Model parameters were adapted to reproduce the experimental percentages of cell cycle phases in different conditions obtained via flow-cytometry measurements. Independent measurements of doubling time and duration of DNA synthesis are further used to constrain model parameters. The model can predict experimental growth curves for Caco-2 cells irradiated in the dose range 2 Gy – 10 Gy. Output parameters have biological significance and can be used to quantify cell radio-resistance in the early response up to   48 hours post-exposure.   In perspective, this theoretical framework can set the basis of a   computational tool to increase the effectiveness of therapeutic strategies for CRC.

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.

Kira Pugh, Swansea University, UK

 Title: Using an in-silico approach to investigate the synergistic effects of DNA damage response inhibitor drugs

Every cell in our bodies faces DNA damage thousands of times per day and the DNA damage response (DDR) is the cellular response to detect and repair this damage. The DDR involves cell cycle checkpoints that require a cell to pass before continuing its progression through the cell cycle. If a damaged cell encounters a checkpoint, then it will get arrested to allow time for repair. These cell cycle checkpoints can be faulty in some cells allowing damaged cells to progress through the cell cycle and if a damaged cell gets replicated and divides this can cause deleterious mutations which could develop into cancer. Here, we discuss a biologically motivated mathematical model that studies damaged and undamaged cancer cells progressing through the cell cycle. By using this model, we can study the effects of two anti-cancer drugs, namely olaparib (a PARP inhibitor) and AZD6738 (an ATR inhibitor drug) as monotherapies and in combination. These drugs work by inhibiting certain proteins involved in the DDR, meaning that cancer cells cannot be repaired, leading to further damage which will eventually lead to cell death. The model findings are consistent with the experimental data showing that when the drugs are used in combination, lower doses and shorter treatment times can be used to induce cell death and growth inhibition of cancer cells.

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.