Biomedical Engineering Reference
In-Depth Information
representations. The following case study demonstrates how PCA and canonical
variate analysis (CVA) can be combined with PNNs to predict physiological states
(PS) during E. col cultivations producing an industrially relevant recombinant
protein at laboratory scale.
Pyrolysis mass spectrometry (PyMS, ) [
60
] was used to reflect the changes in
the composition of the offline biomass samples taken during the cultivation. PyMS
represents a fingerprinting method where the changes in composition of the sample
are detected without necessarily indicating the component responsible for such a
change. This kind of analysis, similarly to NIR spectroscopy, can be highly ben-
eficial in bioprocess monitoring where measurements of individual metabolites
may not fully reflect the PS of the culture even if they were technically and
economically feasible.
Since PyMS yields a large multivariate matrix of measurements, it is necessary
to reduce and cluster the data into individual PSs. PCA-CVA has been applied
successfully to identify patterns in Fourier-transform infrared (FTIR) spectra [
53
]
and is suitable for this purpose. In most analytical studies including PyMS anal-
yses, samples are generally analysed in duplicate or triplicate in order to assess the
reproducibility of sample preparation and analytical conditions. A subset of
spectra, in principle from identical sample material, is referred to as a group. Most
PyMS studies are concerned with identifying the chemical components which
account for the differences between the groups. CVA is able to account for the
information contained in the replicate samples and highlights the differences
between the groups.
In several respects, CVA is similar to PCA. Both result in linear combinations
of variables chosen to maximise a particular quantity. The difference is that PCA
maximises the variance of the derived variables whilst CVA maximises the
covariance or correlation between corresponding members of a pair of derived
variables. The solution in both algorithms is provided by singular value decom-
position (SVD).
CVA can be described briefly as shown in Eq. (
2
).
x
¼
a
k
u
k
y
¼
b
k
v
k
ð
2
Þ
where x and y are the observed variables; a
k
and b
k
are the coefficients which
maximise the correlation between u
k
and v
k
; vectors u
k
and v
k
are the resulting
derived new variables. CVA seeks to maximise the dimensionless correlation
coefficient r
k
between u
k
and v
k
. In PyMS data analysis, CVA is used to maximise
the ratio of between-group to within-group variance.
Figure
7
illustrates the PyMS data resulting from analysing two different
samples from the same cultivation. Samples of consecutive time points (2.5 and
3 h post-inoculation) are shown to demonstrate the differences between individual
samples within the same cultivation. Figure
7
also clearly demonstrates the mul-
tivariate character of the data and indicates the difficulties faced in identifying
changes in the sample composition.
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