Compartmental modeling of ¹⁸F-fluorodeoxyglucose uptake in cancer cells with diffusion considerations

Compartment models are widely used in fields such as epidemiology and biomedicine to describe the exchange of uniformly distributed materials between interconnected compartments. However, their application in biological fluids is limited by the assumption of infinitely large diffusivity. To address this, we develop a diffusion-aware compartment model that maintains the simplicity of traditional compartment models while offering greater accuracy. We conducted experiments on the uptake of ¹⁸F-fluorodeoxyglucose (FDG), a radioactive analog of glucose used for medical imaging, by adherent cells in vitro and found a good agreement between the measured and predicted cellular radioactivity. We demonstrate that the diffusion-aware compartment model reduces to the three-compartment model when FDG diffusion is fast relative to cellular uptake, and it further simplifies to the two-compartment model when sufficient FDG is available in the culture medium. This work establishes a framework to determine the kinetic rate parameters that reflect the biological activity of the cellular transporters and enzymes responsible for the uptake and metabolism of FDG. The semi-analytic solutions of the diffusion-aware compartment model can be easily extended to study other scenarios, such as drug transport and bubble growth dynamics.