Cell kinetics in tumour cords studied by a model with variable cell cycle length

Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185 Rome, Italy.
Mathematical Biosciences (Impact Factor: 1.3). 05/2002; 177-178:103-25. DOI: 10.1016/S0025-5564(01)00114-6
Source: PubMed


A mathematical model is developed that describes the proliferative behaviour at the stationary state of the cell population within a tumour cord, i.e. in a cylindrical arrangement of tumour cells growing around a blood vessel and surrounded by necrosis. The model, that represents the tumour cord as a continuum, accounts for the migration of cells from the inner to the outer zone of the cord and describes the cell cycle by a sequence of maturity compartments plus a possible quiescent compartment. Cell-to-cell variability of cycle phase transit times and changes in the cell kinetic parameters within the cord, related to changes of the microenvironment, can be represented in the model. The theoretical predictions are compared against literature data of the time course of the labelling index and of the fraction of labelled mitoses in an experimental tumour after pulse labelling with 3H-thymidine. It is shown that the presence of cell migration within the cord can lead to a marked underestimation of the actual changes along cord radius of the kinetics of cell cycle progression.

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    • "These structures are observed in sections taken from in vivo primary and experimental tumors, and may be a key organizational structure for vascular tumors at the sub-tissue level [24] [3]. The tumor cord has been investigated mathematically in many contexts as it lends itself to useful assumptions about the symmetry of tumor growth [3] [4]. If one models growth in a thin crosswise section so that significant lengths of the microvessel/tumor extend in both directions, one can make the assumption that the section has axial symmetry. "
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    • "Diffusion and haptotaxis terms account for the spatial dynamics of the system in the models under study. Age, size and/or space structure has also been used in models of tumor cords [17] [18] [19] [26]. Computational and software considerations often limit scientists from incorporating physiological structure directly into a model. "
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    • "The authors concluded that a correct analysis of radioactive labelling data from tumour microregions requires the possible cell migration through the regions to be taken into account. While both the model given by Bertuzzi and Gandolfi (2000) and that given by Bertuzzi et al. (2002) neglected the process of cell death within the tumour cord, a subsequent model given by Bertuzzi et al. (2003) considered the dynamics of tumour cords under the action of a cytotoxic agent. This model incorporated both a random cell death—either spontaneous or induced by the cytotoxic agent—and a cell death which results from insufficient nutrient availability. "
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