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