Help me understand these units please!

Empower2018

I run an assay on my active using an internal standard. So I set the IS against the active and set up the sample set for standards, samples, dilutions etc and the result is working fine but I just don't understand where the method is getting the units of final answer from. Here is the validated calculation:

Area active in sample * Area IS in working standard* Working Std weight(mg) *Sample Volume (mLs) *1000/Average Standard Area in bracketing standards * Area IS in sample *Standard volume (mls) * Standard Dilution * Sampleweight. 


I get that its the typical amount calculation in that you are taking response in sample divided by average response in standards and multiplying by concentration of active in your standard in mcg/mL, then taking into account IS area ratio and finally take into account sampleweight of sample and dilution. Incidentally the sampleweight of my sample is in mg. What I don't get is the *1000 part. It states in the method that the reason is "to convert to mg/g" but if you take out the *1000 then surely your results are in mcg/mL. as in the concentration of the standard is in units of mcg/mL. Surely to get back to mg/g you need to DIVIDE by 1000 to get the result in mg/g? Any insight?

MJS

I've broken down the formula a bit and I am getting µg/g as the final units from what you have provided for information (µg/mL for std concentrations, mg for sample weight).  I've attached a workup of this since the forum formatting doesn't like equations.

If the standard concentration is being entered as mg/mL which is what your original formula actually implies with the (mg) in it, then that changes things a bit and would result in a mg/g final result.  So, could it really just be as simple as not using µg/mL concentrations and using the mg/mL the "validated" formula states to use?

MJS

So, everything to the left of the divisor is in the numerator and everything to the right of the divisor is in the denominator if we were to add parentheses around them, right? 

I'm a little confused by the "standard volume" in the denominator...what is that from in the analysis?  Is that a custom field to address the "concentration" of the IS?  What is the standard dilution value from and what units are there on that?  Maybe an example with actual numbers would help as well.

Empower2018

Hi MJS. Yes, everything to the left is numerator and the right is the denominator. The Std volume refers to the volume that the working standard is made up in so in effect the concentration value needs to go into the Value column. 
We weigh out 12mg of active and dissolve into 50mls for the standard so 50mls for standard volume. Then a dilution of 10mls of this into 100ml to get the final working standard so the final concentration is (12/50)*(10/100)*Purity or 0.024mg/ml or 24mcg/mL. So the other values in the equation like area of internal standard etc are all typical of the Amount calculation but im still confused as to how the output can be seen as mg/g. The value for the concentration in the component editor is treated as mcg/mL with the multiplication by 1000 so surely the end units should be mcg and not g. 

Note: Sampleweight is typically 100mg and is entered against "Sampleweight" for each sample line of the sample set. 

Empower2018

Hi MJS and thanks for your reply. Yes I went through your attachment step by step as well and all the units are exactly what I thought as well. I think there may well be a mistake in the final method (its been through several versions and tech transferred to our lab from people with limited Empower knowledge) because at the end of the day if you enter the component editor value in mg rather than mcg you get an output of mg/g. Strange that this formula got through so many eyes and not getting flagged. 
Ill keep your attachment as a reference, thanks.