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Determination of theophylline in blood serum by UV spectrophotometry and partial least-squares (PLS-1) calibration
Analytica Chimica Acta 384 (1999) 95±103
Determination of theophylline in blood serum by UV spectrophotometry and partial least-squares (PLS-1) calibration HeÂctor C. Goicoecheaa,b, Alejandro C. Olivierib,*, Arsenio MunÄoz de la PenÄac a
Departamento de QuõÂmica, Facultad de BioquõÂmica y Ciencias BioloÂgicas, Universidad Nacional del Litoral, Paraje El Pozo, Santa Fe (3000), Argentina b Departamento de QuõÂmica AnalõÂtica, Facultad de Ciencias BioquõÂmicas y FarmaceÂuticas, Universidad Nacional de Rosario, Suipacha 531, Rosario (2000), Argentina c Departamento de QuõÂmica AnalõÂtica, Campus Universitario, Universidad de Extremadura, Avda. de Elvas s/n, 06071, Badajoz, Spain Received 24 August 1998; received in revised form 10 November 1998; accepted 17 November 1998
Abstract Partial least-squares (PLS-1) multivariate calibration of spectrophotometric data have been applied to the determination of theophylline in blood serum. After sample deproteinization and alkalinization, the electronic absorption spectrum (in the 265± 302 nm region) is processed using a calibration design which includes a series of serum pools spiked with theophylline. The concentrations lay within the therapeutic range (0.0±35.0 mg mlÿ1). All statistical indicators (prediction in validation sets, precision and accuracy) are reasonably good. A comparison of this method with an immuno¯uorescent polarization technique revealed no signi®cant differences in their prediction abilities. Studies in the presence of triglycerides, bilirubin, hemoglobin and caffeine showed that only the latter was able to interfere, as with other theophylline monitoring techniques. # 1999 Elsevier Science B.V. All rights reserved. Keywords: UV spectrophotometry; Multivariate calibration; Partial least-squares; Theophylline monitoring
1. Introduction Theophylline (1,3-dimethylxanthine) has been the cornerstone of asthma management for 70 years. It remains an important drug in the treatment of this disease, especially for patients with moderate-tosevere symptoms [1]. It is commonly prescribed for pediatric patients with asthma, other forms of reactive airway disease, and apnea of prematurity [2].
*Corresponding author. Tel.: +54-41-372704; fax: +54-41372704; e-mail: [email protected]
Recently, it was also reported that theophylline shows a bene®cial effect, both in the treatment and prevention of erythrocytosis in patients with chronic obstructive pulmonary disease [3]. The serum concentration of theophylline must be maintained within a relatively narrow range to achieve optimal therapeutic bene®ts while avoiding toxic side effects. The greatest likelihood of obtaining maximal bronchodilatation with reasonable safety is achieved with peak serum concentrations between 10 and 20 mg mlÿ1 [4,5]. Undesirable side effects, including headaches, dizziness, nervousness, insomnia, anorexia, nausea, vomiting and epigastric pain have been associated with serum
0003-2670/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S0003-2670(98)00834-4
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levels exceeding the recommended therapeutic range. Concentrations >30 mg mlÿ1 carry an increased risk of more serious side effects, including hypokalemia, cardiac dysrhythmia, seizures, coma and death [1,6].
Theophylline has been determined in blood by using spectrophotometry at two wavelengths, with a tedious prior extraction step [7,8]. Other methods have been applied, such as gas chromatography (GC) [9], GC coupled to mass spectrometry (GC/MS) [10], capillary GC [11] and high-performance liquid chromatography. Some of these latter techniques include pre-treatments, such as solvent extraction [12,13], solid-phase extraction [14] and protein precipitation [15±17]. On the other hand, there is a direct micellar liquid chromatographic method which uses a solution of a zwitterionic surfactant as mobile phase for the determination of theophylline in serum [18]. Other methods include isotope dilution MS [19], enzyme electrode amperometry [20], solid-phase extraction [21], and some immunoassays involving homogeneous immunoprecipitation [22,23], latex nephelometry [24], chemiluminescence [25], homogeneous enzyme [26] and homogeneous substratelabeled ¯uorescence [27], and ¯uorescence polarization [28]. Multivariate calibration methods [29±31] applied to both, absorptive and emissive spectral data as well as to electrochemical signals are being increasingly used for the analysis of complex biological mixtures [32]. They have the advantage of using full spectral information, and allow for a rapid determination of mixture components, often with no need of prior separation or sample pre-treatment. Pertinent examples in the ®eld of biomedical analysis are the determination of urinary metabolites of aspirin by spectro¯uorimetry [33,34], salicylic acid and di¯unisal in human serum [35], glucose in blood by near-infrared
[36,37] and Raman [38] spectroscopies, and calcium and magnesium in plasma by UV/visible spectrophotometry [39]. In the present report, we discuss the possibility of determining theophylline in blood serum samples by applying electronic absorption measurements together with partial least-squares (PLS) calibration. As will be shown below, an important degree of spectral overlap exists among theophylline and normal serum components (which may substantially vary among individuals) in the spectral region of interest. The problem thus consists of a single analyte embedded in a highly complex matrix which is dif®cult to reproduce. We have thus explored the use of the PLS-1 formalism for accomplishing this goal, together with a calibration design prepared to take into account the natural variability of the serum samples. To the best of our knowledge, this is the ®rst attempt to determine theophylline in human serum by multivariate calibration of electronic absorption data.
2. Experimental 2.1. Apparatus Electronic absorption measurements were carried out on a Beckman DU-640 spectrophotometer, using 1.00 cm3 quartz cells. All spectra were saved in ASCII format, and transferred to a PC Pentium 166 microcomputer for subsequent manipulation. PLS-1 was then applied using the PLSPLUS package of GRAMS386, version 2.02, which incorporates the algorithm described in Ref. [29]. Polarized immuno¯uorescence measurements were done with an Abbott FPIA TDx equipment at Hospital Provincial de Santa Fe, Argentina. 2.2. Reagents All experiments were performed with analyticalreagent grade chemicals. Stock solutions of theophylline and caffeine containing 1.000 g lÿ1 were prepared by dissolving the compounds in doubly distilled water. Serum samples were prepared by spiking blank sera with appropriate amounts of the stock solution of theophylline.
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Table 1 Composition of the calibration samples used for the determination of theophylline by spectrophotometry/PLS-1 analysis Sample No.
Theophylline (mg mlÿ1)
Pool a
Sample No.
Theophylline (mg mlÿ1)
Pool a
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0
A A A A B B B B C C C C D D D D E E E E F F F F G G G G H H H H I I I I J J J J
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
0.0 10.0 20.0 30.0 10.0 15.0 20.0 25.0 10.0 15.0 20.0 25.0 10.0 15.0 20.0 25.0 5.0 15.0 25.0 35.0 5.0 15.0 25.0 35.0 5.0 15.0 25.0 35.0 5.0 10.0 15.0 20.0 5.0 10.0 15.0 20.0 5.0 10.0 15.0 20.0
K K K K L L L L M M M M N N N N O O O O P P P P Q Q Q Q R R R R S S S S T T T T
a
The letters A±T identify different pools of sera.
2.3. Calibration set It was estimated that the analyte of interest is present within a complex mixture of an unknown but rather large number of components. Therefore, in order to mimic the possible variation in the latter components, serum pools were used for calibration, each of them consisting of sera from 15 different patients. The calibration set was designed with 20
serum pools with added theophylline in the 0.0±35.0 mg mlÿ1 range (Table 1). The selected concentrations cover the therapeutic range of theophylline. 2.4. Validation sets Several validation sets of samples were prepared. Both, the composition and purpose of each set are shown in Table 2.
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Table 2 Composition and purpose of the validation sets Set No.
Purpose
Serum samples
Theophylline added (mg mlÿ1)
1 2 3 4 5 6
validation of the PLS-1 calibration validation of the PLS-1 calibration study of precision and accuracy comparison with the FPIA TDx method study of interference from caffeine study of interference from triglycerides, bilirrubin and hemoglobin
eight different sera three different sera pool of normal sera 23 individual sera pool of normal sera with added caffeine lipemic, icteric and hemolized sera
20.0 15.0, 20.0, 25.0 20.0 0.0±30.0 20.0 20.0
2.5. Technique The appropriate amount of the stock solution of theophylline was added to 1.00 ml of serum in order to obtain the desired concentration. The sample was then homogenized, and 1.00 ml of 24%P/V trichloroacetic acid was added after 15 min. After centrifuging (15 min at 3000 rpm), 1.00 ml of 2 M NaOH was added to 1.00 ml of the supernatant solution, and the electronic absorption spectrum was recorded in the 265± 302 nm region, digitized every 1 nm, which implies working with 38 absorbance data per spectrum. 3. Results and discussion Fig. 1 shows several spectra of human sera, together with a spectrum of an aqueous solution of theophylline containing 20 mg mlÿ1. This ®gure highlights both, the intrinsic variability displayed by basal sera and the high degree of overlapping of the serum signals (even after deproteinization), with the spectrum of theophylline. We found that maximum information concerning theophylline can be gathered by serum deproteinization with trichloroacetic acid, followed by alkalinization with NaOH before the absorption measurements in the 265±302 nm region (Fig. 1 and Section 2). It was found that a proper design of the calibration set required a rather large number of calibration samples, in line with previous works on factor-based analyses in biological ¯uids [36±38], where the blank is intrinsically variable. In the present case, the calibration set shown in Table 1 was prepared, consisting of basal sera containing theophylline in the 0±35 mg mlÿ1 range, with concentrations spaced 5 mg mlÿ1 apart.
Fig. 1. Electronic absorption spectra of: (ÐÐÐ), several blank serum samples and (± ± ±), aqueous solution of theophylline (20.0 mg mlÿ1). Below 265 nm, the serum samples only give uninformative noise.
3.1. Calibration and selection of the optimum number of factors The optimum number of factors to be used within the PLS-1 algorithm is an important parameter to achieve better performance in prediction. This allows to model the system with the optimum amount of information, avoiding over®tting. The cross-validation procedure was applied, consisting of systematically removing one of the training samples in turn, and using only the remaining ones for construction of the latent factors and regression [29]. The predicted concentrations were then compared with the actual ones for each of the calibration serum samples, and the predicted error sum of squares [PRESS P (cact ÿ cpred)2)] was calculated. The PRESS was computed in the same manner, each time a new
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calibration sample is calculated from: , n X 2 F cj m ÿ 1 ecj eci 2
(4)
i6j
where eci is the difference between the actual and estimated concentrations for the ith sample left out during cross validation. The spectral F(aj) ratio for each sample is calculated from: , n m X n X X 2 eaj;k eai;k 2 F aj m ÿ 1 (5) k1
Fig. 2. Calibration of PRESS as a function of the number of PLS-1 factors. Inset shows an expansion of the range between four and eight factors.
factor was added to the PLS model. To select the optimum number of factors, the criteria proposed by Haaland and Thomas [29] was used. In our case, the value of F corresponding to a probability smaller than 0.75 yielded an optimum number of factors of six (Fig. 2). The usual statistical parameters, giving an indication of the quality of ®t of all the data, are the root mean square difference (RMSD), square of the correlation coef®cient (R2) and relative error of prediction (REP%). The expressions for these parameters are: " #1=2 m 1X 2 cact ÿ cpred (1) RMSD m 1 Pm 2 2 1 cact ÿ cpred (2) R 1ÿ P m c 2 1 cact ÿ " #1=2 m 100 1 X 2 cact ÿ cpred (3) REP % c m 1 where cact and cpred are the actual and predicted concentrations during the cross-validation process, m the total number of standard serum samples, and c the average analyte concentration in the m samples. The obtained values using six calibration factors were: RMSD 1.48, R2 0.981 and REP% 9.9%. Outlier analysis was performed on the calibration samples on the basis of both, the concentration and spectral F ratios. The concentration F(cj) ratio for each
i6j k1
where eai,k is the spectral residue of the ith sample left out during cross validation [29]. The ability of the designed calibration in extracting the relevant spectral information for theophylline is shown in Fig. 3, which compares the normalized spectrum of theophylline with the ®rst weight loading vector of the PLS-1 calibration. The latter is the leastsquares approximation to the pure analyte of interest. 3.2. Prediction Sample sets Nos. 1 and 2 (Table 2) were analyzed in accordance with the foregoing procedure, with the results shown in Table 3. Both, the recoveries and values of REP% are acceptable. It is noteworthy that the latter is calculated with the predicted values for the validation sets of samples, and may differ from that cited here for calibration. All predicted samples were checked for the presence of outliers. This is done by PLS-1 on the basis of the calculation of the spectral F(as) ratio, i.e. , n m X n X X 2 eas;k eai;k 2 F as m (6) k1
i1 k1
where eas,k is the spectral residue of the unknown sample and eai,k is the corresponding residue of each of the m calibration samples [29]. 3.3. Precision 3.3.1. Intra-assay variability (repeatability) Ten samples of set No. 3 (Table 2) were analyzed by PLS-1 in order to study the intra-assay variability. The results yielded an average of 19.9 mg mlÿ1, with s 0.9 mg mlÿ1 and CV 4.6%.
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Fig. 3. (ÐÐÐ) First six weight-loading vectors (w1±w6) of the PLS-1 calibration, as indicated; and (± ± ±) normalized electronic absorption spectrum of an aqueous solution of theophylline.
3.3.2. Interassay variability (reproducibility) Four triplicates of set No. 3 (Table 2) were analyzed during four consecutive weeks in order to assess the interassay variability. The results were: average 20.2 mg mlÿ1, s 1.3 mg mlÿ1 and CV 6.4%. 3.4. Accuracy Set No. 3 (Table 2) was analyzed (n 10) with the method of polarized immuno¯uorescence FPIA TDx (Abbott Laboratories, see below), yielding an average of 19.8 mg mlÿ1, with s 0.42 mg mlÿ1 and CV 2.1%. The variances for the immnunomethod and the presently studied one were analyzed. The critical value dcrit to test the difference between sample means was calculated. According to this test, dcrit 0.72 (at 95% con®dence level), whereas jcpred j 0:1; thus, we conclude that the difference is not signi®cant and the present method shows an accuracy comparable to that of FPIA TDx. 3.5. Interferences Table 4 collects the results concerning the possible interference of triglycerides, bilirubin, hemoglobin
and caffeine using set Nos. 5 and 6 (Table 2). No signi®cant interference was detected in the ®rst three cases: the ability of the PLS-1 method in recovering the theophylline content from a lipemic serum is re¯ected in Fig. 4, which compares the latter with a normal one. Only in the case of caffeine a signi®cant interference has been found. It should be noted, however, that other methods available for the determination of theophylline also suffer from the interference of caffeine [16]. This interference may be avoided with an appropriate calibration set, which may involve a three-level two-component (theophylline and caffeine) full factorial design and an adequate number of sera. Another alternative, already described in the literature, is to take samples from patients before any tea or coffee consumption [16]. 3.6. Comparison with the polarized immunofluorescence method A total of 23 samples of the set No. 6 (Table 2) were analyzed by PLS-1 and a reference ¯uorescence polarization immunoanalysis FPIA TDx [28]. The results are shown in Table 5 and in Fig. 5. We have applied two different comparison tests to these data. Since
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Table 3 Results obtained by applying the spectrophotometry/PLS-1 analysis to serum samples spiked with theophylline Sample
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Theophylline/mg mlÿ1 added
found
20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 15.0 15.0 15.0 20.0 20.0 20.0 25.0 25.0 25.0 REP% 7.5%
22.3 21.3 18.6 20.6 23.2 22.9 18.7 21.2 14.5 15.5 15.2 21.2 20.5 21.9 24.0 25.7 25.3
Recovery %
111.5 106.5 93.0 103.0 116.0 114.5 93.5 106.0 96.7 103.3 101.3 106.0 102.5 109.5 96.0 102.8 101.2
Fig. 4. Electronic absorption spectra of: (ÐÐÐ) normal serum samples spiked with theophylline (20.1 mg mlÿ1) and (± ± ±) a lipemic serum sample spiked with theophylline (19.6 mg mlÿ1). Spectral residues are shown (intensities 10 in the 265±302 nm region) for one of the theophyllines containing normal sera, after calibration and prediction using the first six PLS-1 factors.
Table 4 Analysis of interferences in the determination of theophylline in serum by spectrophotometry/PLS-1 analysis Interference Triglycerides Bilirubin Hemoglobin Caffeine
Theophylline/mg mlÿ1
Content ÿ1
10 mg ml 300 mg mlÿ1
10 mg mlÿ1 10 mg mlÿ1
added
found
19.6 20.0 0.0 20.0 20.0
19.5 22.9 3.5 19.5 26.5
approximate standard deviations of both these methods are known, i.e. sPLS-1 0.9 mg mlÿ1 and sFPIA 0.42 mg mlÿ1 (see above), a regression analysis known as constant variance ratio approach for estimating slopes was ®rst applied [40±42]. In this method, errors in both the regressed variables are taken into account, with relative weights which depend on the ratio of the variances corresponding to the tested methods. The result is: m 1.00 (sm 0.06), n 1 (sn 1). As can be seen, using t(0.05,21) 2.08, the con®dence intervals for the slope and intercept (m tsm and n tsn) contain the theoretical values of one and zero, respectively. Further-
more, a recently introduced informational analysis of variance for method comparison was also applied [41]. In this case, the parameter " (1 m2)/ (1 m)2 was computed, whose theoretical value is 1/2. According to Table 5, " 0.500 (s" 0.001), and thus both these methods are again found to be comparable at the 95% con®dence level, since the con®dence interval " ts" contains the expected value of 1/2. 4. Conclusions A simple multivariate calibration spectrophotometric method for the determination of theophlylline in blood serum has been developed. It involves serum deproteinization and alkalinization with NaOH, followed by measurement of the electronic absorption spectrum in the 265±302 nm region. The spectral data are then processed using a partial least-squares (PLS1) calibration, the latter being designed with a series of serum pools spiked with theophylline in the 0.0± 35.0 mg mlÿ1 range. The statistical indicators for the prediction in validation sets of samples, precision and accuracy are all reasonably good. Furthermore, the concentrations predicted by the presently studied method are statistically comparable to those yielded
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Table 5 Results obtained by applying FPIA TDx and spectrophotometry/ PLS-1 analyses to serum samples spiked with theophylline Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Theophylline found (mg mlÿ1) FPIA TDx
PLS-1
0.0 6.5 33.2 9.7 12.2 14.8 20.1 15.6 19.3 16.8 24.2 28.6 0.0 3.9 8.0 11.2 11.4 14.7 16.5 16.6 19.8 19.5 23.0
1.4 5.3 30.6 12.7 14.9 17.7 19.9 18.5 20.4 22.6 27.1 29.8 0.0 1.6 5.7 14.2 15.3 17.5 17.6 19.4 18.7 18.9 21.2
by an immuno¯uorescent polarization technique. Interference studies indicate no signi®cant effects from triglycerides, bilirubin and hemoglobin. Only caffeine has been found to interfere, as in other available methods for the determination of theophylline. In conclusion, the combination of PLS-1 multivariate calibration and spectrophotometric measurements constitutes a valuable tool toward the development of simple methods for monitoring theophylline and other important drugs in blood serum. Acknowledgements Financial support from CONICET (Consejo Nacional de Investigaciones Cientõ®cas y TeÂcnicas), the University of Rosario and FundacioÂn Antorchas is gratefully acknowledged. A. MunÄoz de la PenÄa thanks DGES (Project PB95-1141) for ®nantial support. H.C. Goicoechea thanks FOMEC (Programa para el Mejoramiento de la Calidad de la EnsenÄanza Universitaria)
Fig. 5. Plot of the results obtained by applying spectrophotometry/ PLS-1 vs. those obtained from FPIA TDx analyses of serum samples spiked with theophylline (*). The solid line is the regression line y 1.00x 1, where x,y correspond to FPIA and PLS-1 methods, respectively.
for a fellowship. The authors also thank Abbott Laboratories (Rosario) for the supply of a kit for polarized ¯uorescence immunoassay, and Elisa Kleinsorge and Carlos Mastandrea (Hospital Provincial de Santa Fe) who made the FPIA TDx analyses.
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Determination of theophylline in blood serum by UV spectrophotometry and partial least-squares (PLS-1) calibration HeÂctor C. Goicoecheaa,b, Alejandro C. Olivierib,*, Arsenio MunÄoz de la PenÄac a
Departamento de QuõÂmica, Facultad de BioquõÂmica y Ciencias BioloÂgicas, Universidad Nacional del Litoral, Paraje El Pozo, Santa Fe (3000), Argentina b Departamento de QuõÂmica AnalõÂtica, Facultad de Ciencias BioquõÂmicas y FarmaceÂuticas, Universidad Nacional de Rosario, Suipacha 531, Rosario (2000), Argentina c Departamento de QuõÂmica AnalõÂtica, Campus Universitario, Universidad de Extremadura, Avda. de Elvas s/n, 06071, Badajoz, Spain Received 24 August 1998; received in revised form 10 November 1998; accepted 17 November 1998
Abstract Partial least-squares (PLS-1) multivariate calibration of spectrophotometric data have been applied to the determination of theophylline in blood serum. After sample deproteinization and alkalinization, the electronic absorption spectrum (in the 265± 302 nm region) is processed using a calibration design which includes a series of serum pools spiked with theophylline. The concentrations lay within the therapeutic range (0.0±35.0 mg mlÿ1). All statistical indicators (prediction in validation sets, precision and accuracy) are reasonably good. A comparison of this method with an immuno¯uorescent polarization technique revealed no signi®cant differences in their prediction abilities. Studies in the presence of triglycerides, bilirubin, hemoglobin and caffeine showed that only the latter was able to interfere, as with other theophylline monitoring techniques. # 1999 Elsevier Science B.V. All rights reserved. Keywords: UV spectrophotometry; Multivariate calibration; Partial least-squares; Theophylline monitoring
1. Introduction Theophylline (1,3-dimethylxanthine) has been the cornerstone of asthma management for 70 years. It remains an important drug in the treatment of this disease, especially for patients with moderate-tosevere symptoms [1]. It is commonly prescribed for pediatric patients with asthma, other forms of reactive airway disease, and apnea of prematurity [2].
*Corresponding author. Tel.: +54-41-372704; fax: +54-41372704; e-mail: [email protected]
Recently, it was also reported that theophylline shows a bene®cial effect, both in the treatment and prevention of erythrocytosis in patients with chronic obstructive pulmonary disease [3]. The serum concentration of theophylline must be maintained within a relatively narrow range to achieve optimal therapeutic bene®ts while avoiding toxic side effects. The greatest likelihood of obtaining maximal bronchodilatation with reasonable safety is achieved with peak serum concentrations between 10 and 20 mg mlÿ1 [4,5]. Undesirable side effects, including headaches, dizziness, nervousness, insomnia, anorexia, nausea, vomiting and epigastric pain have been associated with serum
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levels exceeding the recommended therapeutic range. Concentrations >30 mg mlÿ1 carry an increased risk of more serious side effects, including hypokalemia, cardiac dysrhythmia, seizures, coma and death [1,6].
Theophylline has been determined in blood by using spectrophotometry at two wavelengths, with a tedious prior extraction step [7,8]. Other methods have been applied, such as gas chromatography (GC) [9], GC coupled to mass spectrometry (GC/MS) [10], capillary GC [11] and high-performance liquid chromatography. Some of these latter techniques include pre-treatments, such as solvent extraction [12,13], solid-phase extraction [14] and protein precipitation [15±17]. On the other hand, there is a direct micellar liquid chromatographic method which uses a solution of a zwitterionic surfactant as mobile phase for the determination of theophylline in serum [18]. Other methods include isotope dilution MS [19], enzyme electrode amperometry [20], solid-phase extraction [21], and some immunoassays involving homogeneous immunoprecipitation [22,23], latex nephelometry [24], chemiluminescence [25], homogeneous enzyme [26] and homogeneous substratelabeled ¯uorescence [27], and ¯uorescence polarization [28]. Multivariate calibration methods [29±31] applied to both, absorptive and emissive spectral data as well as to electrochemical signals are being increasingly used for the analysis of complex biological mixtures [32]. They have the advantage of using full spectral information, and allow for a rapid determination of mixture components, often with no need of prior separation or sample pre-treatment. Pertinent examples in the ®eld of biomedical analysis are the determination of urinary metabolites of aspirin by spectro¯uorimetry [33,34], salicylic acid and di¯unisal in human serum [35], glucose in blood by near-infrared
[36,37] and Raman [38] spectroscopies, and calcium and magnesium in plasma by UV/visible spectrophotometry [39]. In the present report, we discuss the possibility of determining theophylline in blood serum samples by applying electronic absorption measurements together with partial least-squares (PLS) calibration. As will be shown below, an important degree of spectral overlap exists among theophylline and normal serum components (which may substantially vary among individuals) in the spectral region of interest. The problem thus consists of a single analyte embedded in a highly complex matrix which is dif®cult to reproduce. We have thus explored the use of the PLS-1 formalism for accomplishing this goal, together with a calibration design prepared to take into account the natural variability of the serum samples. To the best of our knowledge, this is the ®rst attempt to determine theophylline in human serum by multivariate calibration of electronic absorption data.
2. Experimental 2.1. Apparatus Electronic absorption measurements were carried out on a Beckman DU-640 spectrophotometer, using 1.00 cm3 quartz cells. All spectra were saved in ASCII format, and transferred to a PC Pentium 166 microcomputer for subsequent manipulation. PLS-1 was then applied using the PLSPLUS package of GRAMS386, version 2.02, which incorporates the algorithm described in Ref. [29]. Polarized immuno¯uorescence measurements were done with an Abbott FPIA TDx equipment at Hospital Provincial de Santa Fe, Argentina. 2.2. Reagents All experiments were performed with analyticalreagent grade chemicals. Stock solutions of theophylline and caffeine containing 1.000 g lÿ1 were prepared by dissolving the compounds in doubly distilled water. Serum samples were prepared by spiking blank sera with appropriate amounts of the stock solution of theophylline.
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Table 1 Composition of the calibration samples used for the determination of theophylline by spectrophotometry/PLS-1 analysis Sample No.
Theophylline (mg mlÿ1)
Pool a
Sample No.
Theophylline (mg mlÿ1)
Pool a
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0
A A A A B B B B C C C C D D D D E E E E F F F F G G G G H H H H I I I I J J J J
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
0.0 10.0 20.0 30.0 10.0 15.0 20.0 25.0 10.0 15.0 20.0 25.0 10.0 15.0 20.0 25.0 5.0 15.0 25.0 35.0 5.0 15.0 25.0 35.0 5.0 15.0 25.0 35.0 5.0 10.0 15.0 20.0 5.0 10.0 15.0 20.0 5.0 10.0 15.0 20.0
K K K K L L L L M M M M N N N N O O O O P P P P Q Q Q Q R R R R S S S S T T T T
a
The letters A±T identify different pools of sera.
2.3. Calibration set It was estimated that the analyte of interest is present within a complex mixture of an unknown but rather large number of components. Therefore, in order to mimic the possible variation in the latter components, serum pools were used for calibration, each of them consisting of sera from 15 different patients. The calibration set was designed with 20
serum pools with added theophylline in the 0.0±35.0 mg mlÿ1 range (Table 1). The selected concentrations cover the therapeutic range of theophylline. 2.4. Validation sets Several validation sets of samples were prepared. Both, the composition and purpose of each set are shown in Table 2.
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Table 2 Composition and purpose of the validation sets Set No.
Purpose
Serum samples
Theophylline added (mg mlÿ1)
1 2 3 4 5 6
validation of the PLS-1 calibration validation of the PLS-1 calibration study of precision and accuracy comparison with the FPIA TDx method study of interference from caffeine study of interference from triglycerides, bilirrubin and hemoglobin
eight different sera three different sera pool of normal sera 23 individual sera pool of normal sera with added caffeine lipemic, icteric and hemolized sera
20.0 15.0, 20.0, 25.0 20.0 0.0±30.0 20.0 20.0
2.5. Technique The appropriate amount of the stock solution of theophylline was added to 1.00 ml of serum in order to obtain the desired concentration. The sample was then homogenized, and 1.00 ml of 24%P/V trichloroacetic acid was added after 15 min. After centrifuging (15 min at 3000 rpm), 1.00 ml of 2 M NaOH was added to 1.00 ml of the supernatant solution, and the electronic absorption spectrum was recorded in the 265± 302 nm region, digitized every 1 nm, which implies working with 38 absorbance data per spectrum. 3. Results and discussion Fig. 1 shows several spectra of human sera, together with a spectrum of an aqueous solution of theophylline containing 20 mg mlÿ1. This ®gure highlights both, the intrinsic variability displayed by basal sera and the high degree of overlapping of the serum signals (even after deproteinization), with the spectrum of theophylline. We found that maximum information concerning theophylline can be gathered by serum deproteinization with trichloroacetic acid, followed by alkalinization with NaOH before the absorption measurements in the 265±302 nm region (Fig. 1 and Section 2). It was found that a proper design of the calibration set required a rather large number of calibration samples, in line with previous works on factor-based analyses in biological ¯uids [36±38], where the blank is intrinsically variable. In the present case, the calibration set shown in Table 1 was prepared, consisting of basal sera containing theophylline in the 0±35 mg mlÿ1 range, with concentrations spaced 5 mg mlÿ1 apart.
Fig. 1. Electronic absorption spectra of: (ÐÐÐ), several blank serum samples and (± ± ±), aqueous solution of theophylline (20.0 mg mlÿ1). Below 265 nm, the serum samples only give uninformative noise.
3.1. Calibration and selection of the optimum number of factors The optimum number of factors to be used within the PLS-1 algorithm is an important parameter to achieve better performance in prediction. This allows to model the system with the optimum amount of information, avoiding over®tting. The cross-validation procedure was applied, consisting of systematically removing one of the training samples in turn, and using only the remaining ones for construction of the latent factors and regression [29]. The predicted concentrations were then compared with the actual ones for each of the calibration serum samples, and the predicted error sum of squares [PRESS P (cact ÿ cpred)2)] was calculated. The PRESS was computed in the same manner, each time a new
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calibration sample is calculated from: , n X 2 F cj m ÿ 1 ecj eci 2
(4)
i6j
where eci is the difference between the actual and estimated concentrations for the ith sample left out during cross validation. The spectral F(aj) ratio for each sample is calculated from: , n m X n X X 2 eaj;k eai;k 2 F aj m ÿ 1 (5) k1
Fig. 2. Calibration of PRESS as a function of the number of PLS-1 factors. Inset shows an expansion of the range between four and eight factors.
factor was added to the PLS model. To select the optimum number of factors, the criteria proposed by Haaland and Thomas [29] was used. In our case, the value of F corresponding to a probability smaller than 0.75 yielded an optimum number of factors of six (Fig. 2). The usual statistical parameters, giving an indication of the quality of ®t of all the data, are the root mean square difference (RMSD), square of the correlation coef®cient (R2) and relative error of prediction (REP%). The expressions for these parameters are: " #1=2 m 1X 2 cact ÿ cpred (1) RMSD m 1 Pm 2 2 1 cact ÿ cpred (2) R 1ÿ P m c 2 1 cact ÿ " #1=2 m 100 1 X 2 cact ÿ cpred (3) REP % c m 1 where cact and cpred are the actual and predicted concentrations during the cross-validation process, m the total number of standard serum samples, and c the average analyte concentration in the m samples. The obtained values using six calibration factors were: RMSD 1.48, R2 0.981 and REP% 9.9%. Outlier analysis was performed on the calibration samples on the basis of both, the concentration and spectral F ratios. The concentration F(cj) ratio for each
i6j k1
where eai,k is the spectral residue of the ith sample left out during cross validation [29]. The ability of the designed calibration in extracting the relevant spectral information for theophylline is shown in Fig. 3, which compares the normalized spectrum of theophylline with the ®rst weight loading vector of the PLS-1 calibration. The latter is the leastsquares approximation to the pure analyte of interest. 3.2. Prediction Sample sets Nos. 1 and 2 (Table 2) were analyzed in accordance with the foregoing procedure, with the results shown in Table 3. Both, the recoveries and values of REP% are acceptable. It is noteworthy that the latter is calculated with the predicted values for the validation sets of samples, and may differ from that cited here for calibration. All predicted samples were checked for the presence of outliers. This is done by PLS-1 on the basis of the calculation of the spectral F(as) ratio, i.e. , n m X n X X 2 eas;k eai;k 2 F as m (6) k1
i1 k1
where eas,k is the spectral residue of the unknown sample and eai,k is the corresponding residue of each of the m calibration samples [29]. 3.3. Precision 3.3.1. Intra-assay variability (repeatability) Ten samples of set No. 3 (Table 2) were analyzed by PLS-1 in order to study the intra-assay variability. The results yielded an average of 19.9 mg mlÿ1, with s 0.9 mg mlÿ1 and CV 4.6%.
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Fig. 3. (ÐÐÐ) First six weight-loading vectors (w1±w6) of the PLS-1 calibration, as indicated; and (± ± ±) normalized electronic absorption spectrum of an aqueous solution of theophylline.
3.3.2. Interassay variability (reproducibility) Four triplicates of set No. 3 (Table 2) were analyzed during four consecutive weeks in order to assess the interassay variability. The results were: average 20.2 mg mlÿ1, s 1.3 mg mlÿ1 and CV 6.4%. 3.4. Accuracy Set No. 3 (Table 2) was analyzed (n 10) with the method of polarized immuno¯uorescence FPIA TDx (Abbott Laboratories, see below), yielding an average of 19.8 mg mlÿ1, with s 0.42 mg mlÿ1 and CV 2.1%. The variances for the immnunomethod and the presently studied one were analyzed. The critical value dcrit to test the difference between sample means was calculated. According to this test, dcrit 0.72 (at 95% con®dence level), whereas jcpred j 0:1; thus, we conclude that the difference is not signi®cant and the present method shows an accuracy comparable to that of FPIA TDx. 3.5. Interferences Table 4 collects the results concerning the possible interference of triglycerides, bilirubin, hemoglobin
and caffeine using set Nos. 5 and 6 (Table 2). No signi®cant interference was detected in the ®rst three cases: the ability of the PLS-1 method in recovering the theophylline content from a lipemic serum is re¯ected in Fig. 4, which compares the latter with a normal one. Only in the case of caffeine a signi®cant interference has been found. It should be noted, however, that other methods available for the determination of theophylline also suffer from the interference of caffeine [16]. This interference may be avoided with an appropriate calibration set, which may involve a three-level two-component (theophylline and caffeine) full factorial design and an adequate number of sera. Another alternative, already described in the literature, is to take samples from patients before any tea or coffee consumption [16]. 3.6. Comparison with the polarized immunofluorescence method A total of 23 samples of the set No. 6 (Table 2) were analyzed by PLS-1 and a reference ¯uorescence polarization immunoanalysis FPIA TDx [28]. The results are shown in Table 5 and in Fig. 5. We have applied two different comparison tests to these data. Since
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Table 3 Results obtained by applying the spectrophotometry/PLS-1 analysis to serum samples spiked with theophylline Sample
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Theophylline/mg mlÿ1 added
found
20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 15.0 15.0 15.0 20.0 20.0 20.0 25.0 25.0 25.0 REP% 7.5%
22.3 21.3 18.6 20.6 23.2 22.9 18.7 21.2 14.5 15.5 15.2 21.2 20.5 21.9 24.0 25.7 25.3
Recovery %
111.5 106.5 93.0 103.0 116.0 114.5 93.5 106.0 96.7 103.3 101.3 106.0 102.5 109.5 96.0 102.8 101.2
Fig. 4. Electronic absorption spectra of: (ÐÐÐ) normal serum samples spiked with theophylline (20.1 mg mlÿ1) and (± ± ±) a lipemic serum sample spiked with theophylline (19.6 mg mlÿ1). Spectral residues are shown (intensities 10 in the 265±302 nm region) for one of the theophyllines containing normal sera, after calibration and prediction using the first six PLS-1 factors.
Table 4 Analysis of interferences in the determination of theophylline in serum by spectrophotometry/PLS-1 analysis Interference Triglycerides Bilirubin Hemoglobin Caffeine
Theophylline/mg mlÿ1
Content ÿ1
10 mg ml 300 mg mlÿ1
10 mg mlÿ1 10 mg mlÿ1
added
found
19.6 20.0 0.0 20.0 20.0
19.5 22.9 3.5 19.5 26.5
approximate standard deviations of both these methods are known, i.e. sPLS-1 0.9 mg mlÿ1 and sFPIA 0.42 mg mlÿ1 (see above), a regression analysis known as constant variance ratio approach for estimating slopes was ®rst applied [40±42]. In this method, errors in both the regressed variables are taken into account, with relative weights which depend on the ratio of the variances corresponding to the tested methods. The result is: m 1.00 (sm 0.06), n 1 (sn 1). As can be seen, using t(0.05,21) 2.08, the con®dence intervals for the slope and intercept (m tsm and n tsn) contain the theoretical values of one and zero, respectively. Further-
more, a recently introduced informational analysis of variance for method comparison was also applied [41]. In this case, the parameter " (1 m2)/ (1 m)2 was computed, whose theoretical value is 1/2. According to Table 5, " 0.500 (s" 0.001), and thus both these methods are again found to be comparable at the 95% con®dence level, since the con®dence interval " ts" contains the expected value of 1/2. 4. Conclusions A simple multivariate calibration spectrophotometric method for the determination of theophlylline in blood serum has been developed. It involves serum deproteinization and alkalinization with NaOH, followed by measurement of the electronic absorption spectrum in the 265±302 nm region. The spectral data are then processed using a partial least-squares (PLS1) calibration, the latter being designed with a series of serum pools spiked with theophylline in the 0.0± 35.0 mg mlÿ1 range. The statistical indicators for the prediction in validation sets of samples, precision and accuracy are all reasonably good. Furthermore, the concentrations predicted by the presently studied method are statistically comparable to those yielded
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Table 5 Results obtained by applying FPIA TDx and spectrophotometry/ PLS-1 analyses to serum samples spiked with theophylline Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Theophylline found (mg mlÿ1) FPIA TDx
PLS-1
0.0 6.5 33.2 9.7 12.2 14.8 20.1 15.6 19.3 16.8 24.2 28.6 0.0 3.9 8.0 11.2 11.4 14.7 16.5 16.6 19.8 19.5 23.0
1.4 5.3 30.6 12.7 14.9 17.7 19.9 18.5 20.4 22.6 27.1 29.8 0.0 1.6 5.7 14.2 15.3 17.5 17.6 19.4 18.7 18.9 21.2
by an immuno¯uorescent polarization technique. Interference studies indicate no signi®cant effects from triglycerides, bilirubin and hemoglobin. Only caffeine has been found to interfere, as in other available methods for the determination of theophylline. In conclusion, the combination of PLS-1 multivariate calibration and spectrophotometric measurements constitutes a valuable tool toward the development of simple methods for monitoring theophylline and other important drugs in blood serum. Acknowledgements Financial support from CONICET (Consejo Nacional de Investigaciones Cientõ®cas y TeÂcnicas), the University of Rosario and FundacioÂn Antorchas is gratefully acknowledged. A. MunÄoz de la PenÄa thanks DGES (Project PB95-1141) for ®nantial support. H.C. Goicoechea thanks FOMEC (Programa para el Mejoramiento de la Calidad de la EnsenÄanza Universitaria)
Fig. 5. Plot of the results obtained by applying spectrophotometry/ PLS-1 vs. those obtained from FPIA TDx analyses of serum samples spiked with theophylline (*). The solid line is the regression line y 1.00x 1, where x,y correspond to FPIA and PLS-1 methods, respectively.
for a fellowship. The authors also thank Abbott Laboratories (Rosario) for the supply of a kit for polarized ¯uorescence immunoassay, and Elisa Kleinsorge and Carlos Mastandrea (Hospital Provincial de Santa Fe) who made the FPIA TDx analyses.
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