Kinetics of Drug Absorption

Most routes of drug administration depend upon the drug dissolving into body fluids and diffusing through one or more membranes to enter the blood plasma.  Therefore, all routes of administration, except intravenous, are classified as extravascular routes.  Drug absorption is defined as the appearance of the drug in plasma.

Oral administration is the most common extravascular route.  Administration of this form, either by solution or by rapidly dissolving solids (i.e. pills) often obey first-order kinetics.  Absorption is characterized by evaluating the absorption rate constant k_a from plasma concentration versus time data graphs.

A kinetic model of first-order absorption is written:

where

D_G = drug at the absorption site (gut)

D_B = drug in the body

D_E = eliminated drug

k_a = first-order absorption rate constant

k_el = overall elimination rate constant

The differential equations describing the rates of change of the three components D_G, D_B and D_E are:

(1)     dD_G/dt = -k_aD_G

(2)     dD_B/dt = k_aD_G - k_elD_B

(3)     dD_E/dt = +k_elD_B

Integrating Eq.1 we get

D_G =D_G^Oexp(-k_at)

where D_G^O is the initial amount of drug presented to the absorbing region of the gut.  The D_G^O is equal to the dosage administered if the absorption is complete.

By substitution, we obtain

dD_B/dt = +k_aD_G^Oexp(-k_at)-k_elD_B

Using Laplace transforms, our equation becomes

where [(D_G^Ok_a)/(k_a-k_el)] represents the amount of drug in the body through extravascular administration.  The two exponential terms represent elimination[exp(-k_elt)] and absorption[exp(-k_at)] of the drug.  By dividing both sides by V_d which is the apparent volume of distribution, we obtain the concentration of the drug within plasma versus time.

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B.7b