Diffusion-aware compartment model of the cellular uptake of ^{18}F-fluorodeoxyglucose

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, especially in environments such as tumors or subcutaneous tissue, where diffusion is considerably lower. 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 ^{18}F-fluorodeoxyglucose (FDG), a radionuclide, by cells grown in culture plates and found a good agreement between the measured and predicted cellular radioactivity. We identify two critical dimensionless parameters that compare the amount of FDG (i) replenished by diffusion and (ii) available in the culture medium to the amount of FDG taken up by cells. 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. The semianalytic solutions of the diffusion-aware compartment model can be easily extended to study other scenarios, such as drug transport and bubble growth dynamics.