Pharmacokinetic-pharmacodynamic modelling of the hypoglycaemic effect of pulsatile administration of human insulin in rats

Abstract

The relationship between the plasma insulin (INS) concentration-time course and plasma glucose concentration-time course during and after pulsatile INS administration to rats was characterized using a pharmacokinetic-pharmacodynamic (PK-PD) model. A total INS dose of 0.5 IU/kg was intravenously injected in 2 to 20 pulses over a 2-h period. Compared with the single bolus administration, the area under the effect-time curve (AUE) increased depending on the number of pulses, and the AUEs for more than four pulses plateaued at a significantly larger value, which was similar to that after the infusion of a total of 0.5 IU/kg of INS over 2 h. No increase in plasma INS concentration occurred after pulsatile administration. Two indirect response models primarily reflecting the receptor-binding process (IR model) or glucose transporter 4 (GLUT4) translocation (GT model) were applied to describe the PK-PD relationship after single intravenous bolus administration of INS. These models could not explain the observed data after pulsatile administration. However, the IR-GT model, which was a combination of the IR and GT models, successfully explained the effects of pulsatile administration and intravenous infusion. These results indicate that the receptor-binding process and GLUT4 translocation are responsible for the change in AUE after pulsatile administration.

Figure 1

The time courses of plasma glucose concentration during and after intravenous pulsatile administration of INS (0.5 IU/kg) in rats. (a) 2 pulses, (b) 3 pulses, (c) 4 pulses, (d) 5 pulses, (e) 10 pulses, (f) 15 pulses, and (g) 20 pulses. The arrows indicate the dosing times. The points represent the mean ± S.E., n = 3–4.

Figure 2

(a) The time courses of plasma glucose concentration after a single intravenous bolus administration of INS (0.5 IU/kg) in rats. (b) The time courses of plasma glucose concentration during and after intravenous infusion administration of INS (0.5 IU/kg) for 2 h in rats. The points represent the mean ± S.E., n = 3–4. (c) The effects of the pulse rate of administration on the AUE after intravenous administration of INS (0.5 IU/kg/2 h) in rats. The data represent the mean ± S.E., n = 3–4. *p < 0.05 compared with single bolus administration by Dunnett’s test.

Figure 3

The time courses of plasma INS (a) and glucose (b, c) concentrations after a single intravenous bolus administration of INS in rats. The doses are 0.05, 0.1, 0.17, 0.25, and 0.5 IU/kg (red, yellow, green, blue, and white, respectively). The points represent the mean ± S.E., n = 3–5. The solid lines are the theoretical curves fitted to the PK model (a), IR model (b), and GT model (c), respectively.

Figure 4

Diagrammatic representation of the PK–PD model for the hypoglycaemic effect. The plasma INS concentration is described by a nonlinear two-compartment open model with Michaelis–Menten type and linear elimination kinetics and zero-order biosynthetic kinetics. Ins1 and Ins2 are the amounts of insulin in the central and peripheral compartments (ng/kg), respectively. k₁₂ and k₂₁ are the first-order rate constants (min^-1) between the central and peripheral compartments, k₁₀ is the first-order rate constant (min^-1) for the linear elimination of INS, V_max (ng/kg/min) and K_m (ng/kg) are Michaelis–Menten kinetic constants, and K_ins is the zero-order constant for the endogenous synthesis of INS. An indirect response model was used to analyse the PK-PD relationship. Glc is the plasma glucose concentration (mg/dL), S_max is the maximum effect, SC₅₀ is the theoretical signal strength producing 50% of S_max, K_Gin is the zero-order rate constant for endogenous glucose production, and k_Gout is the first-order rate constant (min^-1) for glucose elimination. IR and GT models and their combination, the IR-GT model, were used. K_d is the dissociation constant for the receptor and Φ is the ratio of receptor occupancy by INS. G4A is the hypothetical amount of inactive GLUT4 in the intercellular pool, G4B is the hypothetical amount of active GLUT4 on the cell surface, and α is the transit coefficient between the plasma INS concentration and stimulation for translocation. T_AB is the time is takes for G4A to translocate to the cell surface and T_BA is the time over which cells take up glucose from plasma.

Figure 5

Comparison of the IR model-simulated plasma glucose concentration–time courses and the observed data during and after intravenous pulsatile administration of INS (0.5 IU/kg) in rats. (a) 2 pulses, (b) 3 pulses, (c) 5 pulses, (d) 10 pulses. The solid lines are the predicted curves from the IR model. The points represent the observed data and the mean ± S.E., n = 3–4.

Figure 6

Comparison of the GT model-simulated plasma glucose concentration–time courses and the observed data during and after intravenous pulsatile administration of INS (0.5 IU/kg) in rats. (a) 2 pulses, (b) 3 pulses, (c) 5 pulses, (d) 10 pulses. The solid lines are the predicted curves from the GT model. The points represent the observed data and the mean ± S.E., n = 3–4.

Figure 7

Comparison of the IR-GT model-simulated plasma glucose concentration–time courses and the observed data during and after intravenous pulsatile administration of INS (0.5 IU/kg) in rats. (a) 2 pulses, (b) 3 pulses, (c) 5 pulses, (d) 10 pulses. The solid lines are the predicted curves from the IR-GT model. The points represent the observed data and the mean ± S.E., n = 3–4.

Figure 8

Comparison of the IR-GT model-simulated plasma INS (a) and glucose (b) concentration–time courses and the observed data during and after intravenous infusion administration of INS (0.5 IU/kg/2 h) in rats. The solid and dashed lines are the predicted curves from the IR-GT model and a typical indirect response model without the IR and GT models, respectively. The points represent the observed data and the mean ± S.E., n = 3–4.