ArticleActa biotheoretica1995
From passive diffusion to active cellular migration in mathematical models of tumour invasion.
Article in Acta biotheoretica, 1995. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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13 citing papers in PubMed, 92 citations in OpenAlex.
- Tissue stresses caused by invasive tumour: a biomechanical model.Journal of the Royal Society, Interface · 2025Article
- Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist.Frontiers in cell and developmental biology · 2024Review
- Semi-autonomous wound invasion via matrix-deposited, haptotactic cues.Journal of theoretical biology · 2023Article
- Post-Surgery Glioma Growth Modeling from Magnetic Resonance Images for Patients with Treatment.Scientific reports · 2017Article
- Glioma follow white matter tracts: a multiscale DTI-based model.Journal of mathematical biology · 2015Article
- Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model.PloS one · 2015Article
- Simulating radiotherapy effect in high-grade glioma by using diffusive modeling and brain atlases.Journal of biomedicine & biotechnology · 2012Article
- Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy.Journal of biological dynamics · 2012Article
- In silico modelling of tumour margin diffusion and infiltration: review of current status.Computational and mathematical methods in medicine · 2012Review
- In-silico oncology: an approximate model of brain tumor mass effect based on directly manipulated free form deformation.International journal of computer assisted radiology and surgery · 2010Article
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- Front instabilities and invasiveness of simulated avascular tumors.Bulletin of mathematical biology · 2009Article
- Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation.IEEE transactions on medical imaging · 2005Article
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Authors and funding
1 author at 1 institution in 1 country.
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Abstract
Mathematical models of tumour invasion appear as interesting tools for connecting the information extracted from medical imaging techniques and the large amount of data collected at the cellular and molecular levels. Most of the recent studies have used stochastic models of cell translocation for the comparison of computer simulations with histological solid tumour sections in order to discriminate and characterise expansive growth and active cell movements during host tissue invasion. This paper describes how a deterministic approach based on reaction-diffusion models and their generalisation in the mechano-chemical framework developed in the study of biological morphogenesis can be an alternative for analysing tumour morphological patterns. We support these considerations by reviewing two studies. In the first example, successful comparison of simulated brain tumour growth with a time sequence of computerised tomography (CT) scans leads to a quantification of the clinical parameters describing the invasion process and the therapy. The second example considers minimal hypotheses relating cell motility and cell traction forces. Using this model, we can simulate the bifurcation from an homogeneous distribution of cells at the tumour surface toward a nonhomogeneous density pattern which could characterise a pre-invasive stage at the tumour-host tissue interface.
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