Biomedical Engineering Reference
In-Depth Information
shift is proportional to
n
,
G
,and
T
, whereas the
b
-factor is pro-
portional to
n
,
G
2
,and
T
3
, it is preferable to use strong and
short, rather than weak and long, gradient oscillations, as well as a
large number of short gradient oscillations rather than fewer long
ones. Consequently, we chose
G
2ms.Fur-
thermore, another trade-off for using a large number of gradient
oscillations is the increased echo time (TE) needed to accommo-
date these gradients, resulting in a global signal attenuation due
to
T
2
relaxation. We, therefore, experimentally determined that
a value of
n
=
40 mT/m and
T
=
15, corresponding to a minimum TE of 71 ms,
was optimal. With this choice of parameters, a maximum displace-
ment
=
l
max
of 10
μ
m would result in a maximum phase shift
φ
max
≈
π
20%, as estimated from Equa-
tions (14.3) and (14.4) respectively. The resulting
b
-factor is only
9s/mm
2
, thus causing a negligible signal attenuation due to dif-
fusion weighting. Other imaging parameters were chosen as fol-
lows: Repetition time 1000 ms, flip angle 70
o
, field-of-view 12
cm, matrix size 256
and a signal loss
R
≈
128, and slice thickness 5 mm.
Three studies were carried out to assess the dependence of
the LEI signal on the intensity of straight and randomly oriented
electrical currents, as well as its dependence on the synchroniza-
tion between the current and the oscillating gradients for a fixed
current intensity.
The first study was conducted on phantom A to evaluate the
sensitivity of the LEI technique using the simplest geometry. The
phantom was positioned in the magnet with the wire orthogo-
nal to the main magnetic field to maximize the Lorentz effect.
Axial images were acquired with oscillating gradients applied in
the direction orthogonal to both the wire and the main magnetic
field, since the Lorentz force induced displacement occurs in that
direction. Current pulses of 0, 5, 10, 20, 50, 100, 200, and 500
μ
×
A were applied in synchrony with the positive lobes of the oscil-
lating gradients (in separate acquisitions), thus covering the range
of values found in biological systems. Five averages were used for
current intensities up to 20
A to increase the SNR.
The second study was conducted on phantom B to demon-
strate the feasibility of the LEI technique to detect currents
flowing in multiple directions with a more complex geometry.
All parameters were identical to those used in the first study,
except that oscillating gradients were applied along both direc-
tions orthogonal to the main magnetic field. The LEI technique
can detect displacements occurring in multiple directions whether
oscillating gradients are applied along only one axis or both axes
orthogonal to the main magnetic field. In either case, it is most
sensitive to displacements occurring in the direction of the largest
gradient. However, when oscillating gradients are applied along
both axes rather than only one axis, this largest gradient is a factor
μ
√
2 larger (assuming they have the same amplitude along both
axes), and consequently the overall sensitivity is higher.
