Michaelis-Menten Constraints Improved Cerebral Glucose Metabolism and Regional Lumped Constant Measurements with [18F]Fluorodeoxyglucose

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Abstract
In the three-compartment model of transfer of native glucose and [18F]fluorodeoxyglucose (FDG) into brain, both transport across the blood–brain barrier and phosphorylation by hexokinase can be described by the Michaelis-Menten equation. This permits the use of fixed transport (τ = K*1/ K1) and phosphorylation (φ = k*3/ k3) ratios and a common partition volume ( Ve = K1/ k2) for tracer and glucose. By substituting transfer constants of FDG for those of glucose, using τ and φ, the lumped constant was determined directly by positron tomography. The same constraints also eliminated k*2 and k*3 from the model, thus limiting the parameters to K* [equivalent to K*1 k*3/( k*2 + k*3)], K*1, and the cerebral vascular volume ( Vo). In six healthy elderly men (aged 61 ± 5 years), time-activity records of cerebral cortical regions were analyzed with τ = 1.1 and φ = 0.3. The results were compared with those of the conventional FDG method. At 20 min, the goodness of fit by the new equation was as good as that of the conventional method at 45 min. The estimates obtained by the constrained method had stable coefficients of variation. After 20 min, regional differences between the estimates were independent of time, although we observed steady decreases of K* and ( k*3). The decrease strongly suggested dephosphorylation of FDG-6-phosphate, particularly after 20 min. All estimates of variables with the constrained method were more accurate than those of the conventional method, including the cerebral glucose metabolic rate itself, as well as physiologically more meaningful, particularly with respect to k*2 and k*3.