Elimination rate constant

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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

,

where is the blood plasma concentration of drug in the system at a given point in time , is an infinitely small change in time, and 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 via IV bolus injection:

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

Derivation[edit]

In first-order (linear) kinetics, the plasma concentration of a drug at a given time t after single dose administration via IV bolus injection is given by;

where:

  • C0 is the initial concentration (at t=0)
  • t1/2 is the half-life time of the drug, which is the time needed for the plasma drug concentration to drop to its half

Therefore, the amount of drug present in the body at time t is;

where Vd is the apparent volume of distribution

Then, the amount eliminated from the body after time t is;

Then, the rate of elimination at time t is given by the derivative of this function with respect to t;

And since is fraction of the drug that is removed per unit time measured at any particular instant, then if we divide the rate of elimination by the amount of drug in the body at time t, we get;

Sample values and equations[edit]

Characteristic Description Example value Symbol Formula
Dose Amount of drug administered. 500 mg Design parameter
Dosing interval Time between drug dose administrations. 24 h Design parameter
Cmax The peak plasma concentration of a drug after administration. 60.9 mg/L Direct measurement
tmax Time to reach Cmax. 3.9 h Direct measurement
Cmin The lowest (trough) concentration that a drug reaches before the next dose is administered. 27.7 mg/L 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
Concentration Amount of drug in a given volume of plasma. 83.3 mg/L
Elimination half-life The time required for the concentration of the drug to reach half of its original value. 12 h
Elimination rate constant The rate at which a drug is removed from the body. 0.0578 h−1
Infusion rate Rate of infusion required to balance elimination. 50 mg/h
Area under the curve The integral of the concentration-time curve (after a single dose or in steady state). 1,320 mg/L·h
Clearance The volume of plasma cleared of the drug per unit time. 0.38 L/h
Bioavailability The systemically available fraction of a drug. 0.8
Fluctuation Peak trough fluctuation within one dosing interval at steady state 41.8 %
where
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References[edit]