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

Abstract

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.

The effects of hypoxia on the theoretical modelling of tumour control probability

“…The modelled tissues had a 2D geometry that may be regarded as a simplification of the real 3D structure of tissues. However, the results of the simulations may be considered representative for the oxygenation in real tissues as has been shown in Daşu et al [18]. Low values (40 mmHg) were assumed for oxygen tensions in the blood vessels as in tumours they often originate from the venous side of the vasculature [3].…”

“…Tumour tissues with different vascular structures were modelled according to the method described in Daşu et al [18]. Thus, a Monte Carlo technique was used to generate tissues with biologically relevant distributions of intervessel distances centred on 50, 100 and 150 mm, in agreement to the experimental study of Konerding et al [19].…”

Treatment modelling: The influence of micro-environmental conditions

“…Tumour microenvironment was simulated using the method described in Daşu et al [18]. Thus, a Monte Carlo method was used to generate tissues with blood vessels placed according to ranges of experimentally measured distributions of intervascular distances.…”

“…The oxygenation of the tissue was calculated numerically from the differential equation describing the oxygen transport, the result being an oxygenation map which reflects the limited diffusion of oxygen into the tissue and hence the diffusion limited or chronic hypoxia demonstrated experimentally by Thomlinson and Gray [19] and later by Tannock [20]. The temporal component of hypoxia, the perfusion limited or acute hypoxia, suggested by Brown [21] to occur due to the transient collapsing of the tumour blood vessels as the result of increased interstitial pressure or temporary vessel occlusion due to ''rigidised'' blood cells in the acid environment was simulated according to the method described in Daşu et al [18] by the random closure of some blood vessels in the simulated tissue. Several patterns of acute hypoxia were modelled for a treatment simulation as the time-scale for this type of hypoxia ranges from a few minutes to hours and therefore it is not likely to have the same oxygenation pattern through consequent radiation fractions.…”

The Six Rs of Head and Neck Cancer Radiotherapy

“…The two main forms of hypoxia associated with them are known as chronic (diffusion-limited) or acute (perfusion-limited) hypoxia. Thus, chronic hypoxia will occur when the distance from the cells to the nearer capillaries is close to exceeding the maximum oxygen diffusion distance, which under normal rates of oxygen consumption by the cells is expected to be in the order of 100-150 μm as shown by the early studies of Thomlinson and Gray [50] and confirmed later by experimental and modelling studies [51][52][53]. Acute hypoxia arises near the blood vessels temporary occluded, and, by its nature, has a transient character, unless the blood vessels remain blocked a long time period, depriving the cells of oxygen beyond the limit for survival.…”