Application of Chemometrics in
A. C. Duarte
Departamento de Quı ´mica, Universidade de Aveiro, Aveiro, Portugal
Departamento de Ecologia, Universidade de E´vora, E´vora, Portugal
Abstract: Chemometrics aims at extracting maximum information through the appli-
cation of statistics and mathematics to problems of a chemical nature. Over the years,
chemometrics has become an important chemical discipline with a significant impact in
analytical chemistry, including the incorporation of significant improvements in design
and selection of optimal experimental procedures, calibration of analytical instrumen-
tation, and advanced methods for analysis of chemical data.
The application of chemometrics methods to separation science, mainly chromato-
graphy and capillary electrophoresis, has followed the same increasing trend as in
any other field of analytical chemistry. However, reviews on the application of
chemometrics in separation science have been very scarce. Therefore, in this paper,
the development of chemometrics in chromatography and capillary electrophoresis
will be presented with a view of the current state of the-art and with the prospects
for the future.
Keywords: Chemometrics, Chromatography, HPLC, Capillary electrophoresis,
Principal component analysis
The major areas of chemometrics chosen to be reviewed in a recent paper
about the evolution of chemometrics related to analytical chemistry,
included multivariate calibration, pattern recognition, and mathematical
Address correspondence to A. C. Duarte, Departamento de Quı ´mica, Universidade
de Aveiro, 3810-193 Aveiro, Portugal. E-mail: email@example.com
Journal of Liquid Chromatography & Related Technologiesw, 29: 1143–1176, 2006
Copyright # Taylor & Francis Group, LLC
ISSN 1082-6076 print/1520-572X online
mixture resolution. Such a division seems most appropriate to follow also in
this review of applications of chemometrics to separation science for two
main reasons: (a) it becomes easy to compare and follow the evolution of
different studies in a specific area; and (b) for lecturing purposes it is useful
to have a review on this subject structured in well known areas.
In anotherreview paper,specific for optimization methods in chromato-
graphy and capillary electrophoresis, a distinction is made in what concerns
the use of chemometrics methods where no explicit models are required,
and hard modelling when models are available, and, in such a case, optimi-
zation can be performed by regression methods. Hard modelling can not be
left completely out of this review on the application of chemometrics to
separation science, since both the large variety of chromatographic parameters
and the vast number of relationships between them leads to the conclusion that
the combination of chemometrics methods with hard modelling will certainly
bring some improvements to the prediction of retention,[2,3]one of the most
specific application of chemometrics to separation sciences. Besides, if one
considers the general definition of chemometrics as mentioned at the top of
this review, there is no practical reason for making a distinction between
the application of chemometrics, and/or hard modelling to separation
science. They both aim at extracting maximal chemical information through
the application of statistical and mathematical methods.
Various textbooks on the major areas of Chemometrics, as well as
dedicated journals are available, and as a first approach, the review paper
on the evolution of chemometricscan be considered an excellent source
of references to start with, besides containing short introductions to several
relevant methods for multivariate calibration, pattern recognition, and
mixture resolution. Another recent review paperon chemometrics in
Hungary, for the last 10 years, also deserves a special mention as a source
of important information on the work of chemometricians, although only
focused on the Hungarian works.
The specificities of separation science bring into play subjects such as
analysis of peak asymmetry, peak overlapping, and quantitative structure
retention relationship, which are not usually highlighted in reviews of
chemometrics. Although the general accepted classification of major areas
in chemometrics will be used in this review, one must bear in mind that the
same method (such as artificial neural networks) can be used in different
applications (such as multivariate calibration or prediction of retention).
Therefore, this review is an attempt to reach equilibrium between emphasizing
the applications of chemometrics methods, without loosing sight of the
analytical specificities in separation science. As shown in Figure 1,
principal components analysis (PCA) is the most used chemometric
technique in separation science, followed by factorial design (FD), cluster
analysis (CA), artificial neural networks (ANN), and partial least squares
(PLS). The criteria of highlighting the techniques cited more than 5 times
included a plethora of several other techniques under the heading “others”.
A. C. Duarte and S. Capelo1144
The trend in the application of chemometric techniques in separation sciences
can be observed in Figure 2, where the number of cited papers in this review is
plotted against the year of publication. Although the number of citations per
year is not remarkable, the trend to increase is apparent, mainly due to the
application of chemometrics to distinguish or to characterize samples of
different origin or nature. The older publications use chemometrics to
solving separation related problems, such as, peak definition or peak
resolution. In Figure 3, where the number of cited papers for the most cited
chemometric technique (PCA) versus year is presented, it can be observed
that it is in 2004 that most citations appear.
Chemometric techniques versus number of times of appearance in the
Number of appearance of all chemometric techniques versus year.
Application of Chemometrics in Separation Science1145
Peak Asymmetry and Overlapping of Chromatographic Peaks
Peak asymmetry and overlapping of chromatographic peaks are often dealt
with in separation science, and chemometricians have been developing
methods for improving our knowledge on those two subjects for some time
now. Asymmetry of skewness of chromatographic peaks has long been
recognized as extremely important regarding signal processing, since the
deviation of the real peak shape from the symmetrical peak has a significant
impact on the estimation of many chromatographic figures of merit, such as
the retention time, the peak area, the peak width at half peak height, and
even the degree of peak overlapping.
It is fundamental to examine all possible reasons why the real chromato-
graphic peaks are not symmetrical in order to approach the problem; first
by examining deeply its physical chemical nature, then, second by fitting
mathematical functions to characterize the asymmetric factor (skew) of real
chromatographic peaks, and, finally, by assessing the usefulness of the
proposed methodology in real cases. The principal reasons for the observation
of deviation from the ideal symmetrical peak are the column overload,
non homogeneity of the stationary phase, the non homogeneity of the
column packing, the occurrence of slow mass transfer, the effects due to
kinetics of adsorption-desorption, and the dispersion phenomena on the band
profile. Besides the phenomena occurring in the column, there are other
instrumental and operational causes which can play an important role in the
occurrence of asymmetrical peaks and broadening effects observed in sepa-
ration science. Instrumental details such as connections, tubing and fittings
within the chromatographic apparatus, as well as the injection port and
detector characteristics, may increase the width and asymmetry of the peak.
Principal components analysis (PCA) (as the most cited technique) versus
A. C. Duarte and S. Capelo1146
Operational details, such as when the temperature of the injection port in gas
chromatography is not high enough, may cause the occurrence of peaks with
a significant degree of tailing.
The above mentioned approach has been generally followed and conse-
quently, many methods can be found in the literature for the determination
of chromatographic peak parameters and calculation of factors related to
peak shape asymmetry. These methods have been revisited and reviewed to
the point of suggesting a new method for the determination of peak shape
asymmetry in chromatography.First, the real chromatographic peak is
fitted to a mathematical function,and then the peak width of the symmetri-
cal curve is fitted to the measured data with the same peak maximum position
and height of the fitted asymmetrical peak. The differences of the asymmetri-
cal and symmetrical peaks and the areas of the difference curve on the
ascending and descending half parts of the peak characterize the real
asymmetry of the measured peak.The application of this concept to
separation of phenol derivatives by HPLC in the function of flow velocity,
allowed not only determination of asymmetry factors but also suggest that
the examination of asymmetry can give an insight into the physicochemical
processes occurring in the column.The effect of intraparticle mass
transfer resistances on the chromatographic peak shape was studied both
theoretically and experimentally in chromatography of proteins,where
very broad and highly asymmetrical peaks are usually observed.
Besides skewed peaks, it is also usual to observe the occurrence of
overlapped (and skewed) peaks, which further increases the difficulties of
assessing the chromatographic figures of merit. Cai and Wudeveloped a
method for calculating the statistical moments of overlapped peaks by using
a parameter determined from the leading half of the peak to indicate the
peak asymmetry, and the method was successfully applied for the deconvolu-
tion of a series of overlapping peaks. Pa ´pai and Papsuggested a new mathe-
matical equation, result of the product of a Gaussian function and a
polynomial, to fit symmetric, asymmetric, and strongly fronting peaks,
adequate for the determination of chromatographic peak parameters by
nonlinear curve fitting using statistical moments; furthermore, the function
could be used, with acceptable results, for resolution of overlapped peaks,
correction of baseline drift and noise filtering. Fourier transformation (FT)
has been applied to multicomponent chromatograms in order to characterize
retention patterns,to improve the signal to noise ratio of chromatographic
peaksand, at a further stage, to unravel superposition of more complex
retention patterns.A combination of a stochastic model with mobile
phase dispersion has been proposed by Felinger et al.,as the stochastic-
dispersive theory of chromatography, to include the effects of slow mass
transfer or adsorption-desorption kinetics and the band profile axial dispersion
on the full description of the efficiency of separations, as well as the chromato-
graphic peak features. Pietrogrande et al.reported a general method for
evaluating the statistical degree of peak overlapping in a multicomponent
Application of Chemometrics in Separation Science1147
chromatogram, once the retention pattern is determined in advance. The same
basic principles were also used for deconvolution of overlapping skewed
peaks,and for determination of the critical degree of peak overlapin
multicomponent chromatograms. In this case, as the heights of adjacent
peaks may differ widely, no single value of critical peak resolution can be
determined in multicomponent chromatograms. Therefore, only a distribution
of critical peak resolutions can be determined by using the peak height
distribution. A mathematical function has been derived by Fellingerfor
the critical peak resolution, from which the average or maximum probable
peak resolution can be obtained by integration.
Besides further examples of utilization of Fourier transform[17,18]for
decoding complex multicomponent chromatograms, the extended Kalman
filter in frequency domainhas also been a useful method to perform
parameter estimation on the basis of the FT of the signal, and used for the
evaluation of overlapping signals, mainly for noise filtering and for deconvo-
lution by peak sharpening.
Liu and Davisevaluated the predictions of the statistical overlap
theory in the observed peak overlap of 38 neutral compounds by micellar elec-
trokinetic chromatography (MEKC), based on the assumption of an inhomo-
geneous Poisson distribution of migration times. Besides, the probability
distributions and statistical moments in the separation were computed by
Monte Carlo simulation.
Zhang et al.reported the successful application of multilayer percep-
tion artificial neural networks (ANN), based on genetic input selection for
quantification of the unresolved peaks in micellar electrokinetic capillary
Gao et al.modified the non-negative matrix factorization introducing
the characteristics of the chemical signals, such as smoothness of spectra,
unimodality of chromatograms, and sparseness of mass spectra for resolving
overlapping spectra and, therefore, transforming the traditional NMF
algorithm adequate as a resolution method for complex samples.
Hu et al.proposed a singular value ratio (SVR) for resolving peaks in
HPLC-DAD and detecting the presence of impurities in complex mixtures.
This simple chemometric approach is based on the technique of moving
fixed size windows along the retention time axis and extracts information
about selectivity in singular value evolving profiles, in order to more effec-
tively determine peak homogeneity for HPLC-DAD.
Quantitative Structure–(Chromatographic) Retention
Reubsaet and Jinnoon reviewing and discussing the interactions between
an analyte and the stationary phase with relation to the physicochemical
properties of both, concluded that a chemometric approach provides insight
A. C. Duarte and S. Capelo1148
into combinations of these interactions that dominate the retention behaviour
of analytes in RP-HPLC.
He ´berger,on examining QSRR of 20 hydrocarbons (mainly alkylben-
zenes) in silicone oil 550 (moderately polar phase) or bentone 34 (polar phase)
as the stationary phase, when establishing empirical correlations between gas
chromatography retention data and physical or topological properties of solute
molecules, has shown the superiority of a nonlinear fitting equation in describ-
ing retention time using a boiling point (BP) and another topological descrip-
tor. Also, He ´bergerlater proved the excellence of the predictive ability of
this nonlinear model for apolar and slightly polar stationary phases using alkyl
benzenes as model compounds. Finally, He ´berger and Kowalskadeveloped
studies on the thermodynamics of Kova ´ts retention index-boiling point corre-
lations for alkylbenzenes in gas chromatography, which allowed prediction of
retention indices, standard chemical potential of partitioning of one methylene
group of n-alkane, and the average heat of vaporization/solution values for
low and moderately polar stationary phases.
Kaliszanreviewed the combination of available data regarding the
application of affinity CD and HPLC and chemometrics (mainly MLR,
PCA, and Cluster Analysis (CA)) to evaluate the strength of drug-protein
interactions, and to provide information of relevance to molecular pharma-
cology and for drug design. QSRR equations derived for test series of drug
analytes are interpreted in terms of structural specificities of binding sites in
biomacromolecules. In another review on the role of chromatography and
capillary electrophoresis in modelling the basic processes of drug action,
Kaliszanemphasized the combination of separation sciences and chemo-
metrics (such as PCA) for increasing speed and efficiency in establishing
quantitative relationships between the chemical structure of drugs and their
ability to participate in intermolecular interactions with the components of
living systems, besides reducing the research costs with new drugs and the
use of laboratory animals. The principles and methodology of QSRR using
biologically active chemicals are discussed by Kaliszanin the context of
using the chromatographically measured parameters for describing the inter-
actions of drugs with biomolecules, in order to predict quantitative differences
in specific bioactivity parameters of a given pharmacological family, i.e.,
establishing quantitative structure activity relationships (QSAR) with
retention parameters serving as structure parameters.
The retention characteristics of a newly designed cholesterol bound silica
gel stationary phase for RP-HPLC were revealed by analysis of QSRR, which
was derived by multiple regression analysis (MRA), using three groups of
structural descriptors of analytes and the log kwdata determined on the new
Baggiani et al.used PCA combined with PCR to search for corre-
lations between the selectivity of a pentachlorophenol (PCP) imprinted
polymer packed in a HPLC column and the molecular descriptors of 52
PCP-related phenols. The QSRR procedures were applied to correlate the
Application of Chemometrics in Separation Science1149
chromatographic behaviour of several phenols, mainly characterized by their
retention time, with structural parameters determined by molecular mecha-
nisms or semi empirical quantum chemical techniques. The magnitude of
the multivariate model’s parameters shows that selectivity is strongly influ-
enced by molecular descriptors having a structural character, while the
effect of molecular descriptors having an electronic character is much less
Bolliet and Pooleused statistical mixture design techniques associated
to the solvation parameter model, in order to predict retention time in reversed
phase liquid chromatography using ternary mobile phase compositions. The
solvation model is used to obtain system constants characteristic of the
chromatographic capability for defined solvent-solvent and solute-solvent
interactions. The mixture design was used to build system surfaces, for each
system constant for all mobile phase concentrations, which could then be
used in models to predict the retention of a wide group of 36 solutes on a
porous polymer sorbent at a methanol-acetonitrile-water composition not
included in the data used to construct the system surfaces.
Quantum chemical calculations provide acceptable descriptors for
characterization of molecular properties in QSRR. Ko ¨rtve ´lyesi et al.[32,33]
established correlations between the Kova ´ts retention index and quantum
chemical descriptors for aliphatic ketones and aldehydes on stationary phases
of different polarity, besides developing calculations of quantum chemical
descriptors (i.e., van der Waals’ surface areas and volumes), and highlighting
their good correlation with the Kova ´ts retention index for alkanes, alkenes,
and azo compounds. Ko ¨rtve ´lyesi et al.used multiple linear regression
(MLR), cluster analysis (CA), and principal component analysis (PCA) for
the statistical evaluation of the relationships between Kova ´ts retention
indices and the calculated molecular descriptors. Unusual retention relations
have been observed by Kiva ´ly et al.in the gas chromatography of
N,N0-dialkylhydrazones (DAHs), where different correlations are necessary
for calculation of retention indices for aldehyde and ketone DAHs, due to the
different resonance structures in the aldehyde and ketone derivatives.
A PLS model has been built by He ´berger et al.to estimate retention
data of 35 aliphatic ketones and aldehydes at different temperatures (50, 70,
90, and 1108C) and various stationary phases of different polarity, and also
to discriminate between ketones and aldehydes on the basis of their
retention date and physical properties (structural descriptors). Multiple
linear regression (MLR) was also used by Markuszewski et al.to derive
QSRR(relating retention parameters
hydrogen bond descriptors and structural parameters from molecular
modelling) to evaluate the partition mechanism of environmental significant
compounds (mainly nitroaromatics and their transformation products around
former ammunition plants) on new stationary phase materials. Furthermore,
the chromatographic retention data, once subjected to PCA, allowed the
assignment of individual pollutants to defined metabolic routes.
to hydrophobicity parameters,
A. C. Duarte and S. Capelo1150
Canonical correlation analysis (CCA) has been used in QSRR by Forga ´cs
and Cserha ´tion their work to relate retention characteristics with physico-
chemical parameters of barbituric acid derivates on a porous graphitized
carbon column using water-tertrahydrofuran mixtures as solvents, and
concluded that the electronic parameters exerted the highest impact on the
retention, while the hydrophobicity was negligible.
Valko ´ et al.established relationships between the chromatographic
hydrophobicity indices (CHI) and solute descriptors obtained by using
several reversed-phase, diol, nitrile, cyclodextrin, and immobilised artificial
membrane bonded HPLC columns. The CHI data obtained on various
HPLC stationary phases were subjected to multiple regression analysis
(MRA) and PCA.
Since the partitioning of drugs is often mainly ruled by their hydrophobi-
city character, a fast screening of new drug candidates is performed by corre-
lating the logarithm of the retention factors (log k) from classical RP-HPLC
with hydrophobicity expressed by the partition coefficient, log P. The use of
new methods, which include stationary phase models of biological
membranes and micelles in their mobile phase (i.e., micellar liquid chromato-
graphy (MLC), micellar electrokinetic capillary chromatography (MECC)),
are alternatives for providing QSRR (as conventional RP-HPLC does), as
well as quantitative retention activity relationships (QRAR) using biological
parameters and wishfully mimicking biological partitioning.Detroyer
et al.used PCA score plots to differentiate between pharmacological
classes based on their retention characteristics on MLC, MECC, and IAM,
as well as on conventional methods, and concluded that the insertion of
these new methods would allow covering a whole range of retention mecha-
nisms, besides hydrophobicity, very useful to model QRAR. In another work,
Detroyer et al.also explored the potential of PCA, CA, weighted holistic
invariant molecular (WHIM) descriptors (in a variant of PCA), sequential
projection pursuit (SPP) (another variant of PCA) for the classification of
83 substances, from 5 pharmacological families, based on chromatographic
data on 8 HPLC systems.
Artificial neural networks (ANN) were successfully developed by
Jalali-Heravi and Garkani-Nejadfor the modelling and prediction of
electrophoretic mobility of a series of sulfonamides, positively charged at
low pH and negatively charged at high pH, in capillary zone electrophoresis
(CZE) using, for modelling purposes, part of a set of 47 descriptors divided
into four groups of topological, geometric, and physicochemical parameters.
The results obtained using ANN compared very well with the experimental
values and showed some superiority to those obtained by MLR techniques.
Cserha ´ti and Forga ´csapplied PCA to prove that the hydrophobicity
parameters determined by RP-HPLC and RP thin-layer chromatography
(TLC) are slightly different, and herbicides and fungicides could not be
discriminated according to their hydrophobicity parameters. The significance
of this finding in terms of application of QSAR in agrochemical research is
Application of Chemometrics in Separation Science1151
thatdifferencesinthe biologicalactivityofthesepesticidescannot beattributed
to either their hydrophobicity or specific hydrophobic surface area alone.
Farkas et al.compared RI prediction of three groups of saturated O-,
N-, and S-containing heterocycles using variable subset selection (VSS) and
PLS methods to select, from a large data set, the most appropriate independent
descriptors. After choosing the appropriate independent variables, predictive
models were then built, and compared, using MLR and PLS methods. PLS
failed to select boiling point (BP) or molecular mass as descriptors of the
RI, but after including the selected descriptors with BPs, PLS provided
proper models for RI prediction. The main conclusion was that combination
of the MLR for variable selection and PLS for model building should be a
useful methodology for RI prediction.
The support vector machine (SVM) and the heuristic method (HM) were
used by Luan et al.to develop the non-linear and linear models between the
retention time (RT) and five molecular descriptors of 149 volatile organic
compounds (VOCs). The HM was used for the prediction of RT using calcu-
lated structural descriptors and, even after the heuristic reduction, the pool of
descriptors was reduced to 150. In order to avoid over parameterization, a
number of 5 descriptors seemed to be enough for a successful linear model.
From the physical meaning of the descriptors in the linear model, it can be
suggested that the polar interactions and relative reactivity are likely to be
the two major factors controlling the retention behaviour of VOCs on
non-polar stationary phases of DB-1. The SVM was then used to built a
non-linear model based on the same set of descriptors obtained by the HM.
The performance of the SVM proved to have better predictive ability then
that provided by the HM.
SMV was also used, as a nonlinear regression method, by Liu et al.to
develop a nonlinear quantitative structure mobility relationship model of
peptides based on the structural descriptors. MLR and SVM were used
to select the descriptors responsible for the electrophoretic mobility of
peptides and develop linear and non-linear models, respectively, for the
prediction of the electrophoretic mobilities of peptides. The performance of
the SVM model showed a better performance than the MLR, which highlights
that the non-linear model can describe better the relationship between the
structural descriptors and the electrophoretic mobilities of peptides.
Classification of Stationary Phases and Polarity Indicators
The column selection is not a straightforward process and stationary phases
can only be appropriately selected for a given separation when there is a
sound knowledge about the physical meaning and the classification of the
phases. Valko ´ et al.suggested the use of a high throughput chromato-
graphic hidrophicity index (CHI) for characterizing the different selectivities
of stationary phases according to the solute-stationary phase interaction
A. C. Duarte and S. Capelo1152
properties for each specific phase. He ´bergerevaluated polarity indicators
and stationary phases in gas-liquid chromatography using PCA, and
suggested that no single polarity variable can be used on its own. Furthermore,
physical meaning could be associated to the most influential principal com-
ponents: PC1, attributed to polarity defined as usual; PC2, attributed to
hydrogen donating and hydrogen accepting ability with opposite signs; and
PC3, attributed to dipole interactions. He ´berger et al.also used PCA for
assessing polarity indicators and solute-solvent interaction parameters in
order to classify ketones, their oximes, and mixtures as stationary phases in
inverse gas chromatography. Forlay-Frick et al.used PCA, as an unsuper-
vised pattern recognition technique, to unravel patterns, and test the possible
replacement of HPLC systems from data on plate numbers and symmetry
factors measured for three solutes (benzoic acid, N,N0-dimethyl-aniline and
Vancomycin) in various chromatographic systems (stationary phases and
different mobile compositions). Although, the theoretical plate number
(column efficiency) is negatively correlated with the symmetry factor,
Forlay-Frick et al.concluded that both are necessary for proper classifi-
cation and characterization of stationary phases. Iva ´nyi et al.evaluated if
PCA could reduce the number of chromatographic test parameters, while
maintaining the classification of RP-HPLC stationary phases. Fewer para-
meters, only three or four, could be enough for keeping column clustering
and column differentiation without much loss of information and, in some
cases, provided even more detailed results. Poole and Poolealso
recognized the role of PCA and CA to classify the stationary phases, by
their similarity for specific intermolecular interactions, on their study about
the chemometric classification of the solvent properties (selectivity) of
commonly used GC stationary phases.
Gyseghem et al.measured chromatographic parameters representing
hydrophobicity, steric selectivity, efficiency, silanol activity, H-bonding
capacity, and ion exchange capacity, and compared the selection of
RP-HPLC columns with diverse selectivity towards the potential separation
of impurities in drugs. The initial selection was based on the visual inspection
and personal experience and a reevaluation was then performed using the
Pareto-optimality method, PCA, and Derringer’s desirability functions
approach. The selection by the chemometric approaches was found to be
fairly comparable with the initial selection.
Forlay-Frick et al.,for the selection of orthogonal/similar chromato-
graphic systems using retention factor data of drugs, applied the generalized
pairwise correlation method (GPCM) using different statistical tests
(Williams’ t, Conditional Fisher’s, McNemar’s and Chi-square tests), and
the results were compared and validated with those obtained correlation coef-
ficients (Pearson’s product moment correlation coefficient, Spearman’s rho
and Kendall’s tau). The vast majority of retention data for chromatography
is not normally distributed, the classification of the systems was strongly
dependent on the applied method, and a comparison on the basis of the
Application of Chemometrics in Separation Science1153
orthogonality ratios calculated using the different techniques to obtain infor-
mation about the discrepancies existing in the results allowed Forlay-Frick
et al.to use it, even when the distribution of the data is not normal.
Retention data of newly synthesized stationary phases and structural
descriptors derived by molecular modelling of nucleosides and cyclic nucleo-
tides were subjected to PCA, allowing Turowski et al.to conclude that
from the 11 new materials, 8 hydrocarbon bonded silica phases had separation
properties regarding nucleosides and nucleotides similar to a standard
octylsilica phase. Furthermore, PCA of structural descriptors of solutes
facilitate the identification of structure features that affect retention, while
PCA of retention data provides a method for comparison characteristics and
classification of the HPLC systems.
Optimization of Operational Conditions Associated with
The optimization methods applied to parameters of interest in either
chromatography or capillary electrophoresis have been reviewed by Siouffi
and Phan-Tan-Luu.The reviewestablishes a separation between
optimization methods using a chemometric approach and methods based on
models. The conclusion is that chemometrics tools such as the simplex
algorithm, the overlapping resolution maps, the factorial designs, the
response surface methodology, and the neural networks have the great
advantage of not needing an explicit equation for the objective function
with the desired criteria. However, chemometrics methods may require a
large number of experiments, and boundaries of the domain are not easy to
draw. Therefore, when models are available, optimization becomes straight-
forward by regression methods, and the reviewalso concludes, that
among the chemometric methods, the simplex and the overlapping resolution
maps are declining, while the use of artificial neural networks is increasing.
Besides, the factorial designs and central composite designs are becoming
more popular in capillary electrophoresis since the number of parameters to
optimize is much larger than in CG or LC.
The development and validation of a capillary electrophoresis (CE)
method by Wynia et al.involved the use of several chemometric
methods, such as Box-Behnken design, PLS, and MLR, for assessing the suit-
ability of CE in the determination of drug substance, mirtazapine, and five
structurally related substances. The capillary efficiency and the overall
quality of separation of benzodiazepines in CE was assessed by Peyrin and
Guillaumeby means of a new response function, which was maximal
when both efficient separation conditions and a minimum analysis time
were met, and using Box-Benhken design followed by simplex optimization.
Guillaume and Peyrinperformed the optimization of the migration time,
height equivalent to a theoretical plate and separation of a mixture of
A. C. Duarte and S. Capelo1154
imidazole compounds by CE, with a method based on the application of
a simplex to a polynomial derived from preliminary experiments designed
by factorial designs.
Corradini et al.applied a full factorial design to optimize the CZE con-
ditions (temperature, voltage, and percentage of methanol added to the back-
ground electrolyte) for characterization of fructooligosaccharides and inulin at
different degree of polymerization, in order to evaluate their prebiotic
The successful application of fractional factorial design and Plackett-
Burman designs have been reportedwhen addressing the robustness of
an HPLC assay method issued by the United States Pharmacopoeia for ginse-
nosides, in Asian and American ginseng. The interpretation of the effects on
the responses were evaluated both graphically (with a half normal probability
plot) and numerically by a t-test. Perrin et al.also used a Plackett-Burman
design on testing the robustness of enanteomeric separation of a basic
(propanolol), a neutral (praziquantel), and an acidic (warfarin) compound
by CE using highly sulfated cyclodextrins.
A fractional factorial design, together with a star design, were used for
studying the effects of 3 factors (the alkyl chain length, the concentration of
the ion interaction reagent, the concentration of the acetonitrile, and the pH
of mobile phase) and their interactions, in order to develop and optimize a
method of ion-interaction chromatography (IIR-RP-HPLC) for the simul-
taneous separation of 21 polar aromatic sulfonates.The failure to obtain
good predictions with a linear regression algorithm was overcome by using
the Box-Cox transformation after which Marengo et al.located the
optimal experimental conditions for separations.
A fractional factorial design was used by Persson-Stubberud and
A˚stro ¨mfor development and optimization of a capillary electrophoresis
separation of ibuprofen, codeine phosphate, their degradation products and
impurities. In the analysis of ranitidine and related compounds by capillary
electrophoresis. Morris et al.used a strategy involving fractional
factorial designs to screen and determine the significant factors controlling
separation and central composite designs to determine the optimal conditions
for the separations. Models were generated by multilinear regression (MLR)
and canonical analyses were used to calculate the optimum conditions.
Wynia et al.developed and validated a capillary electrophoresis separation
for the assay of antidepressant mirtazapine and five structurally related sub-
stances in a tablet formulation, following a Box-Behnken design and PLS
as multivariate modeling technique for relating the current profiles and both
migration times and peak areas.
The selection of optimum variable separation conditions (pH and concen-
tration of a complexing agent in the buffer electrolyte) of rare earth metal ions
in capillary zone electrophoresis (CZE) was accomplished by Jimidar et al.
by application of a multicriteria approach: the separation method was
optimized using a central composite design for the two variables and the
Application of Chemometrics in Separation Science1155
Derringer’s desirability function was applied to determine the most desirable
combination of separation, sensitivity, and analysis time.
The optimization and comparison of neurotransmitter amino acid separ-
ation in normal micellar electrokinetic chromatography (N-MEKC) and
reversed migration electrokinetic chromatography (RM-MEKC) were
carried by Wan et al.using a central composite design with multivariate
linear regression. A face centred cube central composite design was also
used by Safa and Hadjmohammadito evaluate the effect of the concen-
tration of sodium dodecyl sulfate, propanol content, and pH of the mobile
phase in micellar HPLC separation of chlorophenol isomers. Besides, the
use of the Pareto-optimality method, an approach from the multicriteria
decision making, allowed Safa and Hadjmohammadithe selection of the
best possible combination of separation quality and analysis time, with the
consequent production of chromatograms of superior quality.
A three-step procedure was followed by Brunnkvist et al.in the search
of optimal chromatographic separation conditions of two different capillary
electrophoresis (CE) stationary phases (Hypersil phenyl and Hypersil C18)
for four basic peptides, using peak resolution and peak efficiency as
response function: a) initial studies for determination of the experimental
variables and their respective domains for the two stationary phases; b) appli-
cation of a Plackett-Burman design and PLS models were preferred to MLR’s,
due to their higher predictive ability; and c) optimization according to a
central composite design combined with both MLR and PLS models for
each stationary phase.
Chiralcel OD-R, as a chiral stationary phase with mobile phase containing
acetonitrile (modifier) and sodium perchlorate (buffering component), was
found by Wso ´l and Fellto be the most suitable system for chromato-
graphic enantioresolution of rac-11-dihydrooracin. The Box-Wilson central
composite design was employed to find the optimal conditions of temperature,
modifier concentration, and buffer concentration for new proposals of chroma-
tographic response functions, based on the resolution and the retention time
of the last component eluted.
In terms of sample preparation, extraction, and other conditions prior to
separation, Romva ´ri et al.[68,69]developed a rugged sample preparation
approach, based on Taguchi’s method, which allowed obtaining high
accuracy and reliability in the use of HPLC for the determination of two
main metabolites of albenzadole (albenzadole-sulfoxide and albenzadole-
sulfone) in cow’s milk. Designed experiments according to Taguchi’s
method were also used by Ehmann et al.for investigation of alkaline and
acid prerinsing techniques in capillary preconditioning for analysis of
anions using indirect UV detection in capillary zone electrophoresis.
Keszler and He ´bergerused PCA for studying the influence of extraction
parameters and medium on the efficiency of solid phase microextraction
(SPME) sampling, in the analysis of aliphatic aldehydes by GC-MS. Tukai
et al.used factorial design (for selecting the most significant factors) and
A. C. Duarte and S. Capelo1156
central composite design for optimization of the conditions of microwave
assisted extraction, prior to HPLC-IPMS analysis of arsenic species in
marine macroalgae. Johansen and Rasmussenused a factorial design and
response surface modelling (RSM) for screening and optimization of
dialysis recoveries of antidepressant drugs in human plasma prior to HPLC.
Beijersten and Westerlundoptimized the conditions of derivatization
of dipeptides for separation by micellar electrokinetic chromatography,
using a fractional factorial design for screening experiments and a central
composite design for response surface modeling. A central composite
design was also followed by Daali et al.to optimize the conditions of
chemical hydrolysis (acid concentration, hydrolysis temperature, and hydroly-
sis time) of sialic acid in a soluble caseinoglycomacropeptide, and the sialic
acid release was monitored by high performance anion exchange chromato-
graphy with pulsed amperometric detection (HPAEC-PAD).
The optimization of RP-HPLC separation of p-hydroxybenzoic acid and
its esters, was performed by Guillaume and Peyrinwith a new algorithm
based on Glover’s taboo search (TS), with better results than those obtained
with pure random search and simplex search. A novel chromatographic
response function (CRF) already used by Peyrin and Guillaume,which
was maximal when both efficient separation conditions and a minimum
analysis time were met, allowed obtaining the optimal conditions for
column temperature, the water fraction in the mobile phase, and its flow rate.
In order to avoid a blank chromatographic run, Boelens et al.
developed a two step process, which takes into account the shape and
also the intensity differences of the background eluent spectrum during the
HPLC separation process coupled to spectroscopic detection: first, the
baseline spectra are modelled using a limited number of PCs; subsequently,
an asymmetric least squares regression method allows for correction of the
spectra during elution for the background correction.
Doehlertmatrixdesign, as a chemometric tool, deserves a special mention
since its application to analytical chemistry has been recently reviewed by
Ferreira et al.The review paperdiscusses the advantage of Doehlert
design with other response surface designs, such as central composite and
Box-Behnken designs, and discusses the application of Doehlert matrices in
chromatography, besides a reference to the first demonstration that application
of this design in analytical chemistry is more appropriate and more economi-
cal than the central composite design for optimization of a separation process
using HPLC.Considerable reduction of analysis time in lengthy HPLC was
obtained by Araujowhen the Doehlert design was selected for systematic
and simultaneous optimization of the gradient solvent system and the instru-
mental/experimental variables associated to the HPLC-DAD chromatograms
of chloropigments, chlorophyll a, hydroxyl chlorophyll a, and methoxylac-
tone chlorophyll a. Further applications to the HPLC separation of orto,
meta, and para cresol in antiseptic products, and polyaromatic hydrocarbons
in synthetic mixtures, allowed also a significant reduction in analysis time.
Application of Chemometrics in Separation Science1157
A two factor Doehlert design was also chosen by Garcı ´a et al.to fit a second
order model, and jointly optimize the resolution and the peak width through a
global desirability function for the determination of hormones (diethylstil-
bestrol, hexestrol, dienestrol, nor-testosterone, methyl-testosterone, 17-a-
estradiol, 17-b-estradiol, and 17-a-ethynylestradiol)) by GC-MS without
derivatization. Prior to the optimization step, a design similar to a reflected
Plackett-Burman design was carried out to select, with a reduced number of
experiments, the most important factors and how their responses affect the
resolution and the peak widths.
Farkova ´ et al.has shown that artificial neural networks (ANN) can be
used to estimate peak parameters and, in combination with central composite
design (CCD), can be applied for efficient prediction of optimal conditions in
capillary zone electrophoresis with a lower analytical effort. The application
of ANN in optimization of CZE methods has been examined by Havel
et al.,and a new method has been developed based on the combination
of central composite design (CCD) and ANN with the back propagation
technique, which showed considerable effectiveness.
A chemometric tool, based on the function of mutual information (FUMI)
theory, has been suggested by Kotani et al.for predicting the measurement
uncertainty in HPLC with electrochemical detection (HPLC-ECD) with only
one chromatogram, and consequently allowing the optimization, in a very short
time, of the analytical operational parameters for determination of catechins.
The separation of pharmaceutical residues of environmental concern has
been used by Cela et al.to demonstrate the practical advantages and
working procedures of multiobjective optimization using evolutionary algo-
rithms (EA), which allow easy and direct definition objectives without the
need for chromatographic response functions (CRF), and also provides not
only a single optimum, but a well populated Pareto front of non dominated
solutions. The problem of modelling the CRF for optimization purposes of
HPLC methods has been approached by Dewe ´ et al.using the separation
of S-timolol, R-timolol, and related substances as a case study: a Box-
Behnken experimental design was followed to perform the experiments, a
Derringer’s function was defined for each response, and overall desirability
was derived. Marini et al.assessed the uncertainty associated to an
HPLC method for determination of R-timolol and other related substances
in S-timolol maleate, by applying a two level Placket-Burman design and per-
forming the experiments, which could be assimilated to laboratories from an
interlaboratory exercise; different uncertainty components were estimated
using the data obtained from the robustness test.
Holı ´k and Mannschreckdiscussed the errors involved in the calcu-
lation of the enanteomeric excess determined from overlapping HPLC
peaks when a dual detector, i.e., UV/VIS and circular dichroism (CD), is
used. The best results were obtained when two different methods of calcu-
lation of errors are used, and those errors are about one order lower than the
possible error due to wrong selection of the range of data.
A. C. Duarte and S. Capelo1158
Sanli et al.applied three different model fitting strategies for the
experimental designs, in order to optimize the HPLC resolution of a series
of polyphenolic acids with water-acetonitrile mobile phases: a) nonlinear
regression to all data points; b) four data points; c) only two data points.
The models for the retention behaviour of the polyphenolic acids were
based on the relationships between retention factors of solutes with the pH
and solvatochromic parameter of the mobile phase, and between the
dissociation constants of the compounds and the molar fraction of the
Chemical Analysis: Clustering, Detection, Calibration,
The use of chemometrics for clustering samples, multivariate calibration, and
quantification of analytes is the most common activity among the chemome-
tricians, and in various laboratories is still the main activity of the analytical
chemists interested in chemometrics.
Classical analysis of variance (ANOVA), outliers testing, precision
calculations, and other statistics based on the ISO 5725-2 norm, were applied
by De Beer et al.to evaluate the measurement uncertainty in the HPLC-
DAD analysis of several hydro- and lipo-soluble vitamins in multivitamin
preparations on the results of the analysis. A demonstration of an entire
validation programme, exemplified for an HPLC method for the determination
for the evaluation of several performance characteristics, using several classical
statistics tests (ANOVA, Grubbs test, and regression analysis).
PCA is a popular method used for the purpose of pattern recognition,
classification, modelling, and other aspects of data evaluation with chromato-
graphic retention data. However, Brereton et al.assessed different prepro-
cessing approaches (mean centred data sequential scores, mean centred
sequential loadings, and uncentred data) for determining the number of signifi-
cant factors in window factor analysis using principal component based
methods of chromatographic data, and concluded that the general practice,
in HPLC-DAD, of calculating scores for the sequential (time) direction
should be carefully reviewed, and it is likely that loadings in this dimension
is preferable. The best way is to use a variety of methods for calculating
and compare the results in order to detect eventual anomalies or problems
with the chromatographic data. PCA has been applied by Csomo ´s et al.
to biogenic amines, polyphenols, and resveratrol in Hungarian wines. In this
latest example, PCA was able to characterize wines according to their
biogenic amine and polyphenols contents,while cluster analysis failed to
do so. A classification of German wines was performed by PCA (and CA)
based on the HPLC relative anthocyanin pattern, that is the ratio of antho-
cyanin to each other, and it helped to establish the genuiness regarding the
Application of Chemometrics in Separation Science1159
variety of the different wines.PCA allowed Masino et al.to suggest
some clues on the ageing process of Italian balsamic vinegar by using an
HPLC-Diode array detector to obtain analytical data on the following
furanic compounds: hydroxymethylfurfural, furoic acid, furfural, and
5-acetoxymethylfurfural. PCA was applied by Nemati et al.to classify
and characterize the gelatine components of 14 bovine and 5 porcine
gelatines separted by RP-HPLC-UV after hydrolysis and precolumn derivati-
zation. The application of PCA to HPLC data on chorophyls, pheophytins, and
carotenoids in olive oils, allowed Cichelli and Pertesanato discriminate
olive cultivars and to assess the genuineness of olive oils. PCA and CA of
HPLC separated preparations of soybean and milk proteins and their trypsin
hydrolysates enabled Dziuba et al.to determine the type of milk protein
preparations added to a soybean protein preparation. Nemati et al.used
HPLC data on gelatine components (peak height, area, area percentage and
width) to differentiate between bovine and porcine gelatines. PCA, CA, and
correlation analysis were used by Yawei et al.to investigate the relation-
ship between the methylmercury (determined by HPLC-AFS) and total
mercury contamination in gastropod and bivalve species along the Chinese
Bohai Sea. The data from HPLC-TOF/MS (and
when combined with PCA, could be used to fingerprint endogenous metab-
olites and identify compounds or a group of compounds that can be
assigned as markers for the effects toxins, as in the case of nephrotoxicity
of cyclosporin A in rats.The application of PCA to data on the volatile
organic compounds (VOCs) obtained from the headspace of truffle samples
and fingerprinted by GC-MS, allowed Gioacchini et al.to distinguish
between different species of truffles.
PCA was applied by Lu et al.to HPLC fingerprints of herbal extracts
for distinguishing Chinese Angelica from related umbellifera herbs. Gong
et al.combined GC-MS with heuristic evolving latent projections
(HELP) and iterative optimization procedure for resolving embedded peaks
(IPREP), as a method that could enhance the chromatographic separation
and spectral qualitative ability, as shown in the qualitative and quantitative
determination of volatile compounds in Cortex cinnamoni (traditional
herbal medicine) from four main producing areas. PCA was at first used to
confirm the background and correct the baseline drift. The chromatographic
and electrophoretic techniques commonly used in the instrumental inspection
of herbal medicines, as well as the chemometric methods used for evaluating
the fingerprints of herbal products, such as the method based on information
theory, similarity estimation, chemical pattern recognition, spectral correla-
tive chromatogram, multivariate resolution have been extensively reviewed
by Liang et al.The reviewconcludes that the combination of chroma-
tographic fingerprints of herbal medicines and the chemometric evaluation
could become a powerful tool for discrimination and quality control of
herbal products, but the complex relationship between the chromatographic
fingerprints and efficacy of herbal medicines is yet to be properly approached.
1H NMR spectroscopy),
A. C. Duarte and S. Capelo1160
Hendriks et al.emphasized the importance of the different methods
for preprocessing data (peak alignment, normalization, standardization, trans-
formation) before PCA is performed on HPLC profiles of plant extracts to
clustering and classifying samples from different origins. Furthermore, the
use of weighted PCA is advised, instead of ordinary PCA, since this
technique allows the nonconstant error variances to be analyzed. Chen and
Yudemonstrated the benefits of combining a background constraining
technique to mitigate the influence of relatively common deviations in each
data matrixes of the three way data (for example, such as in the case of
HPLC-DAD) associated to iterative correcting procedures, to prevent the
distortion effect of large unique deviations and nonlinear response in each
of the same data matrices.
Linear discriminant analysis (LDA) has been used by Jakab et al.for
comparative analysis of different plant oils by HPLC atmospheric pressure
chemical ionization mass spectrometry. LDA was able to distinguish the
oils based on their triacylglycerols composition.
The chromatographic data on triglycerides and tocopherols present in
Arabic and Robusta coffees, both green and roasted, were considered as
chemical descriptors and used by Gonza ´lez et al.to discriminate coffee
varieties by application of PCA and LDA. Tocopherols proved to be best
suited for coffee authentication processes, not only because they are easier
to determine, but also they can differentiate coffee varieties even after
roasting. Baiocchi et al.applied PCA and the kth nearest neighbour classi-
fication (KNN) to the analyses by RP-HHPLC-DAD of phenolic compounds
from bark extracts of clones of poplar trees, in order to discriminate among the
clones obtainable from the variation of the phenolic content of the bark
extracts. Klemencapplied PCA, hierarchical clustering (HCA), and k
nearest neighbours (K-NN) on the normalised and scaled analytical data
obtained by GC-MS on heroin samples, with the purpose of searching for
batch links among a limited number of investigated heroin samples. Marini
et al.applied linear discriminant analysis (LDA) and artificial neural
networks (ANN) trained by back propagation algorithm to discriminate rice
bran oils manufactured in three different countries (Italy, Thailand, and
Switzerland) according to their geographical origin, using variables such as
of fatty acids and sylil-ethers derivatives of sterols) and HPLC (triglycerides).
Chemometric optimization based on central composite design was
employed by Gong et al.to find the optimum CE resolution, in terms of
buffer concentration, pH, and concentration of acetonitrile as organic
modifier, for the simultaneous determination of six main nucleosides and
bases, including adenine, uracil, adenosine, guanosine, uridine, and inosine in
natural and cultured Cordyceps. Cluster analyses (CA) based on the
characteristics of the peaks in CE profiles, showed that adenosine and inosine
could be used as discriminators and markers for quality control of natural
and cultured Cordyceps.CA also allowed Alonso-Salces et al.
Application of Chemometrics in Separation Science1161
a preliminary study of the HPLC-DAD data structure obtained from a set of
analyses of the polyphenolic content of extracts of freeze dried apple pulps
and peels, followed by LDA. K-nearest neighbours, soft independent
modelling of class analogy, and multilayer feed-forward artificial neural
networks (MLF-ANN) wereused to develop decision rules for the classification
of apples according to their maturity state based on the polyphenolic
The application of evolving factor analysis (EFA) allowed Pasadakis
et al.the accurate determination of aromatic groups in heavy gas oil
fractions based on their elution times and UV spectrum patterns using
HPLC-UV-DAD, even when strong overlapping of the eluting aromatic
component groups occurred.
Lilley and Wheatused PCA and iteractive target factor analysis
(ITFA) to inspect each electropherogram obtained by capillary electrophoresis
for spectral homogeneity of the peaks and to deconvolute comigrations. The
methodology was tested and demonstrated for drug identification in biological
matrices, i.e., analysis of amphetamine and common interferences in human
Partial least squares (PLS) methodology has been used by He ´berger
et al.on chromatographic retention data of oxo compounds in gas chrom-
atography. PLS regression also enabled Latorre et al.the determination of
amino acids by capillary electrophoresis-DAD, since PLS overcame the
partial overlap of phenylalanine, isoleucine, and tyrosine, and the complete
overlap of histidine and leucine. Mean centring and the selection of a chroma-
tographic region were found advantageous by Frenich et al.,when
applying partial least squares (PLS1 and PLS2) and principal component
regression (PCR), as multivariate calibration methods, to the simultaneous
determination of highly overlapped cypermethrin, fenvalerate, and cis- and
trans-permethrin by HPLC-DAD. Other preprocessing techniques such as
smoothing, baseline correction, and averaging did not make any improve-
ments, whereas differentiation had a detrimental effect.
Sentellas et al.showed that the performance of principal component
regression (PCR), partial least squares (PLS1 and PLS2), and nonlinear PLS
(NL-PLS) were comparable as multivariate calibration methods for quantifi-
cation of strongly overlapped peaks, as is the case of CZE-DAD applied to
the separation of ebrotidine and its metabolites. Furthermore, data pretreat-
ment to correct baseline and spectral drifts and peak shifting should always
be addressed beforehand.
The detection and quantification of residues of simazine, prometon,
atrazine, and propazine in apples by gas chromatography selected ion monitor-
ing (GC-SIM) were performed by Jalali-Heravi and Vosough,using the
generalized rank annihilation method (GRAM). The GRAM, as a second
order calibration technique, allowed obtaining the mass chromatograms and
the true ion abundance of each analyte and to quantify the triazines in
different samples with only one standard data matrix. The application of
A. C. Duarte and S. Capelo1162
GRAM required different steps of data preprocessing, such as background cor-
rection, deskewing, and standardization for rank alignment. The effect of a
relatively high background baseline is removed by a linear background correc-
tion on every data set before further processing. The deskewing and standardi-
zation (for rank alignment) algorithm were used for bilinearity and trilinearity
Gimeno et al.used second order bilinear generalized rank annihil-
ation method (GRAM) for calibration of PAH compounds by HPLC-DAD
where a spiked sample was used instead of a standard solution, because the
complexity of the samples led to the suspicion of the presence of a matrix
effect. The quantification of PAHs in marine sediment samples with the
GRAM calibration compared favourable in various aspects with univariate
standard addition calibration.
Bogomolov and McBrienevaluated the theoretical basis of a new
method of peak matching in a series of simulated HPLC-DAD analyses of
the same mixture obtained under varying separation conditions. The
matching of the main peaks is based on defining a key set of spectra by
interactive key set factor analysis (IFSFA) after PCA, which is then
subjected to validation and selection. The new method, named mutual
automated peak (MAP) matching, shows an appropriate performance under
simulated poor separation conditions, while peak intensities vary enormously.
Walczak and Wuproposed the application of a fuzzy matching
approach to chromatographic signal alignment (or warping), requiring
detection of a few more intense peaks in individual chromatograms only,
and it aligns signals once the correspondence of the detected peaks is
The GRAM was also used by Gross et al.to enhance the selectivity
and quantitative precision of RP-HPLC separations using a parallel column
configuration with two complementary stationary phases, and Comas
et al.used this second order calibration method for identifying and quan-
tifying aromatic sulfonates in water by HPLC-DAD in the presence of
coeluting interferences. In this later case, the problem of the time shift in
different chromatographic runs and improvement of trilinearity necessary to
the application of the GRAM, has been dealt with using iterative target trans-
formation factor analysis (ITTFA). The use of correlation optimised warping
(COW) has been suggested by Nielsen et al.to perform the alignment of
single and multiple wavelength chromatographic profiles prior to chemo-
metric data analysis. The suggested method uses the entire chromatographic
data matrices, only relying on two input parameters which can be estimated
from the observed peak width, and it proved its suitability on processing the
HPLC-DAD chromatograms of fungal extracts.
De Braekeleer et al.analysed tetracycline hydrochloride samples by
HPLC-DAD and assessed the purity of the samples using orthogonal projec-
tion approach (OPA) and the fixed size moving window evolving factor
analysis (FWEFA), followed by resolution of the data matrix by multivariate
Application of Chemometrics in Separation Science1163
curve resolution alternate least squares (MCR-ALS), which allowed obtain-
ment of the pure component spectra and the individual concentration profiles.
HPLC-MS, in combination with NMR analysis, has been used by
Williams et al.to detect differences between normal and obese rats in
order to provide markers of the metabolic disease. Both analytical techniques
were used to obtain metabolite fingerprints for the metabonomic analysis of
urine from rats, and the resulting data were subjected PCA and partial least
squares discriminant analysis to asses the effects of strain differences,
diurnal variation in strains, diurnal variation and gender, and gender on metab-
PCA of reverse-phase HPLC chromatograms and data from individual
free amino acid analysis allowed assessing the effect of defined strain
surface starters on the ripening of Tilsti cheeseand highlighting the
different proteolytic systems associated with the organisms in the different
smears used, as compared to the traditional technique of using smear liquid
from older cheese.
Korany et al.applied derivatives, and derivatives followed by
convolution with discrete Fourier functions, to chromatographic response
data in order to eliminate interferences and improve calibration and statistical
parameters, in a model mixture containing ascorbic acid, paracetamol, and
guaiphenesin subjected to non ideal conditions of operation. Calibration
using Theil’s method, instead of the usual least squares regression,
improved quantification of the chromatographic signals.
A combination of chemometric procedures has been devised by Gong
et al.for correction of retention time shifts for chromatographic finger-
prints of herbal medicines. First, a selection of marked compounds is
performed by fixed size moving window evolving factor analysis (FWEFA),
which then allow to resolve the two-dimensional HPLC-DAD data matrix
into pure chromatograms and spectra profiles with local full rank analysis;
the top points of the pure chromatographic profiles are used as the retention
time points to correct the retention time shifts, and finally reconstruct the chro-
matographic fingerprints with cubic spline interpolation. The application of
PCA to chromatographic fingerprints from real herbal medicines, before and
after correction of time shifts, allowed identifying their inhomogenities and
further improving their interpretation.
A 2 level, full factorial design was used by Gennaro et al.for
assessing the effect of the cheese making process on contents of biogenic
amines, measured by HPLC-UV, in a semi hard Italian cheese (Toma) and
found that the conditions for minimizing the formation of amines were
dependent on the type of amine.
In order to estimate concentration and elution profiles of compounds,
Dunkerley et al.compared several deconvolution methods to a HPLC-
DAD-MS data matrix of 2- and 3-hydroxypyridine at varying pH in the
presence of severely tailing peak shapes. This workcontains an
extensive review and comparison of several methods (i.e., PCA, evolving
A. C. Duarte and S. Capelo1164
factor analysis (EFA), fixed window evolving factor analysis (FWEFA)) of
two way chromatographic data and suggested a deconvolution method,
which allows the inclusion of restrictions prior to the regression analysis,
and it is used only for determination of profiles from the purity curves.
Windighas recently introduced the use of Durbin-Watson criterion as
a tool for reducing the noise and baseline problems in LC/MS of surfactants,
and a similarity index (SIM) for better discriminating between minor differ-
ences in samples, both as improvements of an algorithm called component
detection algorithm (CODA) that selected only low noise and low background
chromatograms from complex LC/MS data and determined which mass
chromatograms are different based on simples logical rules.[134,135]
The predictive ability of artificial neural network was found by Zhao
et al.to be better than PCA and canonical discriminant analysis (CDA)
for the clinical diagnosis of tumours based on capillary electrophoresis of
urinary nucleosides. The structural changes in pine Kraft lignin during
pulping were studied by Malkavaara et al.by applying PCA, PCR, and
projection to latent structures, to data obtained on lignin samples subjected
to alkaline cupric oxide oxidation followed by capillary electrophoretic-UV
Stras ˇı ´k et al.used chemometric procedures (target transformation
factor analysis (TTFA), fixed size moving window-evolving factor analysis
(FSW-EFA), orthogonal projection approach (OPA), and fixed sized
moving window-target transformation factor analysis (FSW-TTFA)) to
assess the feasibility of the use of a wide bore (320m ID) capillary tube,
and also the use of tandem-coupled columns for the detection and identifi-
cation of CZE analytes by optical fiber coupled DAD, even in critical
situations of peak overlapping. Dankova ´ et al.then applied the above
mentioned procedures as referred by Stras ˇı ´k et al.in processing data
acquired by CZE in the separation system with tandem-coupled columns to
the spectral identification and determination of orotic acid in urine by DAD,
coupled to the separation system by optical fibers.
For the development and validation of a method for determination of
pesticides in groundwater, Rodrı ´guez-Cuesta et al.used bilinear-
trilinear multivariate curve resolution alternating least squares (MCR-ALS)
for resolution and calibration of a HPLC-DAD data region where severely
overlapped peaks appeared: vinclozolin, chlorfenvinphos, tebuconazole, and
parathion-ethyl.Pere ´-Trepat et al.
multivariate curve resolution alternating least squares (MCR-ALS) in the
analysis of complex biocide environmental sample mixtures by HPLC-
DAD, showing that the lack of chromatographic resolution and lack of
spectral selectivity of UV-VIS diode array detection is compensated by
chemometric resolution using MCR.
Rodrı ´guez-Cuesta et al.also used PCA for checking the presence of
outliers or influential samples, EFA, and SIMPLISMA for finding out the
proper number of components and the sources of variability, parallel factor
evaluated theapplication of
Application of Chemometrics in Separation Science1165
(PARAFAC) analysis for sources of comparison of the resolution strategy
Xie et al.,based on the difference of the behaviour of the chemical
signal and noise components, proposed the two mode subspace comparison
(TMSC) approach to estimate the chemical rank of three way analytical
data array (such as HPLC-DAD) with two full rank modes. The method
showed great robustness to a very high degree of collinearity between the
chromatograms involved or to a very high level noise contained in a three
way array. Sa ´nchez-Ponce and Rutanincorporated a kinetic based hard
model as constraint in a soft modelling technique, such as multivariate
curve resolution alternating least squares analysis (MCR-ALS) to extract
enzyme kinetic information (such as the Michaelis constant, the maximum
velocity, and the inhibition constants) from three way LC-MS analytical
data from simultaneous incubation of two CYP450 isoenzymes. Webb-
Robertson et al.introduced a new sequential projection pursuit (SPP)
algorithm, a random scan sampling algorithm (RSSA), that significantly
reduces computation time, thus, becoming an attractive alternative to PCA
when performing clustering or classification analysis, since it achieved a
higher accuracy with a lower number of latent variables as shown, for
example, with a data set containing diesel fuel chromatographic signatures.
Kubic ˇka et al.showed that soft independent modelling of classifi-
cation class analogy (SIMCA) could be successfully applied for original
and preprocessed GC-MS data on C10-bicycloalkanes, in order to assist evalu-
ation of kinetic experiments involving complex mixture of C10-hydrocarbons.
Chemometrics provides valuable tools for enhancing the application of
chromatographic separations in chemistry, leading to faster acquisition of data
and better data quality with less laboratory work. This review produces a
in various areas of chemical research, namely the study of peak asymmetry and
overlapping peaks, the quantitative structure–(chromatographic) retention
relationships (QSRR), the classification of stationary phases and polarity indi-
cators, the optimization of operational conditions associated to chromatographic
processes and chemical analysis related subjects such as clustering, detection,
calibration and quantification.
The applications of chemometrics in separation science follow a general
trend: increasing exploration of available well tested techniques, together with
more advanced ones for extracting chemical information obtained with the
help of chromatography. However, there is a promising strategy in biologi-
cally oriented research, resulting from increased speed and efficiency in
establishing quantitative relationships between the chemical structure of
xenobiotics and their ability to participate in intermolecular interactions
A. C. Duarte and S. Capelo1166
with the components of a living system. The development of such work can
lead to a decrease in costs of a search for new drugs and the use of laboratory
animals. The perspectives now are especially attractive because of the
availability of isolated pharmacological receptors obtained by modern
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Received September 27, 2005
Accepted December 21, 2005
A. C. Duarte and S. Capelo 1176