Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
1999-10-25
2001-05-01
Oda, Christine (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
C324S318000, C324S317000, C600S410000
Reexamination Certificate
active
06225804
ABSTRACT:
BACKGROUND OF THE INVENTION
In a conventional two-dimensional Magnetic Resonance Imaging (MRI) scan, a radio-frequency (RF) energy pulse is applied to excite the nuclear spins of the object undergoing scanning. If a slice of the object is selected for scanning, a magnetic field gradient is applied in the direction perpendicular to the slice in conjunction with the RF pulse. As a result, an MRI signal is emitted from the excited slice at the resonant radio frequencies. The magnetic field gradient can be applied in any direction. For simplicity and clarity, the following description assumes that a slice perpendicular to the z-axis is selected for scanning. Thus, to be consistent with the following description, the magnetic field gradient applied with the RF pulse is along the direction of the z-axis.
The emitted MRI signal, denoted as s(k
x
, k
y
) with k
y
set at a constant, represents a one-dimensional spectrum of the slice in two-imensional frequency space, commonly referred to as “k-space”. Prior to detection of the MRI signal, a magnetic filed gradient is applied along a transverse direction, or y-axis direction, in order to induce a shift in the phase of the MRI signal in the y-direction of k-space. Additionally, a second RF pulse is commonly applied to refocus the MRI signal, according to a process referred to as generating “echo” of the spins. A magnetic filed gradient along the third orthogonal dimension, or x-axis direction, is thus activated during collection of the MRI signal. The collected MRI signal therefore constitutes a one-dimensional spectrum of the slice along the x-direction, spaced from the x-axis by an amount proportional to the strength and duration of the magnetic field gradient in the y-direction, as shown in k-space by the solid line
100
of FIG.
1
.
During a scan sequence, the strength of the y-direction gradient is varied to generate a set of MRI signals having a range of phase shifts, which represent a set of one-dimensional spectra in the x-direction, spaced a plurality of predetermined distances from the x-axis center, as shown by the dashed lines
102
of FIG.
1
. The x-direction of k-space is commonly referred to as the “readout” direction, and the y-direction is commonly referred to as the “phase-encoding” direction.
Suppose, for example, that each MRI signal is sampled at a constant interval &Dgr;k
x
, along the x-direction in k-space, to provide n
x
complex data points. The strength of the y-direction gradient can be incrementally varied, at a constant increment, such that the collected signals are separated by a constant frequency interval &Dgr;k
y
along the y-direction in k-space. When a sufficient number, n
y
, of MRI signals
100
are collected, the spectra are uniformly distributed. The spatial distribution of the resulting slice f(x, y) can then be reconstructed using a two-dimensional Fourier transform of the k-space MRI signals. That is,
f
(
x
,
y
)
=
∑
k
y
=
-
n
y
Δ
k
y
/
2
n
y
Δ
k
y
/
2
-
Δ
k
y
∑
k
x
=
-
n
x
Δ
k
x
/
2
n
x
Δ
k
x
/
2
-
Δ
k
x
s
(
k
x
,
k
y
)
exp
{
-
2
π
ⅈ
(
k
x
x
/
n
x
+
k
y
y
/
n
y
)
}
,
(
1
)
where s(k
x
, k
y
) represents the collected MRI signals in k-space, and where f(x,y) represents spatial image data in image-space as described above.
During this process, each collected MRI signal is initially applied to a Fourier transform in the first dimension along the readout direction (x-axis) to generate intermediate results g(x, k
y
) as:
g
(
x
,
k
y
)
=
∑
k
x
=
-
n
x
Δ
k
x
/
2
n
x
Δ
k
x
/
2
-
Δ
k
x
s
(
k
x
,
k
y
)
exp
{
-
2
π
ⅈ
(
k
x
x
/
n
x
)
}
.
(
2
)
The intermediate results g(x, k
y
) are then re-grouped and Fourier transformed in the second dimension along the phase-encoding direction (y-axis) to provide the spatial distribution function f(x, y) of the object:
f
(
x
,
y
)
=
∑
k
y
=
-
n
y
Δ
k
y
/
2
n
y
Δ
k
y
/
2
-
Δ
k
y
g
(
x
,
k
y
)
exp
{
-
2
π
ⅈ
(
k
y
y
/
n
y
)
}
(
3
)
where x and y represent discrete positions in the image plane at spatial intervals of &Dgr;x and &Dgr;y, respectively:
x=−n
x
&Dgr;x/2, −n
x
&Dgr;x/2+&Dgr;x, . . . , −&Dgr;x, 0, &Dgr;x, . . . , n
x
&Dgr;x/2−2&Dgr;x, n
x
&Dgr;x/2−&Dgr;x (4)
y=−n
y
&Dgr;y/2, −n
y
&Dgr;y/2+&Dgr;y, . . . , −&Dgr;y, 0, &Dgr;y, . . . , n
y
&Dgr;y/2−2&Dgr;y, n
y
&Dgr;y/2−&Dgr;y (5)
In other words, the input data are Fourier transformed row-by-row, and then column-by-column, in k-space, to obtain the spatial data f(x, y). The object image p(x, y), is computed as the magnitude of the complex spatial function f(x, y):
p(x, y)=sqrt{f(x, y)f*(x, y)} (6)
where f*(x, y) is the complex conjugate of f(x, y), and “sqrt” represents the square-root function. It should be noted that the MRJ signals s(k
x
, k
y
) are collected as time-domain data. The data representing the spatial function f(x, y) are corresponding to frequency-domain data, where each point of f(x, y) is associated with certain magnetic resonance frequency. The data g(x, k
y
) can be considered as intermediate data with a first dimension in the frequency domain and a second dimension in the time domain.
In the above Equations 1-6, the units are chosen such that the intervals &Dgr;k
x
, &Dgr;k
y
, &Dgr;x, and &Dgr;y correspond to a value of one. In this scale, the discrete values for k
x
, k
y
, x, and y become:
k
x
=−n
x
/2, −n
x
/2+1, . . . , −1, 0, 1, . . . , n
x
/2−2, n
x
/2−1;
k
y
=−n
y
/2, −n
y
/2+1, . . . , −1, 0, 1, . . . , n
y
/2−2, n
y
/2−1;
x=−n
x
/2, −n
x
/2+1, . . . , −1, 0, 1, . . . , n
x
/2−2, n
x
/2−1; and
y=−n
y
/2, −n
y
/2+1, . . . −1, 0, 1, . . . , n
y
/2−2, n
y
/2−1.
The receiver of a typical MRI scanner is optimized to detect minute MRI signals. In the presence of the RF transmitter, the hyper-sensitive RF receiver inevitably detects a finite, albeit small, level of stray transmitter signal referred to as a “feed-through” signal. This RF feed-through signal results in a corresponding DC offset in the collected base-band MRI signal. Unfortunately, at the receiver, this DC offset is indistinguishable from the true MRI signal emitted from the object at the center of the gradient field. As a consequence, a point artifact having a strong intensity level is generated at the center of the resulting image. The true image intensity at the center is thus completely obscured and inseparable from the point artifact. To complicate matters, the amount of RF feed-through does not necessarily remain constant during a scan. As a result, the DC offset may drift slightly from one phase-encoded signal to another. Consequently, the point artifact
106
spreads out along the direction of the y-axis and thus becomes a line artifact
108
peaking at the center
106
of image space as depicted in FIG.
2
. The length l of the line artifact, in other words the number of image pixels affected by the DC offset, depends on the stability of the RF system. For a well-designed system, the length is limited to several pixels.
In addition to RF feed-through, the output of the RF mixer responsible for generating the base-band signal, as well as analog-to-digital converters in the receiver data channels, can also contribute to DC offset. DC offset levels generated by the mixer and the analog-to-digital
Analogic Corporation
McDermott & Will & Emery
Oda Christine
Shrivastav Brij B.
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