Biomedical Engineering Reference
In-Depth Information
T
1
c
) at a given
B
0
can be determined via regressions as a function
of
t
, where both
k
1
and
k
−
2
are replaced by their apparent spin-
lattice relaxation rate and intrinsic spin-lattice relaxation time (see
Eqs. (15.13a)
and
(15.13b)
). Then, the forward rate constants
(
k
1
and
k
−
2) can be calculated by their relations with the apparent
spin-lattice relaxation rate and intrinsic spin-lattice relaxation time
as depicted above.
When a steady-state condition is approached with complete
saturation of
-ATP (i.e.,
dM
a
/dt = 0 and
dM
c
/dt = 0),
Eqs.
(15.13a)
and
(15.13b)
can be further simplified to the following
formulae:
γ
M
a
M
∗
b
M
a
M
∗
b
−
−
a
a
T
1
a
M
∗
b
k
1
=
α
a
=
(15.13c)
M
a
a
M
c
M
∗
b
M
c
M
∗
b
−
−
c
c
T
1
c
M
∗
b
k
−
2
=
α
c
=
(15.13d)
M
c
c
where
M
∗
b
a
and
M
∗
c
are the steady-state magnetizations of a and
c when b is fully saturated. Therefore, the forward rate constants
of
k
1
and
k
−
2
can be calculated by using
Eqs. (15.13c)
and
(15.13d)
. For this case, only two steady-state spectra acquired in
the presence and absence of saturating b are needed to determine
both
k
1
and
k
−
2
,if
T
1
a
and
T
1
c
have already been determined
at a given B
0
through the progressive saturation measurement
accordingly to
Eqs. (15.13a)
and
(15.13b)
. Finally, the forward
fluxes for the CK and ATP
ase
reactions can be determined by the
following relations,
and
F
ATP
ase
f
F
CK
=
k
1
[
PCr
]
=
k
−
2
[
Pi
]
(15.13e)
f
Step 2: Steady-state saturation of Pi for determining CK
reverse rate constant and flux
The second step of the in vivo
31
P MSS MT measurements
is to apply a frequency-selective RF pulse train for completely sat-
urating the Pi resonance peak with a sufficiently long saturation
time resulting in steady-state magnetizations of a and b. For this
case,
M
c
=
0,
dM
a
/
dt
=
0,
dM
b
/
dt
=
0,and
Eqs. (15.12a)
and
(15.12b)
yield
k
−
1
=
α
a
M
∗
c
M
a
M
∗
c
b
1
T
1
a
α
a
a
M
a
−
(15.14a)
k
1
=
α
b
M
∗
c
M
b
M
∗
c
1
T
1
b
α
b
b
M
b
−
(15.14b)
a
