Multiscale Modelling and Analysis of Tumour Growth and Treatment Strategies

A multiscale, agent-based mathematical framework is here used to capture the multiscale nature of solid tumours. Tumour dynamics and treatment responses are modelled and simulated in silico. Details regarding cell cy-cle progression, tumour growth and oxygen distribution are included in the mathematical framework. Treatment responses to conventional anti-cancer therapies, such as chemotherapy and radiotherapy, as well as to more novel drugs, such as hypoxia-activated prodrugs and DNA-damage repair inhibit-ing drugs, are studied. Uncertainty and sensitivity analyses techniques are discussed in order to mitigate model uncertainty and interpret model sen-sitivity to parameter perturbations. This thesis furthermore discusses the role of mathematical modelling in current cancer research

Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia–telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development

Quantifying ERK activity in response to inhibition of the BRAFV600E-MEK-ERK cascade using mathematical modelling

Funding: UK Medical Research Council (Grant Number(s): MR/R017506/1).Background Simultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanism of how vertical inhibition synergistically suppresses intracellular ERK activity, and consequently cell proliferation, are yet to be fully elucidated. Methods We develop a mechanistic mathematical model that describes how the mutant BRAF inhibitor, dabrafenib, and the MEK inhibitor, trametinib, affect BRAFV600E-MEK-ERK signalling. The model is based on a system of chemical reactions that describes cascade signalling dynamics. Using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations that are parameterised by in vitro data and solved numerically to obtain the temporal evolution of cascade component concentrations. Results The model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E-mutant melanoma cells. The model elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated BRAF concentrations generate drug resistance to dabrafenib and trametinib. The computational simulations further suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. Conclusions The model can be used to systematically motivate which dabrafenib–trametinib dose combinations, for treating BRAFV600E-mutated melanoma, warrant experimental investigation.Publisher PDFPeer reviewe

A numerical approach to model the dynamics in a mammalian cell exposed to a carcinogenic compound

When a mammalian cell is exposed to a carcinogen, the carcinogen gives rise to new compounds. In this paper a numerical approach is taken to find the amount of these compounds overtime. The concentration of the compounds are assumed to satisfy the reaction and/or the diffusion equation, techniques used for solving these equations include the one-dimensional finite element method (FEM) and the lumped parameter approach. The mathematically derived results are compared to in-vitro measurements. The mathematical model set up in this paper will prove insufficient

Blackboard-to-bedside:a mathematical modeling bottom-up approach towards personalized cancer treatments

Cancers present with high variability across patients and tumors; thus, cancer care, in terms of disease prevention, detection, and control, can highly benefit from a personalized approach. For a comprehensive personalized oncology practice, this personalization should ideally consider data gathered from various information levels, which range from the macroscale population level down to the microscale tumor level, without omission of the central patient level. Appropriate data mined from each of these levels can significantly contribute in devising personalized treatment plans tailored to the individual patient and tumor. Mathematical models of solid tumors, combined with patient-specific tumor profiles, present a unique opportunity to personalize cancer treatments after detection using a bottom-up approach. Here, we discuss how information harvested from mathematical models and from corresponding in silico experiments can be implemented in preclinical and clinical applications. To conceptually illustrate the power of these models, one such model is presented, and various pertinent tumor and treatment scenarios are demonstrated in silico. The presented model, specifically a multiscale, hybrid cellular automaton, has been fully validated in vitro using multiple cell-line–specific data. We discuss various insights provided by this model and other models like it and their role in designing predictive tools that are both patient, and tumor specific. After refinement and parametrization with appropriate data, such in silico tools have the potential to be used in a clinical setting to aid in treatment protocols and decision making

Uncertainty and Sensitivity Analyses Methods for Agent-Based Mathematical Models: An Introductory Review

Multiscale, agent-based mathematical models of biological systems are often associated with model uncertainty and sensitivity to parameter perturbations. Here, three uncertainty and sensitivity analyses methods, that are suitable to use when working with agent-based models, are discussed. These methods are namely Consistency Analysis, Robustness Analysis and Latin Hypercube Analysis. This introductory review discusses origins, conventions, implementation and result interpretation of the aforementioned methods. Information on how to implement the discussed methods in MATLAB is included.Comment: 41 page

A single-cell mathematical model of SARS-CoV-2 induced pyroptosis and the effects of anti-inflammatory intervention

SJH is supported by the Medical Research Council grant MR/R017506/1. The authors would like to thank the SARS-CoV-2 Tissue Simulation Coalition for ongoing collaboration and feedback on model development. Further, this work is part of the RAMP (Rapid Assistance in Modelling the Pandemic) initiative, coordinated by the Royal Society, UK. The authors would like to thank Prof. Mark A.J. Chaplain (University of St Andrews) for coordinating our RAMP Task Team modelling within-host dynamics. SARS-CoV-2 Tissue Simulation Coalition: http://physicell.org/covid19/. RAMP: https://royalsociety.org/topics-policy/health-and-wellbeing/ramp/.Pyroptosis is an inflammatory mode of cell death that can contribute to the cytokine storm associated with severe cases of coronavirus disease 2019 (COVID-19). The formation of the NLRP3 inflammasome is central to pyroptosis, which may be induced by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Inflammasome formation, and by extension pyroptosis, may be inhibited by certain anti-inflammatory drugs. In this study, we present a single-cell mathematical model that captures the formation of the NLRP3 inflammasome, pyroptotic cell death and responses to anti-inflammatory intervention that hinder the formation of the NLRP3 inflammasome. The model is formulated in terms of a system of ordinary differential equations (ODEs) that describe the dynamics of the key biological components involved in pyroptosis. Our results demonstrate that an anti-inflammatory drug can delay the formation of the NLRP3 inflammasome, and thus may alter the mode of cell death from inflammatory (pyroptosis) to non-inflammatory (e.g., apoptosis). The single-cell model is implemented within a SARS-CoV-2 tissue simulator, in collaboration with a multidisciplinary coalition investigating within host-dynamics of COVID-19. In this paper, we additionally provide an overview of the SARS-CoV-2 tissue simulator and highlight the effects of pyroptosis on a cellular level.Publisher PDFPeer reviewe