Biology Reference
In-Depth Information
Intravenous Bolus Dose
In the simplest one-compartment model, the chemical is introduced directly into the
single compartment, and elimination occurs by a first-order process (
Figure 6.4
). The
single compartment has a volume
V
d
, which in this case is the apparent volume of dis-
tribution. A typical plasma concentration-time curve for a one-compartment system is
shown in
Figure 6.4
. This system is mathematically described by a first-order equation,
in which the rate of removal of the chemical (mass per time) is proportional to the
body load of the chemical (mass),
dA
dt
= −
e
k A
,
(17)
where
A
is the amount of chemical in the body (units of mass) and
k
e
is the first-order
elimination rate constant (units of reciprocal time), which represents the fractional
elimination of chemical per unit time. A solution to Eq. (17) is:
A
A
0
exp
(
k t
),
t
=
−
(18)
e
where
A
t
is the amount of chemical in the body at time
t,
and
A
0
is the amount of
chemical in the body at time 0. More frequently, the concentration rather than the
amount of chemical is measured in plasma, and Eq. (18) is rewritten as:
C
t
=
C
0
exp
(
−
k t
),
(19)
e
where
C
t
and
C
0
are the concentrations (units of mass/volume) of the chemical in
plasma at time
t
and time 0, respectively. Taking the logarithm of both sides of Eq. (19)
yields:
k t
e
log
C
t
=
log
C
.
(20)
0
2 303
.
The graph of log
C
t
vs.
t
has a
y
intercept of
C
0
and a slope of 2
k
e
/2.303; hence
k
e
can be determined from the slope of the log
C
t
vs.
t
graph (
Figure 6.4
). The apparent
volume of distribution,
V
d
, can be determined from the known amount of chemical
introduced into the body by intravenous injection at time 0 and the intercept of the
log
C
t
vs.
t
graph as:
A
C
0
V
d
=
.
(21)
0
The apparent volume of distribution is the volume into which the initial dose (
A
0
)
would have to be dissolved to achieve the initial concentration of the chemical in
plasma,
C
0
.
The elimination half-life (
t
1/2
) of a chemical is the time required for the amount or
concentration in plasma to decrease by one-half, in the absence of additional exposure.
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