Limits that Matter: How LoD and LoQ Shape Analytical Results

In Nuclear Magnetic Resonance (NMR) spectroscopy, each organic molecule has its own unique spectral fingerprint. As molecular detectives, chemists can use these fingerprints to discern the quantity and quality of an analyte in a sample. Limit of Detection (LoD) and Limit of Quantification (LoQ) are validation parameters that set the bounds on what is considered feasible in terms of identifying and quantifying an analyte in a certain matrix, under a specific set of parameters.

The LoD is a parameter relevant to identification of an analyte, which can be determined visually by observing a signal that correlates to the structure of the analyte. The LoD can also be determined mathematically, as an analyte signal possessing a signal-to-noise ratio (SNR) of at least 3.¹

As the name implies, the LoQ is the minimum SNR required for a given method to achieve a specified level of precision. For accurate quantification in NMR, an SNR of 150 or higher yields an uncertainty level lower than 1% in the measurement.² One can set their LoQ lower than 150; however, the consequence of this is a larger uncertainty in the measurement.² Note that we typically recommend an SNR of 250 for quantitative measurements, however, an SNR of 150 is also sufficient.

To illustrate the practical application of these concepts, let’s consider a common household product: toothpaste. Many toothpastes contain fluoride, an ingredient that prevents dental caries (tooth decay), by inhibiting tooth demineralization.³ The accurate detection and quantification of fluoride in toothpaste are essential for ensuring efficacy and safety. By using ¹⁹F NMR spectroscopy, we can determine fluoride concentrations with a high degree of specificity and sensitivity.

700 mg of a commercial toothpaste containing sodium fluoride as an ingredient was added to a vial, followed by 2 mL of deuterium oxide. The resulting slurry was sonicated for 1 hour and then filtered into an NMR tube for analysis (filtrate on the left). Three standard solutions of sodium fluoride, with concentrations of 200 mM, 100 mM, and 50 mM, were prepared to establish a calibration curve for determining the LoD and LoQ of this method.

Figure 1. Stacked ¹⁹F (95.7 MHz) NMR plot of sodium fluoride solutions in deuterium oxide (D₂O).

The acquisition parameters used to establish the calibration curve were the following: spectral width of 200 ppm, spectral center of −120 ppm, 65536 points, 4 scans, acquisition time of 3.4 seconds, and a scan delay of 15 seconds. Further, after the spectra were acquired 1.0 Hz of exponential line broadening, baseline correction, and zero filling (x4) were applied.

Figure 2. Calibration curve using sodium fluoride standards to determine the LoD and LoQ with 4 scans.

In Figure 2, we determined that the LoQ was 161.8 mM by identifying the intersection where the slope meets an SNR of 250. Similarly, the LoD was determined to be 2.7 mM by first extrapolating the slope and then identifying the intersection with an SNR of 3. It is important to highlight that these LoQ and LoD values were determined with the acquisition parameters mentioned above, and if these change, so will the LoD and LoQ. For example, if more scans are used, a lower LoD and LoQ can be established.

From Figure 2, we can also estimate the concentration of the toothpaste extract to be 8.9 mM and since the SNR is proportional to the square root of the number of scans, we can calculate the minimum number of scans necessary for accurate quantification of the toothpaste extract.

Figure 3. Determination of minimum number of scans for quantification of toothpaste extract. The orange line represents the extrapolation of the theoretical relationship between the number of scans and the SNR based on 4 scans of the toothpaste extract.

In Figure 3, it was determined that 2048 scans should be sufficient for quantification based on the theoretical (orange) SNR values of the toothpaste extract.

The most common method for quantification in NMR is performed by using an internal calibrant.⁴ We have discussed quantitative NMR⁵ (qNMR), internal calibrants⁶, and relaxation delays⁷ in the past, so we will skip them in this blog entry.

If you have any questions regarding our benchtop instruments’ ability to determine the LoD and LoQ for your sample experiments, please contact us!

References

[1] Schmidt, J.; Haave, M.; Underhaug, J. Wang, W. Micropl.&Nanopl. 2024, 4 (17)

[2] Guide to NMR Method Development and Validation – Part I: Identification and Quantification; Eurolab, 2023. http://doi.org/10.13140/RG.2.2.30200.83208 (Accessed December 3, 2024)

[3] Featherstone, J. D. Community Dent Oral Epidemiol. 1999, 27, 31-40.

[4] Mattes, A.O.; Russell, D.; Tishchenko, E.; Liu, Y.; Cichewicz, R. H.; Robinson, S. J. Concepts Magn Reson Part A. 2016, 45A, e21422.

[5] https://www.nanalysis.com/nmready-blog/2022/4/28/beyond-structural-elucidation-introduction-to-qnmr-part-i?rq=qnmr (Accessed December 3, 2024)

[6] https://www.nanalysis.com/nmready-blog/2023/9/29/beyond-structure-elucidation-introduction-to-qnmr-part-ii-calibrants?rq=qnmr (Accessed December 3, 2024)

[7] https://www.nanalysis.com/nmready-blog/2019/5/30/beyond-structural-elucidation-introduction-to-qnmr-part-iii-relaxation-delays (Accessed December 3, 2024)