ELIMINATION RATE CONSTANT

Ø  For a drug that follows one compartment kinetics and administered as rapid IV injection, the decline in plasma drug concentration is only due to elimination of drug from the body, the phase being called as elimination phase.

Ø  Elimination phase can be characterized by three parameters

o   Elimination rate constant,

o   Elimination half-life

o   Clearance.

Integration of equation 3 yields

ln X = ln X_o - K_E t                                                                                ------ 4

Where, X_o = amount of drug at time t = o i.e. the initial amount of drug injected.

Equation 4 can also be written in exponential form as:

X = X_o e  ^{-  K}_E^t----- 5

It shows that disposition of drug that follows one compartment kinetics is monoexponential.

Transforming equation 4 into common logarithms (log base 10), we get:

log X = log X_o -  K_E t                                                                          ------ 6

                            2.303

Since it is difficult to determine directly the amount of drug in the body X, advantage is taken of the fact that a constant relationship exist between drug concentration in plasma C (easily measurable) and X;

Thus, X = V_d C                                                                                ------- 7

Where, Vd = proportionality constant popularly known as apparent volume of distribution.

It is a pharmacokinetic parameter that permits the use of plasma drug concentration in place of amount of drug in the body.

The equation 6 therefore becomes:

      log C = log C_o -  K_E t                                                 ------ 8

                                 2.303 

Ø  Equation 8 is that of a straight line and indicates that a semi logarithmic plot of log C versus t will be linear with Y intercept log C_o.

Ø  The elimination rate constant is directly obtained from slope of the line (figure 5 (b)). It has units of min^-1.

Thus a linear plot is easier to handle mathematically than a curve which in this case will be obtained from a plot of C versus t on regular (Cartesian) graph paper Figure.

Ø  Thus, C_o, K_E (and t_1/2) can be readily obtained from log C versus t graph.

Ø  The elimination or removal of the drug from the body is the sum of urinary excretion, metabolism, biliary excretion, pulmonary excretion and other mechanisms involved there in.

Ø  Thus, K_E is an additive property of rate constants for each of these processes and better called as overall elimination rate constant.

K_E = K_e + K_m + K_b + K_P + ....                                                                ------ 9

Ø  The fraction of drug eliminated by a particular route can be evaluated if the number of rate constants involved and their values are known. For example, if a drug is eliminated by urinary excretion and metabolism only, then, the fraction of drug excreted unchanged in urine F_e and fraction of drug metabolized F_m can be given as:

Fe = Ke / KE------- 10a

Fm = Km / Ke  ------ 10b

ELIMINATION HALF-LIFE

Half-life is related to elimination rate constant by the following equation:

                       t_½ = 0.693/Ke------ 11

Most of the drugs are eliminated within 10 half lives.

Ø  Half-life is a secondary parameter that depends upon the primary

parameters clearance and apparent volume of distribution as

follows:

                        t½ = 0.693                                                  ………..11(a)

                                   Cl_T