Biomedical Engineering Reference
In-Depth Information
dissociation phase,
D
fd
, for a single-fractal analysis. This indicates that the dissociation rate
coefficient,
k
d
, is sensitive to the fractal dimension,
D
fd
, or the degree of heterogeneity that
exists on the sensor chip surface.
Figure 10.9g
shows the decrease in the ratio of the binding rate coefficients,
k
2
/
k
1
, with an
increase in the film thickness, in mm, for a dual-fractal analysis. For the data shown in
Figure 10.9g
, the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
1
:
056
0
:
0775
k
2
=
k
1
¼ð
3208
:
88
214
:
51
Þ½
film thickness, inmm
ð
10
:
8g
Þ
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 ratio of the binding rate coefficients,
k
2
/
k
1
, exhibits close to a negative first (equal to
1.056) order of dependence on the film
thickness, in mm. This indicates that the ratio of the binding rate coefficients,
k
2
/
k
1
, is sensi-
tive to the film thickness in the 150-480 mm range analyzed.
Figure 10.9h
and
Tables 10.6
and
10.7
show the increase in the fractal dimension,
D
f1
, with
an increase in the film thickness, in mm, for a dual-fractal analysis. For the data shown in
Figure 10.9h
, the fractal dimension,
D
f1
, is given by:
1
:
753
0
:
105
D
f1
¼ð
3
:
3
10
05
þ
1
:
1
10
09
Þ½
film thickness, inmm
ð
10
:
8h
Þ
The fit is very good. Only three data points are available. The availability of more data points
would lead to a more reliable fit. For a dual-fractal analysis, the fractal dimension,
D
f1
,
exhibits a order of dependence between one and a half and two (equal to 1.753) on the film
thickness in the 150-480 mm range.
Figure 10.9i
and
Tables 10.6
and
10.7
show the increase in the fractal dimension,
D
f2
, with an
increase in the film thickness, in mm, for a dual-fractal analysis. For the data shown in
Figure 10.9i
, the fractal dimension,
D
f2
, is given by:
0
:
3034
0
:
198
D
f2
¼ð
0
:
3368
þ
0
:
0606
Þ½
film thickness, inmm
ð
10
:
8i
Þ
The fit is poor. Only three data points are available. The availability of more data points
would lead to a more reliable fit. For a dual-fractal analysis, the fractal dimension,
D
f2
,
exhibits a 0.3034 order of dependence on the film thickness in the 150-480 mm range. This
indicates that the fractal dimension,
D
f2
, is only mildly sensitive to the film thickness, in mm,
in the 150-480 mm range.
Cao and Duan (2005)
recently developed an optical fiber-based evanescent biosensor for the
detection of ammonia. These authors immobilized the sensing dye, bromocresol purple
