Oxygen consumption dynamics in steady-state tumour models

Oxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the underlying physics limits the resolution to the millimetre domain, whereas oxygen tension varies over a micrometre scale. If the distribution of oxygen in the tumour micro-environment can be accurately estimated, then the effect of potential dose escalation to these hypoxic regions could be better modelled, allowing more realistic simulation of biologically adaptive treatments. Reaction-diffusion models are commonly used for modelling oxygen dynamics, with a variety of functional forms assumed for the dependence of oxygen consumption rate (OCR) on cellular status and local oxygen availability. In this work, we examine reaction-diffusion models of oxygen consumption in spherically and cylindrically symmetric geometries. We consider two different descriptions of oxygen consumption: one in which the rate of consumption is constant and one in which it varies with oxygen tension in a hyperbolic manner. In each case, we derive analytic approximations to the steady-state oxygen distribution, which are shown to closely match the numerical solutions of the equations and accurately predict the extent to which oxygen can diffuse. The derived expressions relate the limit to which oxygen can diffuse into a tissue to the OCR of that tissue. We also demonstrate that differences between these functional forms are likely to be negligible within the range of literature estimates of the hyperbolic oxygen constant, suggesting that the constant consumption rate approximation suffices for modelling oxygen dynamics for most values of OCR. These approximations also allow the rapid identification of situations where hyperbolic consumption forms can result in significant differences from constant consumption rate models, and so can reduce the computational workload associated with numerical solutions, by estimating both the oxygen diffusion distances and resultant oxygen profile. Such analysis may be useful for parameter fitting in large imaging datasets and histological sections, and allows easy quantification of projected differences between functional forms of OCR

Molecular imaging of hypoxia with radiolabelled agents

Tissue hypoxia results from an inadequate supply of oxygen (O2) that compromises biological functions. Structural and functional abnormalities of the tumour vasculature together with altered diffusion conditions inside the tumour seem to be the main causes of tumour hypoxia. Evidence from experimental and clinical studies points to a role for tumour hypoxia in tumour propagation, resistance to therapy and malignant progression. This has led to the development of assays for the detection of hypoxia in patients in order to predict outcome and identify patients with a worse prognosis and/or patients that would benefit from appropriate treatments. A variety of invasive and non-invasive approaches have been developed to measure tumour oxygenation including oxygen-sensitive electrodes and hypoxia marker techniques using various labels that can be detected by different methods such as positron emission tomography (PET), single photon emission computed tomography (SPECT), magnetic resonance imaging (MRI), autoradiography and immunohistochemistry. This review aims to give a detailed overview of non-invasive molecular imaging modalities with radiolabelled PET and SPECT tracers that are available to measure tumour hypoxia