A model to simulate tumour oxygenation and dynamic [18F]-Fmiso PET data.

The microenvironment of a tumour, in particular its hypoxic status, is a crucial factor in its response to radiotherapy. Conventional techniques for measuring hypoxia are either invasive or follow surgical intervention, and thus not ideal. Positron emission tomography allows the non-invasive pre-surgical assessment of oxygen status by measuring the spatiotemporal distribution of hypoxia-specific tracers. However, the relationship between levels of uptake and the underlying oxygen tension are yet to be elucidated. Furthermore, it is not fully understood how changes in the underlying physiology affect the appearance of uptake. This paper presents a modular simulation of the tumour microenvironment, underpinned by a probability density function (PDF) to model the vasculature. The model is solved numerically, to simulate both the steady-state oxygenation of a tumour and the spatiotemporal distribution of the hypoxia-specific tracer, [18F]-fluoromisonidazole (Fmiso), in a 2D environment. The results show that using a PDF to represent the vasculature effectively captures the 'hypoxic island' appearance of oxygen-deficient tissues seen ex vivo. Simulated tissue activity curves (TACs) demonstrate the general two-stage trend of empirical data, with an initial perfusion-dominated uptake, followed by hypoxia-specific binding. In well-perfused tissue, activity follows plasma levels in early stages, with binding of Fmiso only becoming apparent at a later stage. In structurally hypoxic tissue, a more gradual initial increase in activity is observed, followed by the same accumulation slope. We demonstrate the utility of theoretical modelling of tracer uptake, by quantifying the changes in TAC structure that arise as a result of altering key physiological characteristics. For example, by decreasing either the proximity of tissue to the vasculature, or the effective diffusion coefficient of Fmiso, we can observe a shift of TAC structure from corresponding to well-perfused to avascular regions, despite wholly different underlying causes.