Cell kinetics in tumour cords studied by a model with variable cell cycle length.
ABSTRACT 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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ABSTRACT: In this paper we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in the Banach space by using the delay semigroup techniques. The local existence and uniqueness of solution as well as the continuous dependence on initial conditions are obtained by using the general theory of quasi-linear evolution equations in nonreflexive Banach spaces, while the global existence of solution is obtained by the estimates of the solution and the extension theorem.04/2014;
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ABSTRACT: DNA mismatch repair (MMR) is involved in processing DNA damage following treatment with ionising radiation (IR) and various classes of chemotherapy drugs including iododeoxyuridine (IUdR), a known radiosensitiser. In this study, the authors have developed asynchronous probabilistic cell cycle models to assess the isolated effects of IUdR and IR and the combined effects of IUdR + IR treatments on MMR damage processing. The authors used both synchronous and asynchronous MMR-proficient/MMR-deficient cell populations and followed treated cells for up to two cell cycle times. They have observed and quantified differential cell cycle responses to MMR damage processing following IR and IUdR + IR treatments, principally in the duration of both G1 and G2/M cell cycle phases. The models presented in this work form the foundation for the development of an approach to maximise the therapeutic index for IR and IUdR + IR treatments in MMR-deficient (damage tolerant) cancers.IET Systems Biology 08/2013; 7(4):114-24. · 1.67 Impact Factor
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ABSTRACT: Tumour cells growing around blood vessels form cylindrical structures called tumour cords. A nu- merical method is derived for the numerical so- lution of a kind of boundary-value problems for a hyperbolic rst order integro-partial dieren- tial equation describing the stationary state of a tumour cord. Numerical simulations with the method are used for a qualitative study of the best functional form (within a inverse power law class of functions) for the radial dependency of a function that describes the fraction of newborn cells that become quiescent in a model by Bertuzzi and Gandol (3), when compared with experimen- tal eld data.