Mathematical modelling of avascular ellipsoidal tumour growth

Authors:
G. Dassios, F. Kariotou, M. N. Tsampas and B. D. Sleeman

Journal:
Quart. Appl. Math. **70** (2012), 1-24

MSC (2010):
Primary 92C05, 92C50

Published electronically:
September 15, 2011

MathSciNet review:
2920612

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Abstract | References | Similar Articles | Additional Information

Abstract: Breast cancer is the most frequently diagnosed cancer in women. From mammography, Magnetic Resonance Imaging (MRI), and ultrasonography, it is well documented that breast tumours are often ellipsoidal in shape. The World Health Organisation (WHO) has established a criteria based on tumour volume change for classifying response to therapy. Typically the volume of the tumour is measured on the hypothesis that growth is ellipsoidal. This is the Calliper method, and it is widely used throughout the world. This paper initiates an analytical study of ellipsoidal tumour growth based on the pioneering mathematical model of Greenspan. Comparisons are made with the more commonly studied spherical mathematical models.

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Additional Information

**G. Dassios**

Affiliation:
Department of Chemical Engineering, University of Patras, GR 265 04, Patras, Greece and ICE-HT/FORTH, Greece

**F. Kariotou**

Affiliation:
Department of Chemical Engineering, University of Patras, GR 265 04, Patras, Greece

**M. N. Tsampas**

Affiliation:
Department of Chemical Engineering, University of Patras, GR 265 04, Patras, Greece

**B. D. Sleeman**

Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

DOI:
https://doi.org/10.1090/S0033-569X-2011-01240-2

Received by editor(s):
March 18, 2010

Published electronically:
September 15, 2011

Article copyright:
© Copyright 2011
Brown University