Area under the curve (pharmacokinetics)

In the field of pharmacokinetics, the area under the curve (AUC) is the definite integral of the concentration of a drug 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. In pharmacology, the area under the plot of plasma concentration of a drug versus time after dosage (called “area under the curve” or AUC) gives insight into the extent of exposure to a drug and its clearance rate from the body.^[2]

Interpretation and usefulness of AUC values

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.^[3]

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).^{[citation needed][4]}

AUC and bioavailability

In pharmacokinetics, bioavailability generally refers to the fraction of a 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 labelled drugs and AMS (accelerated mass spectrometry).^[5]

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

Absolute bioavailability

Absolute bioavailability refers to the bioavailability of a drug when administered via an extravascular 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.^[6]

${\displaystyle F_{\text{abs}}=\left({\frac {{\text{AUC}}_{\text{non-IV}}}{{\text{AUC}}_{\text{ IV}}}}\ \right)\times \left({\frac {{\text{Dose}}_{\text{ IV}}}{{\text{Dose}}_{\text{non-IV}}}}\ \right)}$

Relative bioavailability

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.

${\displaystyle F_{\text{rel}}=\left({\frac {{\text{AUC}}_{\text{dosageA}}}{{\text{AUC}}_{\text{dosageB}}}}\ \right)\times \left({\frac {{\text{Dose}}_{\text{B}}}{{\text{Dose}}_{\text{A}}}}\ \right)}$

Other applications

AUC of glucose concentration change following food intake is used to calculate the glycemic index.^[7]

Variations

Methodology

The use of trapezoidal rule in AUC calculation was known in literature by no later than 1975, in J.G. Wagner's Fundamentals of Clinical Pharmacokinetics. A 1977 article compares the "classical" trapezoidal method to a number of methods that take into account the typical shape of the concentration plot, caused by first-order kinetics.^[8]

Notwithstanding the above knowledge, a 1994 Diabetes Care article by Mary M. Tai purports to have independently discovered the trapezoidal rule.^[9] In Tai's response to the later letters to the editors, she explained that the rule was new to her colleagues, who relied on grid-counting.^[10] Tai's paper has been discussed as a case of scholarly peer review failure.^[11]

Despite the number of mathematically superior numerical integration schemes (such as those outlined in Wagner & Ayres 1977), the trapezoidal rule remains the convention for AUC calculation. Later focus on improving the accuracy of AUC calculation shifted from improving the method to improving the sampling scheme. An example is a 2019 algorithm known as OTTER: it performs a fit onto sum of exponentials curve for the input data but only uses it to suggest better sample times by finding more highly sloped periods.^[12]

Extensions

The area under the effect curve (AUEC) is an integral of the effect of a drug over time, estimated as a previously-established function of concentration. It was proposed to be used instead of AUC in animal-to-human dose translation, as computer simulation shows that it could cope better with half-life and dosing schedule variations than AUC. This is an example of a PK/PD model, which combines pharmacokinetics and pharmacodynamics.^[13]

See also

• C_max (pharmacology)
• C_mean (pharmacology)
• "Area Under Curve" of the Receiver operating characteristic

References

1. 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. 38 (4). Elsevier BV: 310–318. doi:10.1016/j.clinbiochem.2005.01.014. ISSN 0009-9120. PMID 15766732.
2. Scheff, J. D.; Almon, R. R.; Dubois, D. C.; Jusko, W. J.; Androulakis, I. P. (2011). "Assessment of Pharmacologic Area Under the Curve When Baselines are Variable". Pharmaceutical Research. 28 (5): 1081–1089. doi:10.1007/s11095-010-0363-8. PMC 3152796. PMID 21234658.
3. Hodiamont, Caspar J.; van den Broek, Annemieke K.; de Vroom, Suzanne L.; Prins, Jan M.; Mathôt, Ron A. A.; van Hest, Reinier M. (2022). "Clinical Pharmacokinetics of Gentamicin in Various Patient Populations and Consequences for Optimal Dosing for Gram-Negative Infections: An Updated Review". Clinical Pharmacokinetics. 61 (8): 1075–1094. doi:10.1007/s40262-022-01143-0. ISSN 0312-5963. PMC 9349143. PMID 35754071.
4. "Useful Pharmacokinetic Equations" (PDF). University of Florida.
5. Lappin, Graham; Rowland, Malcolm; Garner, R Colin (2006). "The use of isotopes in the determination of absolute bioavailability of drugs in humans". Expert Opinion on Drug Metabolism & Toxicology. 2 (3): 419–427. doi:10.1517/17425255.2.3.419. PMID 16863443. S2CID 2383402.
6. Srinivasan, V. Srini (2001). "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.
7. Brouns F, Bjorck I, Frayn KN, et al. (June 2005). "Glycaemic index methodology". Nutr Res Rev. 18 (1): 145–71. doi:10.1079/NRR2005100. PMID 19079901.
8. Wagner, JG; Ayres, JW (October 1977). "Bioavailability Assessment: Methods to Estimate Total Area (AUC_0–∞) and Total Amount Excreted (A_e^∞) and Importance of Blood and Urine Sampling Scheme with Application to Digoxin". Journal of Pharmacokinetics and Biopharmaceutics. 5 (5): 533–57. doi:10.1007/BF01061733. hdl:2027.42/45073. PMID 925886. S2CID 24170738.
9. Tai, MM (February 1994). "A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves". Diabetes Care. 17 (2): 152–4. doi:10.2337/diacare.17.2.152. PMID 8137688. S2CID 42761923.
10. Monaco, JH; Anderson, RL (October 1994). "Tai's formula is the trapezoidal rule". Diabetes Care. 17 (10): 1224–5, author reply 1225-7. doi:10.2337/diacare.17.10.1224. PMID 7677819. S2CID 27930861.
11. Knapp, Alex (2011). "Apparently, Calculus Was Invented In 1994". Forbes.
12. Hughes, JH; Upton, RN; Reuter, SE; Phelps, MA; Foster, DJR (November 2019). "Optimising time samples for determining area under the curve of pharmacokinetic data using non-compartmental analysis". The Journal of Pharmacy and Pharmacology. 71 (11): 1635–1644. doi:10.1111/jphp.13154. PMID 31412422.
13. Chen, C; Lavezzi, SM; Iavarone, L (August 2022). "The area under the effect curve as an efficacy determinant for anti-infectives". CPT: Pharmacometrics & Systems Pharmacology. 11 (8): 1029–1044. doi:10.1002/psp4.12811. PMC 9381909. PMID 35638366.