Modelling the Cell Cycle and Cell Movement in Multicellular Tumour Spheroids |
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Authors: | M J Tindall C P Please |
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Institution: | (1) Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, UK;(2) School of Mathematical Studies, The University of Southampton, Southampton, SO17 1BJ, UK |
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Abstract: | This paper analyses a recent mathematical model of avascular tumour spheroid growth which accounts for both cell cycle dynamics
and chemotactic driven cell movement. The model considers cells to exist in one of two compartments: proliferating and quiescent,
as well as accounting for necrosis and apoptosis. One particular focus of this paper is the behaviour created when proliferating
and quiescent cells have different chemotactic responses to an extracellular nutrient supply. Two very different steady-state
behaviours are identified corresponding to those cases where proliferating cells move either more quickly or more slowly than
quiescent cells in response to a gradient in the extracellular nutrient supply. The case where proliferating cells move more
rapidly leads to the commonly accepted spheroid structure of a thin layer of proliferating cells surrounding an inner quiescent
core. In the case where proliferating cells move more slowly than quiescent cells the model predicts an interesting structure
of a thin layer of quiescent cells surrounding an inner core of proliferating and quiescent cells. The sensitivity of this
tumour structure to the cell cycle model parameters is also discussed. In particular variations in the steady-state size of
the tumour and the types of transient behaviour are explored. The model reveals interesting transient behaviour with sharply
delineated regions of proliferating and quiescent cells. |
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Keywords: | Multicellular tumour spheroid Cell cycle distribution Chemotaxis Shocks |
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