Biomedical Engineering Reference
In-Depth Information
with
1
T
app
1
b
1
T
1
b
)
α
b
=
=
(
k
2
+
k
−
1
+
where
M
∗
c
a
and
M
∗
b
are the steady-state magnetizations of a and
b when Pi is fully saturated. Only
Eq. (15.14a)
is needed in the
MSS MT approach to determine the CK reverse rate constant
(
k
−
1
) by using the measured magnetizations (i.e.,
M
a
,
M
∗
c
and
a
M
∗
c
b
α
a
and
T
1
a
), which
are determined by the measurement in Step 1. The reverse flux of
CK reaction can be calculated by the following relation:
) and other relaxation parameters (i.e.,
F
CK
=
k
−
1
[
ATP
]
.
(15.14c)
r
Step 3: Steady-state saturation of PCr for determining
ATP
ase
reverse rate constant and flux
The third step of the in vivo
31
P MSS MT measurements is to
apply a frequency-selective RF pulse train for completely saturat-
ing the PCr resonance peak with a sufficiently long saturation time
resulting in steady-state magnetizations of b and c. For this case,
M
a
=0,
dM
b
/dt=0,
dM
c
/dt=0, and
Eqs. (15.12b)
and
(15.12c)
yield
k
2
=
α
c
M
∗
a
M
c
M
∗
a
b
1
T
1
c
α
c
c
M
c
−
(15.15a)
k
−
2
=
α
b
M
∗
a
M
b
M
∗
a
1
T
1
b
α
b
b
M
b
−
(15.15b)
c
where
M
∗
a
b
and
M
∗
c
are the steady-state magnetizations of b and
c when PCr is fully saturated. Only
Eq. (15.15a)
is needed in the
MSS MT approach to determine the ATP
ase
forward rate constant
(
k
2
) by using the measured magnetizations (i.e.,
M
c
,
M
∗
a
and
c
M
∗
a
b
α
c
and
T
1
c
), which are
determined by the measurement in Step 1. The reverse flux of the
ATP
ase
reaction can be calculated via following relation:
) and other relaxation parameters (i.e.,
F
ATP
ase
=
k
2
[
]
ATP
.
(15.15c)
r
Therefore, by combining these three measurement steps, one is
able to measure all kinetic parameters which determine the entire
exchange of
PCr
Pi
including all four ATP metabolic
fluxes for both forward and reverse reaction directions as schemat-
ically summarized in
Figs. 15.1 and 15.13
. In total, a minimal
number of three selective saturated in vivo
31
Pspectraplusone
control in vivo
31
P spectrum (for quantifying [ATP], [Pi], [PCr],
↔
ATP
↔
