Area-under-the-curve Levels (pharmacokinetics)
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In the field of
pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to describing how the body affects a specific su ...
, the area under the curve (AUC) is the
definite integral In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Int ...
of the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...
of a
drug A drug is any chemical substance other than a nutrient or an essential dietary ingredient, which, when administered to a living organism, produces a biological effect. Consumption of drugs can be via insufflation (medicine), inhalation, drug i ...
in
blood plasma Blood plasma is a light Amber (color), amber-colored liquid component of blood in which blood cells are absent, but which contains Blood protein, proteins and other constituents of whole blood in Suspension (chemistry), suspension. It makes up ...
as a function of time (this can be done using
liquid chromatography–mass spectrometry Liquid chromatography–mass spectrometry (LC–MS) is an analytical chemistry technique that combines the physical separation capabilities of liquid chromatography (or High performance liquid chromatography, HPLC) with the mass analysis capabil ...
). In practice, the drug concentration is measured at certain discrete points in time and the
trapezoidal rule In calculus, the trapezoidal rule (or trapezium rule in British English) is a technique for numerical integration, i.e., approximating the definite integral: \int_a^b f(x) \, dx. The trapezoidal rule works by approximating the region under the ...
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 In criminal justice, clearance rate is calculated by dividing the number of crimes that are "cleared", a criminal charge being laid, or convicted by the total number of crimes recorded. Various groups use clearance rates as a measure of crimes s ...
from the body.


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 Formulation is a term used in various senses in various applications, both the material and the Abstract object, abstract or wikt:formal, formal. Its fundamental meaning is the putting together of components in appropriate relationships or struc ...
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 Therapeutic drug monitoring (TDM) is a branch of clinical chemistry and clinical pharmacology that specializes in the measurement of medication levels in blood. Its main focus is on drugs with a narrow therapeutic range, i.e. drugs that can easily ...
of drugs with a narrow
therapeutic index The therapeutic index (TI; also referred to as therapeutic ratio) is a quantitative measurement of the relative safety of a drug with regard to risk of overdose. It is a comparison of the amount of a therapeutic agent that causes toxicity to the ...
. For example,
gentamicin Gentamicin is an aminoglycoside antibiotic used to treat several types of bacterial infections. This may include bone infections, endocarditis, pelvic inflammatory disease, meningitis, pneumonia, urinary tract infections, and sepsis amo ...
is an
antibiotic An antibiotic is a type of antimicrobial substance active against bacteria. It is the most important type of antibacterial agent for fighting pathogenic bacteria, bacterial infections, and antibiotic medications are widely used in the therapy ...
that can be
nephrotoxic Nephrotoxicity is toxicity in the kidneys. It is a poisonous effect of some substances, both toxic chemicals and medications, on kidney function. There are various forms, and some drugs may affect kidney function in more than one way. Nephrotoxin ...
(
kidney In humans, the kidneys are two reddish-brown bean-shaped blood-filtering organ (anatomy), organs that are a multilobar, multipapillary form of mammalian kidneys, usually without signs of external lobulation. They are located on the left and rig ...
damaging) and
ototoxic Ototoxicity is the property of being toxic to the ear (''oto-''), specifically the cochlea or auditory nerve and sometimes the vestibular system, for example, as a side effect of a drug. The effects of ototoxicity can be reversible and temporar ...
(hearing damaging); measurement of
gentamicin Gentamicin is an aminoglycoside antibiotic used to treat several types of bacterial infections. This may include bone infections, endocarditis, pelvic inflammatory disease, meningitis, pneumonia, urinary tract infections, and sepsis amo ...
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

In
pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to describing how the body affects a specific su ...
,
bioavailability In pharmacology, bioavailability is a subcategory of absorption and is the fraction (%) of an administered drug that reaches the systemic circulation. By definition, when a medication is administered intravenously, its bioavailability is 100%. H ...
generally refers to the fraction of a drug that is absorbed systemically and is thus available to produce a
biological Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, origin, evolution, and distribution of ...
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).
Bioavailability In pharmacology, bioavailability is a subcategory of absorption and is the fraction (%) of an administered drug that reaches the systemic circulation. By definition, when a medication is administered intravenously, its bioavailability is 100%. H ...
can be measured in terms of "absolute bioavailability" or "relative bioavailability".


Absolute bioavailability

''Absolute bioavailability'' refers to the
bioavailability In pharmacology, bioavailability is a subcategory of absorption and is the fraction (%) of an administered drug that reaches the systemic circulation. By definition, when a medication is administered intravenously, its bioavailability is 100%. H ...
of a drug when administered via an
extravascular Blood vessels are the tubular structures of a circulatory system that transport blood throughout many animals’ bodies. Blood vessels transport blood cells, nutrients, and oxygen to most of the tissues of a body. They also take waste and ...
dosage form (i.e. oral tablet,
suppository A suppository is a dosage form used to deliver pharmaceutical drug, medications by insertion into a body orifice (any opening in the body), where it dissolves or melts to exert local or systemic effects. There are three types of suppositories, eac ...
, subcutaneous, etc.) compared with the bioavailability of the same drug administered
intravenously Intravenous therapy (abbreviated as IV therapy) is a medical technique that administers fluids, medications and nutrients directly into a person's vein. The intravenous route of administration is commonly used for rehydration or to provide nutr ...
(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. :F_ = \left( \frac\ \right) \times \left( \frac\ \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. :F_ = \left( \frac\ \right) \times \left( \frac\ \right)


Other applications

AUC of
glucose Glucose is a sugar with the Chemical formula#Molecular formula, molecular formula , which is often abbreviated as Glc. It is overall the most abundant monosaccharide, a subcategory of carbohydrates. It is mainly made by plants and most algae d ...
concentration change following food intake is used to calculate the
glycemic index The glycemic (glycaemic) index (GI; ) is a number from 0 to 100 assigned to a food, with pure glucose arbitrarily given the value of 100, which represents the relative rise in the blood glucose level two hours after consuming that food. The GI of ...
.


Variations


Methodology

The use of
trapezoidal rule In calculus, the trapezoidal rule (or trapezium rule in British English) is a technique for numerical integration, i.e., approximating the definite integral: \int_a^b f(x) \, dx. The trapezoidal rule works by approximating the region under the ...
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 In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and ...
. Notwithstanding the above knowledge, a 1994 ''
Diabetes Care ''Diabetes Care'' is a monthly peer-reviewed medical journal published since 1978 by the American Diabetes Association. The journal covers research in the following five categories: 1) clinical care/education/nutrition/psychosocial research, 2) ep ...
'' article by Mary M. Tai entitled " A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves" purports to have independently discovered the trapezoidal rule. In Tai's response to the later
letters to the editor A letter to the editor (LTE) is a letter sent to a publication about an issue of concern to the reader. Usually, such letters are intended for publication. In many publications, letters to the editor may be sent either through conventional mai ...
s, she explained that the rule was new to her colleagues, who relied on grid-counting. Tai's paper has been discussed as a case of
scholarly peer review Scholarly peer review or academic peer review (also known as refereeing) is the process of having a draft version of a researcher's methods and findings reviewed (usually anonymously) by experts (or "peers") in the same field. Peer review i ...
failure. Despite the number of mathematically superior
numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for "numerical integr ...
schemes (such as those outlined in ), 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 In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
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.


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 Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determin ...
shows that it could cope better with
half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...
and dosing schedule variations than AUC. This is an example of a PK/PD model, which combines
pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to describing how the body affects a specific su ...
and
pharmacodynamics Pharmacodynamics (PD) is the study of the biochemistry, biochemical and physiology, physiologic effects of drugs (especially pharmaceutical drugs). The effects can include those manifested within animals (including humans), microorganisms, or comb ...
.


See also

* Cmax (pharmacology) * Cmean (pharmacology) * "Area Under Curve" of the
Receiver operating characteristic A receiver operating characteristic curve, or ROC curve, is a graph of a function, graphical plot that illustrates the performance of a binary classifier model (can be used for multi class classification as well) at varying threshold values. ROC ...


References

Pharmacokinetics Integrals {{Improve categories, date=May 2023