334
Chapter 8
biomass concentration jc is given by
x
=
{l)e
, and combining the dynamic balances of Eqs. (9) and (10), the
well-known mass balance for biomass is found:
d x
,
= (ji-D )x
(12)
at
With the technique of image analysis, it is possible to determine experimentally the average properties of
the hyphal elements, and the simple model based on average properties may be valuable for extracting the
growth kinetics of hyphal elements. The variance of the properties of the hyphal element is, however,
normally quite large, i.e., the relative standard deviation of the hyphal length is often 50% or more of the
average values. The estimation of the average properties should therefore be based on a large number of
single estimations, i.e., many individual hyphal elements have to be measured. The variance of the
distribution function can be calculated from Eq. (8.11), and if an explicit expression for the variance could
be derived the model predicted variance could be compared with the experimentally determined variance. It
is, however, not possible to derive simple expressions to be used in the calculation of the variances, and the
model is therefore evaluated only by comparison with experimental data for the average properties. It
should, however, be noted that the kinetics derived based on the above model is based on average
properties, and it may therefore not necessarily specify something about the kinetics of individual hyphal
elements. Here it is necessary to study the growth kinetics of individual hyphal elements in a growth
chambers positioned under a microscope equipped with an image analysis system. Using such a system the
growth kinetics of
Aspergillus oryzae
has been studied in great detail (Spohr
etal.
, 1998; Christiansen
etai,
1999).
Nielsen (1993) compared the population model derived above with experimental data for the total hyphal
length and the number of tips obtained during fermentations with
P. chrysogenum.
The model was also used
to examine the influence of the energy input on the morphology of
P. chrysogenum
by comparing model
simulations with experimental data given by Metz
etai.
(1981) and van Suijdam and Metz (1981) [the data
were obtained both during a batch fermentation and in a steady-state chemostat
{D
-0.05 hr 1)]. In Fig. 8.8,
data for the total hyphal length are shown as a function of the energy input for the two cases. The data for
the batch fermentation are the measurements obtained in the exponential growth phase, where//=0.12 hr
The energy input
E
(units of W L"1) was calculated from the stirrer speed as specified by van Suijdam and
Metz (1981). By assuming the linear relation in Eq. (13) between the specific rate of fragmentation and the
energy input, the total hyphal length was calculated from the steady-state form of the balance for
(j)
in Eq.
(10) and a hyphal diameter of 3.6
jjm
(Metz
et ah,
1981).
^ = 2 .M 0 6 - £ + 5 0 .0 1 0 6
(13)
The model is observed to correspond well with the experimental data, except for the two measurements at
very low energy input in the chemostat. Considering the data scatter, and the presence of only two
measurements in this range, it is reasonable to conclude that the rate of fragmentation is linearly correlated
to the energy input (note that the same correlation holds for the two sets of independent experimental data).
previous page 357 Bioreaction Engineering Principles, Second Edition  read online next page 359 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off