Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia.

The tumour microenvironment is considered to be responsible for the outcome of cancer treatment and therefore it is extremely important to characterize and quantify it. Unfortunately, most of the experimental techniques available now are invasive and generally it is not known how this influences the results. Non-invasive methods on the other hand have a geometrical resolution that is not always suited for the modelling of the tumour response. Theoretical simulation of the microenvironment may be an alternative method that can provide quantitative data for accurately describing tumour tissues. This paper presents a computerized model that allows the simulation of the tumour oxygenation. The model simulates numerically the fundamental physical processes of oxygen diffusion and consumption in a two-dimensional geometry in order to study the influence of the different parameters describing the tissue geometry. The paper also presents a novel method to simulate the effects of diffusion-limited (chronic) hypoxia and perfusion-limited (acute) hypoxia. The results show that all the parameters describing tissue vasculature are important for describing tissue oxygenation. Assuming that vascular structure is described by a distribution of inter-vessel distances, both the average and the width of the distribution are needed in order to fully characterize the tissue oxygenation. Incomplete data, such as distributions measured in a non-representative region of the tissue, may not give relevant tissue oxygenation. Theoretical modelling of tumour oxygenation also allows the separation between acutely and chronically hypoxic cells, a distinction that cannot always be seen with other methods. It was observed that the fraction of acutely hypoxic cells depends not only on the fraction of collapsed blood vessels at any particular moment, but also on the distribution of vessels in space as well. All these suggest that theoretical modelling of tissue oxygenation starting from the basic principles is a robust method that can be used to quantify the tissue oxygenation and to provide input parameters for other simulations.