The Interaction of Growth Rates and Diffusion Coefficients in a Three-dimensional Mathematical Model of Gliomas

Patricia K. Burgess, Paul M. Kulesa, James D. Murray, Ellsworth C. Alvord

Type: Article

Publication Date: 1997-06-01

Citations: 125

DOI: https://doi.org/10.1097/00005072-199756060-00008

View Publication

Locations

Journal of Neuropathology & Experimental Neurology - View
PubMed - View

Similar Works

Action	Title	Year	Authors
+	The Interaction of Growth Rates and Diffusion Coefficients in a Three-dimensional Mathematical Model of Gliomas	1997	Patricia K. Burgess Paul M. Kulesa James D. Murray Ellsworth C. Alvord
+ PDF Chat	Diffusive modelling of glioma evolution: a review	2010	Alexandros Roniotis Kostas Marias Vangelis Sakkalis Michalis Zervakis
+	Mathematical Modeling Of Glioma Proliferation And Diffusion.	2009	Mahlet Assefa Russell C. Rockne Mindy D Szeto Kristin R. Swanson
+ PDF Chat	Mathematical modelling of spatio-temporal glioma evolution	2013	Maria Papadogiorgaki Panagiotis Koliou X. Kotsiakis Michalis Zervakis
+	Reaction-Diffusion Models for Glioma Tumor Growth	2017	Miguel Martı́n-Landrove
+	Simulating glioblastoma growth consisting both visible and invisible parts of the tumor using a diffusion–reaction model followed by resection and radiotherapy	2018	Navid Moshtaghi-Kashanian Hanieh Niroomand-Oscuii N. Meghdadi
+	Brain tumor modeling: glioma growth and interaction with chemotherapy	2011	Hossein Yousefi-Banaem Alireza Ahmadian Hooshangh Saberi Alireza Daneshmehr Davood Khodadad
+	A complete mathematical study of a 3D model of heterogeneous and anisotropic glioma evolution	2009	Alexandros Roniotis Kostas Marias Vangelis Sakkalis George D. Tsibidis Michalis Zervakis
+	The mathematical path to develop a heterogeneous, anisotropic and 3-dimensional glioma model using finite differences	2009	Alexandros Roniotis Kostas Marias Vangelis Sakkalis Ioannis Karatzanis Michalis Zervakis
+	A mathematical model of glioma growth: the effect of extent of surgical resection	1996	Diana E. Woodward James A. Cook Philippe Tracqui G. C. Cruywagen J. D. Murray Ellsworth C. Alvord
+ PDF Chat	Mathematical Modeling of Human Glioma Growth Based on Brain Topological Structures: Study of Two Clinical Cases	2012	Cecilia Suárez Felipe Maglietti Mario Colonna Karina Breitburd Guillermo Marshall
+ PDF Chat	MATHEMATICAL MODELLING OF GLIOBLASTOMA TUMOUR DEVELOPMENT: A REVIEW	2005	Haralampos Hatzikirou Andreas Deutsch Carlo Schaller Matthias Simon Kristin R. Swanson
+	In-Depth Analysis and Evaluation of Diffusive Glioma Models	2012	Alexandros Roniotis Vangelis Sakkalis Ioannis Karatzanis Michalis Zervakis Kostas Marias
+ PDF Chat	Computer simulation of glioma growth and morphology	2007	Hermann B. Frieboes John Lowengrub Steven M. Wise Xiaoming Zheng Paul Macklin Elaine L. Bearer Vittorio Cristini
+ PDF Chat	The Evolution of Mathematical Modeling of Glioma Proliferation and Invasion	2007	Hana L.P. Harpold Ellsworth C. Alvord Kristin R. Swanson
+	Computer Modeling of Brain Tumor Growth	2008	André H. Juffer U. Marin O. Niemitalo J. Koivukangas
+ PDF Chat	A Mathematical Model to Simulate Glioma Growth and Radiotherapy at the Microscopic Level	2012	Alina Toma Konstanze Holl‐Ulrich Stefan Becker Andreas Mang Tina Anne Schütz Matteo Mario Bonsanto Volker Tronnier Thorsten M. Buzug
+	MODELLING THREE-DIMENSIONAL GROWTH OF BRAIN TUMOURS FROM TIME SERIES OF SCANS	1999	Philippe Tracqui MAHIDINE MENDJELI
+	Mathematical Model of the Impact of Chemotherapy and Anti-Angiogenic Therapy on Drug Resistance in Glioma Growth	2023	Latifah Hanum Nanang Susyanto Dwi Ertiningsih
+	A mathematical model of glioma growth: the effect of chemotherapy on spatio‐temporal growth	1995	Philippe Tracqui G. C. Cruywagen Diana E. Woodward Gabe T. Bartoo J. D. Murray Ellsworth C. Alvord

Works That Cite This (90)

Action	Title	Year	Authors
+	CTV Delineation for High-Grade Gliomas: Is There Agreement With Tumor Cell Invasion Models?	2022	Wille Häger M. Lazzeroni Mehdi Astaraki Iuliana Toma-Daşu
+ PDF Chat	A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects	2017	Georgios Stamatakos S. Giatili
+	Biocomputing: Numerical simulation of glioblastoma growth and comparison with conventional irradiation margins	2010	Pierre‐Yves Bondiau Ender Konukoğlu Olivier Clatz Hervé Delingette M. Frénay Philippe Paquis
+	Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model	2021	Najma Ahmed Nehad Ali Shah Somaye Taherifar F. D. Zaman
+	Modelling intercellular communication and its effects on tumour invasion	2010	Mathilde Badoual Christophe Deroulers M Aubert B. Grammaticos
+	Modelling Cell Invasion: A Review of What JD Murray and the Embryo Can Teach Us	2021	Paul M. Kulesa Jennifer C. Kasemeier‐Kulesa Jason A. Morrison Rebecca McLennan Mary Cathleen McKinney Caleb M. Bailey
+ PDF Chat	A quantitative model for differential motility of gliomas in grey and white matter	2000	Kristin R. Swanson Ellsworth C. Alvord J. D. Murray
+	On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells	2014	Alexander S. Bratus Svetlana Yu. Kovalenko Elena Fimmel
+ PDF Chat	Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells	2023	Hamzeh Zureigat Mohammed Al‐Smadi Areen Al-Khateeb Shrideh Al‐Omari Sharifah E. Alhazmi
+ PDF Chat	Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy	2002	Kristin R. Swanson Ellsworth C. Alvord J. D. Murray

Works Cited by This (0)

Action	Title	Year	Authors