Synopsis
Theory
predicts that the residual quadrupole interaction of spin-3/2 nuclei with
electrical field gradients and the dipole-dipole interaction of coupled
spin-1/2 nuclei depend similarly on the angle between the privileged direction
and the static magnetic field. In this work, we compare the splitting of the
39K resonance with the splitting of the total creatine resonance in 1H MR
spectroscopy in vivo at human calf muscle. We find similar behavior under
variation of the angle between B0 and tibia. Therefor we conclude that the potassium
ions and creatine are located in an equivalent electromagnetic environments.Purpose
The
feasibility of
in vivo 39K magnetic resonance imaging in humans was proven
recently
1,2. In muscle tissue the resonance of this spin-2/3
nucleus is split due to non-vanishing quadrupole interaction with electrical
field gradients (EFG)
3. In case of axial symmetry, theory predicts that the frequency
shift Δf
Q of the two
satellite resonances depends on the angle
β between the privileged
direction of the EFG and the static magnetic field according to
ΔfQ=e2Qq4ℏ(3cos2β−1), where
ℏ is the
Planck constant,
eQ is the electric quadrupole moment (5.85 fm
2)
4 and
eq is the EFG.
The
dipole-dipole interaction of two coupled spin-1/2 nuclei follows the same
angular dependency. In proton spectroscopy of muscle tissue this was observed
for the total creatine (tCr) resonance
5, 6.
In this
work, the angular dependence of splitting of the
39K resonance is compared
in
vivo to the one of the tCr resonance in
1H spectroscopy.
Methods
All
measurements were performed on a 7 T whole body system (MAGNETOM 7 T, Siemens
AG, Germany) with an accessible patient bore size of 60 cm.
39K MR signal was
acquired with a custom-built surface coil (d = 10 cm, 2 windings) whereas for
1H MR spectroscopy a commercially available surface coil was used (
1H Loop Coil
7 T; SIEMENS AG, Germany). The surface coils were placed in two sessions
between the calves of a healthy volunteer (28y, f) positioned right laterally
(fig. 1). The angle between the static magnetic field B
0 and the front edge of
the tibia was varied from -10° up to +100° in increments of 10° by bending the
knees.
For each
position a
39K spectrum was acquired with the FID sequence (TR = 290 ms, BW =
2000 Hz, bas. res. = 512,
α = 90°, nex. = 1024, TRO = 256 ms, TAQ = 5
min, oversampling 2, fig. 2). The occurring resonances were plotted with the
AMARES algorithm
7, 8. By prior knowledge the intensity and line width of the
two satellite resonances as well as their absolute distance to the central resonance were
assumed to be equal. The angular dependency of the satellites’ frequency shift was
plotted and equation
Δfsatellites=A(3cos2(β−β0)−1) was fitted to the data.
After
performing B
0 shimming and water suppression by a water excitation technique
(WET), a
1H spectrum with a PRESS sequence (TE = 20 ms, TR = 2000 ms, BW = 1200
Hz, bas. res. = 2048,
α = 90, nex. = 92, TRO = 1706 ms, TAQ = 3:04 min,
voxel size 2
× 2
× 2 cm
3 placed in musculus gastrocnemius,
fig. 2) was acquired for different angular positions of the calves. The
distance of the two peaks are plotted in fig. 3 versus the angle between the
tibia and B
0.
Results
The
frequency shift of the satellite resonances (
Δfsatellites) in the
39K spectrum changes with the angle between the tibia and B
0. However, the
splitting never reaches zero with the chosen fit options. The fitting results
in
A=(96±12)1/s and
\beta_0 = (-1 \pm 6)°, representing the
unknown angle between the tibia and the muscle fibers.
The
splitting of the tCr resonance (
\Delta f_{dipole-dipole\ splitting\ tCr}) in the
1H spectrum is only distinguishable for
angles between -10° and 30°. In comparison to the splitting of the
39K
resonance caused by non-vanishing quadrupolar interaction the splitting of the
tCr resonance in the
1H spectrum due to dipole-dipole interaction is one order
of magnitude lower. Nevertheless, their behavior under angle variation is
similar for the data acquired.
Discussion
39K
spectroscopy was performed unlocalized. Therefore signals are likely from
different muscle types. Three resonances were assumed for all spectra to avoid
the subjective decision on when to change the model, even though the resonances
are not clearly visible especially of high angles. Nevertheless, the fitted
model for the angular dependence assuming axial symmetry describes the data
properly.
1H
spectroscopy was compromised by the B
0 shim, especially at large bending angles
when the coil could not be positioned exactly in the isocenter. Therefore the
splitting of the tCr resonance was only observable for angles smaller than 30°.
Conclusion
In
conclusion, the similar behavior of quadrupole splitting of the
39K resonance
and the dipole-dipole splitting of the tCr resonance in the
1H spectrum under
angle variation was shown
in vivo at human calf muscle. The potassium ions and
the creatine seem to be located in an equivalent electromagnetic environment.
Acknowledgements
The
MRUI software package was kindly provided by the participants of the EU Network
programmes: Human Capital and Mobility, CHRX-CT94-0432 and Training and
Mobility of Researchers, ERB-FMRX-CT970160.References
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