Pharmacokinetics: Area under the curve calculations

The area under the concentration vs time curve is a useful description of exposure of drug following administration. There are different ways in which AUC may be calculated, and terminology may vary from one source or text to another. This page summarises the calculations and terminology that may be encountered.

Bioanalytical data consists of a series of concentrations at various time points following dose administration.

The shape under each pair of data points forms a trapezoid. The area of a trapezoid can be calculated using a variety of rules. For example, the Linear Log Trapezoidal rule will draw a linear line between pairs of data points that are prior to C_max, and a logarithmic line between data points following C_max. The linear trapezoidal linear interpolation rule will draw a linear line between each pair of data points:

There are additional rules, and these are specified in our study plans.

The area under each of the trapezoids are summed (shaded area above) to give an AUC:

AUC_0-n = Ʃ[0.5*(t₂-t₁)* (C_p1+C_p2)]

Where a logarithmic trapezoidal rule is employed for a trapezoid, the formula is:

AUC_t1-t2 = (t₂-t₁)*((C_p1-C_p2)/ln(C_p1/C_p2 ))

• AUC_0-last describes the area under the curve up to the last quantifiable time-point (sometimes referred to as AUC_0-t)
• AUC_0-x describes the area under the curve limited to a specific time (e.g. AUC_0-12h). This time may fall between available data points, in which case interpolation is used to make the calculation
• AUC_0-inf extrapolates the area to infinite time. This requires a terminal elimination phase to be characterised. AUC_0-inf comprises AUC_0-last plus the extrapolated area AUC_t-inf which is calculated by

AUC_t-inf  = C_pt / Kel

where C_pt is the plasma concentration at the last quantifiable time point and Kel is the terminal elimination rate constant

• AUC_0-tau describes the area under the curve limited to the end of a dosing interval. The end of the dosing interval may fall between available data points, in which case interpolation is used to make the calculation
• AUC_all describes the area under the curve inclusive of any final time-point that is below the limit of quantitation