Anal. Chem. 1987, 59, 1980-1984
1980
Liquid-Solid Extraction Conditions Predicted by Liquid Chromatography for Selective Isolation of Sulfoconjugated Steroids from Equine Urine Lars 0. G. Weidolf' and Jack D. Henion* Drug Testing a n d Toxicology, New York State College of Veterinary Medicine, Cornell University, 925 Warren Drive, Ithaca, New York 14850
A liquid-solld extraction (LSE) procedure that utlllzes C,8bonded slllca was developed for m e suifoconjugated steroids. Volumes and compositions of the eluents used for the LSE were evaluated with a high-performance liquid chromatographic (HPLC) system and a conventional HPLC column packed with the LSE-cartrldge C18material. Eluents with or without buffer provided sJgnHkantly different retention characteristics for the suifoconjugates which were utlllzed for selective extraction. Following solvolysis and Ilquld-llquld extraction, the released parent sterdds were isolated by LSE. The recoveries of the sulfoconjugates of boldenone, 19-nortestosterone, and testosterone from fortified equlne urine and boldenone from a 12-h postadmlnlstratlon urine were determined as released parent sterokls by HPLC and ranged from 66 to 88% at a concentration of 2 X IO-@ M.
The determination of drugs or drug metabolites in samples of biological origin frequently requires purification prior to introduction into a chromatographic system. Traditionally the method of choice has been liquid-liquid extraction (LLE) giving high recoveries of nonpolar compounds and sufficient selectivity to remove interfering matrix components. Many drugs, however, are extensively metabolized resulting in excretion of very low amounts of parent compound. In these cases confirmation of the drug might have to focus on a metabolite (1). LLE of drug metabolites, and drug conjugates of glucuronic acid and sulfuric acid in particular, may require the use of extreme p H or lipophilic ion-pairing counterions for their isolation. This approach will also increase the amount of coextracted matrix constituents. In recent years the development of disposable cartridges packed with silica-based adsorbents has focused great interest on liquid-solid extraction (LSE) as the mode for cleanup of complex samples (2-4). Applications of LSE range from solvent change (e.g., aqueous to organic) which facilitates evaporation of excess solvent to highly selective methods utilizing different sorbents and mechanisms of retention to yield highly purified extracts with high recoveries. Most application notes and guidelines provided by the manufacturers of LSE cartridges deal with the choice of sorbent or combination of sorbents with an aim to retain the compound of interest while eluting the matrix or vice versa (5-7). Less information is given, however, on the choice or development of suitable solvent compositions for selective retention or elution of the compounds. A general approach based on trial and error suggests the use of different solvents or solvent combinations followed by analysis of the eluates by HPLC to determine whether the compound of interest was eluted (4, 5). On leave from AB Hassle, S-431 83 Molndal, Sweden.
Common methods utilized in the determination of steroids and steroid conjugates involve extraction of the bulk of compounds by Amberlite XAD-2 or silica C18LSE, followed by group fractionation on surface-modified Sephadex (ref 8 and references therein). These methods are general and separate neutral steroids, glucuronides, monosulfates, and disulfates but with low selectivity within these groups. Analysis is usually performed by gas chromatography (GC) or gas chromatography/mass spectrometry (GC/MS) after hydrolysis and derivatization. Sulfoconjugation is a common route of metabolism for steroids (9)and two of the sulfoconjugates used in this study, testosterone sulfate and boldenone sulfate, are reported to be excreted as major metabolites in equine urine (10, 11). This paper presents a highly selective LSE procedure for the direct isolation of some sulfoconjugated steroids from equine urine utilizing C18-bondedsilica cartridges. Selectivity was obtained through alteration of the eluent compositions giving different retention behavior. A new approach to evaluate the solvent compositions was developed by using an HPLC system that included the C18 cartridge adsorbent packed into a conventional HPLC column. The eluent volumes for retention and elution were calculated from common chromatographic parameters obtained with the HPLC system and the bed volume of the LSE cartridges.
EXPERIMENTAL SECTION Chemicals. Structural formulas of the compounds used in this study are given in Figure 1. Boldenone (BO, 1,4-androstadien17@-01-3-one),19-nortestosterone (NT, 4-estren-17@-01-3-one), testosterone (T, 4-androsten-17@-01-3-0ne), and testosterone-@D-glucuronide sodium salt (TG) were purchased from Sigma Chemical Co. (St. Louis, MO). Boldenone sodium sulfate (BOS), 19-nortestosteronesodium sulfate (NTS),and testosterone sodium sulfate (TS) were obtained from Steraloids, Inc. (Wilton, NH). The purity of each compound was checked by HPLC before use. Sulfatase type H-2 from Helix pomatia (sulfatase activity 2-5000 units/mL and @-glucuronidaseactivity 100000 units/mL at pH 5.0) was obtained from Sigma. Acetonitrile, ethyl acetate, methanol, and ammonium acetate of HPLC grade and glacial acetic acid, sulfuric acid, and sodium carbonate of reagent grade were purchased from Fisher Scientific (Rochester, NY). HPLC grade water was obtained from an in-house water purification system (Barnstead Nanopure 11, Boston, MA). Liquid-solid extraction cartridges (J.T. Baker, Phillipsburg, NJ) packed with 200 mg of CIB-bondedsilica (Model 7020-2,40 pm, 60 A) were used with a vacuum manifold equipped to hold 12 cartridges (Supelco, Inc., Bellefont, PA). Equine urine samples were obtained from experimental horses housed within our Drug Testing and Toxicology Program, before and after intramuscular administration of 1.1mg/kg body weight of boldenone undecylenate (Equipoise, E. R. Squibb & Sons, Inc., Princeton, NJ). Enzymatic Hydrolysis. The ability of digestive juices from Helix pomatia to hydrolyze TS and TG was tested in an aqueous model system. To 5 mL of 0.05 M sodium acetate, pH 5.0 (pH adjusted with glacial acetic acid), was added 50 p L of sulfatase H-2 and 10 pg of TS or TG in 0.1 mL of water. The mixtures
0003-2700/87/0359-1980$01.50/0 0 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15, AUGUST 1, 1987
0 &-R
I
0 &-Rll
0
Figure 1. Structures of the investigated compounds: (I) R = H, boldenone (BO); R = SO,-, boldenone sulfate (BOS); ( I f ) R = H, 19-nortestosterone (NT); R = SO3-, 19-nortestosterone sulfate (NTS); (111) R = H, testosterone (T); R = SO,-,testosterone sulfate (TS); R
= C6H,0s-, testosterone glucuronide (TG). were incubated overnight at 37 "C and purified by liquid-solid extraction on CIScartridges conditioned with 2 mL of methanol and 2 mL of water. The sample was applied to the column followed by washing with 2 mL of water and elution with 2 mL of methanol/water (85/15). The eluate was evaporated under a gentle stream of nitrogen at 60 "C and reconstituted in 0.5 mL of mobile phase for HPLC to monitor the conversion to parent steroid. Solvolysis. Solvolysis was performed as reported by Vihko (12) modified to suit the smaller sample volumes used in this study. The conditions were evaluated with standard solutions of TS, TG, BOS, and NTS. Fifty micrograms of TS in 50 pL of methanol was added to 25 mL of ethyl acetate at 50 "C which had been saturated with 2 M sulfuric acid (1/10 vol). Aliquots of 1mL were transferred at 1,5,10,20,30,45,and 65 min to test tubes containing 0.2 mL of 1% ammonium hydroxide in methanol to neutralize the acid. The sample was evaporated, reconstituted in 200 pL of mobile phase, and analyzed by HPLC. TG, BOS, and NTS were treated at 50 "C with 5 mL of ethyl acetate saturated with 2 M sulfuric acid, and only one sample at 50 min was analyzed. Sample Preparation. For BOS and NTS 2 mL of equine urine (or 2 mL of aqueous standard solution) was mixed with 2 mL of methanol/0.65 M ammonium acetate, pH 5.4 (pH adjusted with glacial acetic acid) (20/80), with a vortex mixer for 30 s, and the mixture was sonicated for 25 min and centrifuged at 3000 rpm for 5 min. For TS 2 mL of urine was mixed with 2 mL of 0.024 M ammonium acetate, and the pH was adjusted to 5.5 with glacial acetic acid. The liquid-solid extraction cartridges were conditioned with 2 mL of methanol and 1 mL of 0.024 M ammonium acetate, pH 5.5. The sample was applied in two portions and aqueous standard solutions of BOS, NTS, or TS were added on-column to the first portion. The cartridges were washed with 1 mL of 0.024 M ammonium acetate pH 5.5, 2 mL of methano1/0.024 M ammonium acetate, pH 5.5 (40/60for BOS and NTS, 45/55 for TS), and 3 mL of water. The fraction containing the sulfoconjugated steroids was eluted with 2 mL of methanol/water (35/65 for BOS and NTS, 40/60 for TS). The eluate was diluted with 2 mL of methanol to facilitate evaporation at 60 "C under a gentle stream of nitrogen. The residue was dissolved in 0.1 mL of methanol and the sulfoconjugates were solvolyzed by addition of 5 mL of ethyl acetate saturated with 2 M sulfuric acid with heating to 50 "C for 50 min. The organic layer was washed twice with 2 mL of 0.94 M sodium carbonate, pH 10.3 (pH adjusted with sodium bicarbopate), and once with 3 mL of water. The phases were separated and the organic extract containing the released steroids was evaporated under a gentle stream of nitrogen at 60 "C and transferred with three 0.2-mL portions of methanol/water (50/50) to a conditioned C18cartridge containing 1mL of water. The cartridge was washed with 1 mL of water and 2 mL of methanol/water (55/45) and the steroids were eluted with 2 mL of methanol/water (80/20). After evaporation the residue was dissolved in 100 pL of mobile phase and 20-pL aliquots were subjected to HPLC analysis. Determination of recoveries was made by comparison of the mean area of two to three determinations of the compound in the extract with the mean area of four to six determinations each of
1981
two standard solutions of the compound of the expected concentration at 100% recovery. Liquid Chromatography. The high-performance liquid chromatographic system consisted of two M 6000A pumps controlled by an M 660 solvent programmer, an M 440 UV detector with a fixed wavelength of 254 nm (Waters Associates, Milford, MA), and a Model 7010 injector equipped with a 20-pL sample loop (Rheodyne, Cotati, CA). Chromatograms and peak areas were obtained with a Model 3390A reporting integrator (Hewlett-Packard, Palo Alto, CA). The chromatographic column used was 4.6 mm i.d. X 83 mm Pecosphere-3C C18packed with 3-pm particles (Perkin-Elmer, Wilton, CT). For evaluation of capacity factors and suitable solvent compositions in the liquid-solid extracation procedure a 4.6 mm i.d. X 50 mm column was dry-packed with 40-pm C18bonded silica obtained from the extraction cartridges. For method development the dual-pump system was used with methanol/0.024 M ammonium acetate, pH 5.5 (solvent A, 10/90; solvent B, 90/10), or methanol/water (solvent A, 10/90; solvent B, 90/10), but for analysis of the urinary exracts and in the recovery studies, single pump isocratic conditions were used with acetonitrile/methanol/0.024 M ammonium acetate pH 5.5 (7/50/43) for BO and NT and acetonitrile/0.024 M ammonium acetate, pH 5.5 (40/60), for T. Methanol/O.O24 M ammonium acetate, pH 5.5 (57/43), was used for chromatography of BOS, NTS, and TS. The mobile phases were degassed by sonication and sparging with He and filtered through a 0.45-pm Nylon-66 fiiter (Rainin, Woburn, MA) before use. The flow-rates employed were 2.0 mL/min for the 40-pm column and 1.0 mL/min for the 3-pm column.
RESULTS AND DISCUSSION Sample Preparation. Horse urine often contains high levels of carbonates which may cause extensive foaming from release of carbon dioxide when acidified with strong acid. To avoid foaming, the urine was diluted and mixed with ammonium acetate of high buffering capacity of the desired pH and sonicated. If these precautions were not taken, gas developed when the sample was introduced into the LSE cartridge which appeared to decrease the active sorbent surface resulting in varying recoveries. The use of the high ionic strength ammonium acetate buffer gave high recoveries for BOS and NTS, but for TS a lower ammonium acetate concentration and pH adjustment with glacial acetic acid was needed to obtain comparable recoveries. Dilution of the urine with an equal volume of buffer, sonication, and centrifugation helped remove particulate matter and decreased the risk of cartridge clogging. Isolation of the Sulfoconjugates. The volumes and compositions of eluents used for selective retention and elution of the sulfoconjugates were evaluated by HPLC. A short HPLC column was dry-packed with CI8-bonded silica obtained from the LSE cartridges and eluents of higher or lower solvent strength were easily composed by use of the dual-pump system. Retention of the sulfoconjugates was substantially higher when a buffered mobile phase was used as opposed to methanol/water mixtures. This behavior is probably caused by different retention characteristics in the presence or absence of a supporting electrolyte. In eluents without electrolytes the pores become less accessible to, and partly exclude, ionic species (13). The available surface area and distribution volume within the column decreases for the charged sulfoconjugates and elution can be performed with a solvent of lower methanol content. The retention of the uncharged parent steroids is, however, virtually unaffected by the decrease in ionic strength (14). Solvent compositions for selective retention with methanol/ammonium acetate pH 5.5 were evaluated from the capacity factor (k') for the front of the peak of the compound of interest (Idfront = (VR(front)- Vm)/Vm), where V , is the retention volume and V, is the void volume of the column). pH 5.5 of the ammonium acetate buffer was chosen since the recoveries of BOS, NTS, and TS were higher than those obtained a t pH 5.0 and coextraction of matrix
1982
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15, AUGUST 1, 1987 A kfront
1
i
0.001 A.u.
Table I. Liquid-Solid Extraction Recoveries of Steroids and Sulfoconjugated Steroids recovery
compound
?+
concn,= M
(% f std dev)
n
Aqueous Standard Solutions 0
IO
20
30
k'
1 I llkiaii
0.008 A u
Figure 2. Chromatography of 200 ng of boldenone sulfate: (A) mobile phase, methanoV0.024 M ammonium acetate pH 5.5 (40/60); (8) mobile phase, methanoVwater (35/65).
constituents was lower than at pH 6 7 . V , was estimated from the change in refractive index in the chromatogram when mobile phase diluted with water was injected. k'front was evaluated from the chromatograms and chosen from the first visible deflection from the base line at a sensitivity where the peak height was 50-100% of full-scale deflection of the recorder (Figure 2). The volumes of the eluents t~ be used with the LSE cartridges were then calculated with the rearranged equation V , = V , (k' + 1). The bed volume of C18-bonded 60-8, silica of 40-pm particle diameter is approximately 120 pL/lOO mg ( 5 ) and a V , of 0.25 mL was used for the calculations with the cartridges used in this study. klfrontfor BOS with methanol/0.024 M ammonium acetate (40/60) was 11 (Figure 2A) allowing for a maximum volume of 3 mL to elute interfering compounds from the cartridge while still retaining BOS. Obviously the volume calculated from the capacity factor evaluated from the apex of the peak would have caused severe decreases in the recoveries. The subsequent wash with water removed the buffer and decreased the ionic strength within the cartridge. The volume of 3 mL used was chosen arbitrarily, but an increase of this volume did not increase the recoveries of the compounds. Solvent compositions for elution were evaluated from the capacity factor of the tail of the peak (k'& with methanol/wakr as the mobile phase (Figure 2B). For elution of BOS from the cartridge the predicted volume of methanol/wakr (35/65) was 0.9 mL (k'm = 2.6). However, this volume only produced recoveries of BOS of 3540%. This was due to the fact that the eluent volumes were evaluated from capacity factors obtained with the equilibrated HPLC system at constant flow. In the cartridge, however, the applied volume of methanol/water (35/65) was diluted with the water remaining from the previous wash, thus decreasing the solvent strength. By a 2-fold increase of the calculated volume the water was displaced and elution with a recovery of 89% was obtained. Similar considerations were taken for the development of extraction conditions for NTS and TS. Since elution is made with an eluent of lower solvent strength than the preceding wash, neutral steroids will remain in the cartridge and not interfere with the determination of the sulfoconjugates. The recoveries of BOS, NTS, and TS from aqueous standard solutions were 89-96% as determined by HPLC using an external standard (Table I). Aqueous standard solutions of T G subjected to the procedure showed high recovery with the eluent compositions used for BOS and NTS (Table I). It was not possible to determine the recovery of the compounds from urine by HPLC/UV a t this stage due to the interferences from the coextracted matrix.
boldenone sulfate
19-nortestosteronesulfate testosterone sulfate testosterone glucuronide boldenone 19-nortestosterone testosterone
2.6 X 2.7 X 2.6 x 10-7 4.1 X 3.9 X 4.1 X 4.0 x 10-7
89.3 3.0 96.4 f 2.5 95.4 5.7 98.0 95.2 f 0.7 89.6 f 0.9 95.7 A 0.6
*
3 3 4 2 3 3 3
"Calculated from amount added to 2 mL of aqueous standard solution.
Solvolysis. It is well-known that many steroid sulfates, e.g., 17-oxosteroid sulfates are resistant to hydrolytic cleavage by enzyme preparations (15) and this was also confirmed for TS. While T G was quantitatively converted to T during overnight incubation with digestive juices from Helix pomatia at 37 "C, only 8% TS was converted to T. Instead, solvolysis in ethyl acetate saturated with dilute sulfuric acid was evaluated for the sulfoconjugates studied. The kinetics for solvolysis of steroid hydrogen sulfates have been shown to be first order (16),and a logarithmic plot of the decrease of T S vs. the reaction time accordingly showed a linear relationship ( r = 0.999). The rate constant at 50 "C (0.124 min-l) was evaluated from the slope. Solvolysis for 50 min a t 50 "C corresponds to nine half-lives giving >99% conversion of TS to T and was used throughout the study. BOS and NTS subjected to solvolysis for 50 min a t 50 "C showed no trace of the conjugate, nor was any other compound than released BO or N T detected by HPLC. A sample of TG treated under the same conditions showed that the glycosidic bond between the steroid and the glucuronic acid moieties was stable toward solvolysis and no T was formed. Reference compounds of the glucuronides of BO and N T were not available but are assumed also to be resistant to solvolysis. After solvolysis of the urinary extracts obtained as outlined above, polar compounds not affected by solvolysis (e.g., glucuronide conjugates) were removed and the sulfuric acid was neutralized by washing the ethyl acetate phase with sodium carbonate, pH 10.3, and water (17). Isolation of Released Parent Steroids. For the final LSE purification volumes and compositions of eluents were evaluated by HPLC as described above. Methanol/water (55/45) was used to elute interfering polar compounds while the released parent compounds of the sulfoconjugates were eluted with methanol/water (80/20). The recoveries of BO, NT, and T from aqueous standard solutions were higher than 89% and are given in Table I. Recoveries from urine were not determined due to matrix interferences. Isolation of Sulfoconjugates with Determination as Released Parent Steroids. The recoveries of BOS, NTS, and T S determined as released parent compounds were 76-80% from aqueous standard solutions carried through the LSE procedure (Table 11). A chromatogram of an extract of control urine from a female standardbred horse is shown in Figure 3A. Control urine from the same horse was fortified with 1.4 X lo4 M BOS and NTS (0.51 pg/mL) and subjected to the LSE procedure giving the chromatogram in Figure 3B. No major endogenous compounds interfered with the two target compounds. Steroids are frequently administered intramuscularly as 17@-hydroxyestersdissolved in a vegetable oil to obtain a slow distribution into the circulation with subsequent hydrolysis to the active steroid. The overall metabolism of the steroid is, however, qualitatively inde-
ANALYTICAL CHEMISTRY, VOL. 59, NO. 15, AUGUST 1, 1987
1983
Table 11. Liquid-Solid Extraction Recoveries of Sulfoconjugates Determined as Released Parent Steroids recovery compound
concnp M
(YOf std dev)
n
Aqueous Standard Solutions
4.8
79.0 & 2.3 80.2 f 2.0 76.2 f 5.6
5
78.1 f 2.6 83.5 i 4.4
3 3
19-nortestosterone sulfate
6.2 X lo-? 1.9 X lo4
6.3 X lo-'
87.5 f 4.2
3
testosterone sulfate
1.9 X 10" 1.7 X lo4
87.9 f 2.7 66.4 f 7.3
4
boldenone sulfate 19-nortestosterone sulfate testosterone sulfate
4.7 5.2
X X X
10" lo4 10"
5 5
Fortified Urine boldenone sulfate
3
"Calculated from amount added to 2 mL of aqueous standard solution or urine.
0
2
4
6
8
TIME (min)
Flgure 4. (A) Extract of female equine control urine. (9) Extract of female equine control urlne fortified with 1.7 X lo-' M testosterone sulfate: T, testosterone. Chromatographic condiibns are given in the Experimental Section.
I
6
C
0
.
.
2
.
.
4
(Table 11) which might reflect matrix interference during the workup procedure or in the integration of peak areas.
BO NT
.
6
,
.
8 1 TIME ( m i d
. . . . . . 0
1
2
CONCLUSIONS From the different extraction modes utilized in the proposed procedure it can be concluded that the final methanol/water (80/20) eluate can only contain compounds which have been chemically modified to higher lipophilicity during solvolysis and were not present in the LSE-extract preceding solvolysis. Any compound eluted with methanol J water (35/65) presolvolysis, and extracted by ethyl acetate, should have been discarded with the methanol/water (55/45) wash in the postsolvolysis LSE. As shown for TS, sulfoconjugates of different polarity can be isolated by appropriate adjustments of the eluent compositions in the LSE isolation preceding solvolysis. Consequently, this procedure is highly selective for compounds such as sulfoconjugated steroids, also supported by the significantly different endogenous matrix of female and male horse urine extracts which can be expected from these sex-related compounds (unpublished data).
female equine control urine fortified with boldenone sulfate and 19nortestosterone sulfate (both 1.4 X lo-' M): BO, boldenone; NT, 19-nortestosterone. (C) Extract of female equine urine collected 12 h after an intramuscular therapeutic dose of boldenone undecylenate: BO, boldenone. Chromatographic conditions are given in the Experimental Section.
ACKNOWLEDGMENT We thank J. Patterson of J. T. Baker Chemical Co. for helpful information and G. A. Maylin, Director of the laboratory, for his continued support of this work. Registry NO.BOS, 87331-43-9;NTS, 98804-55-8; TS, 651-45-6; BO, 846-48-0; TG, 1180-25-2;T, 58-22-0; NT, 434-22-0.
pendent of whether it was administered as an ester or as the free steroid (18). Urine from the same horse obtained 12 h after an intramuscular dose of boldenone undecylenate treated according to the suggested procedure clearly showed the presence of BO (Figure 3C), supporting the earlier finding that BOS is excreted in urine after administration of BO to horse (11). A chromatogram of female equine control urine worked up according to the procedure for TS is shown in Figure 4A and after fortification with 1.7 X lo4 M TS (0.62 pg/mL) in Figure 4B. The recoveries of BOS,NTS, and TS from fortified equine control urine as determined by external standardization and HPLC differed slightly from aqueous standard solutions
(1) Houghton, E.; Oxiey, G. A,; Moss, M. S.: Evans, S. Biomed. Mass Spectrom. 1978, 5 , 170-173. (2) McDowall, R. D.; Pearce, J. C.; Murkitt, G. S. J. fharm. Biomed. Anal. 1988, 4 , 3-21. (3) Majors, R. E. LC-GC 1986, 4(10), 972-984. (4) Dimson, P.; Brocato, S.; Majors, R. E. Am. Lab. (Fairfield, Conn.) 1986, 18(10), 82-94. (5) Van Horne, K. C. Sorbent Extraction Technology Handbook; Anaiytichem International, Inc.: Harbor City, 1985. (6) Baker- 10 SPE Applications Guide; J. T. Baker Chemical Co.: Phiilipsburg, NJ, 1982, Vol. I. (7) Baker- 10 SPE Applicatlons Guide; J. T. Baker Chemical Co.: Phillipsburg, NJ, 1984; Voi. 11. (8) Shackieton, C. H. L. J. Chromatogr. 1986, 379,91-156. (9) Bernstein, S.; Solomon, S. Chemical and Blological Aspects of SteroM Conjugation; Springer-Veriag: New York, 1970.
Flgure 3. (A) Extract of female equine control urine. (B) Extract of
LITERATURE CITED
1984
Anal. Chem. 1987, 5 9 , 1984-1987
(IO) Dumasia. M. C.; Houghton, E. Xenobiotica 1981, 1 7 , 323-331. (11) Dumasia, M. C.; Houghton, E.; Bradley, C. V.; Williams, D. H. Biomed. Mass Spectrom. 1983, IO, 434-440. (12) Vihko, R. Acta Endocrinol. (Copenhagen), Suppl. 1966, 109, 29. (13) Berendsen, G.E.; Schoenmakers, P. J.; de Galan, L.; Vigh, G.; VargaPuchony, 2.;Inczedy. J. J , Lk7. ChrOmafOgr. 19809 3, 1669-1686. (14) Sirnonian, M. H.; Capp, M. W. J . Chromafogr. 1984, 287, 97-104. (15) Vestergaard, P. Acta Endocrinol. (Copenhagen), s ~ p p l 1978, . 217, 96-120. (16) Burstein, S.; Lieberman, S. J . A m . Chem. SOC. 1958, 8 0 , 5235-5239. (17) Tuinstra, L. G.M. Th.; Traag, W. A . ; Keukens, H. J.; Van Mazijk, R. J.
J . Chromafogr. 1083, 279, 533-542. (18) Dumasia, M. C.; Houghton, E.; Sinklns, S. J . Chromafogr. 1988, 377, 23-33.
RECEIVED for review December 23, 1986. Accepted April 6, 1987. Financial support for this work was obtained from the Harry M. Zweig Memorial Fund, International Minerals and Chemicals Corp. (Terra Haute, IN), and the New York State Racing and Wagering Board.
Equations for Chromatographic Peak Modeling and Calculation of Peak Area J o e P. Foley
Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803-1804
By use of the exponentially modifled Gausslan (EMG) as the skewed model, emplrlcal equations based on peak height, wldth, and asymmetry measurements have been developed for the accurate and preclse calculation of peak area for symmetrlc (Gaussian) and skewed peaks. These equatlons are useful In determining whether or not an experimental chromatographic peak flts the Gausdan or EMG peak model. They can also be used In quantltatlve analyses when electronlc lntegratlon Is precluded by peak overlap, baselkre drlft, etc. or when electronic lntegratlon Is unavailable. By use of the area equatlons, 40 llquld chromatographic peaks were tested and 90 % were found to fit the Gausslan or EMG model.
Quantitative peak shape analysis is important in many areas of analytical chemistry. In chromatography, as noted recently by Dezaro et. al ( I ) , the degree and nature of peak asymmetry are indicative of problems with stationary phase kinetics, thermodynamics, or extracolumn effects. Two approaches have traditionally been taken for chromatographic peak characterization. The first approach assumes a Gaussian peak shape so that a parameter of interest, e.g., plant count, may be calculated from graphically measurable parameters. The second approach employs statistical moment calculations following data acquisition and makes no assumptions about peak shape. Both of these approaches have serious drawbacks: the Gaussian approach is grossly inaccurate, and the data acquisition/moment approach is frequencly imprecise and moderately inaccurate due to noise (2-5), uncertainties in peak stop/start assignments ( 4 , 6 , 7), and base-line drift (2, 8 ) . In addition, the higher moments are especially sensitive to peak tailing (2). A final drawback of the moment method is that it is not available in every laboratory. Recently some empirical methods based on graphically measurable parameters were introduced (9, 10) for the characterization of chromatographic peaks. They are accurate for both Gaussian and tailed peaks, assuming the tailed peaks fit a widely accepted exponentially modified Gaussian (EMG) peak-shape model. Although the EMG function is usually an adequate model for tailed chromatographic peaks ( I I ) , the adequacy should always be verified before the EMG model is employed. The previous graphical methods for testing the fit of peaks to the EMG model require a comparison of values of several peak
parameters at three peak height fractions (9, IO). Although these peak-testing methods are adequate in most cases, they may lack the precision to reject marginal peaks. In addition, these methods require numerous calculations of several parameters and are thus somewhat impractical. In this paper we report equations for the calculation of the peak area of Gaussian and EMG peaks. These equations can be used to test more accurately and precisely the fit of real peaks to the Gaussian or EMG model. They can also be used to accurately quantitate Gaussian and EMG peaks when peak overlap, base-line errors, noise, etc. preclude electronic integration or when electronic integration is unavailable or is suspect.
EXPERIMENTAL SECTION Computations. Either an Apple 11+ or an Apple Macintosh computer was used for all calculations. Programs were written in BASIC. EMG Peak Generation. The exponentially modified Gaussian (EMG) function results from the convolution of a Gaussian function and an exponential decay function and can be expressed in a variety of ways (12-14). The specific form we used was EMG(t) = A / . exp[(l/2) X z (VG/T)'
- (t - t d / r I
-OD
ex~(-~'/2)/(2n)''' dy (1)
where A is the peak area, tG and UG are the retention time and standard deviation of the Gaussian function, r is the time constant of the exponential decay function, and z = (t - tG)/aG - g G / T . The integral in eq 1 was evaluated by use of an accurate polynomial approximation (11). Note that the ratio i / g G is a fundamental measure of peak asymmetry. As r/aG increases, the tailing of the chromatographicpeak increases. As T / g G approaches 0, the resulting peak approaches that of a Gaussian. Values of A = 1, t G = 100, and UG = 5 were used in eq 1 for peak generation. The 7/00 ratio was varied from 0.3 to 4.2 in 0.1 incrementa producing data equivalent to 40 peaks. A search algorithm described previously (11)was used for the measurement of the retention time, peak height, width, and asymmetry at several peak height fractions (0.1, 0.25, 0.3, 0.5, and 0.75). These parameters are illustrated in Figure l for an EMG peak with T / u C = 2.
Empirical Area Equations. Equations for the accurate calculation of peak area for a wide range of symmetric (Gaussian) and tailed (EMG) peaks were obtained by the least-squares fitting of Atrue/AG vs. b l a from T / U G = 0.3-4.2, where Atrueis the area from eq 1, b l a is the empirical asymmetry factor, and AG is the area calculated by using the Gaussian equation (15) A G = C,hpW, (2)
0003-2700/87/0359-1964$01.50/0@ 1987 American Chemical Society
