Applying Mechanistic Models in Bioprocess Development - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 161

Fig. 11 Elementary effects during growth phase on glucose: estimated mean and standard
deviation of the distributions of elementary effects of the 11 parameters on the model outputs.
The two lines drawn in each subplot correspond to Mean i 2sem i (see text)

EE jk ¼ o sy k
oh j
¼ sy k ð h 1 ; h 2 ; h j þ D ; ... ; h M Þ sy k ð h 1 ; h 2 ; h j ; ... ; h M Þ
D

ð 13 Þ

The results obtained are compared with the mean and the standard deviation of
this distribution. Often, the EEs obtained for each parameter are plotted together
with two lines defined by Mean i ± sem i , where Mean i is the mean effect for output

i and sem i is the standard error of the mean ð sem i ¼ std deviation i = r

p Þ . The EEs

are scaled, and thus a comparison across parameters is possible.
Also this analysis has to be performed for a selected time point, or using a time-
series average. As the cultivation has distinct phases, several time points were
selected. The results for the growth phase on glucose (t = 17.2 h) and the growth
phase on ethanol (t = 27.2 h) are presented in Figs. 11 and 12 , respectively.
Parameters that lie in the area in between the two curves (inside the wedge) are
said to have an insignificant effect on the output, while parameters outside the
wedge have a significant effect. Moreover, nonzero standard deviations indicate
nonlinear effects, implying that parameters with zero standard deviation and
nonzero mean have a linear effect on the outputs.