Environmental Engineering Reference
In-Depth Information
contaminant transfer rate or elimination rate to milk or eggs [d
-1
]
k
a
=
λ
a
=
rate of contaminant degradation plus elimination by pathways other than
excretion of milk or eggs [d
−
1
]
If I
a
is constant with time
, the mass of contaminant in animal is as follows:
1
e
−
(
k
a
+
λ
a
)
×
t
f
abs
,
a
×
I
a
k
a
+
λ
a
e
−
(
k
a
+
λ
a
)
×
t
m
a
,1
(
t
)
=
×
−
+
m
a
,1
(0)
×
(11.9)
and
1
e
−
(
k
a
+
λ
a
)
×
t
f
abs
,
a
×
I
a
m
a
,1
(0)
M
a
,1
(
t
)
×
e
−
(
k
a
+
λ
a
)
×
t
C
a
,1
(
t
)
=
M
a
,1
(
t
)
×
−
+
(11.10)
(
k
a
+
λ
a
)
×
in which
=
C
a,
1
(
t
)
contaminant concentration in animal tissues at time
t
[mg/kg]
M
a
,1
(
t
)
=
weight of the animal tissues at time
t
[kg]
If
m
a
,1
(0)
=
0 then,
1
e
−
(
k
a
+
λ
a
)
×
t
f
abs
,
a
×
I
a
C
a
,1
(
t
)
=
M
a
,1
(
t
)
×
−
(11.11)
(
k
a
+
λ
a
)
×
When the contaminant is mainly accumulated in fat tissue, the fat concentration
can be calculated from the previous equations (
C
a
,1
(
t
)
=
contaminant concentration
in fat tissues and
M
a,
1
(
t
)
weight of fat tissue in the animal at time
t
) and the meat
concentration can be derived from
C
a
,1
by multiplying it by the fraction of fat in
meat.
If I
a
varies with time
,
m
a
,1
has to be integrated on time intervals
=
T
where
I
a
may be regarded as constant:
1
e
−
(
k
a
+
λ
a
)
×
T
f
abs
,
a
×
I
a
(
k
a
+
λ
a
)
×
e
−
(
k
a
+
λ
a
)
×
T
m
a
,1
(
t
)
=
−
+
−
×
m
a
,1
(
t
T
)
(11.12)
and
m
a
,1
(
t
)
M
a
,1
(
t
)
C
a
,1
(
t
)
=
(11.13)
When for very lipophilic contaminants there is neither metabolism, nor elimi-
nation via milk or eggs (e.g., in case of beefs or chickens), concentrations can be
assessed as follows, as elimination via urine is assumed to be low:
t
i
=
0
T
×
(
t
i
−
×
[
I
a
(
t
i
)
t
i
−
1
)]
f
abs
,
a
C
a
,1
(
T
)
=
(11.14)
M
a
,1
(
T
)
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