Mathematical modelling of tumour-induced angiogenesis: network growth and structure.
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Summary
This chapter presents a review of a variety of mathematical models used to describe the formation of capillary networks and focuses on a specific recent model which uses novel mathematical modelling techniques to generate both 2 and 3 dimensional vascular structures.
- Type
- review
- Published
- 2004-01-01
- Cited by
- 44
- References
- 66
- OpenAlex
- https://openalex.org/W60558353
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:25925393
Keywords
Angiogenesis, Fibronectin, Extracellular matrix, Endothelial stem cell, Cell biology
References
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- Effect of plasma and carboxylesterase on the stability, mutagenicity, and DNA cross-linking activity of some direct-acting N-nitroso compounds.
- Chemotaxis of aortic endothelial cells in response to fibronectin.
- Angiogenesis and inflammation
- On Growth and Form: Spatio-temporal Pattern Formation in Biology
- Signaling Vascular Morphogenesis and Maintenance
- Tumor growth and neovascularization: an experimental model using the rabbit cornea.
- Tumor-induced neovascularization in the mouse eye.
- Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development
- Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies.
- A mechanical model for the formation of vascular networks in vitro
- Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies
- Angiogenesis in vitro
- Tumor-related angiogenesis.
- Mechanisms of placental invasion of the uterus and their control.
- Role of the Flt-1 receptor tyrosine kinase in regulating the assembly of vascular endothelium
- Quantitative angiogenesis assays: Progress and problems
- Fibronectins—adhesive glycoproteins of cell surface and blood
Cited by
- A multiscale probabilisitic framework to model early steps in tumor metastasis.
- Building blocks for computational models of angiogenesis
- Capillary characteristics in microfluidic experiments and computational simulation
- Evaluation of Angiogenesis and Osteogenesis
- Mathematical modeling of tumorigenesis: mission possible
- Multiscale Models of Angiogenesis
- In Silico Augmentation of the Drug Development Pipeline: Examples from the study of Acute Inflammation
- Antiangiogenic versus cytotoxic activity in analogues of aeroplysinin-1.
- On the global dynamics of a model for tumor immunotherapy.
- Elongation, proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting
- Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model.
- Nanovehicular Intracellular Delivery Systems
- Cancer: a Systems Biology disease.
- Multiscale Cancer Modeling
- Translational Systems Approaches to the Biology of Inflammation and Healing
- A hybrid continuum–discrete modelling approach to predict and control angiogenesis: analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology
- Mechanisms of organogenesis of primary lymphoid follicles.
- Structural Adaptation and Heterogeneity of Normal and Tumor Microvascular Networks
- Clinically Relevant Modeling of Tumor Growth and Treatment Response
- Role of angiogenesis and angiogenic factors in acute and chronic wound healing
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