Biomedical Engineering Reference
In-Depth Information
TABLE 7.5
Transformed Data from
Table 7.3
Based on the Differential Method
1
:
5
13
29
C
C
1
:
5
C
A
0
L
1
2
13
29
C
C
2
d
C
C
d
C
A
0
L
1
C
C
, mol/L
x
1
:
5
[
2
C
C
L
x
2
[
2
C
C
L
z
[
t
0.59
11.74
27.02
0.02878
1.28
10.28
23.29
0.02857
1.505
9.79
22.08
0.03571
1.935
8.84
19.79
0.03050
2.495
7.59
16.83
0.02429
3.03
6.38
14.04
0.01807
3.535
5.22
11.42
0.02368
3.785
4.64
10.14
0.003125
3.96
4.239
9.24
0.01667
4.21
3.663
7.96
0.01429
4.38
3.271
7.10
0.007778
4.655
2.636
5.71
0.007455
5.005
1.829
3.95
0.005686
5.235
1.299
2.802
0.00340
5.335
1.069
2.304
0.002727
5.385
0.954
2.055
0.002258
The correlation as shown in
Fig. 7.8
is not strongly supportive of the straight line (either
in
Fig. 7.8
aor
Fig. 7.8
b). The data points might have been suggesting that a curve should
have been drawn rather than a straight line. Nevertheless, others may be content with
the regression as the correlation coefficient is at 0.91. Let us take the value of
n
¼
2, then
the kinetic parameters determined from the differential method are given by
n
¼
2 and
k
f
¼
0.001344.
7.8.3. Which Methods to Use: Differential or Integral?
Traditionally, kinetic parameters have been determined through linear regression. One can
observe the physical simplicity a straight-line plot, such as
Fig. 7.7
or
Fig. 7.8
, implied. In
some cases, the regression model is not easily rearranged into a linear form, nonlinear regres-
sion has been used as well. However, the two methods are still held as the only means of
obtaining the kinetic parameters: integral method and differential method. Here an integral
method refers to any procedure of regression that involves converting a differential model to
an algebraic model through analytic integration. In other words, the differential equation is
solved analytically before regression. On the other hand, a differential method refers to any
Search WWH ::
Custom Search