Modeling non-linear kinetics of hyperpolarized [1-(13)C] pyruvate in the crystalloid-perfused rat heart

Hyperpolarized (13)C MR measurements have the potential to display non-linear kinetics. We have developed an approach to describe possible non-first-order kinetics of hyperpolarized [1-(13)C] pyruvate employing a system of differential equations that agrees with the principle of conservation of mass of the hyperpolarized signal. Simultaneous fitting to a second-order model for conversion of [1-(13)C] pyruvate to bicarbonate, lactate and alanine was well described in the isolated rat heart perfused with Krebs buffer containing glucose as sole energy substrate, or glucose supplemented with pyruvate. Second-order modeling yielded significantly improved fits of pyruvate-bicarbonate kinetics compared with the more traditionally used first-order model and suggested time-dependent decreases in pyruvate-bicarbonate flux. Second-order modeling gave time-dependent changes in forward and reverse reaction kinetics of pyruvate-lactate exchange and pyruvate-alanine exchange in both groups of hearts during the infusion of pyruvate; however, the fits were not significantly improved with respect to a traditional first-order model. The mechanism giving rise to second-order pyruvate dehydrogenase (PDH) kinetics was explored experimentally using surface fluorescence measurements of nicotinamide adenine dinucleotide reduced form (NADH) performed under the same conditions, demonstrating a significant increase of NADH during pyruvate infusion. This suggests a simultaneous depletion of available mitochondrial NAD(+) (the cofactor for PDH), consistent with the non-linear nature of the kinetics. NADH levels returned to baseline following cessation of the pyruvate infusion, suggesting this to be a transient effect.