Elimination rate constant

The elimination rate constant K is a value used in pharmacokinetics to describe the rate at which a drug is removed from the system.[1]

It is often abbreviated K or Ke. 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 with the differential equation

C_{t+dt} = C_t - C_t \cdot K \cdot dt,

where C_t is the blood plasma concentration of drug in the system at a given point in time t, 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.

The solution of this differential equation is useful in calculating the concentration after the administration of a single dose of drug:

C_t = C_{0}\cdot e^{-Kt} \,

Sample values and equations

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 AUC_{0 - \infty} = \int_{0}^{\infty}C\, \operatorname{d}t
AUC_{\tau, \text{ss}} = \int_{t}^{t + \tau}C\, \operatorname{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{AUC_\text{po} \cdot D_\text{iv}}{AUC_\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}AUC_{\tau, \text{ss}}

References

  1. ↑ Svensén CH; Brauer KP; Hahn RG et al. (September 2004). "Elimination rate constant describing clearance of infused fluid from plasma is independent of large infusion volumes of 0.9% saline in sheep". Anesthesiology 101 (3): 666–674. doi:10.1097/00000542-200409000-00015. PMID 15329591.