Pharmacokinetic/Pharmacodynamic Model

• Problem Description

  • This example is from an actual pre-clinical drug development modeling project. A combined Pharmacokinetic/Pharmacodynamic (PK/PD) compartment-based model was constructed, consisting of 111 state variables and 436 parameters.

  • Plasma concentrations of the PD target were calculated in the model, following test compound input doses of 200, 500, 1000, 2000, 5000, and 10000 mg.

  • The “data” shown in this example represents the resulting plasma concentrations from the differential equation system, upon addition of the specified dose of the test compound.

• Model Descriptions

  1. Differential Equation Sytem Model

  • A compartment model consisting of 111 state variables and 436 parameters was constructed, which included both the PK effects as well as the target PD effects.

  • Both linear and nonlinear relationships were included in the compartment model.

  2. Nonlinear response function model
  • Response function variables are optimized to find the set that yields response curves to best fit the results from the compartment model.

• Results

  • Resulting curves from the nonlinear response function model are compared to “data,” which are the results of the differential equation system. Model curves are labeled M1, M2, M3, M4, M5, and M6, corresponding to the 200, 500, 1000, 2000, 5000, and 10000 mg input doses. Prediction curves P1 and P2 are also included, corresponding to nonlinear response function predictions using input doses of 1500 and 7500 mg. Resulting plots are shown here.

• Conclusions

  • The nonlinear response function shows an accurate representation of the large-scale nonlinear differential equation system, over the entire range of input test compound dosing.

  • Predictions of the 1500 and 7500 mg doses seem to be in agreement with expected time-course profiles given the results of the nonlinear differential equation system.

  • The nonlinear response function model represents a greatly reduced model compared to the nonlinear differential equation system model, and 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 PK/PD modeling as compared to the traditional compartment modeling/ODE system appraoch.