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Calibration Curves, Part 4: Choosing the Appropriate Model
Jul 1, 2009
By: John W. Dolan
LCGC Europe
 Volume 22, Issue 7
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This is the fourth "LC Troubleshooting" column in a series looking at different aspects of the calibration process for liquid chromatography (LC) methods. We first considered whether or not to force a calibration curve through the origin (x = 0, y = 0).1 The next stop was a discussion of some techniques to determine the limits of detection and quantification.2 Last month,3 we saw how %-error plots could help us visualize possible problems with calibration curves. The present discussion focuses on three different calibration models: external standardization, internal standardization and the method of standard additions. Next month, we will look at the technique of curve weighting.

External Standardization


Table 1: Standard curve data.
The use of external standards is the simplest and probably the most common method of calibration for quantitative LC methods. The technique simply compares the detector response between known concentrations of analyte with the response for samples containing unknown concentrations. A calibration curve (also called a standard curve or sometimes a "line") is generated by injecting a series of calibration standards. For well-behaved methods, as demonstrated by validation studies and narrow ranges, for example, ą10% in concentration, a single-point calibration can be used. In this technique, the response (area) for a known concentration of reference standard is calculated (area/concentration) to generate a calibration factor. This value is divided into the area for an unknown concentration and the result is the concentration of the unknown.


Figure 1: External standard calibration plot from the data in Table 1.
More commonly, calibrators are prepared that cover the expected sample concentration range and the response of these calibration standards is used to generate a calibration curve. This is demonstrated with the data of Table 1. The data of Table 1 simulate the use of a method for which all the calibrators are injected both at the beginning (data set 1) and end (data set 2) of a batch of samples. Calibrators were prepared at 1, 2, 5, 10, 20, 50, 100, 200, 500 and 1000 ng/mL and injected with the batch of samples. The results are combined in Table 1. Using the data system software or spreadsheet software, such as Microsoft Excel, a calibration curve can be plotted, as is shown in Figure 1. Here, concentration (x-axis) is plotted against response (y-axis). The plot is linear (y = 403.7x – 5.2) and the standard error of y (Sy = 25.1) is greater than the y-intercept, so the curve can be forced through zero (y = 403.7x). (See the discussion of reference 1 for more information on zero-intercept decisions.) This regression equation is then rearranged (x = y/403.7) to calculate the concentration of unknown samples. For example, a sample that generates a peak of 36827 area counts (last line, Table 1) would have a concentration of (36827/403.7) = 91.2 ng/mL. A common sense double-check of the calculation shows that in Table 1, 36827 area counts would fall between 50 and 100 ng/mL, so the result seems reasonable.

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