Elimination rate constant

Elimination rate constant is a value used in pharmacokinetics to calculate the rate at which drugs are removed from the system.

It is often abbreviated K or K_e. It is equivalent to the fraction of a substance that is removed per unit time measured at any particular instant and has units of T^-1 This can be expressed mathematically as $C_{t+dt} = C_t - C_t * K_e*dt$, where $C_t$ is the concentration of drug in the system at a given point in time, $dt$ is an infinitely small change in time, and $C_{t+dt}$ is the concentration of drug in the system after the infinitely small change in time.

It is useful in calculating the change in plasma concentration after the administration of a single dose of drug:

$C = C_{0} e^{-Kt} \,$

• C_t is concentration after time t
• C₀ is the initial concentration (t=0)
• k is the elimination rate constant

Sample values and equations

Characteristic	Description	Example value	Abbreviation(s)	Formula
Dose	Loading dose (LD), or steady state / maintenance dose (MD).	500 mg	$\textstyle D$	design parameter
τ	Dosing interval.	24 h	$\textstyle \tau$	design parameter
Volume of distribution	The apparent volume in which a drug is distributed immediately after it has been injected intravenously and equilibrated between plasma and the surrounding tissues.	6.0 L	$\textstyle V_d$	$\textstyle = D / C_0$
Concentration	Initial or steady-state concentration of drug in plasma.	83.3 µg/mL	$\textstyle C_{0} \ or \ C_{ss}$	$\textstyle = D / V_d$
Biological half-life	The time required for the concentration of the drug to reach half of its original value.	12 h	$\textstyle t_{1/2}$	$\textstyle = ln (2) / k_{e}$
Elimination rate constant	The rate at which drugs are removed from the body.	0.0578 h-1	$\textstyle k_e$	$\textstyle = ln (2) / t_{1/2} = CL / V_{d}$
Elimination rate	Rate of infusion required to balance elimination.	50 mg/h	$\textstyle k_{in}$	$\textstyle = C_{ss} \cdot CL$
Area under the curve	The integral of the concentration-time curve (after a single dose or in steady state).	1320 µg/mL×h	$\textstyle AUC_{0-\infty}$ $\textstyle AUC_{\tau,ss}$	$= \int_{0}^{\infty}C\, dt$ $= \int_{t}^{t+\tau}C\, dt$
Clearance	The volume of plasma cleared of the drug per unit time.	0.38 L/h	$\textstyle CL$	$\textstyle= V_{d} \cdot k_{e} = D/AUC$
Bioavailability	The fraction of drug that is absorbed.	0.8	$\textstyle f$	$= \frac{AUC_{po}\cdot D_{iv}}{AUC_{iv}\cdot D_{po}}$
Cmax	The peak plasma concentration of a drug after oral administration.	60.9 µg/mL	$\textstyle C_{max}$	direct measurement
tmax	Time to reach Cmax.	3.9 h	$\textstyle t_{max}$	direct measurement
Cmin	The lowest (trough) concentration that a drug reaches before the next dose is administered.	27.7 µg/mL	$\textstyle C_{min,ss}$	direct measurement
Fluctuation	Peak trough fluctuation within one dosing interval at steady state	41.8 %	$\textstyle %PTF$	$\textstyle =100 \cdot \frac{(C_{max,ss} - C_{min,ss})}{C_{av,ss}}$ where $\textstyle C_{av,ss}=\frac{AUC_{\tau,ss}}{\tau}$