Biomedical Engineering Reference
In-Depth Information
The system can then be represented by the matrix equation:
[
M
] = [
c
] [
X
] (4)
with [
A
] is a 1 by 16 vector containing the total amount of metal bound for each situation, [
c
]
is a 1 by 16 vector containing the contribution coefficients for each site type, and [
X
] is the 16
by 16 matrix describing the types of binding that may be taking place. For example, the row
in the matrix [
X
] corresponding to the previous example (Ni →Zn) would be [ 0 1 1 0 0 0 1 0
0 0 0 0 0 0 0 1 ]. Both [
M
] and [
X
] are therefore known or determined experimentally. The
contribution coefficient matrix, [
c
], can then be calculated by solving the multivariate
equation.
[
M
] [
X
]
T
([
X
] [
X
]
T
)
-1
= [
c
] (5)
The superscripts T and -1 designate the corresponding transposed and inverted matrices,
respectively.
Four matrices were examined using this methodology. The matrix presented in Table 6
includes all of the unique single metal bonds, where appropriate, in the sequential case, and
only the three unique sites plus the common site for the simultaneous case. Tables 7a and b
list the experimentally determined total amounts of metal bound with the predicted
amounts from four separate theoretical calculations. Case 1 shows the results from the
calculations using the matrix shown in Table 6. Case 2 is the same matrix as case 1 except for
the simultaneous row, which now includes all three, three-metal binding sites (coefficients
γ
NiZnCd
, γ
ZnCdNi
, and γ
ZnNiCd
) along with the unique and common sites. Case 3 differs from
case 2 by eliminating the unique sites from the simultaneous portion of the matrix. Case 4 is
distinguished by only including the unique metal site type when the metal is the first metal
introduced to the column.
Upon examining the results presented in Tables 7 a and b, it was evident that case 1 best
approximated the experimental results. Figure 5 illustrates the values of the contribution
coefficients for both the native and the modified (shaded)
D. innoxia
total metal bound
studies.
The most striking and least surprising result of this analysis was the contribution the
common site (δ
0
) made to overall binding for both the native and the modified biomaterial.
Also noteworthy, was the series of positive coefficients present in the two metal ion systems.
For both the native and modified biomaterials, it appears that the presence of a metal ion
enhanced the biomaterial's binding capacity. The lone exception to this was the impact of
the NiZn sequence on the modified material.
The native biomaterial exhibited slight positive coefficients for the unique Cd
2+
and Zn
2+
sites and a moderate apparent inhibition for Ni
2+
. All binary combinations of metal ions
exposed to the native biomass resulted in moderate positive coefficient values. The tertiary
combinations all yielded moderately negative values. This does not necessarily indicate an
absolute inhibition of binding, but can be interpreted in terms of relative inhibition effects.
Review of the experimental data listed in Table 7 b reveals single metal values as all near 50
mol g
-1
(average 50.68). Comparatively, binary combinations ranged from 60 - 70 mol g
-1
(average 66.15), an increase of 15 while tertiary combinations ranged from 65 -75 mol g
-1
(average 68.78), an increase which may not be statistically significant. This suggests some
degree of cooperativity in metal-ion binding while the primary mechanism of metal ion
binding is simple electrostatic (i.e., the dominance of the common sites).
