ArticleBulletin of mathematical biology2019
A Mathematical Framework for Modelling the Metastatic Spread of Cancer.
Article in Bulletin of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 32 papers.
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Who cites it
32 citing papers in PubMed, 103 citations in OpenAlex.
- Computational reactive-diffusive modeling for stratification and prognosis determination of patients with breast cancer receiving Olaparib.Scientific reports · 2023Trial
- Mathematical and Mouse Models Identify Regulatory T Cell Influx as A Key Determinant of Acquired Resistance to PD-1 Immunotherapy.Cancer research · 2026Article
- Phylogeography of Bone Metastasis: Clonal Evolution, Skeletal Niche Adaptation, and Clinical Implications.International journal of molecular sciences · 2026Review
- Digital Twin Meets the Bench: Natural Compounds Reshape the Ovarian Cancer Microenvironment.Biomedicines · 2025Article
- Cancer model with moving extinction threshold reproduces real cancer data.Journal of the Royal Society, Interface · 2025Article
- A stochastic modelling framework for cancer patient trajectories: combining tumour growth, metastasis, and survival.Journal of mathematical biology · 2025Article
- A Network Based Model for Predicting Spatial Progression of Metastasis.Bulletin of mathematical biology · 2025Article
- Breaking boundaries: role of the brain barriers in metastatic process.Fluids and barriers of the CNS · 2025Review
- Tissue stresses caused by invasive tumour: a biomechanical model.Journal of the Royal Society, Interface · 2025Article
- A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation.Cellular and molecular bioengineering · 2024Article
- Experimentally-driven mathematical model to understand the effects of matrix deprivation in breast cancer metastasis.NPJ systems biology and applications · 2024Article
- Cancer cell sedimentation in 3D cultures reveals active migration regulated by self-generated gradients and adhesion sites.PLoS computational biology · 2024Article
- A Genuinely Hybrid, Multiscale 3D Cancer Invasion and Metastasis Modelling Framework.Bulletin of mathematical biology · 2024Article
- A Model for Membrane Degradation Using a Gelatin Invadopodia Assay.Bulletin of mathematical biology · 2024Article
- Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics.Cancer research · 2023Article
- Multiscale model of the different modes of cancer cell invasion.Bioinformatics (Oxford, England) · 2023Article
- Nanoscale Prognosis of Colorectal Cancer Metastasis from AFM Image Processing of Histological Sections.Cancers · 2023Article
- A computational model for the cancer field effect.Frontiers in artificial intelligence · 2023Article
- Revolutionizing anti-cancer drug discovery against breast cancer and lung cancer by modification of natural genistein: an advanced computational and drug design approach.Frontiers in oncology · 2023Article
- Recent progress in molecular mechanisms of postoperative recurrence and metastasis of hepatocellular carcinoma.World journal of gastroenterology · 2022Review
Corrections and comments
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Authors and funding
4 authors at 2 institutions in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
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, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer. To shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner-a multigrid, hybrid, individual-based approach. This framework accounts for the spatiotemporal evolution of mesenchymal- and epithelial-like cancer cells, membrane-type-1 matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase-2 (MMP-2), and for their interactions with the extracellular matrix. Using computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix-degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs such as MMP-2.
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