Medicinal Chemistry Applet
Bioavailability/Area Under Curve (AUC)
Introduction
Special thanks for this exercise go to my wife Karin, who helped me with much (most) of the derivations in this discussion.
For a drug to be convenient for a patient to self-administer, it should be available in an oral form. For a drug to be effective orally, it must be readily absorbed from the gastrointestinal tract. Since the blood that absorbs nutrients passes through the liver before reaching the general circulatory system (the first-pass), the drug should also show some resistance to metabolism by the liver. The ability of a drug to successfully pass from the GI tract to the plasma is called its bioavailability, or F. To mathematically define bioavailability, the area under the curve (AUC) of a Cp vs time plot must be measured. The absolute bioavailability of a drug is formally defined by the AUC of a dose delivered by one method (e.g. oral, inhalation, transdermal, etc...) divided by the AUC of an iv bolus (Equation 1). If different size doses were used, the AUC values must be adjusted accordingly. By definition, administration by iv bolus gives 100% bioavailability.
(1)
AUC values for iv bolus Cp vs time plots are relatively straight-forward to determine under the single-compartment model. The relationship of Cp vs time is shown in Equation 2. Both Cpo and kel can be simply determined from a ln Cp vs time plot. Integration of Equation 2 with respect to time affords Equation 3. If Equation 3 is evaluated from t = 0 to t = ∞, the AUC is expressed very simply by Equation 4.
(2)
(3)
(4)
AUC values for oral Cp vs time plots can be approximated through the rectangle method of area estimation. If the required pharmacokinetic parameters are known, the AUC for an oral dose can be calculated directly. The relationship of Cp vs time for an oral dose is shown in Equation 5. Integration with respect to time gives Equation 6. Evaluation of Equation 6 from from t = 0 to t = ∞ affords Equation 7 for exact calculation of the AUC for an oral dose.
(5)
(6)
(7)
Applet
This applet plots the Cp vs time of both an oral dose and iv bolus using a single-compartment model. The AUC for both curves is calculated and printed on the graph in the legend. If Vd is entered with units of liters and the dose is in milligrams, the units of Cp will be µg/mL. Multiplication factors, if any, will be listed at the very top of the y-axis. While the time unit is explicitly listed as hours, if kel, kab, and the dosage interval are entered with minute units, the x-axis will be in minutes. Likewise, the units of AUC will be µg min mL-1.
Problem information
Cocaine is a drug that is used legally as a dental topical anesthetic, but it is generally associated with illegal recreational use. In illegal use, cocaine affords the user a euphoric sensation. Cocaine is normally administered intranasally by snorting the hydrochloride salt (traditional cocaine) or by inhalation through smoking the free base (crack).
The pharmacokinetic parameters of cocaine are shown below. Note that these values from Goodman and Gilman's disagree with values listed by other sources. The numbers below, while possibly not accurate, are sufficient for the presentation of this exercise.
- kel = 0.8 h-1
- kab = 30 h-1 (inhalation)
- kab = 2.5 h-1 (intranasal)
- Vd = 2.0 L/kg
- F = 57% (smoking)
- F = 80% (intranasal)
Problems
- Assume the desired level for a cocaine high corresponds to a Cp range of 250 to 500 ng/mL with levels above 750 ng/mL leading to restlessness and delusional thinking. Given a 100 mg dose, which administration method, inhalation or intranasal, will give a longer high?
- Of the two common administration routes of cocaine, which will give a faster rise in plasma levels?
- Mathematically, equations 5, 6, and 7 are not completely general. In what special situation will these equations give a nonsense result?
Reference
Goodman and Gilman's The Pharmacological Basis of Therapeutics, 10th ed.; Hardman, J. G., Limbird, L. E., Eds.; McGraw-Hill: New York, 2001.