Biomedical Engineering Reference
In-Depth Information
0.02
AFTER 5 DAY CULTIVATION
SIMULATION 30 DAY
0.01
0.0
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
log M
Figure 12.6
Weight distribution of PEG after
cultivation for 30 days according to the
time-independent model based on the initial
value problems (12.9) and (12.10), and the
degradation rate shown in Figure 12.5. The
experimental result obtained after cultivation
for 5 days is also shown [12, 13].
also shows the weight distribution after cultivation for 5 days. It is appropriate to
set
T
2
. Equation (12.19) was solved numerically with the Newton's
method, and a numerical solution, which was approximately equal to 1.136176,
was found [12] .
=
5
and
Τ
2
=
30
12.3.6
Simulation with Time-Dependent Degradation Rate
Once the degradation rate
is determined, the initial value prob-
lems (12.6) and (12.2) can be solved directly to see how the numerical results and
the experimental results agree. The initial value problem was solved numerically
with techniques based on previous results [3 - 5] .
Given the initial weight distribution shown in Figure 12.4, the degradation rate
β
(,
tM
)
=
σ
() (
t
λ
M
)
λ
(
t
given by Eq. (12.17) with the
value of
a
obtained numerically, the initial value problems (12.6) and (12.2) was
solved numerically with the Adams- Bashforth - Moulton predictor - corrector in
PECE mode in conjunction with the Runge-Kutta method to generate approxi-
mate solutions in the fi rst three steps [24]. Figure 12.7 shows the transition of the
weight distribution for 5 days under cultivation of the microbial consortium E-1.
Figure 12.8 shows the numerical result and the experimental results for the weight
distribution after 1-day cultivation. Note that no information concerning the
weight distribution after 1-day cultivation was used to determine the degradation
(
M
shown in Figure 12.5, and the function
σ
