Phase contrast, line-scanned method for NMR angiography

An NMR angiogram is produced using a line scan data acquisition. Each line of NMR data is acquired twice, once with a velocity sensitizing gradient having a positive first moment and once with a velocity sensitizing gradient having a negative first moment. The two signals from the acquisition are subtracted to cancel signals from stationary spins while enhancing signals from flowing spins. The magnitude of the velocity sensitizing gradient moment is changed during the cardiac cycle so that aliasing does not occur at high blood velocities and the signal strength does not drop too low at low blood velocities. An angiogram is produced by reconstructing an image from line scan data acquired from a series of slices.

BACKGROUND OF THE INVENTION 
The field of the invention is nuclear magnetic resonance (NMR) techniques 
for producing angiograms. 
Any nucleus which 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). 
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 
paramagnetic nuclei in the tissue attempt to align with this 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 components in the 
perpendicular plane (x-y plane) cancel one another. If, however, the 
substance, or tissue, is irradiated with a magnetic field (RF 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 can be rotated into the x-y 
plane to produce a net transverse magnetic moment M.sub.1 which is 
rotating in the x-y plane at the Larmor frequency. 
The practical value of this gyromagnetic phenomena resides in the radio 
signal which is emitted after the RF excitation signal is terminated. When 
the excitation signal is removed, an oscillating sine wave is induced in a 
receiving coil by the rotating field produced by the transverse magnetic 
moment M.sub.1. The frequency of this signal is the Larmor frequency, and 
its initial amplitude, A.sub.0, is determined by the magnitude of M.sub.1. 
The measurements described above are called "pulsed NMR measurements." They 
are divided into a period of excitation and a period of emission. As will 
be discussed in more detail below, this measurement cycle may be repeated 
many times to accumulate different data during each cycle or to make the 
same measurement at different locations in the subject. 
Although NMR measurements are useful in many scientific and engineering 
fields, an important use is in the field of medicine. NMR measurements 
provide a contrast mechanism which is quite different from X-rays, and 
this enables difference between soft tissues to be observed with NMR which 
are completely indiscernible with X-rays. In addition, physiological 
differences can be observed with NMR measurements, whereas X-rays are 
limited particularly to anatomical studies. 
For most medical applications utilizing NMR, an imaging technique must be 
employed to obtain information at specific locations in the subject. The 
foremost NMR imaging technique is referred to as "zeugmatography" and was 
first proposed by P. C. Lauterbur in a publication "Image Formation by 
Induced Local Interactions: Examples Employing Nuclear Magnetic 
Resonance", Nature Vol. 242, Mar. 16, 1973, pp. 190-191. Zeugmatography 
employs one or more additional magnetic fields which have the same 
direction as the polarizing field B.sub.0, but which have a nonzero 
gradient. By varying the strength (G) of these gradients, the net strength 
of the polarizing field B.sub.0 =B.sub.z +G.sub.x X+G.sub.y Y+G.sub.z Z at 
any location can be varied. As a result, if the frequency response of the 
receiver coil and circuitry is narrowed to respond to a single frequency 
.omega..sub.0, then gyromagnetic phenomena will be observed only at a 
location where the net polarizing field B.sub.0 is of the proper strength 
to satisfy the Larmor equation; .omega..sub.0 =.gamma.B.sub.0 : where 
.omega..sub.0 is the Larmor frequency at that location. 
By "linking" the resulting NMR signal with the strengths of the gradients 
(G=G.sub.x, G.sub.y, G.sub.z) at the moment the signal is generated, the 
NMR signal is "tagged", or "sensitized", with position information. Such 
position sensitizing of the NMR signal enables an NMR image to be 
reconstructed from a series of measurements. Such NMR imaging methods have 
been classified as point methods, line methods, plane methods and three 
dimensional methods. These are discussed, for example, by P. Mansfield and 
P. G. Morris in their book NMR Imaging in Biomedicine published in 1982 by 
Academic Press, New York. 
The NMR scanners which implement these techniques are constructed in a 
variety of sizes. Small, specially designed machines are employed to 
examine laboratory animals or to provide images of specific parts of the 
human body. On the other hand, "whole body" NMR scanners are sufficiently 
large to receive an entire human body and produce an image of any portion 
thereof. 
An angiogram is a visualization of blood vessels. Traditionally, angiograms 
are produced by injecting the patient with a radiopaque substance and then 
taking an X-ray of the patient from the desired projection angle. The 
radiopaque substance flowing in the blood vessels is opaque to the X-rays, 
and the cardiovascular system appears brighter than the surrounding 
tissues in the resulting image. While high resolution angiograms may be 
produced with this conventional method, the patient is subjected to 
ionizing radiation. 
Two methods have been used to produce angiograms by exploiting the NMR 
phenomenon. One of these is referred to as the "time of flight" or "inflow 
enhancement" method for contrasting flowing spins from the surrounding 
stationary spins, and the other is referred to as the "phase contrast" 
method. 
Inflow enhancement occurs when unsaturated spins flow into a slice which 
has been excited by many radiofrequency (RF) pulses. If the time between 
RF pulses is much shorter than the T.sub.1 relaxation rate of the tissues, 
the longitudinal magnetization does not have time to recover before the 
next RF pulse is applied. This results in reduced transverse magnetization 
and reduced signal when the magnetization is again tipped into the 
transverse plane by the next RF excitation pulse. The in-flowing blood, on 
the other hand, will have seen no prior RF pulses and will therefore have 
a large longitudinal component of magnetization, which produces a larger 
transverse magnetization and a larger NMR signal. As a result, the flowing 
blood appears brighter in the reconstructed image. 
In order to produce an angiogram, using the time-of-flight method, a series 
of contiguous thin slices oriented perpendicular to the direction of 
primary blood flow is collected. The slices can be collected sequentially 
in a 2D fashion or simultaneously in a 3D fashion. If 3D acquisition is 
used, the slice must be on the order of a few centimeters thick and the 
flip angle of the excitation pulses must be reduced. These measures are 
necessary to prevent saturation of the blood as it traverses the slice. 
Once the NMR data from the slices is collected, a projection is produced 
using a ray tracing technique. The most commonly used technique involves 
tracing a ray through the slice data and retaining the value of the most 
intense pixel encountered. The pixel associated with each ray is then 
mapped to its corresponding position in the projection image. 
In phase contrast angiography, the mechanism for flow contrast is 
modulation of the phase of the transverse magnetization. The objective is 
to alter the phase of the NMR signal produced by the moving spins, while 
at the same time leaving the net phase of the NMR signal produced by the 
stationary spins unchanged. This result can be achieved through the use of 
a bipolar gradient waveform. 
For a bipolar gradient waveform such as that shown in FIG. 3B, with first 
moment M.sub.1 =At, it is well known that the NMR signal produced by a 
spin moving with velocity v along the axis containing the bipolar gradient 
will accumulate a phase given by the following equation: 
EQU .phi.=.gamma.M.sub.1 v (1) 
where .phi. is the phase accumulation and .gamma. is the gyromagnetic 
constant of the spins. 
Because stationary spins have velocity equal to zero, the phase change 
imparted to these spins will be zero. The sign of the phase change 
acquired by a moving spin is dependent on the sign of the amplitude of the 
lobes of the bipolar gradient. Therefore, if two excitation sequences are 
performed, each containing a bipolar gradient of opposite sign, each will 
impart equal but opposite phase shifts to the moving spin. Upon 
subtraction of the NMR data obtained using these two sequences, signal 
from stationary tissues will be cancelled whereas signal from moving spins 
will be reinforced to enhance the image. 
As with the time of flight methods, phase contrast angiograms can be 
obtained using 2D or 3D acquisition schemes. Because with phase contrast 
techniques, the contrast does not rely solely on inflow phenomenon, a much 
larger volume is usually imaged in a single acquisition. In order to 
prevent saturation of the blood, a tip angle of approximately 30.degree. 
is used. The smaller tip angle results in less blood signal than is 
obtainable with the 60.degree. flip angle used in the time of flight 
technique, but because phase contrast is a subtraction method, the 
elimination of signals from stationary tissues makes the contrast 
associated with this technique far superior to that associated with the 
time of flight techniques. 
The above described sequences work well in regions void of respiratory 
motion and vessel motion caused by cardiac pulsatility. However, when 
these techniques are applied to the abdomen or extremities where 
respiration and/or pulsatility are present, they yield images which are 
far from acceptable. One problem is image artifacts caused by the motion 
of spins. As indicated above, movement of the spins imparts a phase change 
to the NMR signal and this is indistinguishable from the phase imparted to 
the NMR signal due to the phase encoding gradient. As a result, when the 
image is reconstructed the position of the spins are misplaced in the 
phase encoding direction to produce ghosting or blurring in the image. A 
common solution to this problem is to employ respiratory or cardiac gating 
to the data acquisition procedure so that NMR data is acquired at times 
during the cycle when movement of the vessels is at a minimum. 
Another problem with angiograms produced by the phase contrast method is 
that the image contrast varies as a function of blood velocity. Thus, NMR 
data acquired during the diastolic portion of the cardiac cycle when blood 
velocity is low will lack contrast. As a result, the blood vessels may not 
differ at all from the stationary background tissues. On the other hand, 
if the first moment M.sub.1 of the bipolar gradient is increased to 
improve contrast at low velocities, then signal strength is lost at high 
blood velocities due to an excessive phase accumulation (i.e. aliasing). 
As a result, the angiogram will show parts of the vascular system very 
brightly and other parts will fade into the background. This problem is 
particularly acute at the extremities where blood velocity varies 
considerably during the cardiac cycle. 
SUMMARY OF THE INVENTION 
The present invention is an NMR method for producing an angiogram which 
employs the phase contrast technique and which is relatively insensitive 
to vessel movement and to variations in blood flow velocity. More 
particularly, the present invention includes: applying a slice select 
magnetic field gradient to the subject which is directed along a first 
axis; applying a selective RF excitation pulse to the subject to produce 
transverse magnetization in a plane perpendicular to the first axis; 
applying a bipolar motion sensitizing magnetic field gradient to the 
subject which has a moment M; acquiring an NMR signal from the subject 
while producing a readout magnetic field gradient along a second axis 
perpendicular to the first axis; repeating the above steps with a bipolar 
motion sensitizing magnetic field gradient that has a moment -M; 
subtracting the two acquired NMR signals and storing the resulting 
difference NMR signals as a row of data points in an array; repeating the 
above steps to acquire additional rows of data points from additional 
planes through the subject; Fourier transforming the rows of data points 
in the array; and producing an image in which the intensity of each pixel 
in the image is determined by a corresponding data point in the 
transformed array. 
Another aspect of the invention is to vary the magnitude of the motion 
sensitizing magnetic field gradient moment M as a function of blood 
velocity. This is accomplished by producing a signal which is indicative 
of the phase of the subject's cardiac cycle; and stepping the moment M 
through a series of values in response to the cardiac phase signal such 
that the difference NMR signals are each acquired with a bipolar motion 
sensitizing magnetic field gradient having a moment M that changes in 
magnitude inversely as a function of blood flow rate. 
A general object of the invention is to reduce motion artifacts in the 
reconstructed image due to the movement of vessels in the subject during 
data acquisition. No phase encoding gradient is used in the sequence, and 
hence, spins are not mispositioned by performing a Fourier transform in 
the phase encoding direction. 
Another object of the invention is to shorten the scan time needed to 
produce an NMR angiogram. Because no phase encoding is used, it is not 
necessary to acquire a large number of NMR signals from the same slice. 
The use of the phase contrast method, which provides adequate contrast 
between the moving blood in the vessels and the surrounding stationary 
tissues permits rapid acquistion of data from the succession of slices 
with little regard to loss of signal due to saturation of the spins. 
Yet another object of the invention is to optimize the phase contrast 
method of NMR angiography. By changing the motion sensitizing magnetic 
field gradient moment M as a function of the cardiac cycle phase, the 
sensitivity of the method can be maximized at all phases of the cardiac 
cycle. During diastole when blood flow is minimal, the moment M is 
increased to a value which produces large phase changes in the 
transversely magnetized spins. On the other hand, during systole when 
blood flow is maximum, the moment M is at a minimum so that the phase 
change will not be excessive and cause aliasing. The result is an NMR 
difference signal which is maximized throughout the cardiac cycle so that 
the cardio-vascular system can be easily seen at all times during the 
cycle. 
The foregoing and other objects 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.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring particularly to FIG. 1, the present invention is embodied in a 
full body NMR imaging system which is capable of receiving a patient and 
producing a two-dimensional image. The position and orientation of the 
image is determined by the magnitude of magnetic field gradients applied 
along the respective X, Y, and Z axes of the NMR imaging system. A set of 
slices 1 are shown in FIG. 1 which are taken through the patient's heart, 
although the magnetic field gradients can be controlled to produce an 
image through any section or volume and from any desired orientation. 
The preferred embodiment of the invention has been incorporated in an NMR 
imaging system which is commercially available from the General Electric 
Company and is sold under the trademark "Signa". This system produces a 
1.5 Tesla polarizing magnetic field B.sub.0. FIG. 2 is a simplified block 
diagram of this NMR imaging system that includes a pulse control module 2 
which receives command signals from a host computer 4. The pulse control 
module 2 provides properly timed pulse waveform signals to magnetic field 
gradient power supplies 5, 6 and 7 which energize respective gradient 
coils 8, 9 and 10 forming a part of a gradient coil assembly which 
surrounds the patient. The gradient coils 8, 9 and 10 produce the G.sub.x, 
G.sub.y and G.sub.z magnetic fields in the direction of the polarizing 
magnetic field B.sub.0, but with gradients directed in the x, y and z 
directions, respectively. The use of the G.sub.x, G.sub.y and G.sub.z 
gradients in NMR imaging applications is well known in the art, and the 
specific use in the present invention will be described in more detail 
below. 
Referring still to FIG. 2, the pulse control module 2 also provides 
activating pulses to an RF frequency synthesizer 12, which is part of an 
RF transceiver system which is indicated generally by dash-line 13. The 
pulse control module 2 also supplies modulating signals to a modulator 14 
which modulates the output of the RF frequency synthesizer 12. The RF 
signals are applied through an RF power amplifier 15 and a 
transmit/receive switch 16 to a coupling network 17. The coupling network 
17 produces two phase displaced RF signals which are applied to an 
excitation coil 18. The two phase displaced RF signals are applied to the 
coil 18 such that the RF excitation field B.sub.1 produced by the coil 18 
has two orthogonal components. Such a quadrature RF drive arrangement has 
been found to be a more efficient means for delivering the RF energy to 
the paramagnetic nuclei and, hence, a means for further shortening the 
duration of the RF pulses while still producing the required tip angle of 
the net magnetization. 
Under the direction of the pulse control module 2, the center frequency and 
the modulation of the RF excitation pulses are controlled to produce the 
desired transverse excitation. The amplitude of the RF pulse determines 
the amount which the net magnetization is tipped. As will be described 
below, in the preferred embodiment of the invention tip angles from 
10.degree. to 90.degree. are employed depending on slice thickness and 
blood velocity. In addition, the RF pulse is modulated and is used in 
combination with a magnetic field gradient, usually G.sub.z, to excite 
spins in a selected plane, or slice, of the patient. The RF pulse 
bandwidth together with the slice selection gradient strength determine 
the slice thickness, and the center frequency of the RF pulse together 
with the strength of the slice select gradient determine the slice 
position. This slice select method using a "selective" RF pulse is 
described in U.S. Pat. No. 4,431,968, which issued on Feb. 4, 1984 and is 
entitled "Method of Three-Dimensional NMR Imaging Using Selective 
Excitation". 
Referring to FIG. 2, the NMR signals from the excited nuclear spins are 
sensed by the RF coil 18 and applied through transmit/receive switch 16 to 
an RF preamplifier 19. The amplified NMR signals are applied to a 
quadrature phase detector 20 and the detected signals are digitized by A/D 
converter 21 and applied to computer 4 for storage and processing in a 
manner to be described below. A typical pulse sequence includes the 
application of one or more RF pulses to the coil 18 with the switch 16 set 
to transmit, followed by the receipt of one or more NMR signals with the 
switch 16 set to receive. 
To monitor the patient's cardiac cycle, an ECG unit 23 is connected to the 
pulse control module 2 on the NMR system. The ECG unit 23 has electrodes 
(not shown) which attach to the patient and which sense the voltages 
produced during the cardiac cycle. One of these voltages is used to 
produce a pulse that is applied to the pulse control module 2 at the 
beginning of each cardiac cycle. This ECG input signal is shown in FIG. 4 
as a series of QRS pulses 25 and the ECG input signal for one cardiac 
cycle is shown at 26. As will now be described in detail, the QRS pulse in 
the ECG signal 26 is used to trigger a series of pulse sequences used to 
acquire NMR data for a series of images. 
The pulse sequence used to acquire the NMR data is shown in FIGS. 3A-3C. It 
is a gradient echo sequence in which a selective RF excitation pulse 30 is 
applied to the subject in the presence of a slice select gradient pulse 
31. In the preferred embodiment slices are selected along the z axis and 
the pulse 31 is produced by a G.sub.z gradient. The tip angle of the 
excitation pulse 30 has a value between .alpha.=10.degree. and 
.alpha.=90.degree. which is adjusted as a function of blood velocity. To 
compensate the NMR signal 33 which is produced after the excitation pulse 
30 for phase shifts caused by the slice select gradient pulse 31 and to 
desensitize the NMR signal 33 to velocity along the slice select axis (z), 
a negative G.sub.z gradient pulse 34 followed by a positive G.sub.z 
gradient pulse 35 are produced by the G.sub.z gradient coils 10 as taught 
in U.S. Pat. No. 4,731,583. For example, a pulse 34 of the same width but 
opposite sign as the pulse 31 is used, and the pulse 35 has the same 
height, but one half the width of slice select pulse 31. More complex 
waveforms are also well known in the art for compensation of acceleration 
and higher orders of motion. 
To position encode the NMR signal 33 along a readout axis (x), a readout 
gradient pulse 37 is produced as the NMR signal 33 is acquired. The 
readout gradient pulse 37 frequency encodes the NMR signal 33 in the well 
known manner such that the location of spins along the readout axis can be 
determined in the reconstructed image. The readout gradient pulse 37 
remains at a constant value during the entire scan. To produce the 
gradient echo NMR signal 33 and to desensitize it to velocity along the 
readout axis, gradient pulses 38 and 39 precede the readout gradient pulse 
37 as taught in U.S. Pat. No. 4,731,583. 
Unlike the conventional gradient echo sequence used to acquire 2D or 3D NMR 
data, the pulse sequence of FIG. 3A does not employ phase encoding. As a 
result, only one pulse sequence, rather than a series of pulse sequences 
with different phase encoding need be executed. Of course, only a one 
dimensional (x axis) rather than a two dimensional (x and y axis) 
distribution of the spins can be reconstructed from this acquired NMR 
data. Referring again to FIG. 1, this means that an image coplanar with 
the slice 1 cannot be produced. Instead, data is acquired from a series of 
slices and a two dimensional projection image lying in the x-z plane is 
produced as shown at 40. The magnitude and phase of the NMR signal at any 
point in this projection image 40 is determined by the sum, or line 
integral, of all the excited spins located along a line parallel to the y 
axis which passes through the x,z point. It can be appreciated, however, 
that the orientation of the slices 1 and, therefore, the orientation of 
the projection images 40 can be changed by altering the orientation of the 
applied magnetic field gradient. 
Referring again to FIGS. 3A-3C, to produce an angiogram, the pulse sequence 
of FIG. 3A is sensitized to motion as taught by U.S. Pat. No. Re 32,701. 
More specifically, bi-polar velocity encoding gradient pulses G.sub.m are 
added to each pulse sequence along one of its gradient axes. These 
velocity encoding gradient pulses are produced by the same coils 8-10 that 
produce the position encoding gradients G.sub.x, G.sub.y, and G.sub.z. 
These bi-polar motion encoding gradient pulses (G.sub.m) are shown in 
FIGS. 3B and 3C, where the first moment (M.sub.1) of the motion encoding 
pulses G.sub.m in FIG. 3B is equal to the area (A) of each pulse 45 and 46 
multiplied by the time interval (t) between the pulses 45 and 46 (i.e. 
M.sub.1 =At). The motion encoding pulses G.sub.m in FIG. 3C have the saem 
area and time interval, but they have opposite polarity and have a first 
moment equal to -M.sub.1. 
The motion encoding gradient pulses G.sub.m are added to the pulse sequence 
of FIG. 3A to sensitize it to velocity along one of the three axes. It is 
added to the slice select gradient as indicated by dashed lines 47 to 
measure the velocity of moving spins along the conventional slice select 
axis (z-axis), it is added to the readout gradient as indicated by dashed 
lines 48 to measure the velocity of moving spins along the readout axis 
(x-axis), and it is added to the phase encoding gradient as indicated by 
dashed lines 49 to measure the velocity of moving spins along the phase 
encoding axis (y-axis). As will now be explained, the NMR pulse sequence 
is repeated six times with the motion encoding gradient G.sub.m applied 
separately along each axis and it is executed twice for each axis, first 
with the positive motion encoding gradient G.sub.m of FIGS. 3B and then 
with the negative motion encoding gradient G.sub.m of FIG. 3C. 
The order in which NMR data is acquired during the scan is illustrated in 
FIG. 4. As the cardiac cycles occur during the scan, three cardiac cycles 
are used to acquire NMR data for each slice. The NMR pulse sequence used 
during the first cardiac cycle employs a motion encoding gradient G.sub.m 
along the readout direction (x-axis), the NMR pulse sequence used during 
the second cardiac cycle employs a motion encoding gradient G.sub.m along 
a phase encoding axis (y-axis) and the third cycle employs a motion 
encoding gradient G.sub.m along the slice select axis (z-axis). After each 
set of three cardiac cycles, the center frequency of the RF excitation 
pulse 30 is changed to select the next slice and the three cycle 
acquisition repeats. When data for the last slice (#n) has been acquired, 
the scan is complete. 
Referring still to FIG. 4, there is ample time during each cardiac cycle to 
acquire data for many images. The number (N) of images which are produced 
is determined by the subject's heart rate, and the data for each image 1 
through N is acquired at the same point, or phase, of the cardiac cycle. 
The QRS pulse 25 initiates the sequence and a pair of pulse sequences (+M 
and -M) are executed for each of the N images. Since the data for each 
image is acquired at substantially the same point in each of the cardiac 
cycles, the anatomical structures are captured at substantially the same 
position in each image. As a result, the images are clear, and when viewed 
in order, they show the cardiovascular system as a sequence of angiograms 
at successive phases of the cardiac cycle. 
An alternative data acquisition sequence which produces twice the number of 
images N during a cardiac cycle is also possible. In this alternative 
sequence, positive motion encoding (+M) is applied along an axis (x, y or 
z) during one cardiac cycle and a negative motion encoding gradient (-M) 
is applied during the next cardiac cycle. Two cardiac cycles are thus 
required for each axis, and a total of six cardiac cycles are required for 
each slice. However, the +M and -M can be acquired at precisely the same 
point in successive cardiac cycles and twice as many pulse sequences can 
be executed to double the number N of images acquired during a cardiac 
cycle. 
The present invention is carried out under the direction of a program which 
is executed by the computer 4. A flow chart of this program is shown in 
FIGS. 6A and 6B and it is executed when an angiogram is to be produced. 
The program is entered at 100 and it executes a number of prescan 
procedures which are indicated collectively at process block 101. These 
include calibrating the RF power and frequency so that precise tip angles 
can be produced. The calibration process also includes producing a moment 
table 102 and a tip angle table 103. These tables 102 and 103 are produced 
in a calibration procedure which includes executing the pulse sequence of 
FIG. 3A for three cardiac cycles. The first cycle is performed with an 
x-axis velocity sensitizing bipolar gradient G.sub.m, the second cycle 
sensitizes to y-axis velocity and the third cardiac cycle sensitizes to 
z-axis velocity. The NMR data is acquired from a central slice through the 
region of interest and from this data a velocity profile, such as that 
shown by the curve 105 in FIG. 4 is calculated. For each interval 1 
through N during which successive image data is acquired during a cardiac 
cycle, a gradient moment magnitude value M is stored in the moment table 
102. As shown at 106 in FIG. 4, these values M are determined by the 
absolute magnitude of the velocity curve 105, such that the gradient 
moment M is smallest at high blood velocities to prevent aliasing and is 
highest at low blood velocities to improve the contrast in the angiogram. 
The tip angle table 103 is produced by storing a series of values which 
indicate the amplitude of the RF excitation pulse 30. Typically, as blood 
velocity decreases during diastole the tip angle may be reduced to prevent 
RF saturation of slow flowing spins. This feature is more important when 
the thickness of the slice is increased and spins remain in the slice for 
longer periods of time. 
Referring again to the flow chart in FIGS. 6A and 6B, after system 
calibration the data structures and counters are initialized at process 
block 110 and a loop is entered at 111 in which the NMR data is acquired 
for each slice. The process waits for the next QRS pulse in the ECG signal 
as indicated at process block 112, and then a second loop is entered at 
113 in which NMR data is acquired for each image. In the loop 113 the 
moment M of the bipolar motion encoding gradient G.sub.m is set at process 
block 114. This is done by using the image number, or count, as an index 
into the moment table 102 and setting the amplitude of the bipolar 
gradient pulses to the indicated magnitude. The pulse sequence of FIG. 3A 
is then executed twice as indicated by process blocks 115 and 116. The 
moment M of the motion encoding gradient G.sub.m is positive in the first 
pulse sequence and it is negative in the second pulse sequence. In 
addition, the direction (x, y or z axis) of the motion encoding gradient 
G.sub.m is determined by an axis counter. A test is then made at decision 
block 117 to determine if the data for all N images has been acquired 
during the current cardiac cycle. If not, the image count is incremented 
at 118 and the system loops back to acquire NMR data for the next image. 
When data for all N images has been acquired during a cardiac cycle checks 
are made at decision block 119 and 120 to determine what data will be 
acquired during the next cardiac cycle. If motion sensitized NMR data has 
not been acquired for all three axes for the current slice, the axis count 
is incremented and the image count is reset at process block 121 before 
the system loops back. On the other hand, when NMR data sensitized in all 
three directions has been acquired the test is made at decision block 120 
to determine if data for another slice is to be acquired. If so, the slice 
count is increased and the image count and axis count are reset as 
indicated at process block 122 before looping back to acquire more data. 
When data for all n slices has been acquired, the data acquisition phase 
of the procedure is complete and the image reconstruction begins. 
The NMR data acquired for one of the n images is illustrated in FIG. 5. It 
includes three n.times.m arrays 125, 126 and 127 of NMR data which have 
been velocity sensitized with a positive moment M and three n.times.m 
arrays 128, 129 and 130 of NMR data which have been velocity sensitized 
with a negative moment -M. The number of rows n corresponds to the number 
of slices acquired, and the number of columns m corresponds to the number 
of digitized samples of each acquired NMR signal. In the preferred 
embodiment n=42 and m=256. 
Referring to FIGS. 5 and 6B, image reconstruction according to the present 
invention begins at process block 135 by subtracting the complex numbers 
in the negative arrays 128, 129 and 130 from their corresponding complex 
numbers in the positive arrays 125, 126 and 127 to produce three n.times.m 
difference arrays 136, 137 and 138. It can be appreciated that the NMR 
signal components produced by stationary spins are the same in both the 
positive and negative arrays and this subtraction step will, therefore, 
substantially null the signal component due to the stationary spins. On 
the other hand, the NMR signal components due to moving spins are 
subjected to a phase shift which is positive in the arrays 125, 126 and 
127 and is negative in the arrays 128, 129 and 130. As a result of the 
subtraction, therefore, the NMR signal components due to moving spins add 
together to enhance their signal strength in the difference arrays 136, 
137, and 138. It is this step which enables the cardiovascular system to 
be sharply contrasted with surrounding tissue in the final angiogram, 
because it is the cardiovascular system which contains the rapidly moving 
spins in the form of blood. 
As indicated at process block 140, the next step is to Fourier transform 
the respective difference arrays 136, 137 and 138 along each row. As is 
well known in the art, this transforms the time domain signals on each row 
to the frequency domain, which in turn corresponds to the position along 
the readout axis (x-axis). The complex numbers in each of the three 
resulting n.times.m image data arrays 141, 142 and 143 indicate the number 
of spins moving along the respective x, y and z axes and the average 
velocity of the movement. 
When all three axes have been transformed as determined at decision block 
145, the process then proceeds to process block 146 to calculate the 
elements of an n.times.m phase display array 147. The phase angle 
indicated by each complex number in the n.times.m image data arrays 141, 
142 and 143 is proportional to the average velocity of the spins along 
respective x, y and z axes at a point in the x-z projection plane. 
EQU .phi.=tan.sup.-1 (q/i) 
Accordingly, by vectorially summing these three phase angles, a value 
proportional to the average spin velocity is calculated for each point in 
the n.times.m phase display array. 
##EQU1## 
Because each image is obtained with a different value of bipolar velocity 
encoding gradient G.sub.m, the values in the phase display array must be 
normalized using the first moment value M corresponding to this image in 
the moment table 102. As a result, when all of the phase display images 
are viewed, they will all accurately reflect the velocity of blood flow by 
the brightness of each pixel on the display screen, even though the NMR 
data for each image may have been acquired with a different velocity 
sensitizing gradient moment M. 
Next, as indicated by process block 150, an n.times.m magnitude display 
array 151 is calculated. This is accomplished by first calculating the 
magnitude (D) of each complex number in each of the image data arrays 141, 
142 and 143. 
##EQU2## 
where: i and q are the real and imaginary components of the complex 
numbers 
Then, these magnitudes D.sub.x, D.sub.y and D.sub.z for each axis are 
vectorially summed at each of the n.times.m data points to produce a 
number D.sub.v which represents the magnitude of the NMR signals produced 
by moving spins: 
##EQU3## 
The resulting magnitude display array 151 is stored in the computer memory 
and may be recalled after the procedure has finished to produce an 
angiogram display. Of course, a series of such images are stored by the 
present procedure, and these may be displayed in sequence to show the 
changes in the cardiovascular system during an entire cardiac cycle. 
The remainder of the procedure uses the acquired NMR data to produce a 
conventional spin density image. Referring again to FIGS. 5 and 6B, this 
is accomplished by Fourier transforming arrays 125-130 along each of their 
rows as indicated at process block 155. Six n.times.m transformed NMR data 
arrays 156 are thus produced. Then, the corresponding complex numbers in 
each of the six arrays 156 are added together at process block 157 to form 
a single, n.times.m image data array 158. A magnitude display array 159 is 
then produced and stored at process block 160 by calculating the square 
root of the sum of the squares of the complex number components in the 
static image array 158. When displayed, this data reveals the density of 
the stationary spins in the projection plane and it is used to locate 
vessels with respect to stationary anatomical structures. For example, the 
radiologist can superimpose the angiogram image produced from either the 
phase display array 147 or the magnitude display array 151 on the image 
produced by the static magnitude display array 159 to precisely locate a 
particular vessel in the patient. 
The process is repeated for each of the N images that are acquired during 
the cardiac cycle. When the last image N has been processed as determined 
at decision block 161, the process is complete, otherwise, it loops back 
through block 162 to process the next image. At the conclusion of the 
scan, the computer stores three display arrays 147, 151, and 159 for each 
of the N images that are acquired during a cardiac cycle. These can be 
looked at separately, played back in sequence or combined in any 
diagnostically useful manner.