Despite having achieved a consensus on the copper PDE (10 µg/day) for oral preparations, major pharmacopeias (ChP, USP, EP, JP) lack uniformity in their recommended analytical protocols. For instance, a conflict exists between USP < 233 > , which designates ICP-based methods as primary, and EP Chapter 2.4.20, which accepts both AAS and ICP techniques. This lack of a unified standard thereby constitutes a key source of inter-laboratory discrepancies, particularly for concentrations near the critical 10 mg/kg compliance threshold. Pharmacopeial copper quantification near regulatory thresholds (e.g., 10 mg/kg) is challenged by method conflicts: high-sensitivity techniques (e.g., ICP-MS) amplify calibration uncertainties, while traditional methods risk false compliance. This study establishes a Linearity-Sensitivity-Uncertainty (LSU) framework to quantify slope-modulated error propagation and resolve these conflicts. Copper was quantified in Paeoniae Radix Alba certified reference material (CRM 9.60 ± 0.62 mg/kg) using microwave, wet, and dry digestion coupled with flame atomic absorption spectrometry (FAAS) or inductively coupled plasma mass spectrometry (ICP-MS). Method performance (accuracy, precision, LOD, LOQ) and measurement uncertainty (following GUM/EURACHEM) were evaluated. The LSU framework introduced the error amplification factor (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$K=\frac{1}{b}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> </mrow> </math></EquationSource> </InlineEquation>) to quantify slope-modulated uncertainty. Microwave digestion FAAS achieved optimal accuracy at 10 mg/kg (bias: -0.03 mg/kg; expanded uncertainty <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$U=0.35$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <mo>=</mo> <mn>0.35</mn> </mrow> </math></EquationSource> </InlineEquation> mg/kg, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$k=2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>). ICP-MS, despite 1000-fold lower LOD (0.0005 mg/kg), exhibited 1.93-fold higher error amplification (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">${K}_{ICP-MS}=13.49$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mrow> <mi>I</mi> <mi>C</mi> <mi>P</mi> <mo>-</mo> <mi>M</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mn>13.49</mn> </mrow> </math></EquationSource> </InlineEquation> vs.<InlineEquation ID="IEq5"> <EquationSource Format="TEX">${K}_{FAAS}=7.00$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mrow> <mi mathvariant="italic">FAAS</mi> </mrow> </msub> <mo>=</mo> <mn>7.00</mn> </mrow> </math></EquationSource> </InlineEquation>) due to its lower slope (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">${b}_{ICP-MS}=0.0741$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>b</mi> <mrow> <mi>I</mi> <mi>C</mi> <mi>P</mi> <mo>-</mo> <mi>M</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mn>0.0741</mn> </mrow> </math></EquationSource> </InlineEquation> vs.<InlineEquation ID="IEq7"> <EquationSource Format="TEX">${b}_{FAAS}=0.14288$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>b</mi> <mrow> <mi mathvariant="italic">FAAS</mi> </mrow> </msub> <mo>=</mo> <mn>0.14288</mn> </mrow> </math></EquationSource> </InlineEquation>), elevating U to 3.70 mg/kg. Linearity-derived uncertainty dominated (> 98 %) the uncertainty budget. Dry ashing degraded slope integrity (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$b$</EquationSource> <EquationSource Format="MATHML"><math> <mi>b</mi> </math></EquationSource> </InlineEquation>↓5.5 %, RSD = 3.7 %), increasing U by 29 % and causing false-positive exceedance (10.05 > 10.00 mg/kg). Conclusion: The LSU framework reconciles sensitivity-reliability conflicts by quantifying slope-governed uncertainty propagation (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">$U\propto =\frac{1}{b}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <mo>∝</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> </mrow> </math></EquationSource> </InlineEquation>). It mandates slope-centric calibration, method-concentration zoning (FAAS for limits, ICP-MS for traces levels < 0.5 mg/kg), and slope stability criteria. This mechanistic approach reduced false-positive risk by 29 % (p < 0.01) compared to traditional methods, advancing pharmacopeial compliance testing standards.

Calibration slope-governed uncertainty framework resolves method conflicts in pharmacopeial copper compliance testing of paeoniae radix alba

期刊论文
发表日期：

2026年1月3日

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Yingjuan Gao

摘要

Despite having achieved a consensus on the copper PDE (10 µg/day) for oral preparations, major pharmacopeias (ChP, USP, EP, JP) lack uniformity in their recommended analytical protocols. For instance, a conflict exists between USP < 233 > , which designates ICP-based methods as primary, and EP Chapter 2.4.20, which accepts both AAS and ICP techniques. This lack of a unified standard thereby constitutes a key source of inter-laboratory discrepancies, particularly for concentrations near the critical 10 mg/kg compliance threshold. Pharmacopeial copper quantification near regulatory thresholds (e.g., 10 mg/kg) is challenged by method conflicts: high-sensitivity techniques (e.g., ICP-MS) amplify calibration uncertainties, while traditional methods risk false compliance. This study establishes a Linearity-Sensitivity-Uncertainty (LSU) framework to quantify slope-modulated error propagation and resolve these conflicts. Copper was quantified in Paeoniae Radix Alba certified reference material (CRM 9.60 ± 0.62 mg/kg) using microwave, wet, and dry digestion coupled with flame atomic absorption spectrometry (FAAS) or inductively coupled plasma mass spectrometry (ICP-MS). Method performance (accuracy, precision, LOD, LOQ) and measurement uncertainty (following GUM/EURACHEM) were evaluated. The LSU framework introduced the error amplification factor ( $K=\frac{1}{b}$ $K = \frac{1}{b}$ ) to quantify slope-modulated uncertainty. Microwave digestion FAAS achieved optimal accuracy at 10 mg/kg (bias: -0.03 mg/kg; expanded uncertainty $U=0.35$ $U = 0.35$ mg/kg, $k=2$ $k = 2$ ). ICP-MS, despite 1000-fold lower LOD (0.0005 mg/kg), exhibited 1.93-fold higher error amplification ( ${K}_{ICP-MS}=13.49$ $K_{I C P - M S} = 13.49$ vs. ${K}_{FAAS}=7.00$ $K_{FAAS} = 7.00$ ) due to its lower slope ( ${b}_{ICP-MS}=0.0741$ $b_{I C P - M S} = 0.0741$ vs. ${b}_{FAAS}=0.14288$ $b_{FAAS} = 0.14288$ ), elevating U to 3.70 mg/kg. Linearity-derived uncertainty dominated (> 98 %) the uncertainty budget. Dry ashing degraded slope integrity ( $b$ $b$ ↓5.5 %, RSD = 3.7 %), increasing U by 29 % and causing false-positive exceedance (10.05 > 10.00 mg/kg). Conclusion: The LSU framework reconciles sensitivity-reliability conflicts by quantifying slope-governed uncertainty propagation ( $U\propto =\frac{1}{b}$ $U \propto = \frac{1}{b}$ ). It mandates slope-centric calibration, method-concentration zoning (FAAS for limits, ICP-MS for traces levels < 0.5 mg/kg), and slope stability criteria. This mechanistic approach reduced false-positive risk by 29 % (p < 0.01) compared to traditional methods, advancing pharmacopeial compliance testing standards.