Biomedical Engineering Reference
In-Depth Information
140
PEG DEGRADATION RATE
130
120
110
100
90
80
70
60
50
40
30
20
10
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 12.5
Degradation rate based on the weight distribution of PEG before and after the
cultivation of the microbial consortium E-1 for 3 days [11, 12].
When the solution W( ,
M
of the initial value problem (12.9), (12.10) satisfi es the
condition (12.11), solution
wtM
τ
)
(, ) of the initial value problems (12.6) and (12.2)
satisfi es the condition (12.3), where
T
∫
Τ=
σ
(
ss
d
(12.12)
0
Note that the inverse problem consisting of (12.9)-(12.11) is essentially identical
to the inverse problems (12.1)-(12.3). Numerical techniques developed for the
latter was applied to the former to fi nd the degradation rate
(
M
based on the
weight distribution before and after cultivation for 3 days [12, 13] (Figure 12.5).
λ
12.3.5
Time Factor of Degradation Rate
A microbial population grows exponentially in a developing stage, and the increase
of biodegradability results from increase of microbial population. It is appropriate
to assume that the time factor of the degradation rate σ
(
t
is an exponential func-
tion of time
σ
()
t
=
at
+
b
(12.13)
In view of Eq. (12.8)
