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BACKGROUND OF THE INVENTION
The field of the invention is nuclear magnetic resonance imaging methods
and systems. More particularly, the invention relates to fast NMR pulse
sequences with enhanced susceptibility weighting in the reconstructed
image.
Any nucleus that possesses a magnetic moment attempts to align itself with
the direction of the magnetic field in which it is located. In doing so,
however, the nucleus precesses around this direction at a characteristic
angular frequency (Larmor frequency) which is dependent on the strength of
the magnetic field and on the properties of the specific nuclear species
(the magnetogyric constant .gamma. of the nucleus). Nuclei that exhibit
this phenomena are referred to herein as "spins".
When a substance such as human tissue is subjected to a uniform magnetic
field (polarizing field B.sub.0), the individual magnetic moments of the
spins in the tissue attempt to align with this polarizing field, but
precess about it in random order at their characteristic Larmor frequency.
A net magnetic moment M.sub.z is produced in the direction of the
polarizing field, but the randomly oriented magnetic components in the
perpendicular, or transverse, plane (x-y plane) cancel one another. If,
however, the substance, or tissue, is subjected to a magnetic field
(excitation field B.sub.1) which is in the x-y plane and which is near the
Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or
"tipped", into the x-y plane to produce a net transverse magnetic moment
M.sub.t, which is rotating, or spinning, in the x-y plane at the Larmor
frequency. The practical value of this phenomenon resides in the signal
that is emitted by the excited spins after the excitation signal B.sub.1
is terminated. There is a wide variety of measurement sequences in which
this nuclear magnetic resonance ("NMR") phenomena is exploited.
In simple systems the excited spins induce an oscillating sine wave signal
in a receiving coil. The frequency of this NMR signal is the Larmor
frequency, and its initial amplitude, A.sub.0, is determined by the
magnitude of the transverse magnetic moment M.sub.xy. The amplitude, A, of
the emission signal decays in an exponential fashion with time, t:
A=A.sub.0 e.sup.-t/T*.sbsp.2
The decay constant 1/T*.sub.2 is inversely proportional to the exponential
rate at which the aligned precession of the spins dephase after removal of
the excitation signal B.sub.1. This dephasing is caused by local magnetic
field inhomogeneities produced in part by the differences in
susceptibility between the spins. The dephasing caused by the spin system
itself is referred to as the "spin-spin relaxation constant" T.sub.2, and
as will be described below, this characteristic is used in medical imaging
to contrast tissues containing spins that exhibit different spin-spin
relaxation times. NMR images that rely on this susceptibility phenomenon
to contrast different tissues are referred to as "T*.sub.2 weighted
images."
When utilizing NMR to produce images, a technique is employed to obtain NMR
signals from specific locations in the subject. Typically, the region
which is to be imaged (region of interest) is scanned by a sequence of NMR
measurement cycles which vary according to the particular localization
method being used. The resulting set of received NMR signals are digitized
and processed to reconstruct the image using one of many well known
reconstruction techniques. To perform such a scan, it is, of course,
necessary to elicit NMR signals from specific locations in the subject.
This is accomplished by employing magnetic fields (G.sub.x, G.sub.y, and
G.sub.z) which have the same direction as the polarizing field B.sub.0,
but which have a gradient along the respective x, y and z axes. By
controlling the strength of these gradients during each NMR cycle, the
spatial distribution of spin excitation can be controlled and the location
of the resulting NMR signals can be identified.
Most NMR scans currently used to produce medical images require many
minutes to acquire the necessary data. The reduction of this scan time is
an important consideration, since reduced scan time increases patient
throughput, improves patient comfort, and improves image quality by
reducing motion artifacts. In addition, if body functions such as brain
activity are to be monitored with a series of images, it is imperative
that each image be acquired in seconds, rather than minutes.
There is a class of fast pulse sequences that have a very short repetition
time (TR) and result in complete scans which can be conducted in seconds
rather than minutes. Whereas the more conventional pulse sequences have
repetition times TR which are much greater than the spin-spin relaxation
constant T.sub.2 so that the transverse magnetization has time to relax
between the phase coherent excitation pulses in successive sequences, the
fast pulse sequences have a repetition time TR which is less than T.sub.2
and which drives the transverse magnetization into a steady-state of
equilibrium. Such techniques are referred to as steady-state free
precession (SSFP) techniques and they are characterized by a cyclic
pattern of transverse magnetization in which the resulting NMR signal
refocuses at each RF excitation pulse to produce an echo signal. This echo
signal includes a first part S+ that is produced after each RF excitation
pulse and a second part S- which forms just prior to the RF excitation
pulse.
One well known SSFP pulse sequence is called gradient refocused acquired
steady-state (GRASS). It utilizes a readout gradient G.sub.x to shift the
peak in the S+ signal that is produced after each RF excitation pulse
toward the center of the pulse sequence. In two-dimensional imaging, a
slice selection gradient pulse is produced by the gradient G.sub.z and is
immediately refocused in the well-known manner. A phase encoding gradient
pulse G.sub.y is produced shortly thereafter to position encode the
acquired NMR data. By using this SSFP pulse sequence, data for a complete
image can be acquired in less than two seconds and a series of such images
can be acquired over a period of time which enable such processes as brain
functions to be dynamically monitored. Each acquired image captures the
state of the monitored function over a relatively short time interval, and
a "time resolution" of less than two seconds per image can be achieved.
As indicated above, a very useful image contrast mechanism in NMR medical
imaging is T*.sub.2 contrast. As described by Peter A. Bandettini et al in
"Time Course EPI of Human Brain Function During Task Activation," Magnetic
Resonance in Medicine, 25, 390-397 (1992), the paramagnetic
characteristics of blood change as a function of its oxygenation and this
is reflected as a change in its T*.sub.2 constant. Thus, a series of NMR
images may show the identical physical structures, but the brightness of
the perfused tissue will differ as a function of the degree of oxygenation
of the blood in the capillary bed. The amount of image contrast depends on
the extent to which the T*.sub.2 changes. In turn, the amount of change in
T*.sub.2 can be enhanced by using paramagnetic contrast agents such as
Gadolinium DPTA, or by increasing the T*.sub.2 sensitivity of the pulse
sequence by lengthening the echo time (TE).
While SSFP pulse sequences provide the desired time resolution for dynamic
monitoring, they are not T*.sub.2 contrast sensitive because of their very
short echo times (TE). Consequently, other pulse sequences, such as echo
planar sequences (EPI), have been employed for dynamic studies because
they provide good time resolution and good T*.sub.2 contrast.
Unfortunately, EPI pulse sequences often require hardware enhancements to
standard NMR systems and their use is, therefore, limited.
SUMMARY OF THE INVENTION
The present invention relates to a method for acquiring a series of NMR
images with good time resolution and with good T*.sub.2 contrast. More
specifically, each image in the series is generated by acquiring the S+
echoes produced from a set of SSFP pulse sequences, each S+ SSFP pulse
sequence produces an echo signal with its peak occurring at time TE after
the generation of an RF excitation pulse, by acquiring an asymmetrical
echo signal such that the echo peak occurs in the latter half of an
acquisition window and a portion of the echo signal following its peak is
not acquired, and reconstructing images from the asymmetrical acquired
echo signals.
A general object of the invention is to improve the T*.sub.2 contrast of an
SSFP pulse sequence without incurring a substantial increase in the total
scan time. By performing a partial echo signal acquisition, its peak can
be delayed to increase the echo time TE and thereby improve the T*.sub.2
contrast of the pulse sequence. The acquisition window is shortened by
terminating the acquisition shortly after the echo signal peak is
acquired, and this also enables a reduction in the pulse sequence
repetition time (TR). As a result, the echo time TE can be increased to
improve T*.sub.2 contrast without a corresponding increase in the
repetition time TR and total scan time.
The foregoing and other objectives and advantages of the invention will
appear from the following description. In the description, reference is
made to the accompanying drawings which form a part hereof, and in which
there is shown by way of illustration a preferred embodiment of the
invention. Such embodiment does not necessarily represent the full scope
of the invention, however, and reference is made therefore to the claims
herein for interpreting the scope of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of an NMR system which employs the present
invention;
FIG. 2 is an electrical block diagram of the transceiver which forms part
of the NMR system of FIG. 1;
FIG. 3 is a graphic representation of a pulse sequence which is executed by
the NMR system of FIG. 1 to practice the present invention;
FIG. 4 is a pictoral representation of the conventional processing of an
acquired NMR data set;
FIG. 5 is a pictorial representation of the NMR data set acquired with the
pulse sequence of FIG. 3; and
FIG. 6 is a flow chart of the processing of the NMR data set of FIG. 5 to
reconstruct an image.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring first to FIG. 1 there is shown the major components of a
preferred NMR system which incorporates the present invention and which is
sold by the General Electric Company under the trademark "SIGNA". The
operation of the system is controlled from an operator console 100 which
includes a console processor 101 that scans a keyboard 102 and receives
inputs from a human operator through a control panel 103 and a plasma
display/touch screen 104. The console processor 101 communicates through a
communications link 116 with an applications interface module 117 in a
separate computer system 107. Through the keyboard 102 and controls 103,
an operator controls the production and display of images by an image
processor 106 in the computer system 107, which connects directly to a
video display 118 on the console 100 through a video cable 105.
The computer system 107 is formed about a backplane bus which conforms with
the VME standards, and it includes a number of modules which communicate
with each other through this backplane. In addition to the application
interface 117 and the image processor 106, these include a CPU module 108
that controls the VME backplane, and an SCSI interface module 109 that
connects the computer system 107 through a bus 110 to a set of peripheral
devices, including disk storage 111 and tape drive 112. The computer
system 107 also includes a memory module 113, known in the art as a frame
buffer for storing image data arrays, and a serial interface module 114
that links the computer system 107 through a high speed serial link 115 to
a system interface module 120 located in a separate system control cabinet
122.
The system control 122 includes a series of modules which are connected
together by a common backplane 118. The backplane 118 is comprised of a
number of bus structures, including a bus structure which is controlled by
a CPU module 119. The serial interface module 120 connects this backplane
118 to the high speed serial link 115, and pulse generator module 121
connects the backplane 118 to the operator console 100 through a serial
link 125. It is through this link 125 that the system control 122 receives
commands from the operator which indicate the scan sequence that is to be
performed.
The pulse generator module 121 operates the system components to carry out
the desired scan sequence. It produces data which indicates the timing,
strength and shape of the RF pulses which are to be produced, and the
timing of and length of the data acquisition window. The pulse generator
module 121 also connects through serial link 126 to a set of gradient
amplifiers 127, and it conveys data thereto which indicates the timing and
shape of the gradient pulses that are to be produced during the scan. The
pulse generator module 121 also receives patient data through a serial
link 128 from a physiological acquisition controller 129. The
physiological acquisition control 129 can receive a signal from a number
of different sensors connected to the patient. For example, it may receive
ECG signals from electrodes or respiratory signals from a bellows and
produce pulses for the pulse generator module 121 that synchronizes the
scan with the patient's cardiac cycle or respiratory cycle. And finally,
the pulse generator module 121 connects through a serial link 132 to scan
room interface circuit 133 which receives signals at inputs 135 from
various sensors associated with the position and condition of the patient
and the magnet system. It is also through the scan room interface circuit
133 that a patient positioning system 134 receives commands which move the
patient cradle and transport the patient to the desired position for the
scan.
The gradient waveforms produced by the pulse generator module 121 are
applied to a gradient amplifier system 127 comprised of G.sub.x, G.sub.y
and G.sub.z amplifiers 136, 137 and 138, respectively. Each amplifier 136,
137 and 138 is utilized to excite a corresponding gradient coil in an
assembly generally designated 139. The gradient coil assembly 139 forms
part of a magnet assembly 141 which includes a polarizing magnet 140 that
produces either a 0.5 or a 1.5 Tesla polarizing field that extends
horizontally through a bore 142. The gradient coils 139 encircle the bore
142, and when energized, they generate magnetic fields in the same
direction as the main polarizing magnetic field, but with gradients
G.sub.x, G.sub.y and G.sub.z directed in the orthogonal x-, y- and z-axis
directions of a Cartesian coordinate system. That is, if the magnetic
field generated by the main magnet 140 is directed in the z direction and
is termed B.sub.0, and the total magnetic field in the z direction is
referred to as B.sub.z, then G.sub.x =.differential.B.sub.z
/.differential.x, G.sub.y =.differential.B.sub.z /.differential.y and
G.sub.z =.differential.B.sub.z /.differential.z, and the magnetic field at
any point (x,y,z) in the bore of the magnet assembly 141 is given by
B(x,y,z)=B.sub.0 +G.sub.x x+G.sub.y yG.sub.z z. The gradient magnetic
fields are utilized to encode spatial information into the NMR signals
emanating from the patient being scanned.
Located within the bore 142 is a circular cylindrical whole-body RF coil
152. This coil 152 produces a circularly polarized RF field in response to
RF pulses provided by a transceiver module 150 in the system control
cabinet 122. These pulses are amplified by an RF amplifier 151 and coupled
to the RF coil 152 by a transmit/receive switch 154 which forms an
integral part of the RF coil assembly. Waveforms and control signals are
provided by the pulse generator module 121 and utilized by the transceiver
module 150 for RF carrier modulation and mode control. The resulting NMR
signals radiated by the excited nuclei in the patient may be sensed by the
same RF coil 152 and coupled through the transmit/receive switch 154 to a
preamplifier 153. The amplified NMR signals are demodulated, filtered, and
digitized in the receiver section of the transceiver 150. The
transmit/receive switch 154 is controlled by a signal from the pulse
generator module 121 to electrically connect the RF amplifier 151 to the
coil 152 during the transmit mode and to connect the preamplifier 153
during the receive mode. The transmit/receive switch 154 also enables a
separate RF coil (for example, a head coil or surface coil) to be used in
either the transmit or receive mode.
In addition to supporting the polarizing magnet 140 and the gradient coils
139 and RF coil 152, the main magnet assembly 141 also supports a set of
shim coil 156 associated with the main magnet 140 and used to correct
inhomogeneities in the polarizing magnet field. The main power supply 157
is utilized to bring the polarizing field produced by the superconductive
main magnet 140 to the proper operating strength and is then removed.
The NMR signals picked up by the RF coil 152 are digitized by the
transceiver module 150 and transferred to a memory module 160 which is
also part of the system control 122. When the scan is completed and an
entire array of data has been acquired in the memory modules 160, an array
processor 161 operates to Fourier transform the data into an array of
image data. This image data is conveyed through the serial link 115 to the
computer system 107 where it is stored in the disk memory 111. In response
to commands received from the operator console 100, this image data may be
archived on the tape drive 112, or it may be further processed by the
image processor 106 and conveyed to the operator console 100 and presented
on the video display 118.
Referring particularly to FIGS. 1 and 2, the transceiver 150 includes
components which produce the RF excitation field B.sub.1 through power
amplifier 151 at a coil 152A and components which receive the resulting
NMR signal induced in a coil 152B. As indicated above, the coils 152A and
B may be separate as shown in FIG. 2, or they may be a single whole-body
coil as shown in FIG. 1. The base, or carrier, frequency of the RF
excitation field is produced under control of a frequency synthesizer 200
which receives a set of digital signals (CF) through the backplane 118
from the CPU module 119 and pulse generator module 121. These digital
signals indicate the frequency and phase of the RF carrier signal which is
produced at an output 201. The commanded RF carrier is applied to a
modulator and up converter 202 where its amplitude is modulated in
response to a signal R(t) also received through the backplane 118 from the
pulse generator module 121. The signal R(t) defines the envelope, and
therefore the bandwidth, of the RF excitation pulse to be produced. It is
produced in the module 121 by sequentially reading out a series of stored
digital values that represent the desired envelope. These stored digital
values may, in turn, be changed from the operator console 100 to enable
any desired RF pulse envelope to be produced. The modulator and up
converter 202 produces an RF pulse at the desired Larmor frequency at an
output 205.
The magnitude of the RF excitation pulse output through line 205 is
attenuated by an exciter attenuator circuit 206 which receives a digital
command, TA, from the backplane 118. The attenuated RF excitation pulses
are applied to the power amplifier 151 that drives the RF coil 152A. For a
more detailed description of this portion of the transceiver 122,
reference is made to U.S. Pat. No. 4,952,877 which is incorporated herein
by reference. Referring still to FIG. 1 and 2 the NMR signal produced by
the subject is picked up by the receiver coil 152B and applied through the
preamplifier 153 to the input of a receiver attenuator 207. The receiver
attenuator 207 further amplifies the NMR signal and this is attenuated by
an amount determined by a digital attenuation signal (RA) received from
the backplane 118. The receive attenuator 207 is also turned on and off by
a signal from the pulse generator module 121 such that it is not
overloaded during RF excitation.
The received NMR signal is at or around the Larmor frequency, which in the
preferred embodiment is around 63.86 MHz for 1.5 Tesla and 21.28 MHz for
0.5 Tesla. This high frequency signal is down converted in a two step
process by a down converter 208 which first mixes the NMR signal with the
carrier signal on line 201 and then mixes the resulting difference signal
with the 2.5 MHz reference signal on line 204. The resulting down
converted NMR signal on line 212 has a maximum bandwidth of 125 kHz and it
is centered at a frequency of 187.5 kHz. The down converted NMR signal is
applied to the input of an analog-to-digital (A/D) converter 209 which
samples and digitizes the analog signal at a rate of 250 kHz. The output
of the A/D converter 209 is applied to a digital detector and signal
processor 210 which produce 16-bit in-phase (I) values and 16-bit
quadrature (Q) values corresponding to the received digital signal. The
resulting stream of digitized I and Q values of the received NMR signal is
output through backplane 118 to the memory module 160 where they are
employed to reconstruct an image.
To preserve the phase information contained in the received NMR signal,
both the modulator and up converter 202 in the exciter section and the
down converter 208 in the receiver section are operated with common
signals. More particularly, the carrier signal at the output 201 of the
frequency synthesizer 200 and the 2.5 MHz reference signal at the output
204 of the reference frequency generator 203 are employed in both
frequency conversion processes. Phase consistency is thus maintained and
phase changes in the detected NMR signal accurately indicate phase changes
produced by the excited spins. The 2.5 MHz reference signal as well as 5,
10 and 60 MHz reference signals are produced by the reference frequency
generator 203 from a common 20 MHz master clock signal. The latter three
reference signals are employed by the frequency synthesizer 200 to produce
the carrier signal on output 201. For a more detailed description of the
receiver, reference is made to U.S. Pat. No. 4,992,736 which is
incorporated herein by reference.
The NMR system of FIG. 1 performs a series of pulse sequences to collect
sufficient NMR data to reconstruct an image. The pulse sequence employed
in the preferred embodiment is an SSFP sequence known as GRASS in which
the S.sup.+ signal is acquired. This pulse sequence is shown in FIG. 3 and
includes a selective RF excitation pulse 300 which is produced in the
presence of a slice select gradient pulse 301. A negative readout gradient
pulse 302 is then applied to dephase the excited spins and this is
followed by a positive readout gradient pulse 303 which refocuses the
spins and produces a gradient recalled NMR echo signal 304 which peaks at
a time TE following the excitation pulse 300. The readout gradient pulse
303 also frequency encodes the signal 304 to provide x-axis position
encoding. In addition, y-axis position encoding is provided by a phase
encoding pulse 305 applied before the acquisition of echo signal 304, and
a corresponding rewinder pulse 306 applied after the acquisition of echo
signal 304. The phase encoding pulses 305 and 306 are stepped through a
set of 128 values during the acquisition of a single image.
The distinguishing characteristic of the pulse sequence of FIG. 3 is the
asymmetric acquisition of the echo signal 304. The data acquisition window
307 is aligned such that 128 samples of the echo signal 304 are acquired
before its peak and only 32 samples are acquired after the peak. This is
accomplished by increasing the area of lobe 302 on the readout gradient to
greater than one-half the area of lobe 303. This asymmetric sampling
enables the peak in the echo signal to be delayed to increase the echo
time TE without significantly increasing the pulse sequence repetition
time TR. For example, at an acquisition bandwidth of .+-.32 kHz the 160
samples can be acquired in 2.56 msecs rather than the 4.096 msecs window
required to acquire 256 samples in a symmetric acquisition. This
acquisition time reduction is reflected as a reduction in TR, which in
turn, reduces the entire scan time and improves the time resolution of
each acquired image. Note that the readout gradient 303 is extended for a
period of time after the end of data acquisition such that the S.sup.-
echo does not form within the data acquisition window.
When the present invention is used to acquire a series of images of the
human brain after the injection of a Gadolinium DPTA contrast agent, for
example, the pulse sequence of FIG. 3 is set to a TE of 12 msecs and the
pulse repetition rate TR can be set to 16 msecs. If special gradient
amplifiers and coils are used, the TR can be further reduced to 14 msecs.
An entire 256.times.128 image can thus be acquired in less than 2 seconds,
enabling brain functions to be accurately monitored for a period of time
after injection of the contrast agent.
When a conventional scan is performed using a GRASS pulse sequence the NMR
data is stored in the data disk 112 (FIG. 1) in the form of two arrays 310
and 311 as shown in FIG. 4. The array 310 contains the in-phase magnitude
values I and the array 311 contains the quadrature values Q. Together
these arrays 310 and 311 form an NMR image data set which defines the
acquired image in what is referred to in the art as "k-space." Both arrays
are completely filled with acquired data, for example 256 rows of data
with 256 samples in each row.
To convert this k-space NMR data set into data which defines the image in
real space (i.e. Cartesian coordinates), a two step Fourier transformation
is performed on the I and Q arrays 310 and 311. The transformation is
performed first in the readout direction which is the horizontal rows of
the arrays 310 and 311 to produce two arrays 312 and 313. The array 312
contains the in-phase data and is labeled I' while the array 313 contains
the quadrature data and is labeled Q'. The I' and Q' arrays 312 and 313
define the acquired image in what is referred to in the art as
"hybrid-space."
The second Fourier transformation is performed in the phase encoding
direction, which is the vertical columns of the arrays 312 and 313 to
produce two arrays 314 and 315. The array 314 contains the transformed
in-phase values and is labeled I", while the array 315 contains the
quadrature values and is labeled Q". The arrays 314 and 315 are a data set
which defines the acquired image in real space and the elements thereof
are used to calculate the intensity values in a image array 316 in
accordance with the following expression:
##EQU1##
The elements of the image array 316 are mapped to the main operator console
116 (FIG. 1) for display on a CRT screen.
As described above, to practice the present invention the NMR echo signal
304 is acquired asymmetrically. This is illustrated in FIG. 5, where 32
samples are acquired after the echo peak and 128 samples are acquired
before the echo peak. Since the acquisition covers only part of k-space, a
special reconstruction method must be used to avoid ringing and blurring
artifacts. In the preferred embodiment the homodyne reconstruction
technique disclosed in co-pending U.S. application Ser. No. 07/693,895
filed on May 1, 1991 and entitled "High Resolution Imaging Using Short TE
And TR Pulse Sequences With Asymmetric NMR Echo Acquisition" is employed.
The effective resolution of the reconstructed image depends on the number
of samples acquired, and it has been found that an image equivalent in
resolution to a 256 sample acquisition can be achieved with 160 samples
when this method is used. In situations where resolution can be
sacrificed, the number of samples can, of course, be reduced to shorten
the data acquisition window and the repetition period TR.
Referring still to FIG. 5, each asymmetrically acquired NMR echo signal 304
is stored on a row of an NMR data set 320. As explained above, separate I
and Q values are actually stored, but for clarity of explanation, only a
single data array 320 is shown in FIG. 5. A complete scan is comprised of
256 views and thus the vertical, or phase encoding dimension of the NMR
data set 320 extends from k.sub.y =-128 to k.sub.y =127. The horizontal
dimension of the NMR data set 320, however, is much larger than the 160
acquired samples. The sample NMR echo signals 304 fill only 60% of each
row and the remaining 40% is filled with zeros. The NMR data set 320
extends from k.sub.x =-128 to k.sub.x =127 in the horizontal, or readout
gradient dimension. The sampled NMR spin-echo signals 304 extend from
k.sub.x =+26 to k.sub.x =-128 to fill the NMR data set 320 only to the
left of the dashed line 321. The elements to the right of the dashed line
321 are filled with zeros.
The NMR data set 320 is employed to produce an image using a homodyne
reconstruction technique. This is accomplished under the direction of a
program which is executed by the computer 101 (FIG. 1) and which is
illustrated in FIG. 6. The first step in the reconstruction process is to
produce two separate data sets (G.sub.L) and (G.sub.H) from the NMR data
set 320 (G.sub.K). This is accomplished by multiplying each row of the NMR
data set 320 by the following low frequency window function W.sub.L :
W.sub.L =(1+e.sup.(k-k.sbsp.1.sup.)/T).sup.-1
-(1+e.sup.(k+k.sbsp.1.sup.)T/).sup.-1 (1)
where:
T=4 in the preferred embodiment;
k.sub.1 =18 in the preferred embodiment; and
k=the position of the value being windowed along the readout dimension
(k.sub.x), where k=-128 to 128.
The 256 values (G.sub.K) in each row of the NMR data set 320 (including the
zero-filled points) are multiplied by the value of the window function
W.sub.L as indicated at process block 350 to produce a separate array
G.sub.L.
G.sub.L =W.sub.L .multidot.G.sub.K (2)
Similarly, as indicated at process block 351, each value G.sub.K in the NMR
data set 320 is also multiplied by a high frequency window W.sub.H as
follows:
G.sub.H =W.sub.H .multidot.G.sub.K (3)
where:
W.sub.H =2-(1+e.sup.(k-k.sbsp.1.sup.)/T).sup.-1
-(1+e.sup.(k+k.sbsp.1.sup.)T/).sup.-1, (4)
T=4
k.sub.1 =18
k=the position of the value being windowed along the readout dimension
(k.sub.x), where k=-128 to 128.
Each of the 256 by 256 element data arrays G.sub.L and G.sub.H are then
separately Fourier transformed as indicated by process blocks 352 and 353.
These are complex Fourier transformations along the horizontal, row
direction as would normally be performed in a 2DFT reconstruction. Two,
separate 256 by 256 element arrays g.sub.H and g.sub.L result. Due to the
hermetian symmetry property of the Fourier transformation process, the
zero filled portion of the NMR data set 320 is filled in by the
transformation process and the transformed data in the array g.sub.H is
complete and sufficient to produce an image. However, spatially dependent
phase shifts present in the image must be corrected. The data in the
transformed data array g.sub.L contains the low frequency phase
information necessary to make this correction. This is based on the
assumption that the spatially dependent phase shifts have primarily a low
frequency variation and can be approximated by the phase of the data array
g.sub.L. The next step in the process, therefore, is to correct the phase
of the array elements g.sub.H as indicated at process block 354. This can
be performed in a number of ways, but it is in essence a process in which
the phase (.phi..sub.H) of each complex element in the transformed array
g.sub.H is changed by the phase (.phi..sub.L) of the corresponding element
in the transformed array g.sub.L. This is performed as follows in the
preferred embodiment:
f.sub.x =g.sub.H .multidot..vertline.g.sub.L .vertline./g.sub.L (5)
where f.sub.x is the complex value of each element in a 256 by 256 element
array (f) which represents the NMR image data in hybrid-space. An image is
produced with the real part of these complex values f.sub.x.
As indicated in FIG. 6 at process block 355, the next step is to Fourier
transform the hybrid-space array f in the column, or phase encoding
direction. This is a complex Fourier transformation as is done in a
conventional 2DFT reconstruction, and it produces two 256 by 256 element
data arrays which correspond to the arrays 314 and 315 in FIG. 4. The
final step, therefore, is to create the image array 316 in the usual
manner as indicated in FIG. 6 at process block 356.
Using a conventional GRASS pulse sequence with symmetric echo signal
acquisition, a TE of 2.6 msecs and a TR of 9.4 msecs are obtained. By
using the present invention with a delayed asymmetric echo signal
acquisition, this TE can be increased to 7.8 msecs and the TR increased to
11.6 msecs. The TE can thus be tripled to enhance the T*.sub.2 sensitivity
of the pulse sequence substantially, while the TR is only increased by
23%. In addition, much of this 23% increase represents increased time to
play out additional gradient lobes and increase dead time for gradient
cooling/duty cycle considerations which can be reduced further with
improved gradient coils and gradient amplifiers.
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