Biomedical Engineering Reference
In-Depth Information
[
116
,
117
]. Small spectral differences are enhanced and overlapping peaks are
separated by the use of derivative pre-treatments.
As a measured spectrum is not a continuous mathematic curve, but rather a
series of equally spaced points, traditional derivative calculation performed by
using the difference in values between two adjacent points has the effect of
reducing the signal-to-noise ratio in the data. It is therefore necessary to include
some form of smoothing in the calculation. One method of calculating the derivate
of the spectra is to use the algorithm described by Savitzky and Golay [
118
]. This
works by taking a narrow window centred at the wavelength of interest, and fitting
a low-order polynomial to the data points in this window using least squares. The
calculated polynomial is a continuous curve of the form y = a ? bx ? cx
2
…,
where x is the wavelength and y is the spectral response. The first and second
derivatives of this fitted curve are then used as estimates of the derivatives of the
underlying spectrum.
The choice of pre-treatment can depend on the type of spectra being analysed;
e.g. Raman and NIR will often have derivative pre-treatments applied [
119
-
121
].
A multi-component mixture or a sample collected online which may be subject to
instrument drift will also be pre-treated with a procedure such as SNV or deriv-
atives. Many other pre-treatments are possible, and the nature of the application
will dictate the most suitable one or indeed combination to choose.
Quantitative Analysis
Interpretation of spectra can be a challenge, as many different components can
have a response in similar regions of the electromagnetic spectrum. This becomes
an issue when the aim is to identify and quantify individual components in a
mixture. The first step in developing a calibration model is to do a simple feasi-
bility study such as that described in the ASTM international standards [
122
] for
each component of interest. The procedure described involves the collection of
spectra from 30-50 samples incorporating the expected variations in particle size,
sample presentation and process conditions which are expected during analysis. If
the results of this simple study are favourable as judged by error values from cross-
validation methods and the required precision was obtained, the study can be
expanded to see if multi-component mixtures can be adequately modelled.
To make a good calibration model, a suitable experimental design must be
employed. The samples used for developing the model are known as the training or
calibration set and should ideally comprise several uniformly distributed con-
centrations for each component of interest. The factors in an experimental design
for a multi-component mixture are the individual components, and these factors
should be mutually independent or orthogonal; i.e. the correlation coefficient
between each pair of factors should be zero [
123
]. There has been some discussion
in the literature on the importance of using uncorrelated samples in the develop-
ment of chemometric models for online metabolite monitoring [
124
-
126
]. As the
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