Quantitative NMR imaging of flow

Concepts in Magnetic Resonance, 1993, 5, 281-302

Quantitative NMR Imaging of Flow

J. M. Pope* and S. Yao

Universitv of New South Wales S&o& of Physics

P. 0. Box I Kensington NSW 2033

Received March 10, 1993; Revised May 25, 1993

The principles of NMR imaging of flow are discussed in detail. Particular emphasis is given to basic concepts. The various methods are classified, and practical details of their implementation are explained. Quantitative flow-imaging techniques are described and illustrated by examples obtained from a simple flow phantom.

INTRODUCTION

Spatial discrimination in conventional magnetic resonance imaging (MRI) is based on the application of magnetic field gradients to distinguish between signal contributions from different parts of a complex sample on the basis of their frequency, their phase, or both ( I , 2). Motion or flow of the nuclear spins during application of these spatial encoding gradients can give rise to image artifacts (3, 4 ) . Conversely, a detailed understanding of the origins of motion artifacts and how to suppress them yields insights into methods for flow sensitization and flow measurement in MRI. We emphasize basic principles, rather than the details of individual techniques, and methods that yield quantitative information about velocity distributions. Techniques that simply discriminate between stationary and flowing material, although of importance in MR angiography (5, 6), are not discussed except in so far as they may be adaptable to quantitative flow measurement.

In this article we outline various approaches to flow imaging.

We confine our attention to Fourier imaging methods that use spin echoes (or gradient echoes) for signal acquisition. A basic spin-echo Fourier imaging sequence, similar to that most commonly used in MRI, is shown in Fig. 1. Spatial discrimination is achieved by applying magnetic field gradients -Gslice, GPhe,,, and G,,-along orthogonal axes x , y, and z in three stages as follows:

(1) To excite spins in a slice that is normal, for example, to the z direction, a magnetic field gradient G,, = G, is applied simultaneously with a narrow bandwidth (soft) 90" rf (radio-frequency) excitation pulse. The position and thickness of the excited slice are controlled by the frequency and bandwidth, respectively, of the excitation pulse and by the strength of the gradient.

* To whom correspondence should be addressed.

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(2) A stepped phase-encoding gradient G,,, = G, is then applied prior to the 180" refocusing pulse. If we consider just the component of the NMR signal that arises from a particular sample volume element (voxel), this modulates the phase of the signal by an amount proportional to the Y coordinate of the voxel from which it is derived.

(3) Finally, the echo signal is acquired in the presence of a readout gradient, G,, E G,, which imparts to each signal component a frequency proportional to the X coordinate of the corresponding voxel. A similar gradient lobe applied symmetrically in advance of the 180" refocusing pulse ensures that stationary spins are refocused at the echo peak.

900 180 O ECHO

I - I I

Figure 1. A standard spin-echo Fourier imaging sequence with slice selection on both 90" and 180" rf pulses and a stepped phase-encoding gradient. None of the gradients is flow compensated.

The total NMR signal S(t ) is then a sum of contributions to the transverse magnetization from all the voxels contained within the sensitive volume of the rf coil. In the limit where the voxels are small enough that we can ignore any phase variations across a voxel (as implicitly assumed above), we can write this sum in the form of an integral:

s(t) = JM(r-,t)ei+(Ls1) d L [11

M ( r , t ) is the transverse component of the sample magnetization at position 1: and time t; +(c, t ) is the corresponding phase angle of the nuclear spin precession.

We will see that each of the above processes used to achieve spatial discrimination in a conventional imaging sequence (slice selection, phase encoding, and frequency encoding) can be adapted to provide flow sensitivity. Thus, flow-imaging methods can be classified into three groups:

(1) inflow/outflow methods, which monitor changes in signal intensity resulting from motion of spins into or out of the selected slice

(2) time-of-flight techniques, which distinguish different velocity components by frequency encoding their displacements during the imaging sequence

(3) phase-encoding methods, which make use of flow-dependent phase shifts to provide velocity information directly

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It follows that to understand the basis of flow-imaging methods we must first consider the effects of time-dependent magnetic field gradients on the NMR signal in the presence of motion of the spins.

MOTION OF SPINS IN A MAGNETIC FIELD GRADIENT

Consider a nuclear spin of magnetogyric ratio y that is subject both to a uniform static magnetic field in the z direction B, = BoZ and to a gradient G = (aB,/ax, aB,/ay, aB,/az), such that the strength of the magnetic field varies with position r according to

- B(r) = l3, + 121

We assume that II. = l3, at the origin ( r = 0). As a rqsult of the gradient, the Larmor precession frequency of the nuclear spin becomes position dependent

where w, = yB, is the precession frequency in the absence of the applied gradient. Hence, a spin at r will gain phase relative to a spin at the origin at a rate

Integrating, we obtain

4 ( t ) = y j S * r d t 141

Now the component z(t) of the spin's position along the direction of the applied gradient G can be expanded in terms of time derivatives of its value at f = 0:

151 n! [""I at , = 0

1 a 2 2 at

z ( t ) = zo + [ % ] , = , r + - [--4 t* + ... + - t n + ... For a spin that starts at zo and moves with initial velocity component vo = (az/at) ,=, along the gradient direction, its phase relative to a stationary spin at the origin will be

qj(t) = yzojG(t)dr + yv,lG(t)tdf + higher terms [61

In general, the phase of the signal will have both position- and motion-dependent contributions. For the case of constant-velocity motion, we have for the position-dependent phase

qj0 = yzojG(Wt = yMozo

qj, = yvojG(t)tdt = yM,v,

[71

and for the flow-dependent phase

[81

M, and M, are the zeroth and first moments of the magnetic field gradient; the n"' moment is defined by

t

M,, = IG(t)t"df 191 0

It is often convenient in NMR to view the precessing magnetization from a frame of reference rotating about the static field B, at a given frequency, which in this case without loss of generality, we can take to be wo. Then the phase angle qj is just the phase acquired by the spins as viewed from this rotating-reference frame.

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Waveform M o m e n t s Applicalionr

Phase encoding (Uncompensaied)

Frequency encoding (Uncompensated)

Flow encoding

IEW slicc sclcct (Uncompensated)

f

Figure 2. Some simple gradient waveforms, with corresponding moment values and typical imaging applications. For simplicity, only waveforms comprising rectangular gradient lobes have been included. In the case of frequency-encoding (readout) gradients, the moment values refer to the echo peak, which is assumed to be at the center of the acquisition lobe.

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GRADIENT MOMENT NULLING

It is clear from Eq. [8] that if the magnetic field gradient is applied in the form of a pulse, which is shaped such that the first moment MI = 0, then the phase of precession of a given nucleus and hence of the NMR signal will be independent of any constant-velocity motion of the spins. This is the principle of gradient moment nulling or flow compensation in conventional MRI (7-20). The process can be extended readily to constant or variable acceleration (jerk) motions, such as are experienced in the case of pulsatile flow, by ensuring that, in addition, the second and third moments of the gradient (M, and M,, respectively) are nulled by suitable choice of shapes for the corresponding gradient pulses or episodes.

Alternatively, by arranging that M,, = 0 (zero net area for the gradient pulse) but M, # 0, the phase becomes flow dependent but position independent, making it possible to distinguish between different spins on the basis of their flow velocity. This result forms the foundation of phase methods for flow imaging and flow velocity measurement. Some examples of simple gradient pulse shapes and their corresponding moment values are shown in Fig. 2. In the case of gradient episodes that include 180" pulses it should be noted that the effect of a 180" rf pulse, which inverts the sample magnetization in the rotating frame, is to reverse the sign of the corresponding phase angle, so that +(t) -, - + ( t ) . Figure 3 is an example of this effect for the case of a conventional 90" - 7 - 180" - 27 - 180" - ... multiple spin-echo sequence applied in the presence of a static-field gradient. In the presence of constant gradient, from Eq. [8], the flow-dependent phase of the transverse magnetization 4, increases as the square of the time elapsed since its creation by the 90" pulse

[lo1 = yvGJtdt = TyvGt2 1

The effect of the 180" pulses then is to bring about periodic reversal of this phase at intervals 27. At the time of the second echo (and subsequent even-numbered echoes), the flow-dependent phase passes through zero ( 2 2 ) .

4

3

2

1

0

-1

-2

-3

- 4

I FIRST ECHO

Figure 3. Variation of the phase &(t) of a moving spin with respect to that of a stationary spin (& = 0). for the case of a 90" (- T - 180" - T -)" multiple-echo sequence applied in the presence of a uniform static magnetic field gradient in the direction of the constant velocity motion. The moving spins are in phase with the stationary spin magnetization at the second echo (and at subsequent even-numbered echoes).

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FLOW IMAGING APPARATUS

To study quantitatively the effects of flow in NMR imaging under controlled conditions, a system capable of maintaining a constant flow rate over periods of minutes or hours is required. We have used the recirculatory flow system of Fig. 4 to obtain a range of images that illustrate some of the basic principles discussed in this article. The apparatus has an upper constant-head reservoir (marked " I " ) , the height of which can be adjusted to control the flow rate and the output from which can be passed through any of a range of flow phantoms. The flowing fluid [usually doped with a paramagnetic salt such as CuSO, (3 mM) to reduce its spin-lattice relaxation time T, ] , is returned to the lower reservoir, 2, from which it is pumped back to the top reservoir. Provided the rate at which the fluid is pumped back to this reservoir exceeds the flow rate through the phantom, the upper reservoir will overflow continuously, maintaining a constant head. The use of gravity to drive the flow through the phantom ensures a steady flow rate over long periods, provided that precautions are taken to remove air bubbles, which can create problems particularly at low flow rates. A typical flow phantom comprises a U tube of 2.2 mm internal diameter surrounded by stationary water in a 14 mm i.d. outer tube. All of the results in this article were obtained using this flow system in conjunction with a 4.7 T, 15 cm diameter, horizontal bore, superconducting magnet; Bruker MSL200 imaginghpectroscopy system; and microimaging probe with built in (unshielded) gradient coils that can achieve magnetic field gradients of up to 50 gausskm.

Reservoir 2

Figure 4. The constant-flow system and U tube flow phantom used to provide steady-state flow conditions for flow-imaging studies. A pump recirculates water from the lower reservoir back to the upper reservoir, the height of which is adjustable and which provides a constant head.

FLOW-COMPENSATED IMAGING SEQUENCES

The slice selection and spatial encoding gradients in the conventional spin-echo imaging sequence of Fig. 1 have not been flow compensated. As a result, signal contributions from moving spins will exhibit additional flow-dependent phase shifts 4l # 0, giving rise to flow or motion artifacts in the resulting image. These include the following two effects. Firstly, a voxel in which the spins exhibit a nonzero average velocity will give rise to a signal contribution whose phase is offset by the corresponding flow-dependent phase shift 41. This will have no effect on the spatial localization of the signal, provided that this phase offset does not change from step to step of the phase-encoding gradient. However, if the motion is cyclic or if the flow is pulsatile, ghost artifacts along the phase-encoding direction will result (3, 4) . Even in the case of steady flow, if the velocity of the spins has a component parallel to the phase-encoding gradient, these spins will be mapped to the wrong position in the phase-encoding direction (unless the gradient is flow compensated), and image distortion will result. Secondly, if there are significant variations

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of flow velocity across a voxel (resulting from regions of high shear in laminar flow, for example), the corresponding phase dispersion will result in loss of signal in the image.

Both of these effects can be removed or reduced by means of gradient moment nulling to yield a flow-compensated imaging sequence such as that illustrated in Fig. 5 . There, all three gradients (slice selection, phase-encoding, and frequency-encoding or readout) satisfy the condition that M, = 0 in each case, so that the phase of the signal at the spin echo peak is independent of any constant-velocity motion. Note that only the 180" rf pulse has been made slice selective in this single-slice imaging sequence. This is done to minimize image artifacts resulting from inflow/outflow effects, which arise because, in the presence of flow normal to the image plane, spins can enter or leave the selected slice during the time between the excitation and the refocusing pulses. If both pulses are slice selective, those spins with relatively high velocity components normal to the image plane may experience only one of the pulses, leading to anomalies in image intensity. However, such problems can be greatly reduced by use of a nonselective (hard) 90" pulse that excites all spins within the volume of the rf coil. An example of the effects of flow compensation on the image of a simple flow phantom obtained with the pulse sequence of Fig. 5 is shown in Fig. 6.

900 180 O ECHO

Figure 5 . Flow-compensated pulse sequence using a hard (nonselective) 90" excitation pulse and a slice selective 180" refocusing pulse. All three spatial encoding gradients have been flow compensated in this case, although in practice it is usually necessary to compensate only the slice- and frequency-encoding (read) gradients because the duration of the phase-encoding gradient is usually short, allowing little time for flow-dependent phase shifts to develop. The flow compensation on the read gradient here corresponds to that shown in Fig. 2(v)(a), which is easiest to implement, but alternatives such as those shown in Fig. 2(v)(b) or Fig. 2(x) are better for suppressing out-of-slice magnetization generated by the hard 90" excitation pulse.

Alternatively, the 90" excitation pulse can be made slice selective, and a nonselective 180" pulse can be used. This offers the advantage that, ideally at least, only the magnetization from the selected slice is tipped into the transverse plane. In practice, rf (B,) and static-field (B,) inhomogeneities will result in an imperfect 180" pulse. As a result there will be a free induction decay (FID) signal after the 180" pulse, which results largely from out-of-slice magnetization. If

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Figure 6. Images of the U tube flow phantom obtained with uncompensated imaging sequences (top) and flow-compensated sequences (bottom). In the images on the left, the flow is normal to the image plane (peak velocity v, = 27 cm s-l). The images on the right show in-plane flow (v, = 14 cm s-I). In this case, the phase-encoding gradient was applied after the 180" pulse for the flow-compensated image and before it for the uncompensated image, leading to substantial geometric distortion in the latter case. Note also the loss of signal, particularly in regions of high-velocity shear, in the uncompensated images.

a symmetric, bipolar, frequency-encoding (read) gradient similar to that of Fig. 5 , [or Fig. 2(v)(a)], were used, this would refocus the FID to a gradient echo, which interferes with the spin echo, giving rise to image artifacts. Similar effects, albeit less severe, can result from out-of- slice magnetization generated by a hard 90" excitation pulse and refocused to a gradient echo by the flow-compensated frequency-encoding gradient of Fig. 2(v)(a). It may be worthwhile to use either the alternative symmetric frequency-encoding gradient of Fig. 2(v)(b) or the asymmetric gradient of Fig. 2(x). These offer the advantage of removing the unwanted gradient echoes, [provided that I G, I > 2G, in the case of Fig. 2(v)(b)], but they require the application of larger gradient amplitudes. In addition, the gradient amplitudes now depend on the separation of the gradient pulses and hence, in general, on echo time TE. Note that for the gradient scheme of Fig. 2(v)(b), by arranging that T, = ( 1 / 3 ) T , and G, = -3G,, moments up to and including the second are nulled. This "binomial" flow-compensated gradient sequence, first described by Keller and Wehrli (9), therefore compensates for constant-acceleration motion as well as for constant- velocity flow. For this reason it is particularly useful for imaging in plane flows where the direction of motion (and hence the component of velocity in the frequency-encoding direction) changes with time.

Flow compensation can correct for signal losses that result from velocity differences (both in magnitude and direction) between different spins within a voxel, but it cannot compensate for the effects of random variations in the velocity of a given spin with time - such as those associated with molecular diffusion, turbulent flow, and perfusion. Such processes give rise to irreversible attenuation of the echo amplitude and to a corresponding loss of signal from those regions of an image where the processes occur. An important consideration in flow imaging is to use as a starting point a basic sequence that is flow compensated, to distinguish such effects from signal losses that result from inadequate flow compensation. Typically, this implies that the slice selection and readout gradients must be flow compensated. Flow compensation of the phase- encoding gradient is less important because its duration is generally short.

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OTHER PRACTICAL CONSIDERATIONS

Another factor that can lead to image distortion in Fourier imaging is the time delay between application of the phase-encoding gradient (which encodes spatial position in one direction in the plane of the image slice) and acquisition of the echo signal in the presence of the readout gradient (which provides spatial discrimination in the second, orthogonal, direction). Image distortion will result when there is motion or flow that exhibits a component of velocity at an oblique angle to these two directions in the plane of the selected slice. The effect can be minimized by locating the phase-encoding gradient after the 180" pulse, in the case of spin-echo imaging, and by reducing the acquisition time by use of large spatial encoding gradients and correspondingly short dwell times. The effects of phase encoding before and after the 180" refocusing pulse on an image of in-plane flow and the effects of flow compensation can be seen in Fig. 6. In the in- plane flow image at top right, the phase-encoding gradient was applied before the 180" refocusing pulse, leading to substantial geometric distortion of the image from the flowing spins, in addition to the loss of signal that results from the absence of flow compensation in this image. In contrast, in the flow-compensated image at bottom right, the phase-encoding gradients were applied after the 180" pulse, leading to greatly reduced image distortion and minimal signal loss. Alternatively, provided that the direction of the oblique flow remains fixed within the image plane, this geometric distortion can be removed by arranging that the first moments of both the frequency-encoding and the phase-encoding gradients are zero at the echo peak (12, 13).

It is worthwhile also to consider the factors that determine the range of velocities that can be measured with MR. The upper limit of molecular displacements that can be observed in practice will be determined by the receiver coil dimension t ; the lower limit is determined by molecular self-diffusion (14). To observe a signal, the spins must remain within the receiver coil over the timescale of the measurement -the echo time 7''. Thus, the maximum velocity that can be measured is written as

For a given rf coil size, shorter echo times are necessary for the measurement of high flow velocities, which in turn implies that gradient echo sequences with short minimum TE values are more appropriate than are spin-echo techniques for imaging high flow rates.

At the other end of the scale, to be observable, the displacements that result from coherent motion or flow must at least be comparable to those of random self-diffusion. Because coherent motion increases linearly with time t (r = vt), whereas for coherent flow the root-mean-square displacement r,,, = m ( D is the self-diffusion coefficient of the spins under observation), the effects of flow are maximized at the longest observation times. In practice, observation times in spin-echo imaging are limited by the spin-spin relaxation time (T,) of the sample; for stimulated echo methods the limit is imposed by the spin-lattice relaxation time (T,). Thus, the minimum observable flow velocities are given by

H

vmin [s] for spin-echo imaging or

for stimulated echo imaging.

1131

In practice, this implies a minimum velocity of approximately 50 pm s-' for free water at room temperature (14).

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INFLOW/OUTFLOW METHODS

Anomalous changes in signal intensity associated with the flow of blood in arteries and veins have been recognized since the beginnings of clinical MRI. If the pulse sequence repetition time TR is too short to allow full recovery of the longitudinal magnetization (TR 7 T,), there will be partial saturation of signals from stationary spins. However, flowing spins that move into the image slice can be unsaturated and appear to be fully relaxed, giving rise to an anomalously enhanced signal intensity in the steady state. Such effects are particularly evident in short TR gradient echo sequences (3, 4) . In contrast, in spin-echo imaging sequences that employ slice- selective 90" and 180" pulses, moving spins that experience the 90" excitation pulse can move out of the selected slice before the slice-selective 180" refocusing pulse is applied. These spins will not contribute to the echo signal, and the corresponding vessel will appear dark in the image.

Enhancement of signal intensity by flow of unsaturated spins into the selected slice has been used by Kose et al. (15) to obtain quantitative profiles of the distribution of water flow velocity in pipes. The imaging sequence was preceded by a slice-selective presaturation pulse and by homospoil gradients (Fig. 7) to saturate stationary spins in the plane of the slice, which was chosen normal to the flow direction. In the version employed by Kose et al . , a double-echo sequence was used to ensure refocusing of the phase of the flowing spins in the presence of both the imaging (slice selection) gradients and the static-field (B,) inhomogeneity . However, provided that the B, field is homogeneous, a single-echo sequence with flow compensation of the slice selection gradient, as shown in Fig. 7, also can be used (16). Hard, nonselective 180" pulses are employed to ensure that transverse magnetization arising from spins flowing into the plane of the selected slice are always refocused to give an echo signal. Kose et al. (15) showed that the signal intensity increased approximately linearly with flow velocity up to a limiting value corresponding to that at which spins flowed completely through the selected slice during the interval 7d between the presaturation pulse and the 90" excitation pulse. However, in view of the fact that the signal intensity in such experiments is a function of spin density and the relaxation times T, and T, as well as of flow, inflow/outflow methods are suitable only for quantitative flow measurement when the sample itself is homogeneous. Even in such cases, it is important to ensure that if the flow path extends beyond the region of homogeneous B, field, the fastest

900 900 180° ECHO

I I

SPOIL I 7 n ' I i G*

Figure 7 . The pulse sequence described by Caprihan and Fukushima (26), which is similar to that used by Kose et al. (25) for quantitative flow imaging by the inflowloutflow method. Spins in the selected slice are saturated by the first 90" pulse and spoiler gradients. A flow-compensated imaging sequence applied to the same slice after a delay T, yields a magnitude image whose intensity is proportional to the number of spins entering the selected slice during this interval.

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flowing spins (velocity v,) have time to fully polarize in the magnetic field before reaching the selected slice. For a total path length L in the magnetic field B,, this implies

L Vm

3 5T, t 141 -

T, is the spin-lattice relaxation time of the flowing fluid.

TIME-OF-FLIGHT METHODS

Time-of-flight methods involve selectively exciting or magnetically tagging a particular group of spins in the flowing fluid and subsequently imaging the displacements of these labeled spins. They differ from inflow/outflow methods in that the slice or region that is imaged is different from that which is excited initially. The excited slice is chosen to be normal to the principal flow direction, whereas the detection slice can be parallel or perpendicular to the flow (Fig. 8). In the former case, the image reveals the distribution of displacements (and hence of velocities) along the line of intersection of slice selection and image planes. The latter maps the spatial distribution of spins with a particular velocity (or with a small range of velocities, determined by the thicknesses of the selected slices). An example of the first type of flow image is shown in Fig. 9. The imaging sequence is a double-echo modification of the spin-echo sequence described by Axel et al. (17) and shown in Fig. 10a. The sample is the simple U tube phantom described previously. In the single-echo sequence of Axel et al . , the 90" pulse is used to select a slice plane normal to the principal direction of flow. The subsequent 180" pulse then refocuses magnetization only from a slice parallel to the flow direction. The distribution of transverse magnetization created in the initial slice is then imaged by application of the usual phase- and frequency-encoding gradients in the plane of the second slice.

The purpose of our double-echo modification (Fig. lob) is twofold. Firstly, the use of the second echo rephases signal contributions from spins that are moving with constant velocity in the presence of static-field gradients, in this case resulting from B, inhomogeneities. Secondly, because the image represents the displacements of spins in a plane parallel to the flow direction, it is preferable to excite only the spins in this plane in order to suppress contributions from out- of-slice magnetization associated with imperfect slice selection pulses. This can be important when (as in biomedical applications) the flowing spins are confined to a small vessel surrounded by a large volume of stationary fluid - a situation modeled in our U tube phantom.

Figure 9 shows the displacement of the flowing water in the two arms of the U tube during the interval T, between the initial excitation and the peak of the second echo. The vertical band across the image represents the signal from stationary water in the outer tube. By locating either the peak or, ideally, the leading edge of the signal intensity along the horizontal flow direction and by measuring its displacement (in number of pixels) relative to the corresponding point of the undisplaced slice, the average flow velocity as a function of vertical position across the phantom can be computed. The only additional information required, besides the echo time T,, is the pixel spacing. In the case of the upper (inflow) arm of the U tube, the velocity distribution is parabolic, consistent with ideal laminar flow in this tube. For Poiseuille flow in a straight tube of circular cross section, radius R, the flow velocity at a point distant r < R from the center is given by

v(r) = TR2 =[1 - [+I2] t 151

Q is the volume flow rate, and the peak flow velocity ( r = 0) is just twice the average value. Under conditions of laminar flow, the flow velocities measured by NMR can be compared readily with calculated values obtained from measurements of the volume flow rate.

The flow profile in the lower (outflow) arm of the U tube deviates from the ideal parabolic In this case, the shape because of the effects of vortices produced by the bend in the tube.

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excitation slice was about 30 mm from the bend. The loss of signal intensity near the walls of the glass tube in the flowing water arises because, in the form of the sequence used here (Fig. lob), the slice selection and spatial-encoding gradients were not flow compensated, giving rise to signal cancellation in regions of high velocity shear.

Labeling slice /

r( / x

profile

L Z Flow

Figure 8. In general, spins are excited in a plane normal to the flow - in this case laminar flow in a cylindrical tube. The image slice can be normal to the flow, but displaced relative to it, to select for spins with a particular velocity or range of velocities, or it can be parallel to the flow direction. More generally, the image slice can be stepped throughout the region of interest to yield a three- dimensional image data set. Inflow-outflow methods can be considered as a special case in which the excitation and image slices are coincident.

Slice selection for time-of-flight imaging.

A major disadvantage of this two-dimensional (2D) time-of-flight imaging sequence is that it is necessary to know the precise location of the vessel of interest prior to imaging. Although this can be derived readily from a conventional transverse image of the sample, if there are several vessels intersecting the region of interest (as would often be the case in biological or medical applications), the flow-imaging sequence must be repeated for each vessel of interest. Alternatively, the image slice can simply be systematically stepped across the region of interest to generate a three-dimensional (3D) data set, although this is more time consuming.

Another approach involves dispensing with slice selection parallel to the flow direction, so that a projection image of the flow displacement across the selected slice, normal to the flow direction, results (18). Although this yields rapid results [particularly in the gradient echo version proposed by Kraft et al. ( I S ) ] , this method suffers from problems of distinguishing flow

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in overlying vessels and, in many practical situations, from dynamic range problems associated with the high signal intensity from stationary spins, where these predominate in the sample.

Figure 9. Time-of-flight image of the U tube phantom (v, = 21 cm s-*) obtained with the pulse sequence of Fig. lob. The bright band across the center of the image is derived from the stationary water in the outer (14 mm i.d.) tube that surrounds the 2.2 mm i.d. U tube. The parabolic flow profile in the upper (inflow) arm of the U tube is characteristic of laminar flow. Distortion of the arofile in the lower (outflow) arm results from the effects of vortices produced by the Ubend

1800 180' ECHO

Figure 10. (a) Single echo sequence similar to that described by Axel et al. (17); (b) double-echo sequence used to obtain the image in Fig. 9. For sequence 10a, the refocusing lobe of the slice selection gradient and the dephase lobe of the frequency-encoding gradient (both G, in this case) are merged. For simplicity, none of the imaging gradients has been flow compensated.

Pulse sequences for time-of-flight flow imaging.

In each case flow is assumed to be parallel to the z direction.

SPATIAL MODULATION OF MAGNETIZATION

A novel form of time-of-flight flow imaging involves tagging spins by presaturating the magnetization in orthogonal sets of planes to form a grid of dark lines across the image plane (19-21). In the form proposed by Mosher and Smith (20) , grid tagging was achieved by application of a DANTE pulse train (22) in conjunction with a magnetic field gradient. The DANTE sequence consists of a series of N equally spaced, unmodulated (hard) rf pulses of

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duration rW/N (rW is the duration of a hard 90" rf pulse). By successively applying two such composite 90" rf pulse trains (Fig. l l ) , in the presence of orthogonal magnetic field gradients (both in the plane of the image slice), the sample magnetization will be saturated in the form of a square or rectangular grid. The separation of lines in the grid is given by

G, is the magnitude of the tagging gradient, and T, is the delay between rf pulses in the DANTE sequence. The width of the grid lines is inversely proportional to the duration of the tagging sequence. This presaturation sequence is then followed (after a suitable delay fd to allow displacement of the tagged spins as a result of translational motion or flow) by a conventional (flow-compensated) imaging sequence (Fig. 11). A typical result obtained with this sequence for our U tube flow phantom is shown in Fig. 12. Note that the grid lines in the stationary water surrounding the U tube are undisplaced, as expected. By repeating the sequence for different values of the delay time fd , quantitative estimates of flow velocity can be obtained from the vertex-to-vertex displacement of the grid lines. The method is limited by the time taken to saturate the grid pattern, which must be short compared with both f,, and the spin-lattice relaxation time T, for the sample under study. Mosher and Smith (20), showed that the tagging time of order NT, could effectively be reduced by phase cycling even-numbered DANTE pulses by 90: which reduces the separation of the grid lines by a factor of four for a given total tagging time. For the reasons outlined above, the method is limited to the visualization and measurement of relatively slow flows. It should also be noted that, where the direction of flow is changing in the plane of the image slice (as in the case of the bend in the U tube), dephasing of the magnetization from the flowing spins and a consequent loss of signal will result, unless the imaging sequence is flow compensated for acceleration as well as for constant-velocity flows (7-10). This in turn inevitably results in longer minimum echo times TE and signal loss, particularly for samples with short T, values.

{T RF

Gt SEQUENCE

G R EAD

Figure 1 1 . The DANTE train of N equally spaced pulses, each of flip angle d 2 N , applied in the presence of a gradient in the plane of flow (and repeated in the presence of the orthogonal gradient, also in the flow plane), results in saturation of the spins in the form of a grid. This presaturation sequence is followed. at time r, later, by a conventional imaging sequence with slice selection gradient normal to the principal flow direction. Motion of the spins during t,, results in distortion of the grid pattern.

Pulse sequence used for the DANTE grid-tagging method (19-21).

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Figure 12. sequence of Fig. 1 1 . minimize turbulence in the bend of the U tube.

Image of the U tube flow phantom obtained with the DANTE grid-tagging Here the peak flow velocity was reduced (v, = 0.9 cm s-') to

PHASE METHODS

We showed previously that the application of a time-dependent magnetic field gradient at), for which the first moment

I

M , = [G(f ) td t

Mo = [Gyt)dt

0

is nonzero, gives rise to a velocity-dependent contribution to the phase of the NMR signal. If, in addition, the zeroth moment

t

0

is zero, this flow-dependent phase will be position independent. The simplest gradient episode that fulfills these conditions is the bipolar gradient of Fig. 2(ii) or Fig. 2(iii) (23). In general, for a bipolar gradient comprising two rectangular gradient pulses of duration 7 and separation T, with equal and opposite amplitudes *G, [or the same amplitude if separated by a 180" rf pulse as in Fig. 2(iii)], the net phase acquired by a spin moving with constant velocity y is given by

Thus, the additional phase generated by such a bipolar "flow-encoding " gradient is proportional to the component of flow velocity in the direction of the gradient. This can be used to measure flow velocity distributions directly by incorporating bipolar gradients in conventional, flow- compensated, imaging sequences. An example of a spin-echo-imaging sequence that incorporates a bipolar flow-encoding gradient in the slice selection gradient direction is shown in Fig. 13. All three spatial encoding gradients have been flow compensated, and the bipolar flow-encoding gradient comprises two lobes of the same sign [Fig. 2(iii)] placed symmetrically on either side of the slice-selective 180" rf pulse. In practice, these can alternatively be superimposed on the flow compensation lobes of the slice selection gradient [Fig. 2(iv)], to reduce the minimum echo time that can be achieved, other conditions being the same.

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900 n

180 O ECHO

Figure 13. A flow-compensated spin-echo imaging sequence with bipolar flow-encoding gradient suitable for flow imaging using the phase methods. Here the bipolar flow- encoding gradient is applied to the slice selection axis for imaging and measurement of through-plane flow. In tbis case it can be combined with the flow compensation lobes of the slice selection gradient. Alternatively, the flow-encoding gradient can be applied to the phase-encoding or readout axis to sensitize the sequence to in-plane components of flow velocity.

There are a number of alternative approaches to flow measurement using the phase-encoding method. They differ in the manner in which the data are acquired and processed. In the simplest approach, known as phase mapping (24), the image data are acquired in the presence of the bipolar gradient, using quadrature detection (25), so that both the in-phase and the quadrature components of the NMR signal are recorded. A complex Fourier transform is then performed in polar mode to generate maps of the magnitude of the NMR signal (the conventional image) and of the spatial variation of phase. Ideally, the signal intensity in a given pixel of this phase map is directly proportional to the local (average) velocity in the corresponding sample voxel, provided that the corresponding phase does not fall outside the limits -7r < I ?r beyond which phase wrapping or aliasing will occur. In practice, there will be other contributions to the signal phase, associated with imperfections in the pulse sequence, eddy current effects, and static (B,) and rf (B,) field inhomogeneity, such that in the absence of the bipolar flow-encoding gradient or of flow, the phase variation across the image will be nonzero and will vary with position. Fortunately, provided that this background phase variation is not so large as to produce phase wrapping, it can be removed by repeating the imaging sequence with the polarity of the bipolar gradient reversed and by subtracting the resulting phase maps obtained after complex Fourier transformation (26). This removes the background phase and yields a phase (or velocity) map proportional to 24".

Figure 14 is an example of such a phase map and of the corresponding raw data (before subtraction). Where there is no signal (e.g., outside the phantom) there are large fluctuations in the background because the phase of the noise is random. Such large signal fluctuations can be distracting, so they are removed by application of a "noise mask," which sets the phase to zero whenever the signal intensity in the corresponding magnitude image is below a predetermined threshold. (This has been done in the subtraction image of Fig. 14.) The method can be applied using spin-echo, gradient-echo (27), or stimulated-echo-imaging sequences. Gradient echo methods are more appropriate for high flow rates; stimulated echoes allow the measurement of

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very slow flow. A major problem with the technique is its limited dynamic range - in this case the requirement that the phase variation within each raw data set remain within the limits - 1 < 9 I a. In principle this requirement can be relaxed by application of phase-unwrapping algorithms, but such techniques are difficult to apply reliably, particularly in the presence of high velocity shear, where the phase can vary rapidly from pixel to pixel.

Figure 14. Flow image of the U tube phantom obtained with the phase-mapping method of Bryant et al. (24) , using the pulse sequence of Fig. 13. The raw phase map is shown at bottom left; the image at bottom right was obtained by reversal of the flow-encoding gradient and subtraction of the resulting phase maps. A noise mask has been applied to this image. The effects of image subtraction on the phase of the stationary signal (and the effects of the noise mask) can be seen in the profiles through the upper tube, shown at the top of the picture (v, = 5.5 cm s?).

An alternative approach (28) steps the magnitude of the velocity-encoding gradient through a range of values symmetrically disposed around that for which the phase of the flowing spins is uniform and independent of flow velocity - the flow-compensated value. Of course, the spatial- encoding (imaging) gradients, especially the slice selection and readout gradients, also should be flow compensated. A sample of stationary spins also can be incorporated and the phases of the flowing spins can be referenced to these as a means of compensating for eddy currents (induced in the cryostat and magnet windings), as a result of which, in practice, the phase of the stationary signal will be nonzero. In this way a phase map is obtained for each value of the flow-encoding- gradient amplitude, and the corresponding velocity map is obtained by linear regression of the phase versus M, on a voxel-by-voxel basis (28). The incremental phase between the steps of the phase-encoding gradient must not exceed f?r to prevent velocity aliasing. The technique can be expected to be more robust and the quantitative results more reliable than the simple 2D phase- mapping method for measurement of steady flows, but because it requires acquisition of a 3D data set it is more time consuming.

The technique can be extended to simultaneous measurements of coherent motion (flow) and incoherent motion (diffusion or perfusion). Note that the pulse sequence of Fig. 13 is an interlace between a flow-compensated imaging sequence (Fig. 5 ) and a conventional pulse field gradient diffusion sequence (29). Although the phase of the resulting echo signals reflects flow or coherent motion, the decay in signal intensity as the flow encode gradient is stepped from its initial value is determined by random incoherent motion, which gives rise to dephasing of the signal from a given voxel. Such phase spreading can arise from true molecular diffusion or from perfusive flow in which the flow within a voxel is distributed isotropically and its magnitude

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changes on a timescale that is short compared with that of the NMR measurement - in this case the separation of the bipolar gradient pulses T (30).

A particularly powerful approach to flow-diffusion imaging is the combined spatial (k-space) and dynamic displacement (q-space) technique of Callaghan el al. (31, 32). Here, k is a spatial frequency defined by

1 2?r k = -yG't

G' is the imaging gradient (i.e., the strength of the phase-encoding gradient Gp or readout gradient G,) and c is the corresponding time of evolution of the spin precession (i.e., the duration of the phase-encoding gradient 7 , or the acquisition time in the presence of the readout gradient t,, measured from the echo peak, respectively). q also is a spatial frequency, defined as

1 = - ~ G T 2?r 1191

where G is the amplitude of the flow-encoding-gradient lobe, of duration T , as defined previously. The Callaghan method differs from the linear phase regression technique essentially only in the manner in which the data are processed to generate flow and diffusion maps. In this case the bipolar flow-encoding gradient is stepped from its initial baseline value (ideally zero), in one direction only. The resulting data set is then Fourier transformed with respect to the spatial (phase-encoding and frequencylreadout) dimensions - the normal k-space transform - to yield a set of images corresponding to each step (q-value) of the flow-encoding gradient. However, this complex 2D Fourier transformation is performed in Cartesian mode, so that two sets of images, real and imaginary, are obtained. On the assumption that the isotropic incoherent motions are stochastic, described by a Brownian diffusion coefficient or, more generally, by a dispersion coefficient D, it can be shown that the resulting signal intensity in a given row of pixels along the q-space dimension, corresponding to a particular spatial location r, varies following (31, 32):

S(q,_r,T) = exp[-4?rZqZDTff] exp[ +i2?rqTv]

where T!, = T - (113)~. The complex q-space transform of this function is convolution

S(R,r,T) = (4?rDI;,,)-"exp

according to the

P O I

then given by the

1211

which corresponds to a Gaussian peak of standard deviation (2DTff))" centered at R = vT, in which R is the dynamic spatial dimension conjugate to q. The function S(R,_r,T) represents the statistical probability that spin in the voxel at _r will be displaced by an amount R in the direction of the flow-encoding gradient during the time interval T. Both the dispersion coefficient D and the average flow velocity v can be extracted in this experiment by performing a complex 3D Fourier transform on the raw data and by fitting the resulting data to a Gaussian function along the flow-encoding dimension, pixel by pixel. In general, the number of steps of the flow- encoding direction n, is kept small (typically 16) to minimize total imaging time, and the data are zero-filled in the q-space (flow-encoding) dimension to N points (typically 128 or 256) before transformation. The pixel value corresponding to the peak of the Gaussian distribution, k,, then yields values for the velocity map, and the mean velocity within the corresponding voxel is given by (32)

v = 2an,k,lNy~TG, I221

G, is the maximum value of the flow-encoding gradient. maximum kFWHM of the peak is related to the diffusion coefficient according to

In addition, the full-width, half-

D = (nDkFwHM)* I [(4Pn21?rZ)yz~2G: NZT] ~ 3 1

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Velocity maps obtained using this technique and displayed as stack plots are shown in Fig. 15. Figure 15a shows flow through our standard U tube phantom (peak velocity v, = 29 cm s-') measured using a gradient echo sequence; Fig. 15b shows flow over a single hollow-fiber membrane (0.8 mm 0.d.) at the center of and concentric with a 3.5 mm i.d. glass tube (v, = 3.94 cm s-'), measured with a spin-echo sequence similar to that in Fig. 13. In the latter case, the return path for the flow was through the annular space between the inner glass tube of approximately 5 mm 0.d. and an outer 7 mm i.d. glass tube.

Figure 15. Flow images obtained by the q-space imaging method of Callaghan et al. (31, 32), shown as stack plots. (a) U tube phantom (v, = 29 cm s-I) obtained with a gradient echo version of the sequence of Fig 13; (b) flow of water over a single hollow fiber (0.8 mm 0.d.) contained within a 3.5 mm i.d. glass tube and obtained with the spin-echo sequence of Fig. 13. v, = 3.94 cm s-'; the return flow is via an outer 7 mm i.d. glass tube.

While the velocity/diffusion-imaging method of Callaghan et al. is powerful and relatively robust, it is time consuming, because it requires acquisition of at least a 3D data set (two spatial dimensions in the plane of the selected slice and a third, q-space or flow/diffusion-encoding dimension). Dumoulin et ul. (33) note that, by acquiring just two 2D data sets, with the flow- encoding gradient reversed in the second set, and by subtracting the resulting data, signals from stationary spins are canceled and that from flowing spins varies sinusoidally with flow velocity (Fig. 16). The method differs from the phase-mapping technique in that data subtraction occurs

\ \ \ \ \

-S(-q,r I \ r 7 S(q.11 V\ \ \

PHASE OF SIGNAL FROM STAT JONAR Y SPINS So

Figure 16. Vector diagram showing the principle of the two-dimensional "phase modulation" version of q-space imaging (34). Signal from moving spins S(*q , r ) acquires additional flow-dependent phase *+" relative to that from stationary spins So. By reversing the polarity of the bipolar flow-encoding gradient (and hence the sign of q) , and by subtracting the resulting (complex) data sets prior to image transformation, the signal from stationary spins is canceled: that from the moving spins gives a resultant whose magnitude is proportional to sin+,.

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in the time domain prior to Fourier transformation. The transformation itself is performed in magnitude mode to yield an image whose intensity is given by

& is the flow-dependent phase of Eq. [17], and S is the amplitude of the signal in the corresponding pixels of the raw data sets. This method has-been adapted by Xia and Callaghan (34) for rapid velocity mapping of slow flows, such as those encountered in the vascular tissues of plants. Using this method they have measured flow rates as low as 45 pm s-' (34).

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Quantitative NMR imaging of flow