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While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.
A mathematical model of the tumour growth along a blood vessel is proposed. The
model employs the mixture theory approach to describe a tissue which consists of cells, extracellular
matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host
tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is
paid to consistent description of oxygen consumption and growth processes based on the energy
balance. A finite difference numerical...
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