Biomedical Engineering Reference
In-Depth Information
0.025
0.008
0.02
0.007
0.015
0.006
0.01
0.005
0.005
0.004
1.2
1.3
1.4
Fractal dimension,
D
f1
1.5
1.6
1.7
1.2
1.4
1.6
Fractal dimension,
D
f
1.8
2
2.2
2.4
2.6
B
A
0.085
0.08
0.075
0.07
0.065
0.06
0.055
1.8
2
2.2
Fractal dimension,
D
f2
2.4
2.6
2.8
3
C
Figure 7.7
(a) Increase in the binding rate coefficient, k with an increase in the fractal dimension, D
f
.
(b) Increase in the binding rate coefficient, k
1
with an increase in the fractal dimension, D
f1
.
(c) Increase in the binding rate coefficient, k
2
with an increase in the fractal dimension, D
f2
.
Figure 7.7b
and
Tables 7.4
and
7.5
show the increase in the binding rate coefficient,
k
1
, with
an increase in the fractal dimension,
D
f1
, for a dual-fractal analysis. For the data shown in
Figure 7.7b
, the binding rate coefficient,
k
1
, is given by:
D
1
:
598
0
:
946
k
1
¼ð
0
:
00367
þ
0
:
00090
Þ
ð
7
:
6b
Þ
f1
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The binding rate coefficient,
k
1
, is sensitive to the
degree of heterogeneity on the biosensor surface or the fractal dimension since it exhibits
an order of dependence between one and one-half and two (equal to 1.598) on the fractal
dimension,
D
f1
on the biosensor surface.
