We propose a simple mathematical model and a practical approach for evaluating the flux constant and the absolute value of flux in the citric acid cycle in perfused organs by 13C-NMR and 1H-NMR spectroscopy. We demonstrate that 13C-NMR glutamate spectra are independent of the relative sizes of the mitochondrial and cytosolic compartments and the exchange rates of glutamates, unless there is a difference in 13C chemical shifts of glutamate carbons between the two compartments. Wistar rat hearts (five beating and four KCl-arrested hearts) were aerobically perfused with 100% enriched [2-(13)C]acetate and the kinetics of glutamate carbon labeling from perchloric acid extracts were studied at various perfusion times. Under our experimental conditions, the citric acid cycle flux constant, which represents the fraction of glutamate in exchange with the citric acid cycle per unit time, is about 0.350 +/- 0.003 min(-1) for beating hearts and 0.0741 +/- 0.004 min(-1) for KCl-arrested hearts. The absolute values of the citric acid flux for beating hearts and for KCl-arrested hearts are 1.06 +/- 0.06 micromol x min(-1) x mg(-1) and 0.21 +/- 0.02 micromol x min(-1) x g(-1), respectively. The fraction of unlabeled acetate determined from the proton signal of the methyl group is small and essentially the same in beating and arrested hearts (7.4 +/- 1.7% and 8.8 +/- 2.1%, respectively). Thus, the large difference in the Glu C2/C4 between beating and arrested hearts is not due to the important contribution from anaplerotic sources in arrested hearts but simply to a substantial difference in citric acid cycle fluxes. Our model fits the experimental data well, indicating a fast exchange between 2-oxoglutarate and glutamate in the mitochondria of rat hearts. Analysis of the flux constant, calculated from the half-time of glutamate C4 labeling given in the literature, allows for a comparison of the citric acid flux for various working conditions in different animal species.