🟪 Extrapolation and Interpolation Methods

Various extrapolation and interpolation methods are used during the calculation of some PK parameters. The mathematical expressions for these methods are shown below.

Linear interpolation

If a concentration value must be interpolated between two observed concentration values using linear interpolation, the following equation will be used:

$$C_{interpolated}=C1+|\frac{T_{interpolated}-T1}{T2-T1}|\ast (C2-C1)$$

Logarithimic interpolation

If a concentration value must be interpolated between two observed concentration values using logarithmic interpolation, the following equation will be used:

$$C_{interpolated}=e^{[ln(C1)+|\frac{T_{interpolated}-T1}{T2-T1}|\ast [ln(C2)-ln(C1)]]}$$

Logarithmic extrapolation for Ctau

If a value of Ctau is not observed in the dataset, it can be estimated by extrapolating from the last observed concentration using the following equation:

$$Ctau=Clast\ast e^{-kel\ast (T_{Tau}-Tlast)}$$

Logarithim extrapolation for C0

Backward extrapolation to estimate the concentration at time 0 is performed using the first 2 measured concentrations following dose administration. The first step is to perform a linear regression and estimating the slope ($m$) and intercept ($b$) using the following equation:

$$y=m\ast [ln(C)]+b$$

Then the value for C0 is calculated using the following equation:

$$C0=e^b$$