Assessment of "total Rs" for chromtography compari

[Rob Burgess]

Hi All,

As a method development blueprint say for LC impurity assays where one is trying to compare the chromatographic merits for a separation of 10 - 20 peaks from 5 or more chromatograms, is there a simple way to do this. I was thinking along the lines of a some form of measurement of the total Rs (separation factor etc) of the entire chromatogram. Does this question make sense or is there no such measurement?

[tom jupille]

Rob, there have been many "figures of merit" proposed (average resolution, average resolution per minute, . . .). I don't like the various forms of "average" resolution (for general use) because one highly-resolved pair of peaks can result in a high value despite many poorly-resolved peaks. In specific cases, you can get around that by counting only certain problematic peak pairs.

I've generally followed the Lloyd Snyder approach and used the critical resolution (resolution between the worst-separated pair of peaks of interest on the chromatogram) on the grounds that if this "worst-case" pair is well enough separated, all other pairs are, by definition, also well enough separated. A variant on this would be to establish a "target" resolution for each peak pair, and then use the worst-case percentage of target.

For specific problems, I've occasionally played around with applying "fudge factors" to certain peak pairs on the basis of things like disparity in peak sizes, but those get so subjective that I've found it easier to simply use "common sense".

[Uwe Neue]

Rob,

I have always thought that there are better ways to deal with this than just using resolution. I got a general method that creates values between 1 and 0. 1 means that you have comfortably reached everything that you want from the method, and you get 0, if at least one of the things that you care about is not present.

I can send you a paper, if you contact me. I may also be able to explain it here, but it will take some writing.

[Victor]

Rob-there is something very similar to what you describe called the chromatographic response function (CRF). This method was very popular when Simplex optimisation of HPLC separations was in vogue. Here you require a single number which represents the quality of the separation; automatic optimisation then requires the computer/automated HPLC to maximise this number. There are many variants of the CRF but one is:

CRF = [sum of resolutions between adjacent peak pairs] + f1 (L) +f2(Ta-Tl) + f3 (T1-T0)

where f1-f3 are user adjusted factors to weight the CRF according to taste.
Ta is the maximum retention time specified
Tl is the retention of the last peak
T1 is the retention of the first peak
T0 is the minimum retention time specified.
L is the number of peaks detected.


For example, if it is essential to separate all the peaks then you can choose a large value of f1, which will penalise separations where many of the peaks overlap. If very long analysis times are highly undesirable you adjust the value of f2 accordingly.

If you search for Simplex, CRF and HPLC you will see many functions of this type, and a better description of their use.

[Rob Burgess]

Thank you all very much for your replies... most informative discussion... cheers!

I quite like the sound of Tom's "common sense" approach. It will be much easier to apply this than trying to put a value on something, that is perhaps, meaningless.

Uwe, I'd be interested in reading that paper. A ref. to it would be great.

Victor, this CRF approach is probably worth a read also. How long ago was this work written about, do you know? Thanks for the info...

[Uwe Neue]

U. D. Neue, E. S. Grumbach, J. R. Mazzeo, K. Tran, D. M. Wagrowski-Diehl, “Method development in reversed-phase chromatographyâ€

[Uwe Neue]

Here is a generic way in which values that describe the value of a chromatographic separation can be normalized to run between 0 and 1. Good is 1, 0 is bad. This in turn permits that these values can be multiplied with each other, so a large group of different value criteria can be combined with each other. The simplest case is a combined criterion for the overall resolution in a chromatogram, not just the worst resolution.

Let us assume that I want to achieve a good resolution between all peak pairs. The first step is to define a critical resolution Rs(crit) that will make me happy. I measure the resolution Rs(i) and determine the criterion C(i) for each peak i:

C(i) = Rs(i) / Rs(crit)

Now we can calculate the quality criterium Q for the entire chromatogram:

Q = Product ( C(i)^n / (1 + C(i)^n) )

This value will always run from 0 (some peak is not resolved at all) to 1 (all peaks well resolved). The speed with which the value converts from 0 to 1 depends on my choice of the power n. High powers (8) are often a better choice than low powers (2).

I can use other criteria as well. For example, I can set up a criterion for a maximum run time and multiply it with my resolution criterion. Or I can combine it with other things that make sense.

The beauty of this parameter Q is that it is 1 when it is good, and 0 when it is bad. A computer can understand this very well, and even I can understand it.

[A.Nonymous]

as an alternative, you can adopt the golf card system described in LC-GC for the purchase of instrumentation.
With some adjustments you can use this approach.

Article:
http://www.lcgcmag.com/lcgc/article/art ... &sk=&date=