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Description  |
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This invention relates to magnetic resonance imaging (MRI) systems, and in
particular to the phase sensitive detection of nuclear magnetic resonance
(NMR) signals in such systems.
In MRI, a common imaging technique is the formation of images of selected
planes, or slices, of the subject being imaged. Typically the subject is
located in the static magnetic field with the physical region of the slice
at the geometric center of the gradient field. The field center is the
point where the gradients of the x, y and z dimensions all have nominal
zero values. Generally, each gradient will exhibit an increasing field
strength on one side of the field center, and a decreasing field strength
on the other side, both variations progressing in the direction of the
particular gradient. The field strength at the field center will thus
correspond to a nominal Larmor frequency for the MRI system, usually equal
to that of the static magnetic field.
The radio frequency (RF) coils which transmit RF excitation pulses to the
subject and receive NMR signals in return are normally tuned about the
nominal Larmor frequency. Correspondingly, the RF transmitters and
receivers are similarly adjusted with bandwidths centered about this
frequency. With the region of the slice located at the field center, the
transmitted and received signals will be in a range about the nominal
frequency.
It is often desirable to acquire several slice images from various regions
of the subject for better diagnostic utility. In order to make efficient
use of the MRI system, techniques have been developed for acquiring image
information from multiple slices simultaneously, such as the techniques
described in concurrently filed U.S. patent application Ser. No. 766,613,
entitled "MULTIPLEXED MAGNETIC RESONANCE IMAGING OF VOLUMETRIC REGIONS".
When multiple slices are imaged simultaneously, one may be located at the
field center, but others will be located elsewhere in the gradient fields.
Thus, a number of slices will be located in field regions of Larmor
frequencies other than the nominal center frequency. The bandwidths of the
transmitting and receiving coils and circuitry must therefore be adjusted
to accommodate the transmission and reception of signals over a wider
range of frequencies.
Multiple slice imaging presents a partricular problem in that slices
located at other than the field center will respond to and emit signals of
different frequencies and frequency bands during excitation and NMR signal
emission. An off-center slice will be selected by an excitation signal of
a frequency other than the nominal system center frequency, but reception
in the presence of a frequency-encoding "read" gradient may still be over
a frequency band centered about the nominal center frequency. The problem
that develops is that frequencies and bandwidths must then be changed
between excitation and NMR signal reception.
A straight-forward approach to the above problem is to transmit at a
selected, narrow frequency band to excite the desired slice, then receive
signals over a broad band, with a center frequency that is always the same
as the nominal center frequency, thereby aligning the receiver band with
the read gradient field. However, the slice will be excited in relation to
both the frequency and phase characteristics of the transmitted excitation
signals. Subsequence encoding of the NMR spin systems proceeds from the
phase reference of the transmitted signal. To properly decode the received
NMR signal information, the phase reference of the transmitted signal must
be utilized during NMR signal reception. But if the frequency is changed
in preparation for reception the phase reference may be lost; the phase
may become "unlocked". Thus, some technique is necessary to maintain the
phase lock between transmission and reception when the frequency is
changed.
One technique is to use a reference frequency source that smoothly changes
frequency while maintaining a known phase characteristic. However, it has
been found that such systems are not always reliable, and that some phase
variation may be experienced from time to time when the frequency is
changed after transmission. This problem is usually not realized until
after the scanning has been completed and it is discovered that the
processing system cannot reconstruct a coherent image.
A second technique is to use a multiple frequency reference source that
provides separate, phase-locked signals for transmission and reception.
One such system would derive the two signals from a high frequency master
reference signal which is divided down in frequency. However, this
arrangement restricts both the spacing of the slices and signal timing to
predetermined choices, a penalty in system flexibility. To overcome this,
the multiple frequency source may attempt to phase-align two completely
variable frequency signals. This too, presents a problem in that signals
of different frequencies may be phase-compared only when they momentarily
achieve phase alignment, which happens only once every inverse difference
frequency. The closer the frequencies of the signals, the less often they
are in alignment, and hence the less often a phase correction can be made.
Yet another technique is to offset the frequency-encoding gradient with a
uniform bias field so that its center frequency matches the center
transmit frequency, as by using the bias coil described in U.S. patent
application Ser. No. 621,396, entitled "OFFSET GRADIENT FIELDS IN NUCLEAR
MAGNETIC RESONANCE IMAGING SYSTEMS", filed June 18, 1984. However, since
any gradient can be a slice-selecting gradient, all gradient coils must
respond identically to gradient pulses of the same rise times and pulse
area integrals. This requires substantial manufacturing precision and
constant adjustment during system use to maintain the necessary gradient
accuracy.
A final technique is to employ a stabilizing circuit for the reference
frequency source which will set the phase to a particular value each time
the frequency is changed. Such a circuit is difficult to produce, and can
suffer from instability which makes it no more reliable than the first
technique.
In accordance with the principles of the present invention, an MRI system
is provided which overcomes the problems of the aforementioned techniques
for phase sensitive detection. In an embodiment of the present invention,
each spatially different image slice is interrogated at its own particular
frequency. A selected common frequency is used for excitation and for
reception of NMR signal information from each particular slice. Since the
frequency is not changed between the transmit and receive cycles the phase
reference is not unlocked between the two cycles. However, the use of a
different frequency reference for each slice causes an apparent left/right
frequency shift in the demodulated information signals. This undesired
shift is corrected by modulating the received signals with the
trigonometric function of the difference frequency of the demodulating
signal and a given reference frequency. By using a common frequency for
both transmission and reception the phase information of the NMR signals
is preserved, and by knowing the frequency offset between the selected
frequency and the given reference frequency the misregistration introduced
by the frequency offset is eliminated.
In the drawings:
FIG. 1 illustrates the frequency differences between two slices of
different spatial location;
FIGS. 2 and 3 illustrate an MRI system constructed in accordance with the
principles of the present invention;
FIG. 4 illustrates a block of material, multiple slices of which are to be
imaged;
FIG. 5 illustrates waveforms involved in the imaging of the multiple slices
of FIG. 5 in accordance with the principles of the present invention;
FIG. 6 illustrates frequency bands of different slices in the
frequency-encoding direction; and
FIG. 7 is a flowchart of a software sequence for performing digital
filtering in accordance with the principles of the present invention.
Referring first to FIG. 1, a block of material 70 containing slices A and B
is shown. The block is oriented with respect to the x, y and z axes drawn
next to the block, with the null point of the gradient fields centered
with respect to slice B. An x-directed gradient G.sub.x is drawn to show
the variation of the gradient field for the x-direction. Its degree of
variation is indicated with respect to an x-axis line 74 drawn in the
plane of and through the center of the slice. A z-directed gradient
G.sub.z is also shown, and for clarity of illustration the G.sub.z
gradient is drawn in the plane of the forward face 72 of the block. The
G.sub.z gradient field has its null point coincident with the x-axis line
74. The center of the slice B at the center of the gradient field thus has
a coordinate value with respect to the gradients of (X.sub.o, Y.sub.o,
Z.sub.o).
The slice B is excited by a radio frequency (RF) signal having a narrow
frequency band centered around frequency F.sub.Zo, as indicated by the
arrow below the slice B. The frequency F.sub.Zo is the characteristic
frequency at the null point of the G.sub.z gradient field. When the NMR
signals resulting from the excited nuclei of the slice are to be read, a
read gradient G.sub.x is applied. The acquired signals are spatially
encoded by frequency variation along the x-direction in a band of
frequencies BW.sub.x. The center of the BW.sub.x band is indicated by a
frequency F.sub.Xo, which is the characteristic frequency at the null
point of the G.sub.z gradient field. Since both center frequencies
F.sub.Zo and F.sub.Xo are at field null points where the field is equal to
the static magnetic field, the two center frequencies are equal, F.sub.Zo
=F.sub.Xo. Thus the use of a common reference frequency for both the
transmitter and receiver, equal to F.sub.Zo and F.sub.Xo, may be used to
generate and demodulate signals from slice B. Since the reference
frequency does not have to be changed, there will be no loss of the phase
reference, or "unlock", when the received signals are demodulated.
The slice A is also shown with respect to the G.sub.x gradient, which is
drawn with reference to an x-axis line 76 passing through the center of
slice A and in the plane of the slice. The center of slice A is also
located at the null point of the G.sub.x gradient field. However, the
G.sub.z gradient in the plane of the face 72 of block 70 is seen to be
below the x-axis line 76, because the slice A is in a field location of
the G.sub.z gradient field which differs from that at the null point.
Thus, the center of the slice A has a coordinate value with respect to the
gradients of (X.sub.o, Y.sub.o, Z.sub.L).
The slice A is excited with respect to the G.sub.z gradient field by an RF
signal having a frequency band centered around frequency F.sub.ZL, as
indicated by the arrow below the slice A. The frequency F.sub.ZL is the
characteristic frequency of the G.sub.z gradient field in the plane of the
x-axis line 76, the slice A plane. When the resulting NMR signals are to
be read, the slice gradient G.sub.z is removed and the read gradient
G.sub.x is applied to the slice A. Spatially encoded signals from slice A
will, as before, occupy a band of frequencies BW.sub.x centered around
frequency F.sub.Xo. The frequency F.sub.Xo is the characteristic frequency
at the null point of the G.sub.x gradient field, while the frequency
F.sub.ZL is characteristic of an off-null point of the G.sub.z gradient
field, such as the point indicated by arrow F.sub.XL. Thus, F.sub.ZL is
not equal to F.sub.Xo.
In prior NMR apparatus, the difference between F.sub.ZL and F.sub.Xo for
slice A was taken into account by using a transmit reference frequency
equal to F.sub.ZL, then switching to a receive reference frequency equal
to F.sub.Xo. As mentioned above, this frequency change can cause a loss of
the phase reference used in the excitation of the slice A. In order to
image the slice A using Fourier transform reconstruction, the acquired NMR
information over a number of scans must correspond to a known common phase
reference. This is because the Fourier processing is essentially a
correlation technique. When the phase reference is unlocked, the phase
references for respective data lines will not be precisely correlated.
Thus the Fourier transform processor will be operating upon spatially
uncorrelated information, and will not accurately reproduce the desired
spatially-encoded slice. The problem will manifest itself in the form of
ghosts in the slice A image or, in extreme cases, in an unrecognizable
image.
In accordance with the principles of the present invention, the phase
unlock problem is overcome by using the same reference signal for both RF
transmission and NMR signal reception and demodulation. In the case of an
off-center slice such as slice A of FIG. 1, however, this creates a
further complication. When a frequency equal to F.sub.ZL is used as the
reference signal for both transmission and reception, the F.sub.ZL
frequency will be at a point on the x-axis reference line 76 which is
other than the center point, since F.sub.Xo is not equal to F.sub.ZL. This
may be a frequency such as the point indicated by the arrow of frequency
F.sub.XL, for instance, where F.sub.XL =F.sub.ZL. Demodulation will thus
occur with respect to a band of frequencies centered about frequency
F.sub.XL. This new band of demodulated frequencies will be offset from the
desired frequency-encoded band of BW.sub.x. This condition of frequency
band offset will be discussed further below.
The NMR techniques of the present invention may be performed by an MRI
system such as that shown in block diagram form in FIGS. 2 and 3.
Referring to FIG. 2, the transmission portion of an MRI system is shown. A
pulse sequencer and memory 18 applies a control signal V.sub.c to a
frequency synthesizer 10. In response to the V.sub.c control signal, the
frequency synthesizer 10 applies and f.sub.s transmit reference signal to
a transmitter 12, where F.sub.s is the center frequency of a transmitted
radio frequency signal. The transmitter 12 produces a timed transmit
F.sub.s signal, which is coupled by way of a controlled transmitter
attenuator 14 to a transmitter amplifier 16. The transmitter 12 and
attenuator 14 are controlled by control signals provided by a
transmit/receive controller 20, which is under control of the pulse
sequencer 18. The F.sub.s signal is amplified by the amplifier 16 and
applied to the RF coil 24 in the magnet 30 in the form of a sequence of
pulses formed under control of the transmit/receive controller 20. The RF
coil 24 applies the F.sub.s pulses to the subject being imaged. In order
to synchronize the timings of the applied signals, timing control signals
are also produced by the frequency synthesizer 10 and coupled to the
transmit/receive controller and the pulse sequencer on line 19.
Also located within the field of the magnet 30 are x, y, and z gradient
coils 26, 28, and 29. These coils receive gradient control signals
G.sub.x, G.sub.y, and G.sub.z from gradient signal amplifier 22. The
control signals are provided by the transmit/receive controller 20.
Turning now to FIG. 3, the NMR signals emitted by the nuclei of the
material being imaged induce F.sub.R return signals in the RF coil 24.
These return signals are coupled by way of an RF matching network 25 to a
pre-amplifier 27, and on to a receiver attenuator 34. The receiver
attenuator is controlled by the transmit/receive controller 20. The
received F.sub.R signals are amplified by an amplifier 36 and applied to
guadrature phase detectors 42 and 44. The phase detectors receive two
phase demodulating signals at respective 0.degree. and 90.degree. phase
angles from a phase shifter 40, which receives reference signal f.sub.R
from the frequency synthesizer 10. The phase detectors 42 and 44 produce a
channel A and a channel B signal, respectively. The baseband channel A and
B signals are filtered by respective low pass filters 46 and 48, and the
filtered signals are then sampled by respective analog to digital
converters 50 and 52 in response to a sampling signal f.sub.sample
produced by the pulse sequencer 18. The resultant channel A and channel B
digital words are stored in the memory of a computer 60. The computer and
memory 60 also exchanges information with the pulse sequencer and memory
18 by way of a data link 68. The channel A and B digital words are
processed, combined and transformed to the frequency domain by a Fourier
transform array processor 62. The resultant image signals are assembled in
an image format by an image processor 64, and the processed image is
displayed on a video monitor 66.
Referring now to FIG. 4 a rectangular block of material 70 which is to be
imaged by the system of FIGS. 3 and 4 is shown. Four slices, A, B, C and
D, of the block are to be imaged using a multi-slice, multi-echo format.
The coordinates of the block are as indicated by the x, y and z coordinate
axes shown adjacent the block 70. One face 172 of the block 70 is
specifically indicated.
FIG. 5 shows waveforms for imaging the four slices of block 170. At the top
of the FIGURE the face 172 of the block is partially shown with reference
to a z-directed gradient G.sub.z. Slice B of the block is centered at the
center, or null point of the G.sub.z gradient field. The null point is the
point at which the G.sub.z gradient makes substantially no contribution to
the static magnetic field (G.sub.z =O). On either side of the null point
the gradient field increases relatively positively or negatively.
Slice A is scanned first by applying a frequency selective 90.degree. RF
pulse 80 together with a slice selecting G.sub.z gradient 84. The
90.degree. pulse 80 exhibits a frequency characteristic .omega..sub.A for
spatial selection of slice A. A preconditioning G.sub.x gradient 102 is
applied to the slice and one level of a level variable phase encoding
G.sub.y gradient 202 is applied to spatially encode the slice in the y
direction. A frequency selective 180.degree. RF pulse 82 is then applied
to the block together with G.sub.z gradient 86, resulting in the later
formation of a spin echo signal 88. The spin echo signal 88 is sampled
during a sampling interval 304 in the presence of a frequency-encoding
read gradient 104 for the x direction, G.sub.x.
A second spin echo signal is acquired from slice A by applying one level of
a second phase-encoding G.sub.y gradient 205 to the block 170, followed by
a second 180.degree. RF pulse 85 in the presence of G.sub.z gradient 87. A
second spin echo signal 89 develops and is sampled during a sampling
period 306 in the presence of a G.sub.x gradient 106. The second G.sub.y
gradient 205 has a level chosen to provide twice the phase-encoding effect
as the first G.sub.y gradient 202, but in an opposite sense. This
compensates for the phase reversal caused by the two 180.degree. RF pulses
82 and 85 and causes the phases of the spin echo signal 89 to be of the
same sense for processing. By effectively flipping the signal phase in the
y-direction, the G.sub.y gradient 205 eliminates ghosts in the second echo
image by causing them to superimpose and cancel.
During this multi-echo scan of slice A, the frequency synthesizer of FIG. 2
is receiving a V.sub.c control signal from the pulse sequencer 18 as
indicated at the bottom of FIG. 5. This control voltage causes the
reference frequency produced by the frequency synthesizer 10, f.sub.s, to
be equal to a frequency f.sub.A as indicated in FIG. 5. The reference
signal for the transmitter 12 is thereby set to f.sub.s =f.sub.A and the
transmitted RF signal is centered about frequency f.sub.A.
Although the received NMR signals will be centered about a reference
frequency f.sub.REF, corresponding to the null point of the G.sub.x
gradient field, they are demodulated by the phase detectors of FIG. 3 by a
reference signal f.sub.R =f.sub.A. This demodulating signal determines the
spatial representation of the frequency-encoded signal information. In
prior apparatus the receiver reference signal was frequency shifted for
reception to the nominal reference frequency f.sub.REF, as indicated by
the broken lines beneath the frequency encoding gradients 104 and 106.
However, this change in frequency would distrub the phase lock of the
reference signals applied to phase detectors 42 and 44, which unlock is
indicated by the arrows on the broken lines at the bottom of FIG. 5. The
phase unlock results in erroneous phase-sensitive detection of the
received NMR signals, and would also unlock the phase reference of the
individual RF pulses in the multi-echo sequence.
The phase unlocking is prevented in apparatus of the present invention by
maintaining the same control signal V.sub.c for the frequency synthesizer
10 during the entire transmit and receive cycle, as indicated by solid
line f.sub.A in FIG. 5. The phase detector 42 and 44 receive reference
signals which are still aligned in phase with the f.sub.s =f.sub.A
reference used during transmission, as f.sub.s =f.sub.A =f.sub.R. The
phase-encoded NMR signal information is thus accurately detected for
precise image reconstruction.
But since the demodulating signal is at a frequency f.sub.R =f.sub.A
instead of the f.sub.REF center of the received signal band, there is a
shift of both the bandwidth and center frequency of the information which
has been frequency-encoded in the x-direction. Unless this frequency shift
is taken into consideration, there will be a spatial shift in the x
direction of the reconstructed image of slice A relative to the
positioning of the other slices. For instance, if the frequency shift is 1
KHz from f.sub.REF to f.sub.A and the image resolution is 100 Hz per image
pixel, the image will be repositioned in the x direction by ten pixels.
The repositioning can be either to the left or the right, depending upon
whether f.sub.A is above or below f.sub.REF.
Continuing on with FIG. 5, a single echo scan is performed on slice B.
Since this slice is centered in the gradient field, the v.sub.c control
signal for the frequency synthesizer 10 sets f.sub.s to f.sub.b, which is
equal to the nominal f.sub.REF reference frequency. The reference
frequency for the frequency synthesizer 10 is thus equal to f.sub.S
=f.sub.B =f.sub.REF. A 90.degree. RF pulse 120 with a frequency spectral
content of .omega..sub.B and centered about f.sub.s =f.sub.b is applied to
block 170 in the presence of a G.sub.z gradient 124. After this selction
of slice B, a G.sub.x gradient 108 and one level of the amplitude variable
G.sub.y gradient 208 are applied to the block for spatial encoding. A
180.degree. RF pulse 122 with frequency spectral content .omega..sub.B is
applied in the presence of G.sub.z gradient 126, which results in the
development of a spin echo signal 128. This signal is sampled during
sampling interval 310 in the presence of a G.sub.x frequency encoding
gradient 110. Since the slice selection and sampling of the frequency
encoded spin echo signal are both done at the nominal center frequency of
f.sub.REF, this slice is effectively interrogated in the same manner as
was done in the prior apparatus. The frequencies f.sub.s, f.sub.R and
f.sub.B are all equal to f.sub.REF.
Slice C is selected next by applying a 90.degree. RF pulse 130 with a
frequency spectral content of .omega..sub.C to the block in the presence
of a G.sub.z gradient 134. For slice C, the V.sub.c control signal is
changed to a level so that the f.sub.s signal of the frequency synthesizer
18 is at a frequency f.sub.C as indicated at the bottom of FIG. 5. This
means that the transmitted RF signal F.sub.s is centered about f.sub.C,
and the reference signal for the phase detectors is equal to f.sub.R
=f.sub.C. After the spatial encoding G.sub.x and G.sub.Y gradients 112 and
212 are applied to the block and a 180.degree. frequency selective RF
pulse 132 is applied in the presence of a G.sub.z gradient 136, the prior
apparatus would have switched the V.sub.c control signal back to the
f.sub.REF level, as indicated by the broken line beneath the frequency
encoding G.sub.x gradient 114. However, in the present apparatus the phase
unlocking resulting from such switching is prevented by maintaining the
demodulating reference frequency at f.sub.R =f.sub.C during this time. A
spin echo signal 138 from slice C is thus phase detected in relation to
the f.sub.C reference frequency during a sampling interval 314 in the
presence of G.sub.x gradient 114.
The fourth slice D is the slice most distant from the null point of the
gradient field. Accordingly, the V.sub.c control signal is switched to an
even greater offset level as shown by the V.sub.c line of FIG. 5, causing
the frequency synthesizer signal f.sub.s to be offset to a frequency
f.sub.D. The slice D is selected by applying a 90.degree. RF pulse 140
with a frequency spectral content .omega..sub.D and centered about
frequency f.sub.D to the block 170 in the presence of G.sub.z gradient
144. A G.sub.x gradient 116 and one level of G.sub.y gradient 216 are
applied to the block, followed by a frequency selective 180.degree. RF
pulse 142 which is applied in the presence of G.sub.z gradient 146. The
resulting spin echo signal 148 is sampled during an interval 318 in the
presence of frequency encoding G.sub.x gradient 118 without switching the
demodulating reference frequency to the f.sub.REF frequency as indicated
by the dashed lines in the V.sub.c signal line.
A scan of all four slices is completed at this point. The sequence of FIG.
4 is then repeated numerous times, each with a variation of the level of
the phase encoding G.sub.y gradients 202-216, until sufficient iterations
have been performed and signals gathered for Fourier transform image
reconstruction of the four slices.
The offsets caused by the changing V.sub.c control signal and attendant
frequency changes are illustrated in FIG. 6. The nominal bandwidth of the
received NMR signals when the demodulating reference frequency is reset to
f.sub.REF during each sampling interval is indicated as BW.sub.REF, with a
center frequency of f.sub.REF. However, when the reference frequency is
maintained during both transmission and reception for phase detection
stability, the detected NMR signals from the four slices occupy different
bands as shown in the FIGURE. The bandwidth of the slice A signals is
offset above the nominal band, as indicated by bandwidth BW.sub.A. Slice
B, which is centered in the gradient field, has a bandwidth BW.sub.B which
is aligned with the nominal band. The bands for slices C and D are offset
below the nominal band, as indicated by bandwidths BW.sub.C and BW.sub.D.
The four frequency bands are seen to occupy a total band extending from
f.sub.L to f.sub.H, instead of the single, narrower BW.sub.REF band of the
prior apparatus. In apparatus constructed in accordance with the present
invention, the bandwidth from f.sub.L to f.sub.H is determined by the
relative strengths (slopes) of the G.sub.x and the G.sub.z gradient fields
for a given spacing of slices.
To sample signals in the broader f.sub.L to f.sub.H band, a higher sampling
frequency is needed than that used for the narrow BW.sub.REF band. The
higher sampling frequency must satisfy the Nyquist criteria for sampling
the broader band without creating aliasing artifacts in the band. The
sampling frequency thus determined is the frequency of the f.sub.sample
signal used for the analog to digital converters in FIG. 3.
As discussed above, there remains the problem of the apparent offset of the
respective slice images in the frequency-encoded direction. This problem
arises during image reconstruction processing of the acquired NMR signal
information. In essence, the mathematical reconstruction algorithms are
designed to anticipate that the image data will be confined to a single,
predetermined frequency band with a known center frequency corresponding
to the center of the image in the frequency-encoded direction. Offsets
from the predetermined band and center frequency result in misregistration
of the reconstructed image in this direction.
In accordance with the principles of a further aspect of the present
invention, this problem is overcome by filtering the NMR signal
information prior to reconstruction. The filter function used is a
function of the frequency offset used to establish the reference frequency
for each slice.
In a preferred embodiment of the present invention, the filter function is
embodied in software used to process the NMR signal information. A measure
of the frequency offset is retained in the computer and memory 60 of FIG.
3. The offset representative information is of the form (V.sub.REF -
V.sub.c), where V.sub.REF represents the control signal for the center
frequency of the nominal frequency band BW.sub.REF, and V.sub.c is the
control signal used for acquisition of information from a particular
slice.
The offset representative signal information is used to digitally filter
the NMR signal information as illustrated by the flowchart of FIG. 7. The
flowcharted routine is executed by the computer and memory 60 in
processing the channel A and channel B NMR signal information. Retained in
memory are parameters ZR, AC, NSL, GZ and .DELTA.t, where ZR is the
separation range between the two end slices of the slices which are to be
imaged; ZC is the location of the center slice along the slice separation
direction with respect to the gradient null; NSL is the number of slices;
GZ represents the strength of the slice selection gradient, int his
example, G.sub.z ; and .DELTA.t is the time interval between sampling
points of the analog to digital converters. Some of these parameter values
are transferred between the computer and memory 60 and the pulse sequencer
and memory 18 over the data link 68, as are other values as discussed
below.
Using the stored parameter values for a given NMR experiment, the computer
calculates a value .DELTA.Z=ZR/NSL, which determines the spacings between
the slices. The center of the group of slices with respect to center of
the z-gradient field is then used to determine the offset of the initial
slice in the z-direction, Z1=-ZR/2+ZC. From these two calculations, the
location of a given slice n is determined by Z(i)=(i-1).DELTA.Z+Z1.
The results of the two previous calculations are used to determine the
frequency offset for a given slice i, which is the difference between the
f.sub.R reference frequency for slice i and f.sub.REF. This calculation
multiplies the z spatial location of a slice i by the G.sub.z gradient
strength and by the gyromagnetic ratio for a given nuclear element in the
NMR system, or .DELTA.f(i)=Z(i)*G.sub.z *Y. This frequency offset
calculation is communicated to the pulse sequencer and memory 18 over data
link 68 where it translates directly into a valve for V.sub.c. The
frequency offset is also used to correct the apparent left/right shift of
the NMR signal information by digitally filtering the acquired data by
sine and cosine terms of the frequency offset.
The NMR signal information in the form of the digitally detected A and B
data values of the channel A and B lines is modified by calculating
A'.sub.n =A.sub.n cos[(n-n/2).DELTA.t.DELTA.f(i)]+B.sub.n
sin[(n-n/2).DELTA.t.DELTA.f(i)]
and
B'.sub.n =B.sub.n cos[(n-n/2).DELTA.t.DELTA.f(i)]-A.sub.n
sin[(n-n/2).DELTA.t.DELTA.f(i)],
where n/2 is equal to half the maximum value attained by n (i.e., is a
constant). The A'.sub.n and B'.sub.n signal information is then stored in
memory for subsequent combination, Fourier transform processing and image
reconstruction. In the form of A'.sub.n and B'.sub.n values, the acquired
signal information is effectively frequency shifted as if it had been
demodulated by an f.sub.REF reference signal. In a simplified form, if the
frequency offset is expressed in radians as .DELTA..omega., the A and B
data values are modified by trigonometric function of the frequency offset
cos.DELTA..omega.t and sin(-.DELTA..omega.)t. The reconstructed slice
images will now be identically oriented on the display 66.
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