Organized by: Kathleen Wilke, Gibin Powathil
Note: this minisymposia has multiple sessions. The other session is MS02-ONCO-1.

• Jana Gevertz The College of New Jersey (Department of Mathematics & Statistics)
  "Guiding model-driven combination dose selection using multi-objective synergy optimization"
The biomedical community has long sought to identify synergistic drugs for which the combined effect is greater than additive. However, lack of consensus on the definition of additivity has complicated this goal, particularly because a combination classified as synergistic by one definition can be classified as antagonistic by another. In this talk, I introduce the Multi-Objective Optimization of Combination Synergy – Dose Selection (MOOCS-DS) method as a rigorous approach to bring clarity and consistency to selecting an optimally synergistic dose for a pre-selected drug combination. MOOCS-DS bridges the gap between efficacy-based additivity definitions focused on improving effectiveness and potency-based definitions focused on reducing toxicity. It does this by identifying the Pareto optimal doses, defined as the set of possible combination doses for which one synergy metric cannot be improved without compromising the other. I demonstrate the potential of this approach to guide dose and schedule selection using a model fit to pre-clinical data of the combination of the PD-1 checkpoint inhibitor pembrolizumab and the antiangiogenic drug bevacizumab on two lung cancer cell lines.
• Mohammad Zahid H. Lee Moffitt Cancer Center & Research Institute (Integrated Mathematical Oncology)
  "Fractionated Photoimmunotherapy to Stimulate an Anti-Tumor Immune Response"
Introduction: Photodynamic therapy (PDT) is an anti-cancer therapy where a photosensitizer (e.g. verteporfin) is delivered to cells and then near-infrared light is used to kill the cells that have taken up the photosensitizer. Current PDT is applied locally but does not discriminate between cancer and non-cancer cells. Photoimmunotherapy (PIT) utilizes photosensitizers conjugated to antibodies targeted against cancer cells with the idea that this will lead to more targeted cancer killing and sparing of other cell types in the area. We aim to use preliminary in vitro measurements to inform a modeling investigation of how PIT may impact tumor-immune dynamics and inform methods of best utilizing PIT to promote an anti-cancer immune response. Materials and Methods: Dose response curves of tumor cells (OVCAR5 ovarian cancer cell line) and T-cells (murine T-cells) to PDT (verteporfin + 665 nm light), PIT (cetuximab-verteporfin + 665 nm light), and chemotherapy (cisplatin) were measured in order to measure relative tumor and T-cell viability. These results were used in conjunction with a mathematical model of tumor and immune effector cell interaction consisting of a system of coupled ordinary differential equations that combine logistic tumor growth, immune-mediated tumor cell kill, and immune exhaustion. This model yields a phase plane that separates all combinations of initial conditions into two basins of attraction corresponding with uncontrolled tumor and immune-mediated cancer control. The in vitro viability analyses were used as inputs to the math model to search for potential dosing regimes and treatment schedules that could lead to immune-mediated cancer control. Results and Discussion: The PDT and chemotherapy treatments showed typical sigmoidal dose response curves with both tumor and T-cell kill increasing with increasing dose. However, in the case of PIT with the cancer-cell targeted immunoconjugate, low intensity light doses (< 10 J/cm2) yielded an increase in T-cell numbers (i.e. immunostimulatory response) relative to the no-treatment control. We leveraged this immunostimulatory regime to simulate fractionated PIT dosing schedules that increase the number of immune effector cells and decreasing the number of tumor cells. Simulation results of tumor-immune dynamics with PIT delivered in 6 fractions of 1 J/cm2 each, where each PIT fraction stimulates T-cell growth, gradually moved the immune state of the system into the cancer control region of the phase plane. We further calculated the minimum number for fractions needed for tumor control for all initial conditions over the entire immunostimulatory dose range from 1-10 J/cm2. These results present hypotheses that can be tested with in vitro co-culture measurements in a feedback loop of experiment and modeling. Conclusions: Here we demonstrated a first application of a simple model of tumor-immune interaction with inputs of in vitro measurements of cell survival in order to motivate fractionated PIT using an immunostimulatory dose regime.
• Kira Pugh Swansea University (Mathematics)
  "In silico approaches to study the synergy of DDR inhibitor drugs"
DNA damage occurs thousands of times per cell per day with the DNA damage response (DDR) pathway aiding detection and repair. Some of the pathways involved in the DDR can be exploited for anti-cancer treatments, whereby inhibitor drugs can be used to cause certain pathways to stop working, facilitating cancer growth inhibition and/or death. The ataxia-telangiectasia and Rad3-related (ATR) inhibitor ceralasertib and the poly (ADP-ribose) polymerase (PARP) inhibitor olaparib have shown synergistic activity, in vitro, in the FaDu ATM-KO cell line. Experimental data shows that when these drugs are combined, lower doses and shorter treatment times can induce greater toxicity in cancer cells than using either drug as a monotherapy. We have developed a biologically-motivated mathematical model including cell cycle-specific interactions for both olaparib and ceralasertib, implemented using both a deterministic ordinary differential equation (ODE) model and a stochastic agent-based model (ABM). We study the differences between using an ODE model that considers a homogenous population of cancer cells and using an ABM where the cell population is heterogeneous as each cell has its own characteristics.
• Kathleen Wilkie Toronto Metropolitan University (Mathematics)
  "Modelling Radiation Cancer Treatment with Ordinary and Fractional Differential Equations"
Fractional calculus has recently been applied to mathematical modelling of tumour growth, but it’s use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.

Organized by: Anuraag Bukkuri, Katerina Stankova
Note: this minisymposia has multiple sessions. The other session is MS02-ONCO-2.

• Helena Coggan University College London (Mathematics)
  "Simulations of 3D organoids suggest inhibitory neighbour-neighbour cell signalling as a possible growth mechanism in early lung cancer"
Cancer is driven by the development of genetic mutations. Some mutations which appear in aggressive lung cancers, particularly in people who have never smoked, have also been found to exist quite harmlessly in perfectly healthy people. Although inflammatory cytokines have been highlighted as important promoters of tumour formation, it is unclear what additional stimuli are required in order to drive a `normal cell' harbouring an oncogenic mutation into an invasive tumour. Game-theoretic models suggest that cell fitness may depend on interactions with neighbouring cells. To examine this hypothesis, we looked at the behaviour of stem cells with an activating mutation in EGFR, L858R, when they were given all the nutrients and space required to grow uninhibited in three dimensions. We used computational simulations to model their growth, and predicted that these cells seemed to be suppressing the division of any other cells they touch. We hypothesise that in the very early stages of cancer development, this mutation gives cells a reproductive advantage by preventing the division of non-mutant cells in their environment and driving down competition for space and resources. This also suggests that the success of these pre-cancerous cells depends on their spatial environment and the surrounding cell ecology. We hope that this insight into early cancer development will drive more research into the consequences of cell-cell interaction dysfunction on early tumour initiation.
• Monica Salvioli - Part 1 Delft University of Technology (Institute for Health Systems Science)
  "Validation of the polymorphic Gompertzian model of advanced cancer through in vitro and in vivo data"
Mathematical modeling plays an important role in forming our understanding of therapy resistance mechanisms in cancer. Gompertzian model, analyzed recently by Viossat and Noble in the context of adaptive cancer therapy, describes a heterogeneous cancer population consisting of therapy-sensitive and -resistant cells interacting with each other. Their mathematical analysis demonstrates advantages of adaptive therapy in such models. However, before the theoretical findings can be implemented to cancer therapy design, the model should be validated with real-world data. In our study, we show that the polymorphic Gompertzian model successfully captures trends in both in vitro and in vivo data on non-small cell lung cancer (NSCLC) dynamics under treatment. Biological interpretation of the model’s fit to in vitro data allowed us to confirm previously reported anti-treatment effects of cancer-associated fibroblasts. For the in vivo data, we showed the superiority of the polymorphic Gompertzian model over the monomorphic classical models in fitting the U-shape trend of tumor dynamics and comparable accuracy in other trend categories. In general, the polymorphic Gompertzian model corresponds well to real-world data, thus, its theoretical conclusions can be implemented to the development of clinical studies on adaptive cancer therapy.
• Christin Nyhoegen Max Planck Institute for Evolutionary Biology (RG Stochastic Evolutionary Dynamics)
  "Mathematical models for the optimization of multi-drug treatment strategies"
The evolution of resistance in bacteria and other pathogens, as well as in cancer, poses a major challenge for patient treatment worldwide. One option to reduce the risk of resistance during treatment is to increase the genetic barrier to resistance, which can, for example, be achieved by increasing the number of drugs applied. Different drugs could be alternated (sequential therapy) or administered simultaneously (combination therapy). With multiple drugs in combination, applying the different drugs at the same concentration as in mono-therapy may not be necessary to clear the population of susceptible cells. In fact, reducing the doses might even be required to avoid toxicity. However, lowering the dose might reduce the benefits of combination therapy in controlling resistance. How should we thus choose the number of drugs and their doses to minimize the risk of resistance while efficiently treating a patient and avoiding side effects? In this talk, I will present a pharmacodynamic model for the combination of multiple antibiotics, which can be adapted to study other resistance problems. This model allows us to compare the probability of resistance under mono-therapy at high drug doses and combination therapies at lower doses, keeping the 'total dose' constant. For most of the parameter space, combination therapy with two drugs leads to a lower probability of resistance than mono-therapy. Still, it is not always superior to the treatment with just one drug. Especially the pharmacodynamic properties and the mode of action of the drugs influence the optimal treatment choice. Our mathematical analysis allows us to disentangle the effects of a strategy on the appearance of mutations from those on their establishment probability, allowing us to understand what leads to a strategy's success.
• Alanna Sholokhova University of Washington (Applied Mathematics)
  "Quantifying neoantigen evolution and response to immunotherapy in colorectal cancer"
Each cancerous colorectal tumor contains tumor-specific antigens (neoantigens). Because these neoantigens are present only in the tumor and not in healthy tissue, they are excellent targets for cancer immunotherapies. Checkpoint-blockade immunotherapy enables the patient’s native immune system to recognize tumor cells that were previously invisible due to immune escape, but this therapy has extremely heterogeneous patient outcomes, ranging from total failure to complete remission. We seek to understand how the mutagenic landscape of the tumor is related to therapeutic outcomes. First, we model neoantigen evolution using a stochastic branching-process model. Next, we use a dynamical model of anti-PD1 checkpoint-blockade therapy to predict response to therapy in these in-silico tumors. We relate therapeutic outcomes to heterogeneity of tumor mutational landscape, quantified by both the number of mutations in the tumor as well as the clonality of the neoantigens present in the tumor. We find that mutational burden, the total number of neoantigenic mutations present in the tumor, is insufficient to determine therapeutic outcome. Neoantigenic clonality, the fraction of tumor cells that contain a particular neoantigen, is key in determining response to therapy.

Organized by: Kathleen Wilke, Gibin Powathil
Note: this minisymposia has multiple sessions. The other session is MS01-ONCO-1.

• Annabelle Ballesta Inserm & Institut Curie (unit 900)
  "Quantitative Systems Pharmacology to Personalize Temozolomide-based Drug Combinations against Brain Tumors."
Objectives: Large inter-patient heterogeneity in anticancer drug response highlights the critical need for personalized cancer management which has favored the generation of multi-type individual patient data. However, quantitative systems pharmacology (QSP) approaches handling the complexity of multiple preclinical and clinical data types for designing patient-specific treatments are critically lacking [1-2]. This study aims to design such methodology, to individualize the combination of cytotoxic drugs with targeted molecules, towards a high benefit for patients. Multiple regulatory pathways may be altered initially or activated upon drug exposure in cancer cells, which advocates for the design of combination therapies simultaneously inhibiting multiple targets [3-4]. Such theoretical considerations are backed up by success stories of associating cytotoxic drugs with targeted therapies. The approach was developed here for Glioblastoma multiforme (GBM), the most frequent and aggressive primary brain tumors in adults, which is associated to a median overall survival <18 months despite intensive treatments combining maximal safe neurosurgery, radiotherapy and temozolomide (TMZ)-based chemotherapy. The objective was to develop a QSP pipeline to potentiate TMZ treatment by priming cancer cells with targeted molecules affecting key intracellular functions. Methods: A mathematical model of TMZ cellular pharmacokinetics-pharmacodynamics (PK-PD) based on ordinary differential equations (ODEs) was designed, building on existing works [5]. The model describes key regulatory networks that count among the most deregulated pathways in GBM according to TCGA [6]. Briefly, TMZ is a methylating agent that is spontaneously activated upon a two-step pH-dependent process. Four types of DNA adduct are formed upon TMZ exposure, which are handled either by base excision repair (BER) or by O6-methylguanine-DNA methyltransferase (MGMT). If these initial processes of DNA repair are unsuccessful, DNA single- or double-strand breaks are created, which triggers Homologous Recombination (HR), ATR/Chk1 and p53 activation, cell cycle arrest and possibly apoptosis. TMZ PK-PD model was connected to an ODE-based cell population model that represented cell viability during drug exposure. Model calibration consisted in a modified least square approach ensuring data best-fit under biologically-sound constraints. The minimization task was performed by the Covariance Matrix Evolutionary Strategy (CMAES) algorithm. The same algorithm was used for therapeutic optimization procedures. Results: Parameters of TMZ PK-PD model were estimated in sequential steps involving the use of longitudinal and dose-dependent datasets, informing on the concentrations of TMZ PK, DNA adducts, MGMT, double-stranded breaks, ATR, Chk1 and p53 phosphorylation, and cell death (295 datapoints in total). Most of the datasets were performed in two LN229 glioblastoma human cell lines: the parental TMZ sensitive (MGMT-) and the MGMT-overexpressing TMZ resistant (MGMT+) cells [7-11]. The model was able to faithfully reproduce these multi-type datasets coming from several independent studies. Next, the calibrated model was used as a powerful tool to investigate new therapeutic targets. As a start, we investigated drug combinations involving TMZ and only one targeted inhibitor, which was computationally represented by decreasing the value of the corresponding model parameter. The only strategy leading to a drastic increase of TMZ efficacy in both parental and resistant cell lines consisted in the complete (>90%) inhibition of the BER pathway, prior to TMZ exposure. Such high level of inhibition being challenging to achieve in the clinics, we further explored the combination of TMZ and two inhibitors. This numerical study revealed three possible parameters to be jointly targeted: MGMT protein level, BER activity, and HR activity. The optimal strategy, defined as the one requiring the smaller percentages of inhibition for both targets, was the combined administration of BER and HR inhibitors, prior to TMZ exposure. This therapeutic strategy was investigated experimentally in both LN229 cell lines and led to a drastic increase in TMZ efficacy. The model prediction of cell viability under exposure of TMZ after either BER inhibitor or HR inhibitor only, were also validated. Conclusions: A model of TMZ PK-PD model was carefully calibrated to data and allowed to identify a non-intuitive TMZ-based drug combination leading to a drastic increase of cell death in initially resistant cells. This QSP model is being personalized using multi-omics datasets available in GBM patient-derived cell lines towards the design of patient-specific therapeutic strategies.
• Kévin Spinicci Swansea University
  "Mathematical modelling of HIF on regulating cancer cells metabolism and migration"
The number of studies on tumour metabolism has increased in the recent years as it appears to differ from normal cells. Effort has been put in order to assess dysregulated mechanisms to design new strategies aiming to target cancer cells specifically. It has been observed that the median oxygen level in tumour is less than 2%. This altered environmental condition leads to an adaptation of the cell energetic metabolism and induces angiogenesis. Furthermore, the literature shows that hypoxic cells are more resistant to radiotherapy and potentially more aggressive. Here, we will present a mathematical model of the Hypoxia Inducible Factor (HIF), the main actor in the cellular response to hypoxia, to study how it drives the cell metabolism [1] and the cell ability to migrate. To that end, we have implemented an agent-based model to simulate tumour growth in an in vitro setting using the PhysiCell software. The model includes ODEs to describe the genetic regulations of metabolic key genes with respect to the effect of HIF on those genes. Cells consumption and secretion are affected by the genetic regulation. The results of the model show the consequences on the Warburg Effect and on cancer cell migration.
• Linh Nguyen Phuong Aix-Marseille University (COMPutational pharmacology and clinical Oncology Team)
  "Mechanistic modeling of the longitudinal tumor and biological markers combined with quantitative cell-free DNA"
Early prediction of resistance to immunotherapy is a major challenge in oncology. The ongoing SChISM (Size Cell-fre DNA (cfDNA) Immunotherapies Signature Monitoring) clinical study proposes an innovative approach based on patented cfDNA quantification methods, providing concentration and size profile fluctuations of plasmatic circulating DNA for early therapeutic management of immune checkpoint inhibitors treated patients. The main interest is that such measures can be performed in a less invasive, less expansive way, and especially much earlier than the first imaging evaluation, thanks to liquid biopsies. Five cancer types are investigated: melanoma, head and neck, renal, bladder and lung cancers, with a total of 260 patients at the end of the study, described by their clinical and classical biological data, and cfDNA features, such as concentration, first and second peak of the cfDNA size distribution, and specific size ranges of cfDNA fragments. We developed a mechanistic model of cfDNA joint kinetics with other longitudinal markers and tumor size imaging to help describe and understand the time dynamics of the quantitative profiles of cfDNA over time. The model consists of a dynamical system of differential equations that estimates specifically the component corresponding to cfDNA production by tumor lesions. Subsequently, the model is embedded within a nonlinear mixed-effects statistical framework in order to quantify inter-patient variability, and calibrated on the data. Future perspective will use machine learning models to predict early progression, progression-free survival or overall survival, combining these dynamic parameters and other variables available at baseline.
• Heiko Enderling Moffitt Cancer Center (Department of Integrated Mathematical Oncology)
  "Mathematical modeling of cancer radiotherapy"
Radiation therapy is a mainstay of cancer treatment, with more than 50% of all cancer patients receiving radiation at some point of their clinical care. Mathematical modeling has a long history in radiation oncology, and recent modeling approaches saw translation into prospective clinical trials. Here, we will present the different mathematical modeling approaches to simulate radiation response, and their implication on personalizing radiation dose and dose fractionation, towards a novel concept of adaptive radiation therapy. We will focus on head and neck cancer, one of the few cancer types rising in incidence, that is routinely treated with definitive radiation. Using the data of 39 head and neck cancer patients, we develop, calibrate, and validate the model before making predictions on novel therapies.

Organized by: Anuraag Bukkuri, Katarina Stankova
Note: this minisymposia has multiple sessions. The other session is MS01-ONCO-2.

• Kanyarat Jitmana The University of Utah (Department of Mathematics)
  "Mathematical modeling of the evolution of resistance and aggressiveness of ovarian cancer from HGSOC patient CA-125 time series."
We use time series of CA-125 levels from high-grade serous ovarian cancer patients from the Australian Ovarian Cancer Study to develop mathematical models of the evolution of resistance and response to therapy. We hypothesize that two key traits determine long-term patient outcomes: resistance as measured by the rate of decline of CA-125 during therapy, and aggressiveness as measured by the rate of CA-125 increase between lines. Statistical analysis shows the level of resistance increases as the number of lines increases. Low initial CA-125, residual disease less than or equal to 1 cm, and a high rate of decline during the first line of therapy predict a longer median of survival of patients after finishing the second line of therapy. We use mathematical models to investigate the mechanisms underlying the differences among HGSOC patients. Our simplest model has two cell types, sensitive and resistant, with resistant cells that could be present before therapy or be generated through mutation from sensitive cells. By fitting the models to HGSOC data using all data points, the first two lines, the first three lines, and the first four lines, these models can successfully capture the dynamic of the CA-125 level of HGSOC patients. Contradictory, the model cannot predict the great detail of the dynamic of CA-125 in the later lines, both the short and long run. By fitting these mathematical models to the clinical data for each patient, we estimate the parameters, which are the growth and death rate of sensitive cells and resistant cells. Despite the inability of the models to predict future CA-125, the patients with the low growth rate of sensitive cells, the low growth rate of the resistant cell, and the high death rate of the resistant cell show better survival chances after finishing the second line of therapy
• Ranjini Bhattacharya Moffitt Cancer Center (Integrated Mathematical Oncology)
  "Angiogenesis: A Tragedy of Commons"
Cancer progression is the result of evolution within the tumor microenvironment. Natural selection selects for cells capable of efficient nutrient uptake. Cancer cells achieve this by overexpressing angiogenic factors (VEGF) that induce the formation of blood vessels that carry nutrients to the tumor. Traditionally, angiogenesis has been viewed as a cooperative phenomenon resulting in the evolution of free-loaders. Using a game theoretic framework, we model VEGF production as an evolutionary strategy and show that the over-production of VEGF is the result of a tragedy of commons. A cell’s investment in VEGF depends on the degree to which it aids its nutrient uptake. If higher production of VEGF leads to higher nutrient uptake, then cells are incentivized to produce VEGF. If nutrients are equally divided within a given neighborhood, an individual cell’s incentive to produce VEGF decreases. Our simulations predict that cancer cells produce 100 times more VEGF than what is typically seen in normal cells, and what would be their collective team optimum. This means that VEGF production by a cancer cell aims to co-opt nutrients from neighboring cells resulting in an evolutionary arms race. Increasing the number of cancer cells in a fixed neighborhood results in lower per-cell VEGF production while exacerbating the tragedy of the commons collectively. We simulate anti-angiogenic therapy and find that while therapy reduces the amount of VEGF in the neighborhood, cells adopt a low VEGF production strategy that can still sustain tumor proliferation. This results in evolutionary rescue. Our model challenges the existing paradigm of angiogenesis as a cooperative activity and provides novel insights into therapy in a clinical setting.
• Monica Salvioli - Part 2 Delft University of Technology (Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands)
  "Using the Stackelberg evolutionary game approach in cancer treatment"
We present a game-theoretic cancer model based on Darwinian dynamics with two cancer cell types and treatment-induced resistance as an evolving trait. We first investigate whether a constant treatment dose can keep cancer at a viable tumor burden. The game is then expanded into a Stackelberg evolutionary game with the physician as its leader, who chooses drug dosage to maximize the patient's quality of life. The quality of life is modeled by an objective function that takes into account the following three aspects of tumor burden: 1) the population of cancer cells at the ecological equilibrium point, 2) the toxicity of the drug, and 3) treatment-induced resistance. In this study, the game's Stackelberg and Nash outcomes are compared to the maximum tolerable dose. We demonstrate that for large ranges of parameters, the Nash and Stackelberg treatment strategies can stabilize the tumor burden at viable levels even when the maximum tolerable dose cannot. As expected, the Stackelberg solution allows us to aim for a higher quality of life than the Nash solution. In general, we demonstrate that determining a patient's treatment dose by employing the Stackelberg evolutionary game approach results in an improvement in the patient's quality of life.
• Shalu Dwivedi Matthias Schleiden Institute, Friedrich Schiller University, Jena (Department of Bioinformatics)
  "Go or grow: Game-theoretical description of metastasis in tumour development"
A medically important feature of several types of cancer is their ability to “decide” between staying at a primary site in the body or to leave it and form metastases. The present theoretical study is aimed at a better understanding of the proximate reasons for this so-called “go-or-grow” dichotomy. To that end, we use game theory, which has turned out to be useful in analyzing the competition between tumours and healthy tissue or among different tumour cells [1]. We start from a game-theoretical model presented by Basanta [2]. We determine the type of game, depending on parameter values, both for the basic model and for five modified variants that we suggest here. For example, in the basic model, the deadlock game, Prisoner’s Dilemma, and hawk-dove game can occur. The modified versions lead to several additional game types such as battle of the sexes, route-choice, and stag-hunt game. For some of the game types, all cells are predicted to stay on their original site (“grow phenotype”), while for other types, only a certain fraction stay and the other cells migrate away (“go phenotype”). If nutrient supply at the distant site is high, all cells are predicted to go. We discuss our predictions in terms of the pros and cons of caloric restriction, limitation of the supply of vitamins or methionine. Our results may help devise treatments that avoid metastases. References: 1. S. Hummert, K. Bohl, D. Basanta, A. Deutsch, S. Werner, G. Theißen, A. Schroeter, S. Schuster (2014). Evolutionary game theory: cells as players. Molecular Biosystems 10 (12), 3044 – 3065. https://doi.org/10.1039/c3mb70602h 2. Basanta, D., Hatzikirou, H., & Deutsch, A. (2008). Studying the emergence of invasiveness in tumours using game theory. The European Physical Journal B, 63(3), 393–397. https://doi.org/10.1140/epjb/e2008-00249-y

Organized by: Mohit Kumar Jolly, Paras Jain
Note: this minisymposia has multiple sessions. The other session is MS04-ONCO-1.

• Amy Brock University of Texas at Austin (Biomedical Engineering)
  "Heritability and plasticity of therapeutic resistance mechanisms within heterogeneous cancer cell populations"
Individual cancer cells within a tumor cell population display distinct responses to chemotherapeutic agents. We have developed a novel genetic tracking technology, ClonMapper to elucidate the pre-existent and de novo cell states that arise from chemotherapeutic intervention. By tracking longitudinal clonal dynamics and cell state changes, we elucidate the contributions of heterogeneity to survival and re-growth of cancer cells following specific selective pressures. Here we will examine the distinct survivorship trajectories that characterize breast cancer cells treated with chemotherapy. Subpopulations differ significantly in growth dynamics and the interactions among heterogeneous subpopulations impact the population composition of surviving cells. Models that include subpopulation interactions may improve the ability to predict the composition and sensitivity of cancer cells under varying therapeutic pressures.
• Morgan Craig Sainte-Justine University Hospital Research Centre / Université de Montréal (Immune Disorders and Cancer / Mathematics and Statistics)
  "Impact of cellular and spatial heterogeneity on immunotherapies to treat glioblastoma"
Glioblastoma is a rare but deadly central nervous system and brain cancer. In most patients, current standard-of-care, which includes maximal safe surgical resection, radiotherapy, and chemotherapy, fails due to recurrences, translating to a median survival of just 15 months. There is therefore high interest in developing improved approaches to treat glioblastoma, including immunotherapies (e.g., immune checkpoint blockade, oncolytic viruses etc.). Unfortunately, clinical trials of immunotherapies to treat glioblastoma have thus far failed to show significant benefits to patients. In this talk, I will discuss the role of spatial and cellular heterogeneity on treatment success through the integration of agent-based modelling with clinical samples from patients. Our results suggest avenues of continued drug development to provide improved patient outcomes.
• Yogesh Goyal Northwestern University (Cell and Developmental Biology)
  "Tracing origin and consequences of rare cell plasticity in cancer drug resistance"
Single cell variations within a genetically homogeneous population of cells can lead to significant differences in cell fate in response to external stimuli. This is particularly relevant in cancer cells, where a small population of cells can evade therapies to develop resistance. In this talk, I will present ongoing work on tracing the origins, nature, and manifestations of single cell variations in response to a variety of cytotoxic chemotherapies and targeted therapies in various cancer models. By combining clonal barcoding-based and imaging-based lineage tracing frameworks with computational analysis, I will discuss the commonalities and differences in cell fate outcomes across cancers and therapies. Our experimental and computational designs will provide a foundation for controlling single-cell variabilities in cancer and other biological contexts, such as stem cell reprogramming.
• Geena Ildefonso University of Southern California (Alfred E. Mann Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA)
  "A data-driven Boolean model explains memory subsets and evolution in CD8+ T cell exhaustion"
T cells play a key role in a variety of immune responses, including infection and cancer. Upon stimulation, naïve CD8+ T cells proliferate and differentiate into a variety of memory and effector cell types; however, failure to clear antigens causes prolonged stimulation of CD8+ T cells, ultimately leading to T cell exhaustion (TCE). The functional and phenotypic changes that occur during CD8+ T cell differentiation are well characterized, but the underlying gene expression state changes are not completely understood. Here, we utilize a previously published data-driven Boolean model of gene regulatory interactions shown to mediate TCE. Our network analysis and modeling reveal the final gene expression states that correspond to TCE, along with the sequence of gene expression patterns that give rise to those final states. With a model that predicts the changes in gene expression that lead to TCE, we could evaluate strategies to inhibit the exhausted state. Overall, we demonstrate that a common pathway model of CD8+ T cell gene regulatory interactions can provide insights into the transcriptional changes underlying the evolution of cell states in TCE.

Organized by: Mohit Kumar Jolly, Paras Jain
Note: this minisymposia has multiple sessions. The other session is MS03-ONCO-1.

• Antara Biswas Rutgers Cancer Institute of New Jersey (Department of Pathology & Laboratory Medicine)
  "Transcriptional heterogeneity and cell state plasticity in urothelial bladder carcinoma."
Intra-tumor heterogeneity contributes towards treatment failure and poor survival in urothelial bladder carcinoma (UBC) patients, but underlying drivers are poorly understood. Analysis of single cell transcriptomic data from UBC patients suggests that intra-tumor transcriptomic heterogeneity is, partly due to, admixtures of tumor cells in epithelial and mesenchymal-like transcriptional states, which covary with other cancer hallmarks. Transition between these cell states likely occurs within and between tumor subclones, adding a layer of phenotypic plasticity and dynamic heterogeneity beyond genetic variations. We model spontaneous and reversible transition between partially heritable epithelial- and mesenchymal-like transcriptional states in UBC cell lines and characterize their population dynamics during in vitro evolution. Nutrient limitation, as in large tumors, and radiation treatment perturb the cell-state dynamics, initially selecting for a transiently resistant phenotype and then reconstituting heterogeneity and growth potential, facilitating adaptive evolution. Our data suggests that transcriptional state dynamics contributes towards phenotypic plasticity and non-genetic intra-tumor heterogeneity, modulating the trajectory of disease progression and adaptive treatment response in UBC.
• Samuel Oliver Swansea University (Department of Mathematics)
  "Cancer as a matter of fat: The role of adipose tissue in tumour progression"
Ovarian cancer has the highest mortality rate of all gynaecological cancers, possessing a 5-year survival rate of less than 50% [1]. Numerous factors are responsible for the poor prognosis, including asymptomatic cases and accelerated chemoresistance. Malignant neoplasms achieve metastasis by interacting with stromal cells in the tumour microenvironment, enhancing proliferation and enabling key phenotypic changes. To quantify these links, we developed an agent-based 3D mathematical model using a PhysiCell framework [2] to simulate tumour growth and its dependence on the microenvironment. In-silico experiments were used to understand the adipose-tumour interactions for SKOV-3 and OVCAR-3 cell lines, with higher levels of fat in the tumour microenvironment being found to cause more aggressive cases of the disease with higher cell viability, EMT, and chemoresistance to paclitaxel treatment. These results, along with a rising abundance of obesity in the global population, underline the need for intensive research into adipose-tumour cell interactions to develop better treatments that hamper cancer progression by tackling the cells of the tumour microenvironment including adipocytes. Mathematical models such as the one used here are key in giving patient specific results by quantifying the impacts of changes in the microenvironment and treatment protocol. [1] G. C. Jayson, E. C. Kohn, H. C. Kitchener, and J. A. Ledermann, “Ovarian cancer,” The Lancet, vol. 384, no. 9951, pp. 1376–1388, 2014. [2] A. Ghaffarizadeh, R. Heiland, S.H. Friedman, S.M. Mumenthaler, and P. Macklin. PhysiCell: an Open Source Physics-Based Cell Simulator for 3-D Multicellular Systems, PLoS Comput. Biol. 14(2): e1005991, 2018.
• Simone Bruno Massachusetts Institute of Technology (Mechanical Engineering)
  "Stochastic analysis of chromatin modification circuits that control epigenetic cell memory"
Epigenetic cell memory is a property of multi-cellular organisms that allows different cells to maintain different phenotypes, encoded by distinct gene expression patterns, despite a common genome. Covalent modifications to chromatin are thought to have a role in dictating the long-term stability of these mutually exclusive gene expression states. However, the underlying mechanisms are not well understood. Here, we analyze a chemical reaction model of the chromatin modification circuit within each gene of the mammalian chromosome and demonstrate how the time scale separation between key constituent processes is implicated in long-term maintenance of gene expression states. To achieve this goal, we use the mathematical framework of singularly perturbed continuous-time Markov chains, where the small parameter quantifies the degree of time-scale separation. Unique to our system, is the fact that the limiting behavior as the small parameter decreases is non-ergodic. We, therefore, developed new tools for the analysis of the behavior of stationary distributions as a function of the small parameter. Furthermore, in order to determine the behavior of these distributions and of mean first passage times as biological parameters are varied, we developed comparison theorems. These theorems, beyond being applicable to our system, provide a general stochastic ordering result that can be applied to chemical reaction networks in general.
• Paras Jain Indian Institute of Science (Centre for BioSystems Science and Engineering)
  "Epigenetic memory acquired during long-term EMT induction governs the recovery to the epithelial state"
Epithelial–mesenchymal transition (EMT) and its reverse mesenchymal–epithelial transition (MET) are critical during embryonic development, wound healing and cancer metastasis. While phenotypic changes during short-term EMT induction are reversible, long-term EMT induction has been often associated with irreversibility. Here, we show that phenotypic changes seen in MCF10A cells upon long-term EMT induction by TGFβ need not be irreversible but have relatively longer time scales of reversibility than those seen in short-term induction. Next, using a phenomenological mathematical model to account for the chromatin-mediated epigenetic silencing of the miR-200 family by ZEB family, we highlight how the epigenetic memory gained during long-term EMT induction can slow the recovery to the epithelial state post-TGFβ withdrawal. Our results suggest that epigenetic modifiers can govern the extent and time scale of EMT reversibility and advise caution against labelling phenotypic changes seen in long-term EMT induction as ‘irreversible’.

Organized by: Guillermo Lorenzo, Chengyue Wu, David A Hormuth II, Ernesto A. B. F. Lima, Lois C. Okereke, Thomas E. Yankeelov

• Stéphane Bordas University of Luxembourg (Department of Engineering Sciences)
  "Digital twinning physiological processes: brain metabolism and cancer growth"
The Legato Team from the Department of Engineering at the University of Luxembourg is pleased to present three cutting-edge applications of bio-engineering that utilize advanced digital twin methods. These applications are focused on in vitro and in vivostudies at various scales, includ- ing cellular aggregate, cellular, and organ levels. The first digital twin application involves the reproduction of an experiment involving multi-cellular tumor spheroids encapsulated within alginate capsules [1]. This study aims to investigate the impact of mechanical forces on tumor growth by analyzing the deformation of the capsules, which provides insights into internal tumor pressure. The poromechanical model used in this study is rigorously calibrated and validated against various capsule geometries, and the results not only faithfully reproduce the experimental findings but also provide a refined interpretation of the ex- perimental results.The second example of digital twin application focuses on reproducing the metabolism of human astrocytes while considering their real 3D geometry [2]. By examining the influence of geometry on internal reaction-diffusion processes, this study provides a deep understanding of astrocyte functionalities in both normal physiological processes and neurodegenerative diseases. This ap- plication sheds light on the complex interactions within astrocytes and their role in neurodegener- ative conditions.The third example of digital twin application is performed in real-time computation under operation room conditions. Using patient 3D scan Lidar and clinical reference maps, the model generates patient-specific pre-operative drawings for breast conservative surgery [3]. This personalized approach has shown promising clinical applications and has the potential to improve surgical outcomes. The Legato Team is excited about the recent advancements in these digital twin applications, which have led to promising clinical applications [4, 5, 6, 7]. These studies demonstrate the po- tential of bio-engineering and digital twin methods to revolutionize medical research and clinical practice. References: 1]Ste ́phaneUrcun,Pierre-YvesRohan,WafaSkalli,PierreNassoy,Ste ́phaneP.A.Bordas,and Giuseppe Sciume`. Digital twinning of cellular capsule technology: Emerging outcomes from the perspective of porous media mechanics. PLOS ONE, 16(7):1–30, 07 2021. [2]SofiaFarina,SusanneClaus,JackSHale,AlexanderSkupin,andSte ́phanePABordas.Acut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing. Advanced Modeling and Simulation in Engineering Sciences, 8:1–32, 2021.[3] Arnaud Mazier, Sophie Ribes, Benjamin Gilles, and Ste ́phane PA Bordas. A rigged model of the breast for preoperative surgical planning. Journal of Biomechanics, 128:110645, 2021. [4] Ste ́phane Urcun, Pierre-Yves Rohan, Giuseppe Sciume`, and Ste ́phane P.A. Bordas. Cor- tex tissue relaxation and slow to medium load rates dependency can be captured by a two- phase flow poroelastic model. Journal of the Mechanical Behavior of Biomedical Materials, 126:104952, 2022. [5] Stephane Urcun, Davide Baroli, Pierre-Yves Rohan, Wafa Skalli, Vincent Lubrano, Ste ́phane PA Bordas, and Giuseppe Sciume. Non-operable glioblastoma: proposition of patient-specific forecasting by image-informed poromechanical model. Brain Multiphysics, page 100067, 2023. [6] Sofia Farina, Vale ́rie Voorsluijs, Sonja Fixemer, David Bouvier, Susanne Claus, Ste ́phane PA Bordas, and Alexander Skupin. Mechanistic multiscale modelling of energy metabolism in hu- man astrocytes indicates morphological effects in alzheimer’s disease. bioRxiv, pages 2022– 07, 2022.[7] Thomas Lavigne, Arnaud Mazier, Antoine Perney, Ste ́phane Pierre Alain Bordas, Franc ̧ois Hild, and Jakub Lengiewicz. Digital volume correlation for large deformations of soft tissues: Pipeline and proof of concept for the application to breast ex vivo deformations. Journal of the mechanical behavior of biomedical materials, 136:105490, 2022.
• Jesús J. Bosque University of Castilla-La Mancha (Spain) (Mathematical Oncology Laboratory (MOLAB))
  "Less is more in glioma treatment: In silico and in vivo evidence towards a clinical trial"
Low-grade gliomas (LGG) are primary brain tumours that arise from glial cells. Patients typically have a prolonged survival (median 7 years), but LGG usually transform into a malignant state, eventually resulting in the patient's death. The alkylating agent temozolomide (TMZ) is the most important weapon used against LGG, but very often the patients end up developing drug resistance. Therefore, the treatment of LGG presents an important medical challenge. To investigate the optimum schedule for the administration of TMZ to LGG patients, we developed mathematical models based on ordinary differential equations and agent-based models. To model the acquisition of drug resistance, we considered an intermediate reversible phenotype of persister cells which evade therapy and turn to fully resistant under repeated TMZ exposure. We parametrised our models using data from mice experiments and magnetic resonance images from patients, and used them to generate cohorts of digital patients in which we tested different protocols of TMZ administration. The results from the in silico clinical trials showed that protocols using individual doses with intermediate rest weeks are more effective than the standard protocol to delay the appearance of resistance and increase the survival of the patients. Moreover, these results were further validated through animal experiments, confirming the efficacy of administration schedules with increased time between doses. Thus, our research lays the foundation for a prospective clinical trial that could improve the standard of care of LGG patients.
• Renee Brady-Nicholls H. Lee Moffitt Cancer Center & Research Institute (Integrated Mathematical Oncology)
  "An In Silico Study of Hormone Therapy in Metastatic Prostate Cancer"
African American (AA) men have the highest incidence and mortality rates of prostate cancer (PCa) compared to any other racial group. The increased incidence as well as mortality are likely due to socioeconomic factors, environmental exposure, access to care, and biologic variations. Deciphering the specific drivers of increased incidence and mortality is difficult due to a scarcity in available data from AA patients. In silico modeling can be used to generate pseudo patient data that can be used to compare response dynamics between groups. Here, we use propensity score matching to conduct a in silico study of hormone treatment in AA and European American (EA) PCa patients. Using longitudinal prostate-specific antigen (PSA) data from 57 metastatic PCa patients (N = 47 EA, N = 10 AA), we used propensity score matching to identify 15 EA patients that most closely matched the 10 AA patients. A simple mathematical model describing stem cell, differentiated cell, and PSA dynamics was calibrated to the data. Model parameters were compared between the matched patients and identified a significantly higher stem cell self-renewal rate in AA patients. Using this, an in silico study was performed by sampling from the race-specific parameter sets to create 100 in silico patients (N = 50 EA, N = 50 AA). Response dynamics during both continuous and adaptive therapy were compared between AA and EA groups and found that patients with higher stem cell self-renewal rates received the most benefit from adaptive treatment. This is an important step in identifying race-specific, patient-specific treatment options that can be used to maximally delay time to progression.
• Chase Christenson University of Texas at Austin (Biomedical Enginering)
  "Fast digital twin construction for modeling the response of breast cancer to therapy using proper orthogonal decomposition."
Introduction: Digital twins provide an avenue to personalize and optimize therapy for cancer by simulating response in the digital space, prior to physical delivery of treatment. Mathematical models that accurately predict spatial response to various therapies have been developed but are limited in their practical application due to their heavy computational loads. Reduced order modeling (ROM) techniques, such as proper orthogonal decomposition, can be used to alleviate this burden and make the construction of digital twins more tractable for clinical application. Methods: Our lab has developed a reaction-diffusion model that describes the spatio-temporal response of breast tumors due to cell invasion, proliferation, and response to neoadjuvant therapy (1). The model is initialized and calibrated with sequential magnetic resonance imaging (MRI) data from 50 patients. The MRI data consists of diffusion-weighted MRI and dynamic contrast enhanced MRI to inform tumor cellularity and drug concentration, respectively. We use a data driven ROM formulation, where patient-specific cellularity estimates are used to determine a reduction basis appropriate for the mathematical model and individual patient. Model parameters (e.g., spatial proliferation rates, global diffusivity, and treatment efficacy) are then estimated by fitting the reduced model to the patient-specific scans. The resulting digital twin is evaluated by its ability to predict future response, and its similarity to the output from a full order model (FOM). Results: The correlation between FOM and ROM for global (i.e., whole tumor ROI) changes in total tumor volume and total tumor cellularity both achieve concordance correlation coefficients >0.99 for the calibrated and predicted time points. At the local level (i.e., individual voxels), the ROM achieves a median percent difference from FOM of 1.59% at calibrated time points, and 6.60% for predictions across the 50 patients. Critically, the ROM output requires only 1.33 minutes, nearly 100× faster than the FOM time of 128.43 minutes. Conclusions: We have developed a computational framework that can accurately calibrate a digital twin to individual patient data in a fraction of the time previously required. This reduced model can then be used to make accurate predictions of spatial response to therapy. References: (1) Wu, Chengyue, et al. 'MRI-based digital models forecast patient-specific treatment responses to neoadjuvant chemotherapy in triple-negative breast cancer.' Cancer Research 82.18 (2022): 3394-3404. Acknowledgements: The authors thank the NIH for funding through NCI U01CA142565, U01CA174706, and U24CA226110. They thank the Cancer Prevention and Research Institute of Texas for support through CPRIT RR160005. T.E. Yankeelov is a CPRIT Scholar in Cancer Research

Organized by: Yangjin Kim, Magdalena Stolarska
Note: this minisymposia has multiple sessions. The other session is MS07-ONCO-1.

• Dumitru Trucu University of Dundee (Mathematics)
  "Multiscale Modelling Glioblastoma Progression within the Fibrous Brain Tissue"
Glioblastoma multiforme (GBM) is the most aggressive brain tumour, with patients having poor survival prospects despite recent surgery, radiotherapy and chemotherapy advancements. A central role in the development and spread of GBM within the brain is played by the collective cancer cell migration within the fibrous brain environment. This talk aims to explore this key invasion aspect through a novel non-local multiscale moving boundary modelling framework that takes into account the intrinsic link between overall macroscale tumour dynamics and both the microscale proteolytic activity at the invasive edge as well as the crucial bulk microdynamics of cancer cell-fibres interactions. T1 weighted and DTI scans are used as initial conditions for our model as well as to parametrize the diffusion tensor. Numerical results will illustrate clinically relevant GBM development patterns.
• Junho Lee Konkuk University (Mathematics / Seoul, Republic of Korea)
  "Role of senescent tumor cell in building a cytokine shield in tumor microenvironment: mathematical models"
Cell aging can promote or inhibit cancer progression. Here, it was shown that the proportion of senescent tumor cells (STCs) in colorectal cancer (CRC) supported cancer growth by inhibiting intratumoral infiltration of CD8+ T cells. It has been found that the expression of C-X-C motif chemokines ligand 12 (CXCL12) and colony stimulating factor 1 (CSF1) in senescent tumor cells is increased, and senescent tumor cells secrete high concentrations of CXCL12 to spread chemokine shields. This inhibits the infiltration of CD8+T cells into tumor by causing loss of CXCR4 in T cells and interfering with directional movement. In this study, we investigate the mutual interactions between the CD8+ T cells and the STCs that prevent T cell invasion by developing a mathematical model that involves taxis-reaction-diffusion equations for the critical components in the interaction. We apply the mathematical model to a Boyden invasion assay used in the experiments to demonstrate that the over-expressed CXCL12 can prevent T cell infiltration into tumor. Moreover, we consider tumor-immune dynamics by a hybrid approach, we investigate the fundamental mechanism of STC-mediated cytokine shield and the impact on the migration patterning of T cells. We show that the model can both reproduce the major experimental observation on T cell infiltration and make several important predictions to guide future experiments with the goal of the development of new anti-tumor strategies.
• Eunjung Kim Korea Institute of Science and Technology (Natural Product Informatics)
  "Acquired resistance shapes the treatment outcomes by modulating the distribution of resistance"
Adaptive therapy (AT) is an evolution-based treatment strategy that exploits cell-cell competition. Acquired resistance can change the competitive nature of cancer cells in a tumor, impacting AT outcomes. We aimed to determine if adaptive therapy can still be effective with cells acquiring resistance. We developed an agent-based model for spatial tumor growth considering three different types of acquired resistance: random genetic mutations during cell division, drug-induced reversible (plastic) phenotypic changes, and drug-induced irreversible phenotypic changes. These three resistance mechanisms lead to different spatial distributions of resistant cells. To quantify the spatial distribution, we propose an extension of Ripley's K-function, Sampled Ripley's K-function (SRKF), which calculates the non-randomness of the resistance distribution over the tumor domain. This model predicts that the emergent spatial distribution of resistance can determine the time to progression under both adaptive and continuous therapy (CT). Notably, a high rate of random genetic mutations leads to quicker progression under AT than CT due to the emergence of many small clumps of resistant cells. Drug-induced phenotypic changes accelerate tumor progression irrespective of the treatment strategy. Low-rate switching to a sensitive state reduces the benefits of AT compared to CT. Furthermore, we also demonstrated that drug-induced resistance necessitates aggressive treatment under CT, regardless of the presence of cancer-associated fibroblasts. However, there is an optimal dose that can most effectively delay tumor relapse under AT by suppressing resistance. In conclusion, this study demonstrates that diverse resistance mechanisms can shape the distribution of resistance and thus determine the efficacy of adaptive therapy.

Organized by: Yangjin Kim, Magdalena Stolarska
Note: this minisymposia has multiple sessions. The other session is MS06-ONCO-1.

• Magdalena Stolarska Univeristy of St. Thomas (Mathematics)
  "On the significance of membrane unfolding and cortical stress generation in cell movement"
Cell motility play a critical role in cancer metastasis. Active deformation of the lipid bilayer and underlying actin cortex are important aspects of cell motility but have generally been overlooked in mathematical models. Membrane dynamics, including unfolding and exocytosis from intracellular reservoirs to the lipid bilayer, is necessary for large changes in cell shape, which occur during cell spreading and motility (Figard & Sokac, BioArchitecture, 2014) and for the release of membrane tension that occurs during these shape changes (Pontes et al., J Cell Bio, 2017). Actomyosin contraction of the underlying cortical layer also locally controls variations in cell shape and modes of motility (Salbreux et al., Cell, 2012). The aim of this work is to understand how active deformation of the membrane allows for large deformations of the cell and to understand how local active deformation of the actin cortex leads to amoeboid cell movement. To do this, two related mathematical models are presented. In both models the cell is treated as a viscous fluid that is surrounded by a viscoelastic membrane-cortex pair. Active deformation of the membrane or cell cortex is incorporated into the model via an additive decomposition of the rate of deformation tensor, the active part of which can depend on mechanical or biochemical components of the model, such as membrane tension or local myosin concentration. Using finite element simulations of the model we show that active membrane deformations, such as unfolding, and myosin-based contractility of the cortical layer are required for controlling various modes of cell motility.
• Jay Stotsky University of Minnesota (School of Mathematics)
  "Cell Cortex Mechanics and Cell Swimming"
The cell-cortex is a dense layer of cytoskeletal proteins lying underneath the cell-membrane of many types of cells. Because of its proximity to the cell-membrane, it exerts forces on the membrane precipitating movement and shape-change in cells. In turn, coordinated movement and shape-change are pivotal in cancer metastasis and in biological development. Thus, understanding the mechanical behavior of the cortex is an important area of study that can yield insights into a broad array of challenging questions in biology and medicine. However, the cortex also exhibits complicated behaviors that cannot be fully explained by present models. It is an active material, meaning that it converts chemical (or other forms of) energy into mechanical stress, and it is continually remodeled as the proteins that make up the cytoskeleton turn over and are recycled. In this talk, I will discuss recent work towards developing more realistic models, and computational tools to study the cell cortex. This area of research is exciting because of the many applications to biology and medicine and because it lies at the intersection of a diverse array of topics including differential geometry, thermodynamics, numerical analysis, and biomechanics.
• Donggu Lee Konkuk University (Mathematics / Seoul, Republic of Korea)
  "Optimal strategies of oncolytic virus-bortezomib therapy"
Proteasome inhibition and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts the degradation of proteins in the cell leading to accumulation of unfolded proteins inducing apoptosis. Oncolytic virotherapy uses genetically modified oncolytic viruses (OV) to infect cancer cells, induce cell lysis, and activate an antitumor response. In this work, optimal control theory is utilized to minimize the cancer cell population by identifying strategic injection protocols of bortezomib and OV. Two different therapeutic protocols are explored: (i) Periodic bortezomib and single administrations of OV therapy; (ii) Alternating sequential combination therapy. These strategies support timely bortezomib and OV injection. Relative doses and administrative costs of the two anti-cancer agents for each approach are qualitatively presented. This study provides potential combination therapeutic strategies in cancer treatment.
• Yangjin Kim Konkuk University (Department of Mathematics)
  "Activated NOTCH induced monocyte recruitment suppresses anti-tumor immunity with virotherapy"
The impact of NOTCH signaling on immune therapy is understudied. We found that activation of NOTCH signaling promotes an MDSC enriched immune suppressive environment in brain tumors that limits the benefit from oncolytic immunotherapy. We developed a mathematical model, based on a system of partial differential equations, for the role of NOTCH signaling and macrophages in regulation of tumor growth dynamics and in control of anti-tumor efficacy in onvolytic virus therapy. Experimental data from RNA sequencing and CHIP-PCR indicated that infected tumor cells induced ADAMTS1 expression via RBP-j mediated canonical NOTCH signaling, which then enhanced macrophage recruitment in tumors. We found that Jag1 (NOTCH ligand) expressing macrophages created a feed forward loop in TME that amplified NOTCH signaling in tumor cells distant from sites of viral infection. Then, we investigated how macrophages are recruited to oHSV treated tumors and how these immune cells induce CCL2 production via TLR activation. The critical phenotypic switch towards an M2 phenotype that were immunosuppressive and induced tumor growth, played a significant role in regulation of the immune-tumor dynamics. We tested several hypotheses on the pharmacologic blockade of NOTCH signaling and possible rescue of a CD8 dependent anti-tumor memory response that enhanced therapeutic efficacy of oHSV therapy.

Organized by: Renee Brady-Nicholls, Harsh Jain, Jason George

• Maximilian Strobl Cleveland Clinic (Department for Translational Hematology and Oncology Research, Lerner Research Institute)
  "Using mathematical modeling to design protocols for preclinical testing of evolutionary therapies"
Over the past two decades it has become clear that cancers are complex and evolving diseases. Genetic and non-genetic processes generate diverse subpopulations of tumor cells which can thrive under a variety of conditions and stressors. This provides a rich pool of variation that by means of natural selection and continued evolution enables adaptation to even the most modern treatments, especially in advanced cancers. Based on this novel understanding, so-called “evolutionary therapy” or “evolution-informed treatment strategies” have emerged which try to leverage, and potentially even steer, tumour evolution by strategically and dynamically sequencing and combining existing therapies and adjusting dose levels. In particular, adaptive therapy, which dynamically changes treatment levels to maintain drug-sensitive cells in order to competitively suppress emerging drug resistance, has produced a number of promising theoretical, preclinical and also clinical results. However, unlike for new drugs for which there are clear established frameworks for translation from bench to bedside, the design of preclinical protocols to ensure efficacy and safety of evolutionary therapies is an open question. In this study, we use mathematical modeling to develop and interpret in vitro experimental protocols and apply them towards the development of an adaptive therapy for Osimertinib for the treatment of Non-Small Cell Lung Cancer. In the first step, we consider the question of how to measure ecological interactions between tumor subpopulations. To do so, we build on the “Game Assay” previously developed by our group, in which cells are co-cultured at different frequencies to measure how a population’s fitness depends on its frequency in the environment. Using an agent-based model of our in vitro experiments, we study how different aspects of the design (number of replicates, number of proportions) and analysis (regression technique, regression window) impact the accuracy and precision of the assay. Subsequently, we use our optimized protocol to quantify the frequency-dependent interactions between Osimertinib sensitive and resistant PC9 cells under different drug levels. In the next step, we use our model to explore whether and how so-obtained fitness differences translate to the ability to steer the composition of the tumor in long-term in vitro experiments, in which cells are co-cultured and passaged at regular intervals. In particular, we explore the role of the population size, passaging frequency, and passage fraction (proportion of cells carried forward to next passage). To conclude, we will present preliminary data in which we use this assay to trial a potential adaptive Osimertinib therapy protocol in vitro. Overall, we demonstrate how mathematical models can help to understand and improve experimental assays, and we contribute towards the important discussion as to how to translate evolutionary therapies from the blackboard to the bedside.
• Rebecca A. Bekker H. Lee Moffitt Cancer Center & Research Institute (Department of Integrated Mathematical Oncology)
  "The Immunological Consequences of Spatially Fractionated Radiotherapy"
Radiotherapy (RT) is the single most frequently used cancer treatment, with approximately 60% of patients undergoing RT alone or in conjunction with other therapeutics. However, many patients develop RT-induced lymphopenia, which has been associated with decreased overall survival in head and neck cancer patients. Thus, it is conceivable that sparing select immune populations may improve patient outcomes. One potential method of minimizing the adverse effects of RT on the immune response is the use of spatially fractionated radiotherapy (SFRT), administered through GRID blocks to create areas of low and high dose exposure. We hypothesize that the regions receiving low dose may act as immune reservoirs wherein the anti-tumor immune population is protected from RT-induced death. We develop and calibrate a mechanistic agent-based model of tumor-immune interactions to investigate the therapeutic utility of SFRT. Initializing the model with the multiplex immunohistochemistry / immunofluorescence slides of 30 patients with head and neck cancer, we identify specific GRID block architectures and treatment schedules that are better suited, with respect to anti-tumor immune infiltration and patient outcome, for specific pre-treatment tumor immune microenvironment states.
• Ibrahim Chamseddine Massachusetts General Hospital, Harvard Medical School (Radiation Oncology)
  "Towards Personalized Oncology: Machine Learning-Driven Radiotherapy Across Multiple Disease Sites"
Radiotherapy (RT) is a prominent modality in cancer treatments, utilized in over half of the patients, either as a standalone therapy or in combination with other treatments. However, current RT planning predominantly focuses on dose prescription, neglecting patient-specific properties and leading to variable responses between patients. This highlights the need for personalized strategies to enhance treatment outcomes. To advance towards personalized RT, we employed machine learning (ML) techniques across hepatocellular carcinoma (HCC), prostate cancer, and brain and head and neck cancers. By leveraging ML feature selection on clinical data, we identified predictors of tumor control, survival, and toxicity. We incorporated medical images in prostate and brain cancers using deep learning to further enhance the predictive models. These models facilitated the stratification of patients into low- and high-risk groups, enabling treatment modifications for those in need. We refined our approach by generating an ML-based decision map for personalized treatment selection in HCC and integrating ML techniques with treatment planning systems to optimize patient-specific therapies. We aimed through ML to identify risk groups in multiple disease sites and adapt therapies accordingly, with the future goal of introducing a paradigm shift towards fully personalized RT.
• Alexander B. Brummer College of Charleston (Department of Physics and Astronomy)
  "Data-driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables"
In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

• Daniel Glazar Moffitt Cancer Center & Research Institute
  "A simulation-based sample size analysis of a joint model of longitudinal and survival data for patients with glioma"
Introduction Patients with recurrent high-grade glioma (rHGG) have poor prognosis with median progression-free survival (PFS) <6 months, and median overall survival <12 months [1]. The Response Assessment in NeuroOncology (RANO) defines radiographic progression as 25% increase in the sum of products of longest diameters of individual lesions (SPD) delineated from MRIs relative to minimum observed SPD [2]. However, there is a wide heterogeneity in response to treatment in these patients with some experiencing disease progression within weeks and others surviving for years. Predicting which patients will progress early or late on different therapeutic regimens may aid the clinician in deciding which regimen with which to treat the patient. Thus, there is an urgent clinical need for a predictive biomarker for patient-specific PFS. To predict PFS and OS, baseline disease characteristics, such molecular markers have been investigated [3]. However, repeated measures of such biomarkers are infeasible due to the invasive procedures involved. To remedy this limitation, predictive mathematical models of patient-specific tumor dynamics in glioma based on non-invasive imaging data have been developed [4–8]. However, most of these do not evaluate PFS by RANO, and those that do only predict PFS as a binary outcome over discrete time horizons [6]. Considering a joint model of longitudinal tumor volume and PFS from a Bayesian perspective has the advantage of predicting PFS as a continuous outcome over continuous time horizons for individual patients while taking into account population-level response dynamics [9–11]. However, before applying such a model to clinical data, we note that due to low incidence and accrual rates of early phase clinical trials for patients with rHGG [12], there is a clinical need to determine the minimum sample size necessary to predict patientspecific TTP using longitudinal tumor volumes. As such, we perform a simulation-based sample size analysis of a joint model of longitudinal tumor volume and PFS on an in silico clinical trial for patients with rHGG. Objectives 1. To develop a joint model of longitudinal tumor volume and PFS for patients with rHGG. This joint model will use tumor volume dynamics as an accurate and precise predictive biomarker of PFS. 2. To perform a sample size analysis on an in silico clinical for patients with rHGG to determine the minimum number of patients needed to make accurate and precise individual Bayesian dynamic predictions of PFS based on longitudinal tumor volumes in order to inform clinical trial design. Methods 1. We developed a joint model of longitudinal tumor volume and TTP for patients with rHGG. Tumor volumes were modeled using a tumor growth inhibition (TGI) model with mixed effects. In it, tumors grow exponentially to replicate the fact that patients inevitably progress before any inflection point in their tumor growth. Tumor response rate declines exponentially due to the inevitable development of therapeutic resistance. TTP was then modeled discretely and defined as the time when tumor volume reached 40% above from nadir, extrapolating from the bi-dimensional 25% threshold in RANO [2]. Due to technical limitations, the hazard function was approximated using a scaled skew normal distribution curve. Population parameter estimates of the developed joint model were estimated using quantile information reported in the literature [13] by maximizing the likelihood of joint order statistics [14]. 2. An in silico clinical trial was conducted to study the effects of sample size on the predictive performance of the developed joint model to dynamically predict patient-specific PFS. We selected sample sizes of 40, 60, 80,..., 200 as most clinically feasible due to the low incidence of rHGG. In silico training and test sets were generated by sampling from model parameter distributions and simulating longitudinal tumor volume and TTP every 6 weeks from treatment initiation with baseline 2 weeks prior to treatment initiation to conform with rHGG clinical trial protocols. Population parameters were estimated using the stochastic approximation of expectation-maximization (SAEM) algorithm [15] and then taken to parameterize a prior distribution to dynamically predict patient-specific TTP for the test patients across landmark times and time horizons [9–11]. Predictive performance was then evaluated using time-dependent Brier score (BS) and area under the receiver operating characteristic curve (AUC) [9,16]. Simulations were performed using the Monolix suite software [17]. Results 1. In estimating population parameters, simulated median PFS was between 24 and 30 weeks, which agrees with clinical observations [6]. Also, the majority of simulated patients had between 3 and 7 observations, also in agreement with clinical observations [6]. 2. For the largest sample size considered (N=200), we evaluated the developed model’s predictive performance for set time horizons of 6, 12, 18, and 24 weeks across all landmark times. The median AUC ranged from 0.55 to 0.63 with median BS ranging from 0.19 to 0.25. We then evaluated the developed model’s performance to predict progression around the median PFS (between 24 and 30 weeks) across landmark times 0, 6, 12, and 18 weeks after treatment initiation. The median AUC ranged from 0.50 to 0.65 with median BS ranging from 0.21 to 0.25. 3. Across all sample sizes tested, there was statistically significant albeit small correlation between sample size and AUC (Pearson’s r=0.20, p<1e-15) across all landmark times and time horizons. However, no statistic significance was reached for the correlation between sample and BS (Pearson’s r=-0.0017, p=0.95). When controlling for landmark time and time horizon, the median Pearson’s correlation between sample size and either AUC or BS were r=0.28, 0.07, respectively. Conclusions We developed a joint model of longitudinal tumor volume and PFS for patients with rHGG and parameterized according to quantile information reported in the literature. The model was able to capture the dynamics and survival profiles of the patient population. The predictive performance of the model was robust across the sample sizes tested. However, the overall predictive performance of the model was only marginally better than chance as measured by AUC and BS. In future studies, we will explore a larger range of sample sizes to investigate how many patients are necessary to meet various performance benchmarks as measured by AUC or BS. To improve model predictive performance, we will include covariates, such as sex, molecular markers, and different treatment arms, which are known to affect rHGG volume dynamics and survival endpoints. We will also consider competing risks in the form of a smooth, continuous hazard function as many patients with rHGG experience progression due to clinical deterioration or new lesion even while exhibiting radiographic response. References: [1] Birzu C, French P, Caccese M, et al. Recurrent Glioblastoma: From Molecular Landscape to New Treatment Perspectives. Cancers. 2021; 13(1):47. https://doi.org/10.3390/cancers13010047. [2] Wen PY, Chang SM, Van den Bent MJ, et al. Response Assessment in Neuro-Oncology Clinical Trials. J Clin Oncol. 2017; 35(21):2439-2449. https://doi:10.1200/JCO.2017.72.7511. [3] Phillips HS, Kharbanda S, Chen R, et al. Molecular subclasses of high-grade glioma predict prognosis, delineate a pattern of disease progression, and resemble stages in neurogenesis. Cancer Cell. 2006; 9(3):157-173. https://doi.org/10.1016/j.ccr.2006.02.019. [4] Swanson KR, Bridge C, Murray JD, et al. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. Journal of the Neurological Sciences. 2003; 216(1):1-10. https://doi.org/10.1016/j.jns.2003.06.001. [5] Br¨uningk SC, Peacock J, Whelan CJ, et al. Intermittent radiotherapy as alternative treatment for recurrent high grade glioma: a modeling study based on longitudinal tumor measurements. Sci Rep. 2021; 11:20219. https://doi.org/10.1038/s41598-021-99507-2. [6] Glazar DJ, Grass GD, Arrington JA, et al. Tumor Volume Dynamics as an Early Biomarker for Patient-Specific Evolution of Resistance and Progression in Recurrent High-Grade Glioma. J Clin Med. 2020; 9(7):2019. https://doi: 10.3390/jcm9072019. [7] Hormuth DA., Al Feghali KA, Elliott AM. et al. Image-based personalization of computational models for predicting response of high-grade glioma to chemoradiation. Sci Rep 2021; 11:8520. https://doi.org/10.1038/s41598-021-87887-4. [8] Dean JA, Tanguturi SK, Cagney D, et al. Phase I study of a novel glioblastoma radiation therapy schedule exploiting cell-state plasticity. Neuro-Oncology. 2022. https://doi.org/10.1093/neuonc/noac253. [9] Rizopoulos D. Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics. 2011; 67(3):819–29. [10] Mbogning C, Bleakley K, Lavielle M. Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation maximization algorithm. J Stat Comput Simul. 2015; 85(8):1512–28. [11] Desm´ee S, Mentr´e F, Veyrat-Follet C, et al. Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer. BMC Med Res Methodol. 2017;17:105. https://doi.org/10.1186/s12874-017-0382-9. [12] Central Brain Tumour Registry of the United States. CBTRUS Statistical Report: Primary brain and central nervous system tumours diagnosed in the United States in 2004–2006. 2010. [13] Stensjøen AL, Solheim O, Kvistad KA, et al. Growth dynamics of untreated glioblastomas in vivo. Neuro-Oncology. 2015; 17(10):1402–11. https://doi.org/10.1093/neuonc/nov029. [14] Reiss RD. Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics. Springer New York. 2012. [15] Delyon B, Lavielle M, Moulines E. Convergence of a stochastic approximation version of the EM algorithm. Ann Stat. 1999; 27:94–128. [16] Schoop R, Graf E, Schumacher M. Quantifying the predictive performance of prognostic models for censored survival data with time-dependent covariates. Biometrics. 2008; 64(2):603–10. [17] Monolix Suite 2023R1, Lixoft SAS, a Simulations Plus company.
• Guillermo Lorenzo University of Pavia, Italy
  "Personalized MRI-informed predictions of prostate cancer growth during active surveillance"
Active surveillance (AS) an established clinical management option for low to intermediate-risk prostate cancer (PCa), which represents almost 70% of newly-diagnosed cases. During AS, patients have their tumor monitored via multiparametric magnetic resonance imaging (mpMRI), serum prostate-specific antigen (PSA), and biopsies. If any of these data reveal tumor progression towards an increased clinical risk, the patient is prescribed a curative treatment. However, clinical decision-making in AS is usually guided by observational and population-based protocols that do not account for the unique, heterogenous nature of each patient’s tumor. This limitation complicates the personalization of monitoring plans and the early detection of tumor progression, which constitute two critical, unresolved problems in AS. To address these issues, we propose to forecast PCa growth using personalized simulations of an mpMRI-informed mechanistic model solved over the 3D anatomy of the patient's prostate. We describe PCa growth via the dynamics of tumor cell density with a diffusion operator, representing tumor cell mobility, and a logistic reaction term, which accounts for tumor cell net proliferation. Model calibration and validation rely on assessing the mismatch between model predictions of the tumor cell density map with respect to corresponding mpMRI-based estimates. Here, we present a preliminary study of our predictive technology in a small cohort of newly-diagnosed PCa patients (n=11) who enrolled in AS and had three mpMRI scans over a period of 2.6 to 5.6 years. Our results show a median concordance correlation coefficient (CCC) and Dice score (DSC) of 0.59 and 0.79, respectively, for the spatial fit of tumor cell density during model calibration using two mpMRI datasets. Then, model validation at the date of a third mpMRI scan resulted in median CCC and DSC of 0.58 and 0.76, respectively. Additionally, the global CCCs for tumor volume and total tumor cell count were 0.87 and 0.95 during model calibration and of 0.95 and 0.88 at forecasting horizon, respectively. Thus, while further improvement and testing in larger cohorts are required, we believe that our results are promising for the potential use of our methods to personalize AS protocols for PCa and predict tumor progression.
• Jason T. George Texas A&M University
  "Physical Modeling of the T Cell-Peptide Interaction: Toward Predictive T Cell Immunotherapy"
Despite substantial research activity, reliable and computationally efficient prediction of therapeutically relevant T cell receptor (TCR)-antigen pairs remains elusive owing to limited availability of training data and the formidable dimensionality of TCR and antigen sequence space. Successful prediction, if possible, would open new fields of research, from a systematic understanding of the adaptive immune response to viral adaptation to the rapid and optimal identification of tumor antigen-specific T cells. This talk will detail our recent probabilistic modeling efforts that characterize a post-selection T cell repertoire’s ability to identify foreign antigenic signatures with a high degree of specificity. This modeling framework is then applied to construct a data-driven inferential statistical model trained on primary TCR and peptide primary sequences along with crystal structures of known strong binding TCR-peptide pairs. When restricted to a common major histocompatibility complex allele variant, we demonstrate that this approach successfully identifies therapeutically relevant TCR-peptide pairs with a high degree of sensitivity and specificity. Lastly, the trained model is applied to TCRs derived from the peripheral blood of AML patients with the ultimate goal of rapid in silico prediction of tumor antigen-specific T cells.
• Jeffrey West Moffitt Cancer Center
  "Markov models predict minimal residual disease in Adult B-Lymphoblastic Leukemia"
Cancer stem cells (CSCs) are hypothesized to promote tumor progression through innate chemoresistance and self-renewal. While ostensible CSCs were first identified via CD34+/CD38- immunophenotyping in acute myeloid leukemia, the temporal variation of CD34 and CD38 expression in B-lymphoblastic leukemia (B-ALL) complicates the search for CSCs in this setting. We present a Markovian mathematical model which combines the concept of CSCs with pattern of B-ALL subpopulation at diagnosis to demonstrate dynamic phenotypic alteration and predict minimal residual disease (MRD). Qualitative flow cytometry performed on diagnostic bone marrow was used to determine the proportions of CD34+/CD38+, CD34+/CD38-, CD34-/CD38+, and CD34-/CD38- cells in 44 patients with B-ALL. An iterative numerical search procedure was used to derive patient-specific Markov matrices, describing the stochastic cell state transitions. Then, these patients were divided into MRD positive (n=9) and MRD negative (n=35) cohorts to compare transition matrix features. Among all patients with adequate (> 3 years) follow-up, all MRD positive patients experienced relapse within 3 years, whereas only 31.3% of MRD negative patients (11/35) experienced relapsed B-ALL. A higher transition probability to CD34+CD38- from CD34+CD38+ was associated with positive MRD . In contrast, higher transition probabilities toward a CD34-CD38+ phenotype strongly favor negative MRD status, irrespective of the starting phenotype of other three patterns (p=0.00286, 0.00112, 0.000494, 0.000915, respectively). Combining these parameters into a simple predictive model achieves a sensitivity of 44.4% and specificity of 97.1% for MRD in this setting. Thus, Markov modeling proves useful in assessment of cell state dynamics in patients with B-ALL, especially to predict MRD and a higher relapse rate of disease.

• Chloe Colson University of Oxford
  "Investigating the impact of growth arrest mechanisms on tumour responses to combinations of radiotherapy and hyperthermia"
Developing targeted and effective treatment strategies for patients is at the forefront of cancer research today. Recently, there has been increased focus on combination therapies, which aim to exploit different anti-cancer effects while minimising detrimental side-effects. Hyperthermia (HT) is a promising candidate for enhancing the efficacy of radiotherapy (RT). However, incomplete understanding of their interactions is hindering their combined use in the clinic. In this work, we investigate tumour responses to fractionated RT and HT individually and in combination, focussing on how two different mechanisms for growth control may impact tumour sensitivity to these treatments. To do so, we extend an existing ordinary differential equation model of tumour growth, which distinguishes between growth arrest due to nutrient insufficiency and competition for space and exhibits three growth regimes: nutrient limited (NL), space limited (SL) and bistable (BS), where both mechanisms for growth arrest coexist. We adopt a time-dependent description of RT that accounts for two different types of tumour cell damage (sub-lethal vs. lethal), damage repair and cell death following insufficient repair. We also model the time-dependent effects of HT, distinguishing between mild HT, which re-oxygenates the tumour via vasodilation and a reduction in the oxygen consumption rates of tumour cells, and, high HT, which causes tumour and endothelial cell damage and an associated angiogenic response. We construct three virtual populations of tumours in the NL, SL and BS regimes and, for each population, we study tumour responses to conventional fractionation schedules for RT, HT, and combined RT and HT. We determine the average response in each regime and assess the biological processes that may explain positive and negative treatment outcomes. We also investigate the impact of the fraction dose and dosing frequency on tumour responses. This allows us to evaluate which treatment (RT, HT or RT+HT) and dosing regimen maximise the reduction in tumour burden. We find that mild HT cannot significantly enhance the tumour responses to RT. In particular, while the addition of mild HT leads to a modest improvement in the RT response of tumours in the SL regime, it typically worsens the RT response of tumours in NL and BS regimes. By contrast, high HT can act as a potent radiosensitiser for all tumours in each virtual cohort, provided that the HT-induced angiogenic response is sufficiently weak. When there is a strong HT-induced angiogenic response, high HT enhances the RT response of a few tumours in the NL and SL regimes, while it worsens the RT response of most tumours in the BS regime. Finally, in cases where combination treatments are advisable, higher doses of HT applied with lower doses of RT maximise treatment efficacy.
• Louis Kunz Massachusetts General Hospital and Harvard Medical School
  "AMBER (Agent-based Modeling of Biophysical Evolution after Radiotherapy): a computational tumor model as the first step to simulate radiation response."
Intro: Cancer evolution and responses to radiotherapy treatments depend on a complex interplay among physical, chemical, and biological processes. In order to capture this and optimize treatments, novel strategies are required. This work aims to develop a multiscale model capable of predicting tumor fates using a bottom-up approach. While existing tumor models address radiation delivery using the linear-quadratic response to radiation, mechanistic models connecting cell- with tumor-scale radiation effects are yet scarce. Our model aims to incorporate radiosensitivity-modifier factors such as angiogenesis, different cell types, hypoxic and necrotic regions, and oxygen concentration. Additionally, our model is intended to include radiation dose in different areas of the tumor calculated through the TOPAS Monte Carlo toolkit. Methods: We developed a hybrid model including agent-based components and continuum-like aspects in a voxelized geometry. Our model uses tumor mechanical and vascular properties and simulates tumor growth and necrosis evolution following a set of mechanistic rules for (i) cell proliferation and migration, (ii) oxygenation, (iii) angiogenesis, and (iv) cell fates, as follows: (i) within each voxel, cells reproduce with division times following a Gamma distribution and diffuse to neighboring voxels, depending on the crowding degree in each voxel. (ii) A pre-generated healthy vasculature provides oxygen to each voxel at the beginning of the simulations. To decide the oxygen each cell takes, we performed sub-voxel size simulations depending on crowding and the density of vessels to calibrate a Beta distribution representative of the cell-wise oxygen distribution within a voxel. (iii) If a cell is not supplied with enough oxygen, it releases VEGF, which triggers angiogenesis. Tumor-induced angiogenesis replaces healthy vasculature through a directed random walk considering crowding and VEGF gradient. The step size in the random walk also depends on local pressure and VEGF gradient. When the step size reaches a lower-bound threshold, the vessel stops growing. The radius of each vessel is updated using Murray’s law with a linear correction for the pressure exerted by the cells. (iv) Finally, at each time step, a simple vitality function determines if cancer cells are cycling, quiescent, or going through apoptosis/necrosis. Results: Our model is capable of mimicking the genesis and early development of a generic tumor, including a necrotic core. The order of magnitude of the highest microvascular density (h-MVD) in our simulations matches values found from in vivo measurements done by Forster et al. [1] of 20-200 mm-2. Our simulated tumors show chronic hypoxia due to the intra-voxel oxygen distribution and acute hypoxia resulting from increased pressure due to tumor growth leading to vasculature damage. The density of cells in the tumor center and the tumor radius increase exponentially until reaching a plateau caused by insufficient oxygen supply. At this point, the simulation of angiogenesis is necessary to allow for further tumor growth. If angiogenesis is turned off, the cells stop dividing and go through necrosis due to the lack of oxygen supply, leading to a shrinkage of the tumor. When adding angiogenesis, the oxygen concentration reaches a stable value allowing for the number of cancer cells and the radius of the tumor to keep increasing linearly. The pressure in the center of the tumor acts as a barrier to angiogenesis, creating a necrotic core. Conclusion: We present AMBER, a flexible and modular model simulating the evolution of a tumor. To match the observations described earlier with in-vivo data corresponding to the anatomical region and the type of cancer of interest, one should try to tune the model parameters linked to angiogenesis and cell-specific characteristics, such as VEGF production rate, cell doubling time, necrosis threshold or necrosis probability. Our model is designed to account for radiation dose by the future addition of radiation bioeffect models. Its design will allow for a wide range of potential applications in radiotherapy, including external beam as well as radiopharmaceutical therapies or brachytherapy. The model's adaptability will allow for seamless integration with existing models for radiation delivery, such as TOPAS and TOPAS-nBio, and with models for DNA damage and DNA repair. [1] Forster, Jake, Wendy Harriss-Phillips, Michael Douglass, and Eva Bezak. “A Review of the Development of Tumor Vasculature and Its Effects on the Tumor Microenvironment.” Hypoxia Volume 5 (April 2017): 21–32. https://doi.org/10.2147/HP.S133231.
• Noemi Andor Moffitt Cancer Center
  "Modeling competition between subpopulations with variable DNA content in resource limited microenvironments"
Resource limitations shape the outcome of competitions between genetically heterogeneous pre-malignant cells. One example of such heterogeneity is in the ploidy (DNA content) of pre-malignant cells. A whole-genome duplication (WGD) transforms a diploid cell into tetraploid one and has been detected in 28-56% of human cancers. If a tetraploid subclone expands, it consistently does so early in tumor evolution, when cell density is still low and competition for nutrients is comparatively weak – an observation confirmed for several tumor types. WGD+ cells need more resources, to synthesize increasing amounts of DNA, RNA and proteins. To quantify resource limitations and how they relate to ploidy we performed a PAN cancer analysis of WGD, PET/CT and MRI scans. Segmentation of >20 different organs from >900 PET/CT scans was performed with MOOSE. We observed a strong correlation between organ-wide population-average estimates of Oxygen and the average ploidy of cancers growing in the respective organ (Pearson R = 0.66; P= 0.001). In-vitro experiments using near-diploid and near-tetraploid lineages derived from a breast cancer cell line supported the hypothesis that DNA-content influences Glucose- and Oxygen dependent proliferation-, death- and migration rates. To model how subpopulations with variable DNA-content compete in the resource limited environment of the human brain we developed a stochastic state space model of the brain (S3MB). The model discretizes the brain into voxels, whereby the state of each voxel is defined by 8+ variables that are updated over time: stiffness, oxygen, phosphate, glucose, vasculature, dead cells, migrating cells and proliferating cells of various DNA content, and treatment conditions such as radiotherapy and chemotherapy. Fokker-Planck partial differential equations govern the distribution of resources and cells across voxels. We applied S3MB on sequencing and imaging data obtained from a primary GBM patient. We performed whole genome sequencing (WGS) of four surgical specimens collected during the 1st and 2nd surgeries of the GBM and used HATCHET to quantify its clonal composition and how it changes between the two surgeries. HATCHET identified two aneuploid subpopulations of ploidy 1.98 and 2.29 respectively. The low-ploidy clone was dominant at the time of the first surgery and became even more dominant upon recurrence. MRI images were available before and after each surgery and registered to MNI space. The S3MB domain was initiated from 4mm^3 voxels of the MNI space. T1 post and T2 flair scans acquired after the 1st surgery informed tumor cell densities per voxel. Magnetic Resonance Elastography scans and PET/CT scans informed stiffness and Glucose access per voxel. We performed a parameter search to recapitulate the GBM’s tumor cell density and ploidy composition before the 2nd surgery. Results suggest that the high-ploidy subpopulation had a higher Glucose-dependent proliferation rate, but a lower Glucose-dependent death rate, resulting in spatial differences in the distribution of the two subpopulations. Understanding how genomics and microenvironments interact to shape cell fate decisions can help pave the way to therapeutic strategies that mimic prognostically favorable microenvironments.
• Paul Macklin Indiana University
  "A new grammar for real-time and reproducible modeling of multicellular interactions in cancer"
Cancer is driven by complex and multiscale interactions among a community of malignant epithelial, stromal, and immune cells. Within these cancer ecosystems, cells exchange a vast array of chemical and physical signals to drive behavioral responses. Agent-based models (ABMs)--which simulate individual cells as software agents with independent states and “rules” that represent how biophysical cues drive their behaviors--are frequently used to simulate and explore these complex systems, but creating these models requires expertise in both biology and computational modeling. ABMs generally require modelers to (1) formulate biological hypotheses on how biophysical signals drive individual behavioral responses, (2) transform these biological hypotheses into mathematics, and (3) implement these mathematical statements into computational code in C++, Python, Java, or other languages. Development of robust models requires close collaboration between computational scientists and experimental and clinical scientists with biological domain expertise. To facilitate collaborative development and assessment of computational models through modeling loops, we have designed a new modeling approach which encourages interaction between teams of multidisciplinary scientists. We present a new modeling grammar based on interpretable hypotheses of how chemical and physical signals affect cell behavior. (e.g., “In M0 macrophages, necrotic cell debris increases transformation to M1 macrophages. In malignant epithelial cells, doxorubicin increases apoptosis.”) These hypotheses statements are directly mapped onto mathematical response functions to automatically generate model code in real time. In our approach, new and prior model hypotheses are automatically merged and annotated for reproducibility. Moreover, we can combine knowledge-based rules with data-driven rules learned through high-throughput genomics, text mining, and other techniques. When combined with a graphical model editor, multidisciplinary teams can formulate, run, visualize, and refine complex cancer models in real time, accelerating the modeling loop from months to minutes. We will demonstrate the grammar with examples in cancer hypoxia, cancer-immune interactions, and response of cancer and immune cells to therapeutic compounds. We will give a live demonstration to develop, run, and refine a cancer model on-the-fly, and discuss implications of this approach for reproducible team science in multicellular cancer systems biology.

• David Basanta Moffitt Cancer Center
  "Using game theory to model somatic evolution in cancer treated in the presence of environmentally mediated protection"
In recent years, game theory has become a valuable tool for studying the evolutionary dynamics of cancer and their response to treatment. In this study, we use an evolutionary game theory model to investigate the interplay between treatment and the environment in the development of drug resistance in tumor populations. The model consists of two tumor populations: a sensitive and a resistant phenotype, and a stromal population that interacts with the tumor cells. We use replicator equations to simulate the evolutionary dynamics of the populations and analyze the effects of different treatment strategies on the development of drug resistance. To validate the model, we integrate experimental data from previous studies that have investigated the role of stromal cells, specifically carcinoma-associated fibroblasts, in weakening the tumor's response to treatment in cancer. We use simulations and analyses to optimize adaptive therapies in this context by adjusting treatment frequency and dosage. Our results demonstrate that adaptive therapies using a combination of drugs can significantly reduce the emergence of drug resistance in the tumor population. Furthermore, our simulations suggest that adjusting the treatment frequency and dosage can further optimize the adaptive therapies, taking into account the interactions between the tumor and stromal cells. These results highlight the importance of considering the evolutionary dynamics of cancer cells when designing treatments. By understanding how selective pressures affect tumor populations and how they respond to treatment, we can develop more effective therapies that can prolong patient survival and improve their quality of life. Moreover, the evolutionary game theory model presented here can be adapted to other cancer types, potentially leading to the development of more personalized and effective treatments.
• Stefano Casarin Houston Methodist Research Institute
  "Improving the Efficacy of Radium223 for Prostate Cancer Bone Metastasis through Targeting β1 Integrin: In Silico Modeling and In Vivo Validation"
Bone metastasis is a lethal consequence for prostate cancer patients, mostly due to the emergence of resistance and therapy failure. Bone-targeting radiotherapy with Radium223 (Rad223), a radioisotope emitting genotoxic alpha-radiation with limited tissue penetrance (∼100 µm), prolongs the survival of patients with metastatic prostate cancer (PCa). The clinical response to Rad223 is often followed by detrimental relapse and progression. Whether Rad223 causes tumor-cell directed cytotoxicity in vivo remains unclear, and, additionally, effective strategies to improve long-term Rad223 efficacy have not been developed yet. Integrins are heterodimeric transmembrane receptors that, through their activity, support cell growth, decrease cell death and enable radio-resistance mechanisms on exposure to ionizing radiation. Anti-β1 integrin (β1I) targeting improves irradiation treatment outcomes in breast cancer cells and other subcutaneous xenografts. We hypothesize that: i) limited radiation penetrance in situ defines outcome, and ii) targeting β1I would improve 223Ra outcome. In vivo approaches have been limited by huge resource demanding, ethical concerns, and paucity of investigation time points during follow-up. The integration of central biological findings with mathematical modeling allows generating in silico pathophysiological profiles suitable for testing preclinically relevant hypotheses, including predictions on the impact of combinatorial treatments on disease progression. Such predictions can guide preclinical and clinical studies towards more successful outcomes and maximize efficacy. Accordingly, we developed an agent-based model of prostate cancer bone metastasis establishment, growth, and response to putative therapies to: i) predict Rad223 effectiveness in lesions of different sizes, ii) identify Rad223 resistance niches, and iii) optimize Rad223- β1I combinatorial regimen. Our model is regulated via Montecarlo stochastic simulations and seeded with bone metastasis cells endowed with mitosis/apoptosis probability densities which drive the model towards different outcome according to the therapeutic regimen tested. Our in silico model predictions were validated in vivo on humanized bone metastasis mouse model Rad223 delayed the growth of tumors (PC3 and C4-2B cell line) in bone. Cancer cell lethality in response to Rad223 was profound but zonally confined along the bone interface compared with the more distant tumor core, which remained unperturbed. In silico simulations predicted greater efficacy of Rad223 on single-cell lesions and minimal effects on larger, as further confirmed in vivo for PC3 and C4-2B tumors. Micro-tumors showed severe growth delay or eradication in response to Rad223, whereas macro-tumors persisted and expanded. The relative inefficacy in controlling large tumors points to application of Rad223 in secondary prevention of early bone-metastatic disease and regimens co-targeting the tumor core. Interference with β1I combined with Rad223 reduced PC3 cell growth in bone and significantly improved overall mouse survival, whereas no change was achieved in C4-2B tumors. Anti-β1I treatment decreased the PC3 tumor cell mitosis index and spatially expanded Rad223 lethal effects 2-fold, in vivo and in silico. Regression was paralleled by decreased expression of radio-resistance mediator. Targeting β1I significantly improves Rad223 outcome and points toward combinatorial application in PCa tumors with high β1I expression.
• Tatiana Miti H. Lee Moffitt Cancer Center
  "Integrating Spatatial statistics and ABMs to Study Stromal Effects on the Remission-Relapse Dynamics of NSCLC and TNBC"
Tumor relapse during therapies is thought to reflect the ability of tumor cells to escape treatment via cell-intrinsic genetic and epigenetic changes, either preexistent or evolved de novo under the drug-imposed cytostatic and cytotoxic selective pressures. Multiple published and unpublished reports, show that at least some of the otherwise drug-sensitive tumor cells might be able to avoid elimination due to microenvironmental factors, such as pro-survival paracrine signals, capable of providing alternative means of survival despite the shutdown of oncogenic signaling. Concurrently, clinical studies indicated that higher stroma-to-tumor content has a poorer prognosis and increased risk of relapse in various cancers. However, despite our advances in deciphering the molecular mechanisms behind tumor progression, our understanding of how stroma contributes to the evolution of tumor resistance and relapse remains limited. Our objective is to build stochastic mathematical models to help understand the stroma-tumor eco-evolutionary interplay so that we can design new therapeutic strategies for tumor elimination or treatments that provide long-term control of tumor growth. The models integrate the spatiotemporal stroma-tumor cells interactions measured using a novel purposely-designed spatial analysis pipeline and combine it with in vivo and in vitro tumor growth dynamics data. We focus on two distinct stromal effects studied in our lab in vitro and in vivo, namely drug-sheltering effects against targeted therapies in Non-Small Cell Lung Cancer (NSCLC) and enhanced tumor cells’ proliferation, indiscriminately of treatment presence, in Triple Negative Breast Cancer (TNBC). The preliminary results show that enhanced proliferation in the vicinity of stroma in TNBC could be sufficient to drive tumor relapse after four cycles of chemotherapy and greatly accelerates relapse in tumors where the treatment has a low killing rate. In the context of NSCLC, the drug-sheltering effects of stroma could lead to tumor relapse in absence of hard-wired resistance, and disrupting the drug-sheltering stromal effects result in a higher rate of tumor eradication. Our results show that by using carefully designed and calibrated mathematical models, we can gain a deeper understanding of the ecological mechanisms that lead to tumor relapse as well as uncover new therapeutic strategies that account for stromal effects and are successful at eradicating tumors.
• Zuping Wang University of Maryland, College Park
  "A mathematical model of TCR T cell therapy for cervical cancer"
Engineered T cell receptor (TCR) T cells are expected to drive strong anti-tumor responses upon recognition of the specific tumor antigen, with rapid expansion and cytotoxic functions, causing tumor cell death. However, although TCR T cell therapy against cancers is promising, it remains difficult to predict which patient will have better therapeutic outcome and why. We develop a mathematical model to re-assess some mechanisms of insufficient efficacy of TCR T cell therapy in HPV+ cervical cancer model of mice. We consider a dynamical system that follows the population of cancer cells, effector TCR T cells, regulatory T cells (Tregs), and 'non-tumor killing' TCR T cells. We demonstrate: 1) the majority of TCR T cell within the tumor is 'non-tumor killing' TCR T cells, such as exhausted cells, which are highly active but contribute little or have no direct cytotoxicity in the tumor microenvironment (TME); 2) there are two important conditions for tumor regression: the reversal of the immunosuppressive TME by depleting Tregs, and the increased proliferation of effector TCR T cells with antitumor activity. Using mathematical modeling, we show that certain treatment protocols have the potential to improve therapy responses.

• Anna Tang University of Utah
  "Mathematical Model of Drug Resistance in Cancer with respect to the Cancer Microenvironment"
One of the main obstacles to treating cancer is its ability to evolve and resist treatment. In this project, we mathematically model how the cancer microenvironment interacts with cancer cells and affects response to therapy in the context of estrogen-receptor positive (ER+) breast cancer, endocrine therapy, and cancer-associated fibroblasts (CAFs). The system is described with ordinary differential equations (ODEs) to investigate the impacts that cancer cells and CAFs have on each other’s population dynamics. We explore two different proposed scenarios of cancer-CAF dynamics: 1) cancer cells can recruit CAFs from an endless supply of fibroblasts, 2) a constant total population of fibroblasts that can switch between healthy and cancer-associated. In each scenario, we analyze stability of fixed points to determine the impacts of endocrine treatment and CAFs on the long-term behavior of cancer to address the questions: What role does estrogen/endocrine therapy play in resistance acquisition? Is resistance inevitable? If not, what can we do to prevent it? If resistance is inevitable, can we reverse it? and how? Both systems exhibit vastly different long-term outcomes dependent on estrogen availability in the system. For example, the models predict that a mere 20-hour difference in the initiation of endocrine therapy dictates the difference between the population of cancer dying off or growing infinitely. Furthermore, constant lower levels of available estrogen or constant small populations of CAFs prolong the systems' periods of slow growth. In the recruitment model, we also find that the existence of enough CAFs is necessary for the cancer population to grow exponentially under endocrine therapy or survive. Thus, the model suggests rapid tumor growth can be delayed by increasing the death rate of CAFs. By including CAFs in our model, we hope to provide new insights into how ER+ breast cancer develops resistance to endocrine therapy.
• Pujan Shrestha Texas A&M University
  "Microenvironmental Modulation of the Cancer-Immune Interaction"
This talk will describe our recent modeling effort to understand the stochastic dynamics of cancer dormancy, which refers to the ability of cancer cells to remain inactive below detection thresholds for prolonged time periods despite therapeutic interventions. There are different types of cancer dormancy, including cellular and immune-mediated dormancy. The balance between pro-tumor and anti-tumor immunity plays a critical role in cancer elimination or progression, resulting in cancer escape, elimination, or equilibrium. This equilibrium phase is associated with immune-mediated dormancy, where T cell killing matches the cancer division rate. Previous mathematical models that have been proposed to study dormancy, such as those using ordinary differential equations (ODEs), have limitations like neglecting the distributional behavior of cells and failing to make predictions with equilibrium population sizes close to zero, which may overlook the extinction probability of this absorbing state. To address these limitations, this talk will present a new stochastic model based on non-linear birth-death processes to more accurately describe dormancy dynamics. The model assumes a cancer population undergoing stochastic birth and death with an exponential growth rate, modified by an immunomodulation function that depends on the population size and an inhibitory element. This modeling framework can be used to identify the immunomodulatory effects of cancer therapy and the tumor microenvironment on the timing and likelihood of cancer elimination.
• Yijia Fan Texas A&M University
  "Stochastic modeling of extracellular matrix spatial and geometric cues in the tumor microenvironment: insights into cancer evasion and T-cell dysfunction"
The identification of optimal cancer therapies is significantly complicated by the dynamic interplay between tumor immune evasion and T-cell exhaustion. Cytotoxic T-cell immunosurveillance plays a vital role in immunoediting cancers, and understanding the effects of immunoediting on cancer progression to escape is an ongoing work in progress. One critical factor that remains poorly understood is how the spatial and geometric cues of the extracellular matrix (ECM) in the tumor microenvironment affect the tumor-T-cell interaction. This is further complicated by ECM remodeling by primary cancer en route to metastasis. To address these challenges, we have developed a dual-agent-based model (ABM) to explore the relationship between ECM fiber geometry, tumor spatial growth, and the adaptive process of T-cell recognition of tumor-associated antigens. Using this model, we demonstrate the influence of ECM fiber orientation on cancer spatiotemporal progression. We compare and contrast the spatial dependence of tumor progression in the setting of circumferentially versus radially packed ECM fibers. By studying the balance of T cell accessibility on tumor recognition and antigen loss. Immune microenvironmental factors, including hypoxia and nutrient concentration, can explain cancer progression secondary to T-cell dysfunction. Overall, our preliminary findings provide a more detailed description of cancer spatiotemporal progression, and our model provides a computational means by which ECM geometry and microenvironmental parameters can be integrated for predicting the outcome of tumor-immune evolution across a number of contexts.
• Zahra S. Ghoreyshi Texas A&M University, College Station, TX, USA
  "Optimal cellular phenotypic adaptation in fluctuating nutrient and drug environments"
Despite recent improvements in cancer therapy, phenotypic adaptation persists as a significant barrier in overcoming therapeutic resistance. Recent experimental efforts have attempted to minimize cancer cell growth by using increasingly sophisticated drug cycling strategies. However, this search has been slowed owing to the sheer complexity in the number of allowable temporally varying policies, thereby necessitating more efficient computational identification of optimal dosing strategies. In this study, we develop a stochastic description of cellular adaptation wherein temporally adaptive cells select their phenotype based on their prior encounter with an uncertain environmental landscape. We first apply this model to explain distinct growth phenotypes observed experimentally in bacterial systems navigating fluctuating nutrient landscapes. We then extend and apply our stochastic model in experimental collaboration to study prostate cell line-specific optimal adaptation to temporally varying enzalutamide therapy. Using this approach, we predict that under specific drug cycling frequencies, adaptive cells' nutrient availability is universally reduced compared to cells in constant ones, which confirms empirical observations about cancer cell growth.