Parameters

Basic parameters

Cmax

Maximum concentration from dose time to dose time + tau (if tau > 0). Firs observation used.

Tmax

Time at maximum concentration from dose time to dose time + tau (if tau > 0). Firs observation used.

Cdose

Concentration at dose time.

AUC / AUMC

Area under Curve / Area under the Moment Curve.

\[AUC = \sum_{n=1}^N AUC_{n}\]

\[AUMC = \sum_{n=1}^N AUMC_{n}\]

Where AUCn/AUMCn- partial AUC/AUMC.

Linear trapezoidal rule

\[AUC\mid_{t_1}^{t_2} = \delta t \times \frac{C_1 + C_2}{2}\]

\[AUMC\mid_{t_1}^{t_2} = \delta t \times \frac{t_1 \times C_1 + t_2 \times C_2}{2}\]

Logarithmic trapezoidal rule

\[AUC\mid_{t_1}^{t_2} = \delta t \times \frac{ C_2 - C_1}{ln(C_2/C_1)}\]

\[AUMC\mid_{t_1}^{t_2} = \delta t \times \frac{t_2 \times C_2 - t_1 \times C_1}{ln(C_2/C_1)} - \delta t^2 \times \frac{ C_2 - C_1}{ln(C_2/C_1)^2}\]

Interpolation

Linear interpolation rule

\[C_x = C_1 + \frac{(t_x-t_1)\times(C_2 - C_1)}{t_2 - t_1}\]

Logarithmic interpolation rule

\[C_x = exp\left(ln(C_1) + \frac{(t_x-t_1)\times(ln(C_2) - ln(C_1))}{t_2 - t_1}\right)\]

AUClast / AUMClast

Area from dose time to last observed concentration (>0).

AUCall / AUMCall

All values used to calculate AUC/AUMC.

𝝺z - elimination constant

Linear regression used for logarithmic transformed concentration data.

Half-Life; T1/2

\[HL = ln(2) / \lambda_z\]

If Kel calculated

AUCinf

\[AUC_\infty = AUC_{last} + \frac{C_{last}}{\lambda_z}\]

AUMCinf

\[AUMC_\infty = AUMC_{last} + \frac{t_{last}\times C_{last}}{\lambda_z} + \frac{C_{last}}{\lambda_z^2}\]

AUCpct

\[AUCpct = (AUC_\infty - AUC_{last}) / AUC_\infty * 100.0 \%\]

If Dose used

Clearance

Cllast

\[CL_{last} = Dose / AUC_{last}\]

Clinf

\[CL_\infty = Dose / AUC_\infty\]

Steady-state parameters (If Tau used)

AUCtau / AUMCtau

Area from dose time to dose time + tau.

Accumulation index

\[Accind = \frac{1}{1 - exp(-\lambda_z \tau)}\]

MRTtauinf

\[MRT_{\tau\inf} = (AUMC_\tau + \tau * (AUC_\infty - AUC_\tau)) / AUC_\tau\]