Biomedical Engineering Reference
In-Depth Information
It is of interest to note that as the fractal dimension or the degree of heterogeneity on the bio-
sensor chip surface decreases by a factor of 4.769 from a value of
D
f1
equal to 2.6494 to
D
f2
equal to 0.5556, the binding rate coefficient decreases by a factor of 51.26 from a value of
k
1
equal to 16.64 to
k
2
equal to 0.3246. The changes in the degree of heterogeneity or the fractal
dimension on the biosensor chip surface and in the binding rate coefficient are in the same
direction.
Figure 14.1b
shows the dose-dependent response of the immobilized cells to 1.33 mM phenol
in solution. Once again, a dual-fractal analysis is required to adequately describe the binding
kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a
single-fractal analysis, and (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal
dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis are given in
Table 14.1
. It is of interest
to note that as the fractal dimension or the degree of heterogeneity on the biosensor chip sur-
face decreases by a factor of 3.283 from a value of
D
f1
equal to 2.0968 to
D
f2
equal to
0.6386, the binding rate coefficient decreases by a factor of 19.03 from a value of
k
1
equal
to 6.7434 to
k
2
equal to 0.3544. Once again, changes in the degree of heterogeneity or the
fractal dimension on the biosensor chip surface and in the binding rate coefficient are in
the same direction.
Figure 14.1c
shows the dose-dependent response of the immobilized cells to 2.66 mM phenol
in solution. In this case, a triple-fractal analysis is required to adequately describe the binding
kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a
single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and (c) the binding rate coefficients,
k
1
,
k
2
, and
k
3
,
and the fractal dimensions,
D
f1
,
D
f2
, and
D
f3
, for a triple-fractal analysis are given in
Table 14.1
. It is of interest to note that as the fractal dimension or the degree of heterogeneity
on the biosensor chip surface changes, the binding rate coefficient too exhibits changes in the
same direction. For example, as the fractal dimension decreases by a factor of 369.8 from a
value of
D
f1
equal to 2.5884 to
D
f2
equal to 0.0072, the binding rate coefficient decreases by
a factor of 199.35 from a value of
k
1
equal to 13.193 to
k
2
equal to 0.06618. Similarly, as the
fractal dimension increases by a factor of 228.2 from a value of
D
f2
equal to 0.0070 to
D
f3
equal to 1.5976, the binding rate coefficient increases by factor of 57.43 from a value of
k
2
equal to 0.06618 to
k
3
equal to 3.8005.
Figure 14.1d
shows the dose-dependent response of the immobilized cells to 5.32 mM phenol
in solution. In this case, a triple-fractal analysis is required to adequately describe the binding
kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a
single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and (c) the binding rate coefficients,
k
1
,
k
2
, and
k
3
,
and the fractal dimensions,
D
f1
,
D
f2
, and
D
f3
, for a triple-fractal analysis are given in
Table 14.1
. It is of interest to note that as the fractal dimension or the degree of heterogeneity
