MATHEMATICAL MODELLING OF AVASCULAR AND VASCULAR TUMOUR GROWTH

2008 ◽  
Author(s):  
P. F. JONES ◽  
B. D. SLEEMAN
Keyword(s):  
Mathematical Modelling ◽  
Tumour Growth ◽  
Vascular Tumour

scholarly journals MATHEMATICAL MODELLING OF GLIOBLASTOMA TUMOUR DEVELOPMENT: A REVIEW

2005 ◽  
Vol 15 (11) ◽  
pp. 1779-1794 ◽  
Author(s):  
HARALAMPOS HATZIKIROU ◽  
ANDREAS DEUTSCH ◽  
CARLO SCHALLER ◽  
MATTHIAS SIMON ◽  
KRISTIN SWANSON
Keyword(s):  
Mathematical Modelling ◽  
Tumour Growth ◽  
State Of The Art ◽  
Vascular Tumour ◽  
Open Problems ◽  
Malignant Brain Tumour ◽  
The Past ◽  
Research Perspectives ◽  
Current State ◽  
New Research

During the past several years mathematical models have been applied to various aspects of cancer dynamics, in particular avascular and vascular tumour growth, invasion, angiogenesis, and metastasis. This paper focuses on the most common and malignant brain tumour, glioblastoma, and surveys the growing number of studies dealing with mathematical modelling of this tumour. We attempt to classify these studies by their biomedical relevance and critically analyse their results. The aim of this review is to provide a meaningful reference, to both biomedical and mathematical researchers, of the current state of the art of glioma tumour modelling. The discussion attempts to identify current open problems as well as new research perspectives in the mathematical modelling of glioblastoma growth.

67: A theoretical modelling of vascular tumour growth to identify optimal combinations of anti-angiogenesis drugs with chemotherapy

2010 ◽  
Vol 97 (1) ◽  
pp. S59
Author(s):  
Lignet Floriane ◽  
Sebastien Benzekry ◽  
Frédérique Billy ◽  
Branka Bernard ◽  
Olivier Saut ◽  
...  
Keyword(s):  
Tumour Growth ◽  
Theoretical Modelling ◽  
Vascular Tumour

Mathematical Modelling and Avascular Tumour Growth

Resonance ◽  
2019 ◽  
Vol 24 (3) ◽  
pp. 313-325
Author(s):  
Jennifer A. Flegg ◽  
Neela Nataraj
Keyword(s):  
Mathematical Modelling ◽  
Tumour Growth

scholarly journals Multiscale Modelling of Vascular Tumour Growth in 3D: The Roles of Domain Size and Boundary Conditions

PLoS ONE ◽  
2011 ◽  
Vol 6 (4) ◽  
pp. e14790 ◽  
Author(s):  
Holger Perfahl ◽  
Helen M. Byrne ◽  
Tingan Chen ◽  
Veronica Estrella ◽  
Tomás Alarcón ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Tumour Growth ◽  
Domain Size ◽  
Multiscale Modelling ◽  
Vascular Tumour

scholarly journals The impact of cell crowding and active cell movement on vascular tumour growth

2006 ◽  
Vol 1 (4) ◽  
pp. 515-535 ◽  
Author(s):  
Russell Betteridge ◽  
◽  
Markus R. Owen ◽  
H.M. Byrne ◽  
Tomás Alarcón ◽  
...  
Keyword(s):  
Tumour Growth ◽  
Cell Movement ◽  
Active Cell ◽  
Vascular Tumour ◽  
The Impact

scholarly journals Mathematical Modelling of the Response of Breast Cancer to Drug Therapy

1997 ◽  
Vol 1 (2) ◽  
pp. 137-151 ◽  
Author(s):  
D. A. Cameron
Keyword(s):  
Breast Cancer ◽  
Mathematical Modelling ◽  
Response Curve ◽  
Growth Response ◽  
Tumour Growth ◽  
Primary Tumour ◽  
Regression Line ◽  
Tumour Response ◽  
Response To Chemotherapy ◽  
Cell Kill

mathematical modelling of tumour response in breast cancer offers the potential for further understanding of the mechanisms involved in a tumour's imperfect response to chemotherapy. Three different models of assessing response are studied; the simplest consisting of fitting a regression line to the logarithm of the tumour volumes; a study using exponential growth and an S-shaped growth response curve; and one that assumes log cell-kill and the possibilitu of primary tumour resistance to therapy. All thre can explain some facets of tumour biology, but it is the introduction of the possibility of resistance that appears to result in correlations with clinical outcome. The issue of Gompertz growth is discussed, since it is considered, although not without controversy, to best describe not only xenograft but also clinical tumour growth, and yet has not been used in any of the three models discussed. It appears that much of the data used to clinically validate Gompertz growth is before the period of maximum deceleratin, and thus the true relevance of this function to clinical tumour growth remains uncertain.

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