ArticleJournal of mathematical biology2006
M5 mesoscopic and macroscopic models for mesenchymal motion.
Article in Journal of mathematical biology, 2006. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 24 papers.
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Who cites it
24 citing papers in PubMed, 134 citations in OpenAlex.
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- Using a probabilistic approach to derive a two-phase model of flow-induced cell migration.Biophysical journal · 2024Article
- Modelling microtube driven invasion of glioma.Journal of mathematical biology · 2023Article
- Immune-checkpoint inhibitor therapy response evaluation using oncophysics-based mathematical models.Wiley interdisciplinary reviews. Nanomedicine and nanobiotechnology · 2023Review
- Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis.Bulletin of mathematical biology · 2022Article
- Mathematical modeling of therapeutic neural stem cell migration in mouse brain with and without brain tumors.Mathematical biosciences and engineering : MBE · 2022Article
- Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment.Journal of mathematical biology · 2021Article
- Cell-Scale Degradation of Peritumoural Extracellular Matrix Fibre Network and Its Role Within Tissue-Scale Cancer Invasion.Bulletin of mathematical biology · 2020Article
- Modelling physical limits of migration by a kinetic model with non-local sensing.Journal of mathematical biology · 2020Article
- The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration.Bulletin of mathematical biology · 2020Article
- Modelling collective cell migration: neural crest as a model paradigm.Journal of mathematical biology · 2020Article
- Kinetic models with non-local sensing determining cell polarization and speed according to independent cues.Journal of mathematical biology · 2020Article
- Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving Boundary Cancer Invasion.Bulletin of mathematical biology · 2019Article
- An investigation of the influence of extracellular matrix anisotropy and cell-matrix interactions on tissue architecture.Journal of mathematical biology · 2016Article
- An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas.Journal of mathematical biology · 2016Article
- Glioma follow white matter tracts: a multiscale DTI-based model.Journal of mathematical biology · 2015Article
- Mathematical and computational modeling in biology at multiple scales.Theoretical biology & medical modelling · 2014Review
- A hybrid model of tumor-stromal interactions in breast cancer.Bulletin of mathematical biology · 2013Article
- Computational modeling of single-cell migration: the leading role of extracellular matrix fibers.Biophysical journal · 2012Article
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Authors and funding
1 author at 1 institution in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
In this paper mesoscopic (individual based) and macroscopic (population based) models for mesenchymal motion of cells in fibre networks are developed. Mesenchymal motion is a form of cellular movement that occurs in three-dimensions through tissues formed from fibre networks, for example the invasion of tumor metastases through collagen networks. The movement of cells is guided by the directionality of the network and in addition, the network is degraded by proteases. The main results of this paper are derivations of mesoscopic and macroscopic models for mesenchymal motion in a timely varying network tissue. The mesoscopic model is based on a transport equation for correlated random walk and the macroscopic model has the form of a drift-diffusion equation where the mean drift velocity is given by the mean orientation of the tissue and the diffusion tensor is given by the variance-covariance matrix of the tissue orientations. The transport equation as well as the drift-diffusion limit are coupled to a differential equation that describes the tissue changes explicitly, where we distinguish the cases of directed and undirected tissues. As a result the drift velocity and the diffusion tensor are timely varying. We discuss relations to existing models and possible applications.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.