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An improved signal-conservative approach to cope with Rayleigh and Raman signals in fluorescence landscapes
Chemometrics and Intelligent Laboratory Systems 187 (2019) 6–10
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Chemometrics and Intelligent Laboratory Systems journal homepage: www.elsevier.com/locate/chemometrics
An improved signal-conservative approach to cope with Rayleigh and Raman signals in fluorescence landscapes Fabricio A. Chiappini a, b, Mirta R. Alcaraz a, b, **, Hector C. Goicoechea a, b, * a Laboratorio de Desarrollo Analítico y Quimiometría (LADAQ), C atedra de Química Analítica I, Facultad de Bioquímica y Ciencias Biologicas, Universidad Nacional del Litoral, Ciudad Universitaria, Santa Fe, S3000ZAA, Argentina b Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Godoy Cruz 2290 CABA, C1425FQB, Argentina
A R T I C L E I N F O
A B S T R A C T
Keywords: Excitation-emission fluorescence matrix Data processing Scattering correction Rayleigh scattering Raman scattering
Fluorescence excitation-emission matrix spectroscopy coupled to multi-way analysis has proved to be a powerful tool for the study of complex systems with analytical purposes. However, scattering phenomena that are usually present in fluorescence landscapes can significantly affect the performance of the chemometric modelling or lead to misinterpretations of the spectral information. In this work, an improved algorithm that collects the strengths of the reported approaches and enhances their performances was developed. The proposed algorithm, which is based on the signal-conservative principle, enables the fluorescence landscapes correction by preserving the inherent particularities of the original. Moreover, corrected second-order data were subjected to trilinear decomposition analysis to assess the performance of the scatter correction in terms of trilinearity and prediction ability. In light of the obtained results, this new strategy showed to be adequate for scattering correction in several experimental situations.
1. Introduction Over the last years, advances in instrumental analytical technology have allowed the generation of multi-way data, which has been accompanied by the evolution of chemometric applications for data treatment and data analysis in several research fields [1]. Different analytical instrumentations enable to obtain diverse data structures depending on the instrumental modes that are available for signal detection. The simplest data structure that can be built is the called zero-order data, in which a unique value is gathered for a given sample. Further, first-order data collect a series of values disposed in a vector structure for a given sample, e.g., a spectrum; and second-order data are signals recorded in two instrumental ways, e.g., an excitation-emission fluorescence matrix [2, 3]. The latter has been extensively used for the analysis of a wide variety of multi-component systems by virtue of the so-called second-order advantage [4–6]. This property enables to selectively identify the components of a mixture even in presence of non-modelled constituents [2, 7]. Fluorescence spectroscopy is one of the most popular analytical techniques that facilitate second-order data generation by means of registering excitation-emission matrices (EEM). The EEM spectroscopic
technique consists in acquiring the fluorescence signal over a specific emission wavelength range by exciting the sample at various wavelengths in a particular spectral region [8]. In combination with chemometrics, the EEM technique represents a valuable tool for extracting significant chemical information of multi-component systems. However, particular issues of the fluorescence landscapes ought to be considered, whose, otherwise, would restrict the chemometric modelling or lead to misinterpretations of the results [9,10]. Rayleigh (Ry) scatter is an elastic light dispersion that is produced by bulk substances oscillating at the same frequency as the incident light. Raman (Rm) scatter is a solvent-dependent inelastic form of dispersion that arises from the bulk substances that cause a constant loss of energy of the incident light. Additionally, higher-order scattering can be observed as the product of the light diffraction by the monochromators [11]. Since all these signals derive from the interaction between the molecules in the solution and the incident light, they do not contain information about the chemical characteristics of the system under study. From the chemometric standpoint, it is important to stress that EEM data have the particularity of fulfilling the concept of low-rank bilinearity, which can be succinctly described as a fundamental property of second-order data whereby, considering a pure component, the total
* Corresponding author. Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Godoy Cruz 2290 CABA, C1425FQB, Argentina. ** Corresponding author. Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Godoy Cruz 2290 CABA, C1425FQB, Argentina. E-mail addresses: [email protected] (M.R. Alcaraz), [email protected] (H.C. Goicoechea). https://doi.org/10.1016/j.chemolab.2019.02.007 Received 27 December 2018; Received in revised form 13 February 2019; Accepted 14 February 2019 Available online 15 February 2019 0169-7439/© 2019 Elsevier B.V. All rights reserved.
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2.3. Data generation
information comprised in the two-dimensional structure can be explained by two individual and independent vector profiles [3]. Following the same criterion, in absence of quenching and/or inner filter effects, a 3-way array built with several EEM matrices from the same system would fulfil the concept of low-rank trilinearity. This property is of vital importance when chemometric algorithms based on trilinear decomposition, such as parallel factor analysis (PARAFAC) [12], are used. However, in presence of Ry or Rm scatter, the data cannot be subjected to bi- and trilinear models due to the fact that the scattering signals lie on a diagonal of the landscape and they do not conform to the low-rank bilinear principle [13]. Therefore, these diagonal patterns must be carefully processed without being detrimental to the information of the system. In the literature, it is possible to find a vast number of strategies that aid to mitigating the Ry and Rm scatter effects [14]. For instance, when scatter lines do not overlap with the signal of interest, the scatter region can be removed or omitted [15–17]. In contrast, in case the fluorophore signal overlaps with one or more scatter lines, the signal must be precisely processed in order to avoid bias in the chemometric resolution or misinterpretation of the spectral information. Among procedures that are usually used for handling Ry and Rm scatter effects, digital corrections by means of mathematical algorithms are the most utilized approaches, despite they require mathematical or programming skills [14, 18–20]. This work is aiming to introduce an innovative and improved algorithm based on a signal-conservative strategy that allows subtracting the scattering signals and maintaining the inherent properties of the spectra.
2.3.1. System A - FQ The EEM were registered in the emission spectral range of 300.0 nm and 600.0 nm, every 0.5 nm, scanning the excitation range of 200.0 nm and 400.0 nm, every 5.0 nm, using a scan rate of 800 nm min1. Excitation and emission monochromator slit widths were set at 5 nm and the photomultiplier tube voltage (PMT) was established at 750 V. In this way, all the registered EEM consisted in 41 602 data points for excitation and emission wavelength modes, respectively. 2.3.2. System B - RES The EEM were registered in the emission spectral range of 500.0 nm and 700.0 nm, every 0.5 nm, covering an excitation range of 450.0 nm and 600.0 nm, every 5.0 nm, applying a scan rate of 1000 nm min1. Excitation and emission monochromator slit widths were set at 5 nm and the PMT at 900 V. All the registered EEM consisted in 51 602 data points for excitation and emission wavelengths mode, respectively. 2.4. Software All the data matrices were used as recorded, thus, no pre-processing steps were performed. Data processing was carried out in MATLAB R2015b [21]. The proposed algorithm was written in MATLAB environment and it is available upon request to the authors. 3. Results and discussion The fluorophores used in this work were chosen as model systems considering the differences between Stokes shifts and fluorescence spectral ranges: system A presents a distinct large Stokes shift in the UV spectral range, and system B presents a noticeable short Stokes shift in the Vis spectral range.
2. Experimental section 2.1. Chemical, reagents and samples The fluoroquinolones (FQ) enoxacin (ENO), flumequine (FLU), norfloxacin (NRF) and ofloxacin (OFL) were provided by Sigma Aldrich (Steinheim, Germany), and resorufin (RES) was kindly provided by the Laboratory of Molecular Devices (Buenos Aires, Argentina). Sodium acetate trihydrate (NaAc) p.a. was acquired from Anedra (La Plata, Argentina); glacial acetic acid (HAc) and sodium hydroxide p.a. were purchased from Cicarelli (San Lorenzo, Argentina). Ultrapure water was obtained from a Milli-Q purification system from Millipore (Bedford, USA). A 0.05 mol L1 HAc buffer solution was prepared by weighing and dissolving the appropriate amount of NaAc in ultrapure water, adjusting the pH at 5.0 with HAc and completing the volume to 100 mL with ultrapure water. Stock standard solutions of each analyte were prepared by dissolving the proper amount of each drug in acetate buffer pH 5.0 for FQ, and in alkalinized ultrapure water (pH > 10) for RES. Working solutions were prepared by transferring the appropriate aliquot of stock solution to 5.00 mL volumetric flask and completing to the mark with acetate buffer pH 5.0 or alkalinized ultrapure water, as appropriate. A fourteen-sample set was built by mixing the corresponding aliquot of each FQ following a random design, four of which were samples of the pure analyte. All the samples were prepared in acetate buffer pH 5.
3.1. Description of the proposed signal-conservative algorithm The presented algorithm collects and enhances the essential particularities of the different scatter correction strategies that are reported in the literature. The algorithm core consists in correcting the scatter signals by following the principle proposed by Eilers and Kroonenberg [19] in combination with the ideas implemented by Bahram et al. [10], while its novelty relies on the introduction of meaningful features that improve the performance and the feasibility of the algorithm in comparison with those reported in the literature. It should be clarified that the correction is carried out over the individual emission spectrum at each excitation wavelength. Moreover, it must be remarked that Ry and Rm peaks are separately corrected in successive cycles, and first- and second-order scatter are independently corrected. The proposed algorithm is based on three main phases: the identification, the modelling and the subtraction of the scattering peak feature. To start with the correction, 5 inputs are needed, three of which correspond to the experimental data (the raw data matrix (Xr), the excitation (ex) and emission (em) wavelength vectors) and the others two are tolerances that are established by the user. These tolerances represent the control points of the algorithm and aid to reaching the best scatter recognition and to performing the best peak modelling. The first, h, represents the intensity threshold below which no correction is performed; thus, only the scatter peaks that have a peak maximum height (PMH) higher than h will be considered for the correction. The second, w, denotes the expected half-width at the base of the scatter peak (PHW) and defines the fitting mathematical model to perform. Then, the first step of the procedure is the identification of the scatter position, which is achieved by using the criteria established by Bahram et al. [10], in which the centre of the Ry signal arises when μem, i ¼ n λexc,i, and the Rm scatter is recognised by following Eq. (1):
2.2. Instrumentation All the experiments were performed on a LS-55 luminescence spectrometer (Perkin Elmer, Waltham, Massachusetts, USA), equipped with FL WinLab software package (Perkin Elmer, Waltham, Massachusetts, USA) to instrument control and data acquisition. All the measurements were done on a 1-cm quartz cuvette at room temperature. pH measurements were carried out with an Orion (Massachusetts, United States) 410A potentiometer equipped with a Boeco BA 17 (Hamburg, Germany) combined glass electrode. 7
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μem;i ¼
107
107 λex;i wnr λex;i
Chemometrics and Intelligent Laboratory Systems 187 (2019) 6–10
a region comprising the remaining signal of the spectrum is obtained. This region, r2, contains the residuals of the Gaussian curve subtraction and, more importantly, the inherent noise of the spectrum (Fig. 1.4). In this regard, if the goodness of the Gaussian curve fitting is not assessed, undesired artefacts can be introduced in the spectra. Last, to recover the proper corrected spectrum, the estimated baseline is added to r2 (Fig. 1.5) and the resultant values are included in the region that was excised from the original spectrum. Therefore, an emission spectrum free of scatter signal is finally achieved.
(1)
where μem;i is the expected position of the Rm signal in the emission spectrum (in nanometers) at the i-th excitation wavelength, λex;i , and wnr is the difference in wavenumbers between Ry and Rm positions in the landscape. For instance, when the medium is water, Rm scatter appears at a frequency wnr ~3600 cm1 lower than the Ry scatter frequency [9,11]. If necessary, the value of wnr can be modified considering the nature of the system under study. Once the peak position is identified, the PMH at μem is calculated as the difference between the intensity at μem and the intensity at μem þ wor μem – w, as appropriate, and compared to h. This step seems to be crucial in those regions where scattering signals are overwhelmed by the target signal or the noise, and no correction is then needed. In case PMH > h, the presence of scatter peak is confirmed and it is isolated for further correction. To perform the correction, the spectral region containing the scatter signal (r0) is temporarily excised from the spectrum. To estimate the spectral window of r0, the value of w is considered. Thereafter, the scatter peak in r0 is subjected to a second control which defines the procedure that is implemented for the subtraction. In this matter, it is worth reminding that w represents the expected half-width at the base of the scatter peak and it can be easily estimated considering the instrumental parameters. Ideally, the left and the right half-width at the base of the scatter peak (PHW) are identical in a Gaussian distribution curve. However, in practice, scatter peaks are either asymmetrical or incomplete. Incomplete peak occurrences are always in the extremes of the EEM and, in consequence, those signals cannot be considered as Gaussian curves. On the other hand, the asymmetry degree observed in the peaks is negligible for this purpose and the signals shall fulfil the Gaussian modelling. To distinguish between complete and incomplete scatter peaks, the following criterion was proposed: a scatter peak is considered as complete when both the right and the left PHW is equal to or higher than 80% of w. Therefore, if PHW<0.8 w, either for the right or the left side, the peak is considered as incomplete and the scatter signal is replaced by missing values and linear interpolation is then accomplished by adding a zero value at the beginning (or the end, as appropriate) of r0. In case PHW0.8 w, the scatter peak is modelled with a Gaussian distribution. In this case, the correction begins with the estimation of the baseline of r0, which is accomplished by using the asymmetric least-squares basedsmoothing procedure proposed by Eilers et al. [22]. The estimated baseline is then subtracted from r0 (Figs. 1.1 and 1.2) and only the scatter peak shall remain in the region (r1) (Fig. 1.3). This process is essential in case of strong overlapping between the scatter peak and the analyte signal since curve fitting would lead to undesired outcomes by possible drifts in the baseline of the estimated curve. Later, a Gaussian curve is fitted to the scatter peak by using the PMH and PHW values as initial estimates, which is then directly subtracted from r1 (Fig. 1.3). In this way,
3.2. Descriptive spectral analysis The two evaluated system models are depicted in Fig. 2. As can be seen for system A, first order Ry lies in the limit of the target signal while first-order Rm and second-order scatterings overlap with the signals of interest. For system B, first-order Ry scatter line is strongly overlapped with the signal of the analyte while first-order Rm is overwhelmed by the signal of the fluorophore; besides, second-order scatterings are not observed in the selected spectral region. In order to evaluate the performance of the proposed algorithm for scattering correction, in terms of spectral features and spectra similarity, a comparative analysis of the data obtained after correction was carried out. For this study, emission spectra obtained after correction were carefully examined and compared with those obtained in conditions where no signal from the Ry or Rm scatter are observable (reference spectrum), aiming for proving whether the information comprised in the corrected spectra is comparable or not with the real pure spectra. For each system, three different regions of the corrected fluorescence landscape were analysed and compared with the reference spectrum. The first spectral region comprises the area where scatter lines do not significantly affect the emission spectra; the second corresponds to the region in which the scatter lines and the emission spectra are partially overlapped, and the last one contains the zone whereby a high overlap between scatter lines and spectra is observed. Fig. 3 shows the results obtained after scatter signal correction by means of the proposed algorithm for the two evaluated systems in comparison to a reference and the original uncorrected spectra. Moreover, in all cases, linear-interpolation based algorithm [9] was used as correction algorithm reference. It is worth mentioning that pure OFL is shown in the representation of system A to facilitate the comprehension and the visualization of the results. It is important to highlight that the spectra corrected through the proposed algorithm comprise the residuals of the subtraction between the scatter signal and the fitted curve in addition to the instrumental noise of the original signal. In this regard, it is worth reiterating that the goodness of the Gaussian curve fitting should be assessed in order to avoid introducing artefacts in the spectra. Moreover, it can be seen that for incomplete scatter signals, interpolation strategy does not introduce significant distortions in the spectra (Fig. 3B1). Otherwise, high overlapping between scatter and fluorescence signals that are particularly narrow or asymmetric (Fig. 3B3) is the most challenging case for signal correction treatments and, to the best of our
Fig. 1. Stages through which a scatter signal is subjected to correction along the procedure by means of the proposed algorithm. (1.) Region excised from the original emission spectrum that comprises Ry peak overlapped to analyte signal, (r0); (2.) Original signal (black line) and the estimated baseline (dashed red line); (3.) Spectral signal after baseline subtraction (black line) and fitted Gauss distribution curve (r1); (4.) Resultant signal after subtraction of the fitted curve from the scatter peak (r2). (5.) Signal obtained from the addition of the corrected signal and the estimated baseline. Green and red colours indicate the remaining and the subtracted areas, respectively. PMH and PHW are the peak maximum height and the peak half-width, respectively.
Fig. 2. Contour plots of experimental fluorescence landscapes obtained for system A (FQ mixture, 1.) and system B (RES, 2.), indicating the first- (blue) and second-order (red) Ry and Rm lines. 8
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Fig. 4. Spectral region of an emission spectrum extracted from (1.) the raw matrix, (2.) the corrected matrix by applying linear-interpolation approach and (3.) the corrected matrix by using the proposed algorithm. Blue boxes indicate the spectral window that was considered for the correction.
3.3. Trilinear decomposition through PARAFAC modelling To assess the performance of the scatter correction in data that are further subjected to chemometric modelling, a validation model was constructed and trilinear data decomposition was performed. In this case, PARAFAC algorithm was chosen as chemometric model since it allows identifying lack of trilinearity in the data set and provides profiles with physically recognizable information. For this purpose, an excitation-emission matrix was recorded for each sample and then corrected by using the proposed algorithm. The corrected matrices were used to build a 3-way object in which 9 samples corresponding to the calibration set and 5 to the prediction set. In this manner, the 3-way object was of 14 41 602 data points for the number of samples, the excitation and the emission wavelength modes, respectively. For the PARAFAC modelling, initial estimates obtained from random initialization were used and non-negativity constrain in the 3 modes was applied in the ALS optimization. The number of components was assessed by core consistency diagnostic analysis (CORCONDIA) and the performance of the modelling was corroborated in terms of the figures of merit obtained after convergence and the predictive ability. The results retrieved from the trilinear decomposition and the prediction study for a different number of components are depicted in Table 1. Fig. 5 shows the obtained PARAFAC spectral profiles and the real pure spectra of each analyte. Notwithstanding CORCONDIA values do not show notable differences between the models, the residual fit and the explained variance are worthy indicators of the success and the reliability of the modelling. Hence, it is possible to conclude that the number of components is in agreement with the real number of spectroscopically active species present in the samples, i.e. N ¼ 4, and that no lack of trilinearity is observed in the 3-way object. Moreover, it is noticeable the strong similarity between the profiles retrieved from PARAFAC and the real pure spectra.
Fig. 3. A. OFL emission spectra extracted from fluorescence landscapes at (1.) 225 nm, (2.) 250 nm and (3.) 290 nm excitation wavelengths. B. RES emission spectra extracted from fluorescence landscapes at (1.) 550 nm, (2.) 565 nm and (3.) 595 nm excitation wavelengths. In all cases, emission spectra before correction are depicted in black lines. Blue lines represent the corrected emission spectra by applying the proposed algorithm. Green lines represent the corrected emission spectra by applying the linear interpolation based algorithm. Red lines indicate the reference emission spectra corresponding to an excitation wavelength of 305 nm and 535 nm for OFL and RES, respectively.
knowledge, there is no technique capable of successfully coping with this kind of situation. However, the proposed strategy enables correcting the spectrum with a high degree of similarity with the reference spectrum, strengthening its applicability in troublesome spectral situations. In contrast, it is worth mentioning that linear interpolation is performed considering only the extremes of the excised region, then, the correction efficiency would strongly depend on the width of the scatter lines and the degree of overlap. The correction seems to be better on broad and symmetric spectra, e.g., emission spectra of OFL, than on narrow and asymmetric signals, for example, emission spectra of RES. It is possible to observe that the presence of high noise level represents an important drawback for the correction. Moreover, evident artefacts are introduced when the maximum of the emission spectra overlaps with the scatter lines since no spectral feature is considered during interpolation. For instance, wider bandwidths of scatter lines lying on the maximum of the spectra would dramatically affect the feature of the corrected spectra. Last, it must be clarified that despite the introduction of new code lines for second-order Rm scatter correction is allowed, the algorithm was implemented as provided and no correction of second-order Rm was accomplished. In all cases, the implementation of the proposed algorithm led to a notable improvement in preserving the original spectral features after correction, in terms of signal noise and spectral shape in comparison to the reported methodologies based on an interpolation-based correction [10,20]. Thus, this strategy demonstrated to be more efficient in cases of high-level noise (Fig. 3A1) or strong signal overlapping (Fig. 3A2). In this matter, the significant advantage needed to be highlighted is the conservation of the intrinsic noise, which does not interrupt the continuous feature of the spectrum. When linear interpolation is performed instead, the corrected data region of the spectra is noiseless and then, the continuous feature of the spectra is significantly interrupted. This outcome is graphically demonstrated in Fig. 4, in which an emission spectrum was subjected to correction by applying the interpolation-based algorithm reported by Bahram et al. [10] in comparison with the proposed algorithm correction.
Table 1 Figures obtained after convergence of the PARAFAC modelling for a system containing 4 analytes. Modelling figures
N ¼ 4a
N¼5
N¼6
Number of iterations SSEb sfitc Explained variance CORCONDIA
22 1.34 107 6.2405 99.8129 99.3629
189 1.08 107 5.6171 99.8487 77.9243
125 8.69 106 5.0439 99.8782 56.224
a b
N: number of components used for the model. I P J P K P SSE: sum of square errors calculated as e2ijk , where eijk collects the i¼1 j¼1 k¼i
model errors.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SSE c sfit: residual fit estimated as , where I is the number of samples, IJK and J and K are the wavelengths in the excitation and emission mode, respectively.
9
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no alterations of the spectroscopic information are introduced. Finally, this work attempts to encourage the development of new methodologies for spectroscopic data treatment as well as the investigations in data correction and data processing which is of paramount interest in several research fields. Acknowledgments The authors are grateful to CONICET (Consejo Nacional de Investigaciones Científicas y Tecnicas, Project PIP 2015–0111) and ANPCyT (Agencia Nacional de Promoci on Científica y Tecnol ogica, Project PICT 2014–0347) for financial support. F.A.C. and M.R.A. thank CONICET for their fellowship.
Fig. 5. (1.) Excitation and (2.) emission spectral profiles retrieved from PARAFAC modelling (solid lines) and the real pure spectra (dashed lines) of FLU (red), ENO (light blue), NRF (blue) and OFL (light brown).
References This observation relies on the assumption that the pre-processing procedure applied for the scatter correction does not affect the spectroscopic information of the original data. For the prediction study, the relative error of prediction (REP %) was estimated for each analyte. Moreover, to appraise whether the average recoveries (Rexp ) are significantly different from 100% or not, a suitable statistic test was performed, in which the acceptance of the null hypothesis asserts the statistical equality between values. This condition is accomplished when the critical t value at a level α for n samples exceeds the experimental texp value, which is estimated by following Eq. (2), pffiffiffi n texp ¼ 100 Rexp ; sr
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(2)
where sr is the standard deviation of the recoveries. The REP% figures were 12%, 10%, 17% and 5% for FLU, ENO, NRF and OFL, respectively, while the null hypothesis for the recovery evaluation was accepted in the all cases considering 95% confidence level since the corresponding texp values were lower that the critical value (t0.05,4 ¼ 2.7908 texp,FLU ¼ 0.0838, texp,ENO ¼ 0.4656, texp,NRF ¼ 0.2123, texp,OFL ¼ 1.1004). Therefore, all these results stress the fact that the bilinearity and trilineratity of the data are fulfilled after correction of the fluorescence landscapes which are of utmost importance for chemometrics in analytical chemistry applications. 4. Conclusions In the present work, a new strategy for the correction of scatter signals in fluorescence landscapes was proposed. Matrices gathered from two fluorophoric systems with different spectral properties were subjected to correction and the performance of the correction was in-depth analysed. Moreover, the performance of the correction of data that are subjected to further chemometric modelling was assessed by means of trilinear decomposition with PARAFAC model. The improved algorithm here presented collects and enhances the essential particularities of different scatter correction strategies that are reported in the literature. The novelty of this algorithm relies on the fact that the correction is accomplished by modelling of the scatter peak with further subtraction instead of interpolation. In this way, only the residuals after subtraction in addition to the instrumental noise of the original signal shall remain in the corrected spectra. All the results support the conclusion that the implementation of this algorithm leads to a notable improvement in preserving the original spectral features, offering the uttermost in efficiency and performance in the cases where other techniques may fail. Besides, it was demonstrated that in case of chemometric modelling is applied after correction, the data pre-processing does not affect the performance of the resolution, asserting the fact that trilinearity is fulfilled after scatter correction, and
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Chemometrics and Intelligent Laboratory Systems journal homepage: www.elsevier.com/locate/chemometrics
An improved signal-conservative approach to cope with Rayleigh and Raman signals in fluorescence landscapes Fabricio A. Chiappini a, b, Mirta R. Alcaraz a, b, **, Hector C. Goicoechea a, b, * a Laboratorio de Desarrollo Analítico y Quimiometría (LADAQ), C atedra de Química Analítica I, Facultad de Bioquímica y Ciencias Biologicas, Universidad Nacional del Litoral, Ciudad Universitaria, Santa Fe, S3000ZAA, Argentina b Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Godoy Cruz 2290 CABA, C1425FQB, Argentina
A R T I C L E I N F O
A B S T R A C T
Keywords: Excitation-emission fluorescence matrix Data processing Scattering correction Rayleigh scattering Raman scattering
Fluorescence excitation-emission matrix spectroscopy coupled to multi-way analysis has proved to be a powerful tool for the study of complex systems with analytical purposes. However, scattering phenomena that are usually present in fluorescence landscapes can significantly affect the performance of the chemometric modelling or lead to misinterpretations of the spectral information. In this work, an improved algorithm that collects the strengths of the reported approaches and enhances their performances was developed. The proposed algorithm, which is based on the signal-conservative principle, enables the fluorescence landscapes correction by preserving the inherent particularities of the original. Moreover, corrected second-order data were subjected to trilinear decomposition analysis to assess the performance of the scatter correction in terms of trilinearity and prediction ability. In light of the obtained results, this new strategy showed to be adequate for scattering correction in several experimental situations.
1. Introduction Over the last years, advances in instrumental analytical technology have allowed the generation of multi-way data, which has been accompanied by the evolution of chemometric applications for data treatment and data analysis in several research fields [1]. Different analytical instrumentations enable to obtain diverse data structures depending on the instrumental modes that are available for signal detection. The simplest data structure that can be built is the called zero-order data, in which a unique value is gathered for a given sample. Further, first-order data collect a series of values disposed in a vector structure for a given sample, e.g., a spectrum; and second-order data are signals recorded in two instrumental ways, e.g., an excitation-emission fluorescence matrix [2, 3]. The latter has been extensively used for the analysis of a wide variety of multi-component systems by virtue of the so-called second-order advantage [4–6]. This property enables to selectively identify the components of a mixture even in presence of non-modelled constituents [2, 7]. Fluorescence spectroscopy is one of the most popular analytical techniques that facilitate second-order data generation by means of registering excitation-emission matrices (EEM). The EEM spectroscopic
technique consists in acquiring the fluorescence signal over a specific emission wavelength range by exciting the sample at various wavelengths in a particular spectral region [8]. In combination with chemometrics, the EEM technique represents a valuable tool for extracting significant chemical information of multi-component systems. However, particular issues of the fluorescence landscapes ought to be considered, whose, otherwise, would restrict the chemometric modelling or lead to misinterpretations of the results [9,10]. Rayleigh (Ry) scatter is an elastic light dispersion that is produced by bulk substances oscillating at the same frequency as the incident light. Raman (Rm) scatter is a solvent-dependent inelastic form of dispersion that arises from the bulk substances that cause a constant loss of energy of the incident light. Additionally, higher-order scattering can be observed as the product of the light diffraction by the monochromators [11]. Since all these signals derive from the interaction between the molecules in the solution and the incident light, they do not contain information about the chemical characteristics of the system under study. From the chemometric standpoint, it is important to stress that EEM data have the particularity of fulfilling the concept of low-rank bilinearity, which can be succinctly described as a fundamental property of second-order data whereby, considering a pure component, the total
* Corresponding author. Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Godoy Cruz 2290 CABA, C1425FQB, Argentina. ** Corresponding author. Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Godoy Cruz 2290 CABA, C1425FQB, Argentina. E-mail addresses: [email protected] (M.R. Alcaraz), [email protected] (H.C. Goicoechea). https://doi.org/10.1016/j.chemolab.2019.02.007 Received 27 December 2018; Received in revised form 13 February 2019; Accepted 14 February 2019 Available online 15 February 2019 0169-7439/© 2019 Elsevier B.V. All rights reserved.
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2.3. Data generation
information comprised in the two-dimensional structure can be explained by two individual and independent vector profiles [3]. Following the same criterion, in absence of quenching and/or inner filter effects, a 3-way array built with several EEM matrices from the same system would fulfil the concept of low-rank trilinearity. This property is of vital importance when chemometric algorithms based on trilinear decomposition, such as parallel factor analysis (PARAFAC) [12], are used. However, in presence of Ry or Rm scatter, the data cannot be subjected to bi- and trilinear models due to the fact that the scattering signals lie on a diagonal of the landscape and they do not conform to the low-rank bilinear principle [13]. Therefore, these diagonal patterns must be carefully processed without being detrimental to the information of the system. In the literature, it is possible to find a vast number of strategies that aid to mitigating the Ry and Rm scatter effects [14]. For instance, when scatter lines do not overlap with the signal of interest, the scatter region can be removed or omitted [15–17]. In contrast, in case the fluorophore signal overlaps with one or more scatter lines, the signal must be precisely processed in order to avoid bias in the chemometric resolution or misinterpretation of the spectral information. Among procedures that are usually used for handling Ry and Rm scatter effects, digital corrections by means of mathematical algorithms are the most utilized approaches, despite they require mathematical or programming skills [14, 18–20]. This work is aiming to introduce an innovative and improved algorithm based on a signal-conservative strategy that allows subtracting the scattering signals and maintaining the inherent properties of the spectra.
2.3.1. System A - FQ The EEM were registered in the emission spectral range of 300.0 nm and 600.0 nm, every 0.5 nm, scanning the excitation range of 200.0 nm and 400.0 nm, every 5.0 nm, using a scan rate of 800 nm min1. Excitation and emission monochromator slit widths were set at 5 nm and the photomultiplier tube voltage (PMT) was established at 750 V. In this way, all the registered EEM consisted in 41 602 data points for excitation and emission wavelength modes, respectively. 2.3.2. System B - RES The EEM were registered in the emission spectral range of 500.0 nm and 700.0 nm, every 0.5 nm, covering an excitation range of 450.0 nm and 600.0 nm, every 5.0 nm, applying a scan rate of 1000 nm min1. Excitation and emission monochromator slit widths were set at 5 nm and the PMT at 900 V. All the registered EEM consisted in 51 602 data points for excitation and emission wavelengths mode, respectively. 2.4. Software All the data matrices were used as recorded, thus, no pre-processing steps were performed. Data processing was carried out in MATLAB R2015b [21]. The proposed algorithm was written in MATLAB environment and it is available upon request to the authors. 3. Results and discussion The fluorophores used in this work were chosen as model systems considering the differences between Stokes shifts and fluorescence spectral ranges: system A presents a distinct large Stokes shift in the UV spectral range, and system B presents a noticeable short Stokes shift in the Vis spectral range.
2. Experimental section 2.1. Chemical, reagents and samples The fluoroquinolones (FQ) enoxacin (ENO), flumequine (FLU), norfloxacin (NRF) and ofloxacin (OFL) were provided by Sigma Aldrich (Steinheim, Germany), and resorufin (RES) was kindly provided by the Laboratory of Molecular Devices (Buenos Aires, Argentina). Sodium acetate trihydrate (NaAc) p.a. was acquired from Anedra (La Plata, Argentina); glacial acetic acid (HAc) and sodium hydroxide p.a. were purchased from Cicarelli (San Lorenzo, Argentina). Ultrapure water was obtained from a Milli-Q purification system from Millipore (Bedford, USA). A 0.05 mol L1 HAc buffer solution was prepared by weighing and dissolving the appropriate amount of NaAc in ultrapure water, adjusting the pH at 5.0 with HAc and completing the volume to 100 mL with ultrapure water. Stock standard solutions of each analyte were prepared by dissolving the proper amount of each drug in acetate buffer pH 5.0 for FQ, and in alkalinized ultrapure water (pH > 10) for RES. Working solutions were prepared by transferring the appropriate aliquot of stock solution to 5.00 mL volumetric flask and completing to the mark with acetate buffer pH 5.0 or alkalinized ultrapure water, as appropriate. A fourteen-sample set was built by mixing the corresponding aliquot of each FQ following a random design, four of which were samples of the pure analyte. All the samples were prepared in acetate buffer pH 5.
3.1. Description of the proposed signal-conservative algorithm The presented algorithm collects and enhances the essential particularities of the different scatter correction strategies that are reported in the literature. The algorithm core consists in correcting the scatter signals by following the principle proposed by Eilers and Kroonenberg [19] in combination with the ideas implemented by Bahram et al. [10], while its novelty relies on the introduction of meaningful features that improve the performance and the feasibility of the algorithm in comparison with those reported in the literature. It should be clarified that the correction is carried out over the individual emission spectrum at each excitation wavelength. Moreover, it must be remarked that Ry and Rm peaks are separately corrected in successive cycles, and first- and second-order scatter are independently corrected. The proposed algorithm is based on three main phases: the identification, the modelling and the subtraction of the scattering peak feature. To start with the correction, 5 inputs are needed, three of which correspond to the experimental data (the raw data matrix (Xr), the excitation (ex) and emission (em) wavelength vectors) and the others two are tolerances that are established by the user. These tolerances represent the control points of the algorithm and aid to reaching the best scatter recognition and to performing the best peak modelling. The first, h, represents the intensity threshold below which no correction is performed; thus, only the scatter peaks that have a peak maximum height (PMH) higher than h will be considered for the correction. The second, w, denotes the expected half-width at the base of the scatter peak (PHW) and defines the fitting mathematical model to perform. Then, the first step of the procedure is the identification of the scatter position, which is achieved by using the criteria established by Bahram et al. [10], in which the centre of the Ry signal arises when μem, i ¼ n λexc,i, and the Rm scatter is recognised by following Eq. (1):
2.2. Instrumentation All the experiments were performed on a LS-55 luminescence spectrometer (Perkin Elmer, Waltham, Massachusetts, USA), equipped with FL WinLab software package (Perkin Elmer, Waltham, Massachusetts, USA) to instrument control and data acquisition. All the measurements were done on a 1-cm quartz cuvette at room temperature. pH measurements were carried out with an Orion (Massachusetts, United States) 410A potentiometer equipped with a Boeco BA 17 (Hamburg, Germany) combined glass electrode. 7
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μem;i ¼
107
107 λex;i wnr λex;i
Chemometrics and Intelligent Laboratory Systems 187 (2019) 6–10
a region comprising the remaining signal of the spectrum is obtained. This region, r2, contains the residuals of the Gaussian curve subtraction and, more importantly, the inherent noise of the spectrum (Fig. 1.4). In this regard, if the goodness of the Gaussian curve fitting is not assessed, undesired artefacts can be introduced in the spectra. Last, to recover the proper corrected spectrum, the estimated baseline is added to r2 (Fig. 1.5) and the resultant values are included in the region that was excised from the original spectrum. Therefore, an emission spectrum free of scatter signal is finally achieved.
(1)
where μem;i is the expected position of the Rm signal in the emission spectrum (in nanometers) at the i-th excitation wavelength, λex;i , and wnr is the difference in wavenumbers between Ry and Rm positions in the landscape. For instance, when the medium is water, Rm scatter appears at a frequency wnr ~3600 cm1 lower than the Ry scatter frequency [9,11]. If necessary, the value of wnr can be modified considering the nature of the system under study. Once the peak position is identified, the PMH at μem is calculated as the difference between the intensity at μem and the intensity at μem þ wor μem – w, as appropriate, and compared to h. This step seems to be crucial in those regions where scattering signals are overwhelmed by the target signal or the noise, and no correction is then needed. In case PMH > h, the presence of scatter peak is confirmed and it is isolated for further correction. To perform the correction, the spectral region containing the scatter signal (r0) is temporarily excised from the spectrum. To estimate the spectral window of r0, the value of w is considered. Thereafter, the scatter peak in r0 is subjected to a second control which defines the procedure that is implemented for the subtraction. In this matter, it is worth reminding that w represents the expected half-width at the base of the scatter peak and it can be easily estimated considering the instrumental parameters. Ideally, the left and the right half-width at the base of the scatter peak (PHW) are identical in a Gaussian distribution curve. However, in practice, scatter peaks are either asymmetrical or incomplete. Incomplete peak occurrences are always in the extremes of the EEM and, in consequence, those signals cannot be considered as Gaussian curves. On the other hand, the asymmetry degree observed in the peaks is negligible for this purpose and the signals shall fulfil the Gaussian modelling. To distinguish between complete and incomplete scatter peaks, the following criterion was proposed: a scatter peak is considered as complete when both the right and the left PHW is equal to or higher than 80% of w. Therefore, if PHW<0.8 w, either for the right or the left side, the peak is considered as incomplete and the scatter signal is replaced by missing values and linear interpolation is then accomplished by adding a zero value at the beginning (or the end, as appropriate) of r0. In case PHW0.8 w, the scatter peak is modelled with a Gaussian distribution. In this case, the correction begins with the estimation of the baseline of r0, which is accomplished by using the asymmetric least-squares basedsmoothing procedure proposed by Eilers et al. [22]. The estimated baseline is then subtracted from r0 (Figs. 1.1 and 1.2) and only the scatter peak shall remain in the region (r1) (Fig. 1.3). This process is essential in case of strong overlapping between the scatter peak and the analyte signal since curve fitting would lead to undesired outcomes by possible drifts in the baseline of the estimated curve. Later, a Gaussian curve is fitted to the scatter peak by using the PMH and PHW values as initial estimates, which is then directly subtracted from r1 (Fig. 1.3). In this way,
3.2. Descriptive spectral analysis The two evaluated system models are depicted in Fig. 2. As can be seen for system A, first order Ry lies in the limit of the target signal while first-order Rm and second-order scatterings overlap with the signals of interest. For system B, first-order Ry scatter line is strongly overlapped with the signal of the analyte while first-order Rm is overwhelmed by the signal of the fluorophore; besides, second-order scatterings are not observed in the selected spectral region. In order to evaluate the performance of the proposed algorithm for scattering correction, in terms of spectral features and spectra similarity, a comparative analysis of the data obtained after correction was carried out. For this study, emission spectra obtained after correction were carefully examined and compared with those obtained in conditions where no signal from the Ry or Rm scatter are observable (reference spectrum), aiming for proving whether the information comprised in the corrected spectra is comparable or not with the real pure spectra. For each system, three different regions of the corrected fluorescence landscape were analysed and compared with the reference spectrum. The first spectral region comprises the area where scatter lines do not significantly affect the emission spectra; the second corresponds to the region in which the scatter lines and the emission spectra are partially overlapped, and the last one contains the zone whereby a high overlap between scatter lines and spectra is observed. Fig. 3 shows the results obtained after scatter signal correction by means of the proposed algorithm for the two evaluated systems in comparison to a reference and the original uncorrected spectra. Moreover, in all cases, linear-interpolation based algorithm [9] was used as correction algorithm reference. It is worth mentioning that pure OFL is shown in the representation of system A to facilitate the comprehension and the visualization of the results. It is important to highlight that the spectra corrected through the proposed algorithm comprise the residuals of the subtraction between the scatter signal and the fitted curve in addition to the instrumental noise of the original signal. In this regard, it is worth reiterating that the goodness of the Gaussian curve fitting should be assessed in order to avoid introducing artefacts in the spectra. Moreover, it can be seen that for incomplete scatter signals, interpolation strategy does not introduce significant distortions in the spectra (Fig. 3B1). Otherwise, high overlapping between scatter and fluorescence signals that are particularly narrow or asymmetric (Fig. 3B3) is the most challenging case for signal correction treatments and, to the best of our
Fig. 1. Stages through which a scatter signal is subjected to correction along the procedure by means of the proposed algorithm. (1.) Region excised from the original emission spectrum that comprises Ry peak overlapped to analyte signal, (r0); (2.) Original signal (black line) and the estimated baseline (dashed red line); (3.) Spectral signal after baseline subtraction (black line) and fitted Gauss distribution curve (r1); (4.) Resultant signal after subtraction of the fitted curve from the scatter peak (r2). (5.) Signal obtained from the addition of the corrected signal and the estimated baseline. Green and red colours indicate the remaining and the subtracted areas, respectively. PMH and PHW are the peak maximum height and the peak half-width, respectively.
Fig. 2. Contour plots of experimental fluorescence landscapes obtained for system A (FQ mixture, 1.) and system B (RES, 2.), indicating the first- (blue) and second-order (red) Ry and Rm lines. 8
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Fig. 4. Spectral region of an emission spectrum extracted from (1.) the raw matrix, (2.) the corrected matrix by applying linear-interpolation approach and (3.) the corrected matrix by using the proposed algorithm. Blue boxes indicate the spectral window that was considered for the correction.
3.3. Trilinear decomposition through PARAFAC modelling To assess the performance of the scatter correction in data that are further subjected to chemometric modelling, a validation model was constructed and trilinear data decomposition was performed. In this case, PARAFAC algorithm was chosen as chemometric model since it allows identifying lack of trilinearity in the data set and provides profiles with physically recognizable information. For this purpose, an excitation-emission matrix was recorded for each sample and then corrected by using the proposed algorithm. The corrected matrices were used to build a 3-way object in which 9 samples corresponding to the calibration set and 5 to the prediction set. In this manner, the 3-way object was of 14 41 602 data points for the number of samples, the excitation and the emission wavelength modes, respectively. For the PARAFAC modelling, initial estimates obtained from random initialization were used and non-negativity constrain in the 3 modes was applied in the ALS optimization. The number of components was assessed by core consistency diagnostic analysis (CORCONDIA) and the performance of the modelling was corroborated in terms of the figures of merit obtained after convergence and the predictive ability. The results retrieved from the trilinear decomposition and the prediction study for a different number of components are depicted in Table 1. Fig. 5 shows the obtained PARAFAC spectral profiles and the real pure spectra of each analyte. Notwithstanding CORCONDIA values do not show notable differences between the models, the residual fit and the explained variance are worthy indicators of the success and the reliability of the modelling. Hence, it is possible to conclude that the number of components is in agreement with the real number of spectroscopically active species present in the samples, i.e. N ¼ 4, and that no lack of trilinearity is observed in the 3-way object. Moreover, it is noticeable the strong similarity between the profiles retrieved from PARAFAC and the real pure spectra.
Fig. 3. A. OFL emission spectra extracted from fluorescence landscapes at (1.) 225 nm, (2.) 250 nm and (3.) 290 nm excitation wavelengths. B. RES emission spectra extracted from fluorescence landscapes at (1.) 550 nm, (2.) 565 nm and (3.) 595 nm excitation wavelengths. In all cases, emission spectra before correction are depicted in black lines. Blue lines represent the corrected emission spectra by applying the proposed algorithm. Green lines represent the corrected emission spectra by applying the linear interpolation based algorithm. Red lines indicate the reference emission spectra corresponding to an excitation wavelength of 305 nm and 535 nm for OFL and RES, respectively.
knowledge, there is no technique capable of successfully coping with this kind of situation. However, the proposed strategy enables correcting the spectrum with a high degree of similarity with the reference spectrum, strengthening its applicability in troublesome spectral situations. In contrast, it is worth mentioning that linear interpolation is performed considering only the extremes of the excised region, then, the correction efficiency would strongly depend on the width of the scatter lines and the degree of overlap. The correction seems to be better on broad and symmetric spectra, e.g., emission spectra of OFL, than on narrow and asymmetric signals, for example, emission spectra of RES. It is possible to observe that the presence of high noise level represents an important drawback for the correction. Moreover, evident artefacts are introduced when the maximum of the emission spectra overlaps with the scatter lines since no spectral feature is considered during interpolation. For instance, wider bandwidths of scatter lines lying on the maximum of the spectra would dramatically affect the feature of the corrected spectra. Last, it must be clarified that despite the introduction of new code lines for second-order Rm scatter correction is allowed, the algorithm was implemented as provided and no correction of second-order Rm was accomplished. In all cases, the implementation of the proposed algorithm led to a notable improvement in preserving the original spectral features after correction, in terms of signal noise and spectral shape in comparison to the reported methodologies based on an interpolation-based correction [10,20]. Thus, this strategy demonstrated to be more efficient in cases of high-level noise (Fig. 3A1) or strong signal overlapping (Fig. 3A2). In this matter, the significant advantage needed to be highlighted is the conservation of the intrinsic noise, which does not interrupt the continuous feature of the spectrum. When linear interpolation is performed instead, the corrected data region of the spectra is noiseless and then, the continuous feature of the spectra is significantly interrupted. This outcome is graphically demonstrated in Fig. 4, in which an emission spectrum was subjected to correction by applying the interpolation-based algorithm reported by Bahram et al. [10] in comparison with the proposed algorithm correction.
Table 1 Figures obtained after convergence of the PARAFAC modelling for a system containing 4 analytes. Modelling figures
N ¼ 4a
N¼5
N¼6
Number of iterations SSEb sfitc Explained variance CORCONDIA
22 1.34 107 6.2405 99.8129 99.3629
189 1.08 107 5.6171 99.8487 77.9243
125 8.69 106 5.0439 99.8782 56.224
a b
N: number of components used for the model. I P J P K P SSE: sum of square errors calculated as e2ijk , where eijk collects the i¼1 j¼1 k¼i
model errors.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SSE c sfit: residual fit estimated as , where I is the number of samples, IJK and J and K are the wavelengths in the excitation and emission mode, respectively.
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no alterations of the spectroscopic information are introduced. Finally, this work attempts to encourage the development of new methodologies for spectroscopic data treatment as well as the investigations in data correction and data processing which is of paramount interest in several research fields. Acknowledgments The authors are grateful to CONICET (Consejo Nacional de Investigaciones Científicas y Tecnicas, Project PIP 2015–0111) and ANPCyT (Agencia Nacional de Promoci on Científica y Tecnol ogica, Project PICT 2014–0347) for financial support. F.A.C. and M.R.A. thank CONICET for their fellowship.
Fig. 5. (1.) Excitation and (2.) emission spectral profiles retrieved from PARAFAC modelling (solid lines) and the real pure spectra (dashed lines) of FLU (red), ENO (light blue), NRF (blue) and OFL (light brown).
References This observation relies on the assumption that the pre-processing procedure applied for the scatter correction does not affect the spectroscopic information of the original data. For the prediction study, the relative error of prediction (REP %) was estimated for each analyte. Moreover, to appraise whether the average recoveries (Rexp ) are significantly different from 100% or not, a suitable statistic test was performed, in which the acceptance of the null hypothesis asserts the statistical equality between values. This condition is accomplished when the critical t value at a level α for n samples exceeds the experimental texp value, which is estimated by following Eq. (2), pffiffiffi n texp ¼ 100 Rexp ; sr
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(2)
where sr is the standard deviation of the recoveries. The REP% figures were 12%, 10%, 17% and 5% for FLU, ENO, NRF and OFL, respectively, while the null hypothesis for the recovery evaluation was accepted in the all cases considering 95% confidence level since the corresponding texp values were lower that the critical value (t0.05,4 ¼ 2.7908 texp,FLU ¼ 0.0838, texp,ENO ¼ 0.4656, texp,NRF ¼ 0.2123, texp,OFL ¼ 1.1004). Therefore, all these results stress the fact that the bilinearity and trilineratity of the data are fulfilled after correction of the fluorescence landscapes which are of utmost importance for chemometrics in analytical chemistry applications. 4. Conclusions In the present work, a new strategy for the correction of scatter signals in fluorescence landscapes was proposed. Matrices gathered from two fluorophoric systems with different spectral properties were subjected to correction and the performance of the correction was in-depth analysed. Moreover, the performance of the correction of data that are subjected to further chemometric modelling was assessed by means of trilinear decomposition with PARAFAC model. The improved algorithm here presented collects and enhances the essential particularities of different scatter correction strategies that are reported in the literature. The novelty of this algorithm relies on the fact that the correction is accomplished by modelling of the scatter peak with further subtraction instead of interpolation. In this way, only the residuals after subtraction in addition to the instrumental noise of the original signal shall remain in the corrected spectra. All the results support the conclusion that the implementation of this algorithm leads to a notable improvement in preserving the original spectral features, offering the uttermost in efficiency and performance in the cases where other techniques may fail. Besides, it was demonstrated that in case of chemometric modelling is applied after correction, the data pre-processing does not affect the performance of the resolution, asserting the fact that trilinearity is fulfilled after scatter correction, and
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