Integral

The area under the curve is a basic application of the integral calculus.

Natural sciences

The term has in most natural sciences do not apply ( so, for example, the distance traveled is the integral of velocity over time) and is bounded on the pharmacokinetics. In this part of the field of pharmacology, the term was introduced as a " principle of corresponding surfaces " Dost.

Medical / pharmacokinetics

In medicine and pharmacology, area under the curve (AUC ) refers to the area under the concentration -time curve of a drug in the blood. It is the size by which the bioavailability of a drug is expressed. The German -language equivalent of " area under the curve " has not prevailed in the literature.

Is measured, the concentration of the drug at certain time intervals in the blood after administration. For an oral medication which results from the measurement of concentration-time curve has a typical profile, resulting from the speed of the transition of the drug into the systemic circulation and from the kinetics of leaving composed (blue area in the figure). When administered intravenously, resulting in a concentration-time curve, which is practically determined only by the precipitation kinetics ( red area).

The value of the AUC [ unit: (mass / volume) × time ] is proportional to the amount of bioavailable drug, that is, the proportion of the total administered dose (D), which comes in the bloodstream, regardless of the mode of administration. For an intravenous substance bioavailability (F) is by definition 100 %. If after oral administration of a drug, the AUC equal to intravenous route, the bioavailability is also 100 %, it is lower, the bioavailability will be less.

Calculation of parameters of a pharmacokinetic model

The example of the Bateman function (concentrations after oral administration in one compartment model )

The AUC is given by integration with respect to time.

Each linear Kompartimentsystem can also be empirically as a sum of Exponentialtermen represent.

In general this

Linear trapezoidal rule

Between the measured concentrations are linearly interpolated; The AUC to the last measured time point is approximated by summation of the areas of trapezoids.

Using the estimated elimination constants, the remaining area is calculated.

The concentration at the last time of collection is fraught usually because of the proximity to the analytical detection limit with the greatest uncertainty. An alternative method of calculating the remaining area thus used instead of the last measured concentration of its estimate.

Log - linear trapezoidal rule

Since the concentrations in the elimination follow an exponential curve, the partial surfaces are systematically overestimated after the time the maximum concentration in use of the linear trapezoidal rule. Remedy the logarithmic interpolation.

The method is however not applicable or when ( in these cases the corresponding part surface is linearly calculated). To avoid rounding errors, the method should be replaced with also in this interval by the linear method. In practice, a combination of the two methods is often used, wherein applied at increasing or constant concentration of the linear trapezoidal rule and with decreasing the log-linear.

Alternative methods

Other methods of numerical integration such as Simpson's rule, cubic splines and Lagrange polynomials have not prevailed in the pharmacokinetic practice and are not available in commercial software packages.

Psychological Assessment

The area under the curve (AUC ) parameter is used in the psychological assessment in order for example to determine the probability of certain score intervals in a psychometric test, as the effect size for ROC analysis, to determine the selectivity, the discriminative validity of an instrument, etc.