Biomedical Engineering Reference
In-Depth Information
65.1
μ
mol/g/min
8.8
μ
mol/g/min
0.30
s
-1
0.18
s
-1
Step 3
Step 1
Step 2
ATPase
F
CK
f
=
k
[
PCr
]
F
=
k
[
Pi
]
R4:
R2:
f
-
2
1
γ
-ATP
PCr
Pi
4.0
mM
CK
3.0 mM
0.9
mM
R3:
F
=
k
[
ATP
]
ATPase
F
=
k
[
ATP
]
R5:
r
-
1
r
2
0.42 s
-1
0.05
s
-1
68.7
μ
mol/g/min
8.2
μ
mol/g/min
ATP
F
CK
F
ase
f
f
=
0
95
±
0
12
(unity)
=
1
08
±
0
21
(unity)
CK
ATP
F
F
ase
r
r
F
total
f
F
CK
f
+
F
ATP
f
ase
=
=
0
96
(unity)
CK
r
CK
ATP
F
F
+
F
ase
r
r
Fig. 15.13. Chart showing the three-step measurements of in vivo
31
PMSSMT
approach for determining the entire ATP kinetic network and associated metabolic rate
constants and fluxes, and the measurement results from the human occipital lobe. Step
1 measures two forward reactions (
R2
and
R4
) along the solid arrows. Step 2 measures
the indirectly coupled reverse reaction (
R3
) along the double-line arrows. Step 3 mea-
sures another reverse reaction (
R5
) along the dotted-line arrows. All results point to the
fact that flux ratios satisfy the chemical equilibrium condition.
and
F
total
0.96) indicating that the total
ATP production flux equals the total ATP utilization flux. These
results lead us to conclude that the fluxes measured by the in vivo
31
P MSS MT approach satisfy the chemical equilibrium condi-
tions for the CK and ATP
ase
reactions in the human brain, and
indicate that the MSS MT approach is able to explicitly deter-
mine four rate constants in the
PCr
is again close to unity (
=
r
Pi
kinetic process
and their associated ATP metabolic fluxes in the brain noninva-
sively. Nevertheless, such equal forward and reverse flux relations
are unable to be obtained for the saturation transfer measurement
if the three-spin
PCr
↔
ATP
↔
Pi
exchange system was treated as
two independent two-spin change systems (i.e.,
PCr
↔
ATP
↔
↔
ATP
and
ATP
Pi
) even when the same experimental MSS MT data were
analyzed
(50)
. These findings clearly indicate that the chemical
exchange system of
PCr
↔
Pi
hastobetreatedasathree-
spin exchange system in order to accurately determine the reverse
rate constants and fluxes for both the CK and ATP
ase
reactions.
The
PCr
↔
ATP
↔
Pi
exchange system in a normal brain likely
reaches chemical equilibrium (or near equilibrium) under most
circumstances. As long as the equilibrium condition is satisfied,
one can further simplify the in vivo
31
P MT measurement proce-
dure by using the chemical equilibrium relation
(50)
. In this case,
only two in vivo
↔
ATP
↔
31
P spectra (one control and another with full
saturation of
γ
-ATP as illustrated in
Fig. 15.11
) are practically
