Based on a presentation to the American Chemical Society Fall Conference, 2016
by Savino Sguera
Calibration and Dynamic Range
Linear Dynamic Range (LDR) is a term used in analytical chemistry to describe the region of the calibration curve that is reproducible and therefore usable for reporting scientific values. As indicated in the previous article, an analytical chemical instrument reads values against a calibration curve or slope that relates known concentrations of the chemical to the instrument’s detector response. As the name implies, calibration curves are not always linear. At very high concentrations, the detector may become saturated and give a smaller response. At very low concentrations, interference from other sources becomes larger than the chemical being detected, and so higher responses may be seen than would be caused by the chemical in question alone. Linear Dynamic Range refers to the region of the curve where the curve is straight, or linear, and behaves predictably and reproducibly. Anything outside of this range should not be used for analysis, as it can have unreliable and unpredictable results.
Figure 3: A graph showing the relationship between concentration of standard and instrument response. The purple line represents the actual relationship between instrument response and concentration, the green line shows a linear approximation for the linear portion of the purple line. The Linear Dynamic Range is represented by the overlap between the purple and green lines.
Figure 3 is designed to illustrate a simple concept that is universal in analytical chemistry: Never use values from outside the Linear Dynamic Range. On the X axis we see the solution concentration, and on the Y axis we see the instrument’s output response. The purple line shows the relationship between instrument response and concentration. Due to noise saturation as the low end, the curve never reaches zero but rather trails off as interfering ions trigger the instrument’s response. On the far right side of the graph, we see that the purple line starts to tail off again as the instrument’s detector becomes oversaturated by the chemicals being detected. The green line represents the calibration curve generated from standards. Although the green line is a very accurate approximation within the Linear Dynamic Range, outside of this range the calibration curve is highly inaccurate.
Some labs use an extrapolated calibration curve. An extrapolated calibration curve attempts to use advanced mathematics to correlate instrument response to concentration outside the Linear Dynamic Range. Although this is potentially useful in academic research papers in certain limited cases, most commercial analytical labs and laboratory certification bodies, such as the ISO, frown upon this practice. Additionally, no reputable analytical laboratory working in the environmental, pharmaceutical, or medical industry uses this technique to report results.
Figure 4 below illustrates a schematic of how to properly quantify any unknown sample without using extrapolated calibration curves or any other technique that requires using data from outside the Linear Dynamic Range.
Figure 4: A chemistry work-flow illustrating how dilutions can be used to keep instrument responses within the instrument’s dynamic range. In this figure, the max dilution within the LDR for the machine is 1.0 mg/ml. Oversaturated solutions can be diluted to produce values within the acceptable LDR, with values multiplied back to meet proper values.
If an unknown is to be tested by a lab and the results are outside the Linear Dynamic Range, then it is declared “over range.” The sample is then diluted and re-run until a value is detected within the Linear Dynamic Range. The analytical chemist should then apply all dilutions to the observed value to determine the concentration in the original sample. At no point does an analytical chemist need to use values taken from outside the instrument’s Linear Dynamic Range. This makes an extrapolated calibration curve technique unnecessary to analyze samples.
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About the Author
Savino Sguera is founder and CSO of Digamma Consulting. Since 2010 he has been an analytical chemist and researcher in the cannabis industry, working with both private and public interests to bring scientific integrity to the business. Savino holds a B.Sci. in Biomedical Engineering from Columbia University.