Biomedical Engineering Reference
In-Depth Information
Figure
2.9.
DOE often involves many variables, and the importance of each variable and
interaction should be ranked. (a) The design space for a flow-through chromatography step
may also need to consider conductivity. (b) A central composite circumscribed design for three
variables is shown. (c) APareto chart can be used to assess the relative importance ofmain effects
and interactions. For each of these, the response (e.g., impurity level) can be normalized and
assigned significance on the basis of the variability of replicates and modeling residuals
(deviations frommodel). The effects described arehypothetical andmay not reflect the behavior
of any product in real chromatography.
broad design space, wider ranges for variables can be set. However, ranges so wide
that multiple experiments fail may require additional experiments with narrower
ranges.
It is likely that more than two variables will be needed in developing a design
space. The addition of conductivity to the design space is shown in Fig. 2.9a. A CCC
design for three variables is shown in Fig. 2.9b. In Fig. 2.9c, a Pareto plot is used to rank
the impact of each variable and all the possible interactions. Analysis of variance
(ANOVA) can be used to assign significance to the effect of variables and interactions.
In this hypothetical scenario, conductivity at the range explored has borderline signifi-
cance. However, the interaction of pH and conductivity has a significant impact on the
impurity level.
Considerations for acceptable DOE [36] may include replicate variability versus
experimental ranges, appropriate transformations of data and/or results, appropriate
choice of models (e.g., main effects, interaction, quadratic), choice of regression
(e.g., partial least squares, multiple linear regression), goodness of fit (R
2
, adjusted
R
2
, Q
2
), and ANOVA (regression fit, lack-of-fit test).
