A comparison of quantitative nuclear magnetic resonance methods: internal, external, and electronic referencing

Research Article

Received: 24 May 2013 Revised: 5 August 2013 Accepted: 8 August 2013 Published online in Wiley Online Library

(wileyonlinelibrary.com) DOI 10.1002/mrc.4004

A comparison of quantitative nuclear magneticresonance methods: internal, external, andelectronic referencingChristopher H. Cullen, G. Joseph Ray and Christina M. Szabo*

The performance of three quantitative NMR methods was compared in terms of short-term and long-term precision andaccuracy, robustness, linear range, and general applicability. The Internal Reference method employs a reference material
co-dissolved with sample; the External Reference method employs a reference material contained in a separate solution;and the third method, known as Electronic REference To access In vivo Concentrations (ERETIC), employs an externallycalibrated digital reference peak. The Internal Reference method results were the most precise and remained stable within0.1% for at least 4weeks. The results from the External Reference and ERETIC methods were practically equivalent to eachother during this time. These methods exhibited small differences relative to the standard set by the Internal Referencemethod and slightly lower precision, establishing them as practical alternatives to the Internal Reference method. In contrastto the Internal Reference method, the External Reference and ERETIC methods possess several advantages that address peakoverlap, flexibility of calibration, and duration of applicability. The study was designed such that each spectrum contained theinformation needed to compare the three methods while all other variables were kept constant. Applicability of pulse widthcompensation is addressed. ERETIC software compensation and minor adjustments to 90° pulse width were concluded to beunnecessary for this system. Although each of the methods was applied here to specifically calculate and compare chemicalpurity values, this evaluation applies generally to absolute quantitation by NMR. Copyright © 2013 John Wiley & Sons, Ltd.
Supporting information may be found in the online version of this article.

Keywords: NMR; 1H; quantitation; purity determination; ERETIC; internal reference; external reference

* Correspondence to: Christina M. Szabo, Baxter Healthcare Corporation, 25212W. Illinois Rt. 120, Round Lake, IL, USA. E-mail: [email protected]

Baxter Healthcare Corporation, 25212 W. Illinois Rt. 120, Round Lake, IL, USA

Introduction

The importance of the ability to accurately, precisely, and easilymeasure quantities and concentrations of chemicals cannot be un-derstated for any empirical field of chemistry. Chemical referencestandards, which are materials of known chemical purity or activitywithin a matrix, are the foundation of most measurements of thesequantities regardless of the analytical method used for measure-ment. Prior to quantifying chemicals, such as the components ina drug formulation, impurities, or extractables and leachables fromdrug containers, often a response factor must be calibrated for ananalyte and the particular method and sample matrix. Theresponse factor is usually calibrated using a standard of the analyteof interest. Quantitative NMR spectroscopy is a useful method todetermine the purity and stability of many of these referencestandards because the linear relationship between the concentra-tion of material analyzed and its corresponding NMR peak areamakes NMR an inherently quantitative technique.

There are two basic kinds of quantitation by NMR: relative andabsolute. Relative quantitation involves measurement of therelative molar concentration of each species. Absolute quantitationis the direct measurement of the actual amount of an analyte,independent of other components contained in that sample. Themeasurement of chemical purity is a common application ofabsolute quantitation, as will be discussed here. There are two basicNMR methods for absolute quantitation based on whether aninternal or external reference standard is used to calibrate theNMR signal. An internal reference method relies on the consistent

Magn. Reson. Chem. (2013)

NMR peak area response for all of the species measured within aspectrum. An external method relies on the consistent NMR peakarea response across all of the spectra obtained. Presented hereare results from a comparison of three absolute quantitative NMRmethods – the Internal Reference method, the External Referencemethod, and the Electronic REference To access In vivo Concentra-tions (ERETIC)[1] method – in their application toward chemicalpurity measurement in solutions using 1H NMR.

The Internal Reference method employs a qualified chemicalreference standard dissolved in the sample solution. It producesaccurate and precise results, so it has been widely used.[2–6] Inthis method, an NMR spectrum is obtained of a solution preparedwith known masses of both the sample and reference materials.From the masses and the measured peak areas, the amount ofanalyte in the solution is determined. A drawback of this methodis that internal reference standard must be weighed into eachsample solution; a step that consumes time, effort, and material,and it is the largest source of error in this quantitative NMRmethod.[7] Additionally, this method requires an up-front invest-ment in method development in order to find a functionalcombination of analyte, solvent, and internal standard for whichthere is no chemical interaction or overlap of the NMR peaks.Chemical reactions are not the only concern in setting up the

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Table 1. Equipment tolerance

Equipment Tolerance

NMR tube ±0.25% max volume variation

Volumetric flask, 1ml ±0.6% (2σ)




Analytical balance, 5-place ±0.1% (3σ)

C. H. Cullen, G. J. Ray and C. M. Szabo

solvent/reference system. Simple chemical exchange betweenwater in the solvent and one of the materials may produce a peakwhose chemical shift, breadth, or both, can cause peak overlap.The use of an external reference method alleviates some of

the drawbacks of the Internal Reference method because thereference standard and the sample are prepared as separatesolutions. There are three variations of this method. Onevariation uses a reference standard solution contained in acoaxial tube that is inserted into an NMR tube containingthe sample test solution. The drawback of this method is thatthe reference standard peak appears within the spectrum ofthe sample, which includes peaks from the analyte as wellas impurities, creating a potential for peak overlap. The othermore classic variation, which is used in this work, circumventsthis drawback by acquiring spectra of separate solutions ofthe reference standard and sample. In this method, theabsolute integral of a reference standard peak is obtained tocalibrate the instrument response under a given set ofconditions, and subsequently, the absolute integrals ofanalyte test peaks are quantified on the basis of thiscalibration. Thus, no reference peak is introduced into theNMR spectrum of the sample. Consequently, the advantagesover the Internal Reference method are no peak overlap, nochemical reactions, and no need to develop a compatible sol-vent/analyte/standard combination. Another advantage is thata single calibration may be reused for multiple samples over along period, provided system suitability is demonstrated onthe day of data acquisition. Finally, reference materials aregenerally symmetric small molecules whose peaks tend tohave longer spin–lattice relaxation times (T1) than those ofthe analyte and require longer interpulse delays duringsignal averaging. Use of an external reference allows morerapid data collection from the test sample solution becausethe calibration spectrum only needs to be acquired once.However, while internal reference methods depend onmasses, external reference methods depend on concentra-tions and thus have an additional error contribution fromvolumetric measurements of the solvents used to preparethe test solutions.The third variation of an external reference method, ERETIC,

was developed for quantitation within a magnetic resonanceimaging slice obtained in magnetic resonance spectroscopy.[1]

Originally, the execution of ERETIC involved insertion of anexternally calibrated RF electronic signal through thehardware into the observed FID during acquisition. DuringFourier transformation of the FID, the signal was convertedinto a peak whose chemical shift within the spectrum waspre-determined by the operator. This peak was then appliedas a reference in the spectra of separate sample solutions.In this study, ERETIC consisted of a digitally generated

Gaussian peak, which was inserted into the spectrum of asample by the software after processing the FID. Because itproduces an artificial quantitative reference with an opera-tor-determined chemical shift, the ERETIC technique sharesthe External Reference method’s advantages over the use ofinternal references. The need to even include an artificialreference peak in the spectrum has been challenged in theliterature,[8–10] although a case has also been made that it isconvenient for record keeping.[8,10] The advantage of ERETIC overthe External Reference method is that the ERETIC-calibratedanalyte integral corresponds directly to the 1H molar concentrationof the analyte.

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Experimental Section

Equipment

A Bruker Avance I NMR spectrometer operating at 400MHz 1Hfrequency (Bruker Biospin Corporation, Billerica, MA) was usedfor most experiments. It was equipped with a 5-mm broadbandinverse probe, Bruker Topspin 2.1 software, and the digital ERETICsoftware module that was available for Topspin 2.1. The temper-ature was stable to within ±0.1 °C.

A Bruker Avance III NMR spectrometer operating at 600MHz 1Hfrequency was used to assess instrument-to-instrument rugged-ness. It was equipped with a 5-mm dual C/H cryoprobe andBruker Topspin 3.0 software. The temperature was stable towithin ±0.1 °C.

Solutions were contained in Wilmad 535-pp-cons 5-mm NMRtubes (Wilmad-LabGlass, Vineland, NJ). These tubes come with aconstriction near the top to facilitate the flame sealing that wascarried out with all the samples in this study. All volumetric flasksand pipettes used for sample preparation were class A. Allweights were recorded with a 5-place Sartorius analyticalbalance. The tolerances of the solution preparation equipmentare given in Table 1.

Materials

Chemicals used in this study were analytical standard grade1,1,2,2-tetrachloroethane (TCE; purchased from Fluka), 99+%cyclooctane (purchased from Aldrich), and 99.8% chloroform-d(CDCl3) and 99.9% deuterated dimethyl sulfoxide (DMSO-d6)(both purchased from Cambridge Isotope Laboratories, Inc). Thetest system consisted of the analyte, cyclooctane, the referencestandard, TCE, and the solvent – a mixture of 5.7 g of DMSO-d6in 200ml of CDCl3. DMSO-d6 had been added to shift a smallpeak due to trace water in the system away from the cyclooctanepeak. The TCE and cyclooctane were selected because they gavesimple, well-resolved NMR spectra and because they were notvolatile or prone to coating out in the headspace of the NMRtube because they are high-boiling liquids.

Test system

The three quantitative NMR methods could be directly comparedbecause of the nature of the test system. Specifically, solutionswere prepared with known masses of both reference materialand test material and co-dissolved in solvent, which satisfiedthe preparation requirements for the Internal Reference method.These amounts had also been weighed directly into volumetricflasks before dilution to the desired concentration, so theconcentrations of both materials were also known, satisfyingthe preparation requirements for both the External Reference

3 John Wiley & Sons, Ltd. Magn. Reson. Chem. (2013)

Comparison of quantitative NMR methods

and ERETIC methods. Because the masses of the reference andtest material were known, the spectrum acquired for each solu-tion contained the information needed to compare all threemethods, while all experimental conditions were kept constant.

This model system was chosen to give well-resolved peakswith high signal-to-noise (S/N) ratios in order to provide abenchmark for the performance of each of the three methodsunder optimum conditions. The system does not realistically rep-resent the frequently encountered conditions such as low S/Nratios and overlapped peaks that would degrade the maximumaccuracy and precision of the measurement.

The attributes of the methods that were studied were theaccuracy and short-term and long-term precision, the linearrange, operator-to-operator ruggedness, general applicability,and stability of the methods. For this purpose, two sets ofsolutions were prepared: one to assess the repeatability of chem-ical purity measurement over time and the other to assess the lin-earity of the methods over a large range of analyte concentration.

Repeatability solutions

A set of ten test solutions was prepared to evaluate the precisionand accuracy of purity measurement, stability over time, and op-erator-to-operator ruggedness. Each solution was prepared with50mg each of TCE and cyclooctane, each from the same lot,weighed into a 2-ml volumetric flask.

For both linearity and repeatability solution preparation, firstthe reference and sample were weighed into a vial, and then theywere diluted to a known volume and thoroughly mixed. Allweights were recorded from a 5-place analytical balance. To en-sure that the 1H coil was filled with solution, 525μl aliquots ofall solutions were transferred to 5-mm NMR tubes. Then, thetubes were immersed in liquid nitrogen, evacuated, and flamesealed.

Linearity solutions

In our experience, we have found that solutions prepared with50mg each of standard and sample in approximately 1ml ofsolvent have often provided sample-to-sample relative standarddeviation (RSD) ranging from 0.0% to 0.3% in triplicate puritydeterminations using the Internal Reference method. The testsolutions consisted of duplicate sets whose concentrationscorresponded to each of the following amounts, in mg/mg, ofTCE/cyclooctane in 1ml of CDCl3: 50/50, 25/25, 10/10, 5/5, 2/2,and 1/1. In order to reduce the gravimetric and volumetric errorsrelative to 1ml preparations without requiring impracticalamounts of material and solvent, twice the weights and 2-mlvolumetric flasks were used. Additionally, serial dilutions wereperformed on the 1/1mg/mg solutions to make 100/100, 10/10,and 1/1μg/μg solutions. One solution was prepared at75/75mg/mg to represent a higher concentration than a typicalmaximum of 50/50mg. The 10, 5, 2, and 1mg/ml solutions wereprepared with 5ml and correspondingly increased targetweights. Serial dilutions were made by diluting 1ml of 1, 0.1,and 0.01mg/ml stock solutions in 10ml flasks.

Data acquisition

Proton spin–lattice relaxation times, T1s, were measured via aninversion recovery pulse sequence. All data were acquired withthe same acquisition parameters, except where noted, keeping

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the absolute integration scale constant throughout the study.The 90° pulse width was measured from the first-run sample eachweek using a 360° pulse width null point divided by four.

The pulse sequence employed was delay–pulse–acquire,observing protons, with GARP 13C broadband decoupling duringacquisition to remove 13C satellites. The decoupler frequencycorresponded to a 13C chemical shift of 45 ppm. A 90° 1H pulsewas used, and the interpulse delay was at least seven times thelongest measured T1, in order to recover at least 99.9% of the fullmagnetization.[11–13] Eight scans were acquired on static samplesat a probe temperature of 25.0 ± 0.1 °C. Samples were allowed toequilibrate for several minutes before gradient shimming andcareful tuning and matching of the probe coil for each solution.The number of points acquired was 64 k for a spectral width of4800Hz and an acquisition time of about 3 s.

Data processing

The data were zero filled once from 64 to 128 k points beforeFourier transformation in order to provide sufficient peakdefinition to give reliable integrals. A Lorentzian line broadeningof 0.3 Hz was applied to all spectra, and the baselines wereflattened using Bruker’s automatic baseline correction, whichapplied a standard fifth-order polynomial correction. Integralcurvature was carefully adjusted to remove baseline slope andbias effects, and because of the high S/N of this system, the peakintegral boundaries were easily set where the integrals effectivelymerged with the baseline. Both relative and absolute integralareas were recorded for the reference and analyte peaks fromeach solution.

Repeatability

During week 1, the ten separate repeatability test solutions wererun within 1 day. The same solutions were rerun approximatelyweekly for a month. Data for the final time point was acquiredat 7months.

Linear range

The linearity test solutions, 75–1mg/ml, were all run within a dayunder the same conditions. Because the S/N ratio of the peakswould have been too small at the lowest concentrations toprovide acceptable precision, the number of scans was increasedfrom 8 to 160, 1000, and 4000 for concentrations of 0.1, 0.01, and0.001mg/ml, respectively, which required acquisition of data tobe extended over several days. The increased number of scansfor these solutions was mathematically compensated for later inthe data processing stage.

Ruggedness, operator-to-operator

One week’s repeatability data were acquired and then processedby an operator using all three quantitative methods. It was thenseparately acquired by another operator, who processed dataaccording to the Internal Reference and External Referencemethods.

Ruggedness, instrument-to-instrument

One week’s repeatability data were acquired on two separate NMRinstruments: one operating at 400MHz 1H frequency with aninverse broadband probe and the other operating at 600MHz with

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a dual carbon–hydrogen cryoprobe. The data were processed suchthat the accuracy and precision of all three quantitative methodscould be compared.

Results and Discussion

Purity calculations

Cyclooctane purity results determined by the three methods ofquantitation were compared.

General purity calculation

Weight% purity is generally defined as

Wt%purity ¼ mA=mSð Þ � 100% (1)

where mA is the mass of the analyte in the sample and mS is thetotal mass of the sample with contributions from the analyte plusany contaminants that may be present in the sample.NMR purity values are generally calculated from Eqn (2)

Wt%purity ¼ PRef � IA=IRefð Þ MA=MRefð Þ NRef=NAð Þ CRef=CSð Þ (2)

using the number of protons (N) and integrals (I) represented byboth analyte and reference peaks, as well as the wt% purity of thereference standard (PRef), the molar masses, (M), and concentra-tions (C) in mg/ml, of the sample and reference material.

Internal Reference method calculations

When an internal reference is used, the ratio of the concentra-tions of the two materials is equivalent to the ratio of theirmasses, because they are both dissolved in the same volume,and Eqn (2) becomes Eqn (3). Using the Internal Referencemethod, the purity values were calculated according to Eqn (3).

Wt%purity ¼ PRef � IA=IRefð Þ MA=MRefð Þ NRef=NAð Þ mRef=mSð Þ (3)

ERETIC method calculations

The calibration of the ERETIC peak is made using a singlereference sample. In this work, the reference peak in thespectrum of the first-run test solution from the first week wasused as the calibration reference signal. During the calibrationprocess, the following values were entered: the reference peakintegral range, the molar concentration of the reference, andthe number of nuclei that the peak represented (2 equiv protonsin the case of TCE). The software then applied the calibration tothe reference peak integral in units of molar proton concentra-tion per integral unit, and it generated a calibrated ERETIC peakat the operator selected chemical shift. Generation of the ERETICpeak in the calibration spectrum is optional and not necessary toestablish the calibration.Using a test spectrum in which the analyte peak has been

integrated, an ERETIC command is executed that applies thecalibration to all integrated peaks. Their integral value thendirectly represents the concentration of protons of theircorresponding species. From this value, the wt% purity ismeasured using Eqn (4).

Wt%purity ¼ IA;ERETIC � MA=NACS (4)

where IA,ERETIC is the analyte peak integral after application of theERETIC calibration, i.e. the calculated proton molar concentration


corresponding to that peak, and CS is the concentration ofsample in terms of mS per unit volume.

External Reference method calculations

As with ERETIC, the External Reference method’s calibration wasestablished from data obtained in the first week. However, thecalibration was not established from a reference peak in a singlesolution, but from an average response for the reference peaks inall ten reference solutions, <R>, where R is the ratio R, of 1H con-centration per absolute integral unit, and CRef is the concentra-tion of reference standard in terms of mRef per unit volume.

R ¼ PRef � NRef � CRefð Þ= IRef �MRefð Þ½ � (5)

The mode of integration most often used in NMR gives a‘relative’ integral that is usually normalized by the operator tothe number of protons in the functional group represented bythe peak. In contrast, the absolute integral is an exact representa-tion of the total signal intensity, which is a result of the sampleconcentration, probe sensitivity, and instrument parameters suchas pulse width, receiver gain, and number of scans. Absoluteintegration is intrinsic to every NMR spectrometer, and theprecision and accuracy of the absolute integral are dependenton the stability of the spectrometer’s electronics. In earlyattempts to use external referencing, it was reported that overallaccuracy was rarely better than ±5%,[14] and this may explain whylittle or no work on external referencing was reported for yearsafterward.[15] The probable cause for the large error in accuracywas presumably the relatively low stability of early spectrome-ters. Since then, the stability of NMR spectrometers has been en-hanced, which has led to an improvement in accuracy as well asprecision (RSD) benchmarks, as can be inferred from reports onthe performance of ERETIC.[16–19]

The calibration determined from the reference peaks usingEqn (5) was applied to the analyte peak absolute integrals,and the corresponding analyte concentrations were derived.These concentrations were then used to calculate wt% purityusing Eqn (6).

Wt%purity ¼< R > � IAMAð Þ= NACSð Þ (6)

The wt% purity was calculated for each of the three techniquesover 4weeks, noting the difference of each method’s resultsrelative to the average of the results established by the InternalReference method on the first week. The sample-to-sampleprecision in a given week as well as the week-to-week precisionfor a given sample was also determined.

Precision and accuracy

The results for the Internal Reference method are shown in Fig. 1,which is a plot of purity values obtained in ten solutions weekly,over a 4-week period, and it shows that the relative week-to-weekprecision is better than the relative sample-to-sample precision.The average week-to-week RSD is 0.09%, while the averagesample-to-sample RSD is 0.33%. The fact that the week-to-weekprecision is better than the sample-to-sample precision indicatesthat most of the error of the method comes from weighing thesample and the reference material. The difference of the averagepurity value of all ten samples measured on all 4weeks – relativeto the average purity value measured for week 1 – ranged from0.00 to �0.12wt%. Another time point was added after 6months



to test the stability over a longer period and the difference was only�0.2% relative to the average value for week 1, while the sample-to-sample RSD remained 0.33%.

Figure 2 shows the purity as determined by the ExternalReference method, for which both the average week-to-weekRSD (0.34%) and sample-to-sample RSD (0.67%) are greater thanthose observed for the Internal Reference method. In practice,the precision is still acceptable for routine use. Its range of weeklydifferences over 4weeks relative to the average given by theInternal Reference method for week 1 was 0.0 to �0.3%, andthe calibration that was made in week 1 was valid for the initial4weeks of this study. After 6months, the difference of theaverage measurement was �1.3%, while the sample-to-sampleRSD increased to 0.75%, so the calibration and precision hadslipped significantly from the end of the first month to the sixthmonth. The calibration was no longer usable at levels of a fractionof a wt% for precision and accuracy. However, for at least amonth, the precision and accuracy were adequate forquantitative measurement for routine use, which indicates thatthe spectrometer was very stable over this time frame.

Figure 3 shows the results for the ERETIC method, which hadbeen calibrated using the first solution from the first week.Similar to the External Method, the average sample-to-sampleRSD for the ERETIC method results was 0.65%. However, fromweek-to-week, the RSD was 1.5%, and from the pattern in Fig. 3,it was evident that the variation was not random. Thus, thedifferences measured were due to a bias of the average purityvalue, which ranged from �1.3 to �4.9wt%, with the largestchange of ~4wt% occurring between week 1 and week 2.

Figure 1. Purity of cyclooctane in ten solutions over 6months using the Intshown as a dotted line as the gauge for comparison of difference.

Figure 2. Purity of cyclooctane in ten solutions over 6months using the Extshown as a dotted line as the gauge for comparison of difference.


An inverse correlation was noted between the magnitude ofthis variation and the pulse width, which had been re-calibratedweekly. The software incorporates a feature, PULCON,[20] thatcompensates for a change in the 90° pulse width from the valueused during calibration. This pulse compensation has been foundto improve the accuracy of quantification of a variety of analytesin aqueous solutions.[10,15,20] PULCON, which is based on thePrinciple of Reciprocity,[21] was meant to compensate peakintensities for losses in coil sensitivity due to sample-to-samplechanges in dielectric, for example, with ionic strength. Accordingto this principle, probe sensitivity is inversely proportional to the90° pulse, for a given pulse power. The signal loss of the analyte(A) relative to the reference (Ref) is proportional to the ratio 90°

Ref/90°A. To compensate for this signal loss, the inverse of thisratio, 90°A/90°Ref, is applied. In this study, the 90° pulses weredetermined as one quarter of the null point of the 360° pulse.[20]

We had made minor adjustments of tenths of a microsecond tothe pulse width when we calibrated the 90° pulse width in eachof the initial 4weeks of this study. Correcting for the automaticcompensation for these adjustments gave the results in Fig. 4,where a marked improvement in precision was observed, givinga week-to-week RSD of 0.35% while the sample-to-sample RSDremained 0.65%. The bias of the average purity value thenranged from �1.3 to �1.6%.

The need for a comparison of external referencing with andwithout PULCON has been previously proposed.[22] Our compar-ison indicates that the PULCON compensation for small pulsewidth adjustments, when applied to non-ionic solutions withsample concentrations up to about 100mg/ml, is detrimental.

ernal Reference method. The average of the values from the first week is

ernal Reference method. The average of the values from the first week is


Figure 3. Purity of cyclooctane in ten solutions over 4weeks using the ERETIC method, calibrated to the first solution in the set. The average of thevalues from the first week is shown as a dotted line as the gauge for comparison of difference.

Figure 4. ERETIC results after correction for PULCON compensation. The average of the values from the first week is shown as a dotted line as thegauge for comparison of difference.


Because the peak amplitude is proportional to the sine of the tipangle, a 90° pulse would have to be mis-set by several percentbefore a loss of 0.1% of the peak amplitude would beregistered.[15] Therefore, once a calibration is established, it isbest to avoid 90° pulse width adjustments of less than a fewpercent, relative. The precision of the week-to-week ERETIC dataprofile after removing PULCON compensation, as well as theprecision of the data from the External Method, providesevidence that the system electronics were quite stable over theinitial 4weeks.Although the precision of the ERETIC data was improved

without the PULCON compensation, a negative bias remained.This bias appeared because the ERETIC calibration for all of thedata had been made to a single spectrum – the spectrum ofthe first sample from week 1 – for lack of a more appropriatesample. Indeed, previous work had suggested an improvementin accuracy by calibrating ERETIC against multiple samples.[23] Inorder to improve the ERETIC calibration, we again used theaverage reference signal response factor, <R>, determined fromthe week 1 External Method data. ERETIC was recalibrated usingthe spectrum that had an R value that was closest to <R>. Theresults of this recalibration are shown in Fig. 5, where the profilepractically matched that of the External method (Fig. 2) and theweek-to-week and sample-to-sample RSDs, 0.35% and 0.65%,respectively, were practically identical to the results obtainedwith the External Method. The two sources of bias were removed,and the remaining difference in average purity values, relative to


week 1 of the Internal Referencemethod, ranged from�0.2 to�0.5%,values that were approximately one order of magnitude greaterprior to removal of PULCON and recalibration. The ERETIC methodwas not evaluated at 6months.

Note that ERETIC could have been calibrated to the exactaverage response of the reference data from week 1 insteadof using the nearest-matching sample, but this requires addi-tional steps given that ERETIC is designed to work on a singlespectrum. If replicate preparations of the reference standardsolutions are used to improve the accuracy, then individualR values and <R> are calculated independent of ERETIC soft-ware according to Eqn (5). To apply this averaged calibrationto an arbitrarily selected reference spectrum, the analyst isprompted by the ERETIC software to enter the correspondingconcentration of the analyte. That concentration of theanalyte needs to be adjusted, Cref,adj, according to Eqn (7) sothat the result of the ERETIC calibration corresponds to theaverage response.

Cref;adj ¼ Cref;1 � < R > =R1

¼ I1� < R >(7)

For example, if the first test solution gave a response, R1, thatwas lower than <R>, then the analyte concentration would beadjusted by the factor <R>/R1 such that Cref,adj would be


Figure 5. ERETIC results after recalibration to an ‘average’ value approximated by sample 8. The average of the values from the first week is shown as adotted line as the gauge for comparison of difference.


proportionally higher to yield the effective R, Reff. In this manner, Reffis equal to the response calibrated to the exact average (Eqn (8)).

Reff ¼ Cref;1 � < R > =R1� �

=Iabs;1 ¼< R > (8)

In contrast to this mathematical adjustment for the calibrationof ERETIC, such a calibration using an average response frommultiple reference standard solutions is inherently included inthe External Reference method.

Error analysis

Equations (3), (4), and (6), which were used to calculate purity forthe three methods, can all be expressed in the form

Wt%purity ¼ PRef � NRefmRef=VRef IRefMRefð Þf g VSIAMA=NAmSð Þ(9)

where VRef and VS are the volumes in which the reference andsample materials are dissolved, respectively. This expression isapplicable to the three methods because (A) for the Internalmethod, VRef = VS; (B) for the External method, all of the‘reference’ variables are directly integrated into the calibrationfactor (in brackets); and (C) for the ERETIC method, all of thesevariables are implicit in the calibrated analyte integral, IA.

Of the terms in the equation, the ones that vary are theintegrals, masses, and volumes, each of which carries anassociated error of measurement. The wt% purity calculated byall three methods includes errors from measurement of theintegrals and weights of both materials. However, because oftheir dependence on material concentration, the externalmethods also include errors from volumetric measurementsduring preparation of both the reference and sample solutions.The external methods are also dependent on the variability ofthe inner diameter (i.d.) of the NMR tubes, which causes variabil-ity in the amount of material contained within the active probecoil volume and affects the peak integrals. Therefore, it isimportant to select high quality NMR tubes with a tight i.d.tolerance. Because the Internal and both external referencemethods share errors from measuring masses and integrals, thedifferences in error between the Internal and external methodsmay be attributed entirely to volumetric measurement andNMR tube i.d. variation in the external methods (Table 1). Thetolerance for flasks represents a 95% confidence interval, i.e.,


the percent relative standard error is equal to one half of thetolerance. An assumption is made that the NMR tube maximumvolume error of ±0.25% corresponds to ±2 standard deviations.Thus, the relative standard error of the 2-ml volumetric flask is0.375%, and the relative standard error of the NMR tube is ~0.1%.This compares with the 0.3% difference in sample-to-sampleprecision seen in the repeatability evaluation between the Inter-nal method and the External and ERETIC methods. By weighingthe solvent instead of measuring the volume, the contributionof error from the volumetric flask can be replaced by smallergravimetric errors.

In order to directly compare the three quantitative NMRmethods, while keeping all other variables constant, test solutionswere prepared so that both the reference and test material wereco-dissolved in solvent as described in the Test System section. Inpractice, the external reference standards would be prepared in asolution that is separate from that of the test material. Therefore,the error from the additional volume measurement for the twoseparate solutions is not taken into account in this study, and theexternal reference methods would theoretically have results withhigher %RSDs.

Ruggedness, operator-to-operator

Data were acquired and processed according to the Internal Refer-ence and External Reference methods. The purities measured byboth operators were comparable (Supporting information Fig. S1).The second operator’s measurements using the Internal Referencemethod and External Referencemethodwere higher on average by0.1% and lower by 0.3%, respectively, than those of the firstoperator. These differences are within a fraction of the respectivesample-to-sample standard deviations for the two methods.

Linear range

For each method, the average of duplicate purity measurementswas plotted versus average concentration (Fig. 6). The curveswere evaluated to establish a linear range, bounded by the pointat which the curve deviated past a relative error limit of 2%. Thislimit was set relative to the average wt% purity established athigh concentration. All methods were essentially linear from 75to 0.1mg/ml, except the Internal Method, which was linear onlyto 1mg/ml. At lower concentrations, spectroscopic imprecisionoutweighs imprecision of sample preparation, and overlapping


Figure 6. Linear range of the three methods. Duplicate solutions were analyzed at each concentration, except 75mg/ml, for which one solution wasanalyzed. The average measured purity for each concentration is shown. The boundaries of linearity are defined by the average purity, as established bythe concentrated solutions, and ±2% limits around this average.

Table 2. Comparison of the three quantitative NMR methods

Method attribute Internal External ERETIC

Accuracy (max difference relative to first week Internal method) �0.1% �0.3% �0.5%

Precision: sample–sample 0.3% 0.7% 0.6%

Precision: week–week (for given sample) 0.1% 0.3% 0.3%

Linearity 75 to <1mg/ml

Chemical interactions Yes No No

Peak overlap Yes No No

Direct measurement of [1H] No No Yes

Single calibration for multiple samples No Yes Yes

Ease of calibration No Yes Yes/No*

* Calibration with multiple replicates of standards to improve accuracy is not inherent.


peaks from the trace organic contaminants from the solvent/glassware begin to contribute significantly toward the measuredanalyte peak area. The amplification of spectroscopic error at lowconcentration applies to both peaks for the Internal Referencemethod but only to the analyte peak for the external methods.

General applicability

For the Internal Reference method, the reference peak has a fixedchemical shift. The shortcoming of the Internal Referencemethod is that the reference peak may overlap an impurity oranalyte peak in the sample, degrading the method’s quantitativeperformance. The peak positions in the External Referencemethod are immaterial. The ERETIC signal can be placed atdifferent positions in the spectrum, and its area is reproducibleto five significant figures (data not shown).A second shortcoming of the Internal Reference method is that

the standard must be co-dissolved with each sample, while bothexternal methods require a single calibration for analysis ofmultiple samples. External calibrations were determined to besuitable for high precision measurements (~0.3% RSD) for at least1month.This evaluation showed that the External Reference and ERETIC

methods are comparable in all respects and have a broader

wileyonlinelibrary.com/journal/mrc Copyright © 2013 John Wiley & Sons, Ltd. Magn. Reson. Chem. (2013

general applicability when compared with the Internal Referencemethod. The External Reference method can be convenientlycalibrated to an average of multiple reference standard solutionpreparations. These results are summarized in Table 2.

Conclusions

Although the Internal Reference method performed the bestaccording to the attributes described in Table 2, both externalreference methods yielded results that were only slightly lessprecise and accurate. The demonstrated precision of the ERETICresults is better than what has been previously reported usinganalog versions of ERETIC on less concentrated, more realisticsample matrices. The ERETIC and External Reference methodswere found to be practical alternatives to the classical InternalReference method with competitive precision and accuracy,and they proved to be applicable to a larger range of concentra-tions and a larger number of samples over a longer period – atleast a month in our case for precision on the order of a fractionof a percent. This is indicative of the stability of currentspectrometers. The results of the present work can be used toestablish a statistically suitable number of solutions againstwhich to calibrate.

)


Acknowledgements

We would like to thank Drs Amy Freund and Eric Johnson fromBruker Biospin Corporation for their helpful discussions and JerryPhillips at Baxter Healthcare for the advice on statistical analysis.

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Documents

A comparison of quantitative nuclear magnetic resonance methods: internal, external, and electronic referencing