NMR multiple-echo phase-contrast blood flow imaging

A method for magnetic resonance imaging of fluid flow, and particularly in vivo blood flow, uses multiple-echo phase-contrast sequences of signals both in the magnetic field gradient in the direction in which fluid flow is to be determined, and in the radio-frequency (RF) magnetic field utilized with the magnetic field gradient. The magnetic field gradient has a pair of phase-encoding pulses having a zero mean value effect upon the sample, either alone or with inversion by an intermediate 180.degree. RF pulse signal. A first multi-echo sequence, provided with the phase-encoding pulse pair, provides information of both the amplitude and phase-shift of each pixel of the imaged flowing material while a second multiple echo sequence, devoid of the phase-encoding-gradient pulses, provides information as to the amplitude and the undesired initial phase-shift of each pixel of both stationary and flowing material. Information provided responsive to the second sequence is subtracted from the information provided responsive to the first sequence to provide an image having an intermediate grey-scale value for stationary sample material and with differential grey-scale encoding for differential flow velocities of fluid passing through the image plane.

BACKGROUND OF THE INVENTION 
The present invention relates to the imaging of liquids flowing in 
heterogeneous objects using nuclear magnetic resonance (NMR) methods and, 
more particularly, to in vivo blood flow imaging wherein image contrast 
enhancement is achieved by exploiting blood flow rate to discriminate 
against the stationary media surrounding the blood flow network. In 
particular, novel methods are disclosed for producing a plan view image of 
blood flow in portions of the human body by providing two-dimensional 
phase-contrast images differentiating between a substantially-stationary 
body portion and a fluid flow velocity, or rate. 
NMR imaging offers significant advantages as a medical diagnostic tool, the 
most important of which are (a) the completely non-invasive nature of the 
technology and (b) the ability to spatially encode the NMR signal data 
with a good degree of precision using field gradients. The term 
"Zeugmatography" has been coined recently to cover an increasing range of 
NMR techniques wherein static magnetic fields (to produce the polarization 
of nuclei) are combined with field gradients (to spatially encode the 
volume of interest) and with RF fields (to spatially reorient polarized 
nuclei) to achieve a wide range of objectives, including imaging. In the 
recent past, the technical and patent literature have burgeoned and have 
reported results of successive advances in the field. While the field has 
progressed steadily, certain intrinsic drawbacks have heretofore limited 
certain uses of NMR high resolution imaging in medicine. Chief among these 
are the comparatively slow nuclear spin relaxation times of human tissue, 
and body motion due both to inherent movements within the body and the 
difficulty of keeping the body stationary for long periods of time. Human 
tissue is known to have a spin-lattice relaxation time, T.sub.1, of 
approximately 0.5 seconds and a spin-spin relaxation time, T.sub.2, of 
approximately 0.05 seconds. Both of these time constants are very slow as 
compared to the speed of the instrumentation available to process NMR 
signals. Also, high resolution imaging requires a large number of pixel 
projections, each of which may be the result of a complete NMR pulse 
sequence, where each NMR sequence is at least influenced, if not limited, 
by these time constants. Therefore, real time (or even near-real time) 
imaging of body tissue has been of somewhat limited resolution, or 
contrast, and two-dimensional plan view maps of moving elements such as 
blood have heretofore only been discussed. High contrast two-dimensional 
imaging of in vivo blood flow in real time has been beyond the reach of 
NMR technologies. 
Over the years, NMR has been used to measure flow, including flow rates in 
a variety of fluids as well as blood flow, but not in an imaging context. 
An early approach to using NMR in general for measuring fluid flow 
(actually liquid flow) is provided in U.S. Pat. No. 3,191,119 to Singer. 
This patent discloses the measurement of flow rates basically by measuring 
the amount of absorption energy needed to restore a transported volume of 
polarized liquid at a downstream location in a conduit, to the amount of 
polarization which was induced in an upstream location. While the 
disclosure recites applicability of the scheme to blood flow, it is clear 
that the apparatus is not conveniently adaptable to in vivo measurement. 
The Singer patent is illustrative of a fair-sized body of prior art using 
similar NMR techniques to measure liquid flow generally confined within 
conduits, around which instrumentation is placed. Recent patents of this 
genre are U.S. Pat. No. 4,259,638 to Krueger et al. and U.S. Pat. No. 
4,110,680 to Bergmann et al. 
Various methods for in vivo flow-encoding using pulsed-gradient NMR have 
been proposed, but most of these methods are sensitive only to a limited 
range of flow velocities. An application Ser. No. 490,605, entitled "NMR 
Blood Flow Imaging", utilizing an in vivo technique for discriminating 
against stationary tissue, was filed on May 2, 1983, assigned to the 
assignee of the present application and is incorporated herein in its 
entirety by reference. U.S. Pat. Nos. 4,431,968 and 4,443,760, even though 
not concerned with flow imaging, are both assigned to the assignee of the 
present application and are each incorporated herein in their entireties 
by reference, especially as to their teachings of NMR imaging systems and 
basic techniques. 
Producing blood flow images of various sorts also may be found in the 
patent literature, but these make extensive use of acoustic or other forms 
of energy. U.S. Pat. No. 4,205,687 to White et al. discloses the 
production of a color-coded television or CRT type display of a portion of 
a blood vessel obtained using a mechanically articulated transducer to 
cover the area of interest on the patient. This approach uses basic 
Doppler processing and produces a velocity/color CRT image. U.S. Pat. No. 
4,182,173 to Papadofrangakis et al. and assigned to the instant assignee, 
also discloses a sonic Doppler technique for imaging portions of the body 
including blood vessels, and produces a real time measurement of flow 
velocity in selected regions of the patient. A B-scan CRT display is 
provided on which cross-sectional view data is presented. 
A method of measuring in vivo blood flow using hard radiation is described 
in U.S. Pat. No. 4,037,585 to Gildenberg. The disclosure recites the use 
of X or gamma ray scanning of the cranium in successive layers or slices 
by a narrow beam, and the subsequent digital processing of the resultant 
signals to build a visual presentation of the slice under examination. 
Additional non-invasive blood flow measuring techniques are taught in U.S. 
Pat. No. 3,809,070 to Doll et al., and in U.S. Pat. No. 4,334,543 to Fehr. 
Despite the significant amount of effort directed toward the tasks of 
imaging human tissue in general, and in particular to the imaging of 
blood, it remains highly desirable to provide a non-invasive, in vivo, 
real time, high contrast NMR fluid-flow imaging method, and especially a 
method which would allow a single data set to substantially-simultaneously 
generate conventional T.sub.1 -weighted images, T.sub.2 images and 
blood-flow images. 
BRIEF SUMMARY OF THE INVENTION 
In accordance with the invention, a method for magnetic resonance imaging 
of fluid flow, and particularly in vivo blood flow, uses multiple-echo 
phase-contrast sequences of signals both in the magnetic field gradient in 
the direction in which fluid flow is to be determined, and in the 
radio-frequency (RF) magnetic field utilized with the magnetic field 
gradient to evoke an imaging response signal from the sample to be imaged. 
In particular, the magnetic field gradient is provided with a pair of 
phase-encoding pulses having a zero mean value effect upon the sample, 
either alone or with inversion by an intermediate 180.degree. RF pulse 
signal. Each echo-providing excitation, in a first multi-echo sequence, is 
provided with the phase-encoding pulse pair, which may be of alternating 
nature if alternating echo response signals are to be evoked. The first 
multi-echo sequence provides information which, upon processing (as by FFT 
techniques and the like), has information of both the amplitude and 
phase-shift of each pixel of the imaged flowing material, plus undesired 
phase-shift of stationary material. The sample is then subjected to a 
second multiple echo sequence, which is devoid of the 
phase-encoding-gradient pulses, but otherwise substantially similar to the 
first sequence, to provide information as to the amplitude and the 
undesired inherent phase-shift of each pixel of imaged material, both 
stationary and flowing. The information provided responsive to the second 
sequence is subtracted from the information provided responsive to the 
first sequence, to remove the inherent phase-shift information of all of 
the imaged material, whereby an image is obtained having enhanced contrast 
values for only the flowing material. An image having an intermediate 
grey-scale value for stationary sample material can thus be provided, 
responsive to sample T1 or T2 data, with differential grey-scale coding 
for differential flow velocities of fluid passing through the image plane. 
In one presently preferred embodiment, the differential phase-contrast 
information is used to provide respective increasing grey-scale (lighter) 
and decreasing grey-scale (darker) values in each pixel corresponding to 
fluid moving respectively parallel and anti-parallel to the flow axis 
established by the magnetic field gradient(s) having the flow-encoding 
pluses therein. 
Accordingly, it is an object of the present invention to provide a novel 
method for providing a fluid flow image utilizing multiple-echo, 
phase-contrast magnetic resonance signals. 
This and other objects of the present invention will become apparent upon 
reading of the following detailed description of the invention, when 
considered in conjunction with the drawings.

DETAILED DESCRIPTION OF THE INVENTION 
Referring initially to FIGS. 1 and 1a, a sample 10, shown of cylindrical 
shape for simplicity, has at least one channel therein through which a 
liquid flows at an unknown velocity, i.e. as a vector quantity having both 
magnitude and direction. Illustratively, sample 10 has a pair of channels 
11 and 12, in which fluid flows in opposite directions. It is desired to 
obtain information as to the velocity of fluid flow at the location of a 
particular planar slab 1Oa of the sample. Advantageously, the fluid flow 
information should be obtained in a form capable of visual presentation, 
for rapid interpretation. That is, the fluid volume 11a flowing in a first 
channel 11 passing through planar sample slab 1Oa is to be presented as a 
first gray-scale region 11' (FIG. 1a) and the fluid volume 12a flowing in 
the other channel 12, through planar slab 1Oa, is to be presented as a 
second gray-scale image portion 12', each having a gray-scale value 
proportional to the magnitude .vertline.V.sub.Z .vertline. of the fluid 
flow velocity V.sub.Z and different from a gray-scale value assigned to a 
gray-scale representation 10' of the stationary portion of slab 1Oa. 
Further, it is desired that flow image portions 11' and 12' have different 
gray-scale values indicative of the direction of fluid flow, i.e. that a 
flow, as of volume 11a in a first direction, e.g. in the direction of the 
Z axis of a Cartesian coordinate system established with its Z axis along 
the elongated axis of the sample 10 (and along which Z axis is impressed a 
static magnetic field of magnitude B.sub.O), has a different gray-scale 
value than the value assigned to the flow of the other volume 12a in an 
opposite direction, i.e. in the -Z direction. This may be accomplished, 
for example, by presenting the stationary portions 10' as a medium-grey 
image portion and presenting the regions 11' and 12' with respective 
lighter or darker grey-scale density responsive to flow in one or the 
other direction (e.g. parallel or antiparallel to the desired direction), 
respectively, and with the grey-scale density difference from the 
medium-grey scale density (of the stationary portion) being equal, but 
opposite, for equal .vertline.V.sub.Z .vertline. in the two different 
directions. 
Previously, most of the NMR methods proposed for utilizing imaging pulse 
sequences to generate quantitative blood flow images have sought to 
selectively irradiate, and thus "tag", protons so that the pixel 
brightness in the resulting NMR image is related to the velocity of the 
flowing protons. Such methods all, in essence, utilize the signal 
amplitude to measure the replacement of saturated or partially-saturated 
protons by unsaturated protons. Although conceptually simple, these 
methods encounter difficulties, as there are many factors besides flow 
velocity that can influence the pixel brightness in a conventional NMR 
image. In fact, it has been noted that the signal amplitude in a flowing 
region is substantially linked to the particular pulse sequence utilized 
for imaging. An alternative method for measuring fluid flow utilizing 
nuclear magnetic resonance requires the monitoring of the phase of the NMR 
response signal, after application of pulse gradients. The pulse gradients 
are typically chosen such that the phase of stationary objects is not 
changed, while the phase of moving objects in altered in simple proportion 
to the velocity. This method, first proposed by Hahn in 1960 to detect the 
motion of seawater, has caused several attempts, in recent years, to 
incorporate a flow-encoding pulse sequence into conventional NMR imaging 
sequences to produce fluid flow images. These flow-encoding schemes have 
hitherto suffered from two problems: the phase in an NMR image varies 
throughout the image plane for a number of reasons, so that the phase 
image, following a flow-encoding pulse, is not related solely to the 
velocity of the flowing fluid; and the range of flow velocities detectable 
with these methods, given the inherent signal-to-noise limitations of an 
NMR image, have been relatively limited. 
Referring to FIGS. 2a and 2b, in the presence of a balanced magnetic field 
gradient, i.e. a magnetic field gradient pulse having a zero mean over a 
finite time, the phase of the nuclear magnetization of the flowing fluid 
is shifted in proportion to both the flow velocity V and the magnetic 
field gradient magnitude G, in the direction of fluid flow. That is, a 
fluid flow in the Z direction imparts a phase shift proportion to the 
G.sub.Z gradient and the fluid velocity V.sub.Z along the Z-axis. The 
balanced gradient sequence of FIG. 2a utilizes a pair of Z-axis gradient 
G.sub.Z pulses 14a and 14b of substantially identical duration .tau., with 
a 180.degree. radio-frequency (RF) pulse 15 applied therebetween; the RF 
magnetic field corresponding to pulse 15 is applied in the X-Y plane, and 
serves to invert the phase rotation produced by the second gradient pulse 
14b. Both pulses 14 are of the same polarity, which can be positive (as 
shown by pulses 14a and 14b) or negative (as shown by pulses 14a' and 
14b'). The equivalent zero-mean balanced gradient can also be applied, 
without the use of an RF magnetic field, by utilizing the bi-polarity 
G.sub.Z pulse sequence of FIG. 2b, wherein the polarity of two sequential 
pulses, of substantially identical duration .tau., are of opposite 
polarity; thus, a first pulse 16a, of positive polarity, is balanced by a 
second, negative-polarity pulse 16b (or a first negative-polarity pulse 
16a' is balanced by a second, positive-polarity pulse 16b'). Each of the 
pulse sequences in FIG. 2a or FIG. 2b shifts the phase of an NMR response 
signal from a flowing fluid by a like amount, if the magnitude and 
direction of the pulses are substantially identical. The phase rotation 
introduced by any gradient sequence, having a zero mean over finite time, 
is represented by .phi.; 
##EQU1## 
where .gamma. is the gyromagnetic ratio for the nuclei under 
investigation, .tau. is the duration of the gradient pulse and the 
time-dependent gradient pulse G(t) is applied along that axis, e.g. Z 
axis, along which the velocity V(t), e.g. velocity V.sub.Z (t), is to be 
measured. For either of the pulse sequences shown in FIG. 2a or 2b, the 
phase shift equation (1) becomes: 
##EQU2## 
It will be seen that, for stationary nuclei, the phase shift given by the 
above equation ideally reduces to zero and there is thus no net phase 
rotation. However, the movement of fluid nuclei in the Z direction with a 
uniform velocity V, over the duration of the gradient pulse, causes a 
phase rotation given by: 
EQU .phi.=.gamma.G.sub.Z V.sub.Z [-.tau..sup.2 /2+2.tau..sup.2 -.tau..sup.2 
/2]=.gamma.G.sub.Z V.sub.Z .tau..sup.2. (3) 
That is, the phase of uniformly-flowing nuclei is rotated independent of 
position and in proportion only to the flow velocity (V.sub.Z), the 
magnitude (G.sub.Z) of the applied magnetic field gradient, and the square 
of the duration (.tau.) of each lobe of the flow-encoding pulses 14 or 16. 
It will also be seen that the sign of the phase change is determined by 
the direction of the flow relative to the gradient direction, so that, for 
a dual-lobe flow-encoding pulse sequence having a positive-polarity for 
first pulse (14a or 16a), flow in the direction of the gradient field 
generates a phase advance, whereas flow antiparallel to the direction of 
the gradient field generates a phase retardation. These sequences are 
known and have, in fact, been proposed by P. R. Moran, in "A Flow Velocity 
Zeugmatographic Interlace for NMR Imaging in Humans", Magnetic Resonance 
Imaging, V. 1, pages 197-203 (1982); Moran's proposal was for 
incorporation of a flow-encoding pulse into an imaging sequence just prior 
to the onset of the read-out gradient and with the resulting spin-echo 
signal utilized for conventional imaging. Moran proposed to sweep the 
magnitude of the flow-encoding pulse over a range of values spaced evenly 
between some maximum and minimum amplitudes and to use such a gradient 
sequence to encode the spins for flow velocity in analogy to the 
phase-encoding utilized for spatial location in spin-warp imaging. The 
method of Moran requires that a complete two-dimensional (2-D) or 
three-dimensional (3-D) imaging sequence be completed and an image be 
generated, utilizing conventional reconstruction methods, for each value 
of the magnitude of the flow-encoding pulse. Thus, Moran requires N 
independent 2-D or 3-D images to be obtained, corresponding to the N 
independent values of the flow-encoding pulse, and with this set of N 
independent images being then Fourier transformed with respect to the 
flow-encoding sequence on a pixel-by-pixel basis to generate a set of N 
flow images. Each image of this set displays all pixels within the object 
moving at a particular flow velocity, where the pixel brightness is 
determined by either the spin-density or the relaxation times in that 
pixel. This approach requires an inordinately long time to generate very 
crude velocity maps and is thus not practical for most clinical 
applications. For example, if 1 minute is required to acquire all data 
necessary for reconstruction of a convention 2-D image of 128.times.128 
pixels, then the use of Moran's method would require 10 minutes to acquire 
all the data needed to generate velocity images with a velocity resolution 
of 1 cm/sec. over a velocity range of .+-.5 cm/sec. This is a relatively 
long acquisition time for such relatively poor velocity resolution; 
further, if both the absolute magnitude and the direction of flow are 
required, rather than just the component or flow along a particular axis, 
then independent flow-encoding sequences must be applied along each axis 
and, for the example presented above, would result in an acquisition time 
of 30 minutes, which obviously renders the technique impractical for most 
clinical applications. 
My novel method for imaging fluid flow utilizes a multi-echo, 
phase-contrast imaging sequence with flow-encoding by at least one pulsed 
gradient field. In broad terms, a fixed flow-encoding pulse is switched on 
and off at each value of an imaging gradient. In the illustrative 
sequences to be described in detail hereinafter, the flow-encoding pulse 
sequence is applied to one of a pair of sequential, modified spin-warp 
imaging sequences. In the absence of the flow-encoding pulse, a first 
(convention) image is formed, where the reconstruction Fourier transforms 
provide the spin-echo data in a plurality, e.g. two or three, of 
dimensions to provide the complex value A.sub.1 (X,Y,Z) of a pixel, at 
location (X,Y,Z), with a spin density .rho.'(X,Y,Z) as may be modified by 
the appropriate relaxation time, and with a phase factor .phi.(X,Y,Z) 
which may vary throughout the imaging plane. That is, 
EQU A.sub.1 (X,Y,Z)=.rho.'(X,Y,Z)exp(i.phi.(X,Y,Z)). (4) 
The phase term .phi.(X,Y,Z) can, for many reasons, be a non-zero term, even 
in the absence of the flow-encoding pulse sequence. For example, if the RF 
magnetic field utilized to excite the nuclear spins generates eddy 
currents within the sample being imaged, then the phase of the exciting RF 
field may vary throughout the imaged plane. Typically, only the modulus of 
A, i.e. .vertline.A.vertline.=.vertline.A(X,Y,Z).vertline., is usually 
displayed to overcome the effects of phase variations throughout the 
imaged plane and provide an unambiguous representation of the spin density 
.rho.'(X,Y,Z). However, in accordance with one principle of my present 
method, even during the spin-warp imaging sequence which is devoid of a 
flow-encoding pulse sequence, the entire set of complex pixel values 
A.sub.1 (X,Y,Z) is retained. The flow-encoding pulse is applied, during 
the one of a pair of modified spin-warp imaging sequences, after the 
phase-encoding pulse and immediately prior to the response signal read-out 
gradient. The same flow-encoding pulse pair is utilized throughout the 
entire flow-encoded imaging sequence such that the spin-echo data for a 
second image represents the spatial Fourier transform of the density 
function .rho.'(X,Y,Z) modulated in phase by the magnitude of flow within 
each pixel, as well as by the phase term .phi.(X,Y,Z). Thus, if a 
flow-encoding pulse of magnitude G and duration .tau. is applied along the 
Z axis, the reconstructed complex value at each pixel of the flow-encoded 
second image is 
EQU A.sub.2 (X,Y,Z)=.rho.'(X,Y,Z)exp(i.gamma.GV.sub.Z 
(X,Y,Z).tau..sup.2)exp(i.phi.(X,Y,Z)). (5) 
In the foregoing equation, V.sub.Z (X,Y,Z) is the component of the fluid 
flow velocity along the Z axis at position (X,Y,Z). It will be seen that 
the only difference between the pair of images formed in accordance with 
equations 4 and 5 is that the phase in each pixel of the second image 
(formed in accordance with equation 5) is rotated with respect to the 
phase of the first image (formed in accordance with equation 4) and is 
rotated in proportion to the flow velocity in each pixel. In pixels where 
there is no flow, the two images are identical. Consequently, the phase 
difference 
between A.sub.2 (X,Y,Z) and A.sub.1 (X,Y,Z) generates an image that is 
directly related to the flow velocity in each pixel. This phase contrast 
image can be computed utilizing the expression 
##EQU3## 
where R.sub.1 =Re(A.sub.1 (X.Y.Z)), R.sub.2 =Re(A.sub.2 (X.Y,Z)),I.sub.1 
=Im(A.sub.1 (X,Y,Z)) and I.sub.2 =Im(A.sub.2 (X,Y,Z)). Thus, the 
differential phase contrast value at each phase-contrast image pixel is 
related to the flow velocity V.sub.Z, at that pixel, by the expression 
EQU .DELTA..phi.(X,Y,Z)=.gamma.GV.sub.Z (X,Y,Z).tau..sup.2. (7) 
Therefore, a flow image is obtainable from the phase contrast image by 
inverting the previous equation to yield the velocity, at a particular 
pixel and in the direction of the gradient, by 
EQU V.sub.Z (X,Y,Z)=.DELTA..phi.(X,Y,Z)/(.gamma.G.tau..sup.2). (8) 
It will be seen that the use of phase contrast greatly reduces the data 
acquisition time for quantitative flow imaging since only one additional 
repetition of the entire imaging sequence is needed to obtain flow 
information. Thus, if a conventional imaging sequence requires 1 minute to 
complete, then only 2 minutes are needed to acquire all the data necessary 
for reconstruction of a flow velocity image along a particular axis. 
Similarly, a complete reconstruction of both magnitude and direction of 
fluid flow requires only 4 minutes, for a basic 1-minute imaging sequence. 
Referring now to FIGS. 3a-3e, the three Cartesian magnetic field gradients 
(G.sub.X, G.sub.Y and G.sub.Z) and the RF excitation signal are 
respectively graphed in FIGS. 3a-3d, in addition to the received NMR 
response imaging signal graphed in FIG. 3e, for one possible 
two-dimensional flow image sequence. Starting at a sequence initial time 
t.sub.O, a slab-selection G.sub.Z gradient pulse lobe 20a, of 
positive-polarity, is provided. During pulse 20a, an RF selective 
90.degree. pulse signal 22, illustratively amplitude-modulated with a 
(sine bt)/bt, where b is a constant and t is time, envelope is utilized to 
confine the selective excitation to the nuclei in the slab 1Oa (FIG. 1); 
the amplitude of pulse 20a selects the Z-axis position of slab 1Oa, while 
the frequency components of RF pulse 22 select the thickness .DELTA.Z, 
about the central Z-axis location, of the slab. At the end of the Z-axis 
slab-definition time interval a.sub.1, the RF pulse signal 22 has 
terminated and gradients are applied in all three Cartesian directions; 
during second time interval b.sub.1, the Z-axis gradient field G.sub.Z is 
applied with an opposite-polarity (negative-polarity) lobe 20b acting to 
rephase the spins across the .DELTA.Z slab 10a, while the Y-axis gradient 
field G.sub.Y is provided with a pulse 24a with a magnitude and polarity 
selecting one of a number of parallel columns of nuclei to be imaged by 
the present sequence, and the X-axis gradient field G.sub.X is supplied 
with a lobe 26 acting to dephase spins in the X-axis direction, such that 
later applications of a G.sub.X gradient field will rephase the nuclei 
spins and provide a subsequent spin-echo imaging response signal 30. The 
gradient pulses 20b, 24a and 26a terminate at the end of time interval 
b.sub.1. In the next time interval c.sub.1, in accordance with one 
principle of the present invention, an additional lobe 20c is utilized in 
the gradient (e.g. gradient Z) of the direction (e.g. the Z-axis) along 
which flow (e.g. .vertline.V.sub.Z .vertline.)is to be imaged. Pulse lobe 
20c has the same polarity as the original slab-selection pulse lobe 20a, 
and is of an amplitude and duration selected to normalize the spins of 
nuclei within the slab 1Oa to be imaged, such that the same amount of 
phase shift is imparted to flowing nuclei and stationary nuclei in that 
slab with no flow-encoding excitation. 
At the termination of time interval c.sub.1, the multiple-echo imaging 
sequence itself commences. A short time interval d.sub.1 is provided to 
assure that all gradients have returned to a substantially zero value. In 
the next time interval e.sub.1, the first of a pair of phase-encoding 
gradient pulses 28a and 28b is provided in the gradient magnetic field 
along the axis in which flow-encoding is to be investigated, e.g. G.sub.Z 
pulse 28a is provided in gradient field G.sub.Z for imaging along the Z 
axis. Pulse 28a is analogous to pulse 14a in FIG. 2a. At the end of time 
interval e.sub.1 (having a duration equal to the duration .tau. of pulse 
14a of FIG. 2a), pulse 28a terminates and a 180.degree. non-selective 
inverting RF signal pulse 22a is provided during time interval f.sub.1 ; 
pulse 22a is analagous to pulse 15 of the sequence in FIG. 2a. In next 
subsequent time interval g.sub.1, a second, similar-polarity gradient 
field pulse 28b is provided in the G.sub.Z field, analagous to pulse 14b 
in FIG. 2a. Thus, because of the inverting pulse 22a, the flow-encoding 
pulse pair 28a and 28b have a zero net mean, but impart a flow-encoding 
phase shift to the spins of flowing nuclei. At the end of time interval 
g.sub.1, the flow-encoding pulse pair 28a and 28b are completed, and a 
read-out X-axis gradient G.sub.X portion 26b-1 is applied, to cause a 
first spin-echo imaging response signal 30a, of a plurality N thereof, to 
appear during response interval h.sub.1. It will be seen that, while the 
X-gradient field dephasing lobe 26a is often of a polarity opposite to the 
read-out gradient portion 26b, lobe 26a in the present sequence, due to 
the presence of a 180.degree. non-selective inversion RF pulse 22a, is 
inverted to have the same polarity as the initial dephasing G.sub.X pulse 
26a and is of the same positive polarity as subsequent read-out pulses 
26b, 26b', 26b", 26b '", etc. 
Advantageously, each phase-encoded X-direction column of the slab is caused 
to provide the plurality N of successive spin-echo response signals 30, to 
facilitate response signal averaging and increase the signal-to-noise 
ratio, as well as to provide information for T.sub.1 and T.sub.2 imaging. 
Therefore, subsequent-echo preparatory time intervals d.sub.2, d.sub.3, 
d.sub.4, . . . are provided before a first flow-encoding pulse 28a', 28a", 
28a'", . . . appears in associated time intervals e.sub.2, e.sub.3, 
e.sub.4, . . . , followed by subsequent 180.degree. non-selective RF 
signal pulses 22a', 22a", 22a'", . . . in associated time intervals 
f.sub.2, f.sub.3, f.sub.4, . . . , and the second phase-encoding pulse 
lobes 28b', 28b", 28b'", . . . associated time intervals g.sub.2, g.sub.3, 
g.sub.4, . . . , before the application of associated read-out G.sub.X 
field portions 26b' , 26b", 26b'", . . . during which the subsequent 
spin-echo signals 30a', 30a", 30a'", . . . are provided by the excited 
spins in selected slab 10a and are received, digitized and processed along 
with the initial spin-echo response signal 30a. 
In accordance with another principle of the present invention, the imaging 
sequence having the flow-encoding pulses (e.g. like-polarity pulses 28a 
and 28b, interspersed with a 180.degree. non-selective inverting RF pulse 
22a) is followed by a similar imaging sequence, for the same Y-direction 
column encoding pulse 24a' amplitude, but without the flow-encoding pulses 
28 in the flow-direction axis magnetic field gradient, e.g. G.sub.Z. Thus, 
starting at time t.sub.O ', the non-phase-encoding multiple-echo sequence 
commences, in first time interval a.sub.1 ', with the .DELTA.Z 
slab-selecting gradient lobe signal 28a', in conjunction with a 90.degree. 
selective RF excitation pulse 22'. In the next time interval b.sub.1 ', 
the Z-rehasing lobe 20b' appears with the G.sub.Y phase-encoding signal 
24a'(of the same magnitude as the signal lobe 24a used in conjunction with 
the flow-encoding sequence), and the X-axis dephasing lobe 26a'(of the 
same magnitude as the signal lobe 26a in the flow-encoding sequence). In 
the next time interval c.sub.1 ', the phase-shift-normalizing G.sub.Z lobe 
signal 20c', analagous to signal 20c in the flow-encoding sequence, is 
present. As no flow-encoding is utilized in the second sequence, time 
intervals analagous to intervals d.sub.1, e.sub.1 and g.sub.1 are not 
utilized. Therefore, the next time interval is f.sub.1 ', in which the 
180.degree. non-selective inverting RF pulse 22b is provided, followed by 
the first imaging signal response read-out time interval h.sub.1 ', 
wherein the G.sub.X read-out gradient portion 26b is applied to cause a 
first spin-echo imaging response signal 30b to be provided. The same 
number N of multiple-echoes is provided for the non-flow-encoding sequence 
as was provided for the flow-encoding sequence. 
It will be understood that the entire two-dimensional image, either of the 
fluid-flow or stationary material, requires that additional 
flow-encoded/non-flow-encoded sequences be consecutively provided; each 
pair of sequences (one having the flow-encoding pulses 28a and 28b and the 
other devoid of the flow-encoding pulses) has one of the required 
additional values and polarities of the G.sub.Y gradient, as shown by the 
broken line gradient lobes for signal portions 24a and 24a", to complete 
imaging over the slab 1Oa. 
It should also be understood that the use of the flow-encoding sequence of 
FIG. 2b, i.e. having a pair of identical-duration, identical-amplitude and 
opposite-polarity lobes 16a and 16b with no 180.degree. RF pulse 
therebetween, can be utilized. In that case, the 180.degree. non-selective 
RF inverting pulse signal is provided, as shown in broken line, as signals 
22c, 22c', 22c", 22c'", . . . in associated time intervals d.sub.1, 
d.sub.2, d.sub.3, d.sub.4, . . . and the signals 22a, 22a', 22a", 22a'", . 
. . are not utilized. This alternating of opposite-polarity flow-encoding 
pulses, following a non-selective 180.degree. RF inverting pulse, is also 
shown in FIGS. 3a'and 3d'. 
The use of alternating polarity for the opposite-polarity flow-encoding 
pulse pairs also allows solution of an additional problem inherent in the 
phase-contrast approach. That is, the problem of the phase .phi., or the 
phase difference .DELTA..phi., being a periodic function uniquely defined 
only over the range -.pi. to +.pi.. That is, if the flow velocity in a 
particular pixel creates a phase advance greater than +.pi., or a phase 
retardation greater than -.pi., then the reconstruction algorithm for flow 
imaging will compute the wrong value for the flow velocity, as these 
conditions represent the classic aliasing problem for a periodic function. 
The aliasing problem can be overcome by using the magnitude and duration 
of the flow-encoding pulses to satisfy the Nyquist criterion, i.e. 
choosing the gradient such that the maximum expected fluid flow velocity 
generates no more than a .+-..pi. radian phase shift. This maximum flow 
velocity must be chosen relatively conservatively to insure that all flow 
velocities are faithfully reproduced. Therefore, many of the velocities of 
interest will be less than the maximum flow velocity and will accordingly 
produce relatively small phase changes, which are difficult to measure due 
to the random phase component superimposed on the actual phase shift, by 
the random noise in the imaging system. It will be seen that the maximum 
measurable flow velocity is set by the Nyquist criterion while the minimum 
measurable flow velocity, as well as velocity resolution, is determined by 
the system signal-to-noise ratio. In many applications, such as 
measurement of flow velocity with high spatial resolution, the 
restrictions imposed may provide a dynamic flow velocity range which is 
inadequate for full use. The dynamic range and velocity resolution can be 
increased in flow measurements without a significant imaging time penalty, 
by utilizing the multi-echo imaging sequence with a pair of sequential 
flow-encoding pulses having alternating initial polarity, to allow a 
plurality of echoes to be summed to increase the signal-to-noise ratio and 
therefore the velocity resolution. In this case, the phase contrast image 
generated for each echo is given by 
EQU .DELTA..phi..sub.n (X,Y,Z)=(-1).sup.n- 1n(.gamma.G.sub.Z V.sub.Z 
(X,Y,Z).tau..sup.2) (9) 
where n is the echo index, i.e. n=1, 2, 3, . . . , N for the plurality N of 
echoes obtained for each pixel at location (X,Y,Z). The flow image 
generated by the sequence is reconstructed by first plotting the phase, 
after correction for the sign reversal (that is, by multiplying each phase 
shift .DELTA..phi..sub.n (X,Y,Z) by ((-1).sup.n-1), as a function of echo 
number N. For velocities near the Nyquist rate, the cumulative phase may 
be aliased on certain echoes although, because there is no aliasing on a 
single echo, the phase difference can be unwrapped as a function of echo 
number for all velocities satisfying the Nyquist criterion. Following the 
phase unwrapping step, the phase difference can be fitted to a straight 
line curve as a function of echo number, with the slope of the fitted 
curve representing the average phase rotation per echo and related to the 
flow velocity by 
EQU X.sub.Z (X,Y,Z)=.phi.(X,Y,Z)/(.gamma.G.tau..sup.2) (10) 
where .phi.(X,Y,Z) is the slope. This processing acts to increase the 
dynamic range by reducing the effect of noise and, in particular, if all 
of the plurality N of echoes are recorded in a time less than the 
spin-spin relaxation time T.sub.2 of the flowing fluid, e.g. blood, then 
the dynamic range is increased approximately by the square root of the 
number of echoes, i.e. by .sqroot.N. Since the spin-spin relaxation time 
T.sub.2 of blood is greater than about 200 milliseconds, 4-6 echoes can be 
recorded in a time sufficiently less than the relaxation time T.sub.2 of 
the flowing blood and therefore the multiple-echo method can easily 
increase both the dynamic range and the velocity resolution of the 
phase-contrast image by a factor of between about 2 and about 2.5. 
It should be further understood that three-dimensional (3-D) flow images 
can be obtained by utilizing phase-encoding on the Z axis, as shown by the 
variable-amplitude, negative-polarity rephasing lobes 20b-1 and 20b-2 for 
the G.sub.Z waveforms of FIG. 3a'; by Hadamard encoding of the selective 
excitation; and by other known methods. If Z-axis phase-encoding is 
utilized, the phase-shift-normalizing G.sub.Z gradient lobes 20c and 20c' 
are generally not required; only the slab selection pulses 20a and 20a' 
and the Z-axis phase-encoding pulses 20b-1 or 20b-2 are provided in the 
Z-axis gradient, prior to the flow-encoding pulses 28, themselves applied 
prior to the read-out gradient 26b, e.g. along the X axis, for each echo. 
It should be further understood that the non-selective 180.degree. 
inverting RF pulses 22a, 22a', 22a", 22a'", . . . or 22c, 22c', 22c", 
22c'", . . . may not contribute exactly the 180.degree. phase shift 
required to invert the flowing spins, and a four-part sequence, such as 
the "chopper" sequence of the aforementioned U.S. Pat. No. 4,443,760, may 
be required. That is, the selective 90.degree. RF pulses 22 and 22' may 
have to be phase alternated for subsequent pairs of 
flow-encoded/non-flow-encoded sequences and alternating sequence pairs of 
the imaging NMR signals may have to be subtracted to allow the desired 
signals, due to the 90.degree. RF pulses, to reinforce while the undesired 
signals produced by the imperfect 180.degree. pulses are cancelled. This 
technique basically requires that the 90.degree. RF pulses 22 and 22' of 
FIG. 3d be utilized respectively with flow-encoding pulses 28 in a 
flow-encoded first sequence followed by a non-flow-encoded second sequence 
devoid of pulses 28, and that the oppositely, or reverse-phased, 
90.degree. RF selective pulses 22r and 22r' (as shown in FIG. 3d') be 
sequentially utilized respectively with a flow-encoded third sequence 
(having flow-encoding pulses 28) and a subsequent non-flow-encoded fourth 
sequence (devoid of flow-encoding pulses 28). Similarly, it is within the 
scope of the present method to utilize a four-part pulse sequencing method 
in which a first multi-echo sequence has the 90.degree. selective pulse 
with a positive phase, in the presence of pulse-encoding pulses 28, 
followed by a second multi-echo sequence with the 90.degree. selective RF 
pulse having a negative phase and with the flow-encoding pulses 28 
present, and then followed by third and fourth multi-echo sequences, each 
devoid of flow-encoding pulses 28, and respectively having the 
positive-phased and negative-phased 90.degree. selective RF pulses, 
respectively. Again, the pair of multiple-echo signals responsive to the 
oppositely-phased selective RF signals for each flow-encoding value would 
be subtracted from one another and two images would be formed for each 
like-positioned echo of the sequence. The amplitude image and the 
phase-contrast image for each echo position can be computed according to 
the formulae: 
EQU A(X,Y)=(A.sub.1.sup.2 +B.sub.1.sup.2).sup.1/2 +(A.sub.2.sup.2 
+B.sub.2.sup.2).sup.178 (11) 
for the amplitude image and 
EQU .DELTA.(X,Y)=tan.sup.-1 ((B.sub.1 A.sub.2 -B.sub.2 A.sub.1)/(A.sub.1 
A.sub.2 +B.sub.1 B.sub.2)) (12) 
for the phase-contrast image, where A.sub.1 and B.sub.1 are respectively 
the real part and the imaginary part, respectively, of the image at a 
two-dimensional point (X,Y) with flow-encoding pulses 28 present; and 
A.sub.2 and B.sub.2 are respectively the real part and the imaginary part, 
respectively, of the image at the same point (X,Y) with flow-encoding 
pulses 28 not present in the imaging sequence. Again, as the sign of both 
the spatial encoding and the flow-encoding phases alternate from echo to 
echo in a sequence, the reconstruction program will invert the 
Y-direction-encoding sequence prior to Fourier transformation and will 
invert the sign of the final phase contrast image for alternate echoes. I 
have found that a four-echo sequence, designed to faithful produce flow 
velocities up to about 100 cm/sec. can also accurately detect (resolve) a 
flow velocity as small as 1 cm/sec. with a system white noise phase-jitter 
of about 4.degree. per pixel. 
Referring now to FIG. 4a, a photograph of the phase-contrast images taken 
of a flow phantom, without and with a liquid flow occurring, is shown. The 
flow phantom consists of eight tubes of four different sizes, arranged 
with decreasing diameter in each column from left to right, from about 16 
millimeters in diameter at the left to about 6 millimeters in diameter at 
the right, with each diameter tubing being provided as a pair of tubes 
arranged one above another in each of two rows. The tubes are connected in 
series and the flow through the phantom is controlled such that for each 
tube diameter there is forward flow in one tube and reverse flow in the 
other tube of that column (and of the same diameter). The length of each 
of the eight tubes is made sufficiently long to insure nearly laminar, 
i.e. non-turbulent, flow under substantially all conditions. Continuous 
flow of the liquid through the phantom is maintained with a mechanical 
pump. As the tubes are connected in series and non-turbulent flow is 
present, the average flow velocity in each tube varies substantially only 
as the inverse of the cross-sectional area of the tube. The flow phantom 
apparatus was positioned within the bore of a 0.15 Tesla (T) imaging 
system magnet, with the direction of flow within the phantom being either 
parallel or anti-parallel to the direction of the main magnetic field, 
i.e. along the Z axis. The phantom was imaged using a two-dimensional, 
partial saturation, multi-echo, phase-contrast sequence in which a pair 
(i.e. N=2) of echoes was obtained. 
With the flow pump turned off, the image at the top of the FIG. 4a 
photograph illustrates that the two-echo average provide grey-scale data, 
which was adjusted to define zero flow to correspond to a zero value and 
an intermediate grey-level, which is substantially identical for all eight 
tubes of the phantom. However, as shown by the grey-scale values of the 
eight flow phantom tubes in the lower portion of FIG. 4a, when the flow 
pump is turned on and set for a flow rate of about 400 cc/min., the images 
obtained by use of a flow-encoding-on/flow-encoding-off sequence clearly 
shows both the grey-level change with changing velocity and with changing 
direction. In particular, the grey scale in this bottom picture is defined 
such that zero flow corresponds to a value of zero and an intermediate 
grey level, with flow into the plane of the image being represented by a 
value greater than zero and a grey level brighter than the median grey, 
and with flow out of the plane of the image being represented by a value 
less than zero and a grey scale darker than the median grey. Thus, in the 
largest diameter tubes, in the left-hand-most column, the lowest fluid 
flow velocities are obtained, with the fluid in the top tube of the pair 
flowing out of the picture (toward the viewer) and the fluid in the bottom 
tube of the pair flowing into the plane of the picture (away from the 
viewer). It will be seen that the slowest flow phantom tubes have 
grey-scale values respectively slightly darker and slightly brighter than 
the flow-off phantoms. In the second-largest pair of tubes, in the column 
immediately to the left of the center of the photograph, the top tube 
contains fluid flowing into the plane of the image, while the bottom tube 
contains fluid flowing out from the plane of the image; it will be seen 
that the brighter top tube image and darker bottom tube image have values 
respectively more bright, and more dark, than the respective bottom and 
top tubes of the largest diameter phantoms. Similarly, the third-largest 
tubes, being the pair of tubes immediately to the right of the photograph 
vertical center line, have a flow into the plane of the image in the 
bottom tube and out from the plane of the image in the top tube; the 
grey-scale levels are substantially proportionally brighter and darker, 
respectively, than the "into" and "out from" grey-scale levels of the 
larger diameter tube pairs. Finally, it will be seen that the 
right-hand-most pair of tubes, having the smallest diameter, have a flow 
magnitude greater than the flow magnitude of any of the other tube pairs, 
with the top tube having a flow into the plane of the image and the bottom 
tube having a flow out of the plane of the image; the brighter and darker 
grey-scale images are again substantially proportional to the flow 
magnitude. 
FIG. 4c graphically illustrates the flow distribution within the tubes, 
where the abscissa 40 is scaled in the diameter, in millimeters, of the 
four tubes (of about 6.2 millimeters, about 9 millimeters, about 12.8 
millimeters and about 15.9 millimeters, respectively) and the ordinate 42 
is scaled in units of flow velocity in cm/sec. Curve 44 is the computed 
average flow velocity expected as a function of the tube diameter, 
assuming laminar flow for a volume flow rate of 400 cc/min. As the tubes 
are connected in series, the average velocity should vary as the inverse 
square of the tube diameter for non-turbulent flow and the standard 
deviations should scale proportional with the average velocity for 
near-laminar flow. The measured mean velocity and standard deviations for 
both forward flow (represented by circular indicators) and reverse flow 
(represented by diamond indicators) clearly indicates that the measured 
mean velocity very closely parallels predicted results for both flow 
directions and that the average deviation does indeed scale with mean 
velocity flow as predicted. 
FIG. 4b is another photograph illustrating the amplitude image in both the 
fluid flow and non-fluid flow conditions, similar to those of FIG. 4a. In 
both cases, at the top and bottom portions of the photograph of FIG. 4b, 
the same two-echo sequence, used for the images of FIG. 4a, was utilized. 
However, in FIG. 4b, the images were obtained by simply averaging the 
image information from both echoes, i.e. the image intensity A is given by 
A(X,Y)=(A.sub.1 (X,Y)+A.sub.2 (X,Y))/2. The phase information was 
discarded. It will be seen that the grey scale, having been set for an 
intermediate (zero) value and grey level, is approximately the same for 
each of the eight tubes, whether the flow pump is off (top photograph 
portion) or the flow pump is on (bottom photograph portion) and the only 
information imaged is the presence and diameter of the flow phantom 
tubing. Thus, it will be seen that spin-spin lattice T.sub.2 images, as 
well as more conventional amplitude images, can also be generated from the 
flow-encoded data. 
Referring to FIG. 5, a multiple-echo, phase-contrast image of a healthy 
adult volunteer is shown. The image was obtained with a simple 
two-dimensional, two-echo sequence and is an axial slice in the abdomenal 
region. While the volunteer subject's right-hand side is at the left-hand 
side of this phase-contrast image, it will be seen that blood flow in the 
inferior vena cava is correctly depicted, as a lighter grey-scale area 
slightly to the left of center, as flowing into the plane of the image, 
while the blood in the abdominal aorta is correctly depicted, in the 
darker grey-scale portion slightly to the right of the vertical midline of 
the picture, as flowing out of the plane of the image. This image was also 
obtained at 0.15 T, with a slice thickness .DELTA.Z of about 1 centimeter 
and with each pixel having a dimension of 3.5 millimeter-squared, with 
data acquisition requiring only 1.5 minutes. The grey-scale information in 
the abdomenal aorta and inferior vena cava areas, when referenced to the 
stationary portion grey-scale level, indicates that the average value of 
blood flow velocity in the vena cava is 10.5 cm/sec. .+-.5.4 cm/sec. (for 
a peak velocity of about 19.6 cm/sec.), a value well within the normal 
range for a healthy adult at this level of the abdomen. In contrast, the 
average value of the velocity in the abdominal aorta is only -8.1 
cm/sec..+-.2.4 cm/sec. (peak velocity equal to about -12.4 cm/sec.), a 
value smaller than the expected average in a healthy adult. It appears 
that this understatement of the aorta flow velocity is related to the 
pulsatile nature of flow in the major arteries. That is, during the 
interval of each cardiac cycle when peak flow is present in the aorta, the 
phase was aliased for the flow-encoding pulse used in this particular 
experiment. The amplitude of the flow-encoding pulse was chosen to produce 
substantial phase shifts for the average flow velocities in the vena cava 
and the aorta and, indeed, during the interval of low flow the phase was 
in fact faithfully measured by the imaging experiment. However, because 
the measurements were not synchronized with the cardiac cycle, the aliased 
measurements averaged with the non-aliased measurements to result in an 
underestimation of the true phase change associated with aortic flow. This 
problem can be completely circumvented by insuring that the flow-direction 
magnetic field gradient, e.g. the Z-axis field gradient G.sub.Z, is chosen 
such that peak flow in the major arteries is not aliased. Nevertheless, 
the result, graphically illustrated in FIG. 5, clearly demonstrates the 
operation and utility of my multiple-echo, phase-contrast method of 
magnetic resonance blood flow imaging. 
While many variations and modification will now occur to those skilled in 
the art, it is my intent to be limited only by the scope of the appending 
claims and not by the few illustrated pulse sequences and other details 
presented by way of explanation of the principles of the inventive method 
herein.