As you all know in Beer’s Law (A= abc) a linear relationship exists between sample concentration and absorbance. My colleague strongly believes that a linear relationship measured by a HPLC integrator dose not truly represents Beer’s Law. In other words, a linear regression of R2>0.99 by HPLC with UV detector and integrator (such as Millennium) may not really linear. According to my colleague, only a chart record can truly measure the linearity. This is because one can not change the scale of chart record. With the integrator, the up limit of detector (scale) can be manually raised. I had hard time to understand this theory. Am I missing something here? Please let me know what you think. Thanks.

p.s. According my colleague that peak area is not equal to ABSORBANCE. Therefore, intergrator can not truly measure the linearity because it measure PEAK AREA.

Do you work with a total jackass or what. The area (or height) of a peak is caclulated using the response of the detector. That calculated value has little to do with the picture on the computer srceen. Also, you can change the scale of most chart recorders, they often have an attenuation setting. If this person is your boss, get a new job, if he/she works for you, get rid of them. Yikes!

This is an older chemist, isn't it? I work with a MUCH older chemist and he had similar reservations about the computer doing his integrations for him--he wanted to attach a chart recorder to our brand new, computer controlled HPLC system so he could measure his peak heights by hand. Needless to say, he doesn't run our HPLC anymore.

And how old is that chart recorder that you can't change it's attenuation?!?! We have some from the 80s that have attenuation settings on them!

just as an aside, your colleague is partially right. Peak Area is NOT equal to absorbance, however, Peak Area IS directly proportional to absorbance, assuming that you have not overloaded the column. Also, r2 is not necessarily strong evidence of linearity. It is however, a good indicator of linearity. r2 and a plot of area(count)/concentration(unit) {y-axis} vs. Log(Concentration (unit)) {x-axis}. if r2 approaches a value of 1 and all data points in the plot are within 0.95Rc - 1.05Rc (where Rc=the average value of Area/concentration) will graphically demonstrate the linear range for the method.

just thought I'd post that for fun.

Actually, it's a little more complicated than that. Peak area is essentially the sum of a series of absorbance measurements taken during the elution of a peak. It is entirely possible for the highest portion of the peak to be outside the linear range of the detector, but to have most of the measurements (before and after the peak maximum) to be within the linear range. Imagine the non-linearity error being "diluted" by the smaller measurements. What this means is that linearity of peak area vs concentration is a weaker indication of overload problems than, say, that of peak height.

This debate may be academic, however. What we are trying to do is quantitate the analyte; if the linearity of area vs analyte concentration is adequate, then the linearity of an intermediate figure such as absorbance is arguably irrelevant.

-- Tom Jupille / LC Resources Inc.

Tom:Thanks for your comments. I developed a HPLC UV method. Its linear regression R2 > 0.999 (area vs concentration), peaks sharp are sharp, and intensity is <0.3. But the boss want me to prove its linearity with a UV photometer or a chart record. Otherwise, I have to change the method by decreasing the concentration to very low so peak area count <500,000. Please see "High Load, Low Load".

Rule #1: The boss is always right.

Rule #2: When the boss is wrong, see Rule #1.

If you were having linearity problems, then checking the linearity of the detector would be useful as a troubleshooting tool. Otherwise, I don't think it's necessary. Having said all that, to address the original question, many pharmaceutical analyses *do* call for two runs (high load for impurities, low load for major products) to avoid potential linearity problems.

If your (injected mass) versus (peak area) line was straight, you're home free. As Tom Jupille points out, a more rigorous test is (injected mas) versus (peak area).

Don't use R^2 as a criterion. It's a lousy test of linearity. The best simple test is to set a straight edge along the plotted data points and see whether they fall on the line, or whether they curve away from the line.

The real question is whether the degree of error seen (whether due to noise scatter or nonlinearity) is tolerable for the assay at hand. We routinely find and prove that a single-point calibration is adequate for our work provided that the peak area of the standard is similar to that of the sample.

I also have a question about high load. When impurity level is too low and you have to inject very high amount of drug substance to detect the impurity. By that time, the main peak is out-of range and flat-top peak occurs. I was told that the peak area integration of flat-top peak is not correct. The impurity level is calaulated as peak area over total peak area excluding solvent peaks. So linearity is not the concern now. Lowing the sensitivity of detector will not work for this case. How to resolve this this problem ?
Thanks

TO M.L.:
Two approches may help for your problems:
1. Using the impurity standard if it is available.
2. Inject a normal concentration (below the saturation level) of the potency compnent separately. Calculate impurity level based predetermined RF of the impurity vs potency component. Or, calculate %peak from the chromatograms of impurity (high load) and potency (low load).

This type of problem has been talked about in GC work since there were GC's. The biggest problem is that unless the chemist knows WHAT the material is, there is no way to determine the response relative to compounds that ARE identified. Hence, the '12 PPM Unknown material', or some variation of that, on a report. Because we use 'specific' detectors extensively in our pesticide work, and see response variations measured in orders of magnitude, we are especially sensitive to this issue.

I think that linearity still must be considered, M.L., and the answer above--calculate a theoretical extended curve based on the necessary dilutions--is perhaps the best if the 'impurities' have not been identified.

One more thought. If you are using a detector that can be made to run in a mode approaching universal detection, it might help to equalize sensitivities. For instance, a UV detector doing this work might give more realistic numbers if it were set to 210 nm. Maybe not, but I'll bet it generates DIFFERENT numbers!

LC/MS will help this problem. The extent of the problem can be visualized more easily, and compound identification will become easier. We still, however, see huge differences in response for the same injection quantities of different materials.

Sometimes, these problems just end up being analysis by definition, and must be taken with many grains of salt.

I would think that for drug work, the FDA--or somebody--must have written guidelines on how to do this analysis.

Sorry for the long posts--I'm not busy enough, apparently.

To help solve the linearity problem, an internal standard at a level approximating the 'impurities' could be added, and the response of the main component ignored, or corrected by using the theoretical curve mentioned earlier.

One of our chemists solved a particularly difficult GC problem (on-column isomerization) by removing the main component with a clean-up step.

I would like to make a brief and some comments about this discussion:
Let’s remember that Beer’s Law is deduced under several assumptions. One of them is that solute should be enough dilute to receive the same intensity in the whole light path. Therefore, if the solution were enough concentrated, the Beer’s Law would not be valid and the peak maximum could be outside from the linear range, as it was indicated by Tom Pupille. Then, impurities would be over estimates if we were using %area/area quantitation.
As is indicated by Wen, it’s better to make 2 runs: 1st run with a diluted reference solution (i.e. 1% of test solution) at the upper limit of impurity. 2nd run with the concentrated test sample (High load) in order to evaluate the impurity peaks. %a/a of impurities can be calculated from each peak area and the peak area from the diluted reference standard.
It be kept in mind that %a/a is not the real %p/p of the impurity because its response factor is generally different from the main component. A very good example is the determination of maleic and fumaric acids as impurities of malic acid. When this difference is strong, it would be better to use an authentic reference of the same substance to quantify, if this were possible.
So, the main question is: What does linearity exactly mean? I would like to have a new point of conversation in this Forum.

To examine possible overload conditions with
respect to linearity how about plotting RESPONSE
FACTOR vs concentration? If the response is truely
linear you should get a straight line is i.e.
slope= 0.