Modelling Approaches for Bio-Manufacturing Operations - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 94

improvements in one being obtained at the expense of others deteriorating. To
ensure that a holistically balanced result is achieved, it may be necessary for several
output metrics to be integrated together into a single objective value. One way to do
this is to use multi-attribute decision making techniques, which combine several
output values—possibly with the inclusion of additional weighting values to
provide greater prominence to the more critical outputs—to generate a single
assessment value to judge the overall feasibility of a process strategy [ 10 ]. This can
apply to both quantitative metrics and qualitative measures including intangible
items such as process reliability and flexibility. By assigning arbitrary, user-defined
numerical values to these and then using multi-attribute decision making to obtain a
single output metric, this can simplify the evaluation of a strategy. Such an
approach can enable multiple conflicting outputs to be traded off to find the most
appropriate final balancing point.
3 Types of Bioprocess Models
3.1 Process Models of Bio-Manufacturing Operations
A convenient way to set up a model is to apply simple percentage step efficiencies
to individual unit operations to determine overall process recoveries. Such an
approach is clearly straightforward and may be valid during the preliminary stages
of assessing project feasibility, but more accurate models that use engineering
understanding are more helpful when specifying operating conditions. Thus
models which rely upon more mathematically 'rigorous' equations (i.e. those
which provide a systematic connection between design/operating parameters and
process outputs) can offer valuable insight. Some of these may be derived from
standard engineering theory, while others may be developed on an empirical or
semi-empirical basis using laboratory data. As indicated above, such models may
be established using spreadsheets if the mathematical basis permits, or alterna-
tively one may need a more specialised numerical solver. The technical modelling
of biopharmaceutical operations draws at least in part upon standard process
engineering concepts for describing mass or momentum transport phenomena.
These may include mixing conditions, aeration rates or impeller specifications (for
fermenters), pressures and the number of passes (for homogenisers), flow rates and
separation surface areas (for centrifuges and membranes), uptake kinetics, equi-
librium or diffusive properties (for chromatography) etc. An exhaustive list of the
equations used to model all the main bioprocess unit operations is beyond the
scope of this chapter, and the exact equations used for specific steps can be found
in numerous texts and journal articles. Specific unit operation models vary in terms
of complexity, with some being relatively straightforward to solve e.g. the first-
order cell rupture expression [ 18 ] or the sigma concept for equating the flow rate-
to-sedimentation area ratio between centrifuges at different scales [ 1 ]. Other