Oxygen Distributions—Evaluation of Computational Methods, Using a Stochastic Model for Large Tumour Vasculature, to Elucidate the Importance of Considering a Complete Vascular Network

Purpose: To 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. Methods: A 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. Results: The 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