Drug Disappearance Curve

There are two ways that a drug can disappear:

1.) ZERO ORDER KINETICS-- after a drug rises to its maximum, it just falls on a

straight line; eliminated at a constant rate. (see handout p. 2)

C(t): plasma drug concentration @ any time (t) after the drug is administered

C(t) = C₀ – k₀t C₀: peak concentration immediately after the drug is delivered

k₀: zero-order rate constant for elimination

t: time after drug administration @ t = 0

-Zero order kinetics occurs only rarely, usually when the elimination mechanisms

are saturated. A prime example of this is with alcohol.

2.) FIRST ORDER KINETICS-- a constant fraction (%) of the concentration is eliminated for a unit time. At each instant the rate of elimination is not constant, but is proportional to the concentration at that instant in time. The more drug present, the faster it goes out; the less drug present, the slower it goes out. So the rate is proportional to the concentration… this leads to exponential decay of the drug concentration. IMPORTANT: the rate is not constant, but always changing (decreasing) with time.

-First order kinetics occurs with most drugs

Equation for First Order Kinetics (p.2 handout, eq. 5-1 Brody)

C₀: peak concentration immediately after the drug is adminstered

e: the base of the natural logarithm (e = 2.718…)

C(t) = C₀e^-kt e^x: ‘exponential function’ sometimes written ‘exp x’

k: first-order rate constant for elimination

t: time after drug administration @ t = 0

Most important parameter associated with the drug disappearance curve is the half–life (t_½). Every drug has its own t_½, it must be given from the drug insert. It depends on the molecular structure and the mechanisms for elimination. So if we have an enzyme that will really crank on that molecule, it will be small. t_½ can vary from person to person, also can vary within a person depending on various conditions (those enzymes might be occupied with something else, ie. metabolizing food or another drug).

Another parameter of the drug disappearance curve is the pharmacologic half-life. That’s the time for half of the pharmacological response, not the plasma concentration. Whats the difference? If the pharmacological mechanism is used by binding to a receptor, the two are really the same because as the drug disappears from the blood the receptors are unbound and the response disappears. But there are other cases where a drug produces a long term effect. Some drugs will produce some covalent bonding, or may permanently damage some enzymes leaving long term effects (ie. LSD flashbacks).

The method of administration effects the maximum value, but not t ½ .

t_½ is independent of initial concentration, so if you change the initial concentration you’d still have the same pathway. (see handout p. 4, item 4).

-whatever concentration you start with, it will go to half of that value in time t_½ , it doesn’t matter what concentration you start with

The concentration at any time will be decreased by half in time t_½. (see handout p. 4, item 5)

The first order rate constant k is related to t_½ as follows (handout p. 4, item 6)

-see p. 4 for derivation

k = 0.69

t_½

PROBLEMS (handout p. 5)

• see handout for examples

• always keep track of time units; when t_½ units are in hours the answer will also be in hours, when t ½ units are in minutes the answer will be in minutes

• ln (e^x) = x

Question: If a dose were doubled, would the amount of time that the drug is active be doubled as well?

Answer: NO! This is the essence of first order kinetics… if the dose is doubled, the effect will last one half-life more.

** if you had zero-order kinetics however, doubling the dose would double the drug’s effects.

Category: Pharmacology Notes