Tag Archives: GC

amandarigdon
The Practical Chemist

Calibration Part II – Evaluating Your Curves

By Amanda Rigdon
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Despite the title, this article is not about weight loss – it is about generating valid analytical data for quantitative analyses. In the last installment of The Practical Chemist, I introduced instrument calibration and covered a few ways we can calibrate our instruments. Just because we have run several standards across a range of concentrations and plotted a curve using the resulting data, it does not mean our curve accurately represents our instrument’s response across that concentration range. In order to be able to claim that our calibration curve accurately represents our instrument response, we have to take a look at a couple of quality indicators for our curve data:

  1. correlation coefficient (r) or coefficient of determination (r2)
  2. back-calculated accuracy (reported as % error)

The r or r2 values that accompany our calibration curve are measurements of how closely our curve matches the data we have generated. The closer the values are to 1.00, the more accurately our curve represents our detector response. Generally, r values ≥0.995 and r2 values ≥ 0.990 are considered ‘good’. Figure 1 shows a few representative curves, their associated data, and r2 values (concentration and response units are arbitrary).

Figure 1: Representative Curves and r2 values
Figure 1: Representative Curves and r2 values

Let’s take a closer look at these curves:

Curve A: This represents a case where the curve perfectly matches the instrument data, meaning our calculated unknown values will be accurate across the entire calibration range.

Curve B: The r2 value is good and visually the curve matches most of the data points pretty well. However, if we look at our two highest calibration points, we can see that they do not match the trend for the rest of the data; the response values should be closer to 1250 and 2500. The fact that they are much lower than they should be could indicate that we are starting to overload our detector at higher calibration levels; we are putting more mass of analyte into the detector than it can reliably detect. This is a common problem when dealing with concentrated samples, so it can occur especially for potency analyses.

Curve C: We can see that although our r2 value is still okay, we are not detecting analytes as we should at the low end of our curve. In fact, at our lowest calibration level, the instrument is not detecting anything at all (0 response at the lowest point). This is a common problem with residual solvent and pesticide analyses where detection levels for some compounds like benzene are very low.

Curve D: It is a perfect example of our curve not representing our instrument response at all. A curve like this indicates a possible problem with the instrument or sample preparation.

So even if our curve looks good, we could be generating inaccurate results for some samples. This brings us to another measure of curve fitness: back-calculated accuracy (expressed as % error). This is an easy way to determine how accurate your results will be without performing a single additional run.

Back-calculated accuracy simply plugs the area values we obtained from our calibrators back into the calibration curve to see how well our curve will calculate these values in relation to the known value. We can do this by reprocessing our calibrators as unknowns or by hand. As an example, let’s back-calculate the concentration of our 500 level calibrator from Curve B. The formula for that curve is: y = 3.543x + 52.805. If we plug 1800 in for y and solve for x, we end up with a calculated concentration of 493. To calculate the error of our calculated value versus the true value, we can use the equation: % Error = [(calculated value – true value)/true value] * 100. This gives us a % error of -1.4%. Acceptable % error values are usually ±15 – 20% depending on analysis type. Let’s see what the % error values are for the curves shown in Figure 1.

practical chemist table 1
Table 1: % Error for Back-Calculated Values for Curves A – D

Our % error values have told us what our r2 values could not. We knew Curve D was unacceptable, but now we can see that Curves B and C will yield inaccurate results for all but the highest levels of analyte – even though the results were skewed at opposite ends of the curves.

There are many more details regarding generating calibration curves and measuring their quality that I did not have room to mention here. Hopefully, these two articles have given you some tools to use in your lab to quickly and easily improve the quality of your data. If you would like to learn more about this topic or have any questions, please don’t hesitate to contact me at amanda.rigdon@restek.com.

The Practical Chemist

Calibration – The Foundation of Quality Data

By Amanda Rigdon
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This column is devoted to helping cannabis analytical labs generate valid data right now with a relatively small amount of additional work. The topic for this article is instrument calibration – truly the foundation of all quality data. Calibration is the basis for all measurement, and it is absolutely necessary for quantitative cannabis analyses including potency, residual solvents, terpenes, and pesticides.

Just like a simple alarm clock, all analytical instruments – no matter how high-tech – will not function properly unless they are calibrated. When we set our alarm clock to 6AM, that alarm clock will sound reproducibly every 24 hours when it reads 6AM, but unless we set the correct current time on the clock based on some known reference, we can’t be sure when exactly the alarm will sound. Analytical instruments are the same. Unless we calibrate the instrument’s signal (the response) from the detector to a known amount of reference material, the instrument will not generate an accurate or valid result.

Without calibration, our result may be reproducible – just like in our alarm clock example – but the result will have no meaning unless the result is calibrated against a known reference. Every instrument that makes a quantitative measurement must be calibrated in order for that measurement to be valid. Luckily, the principle for calibration of chromatographic instruments is the same regardless of detector or technique (GC or LC).

Before we get into the details, I would like to introduce one key concept:

Every calibration curve for chromatographic analyses is expressed in terms of response and concentration. For every detector the relationship between analyte (e.g. a compound we’re analyzing) concentration and response is expressible mathematically – often a linear relationship.

Now that we’ve introduced the key concept behind calibration, let’s talk about the two most common and applicable calibration options.

Single Point Calibration

This is the simplest calibration option. Essentially, we run one known reference concentration (the calibrator) and calculate our sample concentrations based on this single point. Using this method, our curve is defined by two points: our single reference point, and zero. That gives us a nice, straight line defining the relationship between our instrument response and our analyte concentration all the way from zero to infinity. If only things were this easy. There are two fatal flaws of single point calibrations:

  1. We assume a linear detector response across all possible concentrations
  2. We assume at any concentration greater than zero, our response will be greater than zero

Assumption #1 is never true, and assumption #2 is rarely true. Generally, single point calibration curves are used to conduct pass/fail tests where there is a maximum limit for analytes (i.e. residual solvents or pesticide screening). Usually, quantitative values are not reported based on single point calibrations. Instead, reports are generated in relation to our calibrator, which is prepared at a known concentration relating to a regulatory limit, or the instrument’s LOD. Using this calibration method, we can accurately report that the sample contains less than or greater than the regulatory limit of an analyte, but we cannot report exactly how much of the analyte is present. So how can we extend the accuracy range of a calibration curve in order to report quantitative values? The answer to this question brings us to the other common type of calibration curve.

Multi-Point Calibration:

A multi-point calibration curve is the most common type used for quantitative analyses (e.g. analyses where we report a number). This type of curve contains several calibrators (at least 3) prepared over a range of concentrations. This gives us a calibration curve (sometimes a line) defined by several known references, which more accurately expresses the response/concentration relationship of our detector for that analyte. When preparing a multi-point calibration curve, we must be sure to bracket the expected concentration range of our analytes of interest, because once our sample response values move outside the calibration range, the results calculated from the curve are not generally considered quantitative.

The figure below illustrates both kinds of calibration curves, as well as their usable accuracy range:

Calibration Figure 1

This article provides an overview of the two most commonly used types of calibration curves, and discusses how they can be appropriately used to report data. There are two other important topics that were not covered in this article concerning calibration curves: 1) how can we tell whether or not our calibration curve is ‘good’ and 2) calibrations aren’t permanent – instruments must be periodically re-calibrated. In my next article, I’ll cover these two topics to round out our general discussion of calibration – the basis for all measurement. If you have any questions about this article or would like further details on the topic presented here, please feel free to contact me at amanda.rigdon@restek.com.

amandarigdon
The Practical Chemist

Easy Ways to Generate Scientifically Sound Data

By Amanda Rigdon
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amandarigdon

I have been working with the chemical analysis side of the cannabis industry for about six years, and I have seen tremendous scientific growth on the part of cannabis labs over that time. Based on conversations with labs and the presentations and forums held at cannabis analytical conferences, I have seen the cannabis analytical industry move from asking, “how do we do this analysis?” to asking “how do we do this analysis right?” This change of focus represents a milestone in the cannabis industry; it means the industry is growing up. Growing up is not always easy, and that is being reflected now in a new focus on understanding and addressing key issues such as pesticides in cannabis products, and asking important questions about how regulation of cannabis labs will occur.

While sometimes painful, growth is always good. To support this evolution, we are now focusing on the contribution that laboratories make to the safety of the cannabis consumer through the generation of quality data. Much of this focus has been on ensuring scientifically sound data through regulation. But Restek is neither a regulatory nor an accrediting body. Restek is dedicated to helping analytical chemists in all industries and regulatory environments produce scientifically sound data through education, technical support and expert advice regarding instrumentation and supplies. I have the privilege of supporting the cannabis analytical testing industry with this goal in mind, which is why I decided to write a regular column detailing simple ways analytical laboratories can improve the quality of their chromatographic data right now, in ways that are easy to implement and are cost effective.

Anyone with an instrument can perform chromatographic analysis and generate data. Even though results are generated, these results may not be valid. At the cannabis industry’s current state, no burden of proof is placed on the analytical laboratory regarding the validity of its results, and there are few gatekeepers between those results and the consumer who is making decisions based on them. Even though some chromatographic instruments are super fancy and expensive, the fact is that every chromatographic instrument – regardless of whether it costs ten thousand or a million dollars – is designed to spit out a number. It is up to the chemist to ensure that number is valid.

In the first couple of paragraphs of this article, I used terms to describe ‘good’ data like ‘scientifically-sound’ or ‘quality’, but at the end of the day, the definition of ‘good’ data is valid data. If you take the literal meaning, valid data is justifiable, logically correct data. Many of the laboratories I have had the pleasure of working with over the years are genuinely dedicated to the production of valid results, but they also need to minimize costs in order to remain competitive. The good news is that laboratories can generate valid scientific results without breaking the bank.

In each of my future articles, I will focus on one aspect of valid data generation, such as calibration and internal standards, explore it in practical detail and go over how that aspect can be applied to common cannabis analyses. The techniques I will be writing about are applied in many other industries, both regulated and non-regulated, so regardless of where the regulations in your state end up, you can already have a head start on the analytical portion of compliance. That means you have more time to focus on the inevitable paperwork portion of regulatory compliance – lucky you! Stay tuned for my next column on instrument calibration, which is the foundation for producing quality data. I think it will be the start of a really good series and I am looking forward to writing it.