Modelling cell populations with spatial structure: steady state and treatment-induced evolution of tumour cords
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Tumour cells growing around blood vessels form structures called
tumour cords. We review some mathematical models that have been proposed to
describe the stationary state of the cord and the cord evolution after
single-dose cell killing treatment. Whereas the cell population has
been represented with age or maturity structure to describe
the cord stationary state, for the response to treatment a simpler approach
was followed, by representing the cell population by means of the cell volume
fractions. In this latter model, where transport of oxygen is included and
its concentration is critical for cell viability, some constraints to be
imposed on the interface separating the tumour from the necrotic region
have a crucial role. An analysis of experimental data from untreated tumour
cords, which involves modelling by cell age and by volume fractions, and
some results about the cord response to impulsive cell killing, are
also presented.