A Simulation of the Effects of Diffusion on Hyperpolarized [1-¹³C]-Pyruvate Signal Evolution

Hyperpolarized [1-¹³C]-pyruvate magnetic resonance imaging is an emerging metabolic imaging method that offers unprecedented spatiotemporal resolution for monitoring tumor metabolism in vivo. To establish robust imaging biomarkers of metabolism, we must characterize phenomena that may modulate the apparent pyruvate-to-lactate conversion rate (k_PL). Here, we investigate the potential effect of diffusion on pyruvate-to-lactate conversion, as failure to account for diffusion in pharmacokinetic analysis may obscure true intracellular chemical conversion rates.

Changes in hyperpolarized pyruvate and lactate signal were calculated using a finite-difference time domain simulation of a two-dimensional tissue model. Signal evolution curves with intracellular k_PL values from 0.02 to 1.00 s^-1 were analyzed using spatially invariant one-compartment and two-compartment pharmacokinetic models. A second spatially variant simulation incorporating compartmental instantaneous mixing was fit with the same one-compartment model.

When fitting with the one-compartment model, apparent k_PL underestimated intracellular k_PL by approximately 50% at an intracellular k_PL of 0.02 s^-1. This underestimation increased for larger k_PL values. However, fitting the instantaneous mixing curves showed that diffusion accounted for only a small part of this underestimation. Fitting with the two-compartment model yielded more accurate intracellular k_PL values.

This work suggests diffusion is not a significant rate-limiting factor in pyruvate-to-lactate conversion given that our model assumptions hold true. In higher order models, diffusion effects may be accounted for by a term characterizing metabolite transport. Pharmacokinetic models used to analyze hyperpolarized pyruvate signal evolution should focus on carefully selecting the analytical model for fitting rather than accounting for diffusion effects.