Biomedical Engineering Reference
In-Depth Information
0.05
0.025
0.04
0.02
0.03
0.015
0.02
0.01
0.005
0.01
0
0
0
10
20
30
40
50
0
10
20
30
40
A
B
Time (min)
Time (min)
Figure 10.16
Binding and dissociation of different methanol concentrations (in ppm) to a polyimide thin layer
biosensor (
Manera et al., 2006
). Influence of a repeat run: (a) 4980 (b) 4980. When only a solid
line is used (—) then a single-fractal applies. When both a dotted (- - -) and a solid line (—) is used,
then the dotted line is for a single-fractal analysis, and the solid line is for a dual-fractal analysis. In
this case, the dual-fractal analysis provides the better fit.
Figure 10.16b
shows the binding and dissociation of 4980 ppm methanol in air to a polyimide
thin layer biosensor. In this case, a dual-fractal analysis is required to adequately describe the
binding kinetics. A single-fractal analysis is still adequate to describe the dissociation kinet-
ics. Clearly, this cannot be classified as a repeatability run. It is of interest to note that for the
dual-fractal analysis that is required to describe the binding kinetics, as the fractal dimension
decreases by a factor of 105.18 from a value of
D
f1
equal to 1.776 to
D
f2
equal to 0.1690, the
binding rate coefficient,
k
, increases by a factor of 3.146 from a value of
k
1
equal to 0.005381
to
k
2
equal to 0.01690. In this case, changes in the degree of heterogeneity on the polyimide
thin layer biosensor surface and in the binding rate coefficient are in opposite directions.
It is of interest to note that the dissociation rate coefficients for the two consecutive runs for
the 4980 ppm methanol in air are within 23.9% (0.00581; 0.00723) of each other, even
though the binding mechanisms for these two cases are different (single-fractal analysis;
dual-fractal analysis).
Figure 10.17a
and
Tables 10.10
and
10.11
show the increase in the binding rate coefficient,
k
,
with an increase in the fractal dimension,
D
f
, for a single-fractal analysis. For the data shown
in
Figure 10.17a
, the binding rate coefficient,
k
, is given by:
D
5
:
06
2
:
02
f
k
¼ð
:
þ
:
Þ
ð
:
Þ
0
000106
0
000113
10
11a
The fit is reasonable. There is scatter in the data, and this is reflected in the error in the bind-
ing rate coefficient, k. Only the positive error is presented since the binding rate coefficient,
k
, cannot have a negative value. Only three data points are available. The availability of more
data points would lead to a more reliable fit. For a single-fractal analysis, the binding rate
