Biology Reference
In-Depth Information
where V t is the volume of the tissue compartment, C t is the concentration of free
chemical in the tissue compartment, C a is the concentration of free chemical in the
entering arterial blood, and C vt is the concentration of free chemical in the venous
blood exiting the tissue. The concentrations of free chemical in tissue and venous
blood leaving the tissue are related by the tissue-to-blood partition coefficient ( P t ) as:
C
P
t
C
.
vt =
(64)
t
The overall mixed venous blood concentration is:
=
C Q
Q
vt
t
C
,
(65)
v
c
where Q c is cardiac output (i.e., total blood flow or Q t ).
For chemicals that have a distribution that is limited by the rate of diffusion across
the cell membrane rather than by blood flow (i.e., diffusion-rate limited), separate mass
balance equations must be written for the intracellular and extracellular compartments
of the tissue ( Figure 6.12B ). The mass balance equation for the extracellular space is:
C
P
dC
dt
es
t
C
,
(66)
V
=
Q C
(
C
)
+
PA
es
t
a
vt
t
vt
t
where V es and C es are the volume of and the concentration in the extracellular space,
respectively. The mass balance equation for the intracellular space (i.e., tissue matrix) is:
C
P
dC
dt
is =
t
t
PA C
,
(67)
V
is
t
vt
where V is and C is are the volume of and the concentration in the intracellular space,
respectively.
Chemicals may be effectively eliminated from a tissue by metabolism, macromo-
lecular binding, and/or excretion. For these tissues, the mass balance equation is more
complex than those shown in Eqs. (63), (66), and (67). The mass balance equation for a
tissue that metabolizes the chemical (e.g., the liver) is:
V dC
dt
dA
dt
t
met
=
,
(68)
Q C
(
C
)
t
t
a
vt
where d A met /d t is the rate of metabolism. Many enzyme systems are saturable, and:
dA
dt
V C
K
met
max
vt
(69)
=
,
+
C
m
vt
 
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