Magnetic Resonance Imaging, Vol. I I, pp. 585-591, 1993 0730-725X193 $6.00 + .oO

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l Technical Note

FLOW-SELECTIVE PULSE SEQUENCES

J.M. POPE AND s. YAO

School of Physics, The University of New South Wales, P.O. Box 1, Kensington, NSW, Australia 2033

A series of pulse sequences is described which selectively excite signals only from flowing spins. The method is based on the binomial selective excitation sequences employed for solvent suppression in NMR spectroscopy, com- bined with 180“ refocusing of chemical shift and static field inhomogeneity effects and the application of bipolar gradients to distinguish stationary from flowing spins. The effectiveness of the method is demonstrated by experi- ments on a simple flow phantom.

Keywords: Flow selective excitation; Flow imaging; Stationary signal suppression.

INTRODUCTION

Pulse sequences which distinguish between signals from stationary and flowing spins are of interest in a num- ber of applications. In order to image flow in samples containing a high proportion of static spins, it may be necessary to suppress the stationary signal contribution in order that the flowing component may be accurately sampled with an analogue to digital converter of finite resolution. In angiography, it is important to remove the stationary signal so that the blood vessels can be adequately delineated in a projection image. Finally, with suitable static signal suppression it becomes pos- sible to employ techniques for flow monitoring that avoid the need for spatial discrimination, leading to faster sampling times than are available with imaging methods.

Approaches to static signal suppression’ include subtraction methods, in which two data sets are ob- tained for which the static signal contribution is ide- ally the same, while that from the flowing material is modulated, for example, by application of a bipolar “flow-encoding” gradient.1*2 Subtraction of the data sets then removes the contribution from the static spins. Alternatively, for example in steady state free preces- sion (SSFP) methods, it may be possible to saturate the signal from stationary spins, while contributions car- ried into the image plane by flow are refreshed and still contribute.’

In addition, a number of authors have investigated methods for selective excitation of signals from flow-

ing material only. 2zs In general these “flow-selective excitation” sequences are based on the application of a pair of pulses 90, - 7 - 90_, , with a bipolar gradi- ent pulse between them. The overall effect of such a pulse sequence on stationary spin magnetisation is to return it to the static field direction, while that from moving spins which acquires additional phase as a re- sult of the bipolar gradient is tipped partially or wholly into the transverse plane.

In this paper we describe a family of similar pulse sequences based on the “binomial excitation” sequences commonly employed for water or solvent suppression in NMR spectroscopy.6 A simple adaptation of these sequences to incorporate flow-encoding gradients re- sults in a set of pulse sequences for flow selective exci- tation. Analysis of the performance of the sequences, together with that described previously2T5 (which is a particular case of the simplest binomial flow-encoding sequence), shows that the latter is not optimal for flow selective excitation and measurement. Any of the se- quences described can be combined with standard im- aging methods to achieve flow imaging or quantitative flow measurement with stationary signal suppression in a single sequence.

THEORY

The binomial selective excitation methods of Hore6 comprise sequences of hard pulses separated by delays of the form:

RECEIVED 6/25/92; ACCEPTED l/8/93. Address correspondence to J.M. Pope.

585

586 Magnetic Resonance Imaging 0 Volume 11, Number 4, 1993

ex - 7 - kx

f% - 7 - 2e_, - T - ex

ex - r - 38_, - r - 38, - r - e+

where the pulse tip angles 0 are chosen to sum to 90” for each sequence and the sequences can be designated by a shorthand notation, e.g. 1331 for the third se- quence above, where the delays are omitted and the bars imply radiofrequency (RF) phase inversion of the corresponding pulse. In implementing these sequences, the dominant solvent peak is placed on-resonance so that the net effect of each of the sequences is to return the corresponding magnetisation to equilibrium along the static field B,. In contrast, off-resonance contri- butions from spectral components at chemical shift e with respect to the solvent precess during the interval between the pulses by an amount which depends on their frequency offset Ao = yB,a, giving rise to non- zero transverse magnetisation following the sequence. Thus the on-resonance solvent peak is suppressed, while chemically shifted peaks contribute to the, resulting spectrum by an amount which depends on the phase angle $ = Awr, through which the corresponding mag- netisation precesses during the delays between the pulses. These signals are maximised when 6 is an odd multiple of ?r. The sequences differ in the extent to which signals close to resonance are suppressed, the more complex sequences being most effective in sup- pressing a broad solvent resonance.6

The effect of a bipolar gradient pulse applied in the presence of flowing spins is to generate a flow- dependent phase shift 9 given by

4 = -yGAGv (1)

where 6 is the duration of each lobe of the bipolar gra- dient, A is the time between the start of the positive lobe and that of the negative lobe, G is the amplitude of each lobe, (assumed constant here) and v is the component of flow velocity in the gradient direction. Thus appli- cation of a bipolar gradient has a similar effect on flow- ing spins to that of a chemical shift in a stationary sample. By incorporating such bipolar gradients, (which we designate G G), in the binomial excitation sequences therefore, we obtain a family of flow selec- tive pulse sequences of the form:

l-GG-i

I-GG-2-GG-1

l-GG-3-GG-3-GG-I

where we have adopted the shorthand notation of Hare,’ representing an no, pulse by n and using bars to designate RF pulse phase or gradient reversal. Clearly the sequences are entirely analogous to the bi- nomial solvent suppression sequences, except that the phase acquired between pulses results from the action of the bipolar gradients rather than a chemical shift. Consequently, the sequences are flow-selective rather than chemical shift selective. Analysis of the first of these sequences by the product operator method7 shows that if the magnetisation has its equilibrium value M,, along the static field direction prior to appli- cation of the sequence, its components in the rotating frame after the sequence are given by:

M, = MO sin 0 sin 6 (2a)

My = tM,sin28[1 -COST] (2b)

M, = M,,[cos~ 0 + sin2 0 cos $1 @cl

Thus stationary spin magnetisation (4 = 0) is unaf- fected by the sequence and M, = MO (all e). For 0 = 7r/4, these results yield M, = (MO/a) sin 4 and M,, =

(M,/2)( 1 - cos 4) so that when I#I = r M,, = MO and the magnetisation is tipped along the Y axis by the pulse sequence.

The performance of the sequences has also been an- alysed using rotation matrices’ and results are shown in Fig. 1. As anticipated the more complex sequences give better suppression of transverse magnetisation Mxy = w for quasi-stationary and low veloc- ity flow. In all cases the transverse magnetisation in- creases monotonically with flow velocity up to that cor- responding to 6 = ?T, so that, assuming constant spin density and relaxation times for the flowing material, the signal intensity can be employed as a semi-quanti- tative measure of flow velocity, provided this limiting value is not exceeded. Also shown in Fig. 1 are results for the sequence 90, - r - 90_, first proposed by Nishimura et a1.2 Note that this corresponds to the first of the binomial flow selective excitation sequences if the pulse flip angle t9 is increased from 7r/4 to a/2. In this case the transverse magnetisation is maximised for 4 = *7r/2. However, this has the effect of halving the range of phase angles 4 (and hence flow velocities v) which can be accommodated for given gradient strengths and durations before maximum signal is reached. As is clear from Eqs. (2a-c), for this latter se- quence (0 = go”), when 4 = r/2 the net effect is to tip the magnetisation along the X axis in the rotating frame.

Incorporation of the flow selective pulses in conven- tion spin-echo Fourier imaging sequences is very

Flow-selective pulse sequences 0 J.M. POPE AND S. YAO

0 O-2 0.4 O-6 O-8 1 l-2 1.4 1.6 1.8 2 Q/n

Fig. 1. Calculated variation of the transverse magnetisation MXy = dm as a function of the flow-dependent phase angle @I = -yGAGu (see text) following application of the flow selective sequences 0 = 1 - GG - i with 0 = 90”, 0 = 1 - GG - i with 0 = 45”, o = 1 - GG - 2 - GG - 1 with 0 = 22.5”, A = 1 - GG - 3 - GG - 3 - GG - i with 0 = 11.25”. In all cases it is assumed that the sequences are applied on-resonance.

straightforward. For single-slice imaging, we have sim- ply replaced the 90” excitation pulse by one of our flow selective sequences, followed by phase and frequency encoding with slice selection on the 180” pulse in the usual way (Fig. 2A). For applications where the spin density within the flowing material is uniform and flow rates are constant or reproducible, it is also a simple matter to relate the signal intensity in the resulting mag- nitude images directly to flow velocity. Note that the signal intensity is proportional to the transverse mag- netisation Iw,, so that for the 1 - G c - 1 sequence with 8 = 45” we obtain from Eqs. (2a-c):

S(4) = + [sin24 + 2(1 - cos4)1”* (3)

which has a maximum value S, when 4 = ?r. For opti- mum flow sensitivity we choose G, A, and 6 such that the phase angle $J,,, corresponding to the maximum flow velocity lies in the range 7r/2 < b,,, < ?r. By em- ploying nonselective (hard) 8 = 45” excitation pulses, we also avoid inflow/outflow effects which would make S, itself flow dependent. Then by doubling the pulse flip angle to 0 = 90” and repeating the imaging sequence, we obtain a second image for which the sig- nal intensity is given by:

S’(6) =&sin+ . (4)

The signal intensities in this “calibration” image exhibit

maxima for which 6 = n/2. Provided the signal inten- sity/phase relationship for the first image is monotonic (i.e., r#~ < a everywhere), we can then relate these in- tensities directly to the flow-dependent phase angle (b and hence to flow velocity v via Eq. (1). We obtain

S(4) = (S,/&)[sin*6+2(1 -cos$)]“* (5a)

and

4 = cos-1[ -1 + J-=)2] (5b)

where S, = S’(7r/2) is the calibration value.

MATERIALS AND METHODS

The flow selective sequences described above have been implemented on a micro-imaging system based around a Bruker MSL 200 NMR spectrometer and 4.7 T superconducting magnet with 15 cm diameter horizon- tal room temperature bore. A flow phantom was con- structed from a glass capillary tube of 2.2 mm internal diameter and 1 mm wall thickness, bent into a U tube and inserted into a 15 mm diameter NMR tube. The latter was filled with stationary water doped with 3 mM CuS04, while a similar solution flowed through the capillary tube under gravity feed.

588 Magnetic Resonance Imaging 0 Volume 11, Number 4, 1993

ex 8-X 180

RF

GY

GX I

RECEIVER

A

eJ 18Oy OX 180

RF

GZ J I

GY

GX

RECEIVER

B

Fig. 2. Pulse sequences employed for flow imaging in con- junction with (A) 1 - GG - i and (B) 1 - G - 180“, - G - 1 flow-selective excitation sequences.

RESULTS

Typical transverse images of the phantom for the se- quences described are shown in Figure 3. The flow rate was estimated from measurement of the volume flow to be 6.0 cmesec-’ at the capillary tube centre, assum- ing laminar flow. The bipolar flow-encoding gradient strength G was 3.65 gauss/cm for Fig. 3A and 7.3 gauss/cm for Fig. 3B-D, with A = 6 = 1.5 msec in all cases, giving durations for the flow-selective excitation segments ranging from 1.8 msec for 1 - G G - 1 to 10.8 msecforl-GG-3-GG-3-Gd-i.Ineach case the spin echo occurred 9.8 msec after the final 8_, pulse. A sequence repetition time of 0.5 set was em- ployed which, with four excitations per phase-encod- ing step and a 128 x 128 matrix yields a total imaging time of 8 min 32 set for these magnitude calculated images.

Clearly the stationary signal suppression improves for the more complex sequences, as expected, but loss

of signal from slowly flowing material close to the walls of the capillary tube is also evident for these sequences. Poor suppression of signals from stationary material near the walls of the outer tube arises from static mag- netic field (B,) inhomogeneity, which results in mag- netisation from parts of the sample outside the region of homogeneous field acquiring additional phase. This problem can readily be overcome by incorporation of hard 180” refocussing pulses within the selective exci- tation segment3,4 to yield sequences of the form:

1 - G - 180°, - G - 1

1 - G - 180, - G - 2 - G - 180, -G - 1 etc.

Note that if 180, pulses are employed, the gradient re- versal and phase reversal of successive RF pulses must be omitted. The resulting transverse magnetisation then follows the ideal behaviour of Fig. 1. Alternatively, 180, pulses can be incorporated while retaining the RF phase reversals to yield transverse magnetisation of the same magnitude but inverted in sign.

A typical result is shown in Fig. 4 for the sequence 1 - G - 180°, - G - 1 of Fig. 2B, (with a pulse flip angle 8 = 45”), together with a similar image in which a 16-step phase cycle was employed to suppress the cen- tral artifact that arises from baseline offsets in the raw signal data. Also shown for comparison is the image resulting from application of the sequence 1 - G - 1 80°, - G - i , which tips the stationary spin magne- tisation into the transverse plane, (M, = kf, for 6 = 45” and 4 = 0), so that the full stationary spin signal results. Again the flow-encoding gradient strength em- ployed was 7.3 gauss/cm. Here A = 3.0 msec, 6 = 0.6 msec, TE = 14.0 msec, TR = 0.5 set and other condi- tions were identical to those for Fig. 3. Also shown in Fig. 4B is a profile through the centre of the upper cap- illary tube in the image of Fig. 4D. There is some loss of signal intensity in the lower (outflow) arm of the U tube here, which probably results from partial dephas- ing of the transverse magnetisation due to nonlaminar flow effects (Dean vortices) introduced by the bend in the U tube.’ The image plane was only 2-3 cm from the bend in the U tube here-insufficient to completely re-establish laminar flow in this case.

A plot of velocity against position obtained from a profile similar to that of Fig. 4B is shown in Fig. 5. Sig- nal intensities were converted to flow velocities by means of Eqs. (1) and (5), together with a 0 = 90” “cal- ibration image” to identify pixels corresponding to 4 = 7r/2, as described earlier. A parabolic fit to the data is included, consistent with the assumption of laminar flow. This assumption also yielded a maximum flow

Flow-selective pulse sequences l J.M. POPE AND S. YAO 589

Fig. 3. Images obtained from a flow phantom (see text) for comparing the performance of simple binomial flow selective exci- tation sequences (A) 1 - Gd - i with 0 = 90”, (B) 1 - GG - i with 0 = 45”, (C) 1 - GG - 2 - GG - 1 with 19 = 22.5”, and (D)1-Gd-~-G~-3-G~-iwith~=11.250.AllTR=0.5secand4averages.

rate at the centre of the tube of 11.9 cm-set-’ in this

case, based on the measured volume flow rate.

DISCUSSION

The extent to which these flow-selective pulse se-

quences are capable of suppressing signals from non- flowing material is demonstrated in Fig. 4 by the inclusion of the profile that shows the variation in sig- nal intensity along a horizontal line, through the up- per capillary tube of the image in Fig. 4D. Note that the profile includes regions of background noise from both outside the sample and within the wall of the in- ner glass tube. Clearly, the stationary signal is almost completely suppressed across the full field of view. We emphasize that these are all conventional magnitude calculated images and that stationary signal suppres- sion is achieved in a single imaging sequence without flow-encoding gradient reversal. The method can, there- fore, be expected to be inherently less prone to artifacts arising from sample or patient motion than techniques

which rely on addition or subtraction of separate im- ages for stationary signal cancellation. Effectively, with these techniques, the stationary signal is nulled on a timescale of milliseconds. The use of magnitude images also removes problems of phase roll, which result when binomial excitation sequences are employed for solvent suppression in spectroscopy. In view of the excellent stationary signal suppression achieved when 180” re- focussing pulses are included in the basic sequence, there appears little need to employ more complex se- quences such as 1 - G - 180, - G - 2 - G - 180, - G - 1, which inevitably result in longer TE values and corresponding loss of signal intensity for the flowing material. The inclusion of 180” refocussing pulses does, however, render the sequences more sensitive to inho- mogeneity in the RF field B,, although this was not significant in the examples shown here. The more com- plex flow-selective sequences may, however, have ap- plication in MR angiography, where longer TE values would assist in suppression of residual background sig- nals from stationary tissues, which generally have

590 Magnetic Resonance Imaging 0 Volume 11, Number 4, 1993

Fig. 4. Effects of incorporating 180’ re-focussing pulse in the flow-selective sequences. (A) 1 - G - 180”, - G - 1, (C) G- 180”, - G - i, (D) as (A) with a 16-step phase cycle applied. (B) is a profile through the upper capillary tube in (D). TE = 13.8 msec as measured from the first BX pulse and TR = 0.5 sec.

t t

s Y

VELOCITY AGAINST POSITION

12

10

8

6

r,

2

0 1 5 10 15 20 25 30

PIXEL NUMBER

Fig. 5. Variation of flow velocity along a line through the centre of the upper tube (inflow side) of our flow phantom. q = Experimental points obtained from an image similar

to 4(D). + = Parabolic fit to the data based on the assump- tion of laminar flow. In this case the maximum flow rate estimated from the volume flow was 11.9 cm. see-’ . Pixel spacings were approximately 120 pm.

l- All

shorter T2 relaxation times than the corresponding flow material (physiological fluids). In such cases quan- titation of flow velocity profiles may be less important.

While we have chosen to demonstrate the effective- ness of flow-selective excitation sequences by incor- porating them in a conventional spin-echo imaging sequence, they are equally capable of inclusion in se- quences which employ gradient echoes for rapid imag- ing. The ability to obtain quantitative measurements of flow velocity, at least for situations where the spin density is uniform throughout the flowing material, is also significant. Standard phase methods for quanti- tative imaging of flow over a 2-dimensional slice are generally either based on phase mapping” or require a 3-dimensional acquisition in which the flow-encoding gradient is incremented” over a range of values. The phase images obtained with the former method gener- ally suffer from limited signal to noise ratio compared to magnitude images, while the latter methods are very time consuming. Here we have demonstrated a tech- nique for obtaining quantitative flow information

Flow-selective pulse sequences 0 J.M. POPE AND S. YAO 591

which employs only 2-dimensional acquisitions and magnitude transformation of the resulting data sets.

Acknowledgments-The authors wish to thank Mr. D. Jonas for tech- nical assistance and the Australian Research Council for financial support. A preliminary report of this work was presented at the Tenth Annual Meeting of the Society of Magnetic Resonance in Medicine, San Francisco (1991).

REFERENCES

Caprihan, A.; Fukushima, E. Flow measurements by NMR. Phys. Rep. 198195-235; 1990. Nishimura, D.G.; Macovski, A.; Pauly, J.M. Magnetic resonance angiography. IEEE Trans. Med. Imaging Ml- 5:140-151; 1986. Pauly, J.; Nishimura, D.; Macovski, A. Cancellation ex- citation for angiography. In: Book of abstracts: Fifth An- nual Meeting of the Society of Magnetic Resonance in Medicine. Montreal: SMRM; 1986: pp. 70-71. Moran, P.R.; Saloner, D.; Tsui, B.M.W. NMR velocity- selective excitation composites for flow and motion im-

5.

6.

7.

8.

9.

10.

11

aging and suppression of static tissue signal. IEEE Trans. Med. Imaging MI-6:141-147; 1987. Zur, Y.; Zou, X.; Neuringer, L.J. MRangiography with- out subtraction. Magn. Reson. Med. 19:361-372; 1991. Hore, P.J. Solvent suppression in Fourier transform nu- clear magnetic resonance. J. Magn. Reson. 55:283-300; 1983. Sorensen, O.W.; Eich, G.W.; Levitt, M.H.; Boden- hausen, G.; Ernst, R.R. Product operator formalism for the description of NMR pulse experiments. Prog. NMR Spectroscopy 16:163-192; 1983. Mansfield, P.; Morris, P.G. NMR imaging in Biomedi- cine. New York: Academic Press; 1982. Drazin, P.G.; Reid, W.H. Hydrodynamic Stability. Cam- bridge University Press, 198 1. Bryant, D.J.; Payne, J.A.; Firmin, D.N.; Longmore, D.B. Measurement of flow with NMR imaging using a gradient pulse and phase difference technique. .I. Com- put. Assist. Tomogr. 8:588-593; 1984. Callaghan, P.T.; Xia, Y. Velocity and diffusion imaging in dynamic NMR microscopy. .I. Magn. Reson. 91:326- 341; 1991.