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. © 2016 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.