Abstract
PurposeTo develop a general model that utilises a stochastic method to generate a vessel tree based on experimental data, and an associated irregular, macroscopic tumour. These will be used to evaluate two different methods for computing oxygen distribution.MethodsA vessel tree structure, and an associated tumour of 127 cm3, were generated, using a stochastic method and Bresenham’s line algorithm to develop trees on two different scales and fusing them together. The vessel dimensions were adjusted through convolution and thresholding and each vessel voxel was assigned an oxygen value. Diffusion and consumption were modelled using a Green’s function approach together with Michaelis-Menten kinetics. The computations were performed using a combined tree method (CTM) and an individual tree method (ITM). Five tumour sub-sections were compared, to evaluate the methods.ResultsThe oxygen distributions of the same tissue samples, using different methods of computation, were considerably less similar (root mean square deviation, RMSD≈0.02) than the distributions of different samples using CTM (0.001< RMSD<0.01). The deviations of ITM from CTM increase with lower oxygen values, resulting in ITM severely underestimating the level of hypoxia in the tumour. Kolmogorov Smirnov (KS) tests showed that millimetre-scale samples may not represent the whole.ConclusionsThe stochastic model managed to capture the heterogeneous nature of hypoxic fractions and, even though the simplified computation did not considerably alter the oxygen distribution, it leads to an evident underestimation of tumour hypoxia, and thereby radioresistance. For a trustworthy computation of tumour oxygenation, the interaction between adjacent microvessel trees must not be neglected, why evaluation should be made using high resolution and the CTM, applied to the entire tumour.
Highlights
A sufficient tumour vasculature is crucial for tumour cell division and for tumour growth
The deviations of individual tree method (ITM) from combined tree method (CTM) increase with lower oxygen values, resulting in ITM severely underestimating the level of hypoxia in the tumour
Kolmogorov Smirnov (KS) tests showed that millimetre-scale samples may not represent the whole
Summary
A sufficient tumour vasculature is crucial for tumour cell division and for tumour growth. The tumour is able to interfere with its vasculature, through angiogenesis, in order to increase the oxygen delivery to the cells as the tumour volume expands and the distance between blood vessels increases. Depending on the geometry and size of a tumour and the structure of its vasculature, the development of the tumour as well as the feasibility of successful treatment may differ substantially.[1,2] knowledge of the vascular architecture, of tumours in general and of individual tumours in particular, is valuable as it may be a determining factor to whether the tumour is eradicated or not. Many attempts have been made to map and model the behaviour of tumour vasculature. Recent examples include single cell based 2D models,[4] 3D models with constant vessel oxygen level,[5] numerical models using greens functions[6] and models including heterogeneity of vascular oxygen content.[7,8]
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