Mark A J Chaplain

Mark A J Chaplain
University of St Andrews · School of Mathematics and Statistics

BSc (Hons), PhD

About

354
Publications
62,704
Reads
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16,187
Citations
Citations since 2017
73 Research Items
6609 Citations
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201720182019202020212022202302004006008001,0001,200
201720182019202020212022202302004006008001,0001,200
Introduction
Mathematical oncology - various mathematical modelling approaches to all aspects of cancer growth and treatment; Techniques: differential equations (ODEs, PDEs); deterministic and stochastic approaches; individual-based or agent-based models; multiscale approaches Aspects of cancer: avascular solid tumours, vascular tumours, angiogenesis, invasion and metastasis, immune response, chemotherapy and radiotherapy treatment Current interest: invasion and metastasis
Additional affiliations
January 2009 - present
The Ohio State University
September 1996 - December 2012
University of Dundee
September 1996 - April 2015
University of Dundee
Position
  • Ivory Chair of Applied Mathematics
Education
October 1987 - June 1990
University of Dundee
Field of study
  • Applied Mathematics, Mathematical Biology
October 1982 - June 1986
University of Dundee
Field of study
  • Applied Mathematics

Publications

Publications (354)
Article
The contents of this editorial is proposed in three parts devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is as follows: first, a general framework is presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multi...
Preprint
Full-text available
Individual responses to SARS-CoV-2 infection vary significantly, ranging from mild courses of infection that do not require hospitalisation to the development of disease which not only requires hospitalisation but can be fatal. Whilst many immunological studies have revealed fundamental insights into SARS-CoV-2 infection and COVID-19, mathematical...
Article
Rheumatoid arthritis (RA) is a chronic inflammatory disorder that causes pain, swelling and stiffness in the joints, and negatively impacts the life of affected patients. The disease does not have a cure yet, as there are still many aspects of this complex disorder that are not fully understood. While mathematical models can shed light on some of t...
Chapter
This chapter provides an introduction to the contents of this edited book which is devoted to the modelling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. Firstly we report about motivations and objectives of the edited book consistent with the idea that mathematical models sho...
Article
The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis,...
Article
Full-text available
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 governe...
Article
Full-text available
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 eluci...
Article
This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population...
Chapter
A defining feature of cancer is the capability to spread locally into the surrounding tissue, with cancer cells spreading beyond any normal boundaries. Cancer invasion is a complex phenomenon involving many inter-connected processes at different spatial and temporal scales. A key component of invasion is the ability of cancer cells to alter and deg...
Preprint
Full-text available
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 eluci...
Article
Full-text available
Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a...
Article
Full-text available
We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables—tumour cell density, extracellular matrix density and matrix degrading enzyme concentration—in a one-dimensional tissue domain. The first method is a likelihood...
Preprint
The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis,...
Article
Full-text available
We develop a three-dimensional genuinely hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between thes...
Book
This book presents original papers reflecting topics featured at the international symposium entitled “Fusion of Mathematics and Biology” and organized by the editor of the book. The symposium, held in October 2020 at Osaka University in Japan, was the core event for the final year of the research project entitled “Establishing International Resear...
Article
Understanding and designing clinical radiation therapy is one of the most important areas of state-of-the-art oncological treatment regimens. Decades of research have gone into developing sophisticated treatment devices and optimization protocols for schedules and dosages. In this paper, we presented a comprehensive computational platform that faci...
Article
TB is one of the top 10 causes of death worldwide and the leading cause of death from a single infectious agent. Decreasing the length of time for TB treatment is an important step towards the goal of reducing mortality. Mechanistic in silico modelling can provide us with the tools to explore gaps in our knowledge, with the opportunity to model the...
Article
Full-text available
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of tumour cells, the concentration of oxygen and the concentration of a chemotherapeutic agent. In order to disentan...
Preprint
Mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems and describe the physical interactions between cells and their local surroundings. These models generally consist of a balance equation for the cell density, one for the density of the extracellular matrix (ECM), and a force-bal...
Article
Full-text available
Cancer invasion and metastatic spread to secondary sites in the body are facilitated by a complex interplay between cancer cells of different phenotypes and their microenvironment. A trade-off between the cancer cells' ability to invade the tissue and to metastasize, and their ability to proliferate has been observed. This gives rise to the classif...
Preprint
We develop a three-dimensional genuinely hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between thes...
Preprint
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of reaction-diffusion equations for interacting chemical species ("morphogens"), whose heterogeneous distribution...
Article
Full-text available
This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS–CoV–[Formula: see text] Severe Acute Respiratory Syndrome, corona virus n.[Formula: see text]. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from...
Preprint
Full-text available
This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called \textit{SARS--CoV--2 Severe Acute Respiratory Syndrome, corona virus n.2}. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the vi...
Chapter
Cancer is a complex disease, a complicated phenomenon involving many inter-related processes across a wide range of spatial and temporal scales. It is one of the leading causes of morbidity and mortality across the globe, with around 14 million new cases in 2012, and this figure is set to rise over the next 20 years. The latest statistics from the...
Preprint
Full-text available
Understanding and designing clinical radiation therapy is one of the most important areas of state-of-the-art oncological treatment regimens. Decades of research have gone into developing sophisticated treatment devices and optimization protocols for schedules and dosages. In this paper, we presented a comprehensive computational platform that faci...
Article
1. Aphid populations frequently include phenotypes that are resistant to parasitism by hymenopterous parasitoid wasps, which is often attributed to the presence of 'protective' facultative endosymbionts residing in aphid tissues, particularly Hamiltonella defensa. In field conditions, under parasitoid pressure, the observed coexistence of aphids wi...
Article
Full-text available
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population gr...
Article
We present a stochastic individual-based model for the phenotypic evolution of cancer cell populations under chemotherapy. In particular, we consider the case of combination cancer therapy whereby a chemotherapeutic agent is administered as the primary treatment and an epigenetic drug is used as an adjuvant treatment. The cell population is structu...
Article
Full-text available
Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases, mortality. Understanding the biological mechanisms behind the progression of the disease, as well as de...
Preprint
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of tumour cells, the concentration of oxygen and the concentration of a chemotherapeutic agent. In order to disentan...
Article
The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in t...
Preprint
Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which leads to chronic pain, poor life quality and, in some cases, premature mortality. Understanding the biological mechanisms behind the progression of the disease, as...
Preprint
Full-text available
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 we here propose using a data-driven, agent-based model to bridge t...
Preprint
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of a system of non-local parabolic equations that describes the phenotypic evolution of tumour cells and their nonlinear dynamic interactions with oxygen, which is released...
Preprint
Full-text available
Cancer invasion and metastatic spread to secondary sites in the body are facilitated by a complex interplay between cancer cells of different phenotypes and their microenvironment. A trade-off between the cancer cells' ability to invade the tissue and to metastasise, and their ability to proliferate has been observed. This gives rise to the classif...
Preprint
Full-text available
Cancer invasion and metastatic spread to secondary sites in the body are facilitated by a complex interplay between cancer cells of different phenotypes and their microenvironment. A trade-off between the cancer cells' ability to invade the tissue and to metastasise, and their ability to proliferate has been observed. This gives rise to the classif...
Article
Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally focus only on one of these key aspects. We present here a spatial stochastic individual-based model that explicitl...
Preprint
Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally focus only on one of these key aspects. We present here a spatial stochastic individual-based model that explicitl...
Article
Full-text available
Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network, they can spread to distant secondary sites in the body. This process, kno...
Article
Full-text available
We investigate with computer simulations the critical radius of pores in a lipid bilayer membrane. Ilton et al. (2016) recently showed that nucleated pores in a homopolymer film can increase or decrease in size, depending on whether they are larger or smaller than a critical size which scales linearly with film thickness. Using dissipative particle...
Article
Transcription factors are important molecules which control the levels of mRNA and proteins within cells by modulating the process of transcription (the mechanism by which mRNA is produced within cells) and hence translation (the mechanism by which proteins are produced within cells). Transcription factors are part of a wider family of molecular in...
Article
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...
Preprint
We consider a continuum mechanical model of cell invasion through thin membranes, which consists of a transmission problem for a system of nonlinear partial differential equations for the cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting tra...
Chapter
We present a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of oxygen and therapeutic agents in mediating phenotypic selection of cancer c...
Preprint
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population gr...
Article
Full-text available
The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates do...
Data
miR-451-AMPK-mTOR system. Development, parameter estimation, analysis, sensitivity analysis, and theoretical implications of the miR-451-AMPK-mTOR core control system. (PDF)
Data
Supplementary Raw Research Data. This is open data under the CC BY license http://creativecommons.org/licenses/by/4.0/
Preprint
Full-text available
The ability to locally degrade the extracellular matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a critical step in the metastatic spread of the tumour. The invasion of the surrounding tissue involves the coordinated action between cancer cells, the ECM, the matrix degradin...
Article
We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenoty...
Article
A growing body of experimental evidence indicates that immune cells move in an unrestricted search pattern if they are in the pre-activated state, whilst they tend to stay within a more restricted area upon activation induced by the presence of tumour antigens. This change in movement is not often considered in the existing mathematical models of t...
Preprint
If improvements are to be made in tuberculosis (TB) treatment, an increased understanding of disease in the lung is needed. Studies have shown that bacteria in a less metabolically active state, associated with the presence of lipid bodies, are less susceptible to antibiotics, and recent results have highlighted the disparity in concentration of di...
Article
Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the...
Article
Full-text available
If improvements are to be made in tuberculosis (TB) treatment, an increased understanding of disease in the lung is needed. Studies have shown that bacteria in a less metabolically active state, associated with the presence of lipid bodies, are less susceptible to antibiotics, and recent results have highlighted the disparity in concentration of di...
Research
Full-text available
Combined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome , but is difficult to account for using traditional treatment plann...
Article
Full-text available
Combined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planni...
Article
Full-text available
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these pro...
Article
Full-text available
Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell in...
Article
Full-text available
We study angiogenesis using mathematical models describing the dynamics of tip cells. We review the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examine the classical model of Anderson-Chaplain using fundamental concepts of mass transport and ch...
Article
Full-text available
In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell–cell adhesion and cell–matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model cons...
Article
In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model...
Article
The emergence of cooperation is a major conundrum of evolutionary biology. To unravel this evolutionary riddle, several models have been developed within the theoretical framework of spatial game theory, focussing on the interactions between two general classes of player, “cooperators” and “defectors”. Generally, explicit movement in the spatial do...
Article
Full-text available
Royal Society Open Science has been in the vanguard of efforts to improve both transparency and reproducibility in science, since its launch in 2014. Among the wider scientific community, there is a widespread dissatisfaction with the current level of transparency and reproducibility in published research and, as part of our response to this, we s...