Biomedical Engineering Reference
In-Depth Information
40
110
100
35
90
30
80
70
25
60
20
50
15
40
0.8
1
1.2
1.4
1.6
1.8
2
2.3
2.4
2.5
2.6
2.7
2.8
A
B
Figure 10.13
(a) Increase in the binding rate coefficient, k
1
, with an increase in the fractal dimension, D
f1
.
(b) Increase in the binding rate coefficient, k
2
, with an increase in the fractal dimension, D
f2
.
Fractal dimension,
D
f1
Fractal dimension,
D
f2
factor of 1.47 from a value of
D
f1
equal to 1.6806 to
D
f2
equal to 2.4742, the binding rate
coefficient increases by a factor of 2.40 from a value of
k
1
equal to 17.885 to
k
2
equal to
41.489.
Figure 10.13a
and
Table 10.9
show the increase in the binding rate coefficient,
k
1
, with an
increase in the fractal dimension,
D
f1
, for a dual-fractal analysis when the different carrier
gases, air, nitrogen, and argon are used. For the data shown in
Figure 10.13a
, the binding rate
coefficient,
k
1
, is given by:
k
1
¼ð
23
:
29
13
:
36
ÞD
0
:
243
þ
0
:
964
ð
10
:
10a
Þ
f1
The fit is poor. There is scatter in the data, and this is clearly reflected in the error in the
order of the fractal dimension,
D
f1
. Only three data points are available. The availability of
more data points would lead to a more reliable and better fit. The binding rate coefficient,
k
1
, is only mildly sensitive to the fractal dimension,
D
f1
, or the degree of heterogeneity that
exists on the biosensor surface as noted by the close to zero (equal to 0.243) order of depen-
dence exhibited.
Figure 10.13b
and
Table 10.9
show for a dual-fractal analysis the increase in the binding rate
coefficient,
k
2
, with an increase in the fractal dimension,
D
f2
, when the different carrier gases,
air, nitrogen, and argon are used. For the data shown in
Figure 10.13b
, the binding rate co-
efficient,
k
2
, is given by:
D
4
:
71
3
:
20
k
2
¼ð
0
:
770
0
:
339
Þ
ð
10
:
10b
Þ
f2
The fit is good. Only three data points are available. The availability of more data points
would lead to a more reliable and better fit. The binding rate coefficient,
k
2
, exhibits an order
