Pharmacodynamic Analysis of Recombinant Human Erythropoietin Effect on Reticulocyte Production Rate and Age Distribution in Healthy Subjects

Abstract

Objective: To evaluate the effect of recombinant human erythropoietin (rHuEPO) on the reticulocyte production rate and age distribution in healthy subjects.

Methods: Extensive pharmacokinetic and pharmacodynamic data collected from 88 subjects who received a single subcutaneous dose of rHuEPO (dose range 20–160 kIU) were analysed. Four nonlinear mixed-effects models were evaluated to describe the time course of the percentage of reticulocytes and their age distribution in relation to rHuEPO pharmacokinetics. Model A accounted for stimulation of the production of progenitor cells in bone marrow, and model B implemented shortening of differentiation and maturation times of early progenitors in bone marrow. Model C was the combination of models A and B, and model D was the combination of model A with an increase in the maturation times of the circulating reticulocytes. Model evaluation was performed using goodness-of-fit plots, a nonparametric bootstrap and a posterior predictive check.

Results: Model D was selected as the best model, and evidenced accurate and precise estimation of model parameters and prediction of the time course of the percentage of reticulocytes. At baseline, the estimated circulating reticulocyte maturation time was 2.6 days, whereas the lifespan of the precursors in the bone marrow was about 5 days. The rHuEPO potency for the stimulatory effect (7.61 IU/L) was higher than that for the increase in reticulocyte maturation times (56.3 IU/L). There was a significant 1- to 2-day lag time in the reticulocyte response. The effect of rHuEPO on the reticulocyte age distribution consisted of a transient increase in the reticulocyte maturation time from baseline up to 6–7 days, occurring 1 day after administration. The dose-dependent amplitude of the changes in the age distribution lasted for 12–14 days. The model-predicted peak increase in the reticulocyte release rate ranged from 140% to 160% of the baseline value and was maximal on days 7–8 following rHuEPO administration.

Conclusions: A semiphysiological model quantifying the effect of rHuEPO on the reticulocyte production rate and age distribution was developed. The validated model predicts that rHuEPO increases the reticulocyte production rate and modifies the reticulocyte age distribution in a dose-dependent manner.

Appendix

Mean Residence Time for One-Compartment Model with Time-Dependent First-Order Elimination Rate

Consider a one-compartment model where drug amount A is eliminated at the first-order rate k(t), which can depend on time (equation 35):

Let t₀ be an arbitrary time and the amount of drug at this time is A(t₀). For an incrementally small Δt, the number of drug particles comprising A(t₀) that exit the compartment between times t and t + Δt is k(t) · (A(t)/m) · Δt, where m is the mass of a single drug particle. In addition, let t_out denote the time at which a particle exits the compartment. Then t_out can be considered as a random variable, and the probability that a particle will leave the compartment between times t and t + Δt can be calculated as equation 36:

Consequently, the probability density function for the t_out distribution is represented by equation 37: and the expected tout [E(tout)] can be expressed as follows (equation 38):

The time during which a particle of A(t₀) resides in the compartment is the time elapsing between t₀ and t_out. Hence the MRT is (equation 39):

To simplify the integral in equation 38, multiply both sides of equation 35 by t and integrate from t₀ to infinity (equation 40):

Integration by parts implies that (equation 41):

Combining equations 38 and 41 results in equation 42:

Note that introducing a new variable X(t, t₀) = A(t)/A(t₀) [equation 43]: where X(t, t₀) is a solution to equation 44: with the initial condition (equation 45):