Biomedical Engineering Reference
In-Depth Information
Table 5 Identifiable parameter subsets with maximum number of parameters and corresponding
collinearity index
Parameter subset
Collinearity
index
Identifiable
parameter
Set
r
G
;
max
r
E
;
max
Y
Oxid
XG
Y
Red
XG
Y
XE
K
G
K
E
k
L
a
22.34
No
r
G
;
max
r
O
;
max
r
E
;
max
Y
Oxid
XG
Y
Red
XG
Y
XE
K
G
k
L
a
22.10
No
r
G
;
max
r
E
;
max
Y
Oxid
XG
Y
Red
XG
Y
XE
K
G
K
i
k
L
a
22.10
No
r
G
;
max
r
O
;
max
r
E
;
max
Y
XE
K
G
K
E
K
i
k
L
a
2.65
Yes
r
G
;
max
r
E
;
max
Y
Red
XG
Y
XE
K
G
K
E
K
i
k
L
a
2.75
Yes
r
G
;
max
r
E
;
max
Y
XE
K
G
K
O
K
E
K
i
k
L
a
2.75
Yes
r
G
;
max
r
E
;
max
Y
Oxid
XG
Y
XE
K
G
K
E
K
i
k
L
a
2.85
Yes
r
G
;
max
Y
XE
K
G
K
E
K
i
k
L
a
-
-
1.75
Yes
Table 6 Estimated values for the identifiable subset of parameters
Parameter
Initial guess
Estimated value
Units
g G g
-1
Xh
-1
r
G
;
max
3.5
2.9
8 9 10
-3
5.5 9 10
-3
mol O g
-1
Xh
-1
r
O
;
max
g E g
-1
Xh
-1
r
E
;
max
0.24
0.32
g X g
-1
Y
XE
0.72
0.47
E
g G l
-1
K
G
0.5
0.17
g E l
-1
K
E
0.1
0.56
g G l
-1
K
i
0.1
0.31
h
-1
k
L
a
1,000
930
are presented in Table
6
. In Fig.
4
, the model predictions obtained with the estimated
set of parameters are compared with the experimental data.
Generally, the model predictions are in good agreement with the experimental
data. An overprediction of the biomass concentration and a slight underestimation
of the ethanol concentration are however observed. The oxygen profile describes
the drop of the dissolved oxygen concentration during the growth, and a steep
increase upon the depletion of ethanol and the resulting growth arrest. The
dynamics of oxygen described by the model assumes a constant mass transfer
coefficient (k
L
a) and equilibrium between the gas and liquid phases. It is worth
mentioning that the formation of other metabolites (i.e., glycerol and acetate) that
are not considered in the model may explain the discrepancies to some degree. In
fact, the overestimation of biomass which can be observed in Fig.
4
may be caused
by the fact that other carbon-containing metabolites have not been taken into
account.
When assessing the goodness of fit of the mechanistic model, it is important to
consider that the experimental measurements have an associated error as well.
Model predictions may not give a ''perfect'' fit at first sight, but they may well be
within the experimental error. While such error might be relatively low for the
measurement of glucose and ethanol by high-performance liquid chromatography
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