## Integration Problems

Oct 01, 2009
Volume 27, Issue 10, pg 892–899

 John W. Dolan
I recently received an e-mail inquiry from a reader, along with the two chromatograms shown in Figure 1. Although not explicitly stated in the e-mail, it was clear that a debate was raging about how to best integrate this group of peaks. Proper integration procedures is a topic that comes up with surprising regularity, so I would like to look at some aspects of integration in this month's "LC Troubleshooting."

The Best Approach

 Figure 1
In Figure 1, it is possible to distinguish three peaks. Peak 1 is just a shoulder on the front of peak 2, whereas peaks 2 and 3 are distinct peaks. So the question is how to best integrate this set of three peaks to get results that are the most accurate — that is, most closely reflect the true area under the peaks. In Figure 1a, a valley-to-valley integration method is used. On the one hand, it may look like this is a good approach, but it misses peak 1 altogether. And, although the integrated area (above the drawn baseline) clearly belongs to peak 2 or peak 3, there is a gross under-integration of the two peaks. That is because all of the area beneath the integration line is ignored.

The correct way to integrate a group of peaks like this is to draw a perpendicular line from the valley between the peaks to the baseline extended between the normal baseline before and after the group of peaks, as seen in Figure 1b. For peak 1, it takes a bit of imagination to pick the correct point to drop the valley, and as we'll see in a minute, this is probably not appropriate anyway. For peaks 2 and 3, the process is simple. First draw a baseline connecting the real baseline before and after the peak group. Then draw a perpendicular line from the valley between each peak pair to the baseline.

 Figure 2
The errors involved in the perpendicular drop method are as follows: If the peaks are approximately the same size, and tailing or fronting is ignored, the amount of the peak tail from the first peak (peak 2 in the present case) hiding under the second peak (peak 3) should be about the same as the amount of peak front from the second peak hiding under the first. If this is the case, the errors should cancel and peak areas should be fairly accurate. If the second peak fronts significantly or if the first peak has a strong tail, the weighting will be distorted, with corresponding errors. If the peak ratio is large — for example, 20:1 — the larger peak will be little affected by the minor contribution of the smaller peak, but the smaller peak will have excess area contributed by the major peak. In this case, the accuracy for the larger peak should be much better than for the minor peak. When the resolution between the peaks is so small that a clear valley is not present, as in the case for peak 1 in this example, the perpendicular drop will grossly over-integrate the peak. A peak skim is more appropriate for integration of peak 1; see further discussion of Figure 2b below.

A related question is when, if ever, is it appropriate to use a valley-to-valley integration technique? The simple answer is that if a known baseline disturbance is present under a set of eluted peaks, valley-to-valley may be appropriate. In the case of Figure 1a, there would have to be a large, broad peak that is roughly defined by the area under the drawn baselines. This is unlikely to occur, and I can never remember encountering such a situation in my experience in the laboratory. On the other hand, in some gradient runs, there may be a small, broad rise in the baseline of blank runs that is consistent enough to allow valley-to-valley integration. In this case, however, the valleys between peaks should reach nearly to the baseline extended from before to after the peak group. This is also a rare occurrence, so the bottom line here is that valley-to-valley integration seldom is the best approach.