Measurement of benzodiazepine receptor number and affinity in humans using tracer kinetic modeling, positron emission tomography, and [¹¹C]flumazenil

Kinetic methods were used to obtain regional estimates of benzodiazepine receptor concentration (B_max) and equilibrium dissociation constant (K_d) from high and low specific activity (SA) [¹¹C]flumazenil ([¹¹C] Ro 15-1788) positron emission tomography studies of five normal volunteers. The high and low SA data were simultaneously fit to linear and nonlinear three-compartment models, respectively. An additional inhibition study (pretreatment with 0.15 mg/kg of flumazenil) was performed on one of the volunteers, which resulted in an average gray matter K₁/k₂ estimate of 0.68 ± 0.08 ml/ml (linear three-compartment model, nine brain regions). The free fraction of flumazenil in plasma (f₁) was determined for each study (high SA f₁: 0.50 ± 0.03; low SA f₁: 0.48 ± 0.05). The free fraction in brain (f₂) was calculated using the inhibition K₁/k₂ ratio and each volunteer's mean f₁ value (f₂ across volunteers = 0.72 ± 0.03 ml/ml). Three methods (Methods I-III) were examined. Method I determined five kinetic parameters simultaneously [K₁, k₂, K₃ ( = k_onf₂B_max), k₄, and K_onf₂/SA] with no a priori constraints. An average k_on value of 0.030 ± 0.003 nM^-1 min^-1 was estimated for receptor-rich regions using Method I. In Methods II and III, the k_onf₂/SA parameter was specifically constrained using the Method I value of k_on and the volunteer's values of f₂ and low SA (Ci/μmol) Four parameters were determined simultaneously using Method II. In Method III. K₁/k₂ was fixed to the inhibition value and only three parameters were estimated. Method I provided the most variable results and convergence problems for regions with low receptor binding. Method II provided results that were less variable but very similar to the Method I results, without convergence problems. However, the K₁/k₂ ratios obtained by Method II ranged from 1.07 in the occipital cortex to 0.61 in the thalamus. Fixing the K₁/k₂ ratio in Method III provided a method that was physiologically consistent with the fixed value of /, and resulted in parameters with considerably lower variability. The average B_max values obtained using Method III were 100 ± 25 nM in the occipital cortex, 64 ± 18 nM in the cerebellum, and 38 ± 5.5 nM in the thalamus; the average K_d was 8.9 ± 1.0 nM (five brain regions).