title: Estimating oxygen distribution from vasculature in three-dimensional tumour tissue.
abstract: Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution.
authors.affiliation: Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK davidrobert.grimes@oncology.ox.ac.uk.
authors.forename: David Robert
authors.identifier: http://orcid.org/0000-0003-3140-3278
authors.initials: DR
authors.lastname: Grimes
authors.affiliation: Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK.
authors.forename: Pavitra
authors.initials: P
authors.lastname: Kannan
authors.affiliation: Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK.
authors.forename: Daniel R
authors.initials: DR
authors.lastname: Warren
authors.affiliation: Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK.
authors.forename: Bostjan
authors.initials: B
authors.lastname: Markelc
authors.affiliation: Engineering Sciences, University of Oxford, Oxford OX1 3PJ, UK.
authors.forename: Russell
authors.initials: R
authors.lastname: Bates
authors.affiliation: Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK.
authors.forename: Ruth
authors.initials: R
authors.lastname: Muschel
authors.affiliation: Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK.
authors.forename: Mike
authors.initials: M
authors.lastname: Partridge
mesh_terms: D000818:Animals; D021621:Imaging, Three-Dimensional; D008955:Models, Cardiovascular; D009374:Neoplasms, Experimental / Q000098:blood supply / Q000000981:diagnostic imaging / Q000378:metabolism; D009389:Neovascularization, Pathologic / Q000000981:diagnostic imaging / Q000378:metabolism; D010100:Oxygen / Q000378:metabolism*; D049268:Positron-Emission Tomography; D051381:Rats
chemical_list: D010100:Oxygen
keywords: cancer; hypoxia; modelling; oxygen; radiotherapy