Mathematical Oncology

Anderson, Alexander R.A.; Maini, Philip K.

doi:10.1007/s11538-018-0423-5

Cited by 47 publications

(35 citation statements)

References 40 publications

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“…These models can be discrete or continuous. A certain type of model is chosen based on the application and availability of the data [149,150]. Depending on the type of the model, Computer models provide large-scale predictive power by allowing us to simulate clinical trials with sufficient details to study response to various conditions.…”

Section: Discussion and Emerging Applicationsmentioning

confidence: 99%

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Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

et al. 2019

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Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

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Section: Discussion and Emerging Applicationsmentioning

confidence: 99%

“…These models can be discrete or continuous. A certain type of model is chosen based on the application and availability of the data [149,150]. Depending on the type of the model, predictions can be made for the behavior of the signaling system in a qualitative, semi-quantitative or quantitative manner.…”

Section: Discussion and Emerging Applicationsmentioning

confidence: 99%

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

et al. 2019

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“…While tumour heterogeneity is now widely recognised (Merlo et al 2006;Gerlinger et al 2012;Anderson and Maini 2018), we are only beginning to comprehend its implications for cancer progression. The fact that the cells in a tumour are not identical, and instead might act as a collective composed of phenotypically distinct individuals, is particularly important in the context of cancer invasion.…”

Section: Discussionmentioning

confidence: 99%

Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion

et al. 2020

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Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno-and phenotypic intratumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

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“…While tumour heterogeneity is now widely recognised [38,29,3], we are only beginning to comprehend its implications for cancer progression. The fact that the cells in a tumour are not identical, and instead might act as a collective composed of phenotypically distinct individuals, is particularly important in the context of cancer invasion.…”

Section: Discussionmentioning

confidence: 99%