Biomedical Engineering Reference
In-Depth Information
0.08
0.06
0.04
0.02
0
0
1000
2000
3000
Time (s)
4000
5000
6000
Figure 12.12
Binding of sodium ions of Na
0.44x
MnO
2
to a selective sodium ion sensor (
Sauvage et al., 2007
).
It is of interest to note that as the fractal dimension increases by a factor of 1.306 from a
value of
D
f1
equal to 2.0148 to
D
f2
equal to 2.6318, the binding rate coefficient increases
by a factor of 10.78 from a value of
k
1
equal to 0.00123 to
k
2
equal to 0.01326. The changes
in the fractal dimension and in the binding rate coefficient are in the same direction.
The fractal analysis by linking the sensing surface with the “binding” rate coefficient should
assist in understanding the insertion/de-insertion mechanism, and also help in facilitating the
material into a practical Na
þ
sensor (
Sauvage et al., 2007
). Also, more work is required to
help turn this material into a practical Na
þ
sensor.
12.4 Conclusions
A fractal analysis is presented for the binding and dissociation (if applicable) kinetics of dif-
ferent analytes in solution to different biosensing surfaces. The analysis includes: (a) the
binding of different IgG species to a porous SiO
2
interferometric biosensor coated with pro-
tein A (
Schwartz et al., 2007
), (b) binding (hybridization) using differential surface plasmon
resonance (
Boecker et al., 2007
), (c) binding of glucose to a One Touch II blood glucose
meter, and a SERS sensor (
Stuart et al., 2006
), (d) binding of different concentrations (in
nM) of Con A to a colloidal gold coated with a glycolipid/dodecanethiol bilayer (
Guo
et al., 2007
), (e) binding of H9 avian influenza virus to calcium quantum dots (Yun et al.,
2007), and (f) binding of sodium ions of Na
0.44
x
MnO
2
to a selective sodium ion sensor
(
Sauvage et al., 2007
). As in the previous chapters, the fractal analysis provides a quantitative
measure of the degree of heterogeneity on the sensing surface, and links this degree of het-
erogeneity on the sensing surface to the binding and the dissociation (if applicable) rate
coefficients. The versatility of the fractal analysis is, once again, demonstrated by its success-
ful application to the kinetics of different analyte/receptor systems occurring on the different
biosensing systems.
