Comparison of Different Approaches for Estimation of the Detection Limit of Quantitative NMR

doi:10.11938/cjmr20212944

Abstract

Abstract:

Limit of detection (LOD), which indicates the detection ability of an analytical method, is an important parameter used in validating quantitative ¹H nuclear magnetic resonance (NMR) method. Different approaches to evaluate LOD have been reported in literature, including the calibration curve approach, regression parameters-based approach, ASTM approach (proposed by American Society of Testing Materials), EPA approach (established by the United States Environmental Protection Agency) and the signal-to-noise ratio approach. In this study, systemic analyses and summaries of all mentioned approaches were given together with their principles, equations and characteristics. A novel approach based on signal-to-ratio regression curve for determining the detection limit was proposed, which can overcome weaknesses of the signal-to-noise ratio approach. The LOD of liquid-state ¹H NMR method in the determination of sodium formate in aqueous solution was calculated using 5 different approaches. The influence of the number of scans on LOD was discussed. The results showed that the LOD was in the range of 10.4~14.4 μmol/L when the number of scans was 64 with 700 MHz NMR spectrometer. In conclusion, the study can provide a reference for determining the LOD of ¹H quantitative NMR.

Key words: liquid-state nuclear magnetic resonance, quantitative detection, limit of detection (LOD), signal-to-noise regression approach

CLC Number:

O482.53

Lei CHEN,Hong-bing LIU,Hui-li LIU. Comparison of Different Approaches for Estimation of the Detection Limit of Quantitative NMR[J]. Chinese Journal of Magnetic Resonance, 2022, 39(2): 230-242.

Figures/Tables 10

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	16	32	48	64	96	128
a	1.0083	1.9491	3.0226	4.0361	6.1182	8.2802
b	0.0353	0.0708	0.1057	0.1410	0.2110	0.2799
R²	0.9944	0.9959	0.9971	0.9979	0.9982	0.9985
S_y/x	0.2000	0.3450	0.4298	0.4906	0.6853	0.8204
X_C/(μmol/L)	12.0	10.3	8.6	7.4	6.9	6.2
X_D⁽²⁾/(μmol/L)^*	23.6	20.3	17.0	14.6	13.6	12.3
X_D⁽³⁾/(μmol/L)^*	23.4	20.1	16.8	14.4	13.4	12.1
X_D⁽⁴⁾/(μmol/L)^*	24.0	20.7	17.3	14.8	13.8	12.4
X_D⁽⁵⁾/(μmol/L)^*	23.7	20.5	17.1	14.7	13.7	12.4
X_D⁽⁶⁾/(μmol/L)^*	23.8	20.5	17.1	14.7	13.7	12.4

样品浓度/(μmol/L)	自由度ν	标准偏差s	F	${t_{(1 - 0.01, {v_1} + {v_2})}}$	S_pooled	X_D/(μmol/L)
20.5	7	2.943	3.5912	2.6245	2.3530	6.2
34.2	7	1.553	3.5912	2.6245	2.3530	6.2

	16	32	48	64	96	128
${a_{SN}}$	34.0846	50.1219	58.5726	63.4292	70.8545	89.1259
${b_{SN}}$	1.0401	1.5872	2.0016	2.3365	2.9585	3.3478
R²	0.9949	0.9953	0.9956	0.9961	0.9963	0.9964
${S_{y/x - SN}}$	5.6671	8.2389	10.1284	11.1132	13.5773	15.2679
X_D/(μmol/L)	16.3	15.6	15.2	14.3	13.8	13.7

方法	计算公式	检出限/(μmol/L)
校准曲线法	${X_D} = \frac{{\delta (\nu , \alpha , \beta ) \cdot {S_{y/x}}}}{b} \cdot \sqrt {1 + \frac{1}{{I \times J}} + \frac{{{{\bar x}^2}}}{{J\sum\nolimits_{i = 1}^I {{{({x_i} - \bar x)}^2}} }}} $	14.4
校准方程参数法	${X_D} = 3{S_{y/x}}/b$	10.4
数学模型法	${X_D} = ({k_1} + {k_2}) \cdot \bar s/b$	14.1
信噪比回归曲线法	${X_D} = 3{S_{y/x - SN}}/{b_{SN}}$	14.3
EPA法	${X_D} = {t_{(1 - \alpha , {v_1} + {v_2})}}{S_{{\rm{pooled}}}}$	6.2

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