How to determine the detection limit (lower limit) and lower limit of quantification
토픽 개요
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There is no one set way. There are some guidelines.
The analyst should determine the detection limit and lower limit of quantification using a method appropriate to the purpose of the analysis, and write down the lower limit value in the report along with the scientific basis.
About detection limit (lower limit) and lower limit of quantification
①When a blank sample is analyzed and no peaks are detected
②If small peaks are detected
Ion chromatograms for two cases are shown as examples.
ブランク試料の測定例Blank sample measurement example 溶媒ピークsolvent peak 溶媒ピークを検出してからの保持時間Retention time after detection of solvent peak ノイズ幅noise width ブランク値blank value
電気信号のノイズは多少なりとも存在する。ブランク試料に対象成分が全く含まれない場合は、ノイズ幅nを読み取る。
There is some noise in electrical signals. If the blank sample does not contain any target component, read the noise width n.
何らかの理由でブランク試料に対象成分が含まれるなら小さなピークが表れる。そのブランク値bを読み取る。このブランク測定は複数回行い、その標準偏差を求める。
If for some reason the blank sample contains the target component, a small peak will appear. Read that blank value b. This blank measurement is performed multiple times and its standard deviation is determined.
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①When a blank sample is analyzed and no peaks are detected
This is a chromatogram when water-soluble ion components are measured using ion chromatography. If some ionic component is separated, a peak will appear in the electrical conductivity (vertical axis) at some time (horizontal axis). The figure below is a chromatogram of a blank sample (water containing no ionic components), so no ionic component peaks can be seen.
However, if you zoom in on the baseline of the chromatogram, you will see that there is background noise in the electrical conductivity measurements.
ブランク試料の測定例Blank sample measurement example 溶媒ピークsolvent peak バックグラウンドbackground
溶媒ピークを検出してからの保持時間Retention time after detection of solvent peak ノイズ幅noise width
In this way, suppose you measure some environmental sample in a case where no peak appears in the blank measurement. If the sample contains very small amounts of ionic components, you should see a small peak. Is that small peak a significantly large peak relative to the background noise? In order to check it the detection limit conditions are determined.
detection limit：
Set S/N ratio = 3 as the detection limit. Find the average noise width n and set the peak (s) corresponding to 3n as the detection limit. Peaks larger than that are recognized as signals (detected), and peaks smaller than that cannot be determined to be noise or signals (not detected).
バックグラウンドBackground ノイズ幅noise width ノイズ幅の３倍3 times the noise width 検出限界detection limit ノイズ幅の３倍の信号強度Signal strength 3 times the noise width
Lower limit of quantification ：
It is assumed that the detection limit conditions are met. Then, a calibration curve is created by measuring standard samples, and the range plotted on the calibration curve is determined to be quantifiable. However, it is also necessary to ensure reliability (accuracy) through repeated measurements of standard samples. For example, the quantifiable range may be defined as "meeting the detection limit and having an error (coefficient of variation) of less than 5% due to repeated measurements of the standard sample." The lower limit of the quantifiable range is called the lower limit of quantification.
Exceptional measures when standard samples cannot be made
However, in environmental analysis, the concentration of target components in environmental samples is so low that it is sometimes impossible to create standard samples with such low concentrations. For example, it is not possible to create standard gas samples for unstable compounds in the atmosphere (such as diiodomethane). In such cases, S/N ratio = 10 may be set as the lower limit of quantitation. Determine the average noise width n and use a signal (s) of 10n as the lower limit of quantitation.
※ In gas chromatograph mass spectrometry, empirically, if the S/N ratio is 10 or more, the calibration curve is linear and often reproducible. Therefore, S/N=10 may be set as the lower limit of quantification.
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② When there is a signal strength that shows a peak for unknown reasons during blank measurement
Even if you measure a blank sample (a sample that does not contain the target component), peaks may be detected for some reason. This is often caused by contamination of target components from sample processing or analysis lines. In this case, repeat the blank measurement 10 times and find the standard deviation σ of the blank signal intensity.
ブランクを測定しても、ノイズに比べて有意な差を持つ信号強度が得られる場合
When measuring a blank yields a signal strength with a significant difference compared to the noise
分析捜査における汚染が原因Caused by contamination in analytical investigation
If the signal intensity of the peak that appears in the blank measurement is exactly the same no matter how many times it is measured, it is considered that the signal intensity is added by that amount (wearing clogs) even in the unknown sample measurement. If so, you can subtract the signal intensity of the blank from the measurement results of the unknown sample. However, the blank must be measured repeatedly to confirm its repeatability. In particular, it is necessary to check whether there is a significant difference (detected) with respect to the blank.
The figure below shows an example of the results of multiple blank measurements. It was found that there was variation in the size of the peaks observed in blank measurements. In the figure below, "ave" represents the average value from repeated measurements of the blank, and "σ" represents the standard deviation.
ブランク試料の複数回測定の例Example of multiple measurements of blank sample 標準偏差standard deviation 平均average
Taking into account the variation due to blank measurements, a peak that is "average, plus, three times the standard deviation of blank measurements" will be recognized as having a significant difference from the blank peak. Therefore, as shown in the figure below, the detection limit value is set as ave + 3σ. (Depending on the purpose of analysis, it may be set as ave + 10σ, etc.)
ブランク測定の平均＋３σもあれば、ブランクのピークとは有意な差がある（検出した）と認めようIf the blank measurement average + 3σ is also found, it is recognized that there is a significant difference (detected) from the blank peak.
Of course, even if a peak is seen in a blank measurement, the quantifiable range is
"The range that can be plotted on a reliable calibration curve after clearing the detection limit"
The lower limit of quantification is the lower limit of the quantifiable range.
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