ONCO Subgroup Contributed Talks

Gustav Lindwall

Max Planck Institute for Evolutionary Biology

"A Mathematical Model for Pseudo-Progression in CAR-T therapy of B-cell Lymphomas"

CAR-T cell therapy, where patient T cells are genetically modified to target CD19-presenting B cells, has transformed the treatment landscape for several types of B-cell lymphomas. However, this therapy often triggers a strong inflammatory response, which can cause the tumor to temporarily swell in the days following CAR-T infusion — a phenomenon known as pseudo-progression. In this work, we present a dynamical model of CAR-T cell therapy that explicitly incorporates the role of pro-inflammatory cytokines in shaping treatment outcomes. Our model reproduces a wide spectrum of clinical trajectories, including complete remission, treatment failure, and transient pseudo-progression. Importantly, the model’s parameters correspond to measurable patient-specific factors, allowing us to explore how individual patient characteristics influence long-term treatment success. The parametrization of the model maps on to measurable patient characteristics, and we discuss how these parameters impact the long term behavior of the model.

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Rafael Bravo

University of Texas at Austin

"Testing the feasibility of estimating the migration to proliferation rate ratio in glioblastoma from single time-point MRI data"

Introduction: Glioblastoma tumors with a high migration to proliferation ratio (D/k ratio) are more drug resistant, suggesting 1) that estimating D/k ratios can help predict patient responses, and 2) investigating the cellular mechanisms behind D/k ratios can help understand the mechanisms of drug resistance. Here we quantify the identifiability of D/k ratios using synthetic tumor data. Materials and Methods: We used the standard reaction-diffusion model (i.e. logistic growth and diffusion) initialized with a single cell. Using this model, we grew synthetic tumors, saving the density field for calibration once the tumor had filled 10% of the domain. We fixed proliferation (k, 1/day) and used grid search followed by Levenberg-Marquardt optimization to calibrate the diffusion rate (D, mm2/day) and growth time (t, days) that produced density distributions matching the synthetic data as closely as possible. We quantified the ability of the algorithm to accurately and precisely identify D/k ratios in both the presence and absence of Gaussian noise. Results: Our algorithm finds D/k ratios with very high accuracy: 0.95 +/- 0.72% difference from correct D/k with k fixed at 0.01/day. We found that with 5% noise added the ability to accurately recover D/k ratios improved as its magnitude increased: 9.6 +/- 13.38% when D/k = 10-2 mm2 versus 2.7 +/- 3.65% when D/k = 1 mm2 Future Directions: Ongoing work will establish the minimal data requirements to accurately estimate D/k ratios within 10% of the correct values, and then apply the technique to the brain tumor image segmentation (BRATS) dataset. All BRATS patients have a single segmented pre-treatment MRI (N = 103) which we will use to estimate their D/k ratios. A subset of the BRATS patients also has RNA microarray data available (N = 91). We plan to correlate the patients’ D/k ratios with gene set scores derived from their microarray data to identify cellular mechanisms that potentially underly the D/k ratios.

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Aaron Li

University of Minnesota

"Using a pharmacokinetic ctDNA shedding model to develop a biomarker of tumor response to targeted therapy"

Early prediction of response to therapy or lack thereof is essential for efficient treatment planning. Next-gen sequencing (NGS) has made it possible to non-invasively collect and sequence circulating tumor DNA (ctDNA) from longitudinal plasma samples. While ctDNA data continues to be collected on a wide variety of cancers and treatment types, it is still unclear what ctDNA biomarkers are most indicative of treatment success or failure. We present a pharmacokinetic model of ctDNA shedding under targeted therapy. Using this model to simulate a cohort of virtual patients, we demonstrate the predictive potential of a biomarker based on early ctDNA sampling. We compare the performance of the biomarker to that of a neural network classifier as well as existing ctDNA biomarkers. We show that our biomarker is able to match and exceed the performance of alternatives, both in terms of accuracy and earliness of prediction.

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Ruby Nixson

Mathematical Institute, University of Oxford

"A structured-PDE approach to targeting a quiescent sub-population under hypoxia and anti-tumour therapies in paediatric glioma."

Paediatric diffuse midline gliomas are highly aggressive, incurable, childhood tumours. Their location in the brainstem limits treatment to radiotherapy, which allows an average survival time of 9-11 months. A sub-population of quiescent tumour cells are thought to be responsible for the poor outcomes of these patient. Quiescence is often viewed as a reversible resting state in which cells temporarily exit the cell cycle, the process controlling DNA replication and cell division. Radiosensitivity varies during the cell cycle, and quiescent cells exhibit a higher relative level of radio-resistance. Hypoxia (physiologically low levels of oxygen) also impacts cell cycle progression and quiescence, as well as response to radiotherapy, contributing to poor patient outcomes. We build on existing mathematical models of cell cycle progression under treatment which account for the radio-resistance of quiescent cells and their ability to re-enter the cell cycle and proliferate. We derive a system of partial differential equations (PDEs), which structures cells by the time spent in each cell cycle phase and allows transitions to and from a quiescent phase. By considering oxygen-dependent cell cycle progression, we use the model to investigate how the proportion of quiescent cells changes when we impose fluctuating oxygen dynamics and treat with radiotherapy. We extend existing studies that optimise treatment schedules using a balance of treatment outcome and toxicity/cost by incorporating a fixed radiotherapy schedule to investigate the impact of a hypothetical drug that alters the transition dynamics to and/or from quiescence. By considering different mechanisms of action for this hypothetical drug, we use our PDE model to identify candidate drugs with the potential to slow tumour progression and improve patient outcomes. This work will inform our clinical collaborators if such an improvement is possible, and what the design of a suitable drug should be.

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Reshmi Patel

The University of Texas at Austin

"MRI-based mathematical modeling to predict the response of cervical cancer patients to chemoradiation"

Concurrent chemoradiation followed by brachytherapy is the standard-of-care treatment for locally advanced cervical cancer (LACC), but 30% of treated patients experience local recurrence [1], indicating a need for patient-specific, optimized therapeutic regimens to improve outcomes. We aim to predict patient-specific response to chemoradiation by applying our established MRI-based mathematical modeling framework [2]. The study cohort consisted of 10 LACC patients who underwent imaging with T2-weighted MRI, dynamic contrast-enhanced MRI, and diffusion-weighted MRI (DWI) before (V1), after two weeks (V2), and after five weeks (V3) of chemoradiation [3]. We registered all patient-specific MRI data within and between visits, and maps of the number of tumor cells (NTC) were calculated from the DWI-derived apparent diffusion coefficients. Our biology-based reaction-diffusion models characterize the spatiotemporal change in NTC as a function of cell diffusion, proliferation, and therapy-induced death. We consider two model options for cell death: (A) distinct chemotherapy (exponential decay) and radiotherapy (instantaneous decrease according to the linear-quadratic model) terms and (B) a single exponential decay term describing chemoradiation. Proliferation and chemoradiation efficacy rates were calibrated to the V1 and V2 NTC maps, and the calibrated model was run forward to predict the NTC at V3. Using Model (A), the concordance correlation coefficient (CCC) between the observed and predicted V1 to V3 change in total tumor cellularity was 0.87, and the CCC between the observed and predicted change in tumor volume was 0.90; using Model (B), the CCC values were 0.97 and 0.90, respectively. These preliminary findings show the promise of our mathematical modeling framework in predicting LACC response to chemoradiation. References: [1]. CCCMAC. Cochrane Database Syst Rev. 2010. [2]. Jarrett et al. Nat Protoc. 2021. [3]. Bowen et al. J Magn Reson Imaging. 2018.

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Pujan Shrestha

Texas A&M University

"An ODE-SDE Model for Ct-DNA dynamics"

Effective cancer therapies, while continuously improving, are often constrained by lower detection limits of disease. Tumor-immune dynamics in this limit present one of the most pressing knowledge gaps as cancer ultimate escape or elimination are often determined following an intervening period of population equilibrium sustained at low population size. Population dynamics in this small-population limit are affected by intrinsic noise in the tumor-immune interaction, as are estimates of population disease burden by extrinsic noise in acquiring such estimates through associated biomarkers. We present a modeling framework that investigates the interactions between tumor cells and the immune system in the small population regime, focusing on how these interactions influence biomarker levels. The framework combines deterministic elements, which describe tumor growth and immune responses, with stochastic components that capture the inherent variability in biomarker release. We use a system of ordinary differential equations (ODEs) to represent the tumor-immune dynamics between an adaptive immune compartment, immunogenic tumor cells, and evasive tumor cells. The immune system’s role in controlling tumor growth is reflected in the tumor-immune interaction terms. Apoptotic death via tumor-immune interactions and necrotic death via the tumor competition under a shared carrying capacity both contribute to the release of a tumor biomarker. We focus on applying our model to ct-DNA, wherein we frame ct-DNA dynamics using a stochastic differential equation (SDE). This SDE framework accounts for the variability in ct-DNA release due to the dynamic tumor-immune interactions, as well as inherent biological noise, such as DNA degradation and clearance. By coupling the ODE system of equations for tumor-immune dynamics with the SDE for ct-DNA release, we can use the model to study the fluctuations in ct-DNA levels driven by tumor-immune dynamics and exogenous sampling noise.

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Keith Chambers

University of Oxford

"Adipocyte-derived lipids promote phenotypic bistability in a structured population model for melanoma growth"

Melanoma cells exhibit a continuum of proliferative to invasive phenotypes. While single-cell and spatial transcriptomics have enabled biologists to quantify the distribution of phenotype amongst melanoma cells, a complete mechanistic understanding is currently lacking. A key issue is the impact of adipocyte-derived lipids, whose uptake by melanoma cells drives an invasive response that may lead to metastasis. To address this, we have developed a phenotype-structured model for melanoma cell populations that couples the phenotype dynamics to the essential aspects of intracellular lipid metabolism and the extracellular microenvironment. In this talk, I will first introduce a single-cell ODE model that illustrates how lipid uptake gives rise to phenotypic bistability in melanoma cells. I will then show how a phenotype-structured population model, whose advection term is informed by the single-cell model, exhibits a range of qualitative behaviours, including cyclic solutions and bimodal phenotypic distributions. Together, these results increase understanding of the role played by adipocyte-derived lipids and other microenvironment factors in shaping the distribution of phenotype in melanoma cell populations. We speculate that our modelling framework may also be applicable to other lipid-rich tumours (e.g. breast and ovarian cancers) that are commonly associated with increased metastasis.

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Fabian Spill

University of Birmingham

"Regulation of Intra- and Intercellular Metabolite Transport in Cancer Metabolism"

Metabolite transport is essential for cellular homeostasis, energy production, and metabolic adaptation. In cancer, dysregulated transport sustains tumor growth and alters redox balance. The mitochondrial solute carrier SLC25A10 facilitates succinate, malate, and phosphate exchange, influencing central carbon metabolism. However, its transport kinetics and physiological directionality remain poorly understood. We present a mathematical model of SLC25A10 based on a ping-pong kinetic mechanism, capturing competitive dynamics between malate and succinate. Our simulations reveal that under normal conditions, malate flux dominates due to its higher binding affinity. However, in succinate dehydrogenase (SDH) dysfunction, excess succinate induces a transient efflux shift and phosphate flux reversal. If experimentally validated, this metabolic shift could serve as a biomarker for tumors with SDH mutations. Integrating our kinetic model with genome-scale metabolic networks, we highlight the role of mitochondrial transport in cancer metabolism. Specifically, in multiple myeloma, metabolic crosstalk between plasma cells and bone marrow stromal cells is key to tumor progression. Our findings demonstrate the power of mathematical modeling in uncovering transport-mediated metabolic vulnerabilities, offering potential therapeutic targets for cancer and metabolic diseases.

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