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Mathematical modelling of avascular ellipsoidal tumour growth. (English) Zbl 1233.92030

Summary: 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 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 is widely used throughout the world. This paper initiates an analytical study of ellipsoidal tumour growth based on the pioneering mathematical model of H.P. Greenspan [Stud. Appl. Math. 51, 317–340 (1972; Zbl 0257.92001)]. Comparisons are made with the more commonly studied spherical mathematical models.

MSC:

92C50 Medical applications (general)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
65C20 Probabilistic models, generic numerical methods in probability and statistics
93A30 Mathematical modelling of systems (MSC2010)

Citations:

Zbl 0257.92001
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Full Text: DOI

References:

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