Kinetic analysis of drug-target interactions with PET for characterization of pharmacological hysteresis

Abstract

In vivo characterization of the brain pharmacokinetics of novel compounds provides important information for drug development decisions involving dose selection and the determination of administration regimes. In this context, the compound-target affinity is the key parameter to be estimated. However, if compounds exhibit a dynamic lag between plasma and target bound concentrations leading to pharmacological hysteresis, care needs to be taken to ensure the appropriate modeling approach is used so that the system is characterized correctly and that the resultant estimates of affinity are correct. This work focuses on characterizing different pharmacokinetic models that relate the plasma concentration to positron emission tomography outcomes measurements (e.g., volume of distribution and target occupancy) and their performance in estimating the true in vivo affinity. Measured (histamine H3 receptor antagonist--GSK189254) and simulated data sets enabled the investigation of different modeling approaches. An indirect pharmacokinetic-receptor occupancy model was identified as a suitable model for the calculation of affinity when a compound exhibits pharmacological hysteresis.

Figure 1

Direct model applied to three different brain regions. Open circles are the estimated V_T values. Solid line is the Direct PK-RO model fit. V_ND and were constrained across the three regions.

Figure 2

(A) Time course of unlabeled GSK189254 in plasma. (B) Direct and Indirect PK-RO model fits. Open circles are the measured H3 time occupancy curve (TOC) after administration of 1.5 μg/kg unlabeled GSK189254. Receptor occupancy at each time point was obtained from occupancy plots. Dashed and solid lines are the Direct (equation 3) and Indirect (equation 6) model fits respectively.

Figure 3

(A) SSE (sum of square errors) between the Direct PK-RO model fit and the simulated time occupancy curve (TOC). Brighter regions represent a larger error while darker areas represent smaller errors. (B) Error between the true K_d and the Direct PK-RO estimate of K_d expressed as the absolute value in percentage. (C) Four examples of Direct (dashed) and Indirect (solid) model fits corresponding to the points depicted in (A) and (B). The upper left plot represents simulated data using the parameters estimated for GSK189254 from the in vivo experiments. Plots i, ii and iii present clear examples of pharmacological hysterisis.

Figure 4

Effect of the study duration (T_d) on the accuracy of direct (dashed line) and indirect (solid line) estimates K_d for three different values of k_off; (A) 0.001 min⁻¹, (B) 0.005 min⁻¹, and (C) 0.01 min⁻¹.