Biomedical Engineering Reference
In-Depth Information
CMRO
2
H
2
17
O
C
a
(t)
H
2
17
O
C
v
(t)
H
2
17
O
C
b
(t)
Feeding arteriole
Draining venule
Brain tissue space
Fig. 15.3. Schematic illustration of a “complete model” describing three parallel pro-
cesses of the
17
O -labeled metabolic water (H
2
17
O) occurring in the brain when the
17
O-labeled oxygen gas molecules are introduced via an inhalation. In this model, only
the metabolic H
2
17
O is considered because the
17
O-labeled
O
2
is invisible by in vivo
17
ONMR.Ca
(t)
, Cb
(t)
and Cv
(t)
stand for the H
2
17
O concentration in arteriole, brain
tissue and venule, respectively, as a function of the
17
O
2
inhalation time.
washout from the brain, and (iii) Blood recirculation bringing
the metabolically generated H
2
17
O in the entire body back to
the brain. All contributions from these three processes have to be
considered for quantifying CMRO
2
. Based on the Kety - Schmidt
theory
(92-94)
, the mass balance of the isotope labeled H
2
17
O
in the brain tissue during an
17
O
2
gas inhalation can be derived
as
(52, 54, 55, 87)
:
mCBF
f
2
Ca
(
t
)
dCb
(
t
)
dt
nCb
(
t
)
λ
=
2
α
f
1
CMRO
2
+
−
(15.8)
where
C
a
(t)
,
C
b
(t)
and
C
v
(t)
are the metabolic H
2
17
O concen-
trations in excess of the natural abundance of H
2
17
O concentra-
tion in the arterial blood, brain tissue and venous blood respec-
tively, as a function of
17
O
2
inhalation time (
t
, unit = minute);
α
is the
17
O enrichment fraction of the oxygen atoms in the inhaled
17
O
2
gas;
is the brain/blood partition coefficient
(95)
.The
factor of two accounts for the fact that one
O
2
converts to two
H
2
O molecules through oxidative metabolism according to
Eq.
(15.7)
;f
1
and f
2
are two unit conversion factors
(54, 87)
.The
correction factor
m
is used in
Eq. (15.8)
to account for the water
permeability restriction across the brain blood barrier
(96)
,and
n
is another correction factor that accounts for the permeability
restriction occurring when H
2
17
O molecules which are metabol-
ically generated inside the mitochondria across the mitochondrial
membranes
(54, 87)
.Both
m
and
n
depend on CBF
(54, 87)
.The
function of
C
a
(t)
(or artery input function) is determined by the
total metabolic H
2
17
O generated in all aerobic organs of a living
body. It can approximate as a linear function of
17
O
2
inhalation
time (i.e.,
C
a
(t)
=
At
,
A
is a constant)
(52, 54, 78, 87)
. Under this
approximation, the solution for solving the differential equation
of
Eq. (15.8)
is:
λ
