Abstract
Hypoxia occurs when oxygen levels within a tissue drop below normal physiological levels. In tumours, hypoxia is associated with poor prognosis, increased likelihood of metastasis and resistance to therapy. Imaging techniques, for example, positron emission tomography, are increasingly used in the monitoring of tumour hypoxia and have the potential to help in the planning of radiotherapy. For this application, improved understanding of the link between image contrast and quantitative underlying oxygen distribution would be very useful. Mathematical models of tissue hypoxia and image formation can help understand this. Hypoxia is caused by an imbalance between vascular supply and tissue demand. While much work has been dedicated to the quantitative description of tumour vascular networks, consideration of tumour oxygen consumption is largely neglected. Oxidative respiration in standard two-dimensional cell culture has been widely studied. However, two-dimensional culture fails to capture the complexities of growing three-dimensional tissue which could impact on the oxygen usage. In this study, we build on previous descriptions of oxygen consumption and diffusion in three-dimensional tumour spheroids and present a method for estimating rates of oxygen consumption from spheroids, validated using stained spheroid sections. Methods for estimating the local partial pressure of oxygen, the diffusion limit and the extents of the necrotic core, hypoxic region and proliferating rim are also derived. These are validated using experimental data from DLD1 spheroids at different stages of growth. A relatively constant experimentally derived diffusion limit of 232 ± 22 μm and an O2 consumption rate of 7.29 ± 1.4 × 10(-7) m(3) kg(-1) s(-1) for the spheroids studied was measured, in agreement with laboratory measurements.