ArticleJournal of mathematical biology2011
Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation.
Article in Journal of mathematical biology, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 35 papers.
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35 citing papers in PubMed, 164 citations in OpenAlex.
- Computational insights into cancer stem cell dynamics and the urokinase plasminogen activation pathway.Journal of biosciences · 2026Article
- Fuzzy and fractional analysis of cancer tumor dynamics with depression effects on chemotherapy.Scientific reports · 2025Article
- Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy.Bulletin of mathematical biology · 2025Article
- CanSeer: a translational methodology for developing personalized cancer models and therapeutics.Scientific reports · 2025Article
- Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues.NPJ systems biology and applications · 2024Article
- Stochastic differential equation modelling of cancer cell migration and tissue invasion.Journal of mathematical biology · 2023Article
- Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model.PLoS computational biology · 2023Article
- Multiscale modeling of collective cell migration elucidates the mechanism underlying tumor-stromal interactions in different spatiotemporal scales.Scientific reports · 2022Article
- A multi-layered hybrid model for cancer cell invasion.Medical & biological engineering & computing · 2022Article
- Mathematical models for cell migration: a non-local perspective.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2020Review
- Cell-Scale Degradation of Peritumoural Extracellular Matrix Fibre Network and Its Role Within Tissue-Scale Cancer Invasion.Bulletin of mathematical biology · 2020Article
- Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.Bulletin of mathematical biology · 2020Article
- Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis.Frontiers in bioengineering and biotechnology · 2020Review
- Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving Boundary Cancer Invasion.Bulletin of mathematical biology · 2019Article
- A Mathematical Framework for Modelling the Metastatic Spread of Cancer.Bulletin of mathematical biology · 2019Article
- Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm.Frontiers in physiology · 2018Article
- A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis.Journal of mathematical biology · 2018Article
- Structured models of cell migration incorporating molecular binding processes.Journal of mathematical biology · 2017Article
- Model of vascular desmoplastic multispecies tumor growth.Journal of theoretical biology · 2017Article
- Tissue-scale, personalized modeling and simulation of prostate cancer growth.Proceedings of the National Academy of Sciences of the United States of America · 2016Article
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Authors and funding
5 authors at 4 institutions in 4 countries.
Funding
Abstract
The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.
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