Here is the question:

When evaluating linearity during method validation using a HPLC, to build a calibration curve, one would make serial dilutions of your analyte in the matrix and then inject the same amount on your HPLC. Then you plot conc. versus response.....This is what I am used to!
This follows Beers law that basically says A=EbC. i.e Absorbance is proportional to Conc.

how about you make take your analyte in the matrix and then perform different volume injections (using an autosampler) and plot amount (mass) versus response?!!!
My question is that is this a valid calibration curve...my feelings are 50/50..if the method works this way then if you validate it this should be OK. But is this OK with respect to Beers law??!
Do we need to evaluate then the matrix effects since there is variable amounts of matrix in each injection???

Please let me know your thoughts....
Thank you

My lab has performed both. if you can show that the curve is linear with the same slope and Y-intercept as when you use the same injection volumes then you are fine doing it this way. I have changed to weighing each std. conc. out seperately and not doing serial dilutions. By doing this you will be able to see if you made a weighing error, where if you used one stock that was prepared wrong you would never know.

You should have an idea if the stock solutions are made right since you should have calibration standards and QC standards in the same batch which should come from different weighings, unless both of the weighings are not correct. I always make a "stock comparison" (by diluting stocks in mobile phase and inject) before I start extracting matrix samples.

ZZ - The Great Bioanalytical Master

using different injectionvolumes is ok with beer's law but not with chromatography'rule. if your respone is height than there can be an effect off the injection volume, espacialy if your samples are disolved in a strong elluent. There also can be an effect of your autosampler on the learity. So i wlould sugest: validate the protocol you use; make different samples and inject the same volume.

The response is based on peak area NOT height. But I do see your point.
re autosampler linearity....is the error from dilution more than the inherent error in autosampler injections. Also, if the HPLC system is qualified, then maybe the error from the autosampler is not that much....right!

Talking about the Beer's law, you are still working with concentrations even when you introduce different volumes of the standard raither than making a set of standards by serial dilutions. The idea is that when the peak elutes, your compound is diluted with the mobile phase that was delivered through the column. The concentration of this compound may be calculated as follows:
Volume(std)*Original Conc.(std)/Total Volume,
where Total Volume = Volume(std)+Volume(mob.phase)
Since volume of the standard is very low compared to the mobile phase volume, we can consider total volume as volume of mobile phase. Then, since original concentration of the standard and volume of mobile phase are the same for all the injections, final concentration of the compound in the standard will be proportional to the standard's volume (which is volume of your injection). The Beer's law will be in your case A=EbKV(std), wher K = Conc(std)/Volume(mob.phase). So, no mistery here.
This equation does have limitations, and some of them were already pointed out during the discussion. Let me summarize them.

1. The equation above is accurate enough as long as the volume of the standard is significantly lower than the mobile phase volume.

2. Matrix effects have to be evaluated for the reasons you mentioned (being exact, they have to be evaluated any way for method validation).

3. Since only one standard is used for the linear curve, correct preparation of this standard has to be verified somehow.

4. Performance of the autoinjector has to be evaluated no matter what approach you choose. For the serial dilutions injector reproducibility is a concern. For the different injection volumes approach, injector's linearity has to be proved.

Personally, for validation purposes I would choose an old-fashioned way with the serial dilutions (less risk with FDA). For in-lab use, different injection volumes would be OK as long as the items above are addressed.

Good luck!

I'd like to add some comments:

1) “Volume(std)*Original Conc.(std)/Total Volume,
where Total Volume = Volume(std)+Volume(mob.phase)
Since volume of the standard is very low compared to the mobile phase volume...”

The drug concentration in the peak is a function of time. If A(t) is the detector response at time t (this is the peak plotted vs. time), the concentration, according to the Beer’s Law will be given by
c(t)= A(t)/a.b where “a” is the absorptivity and “b” the optical path. If the peak is well retained (k’>2), the mass injected m = C.v (where C is the sample concentration and v the injection vol.) will be diluted only in mobile phase. If “w” is the flow (ml/min), the volume of a short interval of time dt is w.dt and the mass in such interval will be dm=w.c(t).dt. Thus, the total mass is given by the integral (Int) along the whole peak width: m = C.v = Int[w.c(t).dt]= (w/a.b).Int[A(t)dt] ==>
Peak Area=Int[A(t)dt]= C.v.(a.b/w)

The peak area is directly proportional to the sample concentration and to the injection volume and inversely proportional to the column flow (constant flow).
That’s the reason we should always use peak area for quantitation.

2) “1. The equation above is accurate enough as long as the volume of the standard is significantly lower than the mobile phase volume.”
I don’t agree. The problem with high volumes will be chromatographic, like column overload, out of linear range, solvent effects or interactions with mobile phase, etc.

3) I agree with the “old-fashioned” way for testing linearity. If you inject different volumes of the same standard you will be verifying only the linearity of the autosampler. A good autosampler has to be linear. To verify Beer’s Law one should prepare “authentic” standard solutions of different concentrations and injecting the same volume, in order to check the detector performance only.

4) To verify the linearity of the method one should prepare standard samples ranging the whole working range and processing it like calibration samples (in the same way you build the calibration curve during routine analysis). This calibration samples could include the sample matrix (i.e. spiked plasma) or could not include the matrix (i.e. standard solutions for a drug assay in tablets. It will depend how you perform your calibration during routine assay. Matrix effects should be assay in a recovery study, which could be done by linear regression analysis. I mean, you should prepare samples with known amounts of drugs (i.e. spiked plasma samples) and then, they should be assayed like unknown samples, with the routine method.

Now, we could talk about what linearity is from the statistical point of view.

Dear chromatographer,

What is the QC sample and how we prepare it ? and what is its role ina bioanalytical assay method?