Reducing phenotype-structured partial differential equations models of cancer evolution to systems of ordinary differential equations: a generalised moment dynamics approach.

Intratumour phenotypic heterogeneity is understood to play a critical role in disease progression and treatment failure. Accordingly, there has been increasing interest in the development of mathematical models capable of capturing its role in cancer cell adaptation. This can be systematically achieved by means of models comprising phenotype-structured nonlocal partial differential equations, tracking the evolution of the phenotypic density distribution of the cell population, which may be compared to gene and protein expression distributions obtained experimentally.

Identifiability of phenotypic adaptation from low-cell-count experiments and a stochastic model.

Phenotypic plasticity contributes significantly to treatment failure in many cancers. Despite the increased prevalence of experimental studies that interrogate this phenomenon, there remains a lack of applicable quantitative tools to characterise data, and importantly to distinguish between resistance as a discrete phenotype and a continuous distribution of phenotypes. To address this, we develop a stochastic individual-based model of plastic phenotype adaptation through a continuously-structured phenotype space in low-cell-count proliferation assays.

Using virtual patient cohorts to uncover immune response differences in cancer and immunosuppressed COVID-19 patients.

The COVID-19 pandemic caused by the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) resulted in millions of deaths globally. Adults with immunosuppression (e.g.

Spatial computational modelling illuminates the role of the tumour microenvironment for treating glioblastoma with immunotherapies.

Glioblastoma is the most common and deadliest brain tumour in adults, with a median survival of 15 months under the current standard of care. Immunotherapies like immune checkpoint inhibitors and oncolytic viruses have been extensively studied to improve this endpoint. However, most thus far have failed.

Smoothing in linear multicompartment biological processes subject to stochastic input.

Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behavior under what are often highly variable external environments acting as system inputs.

Mathematical modelling of clonal reduction therapeutic strategies in acute myeloid leukemia.

Over the years, the overall survival of older patients diagnosed with acute myeloid leukemia (AML) has not significantly increased. Although standard cytotoxic therapies that rapidly eliminate dividing myeloblasts are used to induce remission, relapse can occur due to surviving therapy-resistant leukemic stem cells (LSCs). Hence, anti-LSC strategies have become a key target to cure AML.

Impact of Resistance on Therapeutic Design: A Moran Model of Cancer Growth.

Resistance of cancers to treatments, such as chemotherapy, largely arise due to cell mutations. These mutations allow cells to resist apoptosis and inevitably lead to recurrence and often progression to more aggressive cancer forms. Sustained-low dose therapies are being considered as an alternative over maximum tolerated dose treatments, whereby a smaller drug dosage is given over a longer period of time.

Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation.

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo.

Mathematical modeling predicts pathways to successful implementation of combination TRAIL-producing oncolytic virus and PAC-1 to treat granulosa cell tumors of the ovary.

The development of new cancer therapies requires multiple rounds of validation from and experiments before they can be considered for clinical trials. Mathematical models assist in this preclinical phase by combining experimental data with human parameters to provide guidance about potential therapeutic regimens to bring forward into trials. However, granulosa cell tumors of the ovary lack a relevant mouse model, complexifying preclinical drug development for this rare tumor.

The effect of chemotaxis on T-cell regulatory dynamics.

Autoimmune diseases, such as Multiple Sclerosis, are often modelled through the dynamics of T-cell interactions. However, the spatial aspect of such diseases, and how dynamics may result in spatially heterogeneous outcomes, is often overlooked. We consider the effects of diffusion and chemotaxis on T-cell regulatory dynamics using a three-species model of effector and regulator T-cell populations, along with a chemical signalling agent.

Agent-Based Modelling Reveals the Role of the Tumor Microenvironment on the Short-Term Success of Combination Temozolomide/Immune Checkpoint Blockade to Treat Glioblastoma.

Glioblastoma is the most common and deadly primary brain tumor in adults. All glioblastoma patients receiving standard-of-care surgery-radiotherapy-chemotherapy (i.e.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians.

Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics.

Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated Bayesians or opportunistic users, applied professionals can now reap many of the benefits afforded by the Bayesian paradigm. In this paper, we touch on six modern opportunities and challenges in applied Bayesian statistics: intelligent data collection, new data sources, federated analysis, inference for implicit models, model transfer and purposeful software products.

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model.

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period.

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions.

The COVID-19 pandemic has revealed the need for the increased integration of modelling and data analysis to public health, experimental, and clinical studies. Throughout the first two years of the pandemic, there has been a concerted effort to improve our understanding of the within-host immune response to the SARS-CoV-2 virus to provide better predictions of COVID-19 severity, treatment and vaccine development questions, and insights into viral evolution and the impacts of variants on immunopathology. Here we provide perspectives on what has been accomplished using quantitative methods, including predictive modelling, population genetics, machine learning, and dimensionality reduction techniques, in the first 26 months of the COVID-19 pandemic approaches, and where we go from here to improve our responses to this and future pandemics.

Efficient inference and identifiability analysis for differential equation models with random parameters.

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped.

Agent-based computational modeling of glioblastoma predicts that stromal density is central to oncolytic virus efficacy.

Oncolytic viruses (OVs) are emerging cancer immunotherapy. Despite notable successes in the treatment of some tumors, OV therapy for central nervous system cancers has failed to show efficacy. We used an tumor model developed from human glioblastoma tissue to evaluate the infiltration of herpes simplex OV rQNestin (oHSV-1) into glioblastoma tumors.

Identifying cell-to-cell variability in internalization using flow cytometry.

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability.

COVID-19 virtual patient cohort suggests immune mechanisms driving disease outcomes.

To understand the diversity of immune responses to SARS-CoV-2 and distinguish features that predispose individuals to severe COVID-19, we developed a mechanistic, within-host mathematical model and virtual patient cohort. Our results suggest that virtual patients with low production rates of infected cell derived IFN subsequently experienced highly inflammatory disease phenotypes, compared to those with early and robust IFN responses. In these in silico patients, the maximum concentration of IL-6 was also a major predictor of CD8+ T cell depletion.

Procaspase-Activating Compound-1 Synergizes with TRAIL to Induce Apoptosis in Established Granulosa Cell Tumor Cell Line (KGN) and Explanted Patient Granulosa Cell Tumor Cells In Vitro.

Granulosa cell tumors (GCT) constitute only ~5% of ovarian neoplasms yet have significant consequences, as up to 80% of women with recurrent GCT will die of the disease. This study investigated the effectiveness of procaspase-activating compound 1 (PAC-1), an activator of procaspase-3, in treating adult GCT (AGCT) in combination with selected apoptosis-inducing agents. Sensitivity of the AGCT cell line KGN to these drugs, alone or in combination with PAC-1, was tested using a viability assay.

In silico trials predict that combination strategies for enhancing vesicular stomatitis oncolytic virus are determined by tumor aggressivity.

Background: Immunotherapies, driven by immune-mediated antitumorigenicity, offer the potential for significant improvements to the treatment of multiple cancer types. Identifying therapeutic strategies that bolster antitumor immunity while limiting immune suppression is critical to selecting treatment combinations and schedules that offer durable therapeutic benefits. Combination oncolytic virus (OV) therapy, wherein complementary OVs are administered in succession, offer such promise, yet their translation from preclinical studies to clinical implementation is a major challenge.

COVID-19 virtual patient cohort reveals immune mechanisms driving disease outcomes.

Unlabelled: To understand the diversity of immune responses to SARS-CoV-2 and distinguish features that predispose individuals to severe COVID-19, we developed a mechanistic, within-host mathematical model and virtual patient cohort. Our results indicate that virtual patients with low production rates of infected cell derived IFN subsequently experienced highly inflammatory disease phenotypes, compared to those with early and robust IFN responses. In these patients, the maximum concentration of IL-6 was also a major predictor of CD8 T cell depletion.

Translational approaches to treating dynamical diseases through in silico clinical trials.

The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies.

Engineering in Medicine To Address the Challenge of Cancer Drug Resistance: From Micro- and Nanotechnologies to Computational and Mathematical Modeling.

Drug resistance has profoundly limited the success of cancer treatment, driving relapse, metastasis, and mortality. Nearly all anticancer drugs and even novel immunotherapies, which recalibrate the immune system for tumor recognition and destruction, have succumbed to resistance development. Engineers have emerged across mechanical, physical, chemical, mathematical, and biological disciplines to address the challenge of drug resistance using a combination of interdisciplinary tools and skill sets.