A mathematical model of cerebral glucose metabolism was developed to analyze the isotopic labeling of carbon atoms C4 and C3 of glutamate following an intravenous infusion of [1-¹³C]glucose. The model consists of a series of coupled metabolic pools representing glucose, glycolytic intermediates, tricarboxylic acid (TCA) cycle intermediates, glutamate, aspartate, and glutamine. Based on the rate of ¹³C isotopic labeling of glutamate C4 measured in a previous study, the TCA cycle rate in rat brain was determined to be 1.58 ± 0.41 μmol min⁻¹ g⁻¹ (mean ± SD, n = 5). Analysis of the difference between the rates of isotopic enrichment of glutamate C4 and C3 permitted the rate of exchange between α-ketoglutarate (α-KG) and glutamate to be assessed in vivo. In rat brain, the exchange rate between α-KG and glutamate is between 89 ± 35 and 126 ± 22 times faster than the TCA cycle rate (mean ± SD, n = 4). The sensitivity of the calculated value of the TCA cycle rate to other metabolic fluxes and to concentrations of glycolytic and TCA cycle intermediates was tested and found to be small.