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

University of Florence, Florens, Tuscany, 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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    ABSTRACT: We investigate a new model of tumor growth in which cell motility is considered an explicitly separate process from growth. Bulk tumor expansion is modeled by individual cell motility in a density-dependent diffusion process. This model is implemented in the context of an in vivo system, the tumor cord. We investigate numerically microscale density distributions of different cell classes and macroscale whole tumor growth rates as functions of the strength of transitions between classes. Our results indicate that the total tumor growth follows a classical von Bertalanffy growth profile, as many in vivo tumors are observed to do. This provides a quick validation for the model hypotheses. The microscale and macroscale properties are both sensitive to fluctuations in the transition parameters, and grossly adopt one of two phenotypic profiles based on their parameter regime. We analyze these profiles and use the observations to classify parameter regimes by their phenotypes. This classification yields a novel hypothesis for the early evolutionary selection of the metastatic phenotype by selecting against less motile cells which grow to higher densities and may therefore induce local collapse of the vascular network.
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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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