Pharmacokinetic Model and Analysis

• Problem Description

  • Pharmacokinetic model and analysis of the dipeptidyl peptidase-4 inhibitor sitagliptin

  • Plasma concentrations were measured following single oral doses of 25, 50, 100, 200, and 400 mg of sitagliptin\(^1\)

• Model Descriptions

  • For each model, parameters or response function variables are optimized to the observed data for the doses 25, 50, 100, 200, and 400 mg.
  1. Two-Compartment model assuming first-order (linear) kinetics
  • Model parameters \((k_1, k_2, k_e)\) are optimized to find the set \((k_1, k_2, k_e)_{opt}\) that yields response curves to best fit the observed data for the doses 25, 50, 100, 200, and 400 mg.
  2. Linear response function model

  • Assume a linear response function with two terms, of the form \(\quad C_p(t) \: = \: dose \left [ c_1 \: e^{\lambda_1} \: + \: c_2 \: e^{\lambda_2} \right ]\)

  • Response function variables \((c_1, \lambda_1, c_2, \lambda_2)\) are optimized to find the set \((c_1, \lambda_1, c_2, \lambda_2)_{opt}\) that yields response curves to best fit the observed data for the doses 25, 50, 100, 200, and 400 mg.

  3. Nonlinear response function model
  • Response function variables are optimized to find the set that yields response curves to best fit the observed data for the doses 25, 50, 100, 200, and 400 mg.
  4. Prediction
  • Two-compartment model and nonlinear response function models are constructed using the 25, 50, 100, and 200 mg dose data. This model is used to predict the response curve for the 400 mg dose.
  5. Prediction using logged data
  • Two-compartment model and nonlinear response function models are constructed using the 25, 50, 100, and 200 mg dose logged data. This model is used to predict the response curve for the 400 mg dose.

• Results

  • For each model, the resulting \(C_p(t)\) curves are generated for each of the input doses

  • Resulting \(C_p(t)\) curves are compared to observed data\(^1\). Model curves are labeled M1, M2, M3, M4, and M5.

  1. Resulting plots for the two-compartment/linear response function model are shown here. These plots for the two-compartment model are the same as those for the linear response function model since the optimized two-compartment model yields the same results as the optimized linear response function model.

  2. Resulting plots for the nonlinear response function model are shown here.

  3. Resulting plots for the 400 mg dose prediction using the two-compartment model are shown here.

  4. Resulting plots for the 400 mg dose prediction using the nonlinear response function model are shown here.

  5. Resulting plots for the 400 mg dose prediction using logged data and the two-compartment model are shown here.

  6. Resulting plots for the 400 mg dose prediction using logged data and the nonlinear response function model are shown here.

• Conclusions

  • Fits to data for the nonlinear response function provide the most accurate fits.

  • Fits to data for the two-compartment/linear reponse function model are not as accurate as the nonlinear response function across the entire range of doses.

  • Extraploation from 200 mg dose to 400 mg dose is improved using logged data, where the nonlinear response function model provides a more accurate prediction that the two-compartment/linear response function model.

  • The nonlinear response function model requires no additional fitting of parameters beyond those which are contained in the response function.

  • The nonlinear response function model represents a more universal formulation for use in pharmacokinetic modeling as compared to the traditional compartment modeling/ODE system appraoch.

1. Bergman A, Mistry GC, Luo WL, et al. Dose-proportionality of a final market image sitagliptin formulation, an oral dipeptidyl peptidase-4 inhibitor, in healthy volunteers. Biopharmaceutics & Drug Disposition 2007; 28: 307-313.