Biomedical Engineering Reference
In-Depth Information
ensuing analysis. The total metal-bound data from the simultaneous exposure of all three
metals to the biomaterial were indicative of situations in which all three unique metal
binding sites (X
Cd
, X
Ni
, and X
Zn
) are used along with only the common site, X
Common
. This
enabled the isolation of the common site from any binding enhancement or inhibition that
could be attributed to metal history. By using the total amounts of each metal bound for
each stage in the sequences and the amount of metal bound during the simultaneous
exposure of the material to the three metals, 16 equations for metal binding can be written.
The variables X
Cd
through X
common
can have values of either 1 (the site-type is involved) or 0
(the site-type is not involved). These can then be combined into a single, 16 by 16 matrix (
X
in Table 6) with the corresponding coefficients comprising the contents of 1 by 16 vector (
c
).
For each stage in the sequences the common site, the individual metal-ion sites, and the
corresponding sequential site will make contributions to the total metal bound. For example,
the total metal bound at the sequence stage Ni
2+
Zn
2+
can be represented by the equation:
M
Total
= α
Ni
+ α
Zn
+ β
NiZn
+ δ
0
(2)
And the simultaneous exposure of all three metals can be represented by:
M
Total
= α
Cd
+ α
Ni
+ α
Zn
+ δ
0
(3)
Where M
Total
is the total metal bound and the coefficients (α, β, γ, and δ) indicate the
contribution of each site-type to the total metal bound.
γ
Cd
Ni
Zn
β
Cd
Ni
β
Cd
Ni
β
Cd
Ni
β
Cd
Ni
β
Cd
Ni
β
Cd
Ni
γ
CdZn
Ni
γ
NiCd
Zn
γ
NiZn
Cd
γ
ZnCd
Ni
γ
ZnNi
Cd
α
Cd
α
Ni
α
Zn
δ
0
Cd
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Ni
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Zn
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
CdNi
1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1
CdZn
1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1
NiCd
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1
NiZn
0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1
ZnCd
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1
ZnNi
0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1
CdNiZn
1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1
CdZnNi
1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1
NiCdZn
1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1
NiZnCd
1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1
ZnCdNi
1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1
ZnNiCd
1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1
Simultaneous
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
Table 6. Matrix representing the contributions to total metal ion bound to the immobilized
D. innoxia at each stage of influent metal ion exposure in the sequential experiments. A '1'
indicates a contribution to total metal binding at the particular stage, a '0' indicates the site
is not involved.
