Biomedical Engineering Reference
In-Depth Information
Figure 14.11d
and
Table 14.8
show the increase in the ratio of the binding rate coefficients,
k
2
/
k
1
, with an increase in the ratio of the fractal dimensions,
D
f2
/
D
f1
. For the data shown in
Figure 14.11d
, the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
0
:
5946
0
:
2834
k
2
=
k
1
¼ð
1
:
092
0
:
349
Þð
D
f2
=
D
f1
Þ
ð
14
:
7d
Þ
There is scatter in the data. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The ratio of the binding rate coefficients,
k
2
/
k
1
,
exhibits slightly greater than one half (equal to 0.5946) order of dependence on the ratio of
fractal dimensions,
D
f2
/
D
f1
, present on the sensor chip surface.
Figure 14.11e
and
Table 14.8
show the decrease in the ratio of the fractal dimensions,
D
f2
/
D
f1
, with an increase in the STX concentration (in ng/mL) in solution for a dual-fractal anal-
ysis. For the data shown in
Figure 14.11e
, the ratio of the fractal dimensions,
D
f2
/
D
f1
, is given
by:
0
:
01943
0
:
0077
D
f2
=
D
f1
¼ð
2
:
874
0
:
121
Þ½
STX, in ng
=
mL
ð
14
:
7e
Þ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The ratio of the fractal dimensions,
D
f2
/
D
f1
, is only
very mildly dependent on the STX concentration (in ng/mL) in the range studied as noted by
the
0.01943 order of dependence exhibited.
Figure 14.11f
and
Table 14.8
show the decrease in the ratio of the binding rate coefficients,
k
2
/
k
1
, with an increase in the STX concentration (in ng/mL) in solution for a dual-fractal
analysis. For the data shown in
Figure 14.11f
, the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
0
:
0166
0
:
00863
k
2
=
k
1
¼ð
58
:
461
2
:
779
Þ½
STX, in ng
=
mL
ð
14
:
7f
Þ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The ratio of the fractal dimensions,
k
2
/
k
1
, is only very
mildly dependent on the STX concentration (in ng/mL) in the range studied as noted by the
0.0166 order of dependence exhibited.
14.4 Conclusions
A fractal analysis is presented for the binding and dissociation (if applicable) of toxins
and pollutants in solution to appropriate receptors immobilized on biosensor surfaces. Both
single- and dual-fractal analysis are used to model the binding and dissociation kinetics. The
dual-fractal analysis is used only when the single-fractal analysis does not provide an adequate
fit. This was done by the regression analysis provided by Corel Quattro Pro 8.0 (1997).
