To improve the measurements of glucose metabolism in the human brain, we imposed biologic constraints on the deoxyglucose model with and without dephosphorylation of FDG-6-phosphate (the k4*- and k3*-models). The constraints included constant transport and phosphorylation ratios (tau and phi) and a common partition volume (K1/k2) for tracer [18F]FDG and glucose. In the presence of significant dephosphorylation, the k3*-model yielded time-dependent estimates of the phosphorylation coefficient (k3*), while the K4*-model yielded time-independent estimates. However, the two models yielded practically identical measurements of regional cerebral glucose metabolism in PET studies of six normal volunteers when the phosphorylation affinity ratio (the k3*/k3 ratio of FDG and glucose) and tracer circulation time were 0.30 and 20 min for the k3*-model and 0.33 and 45 min for the k4*-model.