Numerical simulation method for the assessment of the effect of molar activity on the pharmacokinetics of radioligands in small animals

Abstract

Background: It is well recognized that the molar activity of a radioligand is an important pharmacokinetic parameter, especially in positron emission tomography (PET) of small animals. Occupation of a significant number of binding sites by radioligand molecules results in low radioligand accumulation in a target region (mass effect). Nevertheless, small-animal PET studies have often been performed without consideration of the molar activity or molar dose of radioligands. A simulation study would therefore help to assess the importance of the mass effect in small-animal PET. Here, we introduce a new compartmental model-based numerical method, which runs on commonly used spreadsheet software, to simulate the effect of molar activity or molar dose on the pharmacokinetics of radioligands.

Results: Assuming a two-tissue compartmental model, time-concentration curves of a radioligand were generated using four simulation methods and the well-known Runge-Kutta numerical method. The values were compared with theoretical values obtained under an ultra-high molar activity condition (pseudo-first-order binding kinetics), a steady-state condition and an equilibrium condition (second-order binding kinetics). For all conditions, the simulation method using the simplest calculation yielded values closest to the theoretical values and comparable with those obtained using the Runge-Kutta method. To satisfy a maximum occupancy less than 5%, simulations showed that a molar activity greater than 150 GBq/μmol is required for a model radioligand when 20 MBq is administered to a 250 g rat and when the concentration of binding sites in target regions is greater than 1.25 nM.

Conclusions: The simulation method used in this study is based on a very simple calculation and runs on widely used spreadsheet software. Therefore, simulation of radioligand pharmacokinetics using this method can be performed on a personal computer and help to assess the importance of the mass effect in small-animal PET. This simulation method also enables the generation of a model time-activity curve for the evaluation of kinetic analysis methods.

Keywords: Mass effect; Molar activity; Numerical method; Simulation.

Fig. 1

Compartmental model for the simulation of radioligand kinetics. C_p, C_f and C_b are the concentrations of the radioligand in plasma, the free radioligand in an ROI and the bound radioligand in an ROI, respectively. B_avail is the concentration of available binding sites. K₁, k₂, k₃ (= k_onB_avail) and k₄ (= k_off) are rate constants

Fig. 2

Time-activity curve (TAC) for C_p (A) and theoretical TACs for C_t in an ROI (B) used for Validation 1. Panels C and D show the relative errors of simulated values for B_max = 5 nM and B_max = 50 nM, respectively, when ∆t = 0.01 min throughout the observation period (5–60 min). Panels E and F show them when ∆t = 0.001 min for 0–5 min and ∆t = 0.01 min for 5–60 min. The relative errors simulated using Methods 1‒3 in the panels C and D almost completely overlap

Fig. 3

TAC in plasma used for Validation 2 (A), simulated TACs in an ROI generated using Method 4 (B), TAC in plasma used for Validation 3 (C) and simulated TACs in an ROI generated using Method 4 (D)

Fig. 4

TACs generated using Method 4 for B_max = 5 nM (A) and B_max = 50 nM (C) and time-courses of occupancies for B_max = 5 nM (B) and B_max = 50 nM (D), simulated using a molar activity (A_m) in the 6.25–400 GBq/μmol range

Fig. 5

Relationships between A_m and the maximum occupancy (A) and between A_m and C_t(60) (B) for B_max values in the 1.25–160 nM range

Fig. 6

The effect of k_on, k₄ and K_D on the relationship between A_m and maximum occupancy for B_max = 5 nM (A) and B_max = 50 nM (B). The same color represents the same K_D value. The same symbol represents the same k_on value. In panel B, the values for k_on = 0.0125 and k₄ = 0.0125 and for k_on = 0.025 and k₄ = 0.05 almost completely overlap, and the values for k_on = 0.05 and k₄ = 0.05 and for k_on = 0.025 and k₄ = 0.0125 almost completely overlap

Fig. 7

Curve fitting of C_t(t) data simulated using Method 4 for B_max = 5 nM (A) and B_max = 50 nM (B). Symbols show simulated C_t(t) and C_b(t) values. Some simulated data points have been omitted to enable the fitted curves to be seen clearly. Lines for C_t(t) show the fitted curves, and lines for C_b(t) show the curves generated using the kinetic parameters estimated by fitting the C_t(t) curve