Biomedical Engineering Reference
In-Depth Information
The fractal analysis is used to analyze the binding (and dissociation, if applicable) kinetics of
(a) the binding (dose-response) of different concentrations (in mM) of phenol in solution to
cells immobilized on a bio-MEMS based cell-chip (
Yoo et al., 2007
), (b) binding and dissoci-
ation of 0.88 mM hydrogen peroxide mixed with GC2 (
E. coli
strain) immobilized microcell
chip (
Yoo et al., 2007
), (c) binding of catechol to bentonite-vanadium (V) oxide xerogels
(
Anaissi and Toma, 2005
), (d) binding and dissociation of ethanol vapors in 40% RH to a
CTO (powdered sample of Cr
1.8
Ti
0.2
O
3
; titanium substituted chromium oxide) thick film in
a sol-gel-derived polycrystalline biosensor (
Pokhrel et al., 2007
)
,
(e) binding and dissociation
of different concentrations of SEB in solution to the antibody-functionalized microbeads on a
sensor chip (
Haes et al., 2006
).
The fractal analysis is used to provide a better understanding of the kinetics of reactions
(involving pollutants and toxins in solution), and to relate the binding and the dissociation
rate coefficients with the fractal dimension or the degree of heterogeneity that exists on the
sensor chip surface. The fractal analysis provides a quantitative indication of the state of dis-
order (fractal dimension) and the binding (and dissociation) rate coefficient values on the bio-
sensor surface. In accord with the prefactor analysis for fractal aggregates (Sorenson and
Roberts, 1997), quantitative (predictive) expressions are developed for (a) the binding rate
coefficient,
k
1
, as a function of the fractal dimension,
D
f1
, for the dose-dependent response
of immobilized cells to different phenol concentrations (in mM) in solution (
Yoo et al.,
2007
), (b) the ratio of the binding rate coefficients,
k
2
/
k
1
, as a function of the ratio of the frac-
tal dimensions,
D
f2
/
D
f1
, for the dose-dependent response of immobilized cells to different
phenol concentrations (in mM) in solution (
Yoo et al., 2007
), (c) the binding rate coefficient,
k
2
, as a function of the fractal dimension,
D
f2
, for the binding and dissociation kinetics of
alcohol vapors to a TFE-850 sensor (
Pokhrel et al., 2007
), (d) the dissociation rate coeffi-
cient,
k
d
,
k
d1
, and
k
d2
, as a function of the fractal dimensions,
D
fd
,
D
fd1
, and
D
fd2
, respec-
tively, for the dissociation kinetics of alcohol vapors to a TFE-850 sensor (
Pokhrel et al.,
2007
), (e) the binding rate coefficient,
k
, as a function of the SEB concentration (in fM) in
solution (
Haes et al., 2006
), and (f) the dissociation rate coefficient,
k
d
, as a function of the
SEB concentration (in fM) in solution (
Haes et al., 2006
).
The fractal dimension is not a classical independent variable such as analyte concentration in
solution. Nevertheless, the expressions obtained for the binding (and the dissociation) rate
coefficients for a single- and for a dual-fractal analysis as a function of the fractal dimension
are valuable as they provide a means by which these rate coefficients may be manipulated by
changing the degree of heterogeneity or the fractal dimension on the sensor chip surface.
The present analysis is applicable to other pollutant/toxin reactions occurring on different
types of biosensor surfaces. Here it hoped that the kinetic analysis (albeit using fractals)
would help shed some physical insights into these types of interactions occurring on biosen-
sor surfaces. Pollution is a serious problem and the early detection of the different types of
