1 0 3 2 LCGC HORTH AMERICA VOLUME 26 NUMBESIO OaOBER200a wwwxhroma tograp hyan I i ne.cam

Review and Optimization of Linearityand Precision in QuantitativeHPLC-ELSD with Chemometrics

Wayne O. Aruda*, Steven^ and Ira S. Krull§

*Agrenetics; Wilmington, MA.

tStatistical Outsourcing Services;OIney. MD

§Northeastern University; Boston, MA

Please direct correspondence foaruda@3grer)etics.com

Recent improvements in ELSD instrumentation and a better understandingof the limitations and advantages of this detection method areincreasing its popularity, especially for the analysis of molecules lackingchromophores and as an economical surrogate mass spectrometrydetector during method development. However, ELSD instrument settingsmust be appropriate for the physicochemical properties of the analyte andanalyte-specific standard. Also, the nonlinear response of this detertionmethod in gradient elution requires careful calibration and properchemometrics to obtain reliable quantitation.

H igh performance liquid chro-matography (HPLC) with evapo-rative light scattering detection

(ELSD) continues to grow in popularity asa "quasi-universal" detector as shown inTable I (1-88 please see the complete cablein the online version of this article atht tp: / /chromarographyonline.f ind 'pharma.com/lcgc/issue/issueDetail.jsp?id=15886). Improvements in ELSD instru-ment design, including low-temperatureevaporation, have been commercializedrecently (40). Potential improvementsthat are currently patent applications(39,41,52) or laboratory experiments (33),including condensation nucleation light-scattering prototypes (42), along with tech-niques such as volatile mobile phase addi-tives (9,28.32) and higher molecularweight perfluorinated ion-pairing reagents(25,61-68), can further enhance the sensi-tivity of ELSD. Two overviews of ELSDhave been published in LCGC (59,60) in2003 and 2004, and an excellent review(38) of 20 years of progress in ELSD up tomid-2005 has been published. A morerecent review, which includes a graph oftheincrease in ELSD publications versus time,also has been published (97), so our reviewof selected publications covering quantita-

tive HPLC-ELSD begins in late 2004.HPLC-ELSD is a simple, robust

technique. It is especially useful for ana-lytes without significant chromophores,or with mobile phases that have UVchromophores (43,51,79). It also hasbeen used as a surrogate mass spectrom-etry (MS) detector during methoddevelopment, albeit with lower sensitiv-ity. It is a mass flow sensitive detectionmethod — it responds to largeramounts (quantities) of analytes, and itgives a larger relative response the largerthe amount or mass of the analytepassing through the detector — ratherthan a concentration detection method,as is UV detection. QuantitativeHPLC-ELSD has been used recently tostudy analytes from dried leeches (44),fungi (13), and medicinal plants(7,14-16,18,22,26,27,29,45,48,49,88-92), human intestinal (28) and bron-choalveolar (2) fluids and humanbreast milk (72), as well as blood(12,57), bile acids (24), underivatizedamino acids (44,62), sugars (46,75),lipids (4,9,12,19,24,28,50,55,56,72,76,79),foods (3,4,50,55-56,76,79-87), antibi-otics (17,25,54,63-68), pharmaceuticalexcipients (9,11,20,21,47,58,70), sur-

1034 LCGC NORTH AMERO VOLUME 26 NUMBER 10 OaOBEB200B www.chromatograp hyo niine.com

factancs (73), detergents (74), nutritionalsupplements (19,30,61), polymers (6,69),and many "traditional" pharmaceuticalcompounds (1,53,57,77). However, ithas been unsuccessfiil with some combi-natorial chemical libraries (5.8,36) todate. As a vote of confidence in quanti-tative ELSD, in 2006, NIST (30) publishedtwo cross-validated quantitative HPLCmethods (LC-MS and HPLC-ELSD withisocratic elution) for the analysis of itsStandard Reference Material 3280,Biotin. Although the LC-MS methodwas far superior in terms of quantitativesensitivity (LOD, LOQ), both methodsproduced similar quantitative results.NIST concluded tbat either methodalone could be used potentially as a ref-erence method for the quantification ofbiotin in midrivitamin tablets.

Instrumental Advances andSample and MethodConsiderationsResponse factor and gradients: Anappealing characteristic of HPLC-ELSDis that, unlike UV detection (especially atlow wavelengths) with gradient elution,the baseline might not drift. Table Ishows that the majority of recent publi-cations employed gradient elution forHPLC-ELSD. However, the responsefactor for the anaiyte is not constantacross the gradient in ELSD. This is afact that might not be known by themajority of researchers who have pub-lished on quantitative HPLC-ELSDusing gradient elution. However, recentpublications (5,8,41,71) have empba-sized this limitation and some haveattempted to correct for tbis behaviorwith additional calibration curvesthrough the entire range of mobile phasecomposition (for example, 0-100% A).During a gradient, the response factorfor a constant amount of analyte canvary as much as 10 times in magnitude(71). Increasing the organic content ofthe mobile phase increases the transportefficiency of the nebulizer, allowing agreater number of particles to reach thedetection chamber, and also influencesthe particle size distribution of thedroplets. Furthermore, difFerent amountsof material can be delivered cither as amote concentrated solution or as a greatervolume ofthe same solution, so ELSDarea ratio is predicted to (and does)

O Í

o

. iT

4.5-14.0-3.5-3.0-2.5-2.0-1.5-1.0-

-1-0.5--1.0-1

•

1 2 3 4 5

LogX

Figure 1: Plot of log-log calibration curves with error bars on triplicates.

change with injection volume (66).Therefore, strictly relevant calibration isrequired to enable quantitative use ofELSD. Single calibrant detectionschemes require that all analytes bavesimilar response coefficients to those ofthe reference compound. Unless theanalyst can calibrate raw peak area ratiosby knowing the response coefficients ofeach compound, and not just a singlecalibrant, then significant errors inquantification will occur (8). Pfizer (4l)has an assigned patent application on "amethod and data processing apparatus"to calibrate ELSD and correct the datafor variations in the solvent concentra-tion during gradient elution. This limi-tation is not unique to ELSD, but alsohas been documented to occur withcharged aerosol detection (34), and onecan speculate that it might occur inother techniques using aerosol forma-tion, including electrospray ionization(ESI) in MS. although the authors arenot aware of publications documentingchis effect in ESI-MS.

Particle size and signal: There issome question about whether the diam-eters ofthe particles that reach the opti-cal system of the newest ELSD instru-ments are approximately equal to thewavelength ofthe incident light, result-ing in predominantly Mic scattering(33), or whether the particles are some-what larger, resulting in reflection—refrac-tion scattering, or a mixture of both

mechanisms. While the instruments canbe designed to optimize the amount oflight that is reflected-refracted, thatmechanism might not dominate in allapplications. To some extent, if thereare mixed mechanisms of scattering,this contributes to nonlinear calibrationplots as the percent composition of suchmechanisms changes with concentra-tion. The intensity of the scattered lightis proportional to the size of the soluteparticles. Because tbe concentration ofthe analyte is changing over the dura-tion ofthe peak, the particle size that isproportional to the concentration willchange over the course ofthe peak. Notonly does the response cbange with theconcentration of the sample injected, italso changes within the peak. This ismore pronounced with broad peaks > 3s. Tbe size of tbe particles depends uponthe initial size and analyte concentra-tion in the droplets formed by the neb-ulizer (43). However, the droplet sizedistribution from tbe nebulizer is trans-formed further by selective focusing ofthe larger drops to waste and the trans-fer function of the evaporator, but theextent of these two effects will varybetween detector designs and is mini-mal compared with the initial dropletsize and concentration in the droplet.

Larsen (52) disclosed an invention fora "focused droplet nebulizer," animprovement over conventional nebu-lizers that produce variable sizes of

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Table I: For complete table, please see www.chromatographyonline.coin

Analyte Reference, Qradient(G) or IsDaatic(l) Mettt Intra-day %RSD

podium Valproatel, GI

Primidone

CarbamazepinePiracetamHuman Surfactant Protein

Macranthoidin B 7, G

Macranthoidin A

Dipsacoside B

HedcragenJn-28-O-b-D-glucopyranosyl(6à1)'O-b-D'glucopyranosyl ester

Macranthoside B

Macranthoside A

Hederagenin-3-O-a-L-arabinopyranosyl[2á1)-O-a-L-rhamnopyranosidePhosphatidylethanolamine 9, G

PhosphatidylcholineLyso phosphatidylethanolamine

Lyso-phosphatidylcholine• Cyclodextrin 11. G

2*hydroxy propy l-cyclodextr i n

Poly {methyl vinyl etherco-maleic) anhydrideAlternada alternata lycopersici toxins 13, G

Solanesol 14, I 41-42

Jujuboside A 15, G

valproic acicbp20 128-130

281 - 282190- 193151.5-152.5

hydratemp>260 (dec.)267 (dec.)

115

45

55

75

Laurie acid

Myristic acid

Palmitoleic acid

Linoleic acid

Palmitic acid

Oleic acid

Stearic acidArachidic acid (Eicosanoic acid)

Docosanoic acid

Priverosaponin B-22-acetate 16,

Primulasaponin II

Primulasaponin I

Spectinomycin 17, I

Tenacissoside A 18, G

Tenacissoside B

Tenacissoside G

Tenacissoside H

Tenacissoside I

Marsdenoside C

Marsdenoside G

Stigmasterol 19, I

-5itosterol

Stigmastanol

Mannitoi 20, I

oloxamer 188 {Pluronic F68) 21, I

184- 194(amorphous

LSOlid)

40

80

100170

140

144 -145

166-168 30

50 (minimum) 40

0.56 - 22.01 pg

0,54-21.63 pg

0.46-18.42 Mg0.38 - 15.66 Mg

0.42 - 16.82 Mg

0.40- 16.02 Mg

0.42 - 16.46 Mg

0,03 -0.34 mM

0.45-3.72 mM0.02 - 0,22 mM

0.06- 1.84 mM

400 -4000 ng

0.994

0.9922

0.9958

0.9961

0.9989

0.9977

0.9982

0.9935

0.99590.9982

0.99910 9999

0.9989

0.998

0.9983

0.13

2,4

2.24

nd

1.7

2.45

trace

0,1-1.5 mg/ml 0.9998 3.25

0.0229 - 0.1375 pg 0.9983 4.37

0,0208-0.1249 Mg

0.1380-1.1043 pg

0,0458 - 0,2750 pg

0.2104-1.2615 Mg

0,0609-1,4625 pg

0.0158-0.1900 Mg

0.0440 - 0.8792 Mg

0.0271 - 0.3250 Mg0,0406 - 0,4875 Mg

0-0313 0.2000 Mg

0-07 - 3,8 mg/ml

2,019-60,564 Mg

2.124-63.712 Mg

2.313-69,391 Mg

2.296 - 68.876 Mg

1.755 -52,655 M9

2.024 - 60.698 Mg

1.973-59,178 Mg

10-100pg/ml

10-lOOMg/mi

10-100 Mg/ml

0,01 - 0,4 mg/ml

0,1 -0,3 mg/ml

0,9993

0.9955

0.9985

0.9989

0.9984

0.9981

0,999

0.99830.9976

0.9973

0.9985

0.9993

0.999

0.9997

0.9992

0,9996

0.9993

0.9993

0 9997

0.9994

0.9993

0.9987

0,9947

0,9989

0.9999

0,997

2,54

0.83

2,11

3.17

3.41

1.36

2.84

2.782,15

2-99

4,98

4,51

1

3,04

3.58

1,5

2.58

3,16

2.43

1,78

1,71

1.47

1.29

2,5

1.5

2.23

3,04

5-2

nd

4.7

5.72

trace

4-6

2.11

2.44

0.93

3.85

3.68

1.08

2.92

3-33

1.243,04

3.15

2.09

0.16

0.S1 g

0,08 g

0.10 g0.09 g* S/N >3,30 ng

0,88 jjg

0.72 pg

0,34 Mg

0.24 Mg

0,20 Mg

0.22 iig

200 ng

100 ng300 ng

300 ng0.2 mg/mi

0.2 mg/ml

0.05 mg/ml

80

18.3 ng

16.7 ng

110.0 ng

22.9 ng

84.2 ng

30.5 ng

12.7 ng

41.6 ng

21.7 ng54.2 ng

20.8 ng

3.72

3.69

3.14

3.43

3.91

3.38

2-18

1.06

2,03

0.79

N,R,

1,463 M9

1.326 pg

1,218 pg

1,294 Mg

1,605 pg

1.012 pg

1,687 Mg

5 Mg/ml

5 Mg/Til

5 pg/ml

0,01 mg/ml

25 ua/ml

1 0 3 6 tCGC NORTH A M E R O VOtUME 26 NUMBER 10 OCTOBER ZOOB www. chroma tographyon line, corn

Table II: Simulation results for number of standards

Number of Standards Intercept

Full set (n = 10)

Remove middle stan-dard [n = 9)

Remove largest stan-dard (n = 9)

Remove smallest(n = 9)

Remove 2nd, 4th, 6th,8th, 10th (n = 5)

Remove 2nd, 4th, 6th,8th (n = 6)

0.864

0.908

0.844

0,791

0.895

0.929

^ope

0.696

0.693

0.653

0.731

0.642

0.695

R-sq

0.9102

0.9186

0,8786

0.9057

0.9378

0.9538

0.5

1.46

1.53

1-48

1.33

1.57

1.56

25.31

26.18

21,43

26.50

21.73

26.92

of 0.5

105

101

91

107

107

%of30

100

103

85

105

86

106

droplets with an expanding trajectory(divergent spray). Droplets that are toosmall to carry sufficient analyre do notcontribute to the detection signal, and apercentage of properly sized dropletswith analyte are lost in the divergentspray that exits via the outlet drain. Thedroplet distribution strongly dependsupon three factors: mobile phase com-position, mobile phase flow rate, andcarrier gas flow rate. This dependence ishighly interactive, which makes thespray hard to control and causes thedroplets to change in size and numberrandomly with time.

Larsens invention uses an electronicallycontrolled piezo membrane micropumpwith a check-valve system to produce uni-form droplets of a predetermined size,selected within an "optimum" ELSD rangeof 10-100 (Jim with a very narrow si?.e dis-tribution (5% standard deviation). Thedroplet size is independent of droplet pro-duction rate and is not strongly dependentupon liquid composition. Furthermore,there is little spray divergence in the dropletpath (1-2 degrees standard deviation), andoperation can be independent of the flowrate of the carrier gas. However, it appearsthat HPLC columns using typical flowrates of 1 mL/min wotJd need a flow split-ter to lower the liquid flow rate into thenebulizer. Alternatively, the new sub-2-)i,m, 50 mm X 2.1 mm. HPLC columnscan be used with conventional HPLCequipment witb mobile phase flow rates of200-300 H.L/ min. These columns pro-

duce excellent ehromatographic separa-tions with short run times, and could beconnected directly to this nebulizer, thus,improving sensitivity.

Peak shape and nonlinear response:The particle size is mfluenced by severalother factors, including solute concen-tration along the peak profile. In fact,the use of a high gradient slope can bean advantage, resulting in sharp peaksand, thus, contributing to increasedsensitivity (1 1). Peak broadening andasymmetry result in a decrease of ELSDresponse factor (17,25)66). Zhang andcolleagues (51) used enantlomeric mix-tures and chiral column isocratic .separa-tions with UV and ELSD quantitationof peak areas to demonstrate the varia-tion that occurs with peak broadening,and the "peak shaving" effect of ELSDversus UV. This can be responsible fordisproportionate peak areas of twoenantiomers resolved from a racemicmixture when measured by ELSD, butnot by UV: "When two peaks, evenwith equal true peak areas, are shapeddifferently, they are shaved differentlyin ELSD and the larger the peak inter-val, the greater the disparity in peakshape for a given pair of compounds"(51). The expanding use of sub-2-jJLmparticle size columns, with their sharperpeaks, also can improve sensitivity,assuming that the rest of the ELSDpneumatics and fluidics do not result inband broadening. Nebulizers also mustbe tuned for specific flow rates and

evaporation chambers are likewisetuned for flow.

Dolan (94) has reiterated recentlythat reduction of the column length orthe column diameter will improve thelimit of detection (LOD). For example.reduction from a 4.6-mm i.d. columnto a 2.1-mm i.d. column theoreticallymeans a fivefold reduction in peakwidth and, thus, a fivefold increase inpeak height. A twofold reduction in col-umn length theoretically would result ina 1.4-fold gain in LOD, assuming theextracolumn dispersion is small. Like-wise, reduction in retention time willhelp reduce the LOD because the peakstypically are narrower at shorter reten-tion times. Reducing the column vol-ume requires a proportional reductionin solvent flow rate to maintain linearvelocity through the column. It is thisreduction in solvent volume thatimproves the sensitivity of ELSD alongwith narrow peak widths that limit peakshaving. Most ELSD instruments todayare designed to operate at both 1mL/min and 0.2 mL/min without theneed for modification to overcomeadditional dispersion effects. Dispersioneffects become important at microliterflow rates. None of the researchers inTable 1 used columns packed with sub-2-̂ Lm particles, and the majority used4.6-mm i.d. coiumns.

As a starting point, typically we usesub-2-p.m particle size columns (50 mmX 2.1 mm) on conventional HPLCequipment with a column oven at30-40 °C and a water-acetonitrilemobile phase at flow rates of 0.2-0.4mL/min for all new method develop-ment. The backpressure under theseconditions typically is less than 4200psi, and we use 0.0025-in. i.d. tubing ofthe shortest practical length from theinjector to the column and from thecolumn to the ELSD system, usuallybypassing the UV detector. These con-ditions usually transfer well to LC-ESI-MS. The UV detector manufacturershave modified their flow cells to reducethe volume by a factor of four, thusminimizing band broadening of thesevery narrow peaks. Typically, mostELSD instrument manufacturers stillhave tubing dimensions with internaldiameters from inlet to nozzle of 0.007in. and a length of 7.5 in., or an inter-

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Table til: Effect of slope difference on sensitivity

1000

1500

Difference

864.8

1297.2

432.4

1247.9

1871.85

623.95

nal diameter of 0.005 in. and a lengthof 10 in. This means up ro an eightfoldincrease in cross-sectional area of thetubing and significant band broaden-ing, resulting in los.s of resolution andsensitivity and conttibutmg to nonlin-earity due to peak widening, as dis-cussed previously. Substitution of 0.0025-in. i.d. tubing internally for the existinglarger diameter tubing would requirerecalibration of the instruments by themajiufacturers (or introduction of newmodels) because this would affect tbenehulization process, rbe evaporationchamber process, and would requiretuning of the entire ELSD system. How-ever, dispersion effects within the evapo-rator tube should be minimal if the rubeis short and laminar flow is present.Additionally, higher sampling rates andlaster filtering will be required as theefficiency of the separations is improved.However, tbis straightforward improve-ment would be of particular benefit tothe ELSD metbod.

Light intensity: Larger particles scattermore light, and longer residence times ofthe particles in tbe light beam (affectedby tbe gas flow rate) enhance scattering.Tbe intensity of tbe light has a signifi-cant effect on tbe sensitivity. Gaudin andcolleagues (33) reported a 16-foldincrease in the LOD of ceramide whenthey replaced the tungsten bulb witb axenon arc lamp. Lane and colleagues (8)reported a 3-I0-fo!d improvement insensitivity with a blue LED (3-5 mW)light source at 480 nm for a wide rangeoí compounds compared with a tungstenlamp. Larsen and colleagues (39) havedesigned a prototype high-sensitivitylight-scattering detector utilizing a polar-ized laser and improved optical detec-tion, whicb gave a 224-fold increase insensitivity for hydrocortisone.

Mathews and colleagues (71) com-pared three detectors, using crystal vio-let as the analyte. One, which uses a redlaser light source, produced a very ele-

vated response. Anotber, wbicb uses ablue ligbt source, produced a greatlysuppressed tesponse. A tbird, wbicbuses a white ligbt source, produced anormal response. Tbey proposed tbatbecause of the intense violet color ofthis compound, tbe red light source(670 nm) causes the molecule to Huo-resce, boosting the ELSD signal. Theblue light (480 nm) is absorbed selec-tively and not scattered, and the wbiteligbt source produces a normal signal

Melting point and volatility ofanalyte: If particle size matters, thenature of the particle — color, refractiveindex, solid, crystalline, amorphous orliquid •— also is important. Recently,more attention bas been focused on tbeELSD temperature settings (that is,nebulizer and evaporator) and the melt-ing point (and in tare cases, the molarheat of vaporization) of tbe analytes(31). New ELSD instrument modelsoffer subambient operation from 40 °Cdown to 10 °C. However, Table 1 illus-trates several analytes witb (unreported)melting points close to or below tbeevaporator temperature selected foranalysis, but tbese studies generally wereperformed witb older ELSD instru-ments tbat did not bave tbe subambientcapabilities tbat reduce backgroundnoise and facilitate lower evaporatoroperating temperatures. Cooiing of tbenebulizer occurs as a result of aerosolformation, and active cooling ensurestbat the nebulizer stabilizes quickly.Loss of semivolatile analytes is bigbiyproblematic because the vapor pressureof solids rarely is included in the refer-ence literature unless the compound isknown to sublime. Subambient evapo-ration temperatures can be set to evapo-rate warer at 15-20 "C, wbicb reducestbe degradation of rbermally sensitivecompounds. Note that cooling the neb-ulizer is not subambient ELSD and onlyaids in controlling rhe amount of vaporreaching tbe optical cbamber. It does

not aid in increasing tbe detector's sen-sitivity to semivolatile compounds. Tbemost productive approacb is to tune theevaporation temperature to tbe lowestvalue that minimizes background scat-tering. Lane and colleagues (8) clearlydemonstrated tbe important effect onaccuracy and variability that tbe "esti-mated (calculated) boiling point" of tbeanalyte can bave on ELSD. Meltingpoint also can be used as a marker forestimated boiling point in some cases(8,9,31). However, tbere are analyteswith different physicochemical proper-ties (that is, volatility) tbat can lead tounexpected results in ELSD when theseproperties are not considered carefullybefore developing tbe metbod. Eorexample. Fries and colleagues (5) used astructurally similar compound, 7-hydrox-ycoumarin (unreported melting point[mp] 230 °C [dec] sublimes) as a stan-dard to quantitate 7-etboxycoumarin(unreported mp 88-90 "C) witb an evap-orator temperature of 40 "C, a nebulizertemperature of 35 °C, and a gas flow of0.8 L/min. Tbey found "insufficient sen-sitivity" and an "inconsistent inter-ana-lyte" response. Lane and colleagues (8)found response factors of unknownimpurities can differ significantly fromthose of each otber and of tbe target com-pound. At low levels of analyte, impuri-ties present at 1% m/m (mass to mass)migbt only contribute 0.2% of total areaif measured by an uncaÜbrated area %ELSD method.

Pennanec and colleagues (35) used alow-temperature ELSD technique tocompare sensitivity in detecting caffeine(mp 234-236 °C, sublimes) at 30 "Cevaporator temperature versus 50 "Cand found a 10-fold increase in peakbeigbt. Tbey also found tbat tbe sensi-tivity of the detector improved bygreater tban a factor of 10 for urea (mp133-135 "C, thermosensitive) at 25 °Cversus 39 °C. Solutes in solid state scat-ter light more efficiently tban in tbe liq-uid state. Therefore, tbe responsedecreases wben the temperature of theevaporator (that is, drift tube) increases,and solutes have varying responsesdepending upon tbeir melting point otmolar beat of vaporization (31). As longas the temperature is not too high, theanalyte remains as particles. The size ofthe particles depends upon the initial

1 0 3 8 LCGC NORTH AMERICA VOLUME 26 »UMBER ID OCTOBER Z0D8 www. chramatographyonline.com

size and concentration in the droplets(43). An increase in temperattire (at orabove mp) results in the formation ofliquid particles, and a solute can vapor-ize partially, leading to a decrease ofparticle size (32).

Mobile phase additives: Nevertheless,many analytes are liquids at ambient tem-perature, and general methods to enhancethe sensitivity of ELSD have includedvolatile additives to the mohile phase.Deschamps and colleagues (32) used cri-ethylamine (TEA) and formic acidtogether in equimolar amounts in themobile phase (0.1 % v/v) and obtainedresponse enhancement independent ofpeak geometry modification. If the soluteis capable of noncovaient interactions withTEA-formic ion pairs, some TEA-formicassociation complexes still could be presentinside the droplet, thus increasing its massand ELSD response. These types ofadducts are well known in LC-MS. How-ever, these adducts are highly dependentupon solutes, and similar compounds canexhibit very different response enhance-ment (32). Karlsson and colleagues (75)replaced ammonium acetare with ammo-nium formate in the mobile phase becauseof a slightly higher response to monosac-charides with ELSD when using the samedetector settings. Galanalds and colleagues(25) noted thar an increase in the molecu-lar mass of an ion pairing reagent led to anincrease in response íaCTor, possibly due tothe inclusion of anions in the particles,resulting in an increase in the particle mass.In the analysis of amikacin, they found thatnonafluoropentanoic acid gave a 3-4-foldincrease in peak area versus trifluoroaceticacid (that is, increased sensitivity).

ChemometricsDouble logarithmic calibration: Exceptfor limited concentration ranges insome applications (47,48,72), a nonlin-ear response generally is observed inELSD as a consequence of the analyteconcentration influencing the averageparticle size. Low amounts of com-pounds in the detector give responsesthat are much lower than expected.Also, the onset and the tail of a peak arerecorded too tow compared to the top;that is, peaks look sharper (shaved) andseparation efficiency is artificiallyhigher. Chromatograms are distorted ina complex manner (69). The area ofthe

Chromatographie peak {A) correlates

with the analyte mass (m) according to

A = ané

where a and b are coefficients depend-ent upon the ELSD instrument and set-tings, and the mohile phase. Coefficientb can vary between 0.9 and 2 (38), andexcept for cases in which b = 1 (wherea linear curve can be constructed), dou-ble logarithmic coordinates are necessaryto obtain a linear calibration curve, or asecond- or third-order polynomial tofit the data for calibration curves.Clarot (68) points out that such math-ematical transformation is allowed bythe ICH validation description, andNIST strongly recommends it in itsSRM application (30). However, Koup-paris' group (61) notes that the logarith-mic nature of the calibration curverequires a relatively high number ofstandards to construct, and others (70)have noted that using a second-orderpolynomial fit (while giving a somewhathetter correlation coefficient than dou-ble logarithm plots) presented tediousdata processing for quantitation.

Number and location of standardsrequired: 1 he number oí standardsused to calculate the standard curvevaries between five and 10 whenreported. There is a tradeoff betweenobtaining better accuracy and precisionwith the costs involved in additionalstandards preparation. Using simula-tion analysis, an optimal number ofstandards can be obtained using thedouble logarithmic function. Assum-ing AT-values with a range from 0.1 to51.2 (using serial dilution) to createthe 10 standard values, a double loga-rithmic model is fit to generate ran-dom vahies of j that should lead to alinear curve. Table II gives the slopeand intercept of the model includingR^ when using w — 3 for each standardlevel. The last four columns are thebackfits of two "controls" within therange of the standard curve and thepercent difference from the full set ofstandards. It is not clear ¡f there is astatistical difference berween internaland external standards, as many of thereferences did not report the source ofstandards, but the expectation is thatboth sets of standards will be colinear.

From Table II it becomes evidentchat the number of standards is lessimportant than the location of thosestandards. Removal of either the loweststandard or the highest standard isdetrimental ro the curve. Tbe cost/ben-eUt would seem to he no less than sixstandards well spaced across thedynamic range of the assay. Addingadditional samples does not improvethe fit. Figure 1 shows the full calibra-tion curve [n = 10) with error bars onthe triplicate readings.

Of 58 references reviewed in Table 1,32 used gradient elution while 26 usedisocratic. Though one might expect ahigher variation in gradient elution ver-sus the isocratic elution, based upon thedata presented in the references, theisocratic elution showed higher impre-cision and a slightly worse R^ whencompared to the gradient elution.Additionally, between analytes andpooling across rhe references, the iso-cratic elution IS much more variable.The range of iP from the linear modelsfor isocratic is 0.85-1.0 while the rangefor the gradient is 0.98-1.0. Tbese dif-ferences were not statistically different.It is clear that many factors such as ana-lyte and reportable range affect theseresults. The differences in R^ valuescould be a function of poor model fitsor influential observations in the cali-bration curve.

Precision analysis: Variance compo-nents or decomposition of variance is astatistical method to partition the dif-ferent sources of variation into theirrespective components. A book by Box,Hunter, and Hunter (95) is an excellentsource for additional information onbow ro calculate variance components.It is important to remember that vari-ances can be added or averaged, but notthe standard deviations. Variance com-ponents allow you to calculate intra-assay and interassay precision. For awell designed experiment, reproducibil-ity and repeatability of the method isassessed independently. For example,several publications (20,23.25) reportthe percent relarive standard deviation(%RSD) incorrectly because many ofthe effects are confounded and thereported value is an overstatement ofthe rrue precision of the method. Thepurpose of our precision analysis is not

www.chromatographyonline.com OaOBER Î008 LCGC NORTHAMERICA VOLUME 26 NUMBEfl 10 1039

[Q show that ELSD is better than othertechniques, but rather to state thatmany of the claims of precision forKLSD are calculated incorrectly.

Slope and intercept: The slope andintercept of a log-log transformed lin-ear model are critical parameters forpredicted concentration based upon anobserved response. The slope or rate ofchange is the change in the y variablefor a 1-unit increase in the -Y variable. Asteep slope is indicative of a highly sen-sitive method because a small increasein the X variable would have a largechange in the y variable. Fot example,the slope for cholic acid (23) is 1.2479,while the slope of the cholic acid fromanother reference (26) is 0.8648. Table111 shows the difference in sensitivitybetween these two methods. For a 500-unit change in the concentration, thelarger slope gives more than a 44%larger response.

The intercept can be interpreted asthe limit of detection (LOD) if weassume that zero is part of the range ofthe assay. The intercept is the value oíy,when X is equal to zero. If the rangedoes not include zero, it ¡s prudent tofit the standard curve as a no-interceptmodel, especially if the intercept ¡s notstatistically different than zero.

Why not use a log-log? Order magni-tude of Jr values: Some authors prefernot to use a log-log transformation to Htthe standard curve (77). Using simplelinear regression without a transforma-tion makes sense when the order ofmagnitude of the x values is less than 1log scale. Additionally, if the assay rangeonly includes the linear portion of theassay, the log-log transformation mightnot be necessary. A simple lack of fit testwould confirm if the linear model with-out the transformation is ideal.

It has been noted (98) that the correla-tion between the response index meas-ured from the slope of the curve and thelog of the response is a linear function.Based upon the intrinsic relationshipbetween the analyte response and analyteconcentration, a transformation can beused in lieu of a log-log transformation.This relationship helps in the quantifica-tion when standards do not exist for anLuialytc (îr mixtures of analytes.

Detection limit and quantitationlimits: The detection limit of an indi-

vidual analytical procedure is the lowestamount of analyte in a sample that canbe detected but not necessarily quanti-tated as an exact value. The quantita-tion limit of an individual analyticalprocedure is the lowest amount of ana-lyte in a sample that can be determinedquantitatively with suitable precisionand accuracy. The quantitation limit isa patameter of quantitative assays forIow levels of compounds in samplematrices, and is used particularly forthe determination of impurities ordegradation products (96). The ICHguideline gives several suggested meth-ods for assessing LOD and LOQ. Themost liberal approach is the visual eval-uation that is reserved usually for non-instrumental methods but also can beused with instrumental methods. Thedetection limit Is determined by theanalysis of samples with known concen-trations of analyte and by establishingthe minimum level at which the analytecan be detected reliably. The signal-to-noise ratio (S/N) usually can be usedwith analytical procedures that exhibitbaseline noise such as ELSD. Determi-nation of S/N is performed by compar-ing measured signals from samples withknown low concentrations of analytewith those of blank samples and estab-lishing the minimum concentration atwhich the analyte can be detected reli-ably. Signal-to-noise ratios of .3:1 and10:1 generally are considered accept-able for estimating the detection limitand quantitification limit, respectively.The meaning of a 3:1 or 10:1 ratiomeans that the signal needs to be,respectively, at least three times or 10times larger than the signal ofthe back-gtound sample. The method basedupon the standard deviation of theresponse and the slope is perhaps theleast understood regularly usedapproach. The slope is estimated fromthe calibration curve, while the stan-dard deviation can be on the calibrationcurve or based upon the standard devi-ation of a blank. It is clear that estimat-ing the standard deviation from the cal-ibration curve (sometimes called theroot mean squared error) makes sensebecause the slope estimate comes fromthe same curve. The root mean squarederror is an estimate of the variation inthe calibration curve and is used in the

estimation in the standard error of theslope estimate. Using the standard devi-ation of a blank sample combined withthe slope of a calibration curve is dis-jointed. Choosing to estimate the stan-dard deviation of a blank would not bedifferent than doing the analysis of sig-nal to noise (S/N), as the standard devi-ation of a blank also would be an esti-mate of the noise in the method. Agood rule of thumb is to use S/N whenyou have eithet samples or standardsclose to the blank, and use the standarddeviation of the response and slope forthose methods in which the expectedvalues are not close to the noise of thesystem. Regardless of the method cho-sen, the same approach should be uti-lized with both the LOD and LOQ.

Several different analysis methodshave been proposed to determine LODand LOQ including percent recovery,minimum difference from baseline, andanalysis of variance. Currently there aredifferences in opinion regarding theappropriateness of using analysis of vari-ance for showing a difference betweenbaseline and a spiked sample. The goalis not to find statistically significant dif-ferences that have no practical value,but to find statistical differences thathave meaningful implications on assayperformance. One proposed methodthat combines both the statistical rigorof analysis of variance and the appropri-ateness of meaningful differences frombaseline is the use of equivocal tests.

ConclusionThe recent trend in the majority ofpublications reviewed for this articledemonstrates a better understanding ofthe limitations and possibilities of usingHPLC—ELSD for quantitation of ana-lytes lacking chromophores, and signif-icant improvements in ELSD instru-mentation. One should use the bestpractices of this technique in designingquantitative analytical methods, whichinclude prior knowledge of the analytevolatitilty and melting point, properselection of isocratic or gradient elutionwith analyte-specific standards and cor-rection factors across the gradientwhere appropriate, and correct statisti-cal methods to properly analyze thedara collected, keeping in mind the log-arithmic nature ofthe technique.

1 0 4 0 LCGC NORTH AMERICA VOLUME 26 NUMBER 10 OCTOBER 2008 www.chromatographyanline.cam

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