Dynamics of tumour cords following changes in oxygen availability: A model including a delayed exit from quiescence

Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.

The dynamics of tumour-vasculature interaction suggests low-dose, time-dense anti-angiogenic schedulings

OBJECTIVES

The administration schedule appears to be a particularly relevant factor in determining the effectiveness of an antiangiogenic drug. A better quantitative knowledge of the interactions between tumour growth and the development of its vasculature could help to design effective therapies.

MATERIAL AND METHODS

Biological and clinical inferences were derived from the analysis of a mathematical model proposed by Hahnfeldt et al. (1999), and some of its variants. In particular, we compared the effect of constant continuous infusion of an anti-angiogenic drug that induces vascular loss, to the effect of periodic, bolus-based therapy.

RESULTS AND CONCLUSIONS

The role of drug elimination rate and of dose fractionation was investigated, and we show that different schedulings, guaranteeing the same mean value of drug concentration, may exhibit very different long-term responses according to their concentration vs. time profile. For a large class of tumour growth laws, the profiles that approach the constant one are the most effective. This behaviour appears to depend on the 'cooperativity' of the tumour-vasculature interaction and on the functional form of the relationship between tumour growth and vasculature extent. Moreover, we suggest that a therapy approaching constant drug infusion might be advantageous also in the case of cytostatic anti-angiogenic drugs.

Cell resensitization after delivery of a cycle-specific anticancer drug and effect of dose splitting: Learning from tumour cords

After a single dose of an anticancer agent, changes due to cell death are expected to occur in the distribution of cells between proliferating and quiescent compartment as well as in the oxygenation and nutritional state of surviving cells. These changes are transient because tumour regrowth tends to restore the pretreatment status. The reoxygenation due to the decrease of oxygen consumption is expected to induce cell recruitment from quiescence into proliferation, and consequently to increase the sensitivity of the cell population to a successive treatment by a cycle-specific drug. In previous papers we proposed a model of the response of tumour cords (cylindrical arrangements of tumour cells growing around a blood vessel of the tumour) to single-dose treatments. The model included the motion of cells and oxygen diffusion and consumption. On the basis of that model suitably extended to better account for the action of anticancer drugs, we study the time course of the oxygenation and of the redistribution of cells between the proliferating and quiescent compartments. By means of simulations of the response to a dose delivered as two spaced equal fractions, we investigate the dependence of tumour response on the spacing between the fractions and on the main parameters of the system. A time window may be found in which the delivery of two fractions is more effective than the delivery of the undivided dose.