Biomedical Engineering Reference
In-Depth Information
0
L
(
x
,
z
) d
x
d
z
2
0
L
(
x
,
z
) d
x
d
z
2
ρ
(
z
) cos
ρ
(
z
) sin
φ
+
φ
−
/
−
/
l
max
(
M
z
)
M
l
max
(
M
z
)
M
=
R
0
0
ρ
d
x
d
z
φ
max
φ
max
2
2
1
sin
α
1
−
cos
α
=
d
α
+
d
α
, (14.4)
|
φ
|
α
α
max
0
0
where
l
max
). Because of the complex nature of the
compression of the elastic medium, the derivation of an analytical
solution for a more general case is more difficult. Nevertheless,
the simplified model developed here does give an insight into the
signal loss mechanism of the LEI technique, while also providing
a preliminary theoretical foundation for the quantitative evalua-
tion of small electrical activity-induced MR signal changes as a
function of the spatially incoherent displacement.
φ
max
= φ
(
3. Methods
Building upon this initial theoretical analysis, phantom and in vivo
experiments were designed and carried out to examine the con-
trast mechanism of the LEI technique, demonstrate its high spa-
tial and temporal resolution, and assess its sensitivity for potential
applications in biological systems.
3.1. Phantom
Experiments
Two spherical gel phantoms (diameter 10 cm, 2.2% gelatin) were
constructed. Phantom A contained a straight bundle of carbon
wires (overall diameter 500
μ
m), whereas phantom B contained
ten wires (diameter 100
m) connected in parallel and oriented
in random directions in three dimensions. The wires were
connected via shielded cables to a square-wave pulse generator
triggered by the positive lobes of the oscillating gradients, with
a large resistor (
μ
) connected in series to minimize any
current induced by the switching gradients that could contribute
to the Lorentz effect.
All experiments were performed on a 4 T whole-body
MRI scanner (General Electric Medical Systems, Milwaukee,
WI, USA) equipped with a high power gradient system
(40 mT/m maximum amplitude, 150 T/m/s slew rate), using a
shielded quadrature birdcage head coil. The acquisition param-
eters were optimized based on the following considerations.
Equation (14.3)
shows that large values for
n
,
G
,and
T
should
be used to amplify the loss of phase coherence and thus the result-
ing signal decay due to the Lorentz force-induced displacement.
However, the increased diffusion weighting, quantified by the
following
b
-factor:
b
>
1
K
2
G
2
T
3
(for one gradient axis)
(27)
, would result in a global signal attenuation. Since the phase
=
(2
/
3)
n
γ
