Modelling Approaches for Bio-Manufacturing Operations - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 102

mathematical structure, it may be relatively intuitive to work out the most critical
inputs by visual inspection. On the other hand, where there are many terms and
when numerous or complicated mathematical equations are involved (e.g. a series
of highly non-linear or differential equations), inspection may be impossible and
more sophisticated approaches such as sensitivity analysis techniques are required.
These enable the identification of critical variables, thus reducing the dimen-
sionality of the search space and decreasing the scope of both modelling and
subsequently experimental work.
Sensitivity analysis methods involve determining how variations in model
outputs are affected by input changes. Local sensitivity analysis (LSA), for
example, involves determining the importance of a given input by computing the
partial derivative at a specific point on an output function. Although this is useful
in providing sensitivity information about that location and its immediate prox-
imity, it is not satisfactory for describing model characteristics elsewhere. In such
instances, partial derivatives would need to be evaluated at every point of interest,
which depending upon the type of model and the number of points could be
computationally intensive. Additionally, local sensitivity analysis is restricted to
analysing only one input at a time, meaning that complete characterisation would
necessitate separate calculations for every variable. Alternatively, global sensi-
tivity analysis (GSA) is a more powerful method that assesses all input variables
simultaneously over the whole model and ranks them to determine the average
contribution made by every parameter over a stipulated set of input ranges. Var-
iable rankings quantify both the impact of individual variables as well as their
interactions. King et al. [ 23 ] showed how GSA could be applied with beneficial
effects in bioprocess development when determining sensitivities during the disk-
stack centrifugation of mammalian and yeast cell culture broths. The impact of
feed flow rate, particle size, solid-liquid density difference and viscosity on the
achievable clarification was quantified using a validated centrifuge model. Vari-
ation in the values of process sensitivities as a consequence of making significant
changes to the manufacturing set-point conditions could also be investigated. This
can be important when dealing with post-approval process changes; For example,
if upstream improvements result in higher cell densities, this may change the
product-impurity profile that passes into the recovery and purification process,
necessitating downstream changes to maintain product quality at its validated
level. As these changes occur, it can be useful to determine whether previously
important variables remain critical or whether other ones become more significant.
This can prompt changes in either the design or the control mechanisms down-
stream to avoid ill effects caused by variations in specific parameters, thus
maintaining satisfactory process robustness.
Multivariable analysis such as GSA is consistent with other approaches such as
factorial design where one seeks to explore the influence of all variables over their
full ranges to determine whether any synergistic effects exist between parameters.
Where one has potentially several variables in a factorial design and depending
upon the number of levels for each factor, this can result in fairly large experi-
mental matrices. If a model of the experimental system exists already, the