Forking lemma

Characteristic	Description	Example value	Symbol	Formula
Dose	Amount of drug administered.	500 mg	$D$	Design parameter
Dosing interval	Time between drug dose administrations.	24 h	$\tau$	Design parameter
Cmax	The peak plasma concentration of a drug after administration.	60.9 mg/L	$C_{\text{max}}$	Direct measurement
tmax	Time to reach Cmax.	3.9 h	$t_{\text{max}}$	Direct measurement
Cmin	The lowest (trough) concentration that a drug reaches before the next dose is administered.	27.7 mg/L	$C_{\text{min},\text{ss}}$	Direct measurement
Volume of distribution	The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration to drug amount in the body).	6.0 L	$V_{\text{d}}$	$=\frac{D}{C_0}$
Concentration	Amount of drug in a given volume of plasma.	83.3 mg/L	$C_0,C_{\text{ss}}$	$=\frac{D}{V_{\text{d}}}$
Elimination half-life	The time required for the concentration of the drug to reach half of its original value.	12 h	$t_{\frac{1}{2}}$	$=\frac{ln(2)}{k_{\text{e}}}$
Elimination rate constant	The rate at which a drug is removed from the body.	0.0578 h−1	$k_{\text{e}}$	$=\frac{ln(2)}{t_{\frac{1}{2}}}=\frac{CL}{V_{\text{d}}}$
Infusion rate	Rate of infusion required to balance elimination.	50 mg/h	$k_{\text{in}}$	$=C_{\text{ss}}\cdot CL$
Area under the curve	The integral of the concentration-time curve (after a single dose or in steady state).	1,320 mg/L·h	$AU{C}_{0-\mathrm{\infty }}$	$=\underset{0}{\overset{\mathrm{\infty }}{\int }}C\mathrm{d}t$
			$AU{C}_{\tau ,\text{ss}}$	$=\underset{t}{\overset{t+\tau }{\int }}C\mathrm{d}t$
Clearance	The volume of plasma cleared of the drug per unit time.	0.38 L/h	$CL$	$=V_{\text{d}}\cdot k_{\text{e}}=\frac{D}{AUC}$
Bioavailability	The systemically available fraction of a drug.	0.8	$f$	$=\frac{AU{C}_{\text{po}}\cdot D_{\text{iv}}}{AU{C}_{\text{iv}}\cdot D_{\text{po}}}$
Fluctuation	Peak trough fluctuation within one dosing interval at steady state	41.8 %	$\%PTF$	$=\frac{C_{\text{max},\text{ss}}-C_{\text{min},\text{ss}}}{C_{\text{av},\text{ss}}}\cdot 100$ where $C_{\text{av},\text{ss}}=\frac{1}{\tau }AU{C}_{\tau ,\text{ss}}$