Area under the curve

This page explains how to compute the area under the curve. This analysis gives you one value for the area under the entire curve, as well as the area under well-defined peaks. A separate Prism analysis integrates a curve, resulting in another curve showing cumulative area.

The area under the curve is an integrated measurement of a measurable effect or phenomenon. It is used as a cumulative measurement of drug effect in pharmacokinetics and as a means to compare peaks in chromatography.

Start from a data or results table that represents a curve. Click Analyze and choose Area under the curve from the list of XY analyses.

If your data come from chromatography or spectroscopy, Prism can break the data into separate regions and determine the highest point (peak) of each. Prism can only do this, however, if the regions are clearly defined: the signal, or graphic representation of the effect or phenomenon, must go below the baseline between regions and the peaks cannot overlap.

For each region, Prism shows the area in units of the X axis times units of the Y axis. Prism also shows each region as a fraction of the total area under all regions combined. The area is computed using the trapezoid rule. It simply connects a straight line between every set of adjacent points defining the curve, and sums up the areas beneath these areas.

Next, Prism identifies the peak of each region. This is reported as the X and Y coordinates of the highest point in the region and the two X coordinates that represent the beginning and end of the region.

Prism may identify more regions than you are interested in. In this case, go back to the Parameters dialog box and enter a larger value for the minimum width of a region and/or the minimum height of a peak.

•	Prism will not separate overlapping peaks. The program will not distinguish two adjacent peaks unless the signal descends all the way to the baseline between those two peaks. Likewise, Prism will not identify a peak within a shoulder of another peak.

•	If the signal starts (or ends) above the baseline, the first (or last) peak will be incomplete. Prism will report the area under the tails it “sees”.

Prism computes the area under the curve using the trapezoid rule, illustrated in the figure below.

In Prism, a curve is simply a series of connected XY points, with equally spaced X values. The left part of the figure above shows two of these points and the baseline as a dotted line. The area under that portion of the curve, a trapezoid, is shaded. The middle portion of the figure shows how Prism computes the area. The two triangles in the middle panel have the same area, so the area of the trapezoid on the left is the same as the area of the rectangle on the right (whose area is easier to calculate). The area, therefore, is ΔX*(Y1+Y2)/2. Prism uses this formula repeatedly for each adjacent pair of points defining the curve.