MS05 - MFBM-16

Mathematical Modelling in Disease and Therapy: Integrating Quantitative Frameworks for Deeper Insights

Wednesday, July 16 at 10:20am

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Maria Kleshnina (Queensland University of Technology), Mason Lacy (Queensland University of Technology), Luke Filippini (Queensland University of Technology)

Description:

Mathematical modelling plays a crucial role in advancing our understanding of disease dynamics and optimizing therapeutic strategies. This mini symposium brings together innovative approaches that integrate mathematical frameworks with experimental and clinical data to inform disease modelling and therapy design. The talks will explore how stochastic and continuum models can capture complex cellular behaviours, from immune cell expansion in cancer therapy to anisotropic movement in brain tissue. Algebraic and game-theoretic methods will provide insights into treatment resistance and optimal intervention strategies, while data-driven Boolean network models will shed light on cancer progression at the single-cell level. By combining mathematical techniques with cutting-edge biological data, this symposium will highlight how quantitative approaches can uncover fundamental mechanisms of disease and guide more effective treatment strategies.

Luke Filippini

Queensland University of Technology

"Data-informed stochastic frameworks of anisotropic movement in the brain"

Neurological diseases and disorders are the subject of an extensive area of research that is of significant importance to the scientific community and wider population. Notable examples include autism, multiple sclerosis, and nervous system cancers, such as glioblastoma, which currently remain incurable. This is primarily due to the structural complexity of the nervous system and the impracticalities of surgical examination and/or resection. Hence, indirect methods, such as magnetic resonance imaging and mathematical modelling, are frequently relied upon to yield meaningful insight into the physiological processes that drive disease progression. In this talk, we discuss methods for deriving data-informed stochastic models from deterministic frameworks of anisotropic particle diffusion, motivated by applications to neurological diseases and disorders. We consider on-lattice stochastic models derived from a finite volume discretisation of the diffusion equation coupled with diffusion tensor imaging data. Furthermore, we discuss the limitations of using a traditional square or rectangular lattice, in terms of obtaining non-negative transition probabilities, and present a more promising approach using a hexagonal lattice. Most notably, the latter approach yields non-negative transition probabilities for any valid diffusion tensor.

Moriah Echlin

Tampere University

"Using Single-Cell Data-driven Boolean Network Models to Analyze Prostate Cancer Progression"

Cancer is a multifaceted disease, with many unique drivers; yet all cancers have a common foundation – the abnormal and malignant behavior of the body’s cells. Broadly, cellular behaviors result from the dynamics of the gene regulatory network (GRN) and genetic mutations can force the GRN into irregular dynamics. Thus, cells can exhibit the pathological properties associated with cancer: unchecked growth, immune evasion, and metastasis. To understand the origins and ramifications of malignant changes to the GRN, we combine clinically relevant single-cell transcriptomic data with a dynamical systems theoretical framework. This approach takes advantage of the system-wide gene correlations and cell state heterogeneity captured in single-cell ‘omics and the temporal and functional structure provided by dynamical systems models. Specifically, we use a Boolean network architecture to convert distinct cellular profiles to dynamical states. Our work focuses on the conversion of single-cell transcriptomic data to informative Boolean states and their subsequent analysis with the aim of identifying disease-relevant genes, inter-gene dependencies, and cell state dynamics that would not be evident in the original unstructured data. In particular, we highlight changes to the cell state structure that occur as cancer progresses from a primary indolent tumor to metastatic treatment-resistant disease.

Louise Spekking

TU Delft

"Improving cancer therapy through migrastatics and estimating tumor composition"

Adaptive therapy, which anticipates and forestalls the evolution of resistance in cancer cells, has gained significant traction, especially following the success of the Zhang et al.'s protocol in treating metastatic castrate-resistant prostate cancer. While several adaptive therapies have now advanced to clinical trials, none currently incorporates migrastatics, i.e. treatments designed to inhibit cancer cell metastasis. In this study, we propose the integration of migrastatics into adaptive therapy protocols and an evaluation of the potential benefits of employing a game-theoretic spatial model. Our results demonstrate that the combination of adaptive therapy with migrastatics effectively delays the onset of metastasis and reduces both the number and size of metastases across the majority of cancer scenarios . This approach not only extends the time to the first metastasis but also enhances the overall efficacy of adaptive therapies. Our findings suggest a promising new direction for cancer treatment, where adaptive therapy, in conjunction with migrastatic agents, can target both the evolution of resistance and the metastatic spread of cancer cells. In treatment of cancers, success strongly depends on our ability to capture how the disease evolves in response to treatment, both in terms of the size and composition. Understanding the changes in these compositions and the composition of the tumor will aid in developing new therapies in the future. In the second part of the talk, we will assess different machine learning methods on the deconvolution of cells based on microarray RNA sequencing data of glioblastoma organoids. Here, we show that the proportion of cell types changes over time with treatment and that these changes differ between organoids. We believe that this methodology can help in designing better therapies through testing evolutionary responses in patient-derived organoids, while in parallel the ecological response can be tracked through serum biomarkers and imaging in the corresponding patients. This will improve the adoption of adaptive therapies in clinical practice. Joint work with Jan Brábek, Joel S. Brown, Rachel Cavill, Robert A. Gatenby, Christopher Hubert, Weronika Jung, Christer Lohk, Barbora Peltanová, Daniel Rösel, Katharina Schneider, Maikel Verduin, Marc Vooijs, Sepinoud Azimi and Kateřina Staňková.

Noa Levi

University of Melbourne

"Leveraging algebraic approaches to inform therapeutic intervention"

The propensity for biological systems to exhibit adaptation is thought to play an important role in many treatment failures, especially in the context of cancer, since the underlying signalling networks under which cancer thrives are frequently able to adapt to the therapy. Here we present a general mathematical framework to study the effect of targeted pharmacological intervention in intracellular signalling networks which exhibit adaptation. This framework combines methods from graph theory and algebraic geometry to explain why treatment often fails, while illuminating alternative treatment strategies which may offer more success.

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Annual Meeting for the Society for Mathematical Biology, 2025.