GB2164155A - Flow imaging by means of nuclear magnetic resonance - Google Patents

Abstract

To form an image (velocity profile) of fluid flowing in a vessel, the fluid is stimulated to produce a time-dependent magnetic resonance signal which is subjected to Fourier- transform. The stimulating is done so as to introduce spatially-dependent phase information indicative of the velocity profile of the fluid. Thus in Fig. 5, for measuring velocity in the x-direction within a z- slice, after selective oxidation of the slice, a long gradient bx (1) is applied, followed by a pi pulse. A second frequency dispersing bx gradient bx (2) is present in a period embracing the echo signal, following a phase encoding gradient by (1). Slice section may be omitted for projection imaging, and an image of fluid flow can be obtained by generating two data sets encoded with phase information indicative of two different velocity profiles of the fluid (taken at different times), combining the data sets, and displaying the resulting data set as an image. By analysing the signal over a period not centred at the middle of the echo signal, a frequency offset is introduced giving the image a striped appearance, the strips being curved in the presence of fluid flow. <IMAGE>

Description

SPECIFICATION Flow imaging by means of nuclear magnetic resonance Description This invention relates to nuclear magnetic resonance (NMR) imaging.

NMR imaging techniques can be used to form a picture of a cross-section of a threedimensional object (for example, a human organ) in which its structure is indicated by variations in intensity or colour of the picture.

One common technique for forming such an image uses a first magnetic field pulse having a linear gradient along a z-axis (G,) to select the "slice" corresponding to the desired cross-section, a second pulse (called a phaseencoding pulse) having a linear gradient along the y-axis (guv) to encode nuclei at different y-axis positions with different precessional phases, and a third linear gradient pulse (called a frequency-encoding pulse) along the x-axis (Gx) to encode nuclei at different x-axis positions with different frequencies. An appropriately modulated RF signal generator imposes a 90" RF pulse followed (after an appropriate interval) by a 1800 pulse. The resulting time-dependent resonance spin-echo signal is measured and stored.The process is repeated to obtain a family of spin-echo signals each based upon a different magnitude of phase-encoding gradi;nt Gy. The family represents a two-dimensional array of time-dependent pp. 42-44, July 1982, discloses selective projective is proposed to be used in displaying moving blood without displaying the surrounding tissue. In particular, Macovski proposes to use a temporal subtraction approach in which data would be acquired at two different portions of the heart cycle corresponding to different velocities in the vessel and the data would be subtracted in order to cancel all static material and visualize the vessels.

Carr, HY, and Purcell, EM, 1954 Phys. Rev.

94, p. 630, recognized that the motion of nuclei in a magnetic gradient will modify their phases in a way which is reflected in a shift in phase at the centre of the spin echo.

According to a first aspect of the present invention, there is provided nuclear magnetic resonance apparatus adapted for forming an image representative of a velocity profile of a fluid flowing in a vessel, the apparatus comprising: means for stimulating the fluid to produce a time-dependent magnetic resonance signal; means for producing Fourier-transformed data from said time-dependent magnetic resonance signal; said stimulating means including means for introducing into a predetermined component of said Fourier-transformed data, spatially dependent phase information indicative of said velocity profile of said fluid; and extracting means for extracting said predetermined component of said Fouriertransformed data for display as said image representative of said velocity profile.

In a second and alternative aspect of the invention, there is provided a method for using nuclear magnetic resonance to form an image representative of a velocity profile of a fluid flowing in a vessel, the method comprising the steps of: stimulating the fluid to produce a time-dependent magnetic resonance signal; producing Fourier-transformed data from said time-dependent magnetic resonance signal; introducing into a predetermined component of said Fourier-transformed data, spatially dependent phase information indicative of said velocity profile of said fluid; and extracting said predetermined component of said Fourier-transformed data for display as said image representative of said velocity profile.

In preferred arrangements, the phase information includes phase values for an array of positions in the fluid, the image comprises an array of display points each characterised by a visual parameter (e.g., intensity) whose magnitude represents the phase value for a corresponding position in the fluid, and phase offset amounts are imposed on the phase values to impart a visible pattern (e.g., parallel, evenly spaced stripes) to the velocity information in the image; the phase offset amounts increase linearly with distance along a predetermined direction in the fluid, and the stripes are spaced along one dimension of the image corresponding to the predetermined direction; and the Fourier transformation is calculated from a selected time segment of the timedependent resonance signal (e.g., a spin-echo signal), and the selected time segment is offcentre with respect to the centre time point of the resonance signal.

Also in preferred arrangements, a first magnetic gradient pulse is imposed along one direction introducing phase information indicative of velocity of the fluid along the one direction, and a second magnetic gradient pulse is imposed along a second direction (e.g., perpendicular to the one direction), the durations of the pulses are regulated so that the first magnetic gradient pulse is longer (e.g., at least five times longer) than the second magnetic gradient pulse to cause velocity of the fluid along the one direction to have greater influence on the image than velocity of the fluid along the second direction; the vessel is oriented with the predominant direction of flow aligned with the one direction; the first pulse is imposed immediately after the second pulse to reduce the effect on the image of velocity of the fluid along the second direction; and the predetermined component is the real component of said Fourier-transformed data.

Also in preferred arrangements, projection images are produced of a vessel which is part of a larger specimen, the specimen includes stationary portions, the Fouriertransformed data includes a component which carries phase information derived from the stationary portions, and a component is derived from the Fourier-transformed data for display which reduces the effect of the stationary portions on the image; and the component for display is 90" out of phase from the component which carries the phase information from the stationary portions.

The velocity profile images are easily obtained without requiring special velocity-encoding gradient pulses in addition to the phaseencoding and frequency-encoding pulses, and without requiring special processing of the spin-echo signals. The images are produced from the readily available real component of the Fourier-transformed data. For arrangements in which there is an additional background phase offset, the images are in the form of stripes across the vessels which are easy to read both conceptually and for the purpose of actual velocity measurements. For embodiments in which a projection image is formed, the selection of a display component 90 out of phase from the predominant stationary fluid component, makes it easier to see the effects of the moving fluid.

Triggering the frequency-encoding gradient immediately after the phase-encoding gradient reduces the effect of motion which might otherwise occur between the two pulses. Arranging the pulses to produce a high ratio of phase shift to velocity enables good resolution of velocity. Aligning the axis of motion with the axis of the frequency-encoding pulse and making the frequency-encoding pulse longer than the phase-encoding pulse enhances sensitivity to the velocity components of particular interest.

In a third alternative aspect of this invention, there is provided nuclear magnetic resonance apparatus adapted for forming an image representative of fluid flow in a vessel situated within a matrix, said fluid flowing with a first velocity profile at a first time and with a second velocity profile, different from said first velocity profile, at a second time; the apparatus comprising:. stimulating means for stimulating said fluid, vessel, and matrix to produce a time-dependent magnetic resonance signal; means for deriving data from said time dependent magnetic resonance signal; said stimulating means including means for introducing into said data phase information indicative of said velocity profile of said fluid as of a given time; means for extracting said phase information as a data set representative of a projection image of said fluid, vessel, and matrix as of said given time; means for causing said apparatus to generate two said data sets corresponding to two projection images respectively as of said first and second times, and to combine said data sets to form a resulting data set; and means for displaying said resulting data set as said image representative of said fluid flow in said vessel.

In a fourth alternative aspect of the present invention, we provide a method for forming an image representative of fluid flow in a vessel situated within a matrix, said fluid flowing with a first velocity profile at a first time and with a second velocity profile, different from said first velocity profile, at a second time, the method comprising: stimulating the fluid, vessel, and matrix to produce a time-dependent magnetic resonance signal; producing Fouriertransformed data from said time-dependent magnetic resonance signal; introducing into said data phase information indicative of said velocity profile of said fluid as of a given time; extracting said phase information as a data set representative of a projection image of said fluid, vessel, and matrix, as of said given time; generating two said data sets corresponding to two projection images respectively as of said first and second times, and combining said data sets to form a resulting data set; and displaying said resulting data set as said image representative of said fluid flow in said vessel.

Preferred arrangements incorporate the following features: A sequence of RF and magnetic gradient pulses is imparted to the fluid, vessel, and matrix beginning at a predetermined time to produce the resonance signal, and the sequences used to generate the two data sets are identical. The first velocity profile includes a first range of velocities, the second velocity profile includes a second range of velocities higher than the first range, and phases are imparted to protons in the fluid with respect to the first velocity profile that are within a predetermined angle of the phases imparted to protons in the vessel and matrix, and random phases are imparted to protons in the fluid with respect to the second velocity profile.The phase shifts are imparted in protons in the fluid at a rate of 2n radians for a predetermined velocity level of the fluid that is higher than the first range of velocities and lower than the second range of velocities. The fluid is blood, the first range of velocities are the velocities of blood flowing in diastole, and the second range of velocities are the velocities of blood flowing in systole.

The first data set is based on the occurrence of diastole (e.g., follows a QRS complex by 10 milliseconds), and the second time follows diastole by a predetermined interval (between 100 and 300 milliseconds after QRS complex) based on the location of the vessel relative to the heart. The pulse sequence is a two-dimensional Fourier transform spin echo pulse sequence, that includes 90" and 1800 RF pulses, and a pair of magnetic gradient pulses along an axis of the vessel, the gradient pulses comprising a compensating pulse preceding the 1800 RF pulse and a readout pulse following the 1800 RF pulse, the two magnetic gradient pulses being of magnitudes and durations such that for static protons the phase shift imposed by one gradient pulse is exactly cancelled by the phase shift imposed by the other gradient pulse. The spin echo occurs no later than 15 milliseconds after the 90" RF pulse. The vessel is an artery. The matrix is a tissue. The fluid flow is pulsatile. The data produced from the resonance signal is Fourier transformed data. The resulting projection image has high contrast and high resolution. The vascular system is shown in detail while the static matrix is suppressed.

The projection images are easily obtained without requiring special velocity-encoding gradient pulses in addition to the phase-encoding and frequency-encoding pulses. The images are produced from the readily available real component of the Fourier-transformed data.

The invention in its several aspects is hereinafter more particularly described by way of example only with reference to the accompanying drawings, in which: Fig. 1 is an isometric view of a short segment of a blood vessel and surrounding tissue; Fig. 2 is a block diagram of NMR apparatus;, Fig. 3 is a block diagram of portions of the computer processor of Fig. 2; Fig. 4 is a flow chart of data gathering and processing and display steps; Fig. 5 is a timing chart (not to scale) of a pulse sequence for slice-selective imaging; Fig. 6 is a graph of spin-echo signal data; Fig. 7 is an image of two parallel tubes respectively containing static fluid and moving fluid; Fig. 8 shows images of bifurcating tubes respectively containing moving fluid and static fluid, and recombining tubes containing moving fluid;; Fig. 9 shows images of constricted tubes respectively containing moving fluid and static fluid; Fig. 10 is a timing chart of a pulse sequence fgr projection imaging; Fig. 11 shows projection images of a bifurcating tube which contains moving fluid and is immersed in a container of water; Fig. 12 shows a projection image of a rotating disk; Fig. 13 is a timing chart (not to scaie) of a pulse sequence for subtractive projective imaging; Fig. 14 is an isometric diagram of projective imaging Figs. 15, 16 are isgmetric diagrams of the proton phases in diastole and systole voxels; Figs. 1 7 to 23, 25, and 26 are projection images of human subjects; Fig. 24 is an x-ray image corresponding to Figs. 25, 26; and Figs. 27, 28 show block diagrams of portions of the structure of Fig. 3.

Referring to Fig. 1, blood vessel 10 lies within a matrix of tissue 12 and carries blood flowing in the direction indicated by arrow 14.

The velocity of the blood in direction 14 tends to vary depending on how close it is to wall 16 of vessel 10. For example, in certain types of laminar flow the veiocity of the blood is smallest at wall 16 and increases to a maximum at the central axis x of vessel 10. Thus, for a particular imaginary planar slice 18 (having a particular location along axis z) the blood velocity component in the direction might vary from small to large to small as one traverses the slice from one wall to the opposite wall in a direction indicated by axis y.

Referring to Fig. 2, nuclear magnetic resonance apparatus 30 has a magnet 32 for imposing a uniform constant magnetic field B0 on vessel 10 and tissue 12. A G, gradient coil 34 (arranged to provide a linear magnetic field gradient along the z-axis) is connected to a driver 36, which can provide selected levels of power at selected times to coil 34. Likewise, G, gradient coil 38 and Gv gradient coil 40, which can provide linear magnetic field gradients respectively along the x-axis and y-axis, are respectively connected to G, driver 42 and Gy driver 44, for providing power to the coils.

An RF antenna 50 (arranged to transmit and receive an RF signal to and from blood vessel 10 and tissue 12) is connected to modulator 52 which is in turn connected to an RF signal generator 54 and is arranged to impose an RF signal at a selected frequency and at selected times upon vessel 10 and tissue 12. RF antenna 50 is also connected via amplifier 57 to demodulator 58, which is arranged to demodulate received signals (from vessel 10 and tissue 12) into quadrature real and imaginary components (indicated by the doubling of line 60).

Computer processor 70 is connected via I/O interface 71 to G,, Gy, and G, drivers 42, 44, 36, to control the magnitude and timing of the linear gradient pulses imposed along the three axes upon vessel 10 and tissue 12, and to signal generator 54 to control the frequency, magnitude, and timing of the RF pulses.

Processor 70 is also connected via I/O interface 71 to demodulator 58 to receive the real and imaginary components of the demodulated received RF signal.

Processor 70 is further connected to a memory 72 (which stores software to control the operation of the system and data representing the received RF signals), to a CRT 74 (which displays images representing the received RF signal, as well as information needed by the operator to control the system), and to a keyboard 76 (by which the operator can enter data and information to control the entire operation of the system). A camera 75 attached to CRT 74 takes photographs of the displayed images.

Referring to Fig. 3, processor 70 includes G, pulse magnitude and timing control 90 which is connected to trigger G, driver 36 to apply selected levels of gradient at selected times.

Likewise Gx and Gy pulse magnitude and timing controls 92, 94 are connected to trigger respectively G, and Gy drivers 42, 44.

Similarly RF signal generator frequency, magnitude, and timing control 96 is connected to trigger RF signal generator 54 to provide an RF pulse having a selected frequency and magnitude, at selected times.

Controls 90, 92, 94, 96 are all connected to a sequencer 100 which provides the necessary specific magnitude, timing, and frequency parameters at the proper times for a given NMR field pulse sequence.

Sequencer 100 is connected to a user-entered parameter processor 102 which receives parameters from the keyboard and converts them to a form usable by sequencer 100.

Sequencer 100 is also connected to control an A-to-D converter 104 which is in turn connected to demodulator 58 to digitize the real and imaginary components of the received RF signal. A sampler 106 is connected to the converter 104 to sample the digitized signal components and to memory 72 to store the samples for later processing.

A Fourier transform element 108 is connected to memory 72 for performing a complex two-dimensional Fourier transform on a family of received signal samples to produce real and imaginary components of a two-dimensional array of data in the frequency domain. The parameters in accordance with which the Fourier transform is performed are received from processor 102 based on user entered information. transform element 108 to organize and process the frequency domain data into image information for delivery to CRT 74, again in accordance with parameters received from processor 102 as provided by the user.

Sequencer 100 is also connected to gating circuitry 112 which provides signals enabling the sequencer to synchronize successive pulse sequences to occur at the same point in successive heart beats.

The invention can be implemented by appropriately connecting and configuring available hardware and by specifying operating parameters for available related software, in accordance with the foregoing and following description (for example, NMR imaging hardware and software available from Technicare Corporation, Solon, Ohio, or similar systems available from other vendors).

Referring to Figs. 4, 5, in order to generate blood velocity profile images corresponding to planar slice 18 (Fig. 1), vessel 10 is oriented as nearly is possible to lie in the x-y plane with the predominant direction of its axis lying along the x-axis, and the system parameters are configured to perform two series of steps, one for data gathering and the other for processing and display. In the data gathering series (120), the blood pulse timing is first determined (122). At a preselected time (t1) relative to the blood pulse a signal pulse sequence is begun (124) by applying a slice selective field gradient pulse G,(1) (126). While the slice selective gradient is being applied, a 90 RF pulse is applied during the period between times t2 and t3(126).Thy effect of the G, and RF pulses is to excite only those nuclei within planar slice 18, the slice of interest.

During the period between times t3 and t4 a gradient G,(2) of opposite polarity to G,(1) is applied. At time t4, a refocusing gradient pulse Go(1) is applied (128). At time t5, a 1800 RF signal pulse is applied (130) to flip the magnetization vector of the nuclei, causing their phases to tend to reconverge.

In the interval between times t6 and t7 a linear phase-encoding pulse gradient Gy at a selected level (e.g., level Gy(1) on Fig. 5) is applied (132) to encode the nuclei along the y-axis with different phases. Immediately thereafter and during the interval between times t7 and t8, a linear frequency-encoding gradient "read" pulse G,(2) is applied (134) which imparts different frequencies to different nuclei along the x-axis. Pulse Go(2) is timed to occur over an interval which spans the spinecho signal 136, whose center point occurs at t,.

The time durations of the Gx, Gyt and G, gradient pulses are shown only schematically in Fig. 5. Preferably pulse Gy is about two to three times as long as pulse G,, and pulse G, is about 5 to 20 times as long as pulse Gy.

Thus for G2 between 1 and 2 milliseconds, Gy would be between 2 and 3 milliseconds, and G, between 10 and 20 milliseconds. It can be shown (as suggesteg in the Hahn article cited above) that the phase shift in a spin echo experiment depends on the square of the time duration of the gradient pulse. The contribution of the x-axis gradient pulse and hence of the velocity component along the x-axis is thus caused to dominate the total phase shift.

For example, with G, lasting 10 times longer than Gyt the x-axis velocity will be weighted by a factor of 100 in the phase shift.

Referring again to Figs. 4, 5, spin-echo signal 136 is sensed, A-to-D converted and sampled, and the samples (representing a time sequence of signal amplitude levels) are stored (138). That completes the data gathering steps for one time dependent set of signal samples. (The identical steps can be repeated several times with the results being averaged to improve the signal-to-noise ratio.) A family of such signal sample sets is obtained by repeating the steps a number of times, each time using a different magnitude for the phase-encoding gradient pulse G,. Thus, between iterations, the level of Gy is reset and a delay period is allowed to pass (140) before the next iteration begins. The delay period can be selected to synchronize each iteration with the heart beat.

Once the family of signal sample sets are taken and stored, they are processed and displayed (150). A complex two-dimensional Fourier transformation is performed (152) to give spatially dependent real and imaginary components in the frequency domain for a two-dimensional array of pixels, and the real component array is displayed (154) as an image; regresentative of the velocity profile of the blood over planar slice 18. In tne image, the intensity represents the real part of the ccmplex image datum at each pixel. The midpoint of the greyscale represents the zero value. Data with real parts greater than zero (corresponding to phase angles with positive cosines) give an image intensity value greater than the zero value. Data with negative real parts give image values less than the zero value.

Referring to Fig. 6, in performing the Fourier transformation, the set of signal samples which are used for the computation span a time interval whose center time (tis) is different by a small offset amount 160 from the center of the soin-echo signal (t,). The effect of the offset in the Fourier transformation process is that the image data is multiplied by a phase factor that depends linearly on the frequencyencoded coordinate, x. For each sampling interval (e.g., 30 microseconds) within the offset amount there is produced 1800 of total background phase variation across the image in the x direction. The result is a striping of the image which improves readability.

Information about the motion of the blood through vessel 10 during the course of each pulse sequence can be shown to be carried through to the Fourier transformed spatially dependent data in the form of apparent phase shifts, whose magnitudes depend on the velocities of the nuclei. The reai component of the Fourier transformed data preserves this phase shift information, so that a display of the real component will show variations in the phase shift in a pattern which will reflect the velocity profile within vessel 10. By orienting the length of the blood vessel along the same axis (the x-axis) as the frequency encoding gradient pulse, and by making the frequency encoding gradient pulse longer than the phase encoding pulse, the resulting Fourier transformed image data is made more sensitive to velocity along the x-axis than along the y-axis.

Offsetting the sample interval relative to the center of the spin-echo signal has the effect of adding a linearly increasing phase shift in the x-axis direction which produces a highly useful striping of the image as explained below. Placing the phase-encoding pulse Gy close in time to the frequency-encoding pulse G, reduces any error which might occur as a result of the nuclei changing position between the two pulses.

In one example, a velocity profile image was formed of water flowing through a 7/16" (1.1cm) inside diameter tube. Flow was constant, gravity driven, and calibrated with a Mettler top-loading scale. The water was doped with CuSO4 to have a relaxation constant T, of approximately 300 milliseconds at 20 megaherz. The tube was placed in the magnetic field with its axis aligned with the direction of the frequency-encoding gradient (i.e., along the x-axis). Because the flow was constant, rather than pulsatile, the pulse sequences were not gated to flow pulses, but were simply repeated every 300 milliseconds.

The frequency encoding gradient strength was 6 X 103 Hz/cm. The resulting phase shift as a function of velocity of the nuclei can be calculated as 8.2 radians/cm/sec. The ratio depends on the pulse sequence which is preferably arranged so that the ratio will produce an image with striping which is useful for the flow velocities of interest. Ratios of at least 0.2 radians/cm/sec. appear to be useful. The magnet was a 1.44 T. (61.5 MHz) 8 cm superconducting magnet (fabricated by Technicare, Solon, Ohio).

Referring to Fig. 7, the upper half 170 is a display of the real component of the Fourier transformed data resulting from fluid flow in the tube, while the lower half 172 resulted from an identical tube with the fluid not flowing.

The lower half image 172 shows a stripe pattern with the stripes orthogonal to the xaxis. The stripes represent a background phase which increases linearly with distances along the x-axis. Each black or white stripe represents a background phase shift of 1800 (R radians). In upper half image 170, the phase shift due to the motion of the fluid is superimposed over the linear background phase shift. Thus the image gives an easily seen representation that the velocity along the central axis of the tube is higher than along the wall (because at the central axis the phase shift per unit length along the x-axis is greater).Further, because each stripe represents 1800 of phase shift, it is possible to measure the difference between the phases at the wall and at the central axis at one position (174) along the x-axis by counting the number of stripes which must be traversed along the central x-axis in order to reach the stripe which begins at line 174 at the wail of the tube. Here there are 3 stripes between points 176, 178, which amounts to a 3z radians phase shift which translates to a maximum flow velocity of 1.2 cm/sec (3it radians 1.2 cm/sec) or an average flow velocity of 8.2 radians/cm/sec 0.6 cm/sec, which is within 15% of the mechanically calibrated average velocity.

The display format enables direct inference from striping of data phase with a precision of +90 , which is acceptable if small compared with typical phase shifts being studied. By using pulse sequences whose magnitude and du ration produce relatively high phase shift/velocity ratios, phase shifts of many times 360" can be obtained.

Referring to Fig. 8, in another example, the phase image produced by non-moving fluid in a bifurcating tube is shown in the lower left (180), and produces a set of parallel stripes representing the background phase offset.

When the fluid is moving (182), the stripe pattern is shifted to reflect the velocity profile of the fluid. An image of fluid moving through tubes which recombine is shown in the upper right of Fig. 8 (184). In Fig. 8, the tube diameter is 1/2" (1.27cm),and flow rate is 100cc/min. The maximum phase shift discernible on the images is 10 w radians corresponding to a maximum velocity of 3.83 cm/sec. The maximum expect velocity (based on fluid mechanics) is 4.0 cm/sec., within about 2% of the measured figure.

Referring to Fig. 9 in another example, images of a 3/16" (0.48cm) inside diameter tube with a 3/32 inch (0.24cm) stenosis (constriction) are shown for non-moving (190) and moving fluid (192).

In the images of moving fluid, velocity is inferred from the displacement of the stripes left or right, with the slopes of the stripes representing changes in flow velocity. Phase stripes which show forward concavity thus do not imply retrograde flow, but rather the existence of higher shear rates near the central axis compared with the tube wall (as in laminar flow).

Pixels where the phase becomes indistinct correspond to points where the velocity gradient is high enough that different velocity values coexist within one pixel. Interference of the resulting phases caused loss of signal, an effect which can be reduced by increasing the spatial resolution. Alternately, as explained below, such interference can be exploited to produce high contrast projection images of blood flow.

Introduction of a background phase offset into the imaging phase enhances the readability of phase shifts for four reasons. First, phase shifts can be calculated in two ways: stripe count or X displacement. Accuracy and precision are improved by this redundancy.

Second, two-dimensional Fourier transform images have better resolution in X than in Y which gives the X displacement method the advantage. Third, background offset exposes any imperfections in the background phase, enabling correction by the reader. Fourth, in consequence of the first three advantages, phase offset enables the implementation of pulse sequences with higher characteristic velocity/phase shift ratios, reducing the importance of any residual phase ambiguity.

The system can also be used to generate so-called projection images, in which data from a number of stacked planar slices are effectively accumulated into one array. For example, a projection image of Fig. 1 would represent not only slice 18 but slices above and below it along the z-axis.

Referring to Fig. 10, the pulse sequence for taking a set of samples for a projection image begins at time q1 with the start of a long frequency-encoding gradient pulse 200..-No slice-selective gradient pulse G, is used since the image is not meant to be slice-selective.

At time q2 (while the G, pulse continues) a 90" RF pulse is imposed, followed by a 1800 pulse at time q3, and a phase encoding gradient pulse 202 beginning at time q4. The spinecho signal is centered at time q,. Gradient pulse 200 ends at time q5, after which a delay occurs before the next pulse sequence begins.

Thus, the projection images are obtained without either slice selection or z-axis encoding.

The Fourier transformation of the sets of data samples is performed without imposing the background-phase offset used for the slice-selective images. Instead, the data component 90" away from the phase of the stationary nuclei in the object being imaged is the one used to form the image. This in effect suppresses the contribution of the stationary nuclei to the final image, while emphasizing the contribution of the moving nuclei. A greater than 90% reduction in stationary nuclei signal intensity has been achieved, permitting the imaging of flow velocities greater than 10 cm/sec with vessel diameter to total diameter ratios greater than 1/20.

Referring to Fig. 11, the upper portion 210 shows a projection image of a bifurcating and recombining tube through which fluid is flowing at 300 cc/min. The 1/2" (1.27cm) inside diameter tubing lies within an 8"X10"X12" (20.32cm X25.4cm X 30.48cm) cavity of stationary water. The measured maximum phase shift is 5z radians which implies a maximum velocity of V,,,, = 6.44 cm/sec. The expected value of V,,, is 12.0 cm/sec, illustrating that projection imaging underestimates velocities. In this case, however, it would be more reasonable to expect projection images to represent the average velocity, Vat9, rather than Vma, since the entire tube diameter contributes to the observed phase shift. In this experiment V,,, = 6.0 cm/sec, close to the observed velocity value.

Fig. 12 is another example of projection imaging, this time of a rotating disc, with the axis of rotation aligned with the z-axis. The disc is composed of water-saturated towels inside a plastic container 20 cm in diameter and 1.5 cm thick. The disk is rotating at 30 rpm corresponding to a maximum tangential velocity of 1 0it cm/sec. A rigid body rotating in the x-y plane at frequency w has the pro perty that at any Point (x,y), the velocity V(x,y) = 2it/w/ (y,-x). Therefore the x velocity component is proportional to y, and points of equal phase shift lie on horizontal lines (constant y) because they sustain equal x velocities.The pulse sequence was repeated every 300 msec, t, = 10.0 msec, the frequency encoding gradient was Gx = 3 X 103 Hz/cm and the calculated ratio of phase to velocity was P(te)/VX = .28 radians/cm/sec.

At 30 cm/sec, this corresponds to a total phase shift of 3n radians which is in reasonable accord with the experiment. This demonstrates that high velocity can yield good signal intensity without spatial distortion.

Projection imaging is highly efficient, enabling three-dimensional volume to be surveyed in times characteristic of two-dimensional imaging experiments.

In another technique for generating projection images, two distinct sets of data are accumulated, then subtracted to form a resulting image. The two data sets are derived in such a manner that, for static portions of tissue, the data are identical and cancel, while for moving portions (such as blood) the two data sets differ. One data set is taken during systole, the other during diastole. In the resulting image the blood, and implicitly the vessels in which it flows, are seen clearly, while the static tissue is suppressed.

Referring to Fig. 13, the pulse sequences (a two-dimensional Fourier transfotm sequence) begins at a time s, when the QRS complex occurs in the electrocardiogram (ECG). At time 52, after an appropriate gate delay whose duration is based (in a manner described below) on whether the data is being taken for systole or diastole, a 90" RF pulse is imposed. Thereafter; in the interval between 53 and s,, a compensating gradient pulse G, is applied simultaneously with a phase encoding pulse Gy at a selected one of 256 different levels.

Next, at time 55 (i.e., 4.5 milliseconds after 52 or half the 9 millisecond interval between 52 and the echo signal --s,) a 1800 RF pulse is imposed. The spin echo signal is spanned by a frequency encoding readout gradient pulse G, (equivalent to 1 ,000 Hz/cm) in the interval between S6 and 87. The spin echo signal is centered at time s,. The readout period occurs between s, and sg.

The combined effect of the compensating G, pulse and the readout G, pulse, which straddle the 1800 RF pulse is to cause no net phase component to be imparted to static protons but to cause a net pnase component to be imparted to each moving proton. The net component depends on the fact that because the proton moves to a new x position in the time between the occurrences of the two G, pulses, it is subjected to different magnitudes of phase shifting by the two G, pulses; those magnitudes (which in static protons would be equal and therefore cancel) do not cancel.

Following the readout period with respect to one pulse sequence, a new pulse sequence (using a different value for the Gy gradient) is begun at time So upon the occurrence of the next QRS complex. A succession of 256 pulse sequences one for each different value of Gy is used with a gate delay appropriate to diastole to obtain a first data set. A second succession of 256 pulse sequences is used with a gate delay appropriate to systole to obtain a second data set. The pulse sequences used to obtain the two data sets are identical. Referring to Fig. 27; tne respective gating delays for systole and diastole are both provided by gating circuitry 112 to a switch 113 that passes the appropriate delay to sequencer 100.Referring to Fig. 28, processor 70 performs a two-dimensional complex Fourier analysis (in element 108) of the resulting two arrays, producing two corresponding images of the same subject respectively gated to diastole and systole 109, 111. The images are subtracted from each other (in element 115) to obtain a clear resulting blood flow image of high contrast and high resolution in which the static tissue is suppressed. In practice, it has been found necessary to weight the two data sets before subtraction in order to maximize the cancellation of the static proton signals and hence the image contrast. The weighting has been done empirically by applying different weights to a background region of the data sets until the minimum background image intensity is obtained.

The pulse sequence of Fig. 13 is designed to generate velocity-dependent proton phase shifts in the blood of 1 cycle per meter per second. This is accomplished, in particular, by arranging the echo time (i.e., the interval between s2 and s,) to be no greater than 15 milliseconds, preferably no greater than 10 milliseconds. This value results in the relative preservation of the blood proton signal for diastolic flow velocities (which are, e.g., typically less than 0.1 meters per second) because the velocity imposed phase shifts are quite small and the blood proton phases reinforce each other in the projected image.Conversely, the value of 1 cycle per meter per second produces a relative loss of the blood proton signal for systolic flow velocities (which are typically between 0.5 and 1.5 meter per second) because the velocity imposed phase shifts are large enough to cause a randomization of and hence cancellation of phases in the projection image. When the systole and diastole images are subtracted, the static tissue phases (which are identical in the two images) cancel while the blood phase in diastole remains highly visible as an indicator of blood flow.

Referring to Fig. 14, eacn projected image lies in an x-y plane 200 which includes a grid of 256 by 256 pixels (e.g., pixel 202, shown out of scale) in an area of 50 cm by 50 cm.

Each pixel represents a projection of the proton signal from all protons in a voxel (volume element) 204 located at the same x and y coordinatcs as the resulting pixel 202 but spanning all z coordinate values in a sample that includes tissue 206, an artery 208, and moving blood 210 within the artery. voxel 204 thus includes portions 212, 214, 216, 218, 220, that lie respectively in tissue, vessel, blood, vessel, and tissue.

Referring to Fig. 15, in each projective pixel 202, the resulting proton signal 230 has two constituents: a larger coherent part originating in the stationary background material 212, 214, 218, 220, and a smaller part originating in the blood protons 216 whose coherence depends on the flow velocity. At diastolic flow velocities the imaging pulse sequence produces phase shifts smaller than 0.1 cycle.

In that case, the blood proton signal behaves coherently (as represented by the phase arrows in section 216 of Fig. 15, which point in generally the same direction) and adds to the background signal to form an additive resulting proton signal 230.

Referring to Fig. 16, in systole, peak velocities generate phase shifts of 0.5 to 1.5 cycles in moving blood protons 216. Each voxel 204, however, intersects the blood in vessel 208 along a chord of points (section 216 in Fig. 16) and so all velocities between zero and the maximum are sampied by partial volume averaging. This range of velocities yields a blood signal which behaves incoherently (as represented by the randomly directed phase arrows in segment 216 of Fig. 16) and makes little or no contribution to the net proton signal 232 for the pixel 202. Systole signal 232 is thus considerably smaller than diastole signal 230 (Fig. 15).

This subtractive projective imaging technique is performed in a 0.6 T (25 MHz, proton) superconducting imaging system (Technicare Corporation, Solon, OH). The brief duration of the data acquisition window (6 msec between Ss and S, in Fig. 13) requires a comparatively large readout gradient G, of 0.25 Gauss per centimeter (corresponding to 1 kHz per centimeter, proton) and the use of a correspondingly broadband time-domain signal filter (50 kHz). To produce the two images for diastole and systole, data acquisition times for both data sets average 8 minutes (512 cardiac cycles in subjects with a normal pulse).

Artifacts caused by patient movement between the two data sets could be reduced by interleaving the systole and diastole pulse sequences, but the time between successive pulse sequences would have to be increased to accommodate the time required to switch the gating, thus increasing the aggregate time required for data acquisition. Respiratory artifacts could be removed by timing the pulse sequences to occur at the same times relative to the respiration cycles.

For example, Figs. 17, 18, and 19 show respectively the diastolic, systolic, and resulting subtraction flow images of a human chest in a 45" right oblique projection in which the x coordinate (Fig. 14) appears vertically. The diastolic and systolic gate delays (S, to S2 in Fig. 13) were respectively 10 and 150 milliseconds. Blood vessels seen in the flow image (Fig. 19) are labeled aa (ascending aorta), da (descending aorta), pa (pulmonary artery), pas (right pulmonary segmental branches), rca and Ica (right and left carotid arteries), rsc and lsc (right and left subclavian arteries).

In another example, Fig;. 20, 21, 22, 23 show systolic (Figs. 20, 22) and resulting flow images (Figs. 21, 23) of thighs (Figs. 20, 21) and knees (Figs. 22, 23) of a human subject, projective to the coronal plane. The x coordinate is vertical. Diastolic gate delays of 10 msec were used for both knees and thighs; systolic delays of 250 and 300 msec were used at the thighs and knees respectively in this individual (height 180 cm). Arrows mark the superficial (sf) and deep (df) femoral arteries of the thigh and the popliteal (pop), anterior tibial (ta), posterior tibial (tp), and peroneal (per) of the knee and calf.

In another example, Figs. 24, 25, 26 show x-ray (Fig. 24) and NMR systolic and flow (Figs. 25, 26) images of atherosclerotic occlusions of the superficial femoral arteries, using gate delays of 10 (diastolic) and 300 (systolic) milliseconds. Arterial segments are marked as for Figs. 17, 18, 19. Proximal and distal points of occluded segments are marked "0.

prox" and "0. dist" (Fig. 24). The appearance of the popliteal arteries reconstituted by collateral flow images implies they are pulsatile (as was confirmed by Doppler ultrasound examination). The poor appearance of the right proximal superficial femoral artery is consistent with angiographically proven poor runoff in this vessel.

In these examples, one image parameter was tailored for each application: the systolic gate delay. Apart from individuais with ventricular dysrhythmias, the QRS complex itself coincides with arterial diastole so the diastole gating delay is always set at 10 milliseconds regardless of the location of the artery within the body. However, the arrival time of peak systolic flow is variable. In normal individuals arrival times increase with distance from the heart. Disease processes may either retard the pulse wave (e.g., aneurysm, occlusion) or accelerate it (e.g., nonocclusive atherosclerosis).

The systolic gate delay was selected empirically in each case by performing between 1 and 4 brief (1 minute) low resolution (64 X 256 pixels) localization images. Typically the gate delay is between 100 and 300 milliseconds. Best results were obtained by exploring the likely range of gate delays in 50 msec increments.

Several factors will affect the contrast of the subtraction image, including the following.

First, because the fraction of velocity which produces phase shifts (and hence contrast) varies as the cosine of the angle between the direction of blood flow and the x axis, vessels oriented at large angles to the x axis may be unobserved in the flow image due to an undiminished systolic signal. Two resulting flow images could be acquired, separated by a 90" rotation in the x-y plane. Each vessel will have a satisfactory orientation in at least one of these images. Second, flow contrast may be undercut by substantial diastolic flow velocities (greater than 0.1 meter per second) which reduce the diastolic blood signal. Doppler ultrasound data have shown that such diastolic flows occur at certain anatomic locations, notably in the arterial supplies of the brain and the visceral organs.Maximum contrast could be recouped by a diastolic acquisition with reduced phase shift. Third, a portion of the arterial blood protons are replaced during each interpulse interval (between 57 and saO in Fig.

13) by unsaturated protons formerly outside the RF coil (proton refreshment). The saturated proton signal is less intense than the unsaturated proton signal by a factor [1 -exp (57 - sio)] T 1 blood (where T 1 denotes the longitudinal relaxation time). Affected arterial segments will have proportionally enhanced intensity in the flow image. Whether gating is systolic or diastolic, the interval between successive pulse sequences represents one cardiac cycle. Therefore, the physical locations in the vessel that are subject to proton replacement are welldefined. Image subtraction will subtract saturated protons in one data set from saturated protons in the other data set, and will likewise subtract unsaturated from unsaturated.Relative to image subtraction, proton refreshment thus resembles a static variable such as proton density more than a dynamic variable such as phase contrast.

Vascular imaging in the projective format efficient. Neither tomography nor existing 3dimensional imaging techniques can present such detailed anatomy from such large territories in so compact and accessible a form. Projective imaging also yields purely technical benefits. Magnetic resonance imaging times grow exponentially with the dimensionality of the experiment. Though projective images are sensitive throughout a 3-dimensional volume, their data acquisition and processing require ments are those of 2-dimensional imaging. A related economy of this method is its reliance on ccmpletely conventional imaging pulse se quences and reconstruction. From a clinical standpoint, the non-invasiveness of this method may allow its application outside the compass of current indications for angiogra phy. An example might be the periodic assessment of arterial bypass grafts. Pulsatility, tne ultimate source of contrast, tells something more specific about functional capability than simple patency.

Other arrangements are possible. Veins in which blood flow is pulsatile (or any vessel containing pulsatile flow of a fluid) can also be imaged.

Claims (53)

1. Nuclear magnetic resonance apparatus adapted for forming an image representative of a velocity profile of a fluid flowing in a vessel, the apparatus comprising: means for stimulating the fluid to produce a time-dependent magnetic resonance signal; means for producing Fourier-transformed data from said time-dependent magnetic resonance signal; said stimulating means including means for introducing into a predetermined component of said Fourier-transformed data, spatially dependent phase information indicative of said velocity profile of said fluid; and extracting means for extracting said predetermined component of said Fourier-transformed data for display as said image representative of said velocity profile.

2. Apparatus according to Claim 1, wherein said phase information includes phase values for an array of positions in said fluid; said image comprises an array of display points each characterised by a visual parameter whose magnitude represents said phase value for a corresponding position in said fluid; and said means for producing said Fourier-transformed data includes means for imposing, on said phase values, phase offset amounts to impart a visible pattern to the velocity information represented in said image.

3. Apparatus according to Claim 2, wherein said visual parameter is intensity of the image.

4. Apparatus according to Claims 2 or 3, wherein said phase offset amounts operatively imposed increase linearly with distance along a predetermined direction in said fluid, and said visible pattern operatively imparted is a set of stripes spaced along one dimension of said image corresponding to said predetermined direction.

5. Apparatus according to Claim 4, wherein in the absence of flow, said stripes operatively produced are parallel, evenly spaced along and perpendicular to said dimension.

6. Apparatus according to Claims 4 or 5, wherein for fluid flowing with different velocities at different positions, the velocity profile is operatively represented by the contours and locations of said stripes on said image.

7. Apparatus according to any of Claims 4, 5 or 6, wherein the distance between opposite edges of one said stripe represents a phase difference of 1800.

8. Apparatus according to any of Claims 2 to 7, wherein said means for producing Fourier-transformed data includes means for calcu lating a Fourier transformation from a selected time segment of said time-dependent resonance signal, and means for selecting the beginning and end of said time segment to produce said phase offset amounts.

9. Apparatus according to Claim 8, wherein said stimulating means includes means for causing a spin-echo signal having a centre time point of maximum magnitude, and said time segment is operatively selected to be offcentre by an offset value with respect to said centre time point of said spin-echo signal.

10. Apparatus according to Claim 9, wherein said visible pattern operatively produced depends on the size of said offset value operatively selected.

11. Apparatus according to any of Claims 4 to 10, wherein said vessel is operatively arranged with the predominant direction of flow of said fluid aligned with said predetermined direction.

12. Apparatus according to Claim 1, wherein said stimulating means includes: means for imposing on said vessel a first magnetic gradient pulse along one direction for introducing phase information indicative of velocity of said fluid along said one direction, and a second magnetic gradient pulse along a second direction; and means for regulating the durations of said pulses so that said first magnetic gradient pulse is longer than said second magnetic gradient pulse to cause velocity of said fluid along said one direction to have greater influence on said image than velocity of said fluid along said second direction.

13. Apparatus according to Claim 1, wherein said stimulating means includes: means for imposing on said vessel a first magnetic gradient pulse along one direction for introducing phase information indicative of velocity of said fluid along said one direction, and a second magnetic gradient pulse along a second direction; and means for reguiating the timing of the occurrence of said pulses to reduce the effect on said image of velocity of said fluid along said second direction.

14. Apparatus according to Claims 12 or 13, wherein said one direction and said second direction are perpendicular to one another.

15. Apparatus according to any of Claims 12, 13 or 14, wherein said apparatus is operatively arranged such that said first magnetic pulse is at least five times longer than said second magnetic gradient pulse.

16. Apparatus according to any of Claims 12 to 15, further comprising means for orienting said vessel with the predominant direction of flow aligned with said one direction.

17. Apparatus according to any of Claims 12 to 16, wherein said first pulse is arranged to be imposed immediately after said second pulse.

18. Apparatus according to any preceding claim, wherein said means for producing Fourier-transformed data includes means for phase-sensitive detection of real and imaginary components of said time-dependent magnetic resonance signal, and said predetermined component is the real component of said Fourier-transformed data.

19. Apparatus according to any preceding claim, wherein said stimulating means is adapted to impose magnetic pulses of a magnitude and timing to produce a selected ratio between velocity of said fluid along one direction and corresponding phase values within said phase information.

20. Apparatus according to Claim 19, wherein said ratio is selected on the basis of the predominant velocity of interest of said fluid.

21. Apparatus according to Claim 19 or Claim 20, wherein said ratio is at least 0.2 radians per centimeter per second.

22. Apparatus according to any preceding claim, wherein said apparatus is adapted for producing a projection image representative of said velocity profile; said vessel comprises part of a larger specimen which includes stationary portions; said Fourier-transformed data includes a component which carries phase information derived from said stationary portions; and said extracting means includes deriving means for deriving a component from said Fourier-transformed data which reduces the effect of said stationary portions on said image.

23. Apparatus according to Claim 22, wherein said component operatively derived by said deriving means is 90 out of phase from said component which carries said phase information from said stationary portions.

24. Apparatus according to Claim 1, wherein said fluid has a predominant direction of flow in said vessel; and said stimulating means is adapted to introduce phase information indicative of said velocity profile for velocities along a particular direction and includes means for orienting said vessel with said predominant direction of flow aligned with said particular direction.

25. Apparatus according to Claim 1, wherein said Fourier-transformed data is operatively produced by means of a complex twodimensional Fourier transformation.

26. Apparatus according to Claim 1, wherein said stimulating means includes means for imposing RF pulses on said vessel, said time-dependent magnetic resonance signals being spin-echo signals resulting from said RF pulses.

27. Apparatus according to Claim 1, wherein said stimulating means includes means for imposing on said vessel a first gradient pulse along an axis (y) and means for imposing on said vessel a second gradient pulse along an axis (x) orthogonal to said yaxis; and wherein said Fourier-transformed data includes a two-dimensional array of data points, and said image is two-dimensional.

28. Apparatus according to Claim 27, wherein said first pulse is a frequency-encoding pulse and said second pulse is a phaseencoding pulse.

29. Apparatus according to Claim 27, wherein said stimulating means further includes means for imposing on said vessel a slice-selecting magnetic field gradient pulse along an axis (z) orthogonal to said x- and yaxes; and wherein said image corresponds to the velocity profile in a slice through said vessel, said slice being in the x-y plane and at a location along the z-axis based upon said slice-selecting magnetic field gradient pulse.

30. Apparatus according to Claim 1, wherein said stimulating means includes means for imposing on said vessel a frequency-encoding gradient pulse along a y-axis, means for imposing on said vessel a phaseencoding gradient pulse along an x-axis orthogonal to said y-axis, said frequency-encoding gradient pulse being longer than, and occurring immediately after, said phase-encoding pulse, and means for imposing RF pulses on said vessel to produce, as said time-dependent magnetic resonance signal, a spin-echo signal; wherein said phase information includes phase values for an array of positions in said fluid and said image comprises an array of display points each characterised by a visual parameter whose magnitude represents said phase value for a corresponding position in said fluid; and wherein said means for producing Fourier-transformed data includes means for phase-sensitive detection of real and imaginary components of said spin-echo signal, and means for imposing on said phase values phase offset amounts which increase linearly with distance along said x-axis to impart in said image a visible pattern of stripes spaced along one dimension of said image to enhance the velocity information presented in said image.

31. A method for using nuclear magnetic resonance to form an image representative of a velocity profile of a fluid flowing in a vessel, the method comprising the steps of: stimulating the fluid to produce a time-dependent magnetic resonance signal; producing Fouriertransformed data from said time-dependent magnetic resonance signal; introducing into a predetermined component of said Fouriertransformed data, spatially dependent phase information indicative of said velocity profile of said fluid; and extracting said predetermined component of said Fourier-transformed data for display as said image representative of said velocity profile.

32. A method according to Claim 31, further comprising imposing on said phase information phase offset amounts to impart in said image a visible pattern related to velocity information in said image.

33. Nuclear magnetic resonance apparatus adapted for forming an image representative of fluid flow in a vessel situated within a matrix, said fluid flowing with a first velocity profile at a first time and with a second velocity profile, different from said first velocity profile, at a second time; the apparatus comprising: stimulating means for stimulating said fluid, vessel, and matrix to produce a time-dependent magnetic resonance signal; means for deriving data from said time dependent magnetic resonance signal; said stimulating means including means for introducing into said data phase information indicative of said velocity profile of said fluid as of a given time; means for extracting said phase information as a data set representative of a projection image of said fluid, vessel, and matrix as of said given time; means for causing said apparatus to generate two said data sets corresponding to two projection images respectively as of said first and second times, and to combine said data sets to form a resulting data set; and means for displaying said resulting data set as said image representative of said fluid flow in said vessel.

34. Apparatus according to Claim 33, wherein said stimulating means further comprises means adapted to impart a sequence of RF and magnetic gradient pulses to said fluid, vessel, and matrix beginning at a predetermined time to produce said resonance signal, the arrangement being such that said sequences used to generate said two data sets are identical.

35. Apparatus according to Claim 34, wherein said sequence comprises a two-dimensional Fourier-transform spin echo pulse sequence.

36. Apparatus according to Claim 35, wherein said spinecho pulse sequence comprises 90" and 1800 RF pulses, and a pair of magnetic gradient pulses along an axis of said vessel, said gradient pulses comprising a compensating pulse preceding said 1800 RF pulse and a readout pulse following said 1800 RF pulse, said two magnetic gradient pulses being of magnitudes and durations such that for static protons the phase shift imposed by one said gradient pulse is exactly cancelled by the phase shift imposed by the other said gradient pulse.

37. Apparatus according to Claim 36, arranged such that a spin echo operatively occurs no later than 15 milliseconds after said 90" RF pulse.

38. Apparatus according to Claim 33, wherein said first velocity profile includes a first range of velocities, and said second velocity profile includes a second range of velocities higher than said first range, and said means stimulating means includes imparting means adapted to impart to protons in said fluid with respect to said first velocity profile, phases that are within a predetermined angle of the phases imparted to protons in said ves sel and matrix, and to impart random phases to protons in said fluid with respect to said second velocity profile.

39. Apparatus according to Claim 38, wherein said imparting means is adapted to impart a sequence of RF and magnetic gradient pulses to said fluid, vessel, and matrix that generates a phase shift in protons in said fluid at a rate of 2n radians for a predetermined velocity level of said fluid that is higher than said first range of velocities and lower than said second range of velocities.

40. Apparatus according to Claims 38 or 39, wherein said fluid is blood, said first range of velocities being selected to correspond to the velocities of blood flowing in systole.

41. Apparatus according to any of Claims 33 to 40, wherein said fluid is blood, said first time is diastole, said second time is systole, and said apparatus further comprises means adapted to trigger said stimulating means at said first time based on the occurrence of said diastole, or at said second time based on the occurrence of said systole.

42. Apparatus according to Claim 41, arranged such that said second time operatively follows said diastole by a predetermined interval based on the location of said vessel relative to the heart.

43. Apparatus according to Claims 41 or 42, arranged such that said first time follows a QRS complex by 10 milliseconds.

44. Apparatus according to any of Claims 41 to 43, arranged such that said second time operatively follows said QRS complex by between 100 and 300 milliseconds.

45. Apparatus according to any of Claims 33 to 44, wherein said data operatively derived from said resonance signal comprises Fourier transformed data.

46. A method for forming an image representative of fluid flow in a vessel situated within a matrix, said fluid flowing with a first velocity profile at a first time and with a second velocity profile, different from said first velocity profile, at a second time, the method comprising: stimulating the fluid, vessel, and matrix to produce a time-dependent magnetic resonance signal; producing Fourier-transformed data from said time-dependent magnetic resonance signal; introducing into said data phase information indicative of said velocity profile of said fluid as of a given time; extracting said phase information as a data set representative of a projection image of said fluid, vessel, and matrix, as of said given time; generating two said data sets corresponding to two projection images respectively as of said first and second times, and combining said data sets to form a resulting data set; and displaying said resulting data set as said image representative of said fluid flow in said vessel.

47. A method according to Claim 46, wherein said fluid flow is pulsatile.

48. A method for forming an image representative of blood flow in a vein or artery, comprising performing a method according to Claim 46 wherein said vessel consists of the said vein or artery and said matrix consists of the surrounding tissue.

49. A method for forming an image representative of the velocity profile of blood flow in a vein or artery, comprising performing a method according to Claim 31 or Claim 32 wherein said vessel consists of the said vein or artery.

50. Nuclear magnetic resonance apparatus substantially as hereinbefore described with reference to and as shown in the accompanying drawings.

51. A method for using nuclear magnetic resonance to form an image representative of a velocity profile of a fluid flowing in a vessel, the method being substantially as hereinbefore described with reference to the accompanying drawings.

52. A method for forming an image representative of fluid flow in a vessel situated within a matrix, the said method being substantially as hereinbefore described with reference to the accompanying drawings.

53. A method for forming an image representative of blood flow in a vein or artery, substantially as hereinbefore described with reference to the accompanying drawings.