Advanced In Vivo Heteronuclear MRS Approaches for Studying Brain Bioenergetics Driven by Mitochondria - Dynamic Brain Imaging - page 325

measurements of the reverse CK flux ( ATP PCr )usingCST

(i.e., by saturating PCr) resulted in an inequality between the
forward and reverse CK fluxes (112-114) , which is paradoxi-
cal, in the sense that the CK fluxes into and out of the PCr
pool must be equal when the CK reaction is under chemical
equilibrium condition. One possible explanation is that the ATP
metabolism involves other chemical exchange reactions besides
the CK reaction, for example the ATP hydrolysis reaction (115) .
Consequently, neglecting ATP hydrolysis may lead to an error in
estimating the reverse CK flux. Therefore, it is necessary to con-
sider PCr

→

Pi as a three-spin chemical exchange system in
order to accurately determine all kinetic parameters; in particular,
the reverse rate constants and fluxes (45, 46, 50, 115, 116) .
We will discuss a newly introduced in vivo 31 PMTapproach
being able to noninvasively study the PCr

→ ATP ↔

Pi exchange
in the brain explicitly through the in vivo measurements of the
following rate constants and fluxes associated with four coupled
reactions in different subcellular compartments (50) :
(i) The forward flux ( F ATP as f )ofATP ase reaction (i.e., R2 in
Figs. 15.1 and 15.13 ) occurring inside the mitochondria;
(ii) The

↔ ATP ↔

( F CK
f

forward flux ) of CK reaction (i.e., R4 in

Figs. 15.1 and 15.13 ),
(iii) The reverse flux ( F ATP as r )ofATP ase reaction (i.e., R5 in
Figs. 15.1 and 15.13 ) occurring in the cytosol space;
(iv) The reverse flux ( F CK

) of CK reaction (i.e., R3 in Figs.

r

15.1 and 15.13 ).

A newly introduced in vivo 31 P MT approach for determining
all kinetic parameters of the PCr

4.1. In vivo 31 PMT
Approach for
Determining Entire
PCr

Pi exchange is called
the Multiple Single-site Saturation (MSS) MT approach (50) .
The MSS approach requires a total of four in vivo 31 P spectra:
one control spectrum in the absence of RF saturation plus three
single-site, RF-saturated spectra with the saturation frequency on
PCr,

↔ ATP ↔

↔ ATP ↔ Pi

Exchange

-ATP and Pi, respectively (50) . The quantification of the
ATP metabolic fluxes relies on solving three coupled Bloch equa-
tions based on the three-spin chemical exchange model. For sim-
plifying the mathematical derivation, the symbols of a, b and c
were used which stand for PCr, ATP and Pi, respectively. The
Bloch equations describing the magnetizations of a, b and c and
their changes as a function of time are given by (43) ,

γ

k 2
k − 2

k 1
k − 1 γ −

PCr ATP P i

a b c

M a )
T 1 a

dM a
dt

( M a −

=− − k 1 M a + k − 1 M b (15.12a)