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.

Image-based modelling of skeletal muscle oxygenation

“…Complexity of experiments and lack of available resources are most likely the reasons for this. The method employed by Grimes et al [145] stains for hypoxic regions in tumour tissue; however, for healthy soft tissue this can pose a problem as no hypoxic regions should in theory be present. Instead, a tissue stain to mark oxygenation could be used, allowing validation of the results from computational modelling by use of gold standard light microscopy.…”

“…The only mathematical model presented in this section, validated against experimental data, is the rsif.royalsocietypublishing.org J. R. Soc. Interface 14: 20160992 tumour oxygenation model presented by Grimes et al [145]. Complexity of experiments and lack of available resources are most likely the reasons for this.…”

“…Interface 14: 20160992 realistic predictions of concentration distributions (here of the drug; in our case oxygen) the computation would ideally be performed on experimentally derived images of tumour vasculature, and the results would need to be validated against experimental data. In a novel approach, Grimes et al [145] investigated tumour oxygenation by deriving an oxygenation kernel model, allowing straight vessel segments to diffuse oxygen in a spherical fashion as an array of discrete point sources. Two spherical, scalable kernels were computed; one for a well-perfused tumour network and one for a poorly perfused one, i.e.…”

Visualization and quantification of tumour biology for personalized radiotherapy

“…Small studies testing temporal stability of hypoxia in NSCLC have so far found inconclusive results. Some studies have observed stable hypoxia [39,40], whereas others have reported a decrease in hypoxia [26,41], or a mix of stable and dynamic hypoxia [42]. Lin et al [43] showed in head and neck cancer that when there is a spatial shift, dose painting of the initial subvolume still results in improved equivalent uniform dose on a later scan.…”

“…To acquire knowledge about vascular permeability, the DCE-CT scans should include images acquired around two to ten minutes after injection that will show this transition from the vascular to the extravascular space and back [38,39]. …”