Biomedical Engineering Reference
In-Depth Information
“transition” region, if care is taken to select the correct number of points for the two regions.
In this case,
the product
(antibody-antigen; or analyte-receptor complex, Ab Ag or
analyte
receptor) is given by:
<
t ð 3 D f1 , bind Þ= 2
t p 1 ,
¼
t
<
t 1
t ð 3 D f2 , bind Þ= 2
ð
Ab
Ag
Þ
t p 2 ,
ð
10
:
3
Þ
¼
t 1 <
t
<
t 2 ¼
t c
:
t 1 = 2 ,
t
>
t c
In some cases, as mentioned above, a triple-fractal analysis with six parameters ( k 1 , k 2 , k 3 ,
D f1 , D f2 , and D f3 ) may be required to adequately model the binding kinetics. This is when
the binding curve exhibits convolutions and complexities in its shape due perhaps to the very
dilute nature of the analyte (in some of the cases to be presented) or for some other reasons.
Also, in some cases, a dual-fractal analysis may be required to describe the dissociation
kinetics.
10.3 Results
A fractal analysis is presented for (a) the binding of LPG to zinc oxide films prepared by the
spray pyrolysis method onto a glass substrate ( Shinde et al., 2007 ) (b) the binding and disso-
ciation of different NH 3 concentrations in air to a sol-gel derived thin film ( Roy et al., 2005 ),
(c) binding of NH 3 to an optical fiber-based evanescent sensor ( Cao and Duan, 2005 ),
(d) binding to a nc-Fe 3 O 4 /Si-NPA humidity sensor ( Wang and Li, 2005 ), and (e) the binding
and dissociation of different methanol concentrations (in ppm) to a polyimide thin layer
biosensor ( Manera et al., 2006 ).
Alternative expressions for fitting the data are available that include saturation, first-order
reaction, and no diffusion limitations, but these expressions are apparently deficient in
describing the heterogeneity that inherently exists on the surface. One might justifiably argue
that the appropriate modeling may be achieved by using a Langmuirian or other approach.
The Langmuirian approach may be used to model the data presented if one assumes the pres-
ence of discrete classes of sites (e.g., double exponential analysis as compared with a single-
fractal analysis). Lee and Lee (1995) report that the fractal approach has been applied to
surface science, for example, adsorption and reaction processes. These authors point out that
the fractal approach provides a convenient means to represent the different structures and the
morphology at the reaction surface. They also draw attention to using the fractal approach to
develop optimal structures and as a predictive approach. Another advantage of the fractal
technique is that the analyte-receptor association (as well as the dissociation reaction) is a
complex reaction, and the fractal analysis via the fractal dimension and the rate coefficient
provide a useful lumped parameter(s) analysis of the diffusion-limited reaction occurring
on a heterogeneous surface.
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