Biomedical Engineering Reference
In-Depth Information
The fit is good. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient,
k
d
, for a single-fractal
analysis is sensitive to the film thickness, in mm, since it exhibits close to a two and a half
order (equal to 2.47) of dependence on the film thickness, in mm. Once again, the non-
integer order of dependence exhibited by the dissociation rate coefficient,
k
d
, on the film
thickness, in mm lends support to the fractal nature of the system.
Figure 10.9d
and
Tables 10.6
and
10.7
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 10.9d
, the binding rate coefficient,
k
1
, is given by:
D
1
:
81
0
:
506
k
1
¼ð
0
:
724
þ
0
:
795
Þ
ð
10
:
8d
Þ
f1
The fit is good. 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
, exhibits an order of depen-
dence between one and a half and two (equal to 1.81) on the fractal dimension,
D
f1
, or the
degree of heterogeneity that exists on the biosensor surface. This indicates that the binding
rate coefficient,
k
1
, is sensitive to the degree of heterogeneity that exists on the biosensor
surface.
Figure 10.9e
and
Tables 10.6
and
10.7
show the increase in the binding rate coefficient,
k
2
,
with an increase in the fractal dimension,
D
f2
, for a dual-fractal analysis. For the data shown
in
Figure 10.9e
, the binding rate coefficient,
k
2
, is equal to:
D
3
:
48
2
:
86
k
2
¼ð
0
:
0697
þ
0
:
9961
Þ
ð
10
:
8e
Þ
f2
The fit is not good. There is scatter in the data, and this is reflected in the error in the binding rate
coefficient,
k
2
. Only the positive value of the error is presented since the binding rate coeffi-
cient,
k
2
cannot have a negative value. Only three data points are available. The availability
of more data points would lead to a more reliable fit. The binding rate coefficient,
k
2
, is sensitive
to the fractal dimension,
D
f2
, or the degree of heterogeneity present on the biosensor surface as
noted by the close to three and a half (equal to 3.48) order of dependence exhibited.
Figure 10.9f
and
Tables 10.6
and
10.7
show the increase in the dissociation rate coefficient,
k
d
, with an increase in the fractal dimension in the dissociation phase,
D
fd
, for a single-fractal
analysis. For the data shown in
Figure 10.9f
, the dissociation rate coefficient,
k
d
, is given by:
D
1
:
48
0
:
349
k
d
¼ð
1
:
026
0
:
528
Þ
ð
10
:
8f
Þ
fd
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The dissociation rate coefficient,
k
d
, exhibits close
to a one and a half (equal to 1.480) order of dependence on the fractal dimension in the
