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Anal. Chem. 1988, 6 0 , 2666-267 1
Optical Fiber Spectrometry in Turbid Solutions by Multivariate Calibration Applied to Tablet Dissolution Testing Mats Josefson,* Erik Johansson, and Arne Torstensson Analytical Chemistry, A B Hassle, S-431 83 Molndal, Sweden
A probe connected wlth optkai flbers to a spectrophotometer provkles a convenient way to measure the concentrations In opaque solutions wlthout any prevlous filtering of the sample. This is posslbie by measuring spectra instead of single wavelengths. The statistical method pairtlai least squares (PLS) is used to correct for the disturbance caused by the turbldlty of the solution. This requhes a callbration where a set of spectra from turbid samples are palred wlth manually filtered single wavelength meaewements of the same samples. The procedure is a m e d In tablet dissdutbn tests. The error of the callbration Is small compared with the varlaUon between individual tablets. Wlth the Increased amount of informatlon In spectra compared to slngle wavelength measurements, It ls also possible to monltor the quality of the measurement by residuals and scatter plots. Automation will be posslbie by a robot moving the probe.
A novel analysis method for dissolution tests of tablets is described and applied to felodipine, an antihypertensive drug in an extended release formulation ( I ) . The method involves spectrophotometric measurements by means of fiber optics made in turbid solutions without previous filtering of the sample. The turbidity interference is compensated for by multivariate analysis. In dissolution testing, the rate and extent of drug release of a pharmaceuticalproduct are measured in an in vitro system (2). The results from the in vitro system are then correlated with in vivo measurements to obtain a test that can replace the in vivo process for quality control purposes. The dissolution test gives a good estimate of batch-to-batch consistency during production, is well established as a screening tool for formulation development, and is also used to verify that the tablet composition keeps the same properties until its expiration date. The common way to obtain samples from dissolution tests is by manual sample withdrawal or with a flow system that removes aliquots at preprogrammed times. The detection method is usually spectrophotometry, sometimes preceded by a chromatographic separation. Manual sample withdrawal is, however, not convenient for tablets made with a slow release rate of the drug because the dissolution test may take up to 24 h to complete. The flow approach has drawbacks too, since this drug is very hydrophobic and adsorbs to the plastic tubing commonly used in flow systems. It is also difficult to switch filters automatically in a flow system when the filter becomes clogged by the particles and colloids from the tablet matrix. To circumvent the adsorption of the drug in the tubings of the flow system, the spectrophotometer cell was moved into the vessel of the dissolution test with the aid of an optical fiber spectrophotometer as suggested by Munson (3). The mechanical filtering of samples was replaced by multivariate calibration with partial least squares (PLS) (4-6). PLS was used to extract the real absorbance of the drug from the bulk of information which consisted of a mixture of the drug 0003-2700/88/0360-2666$01.50/0
spectrum and the opacity “spectrum”. The amount of information gathered in the spectra also made detection of errors possible by inspection of the residuals. This is more readily done with PLS than with ordinary multiple regression (MR). MR is the most common tool for multivariate analysis but was not selected since collinearity between the variables has to be avoided (5). Usually this is accomplished by a manual selection of the most important variables. That is not favorable since information is wasted and possibly biased in this selection. The PLS algorithm bases the calculation of the result on all relevant parts of the measured spectrum. As opposed to MR this leads to better statistical properties of the calibration than if only the absorbance at a few wavelengths were used to determine the fiial result. The relevance of different parts of the spectrum is determined by the design of the calibration set. Matrix algebra based on Beer’s law is ruled out since it presumes a constant shape of the opacity “spectrum” independent of the concentration of the tablet excipients. Attempts to apply an explicitly known shape of the opacity “spectrum” by scaling of a standard failed. So did attempts to do curve fitting with shapes known from particle size measurement theory. The advantage with PLS is that it only requires the opacity ”spectrum” to behave in a reproducible manner at the dissolution runs. No explicitly known shape is necessary. Previously, derivative spectroscopy has been used to compensate for turbidity in absorbance measurements (7). That method is not used here since derivatives are more sensitive to noise than the original signal since the dynamic range is wasted in the cancellation effect when the differences between consecutive points are created. The use of the optical fibers introduces more noise than that obtained from a normal spectrophotometer due to the movements of the optical fiber.
EXPERIMENTAL SECTION Reagents. Standard solutions of felodipine, 4-(2,3-dichlorophenyl)-l,4-dihydro-2,6-dimethyl-3,5-pyridinedicarboxylic ethyl methyl ester, were prepared from an ethanolic stock solution containing 0.25 mg of felodipine per milliliter to an appropriate concentration with the buffer used in the dissolution test. The dissolution medium was a phosphate buffer (0.1 M) pH 6.5 containing 1.0% sodium lauryl sulfate (BDH, England). Two different tablet compositions were used either a 5-mg felodipine extended-release tablet or a 10-mg felodipine extended-release tablet. The tablets have about the same size but differ somewhat in the color of the film-coating. Dissolution Apparatus. Dissolution tests were performed on individual tablets by using a modified United States Pharshown in macopeia (USP)apparatus 2 (the paddle method) (8), Figure 1. The modification consisted of a special-made basket in order to place the nondisintegratingtablet into a predetermined position. This approach has also been used by Shenouda et al. (9) for similar formulations that otherwise stick to the wall in an irreproducible manner. The quadrangular basket (10 X 25 X 25 mm) was made of stainless steel gauze wire with a sieve opening of 2.4 mm. The basket is soldered in one of its upper narrow sides to the end of a stainless steel rod (length 150 mm, diameter 6 mm). The rod is brought through the cover of the dissolution vessel and fixed by means of two Teflon nuts, 32 mm from the center 0 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 80. NO. 24. DECEMBER 15, 1988 2867
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250 300 350 400 450 5 0 0 Fbum 1. Dissolution vesssl with me basket fw me dissolving tablet.
of the vessel. The lower edge of the bottom of the basket is adjusted to be 10 mm above the paddle. The basket is directed along the flow stream with the tablet under test standing on its edge. The tests were performed in 500 mL of dissolution medium at a temperature of 37 OC and with a rotation speed of 50 rpm. Spectrophotometry. The optical fiber spectrophotometer was asingle-beam Guided Wave (Model 200, Guided Wave, Inc.) with connectors for optical fibers. The spectrophotometer had a motor-driven grating mirror that is controlled by an IBM compatible computer (Vectra, HewlettPackmd). The detector used in the experimentswas a silicon detector for ultraviolet and visible light. The light from a D2lamp w a ~ filtered through a cutoff fdter at 225 nm (Guided Wave F225-L) before it entered the fiber in order to prevent damage of the fiber from the low wavelength UV radiation. The probe was a ‘six-bone” probe (Guided Wave WW100-1) made of stainless steel with a saphire window and a screw tip with a focusing zirconium mirror. The light entered the probe through one optical fiber and was collected from the mirmr by six fibers to increasethe amount of light to the detector. The probe had a spectral range from 250 to 800 nm. A cell with an optical path length of 10 mm was used. The probe was dipped manually in the six dissolution vessels during 20 s for each sampling occasion. A standard spectrophotometer (Spectronic 1001, Baush and Lomb, West Germany) was used for the filtered solutions in the calibration. It bad a spectral resolution of 2 nm. Software. A program for data collection was provided by Guided Wave. This program controlled the motor-driven grating mirror and collected the spectra. A blank spectrum was stored and subtracted from all other collected spectra. A program to calculate the principal components and partial least squares regression (PLS) was developed. The PLS algorithm was cross-tested with the SIMCA 3 8 software by Wold et al. (IO) in order to produce the same numerical results. The developed pmgram is handed through commands from the terminal or from command files to facilitate routine work. The third program is the report producer. The result is converted from absorbance units to the percentage of the labeled amount released versus time. The multivariate analysis program handles the same data format as the SIMCA 3 8 software. the format of the files from the spectrophotometer,and one additional format. The prcpam is written in Pascal and runs on IBM PC/AT compatibles and VAX. The maximum data capacity for MS-DOS 3.1 is 150 times 150 floating point numbers for independent data and the same amount for dependent data. The VAX version will be available for nonprofit use through Digital Equipment‘s users group ( D E CUS). Multivariate Calibration. The use of PLS can he divided into two steps: first, the calibration model has to be developed; second, this calibration model is used for dissolution tests. The model is built up by measuring the samples both with the optical fiber spectrophotometer and with a spectrophotometric method where the samples are fdtered and mensured at a single wavelength in the traditional manner. The PLS calibration is used to translate the information in a spectrum from a turbid solution to a single absorbance value at 362 nm as measured in a clear solution. To avoid extrapolation, calibration samples are selected to cover the
nrn
Felonpine spectra: (dotted line) standard In clear solutlm. (solid lines) dissolution test after 1. 2. 4. and 6 h. Note the lncreass whh time of the levels above 410 nm due to inaeased turbidity. Flgure 2.
entire range of future possible measurements. To stabilize the model for different turbidities, standards in clear solutions and tablets containing 5 and 10 mg of active substance are used for the same model. Finally the percentage of felodipine released at each sampling time is calculated from the obtained absorbance value, the absorbance of the standard, and the stated amount of felodipine in the tablet. Figure 2 shows an image of the spectra obtained from the spectrophotometer. Spectra are collected with a wavelength range of 25W500 nm with a resolution of 2 nm, which makes 126 data points per spectrum. The experiments were done on three different days. One spectrum was obtained per veasel and sampling time. Sampling times were 2,6, and 10 h. Spectra were obtained from 24 vessels, where 18 contained the 5-mg tablet and 6 contained the 10-mgtablet. A completely dissolved IO-mgtablet gave a concentration of 20 ,tg/mL. Five spectra from standards of felodipiue with the concentrations 6.1, 13.4,19.5,26.8, and 32.9 ,tg/mL were obtained. Standard spectra were also obtained at each sampling time to check the spectrophotometer. The 2 h values for 12 vessels with 5-mg tablets were discarded due to abnormal drift of the UV lamp. In total 65 spectra were used. The collected spectra were divided in two groups where the day for the run and the samplingtime were evenly distributed between the two groups. One group was wed to make the model and the other group was used as the samples to he predicted. AU spectra are precorrected by subtraction of the mean between 410 and 500 nm in order to correct for the offset errors in the spectrophotometer. This means that the wavelength-invariant part of the turbidity is subtracted away from each spectrum. In multivariate calibration it is sometimes common to center the data by subtraction of a mean spectrum and common to weigh the data to give the contribution of each wavelength equal importance. These operations are not performed here. The omission of centering puts the demand on the data that the absorbance is approximately zero when no absorbing substance is present. This is fulfilled. The omission of the weighing increases the importance of the wavelengths where the absorbanceis high, such as spectral peaks. and decreases the importanceof the wavelengths where the absorbance is low, such as base-line regions. The Calibration model is created as shown in Figure 3. The 33 precorrected spectra are put as rows in the X block. The columns will then contain the 126 predictor variables to be translated for each spectrum. Each spectrum is then paired with the corresponding response measurement of the absorbance in the fdtered solution. The response measurementsform the column Y in Figure 3. The model consisted of three PLS components, which means that three successive linear submodels were needed to translate the spectra into absorbances from filtered solutions. The number of components were verified through the cross-validation scheme provided by the SIMCA 3B software (11). The total standard deviation of the response variable was set to 100% before any componentswere generated. After the first component 86% of the total standard deviation was modeled. The same figures after the second and third components were 98.5% and
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
t
T
I
0
0.4t
0
U
E:;
4 PI
- 93
B
p3
-0.24 0.0
Q
P
.. 0.5
1.0
1.5
2.0
U =T'B + H y
x = T*P+E
= U'Q
t l
+F
Flgure 3. A general view of the PLS model in matrix form. The matrices T and P model the X block similarly to an ordinary principal components model, whk the matrix U and the column vector Q models the Y column vector. The connection between X and Y Is modeled as a relation between the U and T matrlces by means of a diagonal matrix E. E and F contain the residuals for X and Y. H contains the residual for the inner relation between U and T.
98.9%. The amount of time necessary for the statistical part of the calibration was for the routine case in the order of 1 h. After the calibration step, the model is used for calculations of new absorbances. The new spectra are precorrected in the same way, with the subtraction of the mean of the spectrum between 410 and 500 nm. Recalibration is necessary when the lamp, the probe, or the tablet composition is changed. Every third month, the calibration is checked by the measurement of the filtered solutions and compared with the values obtained from the calibration model. In this comparison no single error should exceed 2 % of the total amount of active substance in the tablet. 0therwise recalibration is performed. The results from the samples that are used in the checking procedure can also be used in the new recalibration together with results from two additional days of dissolution tests. Every successive component (linear submodel) of the spectra in the total model consists of the vector of loadings, denoted by p, and the scores, denoted by t. For the current case where the variables are absorbances at the wavelengths of the spectra, the loadings p, which are normalized, can be interpreted as a kind of average spectrum of all spectra in the model. The score t, for a new spectrum is the scaling factor used to multiply all the loadingswith to fit the normalized loadingswith the new spectrum. Since the model contains three linear submodels, there are three loading vectors (pl, pz, ps) which are weighed together by the three scores (tl, t2, t 3 ) for each spectrum in order to make a model that fits close to the set of possible spectra (eq 1)in the dissolution tests. spectrum = tlpl t2p2+ t3p3 residual (1)
+
+
The spectrum and the residual are vectors and the scores for one spectrum are scalars here. During the use of the calibration the residual is used as a measure of how well a new spectrum fits in the calibration model. The residual is represented both as the residual spectrum and as the residual error, a scalar expressing the total variance left, not explained by the model (s2) as shown in s2 = Z(residualJ2/(n - comp)
(2)
where the residuali are all the n elements of the residual spectrum from eq 1 and comp is a scalar for the number of components used in the model. The full algorithm is shown in the Appendix. Further details are given by Geladi and Kowalski (12).
RESULTS AND DISCUSSION When multivariate calibration is going to be used, the measured data have to be projected into another data space. This projection is generated by a collection of measurements of the predictor variables paired with their corresponding response values. This means that the magnitudes of the response variables are needed in the calibration step to produce the projection. Secondary when the calibration model is used, the new measured predictor variables are combined
values
Flgure 4. Spectra from the final calibration set projected on a plane defined by the first two components of the model: standards In clear solution (circles),IO-mgtablets (squares),and 5ing tablets (triangles).
with the calibration model to give calculated magnitudes for the response variables. In order to define the projection well, the calibration model must be valid for all cases that occur during the use of the model. This must be taken into consideration during the design of the calibration set. In order to provide a stable design of the calibration set, spectra from different runs should be included to account for the experiment-to-experiment variation. Moreover, to compensate for varying levels of turbidity a t the same concentration of the analyte, the amount of turbidity has to be varied independently of the analyte concentration (13). This can be done in a practical way since two kinds of tablets are available with approximately the same tablet matrix but one with the double concentration of the analyte. When only one kind of tablet is in the calibration set, the resolution of the turbidity from the analyte is caused mainly by differences in the behavior of the turbidity at the same sampling point of the dissolution curve for different samples. Since the behavior of the matrix is almost the same for the same kind of tablet, this would be an unstable calibration. Figure 4 shows a plot of the first two components for a calibration set with two kinds of tablets. The tl axis mainly resolves absorbance differences of the analyte while the t2axis resolves the variation of the turbidity from the analyte variation. The difference in the relation between the turbidity and the absorbance of the analyte from the two kinds of tablets can be seen as lines going from a common starting point diverging as the difference in turbidity increases with the time of the tablet dissolution experiment. The line with squares is from the dissolving 10-mg tablet and the line with the triangles is from the 5-mg tablet. Note that the 10-mg tablet goes higher on the tl absorbance axis than the 5-mgtablet does for the same sampling times in the dissolution test. To stabilize the design of the calibration set further, standards without any turbidity were measured and included in the calibration set. They fall on a line above the 10-mg tablets (circles) and have the same common starting point as the tablets. It was not beneficial to include standards above the concentration of the final concentration of the 10-mg tablet. This only increased the error in the turbidity-corrected absorbance values. When all standards above the final 10-mg concentration were deleted from the calibration set, the result became a calibration with better ability to handle variations of the turbidity and with approximately the same amount of prediction error as the calibration that combined the 5-mg and the 10-mg tablets. An attempt was also made to mix the pure tablet matrix in granulate form with standards to control the design of the calibration set in a simple way without the necessity to run the dissolution tests for the entire design. This was not successful because the shape of the turbidity signal did not become the same as in the dissolution procedure. This is not so surprising since the particles causing the turbidity in the
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988 A r
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b 0.
0
r -0.
b a
i
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t -0.4
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e
250 300 350 400 450 500
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F l g w 5. Fkst loading vector, p,, solid c w e , mcdeis the total variation of both the felodiplne absorbance and the turbdity. p2,dashed curve, models the difference between the absorbance and the turbidity. This can be seen on the positive slope above 410 nm whlch cancels the negative slope of the turbidity signal of p,. pa, dotted curve, right y
axis, tunes the calibration with a positive slope between 290 and 370 nm.
0.0
nm
Flgure 7. (Solid curve) Spectrum with one extra analyte; residual, 0.0026. (Dotted curve) Interpretation by calibration model. 0.5i V 2
0 0
L
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A
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e
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t l values 2 5 0 3 0 0 3 5 0 400 450 500
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Flguro 8. (Solid curve, left y axis) Normal spectrum not Included in the calibration set; residual, 0.000 001 4. (Dotted curve, right y axis) Interpretation by calibration model. The shape is smoothed by cancellation of noise between the spectra In the model. dissolution test are constantly stirred and hence have a different history than the laboratory-made mixture. This fact also indicated that the in situ measurement in the stirred vessel with an optical fiber probe gives a more reproducible turbidity than if samples were withdrawn and measured without filtering at a later time with a normal spectrophotometer. Hence the in situ method was preferred for use with the multivariate calibration since the conditions for the measurement were more stable. The model, which is constructed from the calibration set, consists of a set of vectors for each component of the total model. One of these vedors is the loading vector, p. If spectra are used as predictor variables, the loading vectors can be interpreted as decompositions of the main features of the original set of spectra used in the calibration. The first loading vector will account for most of the total variation in the calibration. Later loading vectors will be of the difference spectrum type in order to tune the f i t rough linear estimate. Each successive loading vector will contain less information and more noise than the previous one. All loading vectors shown in Figure 5 are normalized. This means that their scale does not represent their relative importances in the model. The relative importance for the model is instead found as the magnitude of the score values, t . The p1 vector (solid curve) is mainly the spectrum of felodipine plus the turbidity spectrum, the pz vector (dashed curve) is the correction for the turbidity, and the p3 vector (dotted curve) is noisy and contains an artifact due to a line from the D2lamp. Those loading vectors are weighted together to simulate all experimental spectra for samples covered by the design of the calibration.
Figure 8. Projection, d , of the deviating spectrum from Figure 7 related to the positions in the t,-t2 plane of the spectra from the calibration model. Figure 6 shows the model interpretation of a spectrum together with the measured spectrum. Distortions of measured spectra due to detection failures, wavelength shifts, or interfering analytes, will cause a misfit of the loading vectors. The current calibration model has no means to calculate a correct dependent value from a distorted spectrum. Instead a high value for the remaining residual (eq 1)flags the misfit. An extra analyte present with approximately the same amount of absorbance as from the measured substance (Figure 7) will cause a rise of the residual error by 3 orders of magnitude. Then the erroneous spectrum can be plotted together with the interpretation of this spectrum used by the model to calculate the value for the resulting response variable. Spikes were inserted artificially into spectra both on the peak at 350 nm and beside the peak at 450 nm. These spikes gave an increase of the residual: 0.0056 for the spike at the peak and O.OOO69 for the spike beside the peak. These artifacts show a less but still significant increase of the residual error. The correctness of the response value will be affected more by the spike on the peak than by the spike beside the peak. This is also reflected in the sizes of the residual errors. Further, the potential misfit of spectra is shown in the tl versus t2plot (Figure 8) where the deviating spectrum from Figure 7 will be projected far from the calibration set. The difference between the result calculated from the PLS model and the result obtained by the standard spectrophotometer from the filtered samples is shown in Figure 9. Squares denote the differences between values calculated from spectra used to build the PLS model and their corresponding directly measured values in Y for the calibration. Triangles denote the same difference for values calculated by the PLS model but not used to build the model. The standards of felodipine in clear solutions that are included in the model have no sampling time but are plotted at time zero for comparisons. As can be seen from the figure there is only a s m a l l
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
aration with liquid chromatographyin many dissolution tests.
t
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o A A
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Flgure 9. Differences between the results obtained from the PLS algorithm and the results from the filtered samples. Squares originate from spectra that generate the model. Triangles originate from spectra that were not included in the model. ~~~
Table I. &laGve Standard Deviation for Turbid and Filtered Samples (n = 3) felodipine content, sampling clear samples turbid samples mg time, h mean (A) RSD,’ % mean (A) RSD,’ % 5 10 5 10 5 10 a
2 2 6 6 10 10
0.034 0.059 0.120 0.206 0.185 0.316
9.0 4.8 3.4 2.5 3.9 1.0
0.033 0.059 0.119 0.207 0.189 0.312
6.4 4.2 4.9 2.7 3.3 1.2
Relative standard deviations.
difference in the pattern of spreading between the error for samples generating the model and for samples not generating the model. Each individual absorbance value from the standard spectrophotometer is taken as the true absorbance for that sample. The predicted absorbance measurements of the samples not included in the model are converted to concentration units. The absolute accuracies for the mean of the 2-, 6-, and 10-h measurements becomes -0.009, -0.019, and -0.014 pg/mL (n = 6). If the data set is divided tabletwise rather than timewise, the absolute accuracies for the mean of the 5-mg and 10-mgtablets become -0.066 and 0.049 p g / d (n = 9). The relative standard deviation for a set of three measurements at each sampling time for each kind of tablet is shown in Table I. The standard deviations are relative to the corresponding mean values stated in the table. The precision of the measurement is of the same magnitude at all sampling times thus giving rise to a decrease of the relative standard deviation with increased absorbance. The comparison of the two relative standard deviation columns in Table I shows that the precision of the measurement is unharmed by the multivariate calibration step for the turbid solutions. In the calculation of the percentage of released active substance a standard is used. The additional error introduced by the standard measurement is neglectable compared to the errors in Figure 9.
CONCLUSIONS The combination of optical fibers and multivariate calibration in connection with dissolution testing is time saving. Man power can further be reduced by automation with robotics (14,15),especially for tests over the working day. The procedure can also resolve several overlapping spectra if they have different shapes and thereby replace the need for sep-
APPENDIX Description of the PLS Algorithm for One Response Variable. This is the exact implementation of the PLS algorithm used in this paper. Here all details are shown as opposed to Figure 3, where only the general outline is shown. The assignments 1-10 describe the details of the model creation for one component. X is a matrix for the predictor variables (each column is a variable) where each spectrum is placed as a row. The vector Y contains the values for the response variable. These are the measurements obtained by an independent measurementmethod for each spectrum. The vectors p and w have the same length as the rows of X. The vectors t and Y have the same length as the columns of x. The d is a scalar for each component. Analogously to the power method (4) the vector Y is projected by the matrix x and scaled in assignment 1to give the vector w. Then w is normalized to unit length in assignment 2. After that w is projected back through X to give the vector t, the scores for the current component. Further the t vector is multiplied with the X matrix and scaled to give the vector p, the loadings for the current component in assignment 4. Then p is normalized to unit length: pnew(assignment 5) and the w and t are scaled by the norm of the old p (assignments 6, 7). The scalar d is calculated as the regression coefficient o f t in Y (assignment8). Finally the model of this component is subtracted from the original X and Y, yielding the residuals XneW and Yne, in assignments 9 and 10. This is not the most compact algorithm but it gives the possibility of working with missing values in X. Consecutive components are calculated by the use of the residuals X,, and Y, in place of the previous X and Y. The additional components are added to the model by repetitions of the assignments 1-10. A new set of w, p, and d is saved for each repetition.
---
YTX/YTY w/llwll
w
w
Xw-t tTX/tTt
P/IIPII tllpll
(1) (2)
(3)
p
(4)
Pnew
(5)
t
tTy/tTt T
x - tPnew Y - td
d
Xnew
(9)
Y,,,
(10) Using the model: The vectors w and p and the scalar d for each component are retained as the representation of the model. The vector Y is initially filled with zeroes in assignment 11. Then the new spectra are placed as rows in the X matrix and multiplied by the vector w (assignment 12). For each new component the vector t is multiplied with d and added to the old contents of Y as shown in assignment 13. The contribution of the current component to the final shape of the spectra is subtracted from all spectra in X in assignment 14. Additional components may contribute to the result accumulated in Y by repetitions of the assignments 12-14 with new sets of retained w, p, and d. X and Y are replaced by X,,, and Y,,, for each iteration. 0-Y (11)
Xw-t
(12)
Y
-
+ td
-
Anal. Chem. 1008, 60, 2677-2674
Y,,
NOMENCLATURE
= the assignment operator vT = the transpose of the vector v vTv = the vector product of the vector v llvll = the norm of the vedor v is the square root of the vector product Registry No. Felodipine, 72509-76-3.
LITERATURE CITED (1) Ljung, B. Drugs 1985, 29(suppl 2), 46-58. (2) Mlller, James A. Pharm. Techno/. 1977, l(2). 19-42. (3) Munson. J. P. J . Pharm. Ebmed. Anal. 1988, 4 , 717-724. (4) Wold, H. Research Papers in Statlstics; DavM, F. N., Ed.; Wlley: New YO&. 1966; pp 411-444. (5) Naes, T.; Irgens, C.; Martens, H. J . R. Statist. SOC.,C 1986, 35. 195-206.
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(6) Wold, S.; Albano, C.; Dunn. W. J., 111; Edlund, U.; Esbensen. K.; Geladi, P.; Hellberg, S.; Johansson, E.; Lindberg, W.; Sjbtrom, M. Chemomeffics. Mathematics and Staffsticsh ChemMy; Kowalski, B. R.. Ed.; D. Reidel: Dordrecht, 1984; pp 225-250. (7) Welser, W. E.; Pardue, H. L. Clin. Chem. (Winston-Sahsm, N . C . ) 1983. 2 9 , 1673-1677. (8) The United States Pharmcopsia, 21th rev.; U.S. Pharmacopeia1 Convention, Inc.: Rockvllle. MD, 1985; p 1244. (9) Shenouda, L. S.;Adarns. K. A.; Alcorn, G. J.; Zogllo, M. A. Drug Dev. Ind. Pharm. 1986. 12, 1227-1239.
(IO) Sjostrom, M.; Wold, S.; Llndberg, W.; Persson, J. A.; Martens, H. Anal.
Chim. Acta 1983, 150, 61-70. ( 1 1 ) Persson, J. A.; Johansson, E.; Albano, C. Anal. Chem. 1986, 5 8 , 1173-1 178. (12) Geladl, P.; Kowalskl, B. Anal. Chim. Acta 1988, 185, 1-17. (13) Box, G. E. P.; Hunter, W. G.; Hunter, J. S. StaffsHCsforGper/mentm; Wlley: New York, 1978; pp 4-7. (14) Papas, A. N.; Alpert, M. Y.; Marchese, S. M.; Fitzgerald, J. W.; Deb ney, M. F. Anal. Chem. 1985, 5 7 , 1408-1411. (15) Ecksteln, R. J.; Owens, 0. D.; Balm, M. A.; Hudson, D. A. Anal. Chem. 1988, 5 8 , 2116-2320.
RECEIVED for review January 6,1988. Resubmitted June 17, 1988. Accepted August 31,1988.
Fiber-optic Sensor for the Determination of Glucose Using Micellar Enhanced ChemiIuminescence of the Peroxyoxalate Reaction Monzir S. Abdel-Latif a n d George G. Guilbault*
Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148
The use of cetyltrlmethylammonlum bromlde (CTAB) as a surfactant to enhance the chemllumlnescence (CL) generated from the reactlon ol bls(2,4,6trlchIorophenyl) oxalate (TCPO) with hydrogen peroxlde has been lnvestlgated In the presence of perylene with Incorporation of flber optics. I n the presence of 2 X M CTAB, problems of mlxlng, and hence reproduclblllty, Involved In the peroxyoxalate system were ellmlnated, and the CL Intensity Is llnearly proportlonal to the concentratlon of peroxlde In the range of 8 X lo4 to 8 X lo9 M H202with a llmit of detection equal to 2.5 X lo-' M H2OP The coefflclent of varlatlon (five measurements) Is 0.3% for lo-' M H202. Uslng glucose oxidase (GOx) lmmoblllred on an lmmunodyne membrane, glucose could be assayed by measurlng the concentratlon of the enzymatically generated peroxlde. The callbratlon curve was h e a r In the range of 3 X to 3 X lo-' All glucose and the llmlt of detection was 6 X lo-' M glucose. The coefflclent of varlatlon (five measurements) was 0.3% for lo-' M glucose.
Peroxyoxalate CL is known to be the most efficient nonenzymatic CL reaction with quantum yields of about 25% (1). Hydrogen peroxide and TCPO react to give an intermediate that is capable of transferring 105 kcal/mol of energy to a fluorescent acceptor (2). This energy transferred excites the fluorescent acceptor, which then emits light. The light emitted is proportional to the concentrationof hydrogen peroxide. The reaction sequence can be represented by the following scheme: 0003-2700/88/0360-2671$01.50/0
0-0
I I
+ Fluorescer-
/F-f\ 0 0 *
(Fluorescer)
muorescer*) + 2 co,
-
Fluorescer + h v
The light emitted has a A, dependent on the type of the fluorescer used. The peroxyoxalate CL reaction has been used by Seitz (3) to detect hydrogen peroxide generated from the glucose/ glucose oxidase reaction. However, dissolution problems of organic solvents in aqueous solvents were encountered, and the reproducibility of the system limits its use to a static manner. Also, the stability of TCPO in ethyl acetate, when methanol is added to improve the mixing, was a significant problem. This may be attributed to the fact that most commercial ethyl acetate preparations have acetic acid as an impurity. This catalyzes a nucleophilic attack on the TCPO. For the above-mentioned reason, a t least in part, flow injection and high-performance liquid chromatography (HPLC) have been used to eliminate the problems associated with the reaction system. The CL of the peroxyoxalate systems has been used to quantify substrates of several enzymatic systems (4-11) by measuring the HzOz generated. The use of surfactants to improve the analytical performance of various spectroscopic technqiues has been reported 0 1988 American Chemical Society
