To Örebro University

Purpose: To develop a general course of action for oxygen distribution calculations, in macroscopic tumours, using Graphics Processing Units (GPU) for parallel computation.

Methods: A vessel tree structure and an associated macroscopic (about 100 g) tumour were generated, using a stochastic method and Bresenham’s line algorithm. The vessel dimensions were adjusted to correspond to measured values and each vessel voxel was assigned an oxygen value, based on its distance from an incoming large vessel. Diffusion and consumption were modelled using a Green’s function approach together with Michaelis-Menten kinetics. The tumour was inscribed in a matrix of 10¹² elements. The computations were performed using a parallel method (CUDA), where the tumour was sectioned into about 18000 sub-matrices, overlapping to avoid edge effects, which were processed individually by three GPU: s. The result matrices were cropped to original size to enable concatenation.

Results: The entire process took approximately 48 hours, corresponding to 20 seconds per sub-matrix, which is more than fifty times faster when compared to the equivalent CPU calculation. Sample images illustrate the oxygen distribution of our poorly vascularised example tumour.

Conclusions: Regardless of the model accuracy and performance, the improvement in computation time using GPU calculations is highly advantageous. The preferred, parallel calculation method lowers the computation time by over 98% in this example, while maintaining full quality of performance. This is a remarkable improvement, which makes it possible to test and develop relevant models significantly faster. This computation approach does not depend on how the tumour model was created, nor is it limited to the type of model used here, but may be applied to a variety of problems, involving element-wise operations on large matrices.