Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions

Helen M. Byrne, Mark A. J. Chaplain

Type: Article

Publication Date: 1995-05-01

Citations: 159

DOI: https://doi.org/10.1007/bf02460635

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Locations

Bulletin of Mathematical Biology - View
PubMed - View

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Works That Cite This (129)

Action	Title	Year	Authors
+ PDF Chat	Mesoscopic and continuum modelling of angiogenesis	2014	Fabian Spill Pilar Guerrero Tomás Alarcón P. K. Maini Helen M. Byrne
+	A Fokker–Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis	2022	Souvik Roy Zui Pan Suvra Pal
+	Mathematical modelling of angiogenesis.	2000	Mark A. J. Chaplain
+	Numerical interactions of random and directed motility during cancer invasion	1999	Abbey J. Perumpanani John W. Norbury
+	A Hybrid Discrete-Continuum Model of Tumour Induced Angiogenesis	2011	Alexander R.A. Anderson Mark A. J. Chaplain S. R. McDougall
+	A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies	2003	Michael J. Plank
+	Multiscale Angiogenesis Modeling Using Mixed Finite Element Methods	2005	Shuyu Sun Mary F. Wheeler Mandri Obeyesekere C. Patrick
+	On a class of Keller–Segel chemotaxis systems with cross-diffusion	2015	Tian Xiang
+	Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth	2009	Michael Welter K. Bartha Heiko Rieger
+	A multilevel approach to cancer growth modeling	2007	P. P. Delsanto C. A. Condat Nicola M. Pugno Antonio S. Gliozzi Michele Griffa

Works Cited by This (11)

Action	Title	Year	Authors
+	The propagation of fungal colonies: a model for tissue growth	1982	Leah Edelstein
+	Tumor-related angiogenesis	1989	Neidhard Paweletz Martin Knierim
+	Diffusion regulated growth characteristics of a spherical prevascular carcinoma.	1990	John A. Adam Sophia Maggelakis
+	Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis	1991	Cynthia L. Stokes Douglas A. Lauffenburger
+	A Mathematical Model for the Diffusion of Tumour Angiogenesis Factor into the Surrounding Host Tissue	1991	Mark A. J. Chaplain Andrew M. Stuart
+	A mathematical model of tumour-induced capillary growth	1985	David J. Balding D. L. S. McElwain
+	A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor	1993	Mark A. J. Chaplain Andrew M. Stuart
+ PDF Chat	Migration of individual microvessel endothelial cells: stochastic model and parameter measurement	1991	Cynthia L. Stokes Douglas A. Lauffenburger Stuart K. Williams
+	Traveling wave solutions to reaction-diffusion systems modeling combustion	1983	Henri Berestycki B. Nicolaenko Bruno Scheurer
+	Partial differential equations	1980	Bill Williams