Biomedical Engineering Reference
In-Depth Information
Figure 4.2c and Table 4.1 show the increase in the dissociation rate coefficient, k d , with an
increase in the C a concentration (in nM) in the 0-50 nM range in solution for a single-fractal
analysis. For the data shown in Figure 4.2c , the dissociation rate coefficient, k d , is given by:
0
:
569
0
:
137
k d ¼ð
0
:
364
0
:
098
Þ½
C a ,nM
ð
4
:
4c
Þ
The fit is very good. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient, k d , exhibits an order of
dependence between one-half and one (equal to 0.569) on the C a concentration in solution
in the 0-50 nM concentration range.
Figure 4.2d and Table 4.2 show the increase in the fractal dimension, D f1 , with an increase in
the C a concentration (in nM) in the 0-50 nM range in solution for a dual-fractal analysis. For
the data shown in Figure 4.2d , the fractal dimension, D f1 , is given by:
0
:
122
0
:
0519
D f1 ¼ð
1
:
166
0
:
155
Þ½
C a ,nM
ð
4
:
4d
Þ
The fit is reasonable. Only five data points are available. The availability of more data points
would lead to a more reliable fit. The fractal dimension, D f1 , exhibits an order of dependence
close to zero (equal to 0.122) on the C a concentration in solution in the 0-50 nM range.
Figure 4.2e and Table 4.2 show the increase in the fractal dimension, D f2 , with an increase in
the C a concentration (in nM) in the 0-50 nM range in solution for a dual-fractal analysis. For
the data shown in Figure 4.2e , the fractal dimension, D f2 , is given by:
0
:
0314
0
:
0115
D f2
¼ð
:
:
Þ½
ð
:
Þ
2
481
0
07
C a ,nM
4
4e
The fit is reasonable. Only five data points are available. The availability of more data points
would lead to a more reliable fit. The fractal dimension, D f1 , exhibits an order of dependence
very close to zero (equal to 0.0314) on the C a concentration in solution in the 0-50 nM range.
Note that the fractal dimension is based on a log scale, and thus even very small changes in
the fractal dimension value lead to noticeable changes in the degree of heterogeneity on the
biosensor chip surface.
Figure 4.2f and Tables 4.1 and 4.2 show the increase in the binding rate coefficient, k 1 with
an increase in the fractal dimension, D f1 for the C a concentration (in nM) in the 0-50 nM
range in solution for a dual-fractal analysis. For the data shown in Figure 4.2f , the binding
rate coefficient, k 1 , is given by:
D 7 : 351 2 : 167
k 1 ¼ð
0
:
0364
0
:
044
Þ
ð
4
:
4f
Þ
f1
The fit is very good. Only five data points are available. The availability of more data points
would lead to a more reliable fit. The binding rate coefficient, k 1 , exhibits an order of
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