## 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 bodyD

_{E}= eliminated drugk

_{a }= first-order absorption rate constantk

_{el }= overall elimination rate constantThe differential equations describing the rates of change of the three components D

_{G}, D_{B}and D_{E}are:(1) dD_{G}/dt = -k_{a}D_{G}(2) dD

_{B}/dt = k_{a}D_{G}- k_{el}D_{B}(3) dD

_{E}/dt = +k_{el}D_{B}## Integrating Eq.1 we get

## D

_{G}=D_{G}^{O}exp(-k_{a}t)## 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_{a}D_{G}^{O}exp(-k_{a}t)-k_{el}D_{B}## Using Laplace transforms, our equation becomes

## where [(D

_{G}^{O}k_{a})/(k_{a}-k_{el})] represents the amount of drug in the body through extravascular administration. The two exponential terms represent elimination[exp(-k_{el}t)] and absorption[exp(-k_{a}t)] 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.

B.7b