how to find area under a curve

In the field of pharmacokinetics, the area under the curve (AUC) is the definite integral of a curve that describes the variation of a drug concentration in blood plasma as a function of time (this can be done using liquid chromatography–mass spectrometry^[1]). In practice, the drug concentration is measured at certain discrete points in time and the trapezoidal rule is used to estimate AUC.

Interpretation and usefulness of AUC values [edit]

The AUC (from zero to infinity) represents the total drug exposure across time. AUC is a useful metric when trying to determine whether two formulations of the same dose (for example a capsule and a tablet) result in equal amounts of tissue or plasma exposure. Another use is in the therapeutic drug monitoring of drugs with a narrow therapeutic index. For example, gentamicin is an antibiotic that can be nephrotoxic (kidney damaging) and ototoxic (hearing damaging); measurement of gentamicin through concentrations in a patient's plasma and calculation of the AUC is used to guide the dosage of this drug.

AUC becomes useful for knowing the average concentration over a time interval, AUC/t. Also, AUC is referenced when talking about elimination. The amount eliminated by the body (mass) = clearance (volume/time) * AUC (mass*time/volume).

AUC and bioavailability [edit]

In pharmacokinetics, bioavailability generally refers to the fraction of drug that is absorbed systemically and is thus available to produce a biological effect. This is often measured by quantifying the "AUC". In order to determine the respective AUCs, the serum concentration vs. time plots are typically gathered using C-14 labeled drugs and AMS (accelerated mass spectrometry).^[2]

Bioavailability can be measured in terms of "absolute bioavailability" or "relative bioavailability".

Absolute bioavailability [edit]

Absolute bioavailablity refers to the bioavailability of drug when administered via a non-intravenous (non-IV) dosage form (i.e. oral tablet, suppository, subcutaneous, etc.) compared with the bioavailability of the same drug administered intravenously (IV). This is done by comparing the AUC of the non-intravenous dosage form with the AUC for the drug administered intravenously. This fraction is normalized by multiplying by each dosage form's respective dose.^[3]

F_{abs}=\left({\frac {AUC_{non-IV}}{AUC_{IV}}}\ \right)\times \left({\frac {Dose_{IV}}{Dose_{non-IV}}}\ \right)

Relative bioavailability [edit]

Relative bioavailability compares the bioavailability between two different dosage forms. Again, the relative AUCs are used to make this comparison and relative doses are used to normalize the calculation.

F_{rel}=\left({\frac {AUC_{dosageA}}{AUC_{dosageB}}}\ \right)\times \left({\frac {Dose_{B}}{Dose_{A}}}\ \right)

References [edit]

^ Maurer, Hans H. (2005). "Multi-analyte procedures for screening for and quantification of drugs in blood, plasma, or serum by liquid chromatography-single stage or tandem mass spectrometry (LC-MS or LC-MS/MS) relevant to clinical and forensic toxicology". Clinical biochemistry. Elsevier BV. 38 (4): 310–318. doi:10.1016/j.clinbiochem.2005.01.014. ISSN 0009-9120. PMID 15766732.
^ Lappin, Graham; Rowland, Malcolm; Garner, R Colin (2006). [1] "The use of isotopes in the determination of absolute bioavailability of drugs in humans". Expert Opinion on Drug Metabolism & Toxicology 2 (3): 419–27.
^ Srinivasan, V. Srini (2001). [2] "Bioavailability of Nutrients: A Practical Approach to In Vitro Demonstration of the Availability of Nutrients in Multivitamin-Mineral Combination Products". The Journal of Nutrition 131 (4 Suppl): 1349S–1350S.