Analysing mixtures with Curve Resolution: applications of OPA
S. Gourvénec, E. Van Gyseghem, Y. Vander Heyden, D. L. Massart
ChemoAC, Pharmaceutical Institute, Vrije Universiteit Brussel,
Laarbeeklaan 103, B-1090 Brussel, Belgium - email: email@example.com
The Orthogonal Projection Approach (OPA) [1,2] is a stepwise approach based on the Gram-
Schmidt orthogonalisation, and on the assumption that the purest spectra in the data matrix are
mutually more dissimilar than the corresponding mixture spectra. OPA is applied on data matrices to select the most dissimilar rows or columns in the data set.
Initial y, the dissimilarity of each spectrum with respect to the mean spectrum is calculated. The
dissimilarity of each spectrum, d i, is given by the determinant of the dispersion matrix Yi, a matrix
consisting of the mean spectrum and each individual spectrum of the matrix X (d i = det (Yi .Yi))
The spectrum that gives the highest determinant, xs1, is then selected. In a second step, the
dissimilarity of each individual spectrum of X with respect to xs1 is calculated. The most dissimilar
spectrum, xs2, is then selected and included in each matrix Yi. The process is repeated iteratively,
by comparing each spectrum of X with the spectra that have already been selected. At each step,
the dissimilarity of the newly selected spectrum is plotted as a function of time. A random profile of
the dissimilarity plot indicates that a number of spectra equal to the number of components present
After the selection of the "pure" components, Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS) is applied with or without constraints to resolve the data matrix X into
Combining plots C and S, it can be calculated which peak is corresponding to which substance of
the pure component spectra (S) and their related individual concentration profiles (C) using an
the mixture, and at which elution time (color identification between peak and spectrum).
iterative procedure and a pre-defined convergence limit.
The OPA approach applied to such data works and provides interesting results. It al ows the
determination and the identification of substances. Moreover, by using OPA, throughput could be
Batch processes play an important role in the production of high added value products. They are
often characterised by reaction(s) between materials that are charged in predefined proportions in
OPA can be applied to different situations and to different data set. Two cases are presented here
a reactor and react for a finite duration. There is a need to control the process and to detect as
soon as possible if the batch is going in a wrong direction, and also to detect the end point of a
reaction. One of the traditional approaches to control batch processes is to inspect the final product
and screen out items not meeting specifications. This strategy is wasteful because it involves a
posteriori inspection when the production has already occurred. Another possible approach is to use
As impurities in drug substances can cause undesired side effects, it is important that they al can
control charts. In the literature, several multivariate control charts can be found, mostly based on
be quantified and/or identified, as prescribed by ICH. In the pharmaceutical industry the FDA for
PCA and PLS, sometimes extended to three-way methods like PARAFAC and Multiway PCA. Control
instance, demands that when different substances co-elute, methods must be available to separate,
charts use historical data from successful batches and compare projections of variables (of the new
identify and quantify them. Therefore, it is useful to develop a set of orthogonal systems so that, as
batch being processed) in the reduced space with the statistical distribution of the trajectories of a
a result of their different selectivity, the application of a (new) drug-impurities mixture on each of
set of past successful batches. With these tools, it is possible to compare batch trajectories between
these systems might reveal al substances at least once. In RP-chromatography, the stationary
themselves but it is not possible to fol ow the evolution of the concentrations of products within the
phases, the mobile phase characteristics like organic modifier and buffer pH, or other factors like
temperature, can cause or improve orthogonality between systems. A generic set of 68 drugs was
One way of reaching this goal is to use spectroscopy
selected to determine orthogonality of the chromatographic systems.
implemented on-line, like Near Infrared (NIR) coupled
Determining orthogonal systems: correlation
Spectroscopic techniques can provide a rich source of
information about conditions within a chemical system,
but also chemical information such as the concentration
The matrix of correlation coefficients r(k)
of species present in the reaction, changes in solvent
between the retention factor k for the set of
tested chromatographic systems (CS). The colors in the bar next to the map
express r(k). Blue colors indicate a low r(k)
Self-modelling Curve Resolution can resolve the data matrix into the concentration profiles and the spectra of the components present. Advantage is that no prior information
orthogonal. Pairs with similar selectivity are
about the shape of pure spectra and/or concentration profiles is required.
characterised by a high r(k) (red colors) and
Results for one representative batch of a process:
Resolution of one representative batch in C and S matrices al ows to find initial estimates for
analysis of several batches together with MCR-ALS. However it is not enough to ensure the
In order to increase the throughput of analysis, the substances were injected as 3-4 components
mixtures. The injection of mixtures can introduce co-elution, while one has to determine the elution
time of each substance, so hyphenated techniques are needed to gain multidimensional data, and
peak purity techniques have to be applied to resolve the peaks. The Orthogonal Projection Approach (OPA) is used on hyphenated HPLC with diode array detection (DAD) data.
Performing the HPLC-DAD experiments leads to a matrix
(absorptions measured every 3 nm, in the interval 197-400
nm and every 0.64 sec during 25 min).
Results for several batches and on-line prediction of a new batch:Several batches are analysed together to obtain more representative pure spectra that can be
afterwards used to predict concentration profiles of new batches.
The dissimilarity criterion enables to retrieve the correct number of components. In this application,
the number of components is known and a reference spectrum is available.
The first step of OPA is performed with calculation of different dissimilarity plots. As dissimilarities
were randomly distributed in the fifth dissimilarity plot, the selection stops. It turns out that the
number of selected spectra is equal to the number of components in the mixture.
The example emphasizes that OPA should be capable of selecting the correct number of
components in an unknown mixture. This is very important during application of orthogonal sets
when al impurities in new drug substances have to be detected.
Afterwards, the iterative alternating least squares calculations start to find the purest spectra.
 - F.C. Sánchez, J.Toft, B. Van den Bogaert, D.L. Massart, Analytical Chemistry, 68 (1996) 79-85
 - F.C. Sánchez, B.G.M. Vandeginste, T.M. Hancewicz, D.L. Massart, Analytical Chemistry, 69 (1997) 1477-1484
 - E. Van Gyseghem, I. Crosiers, S. Gourvénec, D.L. Massart, Y. Vander Heyden, Journal of Chromatography A, accepted
 - S. Gourvénec, C.Lamotte, P.Pestiaux, D.L.Massart, Applied Spectroscopy, 57 (2003), 80-87
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