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 Kinetica - Indirect Response III

  Indirect Response Model III – Stimulation of Production Process for 2 Doses
Download the Indirect Response – Stimulation of Dissipation Process for 2 doses in Kinetica 

Model description
Indirect response (IDR) Model III describes the time pattern of the mediator or response variable (R) that is affected by a drug, which stimulates the production process (Kin), normally controlling endogenous levels of R [1]. The response is produced at the zero-order rate and lost at the first-order rate (Kout) as shown in Fig.1.
Basic Schema for IDR model III
Figure 1. Basic scheme for indirect response Model III.


The equation describing IDR Model III is as follows:
dR              Smax . Cp
── = Kin .(1+ ──────── ) - Kout . R
dt                SC50 + Cp

where:

  • R – drug response
  • Kin – zero-order rate constant for production of drug response
  • kout – first-order rate constant for loss of drug response
  • Cp – plasma drug concentration
  • Smax – maximum stimulatory factor attributed to drug (Smax>0)
  • SC50 – drug concentration producing 50% of maximum stimulation

In the absence of drug the response stays at the baseline value (R0):

R0   Kin
= ──
  Kout

Estimation of model parameters
It is assumed that drug plasma concentrations (Cp) for two doses are known prior to pharmacodynamic data analysis. The drug kinetics is incorporated into the model via explicit equation for Cp e.g. for the monoexponential kinetics:

Cp = D  
──  .e-Kel.t
V  

where:

  • D = dose
  • V = volume of distribution
  • Kel = elimination rate constant

or via differential equation:

dCp    -Kel.Cp
── =
dt  

The entire set of pharmacokinetic parameters (e.g.,D1, D2, V, Kel) must be known and available for an input. Pharmacodynamic parameters for IDR Model III are: R0, Smax, SC50, Kout, and Kin.

  • R0: If the baseline response is known, then R0 must be fixed at the baseline value, otherwise R0 can be estimated.
  • Smax : The maximum stimulation value must be higher than 0
  • Kout and SC50: These parameters are recommended to be fitted
  • Kin: The rate of production of response is calculated from the baseline equation: Kin=Kout.R0


The initial values of the pharmacodynamic parameters can be derived from the observed response data [2].

Equation 3 for monoexponential kinetics and Equation 1 for IDR Model III were used for simulations. The values of D1=100 mg, D2 =10 000 mg, V=1l and kel= 0.3 h-1 were used to simulate the plasma concentration-time profile, whereas R0=100 units, Kout=0.1 h-1, SC50=1.0 mg/l and Smax=1.2 were used to simulate the response versus time profile. The 10% noise was introduced to the simulated data of drug response. Kinetica was utilized to estimate pharmacodynamic parameters by fitting Eq. 1 to the noisy data. The model parameters are listed in Table 1 and Fig. 2 shows the predicted response vs. time curve.
 

Parameter True Value Estimated Value C.V. (%)
Kout (h-1) 0.10 0.09 7.74
SC50 mg/l 1.00 1.77 29.61
Smax 1.20 1.33 6.16

Table 1. Pharmacodynamic parameters for IDR Model III estimated with Kinetica (R0=100 units, D1=100 mg, D2=10 000 mg, V=1l, and kel=0.3 h-1).

IDR Model III fitting for 2 doses


Figure 2. IDR Model III fitting for two doses: D1= 100 mg (•) and D2 = 10 000 mg (0) to the simulated data with 10% random noise for a drug with monoexponential pharmacokinetics.


References

  1. Dayneka NL, Garg V, JuskoWJ. Comparison of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 1993;21:457-478.
  2. Sharma A, Jusko WJ. Characterization of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 1996;24:611-635.