Predicting the influence of microvascular structure on tumour response to radiotherapy

Objective: The purpose of this study is to investigate how theoretical predictions of tumour response to radiotherapy depend on the morphology and spatial representation of the microvascular network. Methods: A hybrid multiscale model, that couples a cellular automaton model of tumour growth with a model for oxygen transport from blood vessels, is used to predict the viable fraction of cells following one week of simulated radiotherapy. Both artificial and biologically derived three-dimensional vessel networks of well vascularized tumours are considered and predictions compared with two-dimensional descriptions. Results: For literature-derived values of the cellular oxygen consumption rate there is little difference in predicted viable fraction when three-dimensional network representations of biological or artificial vessel networks are employed. Different two-dimensional representations are shown to either over- or under-estimate viable fractions relative to the three-dimensional cases, with predictions based on point-wise descriptions shown to have greater sensitivity to vessel network morphology. Conclusion: The predicted radiotherapy response is relatively insensitive to the morphology of the microvessel network when threedimensional representations are adopted, however sensitivity is greater in certain two-dimensional representations. Significance: By using realistic three-dimensional vessel network geometries this study shows that real and artificial network descriptions and assumptions of spatially uniform oxygen distributions lead to similar radiotherapy response predictions in relatively small tissue volumes. This suggests that either a more detailed description of oxygen transport in the microvasculature is required or that the oxygen enhancement ratio used in the well known linearquadratic radiotherapy response model is relatively insensitive to microvascular structure.