Log/Log vs quadratic for ELSD

[domino1]

I am sure a discussion on this topic has taken place but I can't seem to find it!

I seem to see most literature references to a log/log relationship for ELSD. However, in our case, a quadratic fits the data better (three 9's instead of two). Is the relationship moleclue dependent? Should we choose the relationship that gives us the best correlation or just go with the log/log.

I am curious as to what you all think.

Thanks!!

[juddc]

Based upon your post, I replotted a recent ELSD calibration I have for trehalose both ways and saw almost precisely the same correlation coefficient for both.

FYI, I ran 10 points evenly distributed over 1 order of magnitude concentration and the %RSD on system suitability at midpoint = 0.83% with 6 injections. Log/log yielded 0.999598 and quadratic yielded 0.999648. Interpolation of an unknown from either curve (predictably) gave indistinguishable data.

It may be molecule dependent in some cases, but I'm not seeing that with my data.

I suspect that it's based upon what folks are comfy with and generally most people like to see and calculate from straight lines, which log/log will give you.

Merely my $0.02, and not based upon any great knowledge of ELSD or arithmetic!

[domino1]

All information is helpful!

I agree that the two are very close. It's all about the math!

Thanks again!

[Mark Tracy]

On the log-log plots, what is the slope? For a curve of y=c*x^n, the slope of the log-log plot will be n with an intercept of log(c). However if the curve is y=c0 + c1*x + c2*x^2 + ... the log-log plot will not be a very good fit.

[domino1]

We are plotting the log of area vs the log of concentration so the resulting correlation is linear y = mx + b.

[Mark Tracy]

Let me clarify. Log-log plots are a transformation of the original response curve. When you transform a quadratic response into log-log space, you get a linear correlation. That is convenient for many reasons. One reason is that the slope in log-log space is the exponent in the original untransformed space. The reason for my original question is to find out how close to linear is the original response curve; a log-log slope != 1.0 means that the original data is not linear.

[domino1]

The log/log slope is 1.65 - does that clarify?

Thanks!

[Mark Tracy]

Yes, thank you. What that means is that your original response curve is non-linear. Since the log-log slope is not an integer, it means that either your original data has a response function of area = amount^1.65 (unlikely), or you have tried to fit a line to the log of a polynomial function (which is a poor fit). Since you report that the quadratic fit is superior to the log-log fit, I think you can safely use (justify the use of) the quadratic. In general, log-log plots are good for showing certain things, but don't make the best calibration curves.

[domino1]

A bit more information...

I am a new user to ELSD so I am researching my options (what I am trying to say is pardon my ignorance!).

I took my data and used the polynomial and log/log curves to calculate purity (obviously can't use straight area percent due to the lack of linearity). Even though the plots gave fairly similar correlations, the calculated purities were dramatically different (78% by log/log, 87% by polynomial, 94% by area normalization assuming linear response (which is non-linear)). In the log/log plot, more weight is given to the low on-column load samples in the line which led to a more dramatic increase in the calculated amount of each impurity.

My thoughts are that this is closer to the true value than using the polynomial plot. When I just look at the response factor at each level I see that my lowest point on my curve is only 8% of the response factor of my nominal load. Therefore it makes sense that there is such an extreme increase in the calculated amounts as compared to just area normalization.

The good news is that we are also collecting UV data for the main peak so we know that the UV data is linear and that the drop off in the ELSD is due to the detector and not due to sample loss to surfaces etc (as I have seen with some molecules).

Going forward we would like to generate a standard curve with the parent compound, transform it to log/log, and then use the curve caluculate the amount of each impuity/related species present. Then use those amounts to calculate the impurity profile. Just like in straight UV, we would be making the assumption that the impurities/RS behave the same as the parent compound.

Does all of this seem to jive with what others have seen when calculating purity by ELSD? Again, I am new to this so any input is appreciated!

Happy Thanksgiving all!

[Mark Tracy]

I disagree. You are trying to find one calibration function that will span the entire dynamic range, and I don't think you can do it under these circumstances. (UV is so nice and linear, and it trains your intuition to assume that. Unfortunately, that is not true for many other detectors.)

Recently, I was working on a technique with conductivity detection. Reluctantly I had to conclude that while the method has a useful dynamic range of 3 orders of magnitude, the quantitation range was only 1 order of magnitude anywhere within the larger range. Even with quadratic fitting. I recommend you do something similar, and have a low-range curve and a high-range curve.

One bit of good news: the assumption that related substances have similar responses is actually better for ELSD than for UV.

[domino1]

Well the good news was that if we used the equation to do the purity analysis we got mass balance with the UV data. For example our main peak areas by UV decreased by 75% (with no related species seen since they are UV transparent). Using the equation for the corresonding ELSD data, we saw an increase of impurities by 25% (it was only 5% if we assumed a linear correlation). So, it does seem to work.

I will however, have my person compare a single calibration curve vs a high/low curve. We are trying to keep it as simple as possible from QC perspective but we do want to be reporting the correct values.

Thanks for the feedback.

[domino1]

Ok, I ran the numbers.

If we use the log/log plot we get essentially the same purity values whether we use a single plot (all points) or one all point plot for the main peak and then a low level point plot for the related species. Good news.

Using the polynominal, you do need two plots. When we use the all point plot for the main peak and then a low level point plot for the related species, we finally get an impurity profile that looks like the one generated by the log/log plot.

Since the log/log plot seems to work pretty well, and we may be able to get away with a single plot, then we will most likely stick with that.