NMR imaging with a rotary field gradient

JOCRNAL OF MAGNETIC RESONANCE

70, 157-162 (1986)

COMMUNICATIONS NMR Imaging with a Rotary Field Gradient SHIGERUMATSUIANDHIDEKIKOHNO Central Research Laboratory, Hitachi, Ltd., P.O. Box 2, Kokubunji, Tokyo 18.5,Japan Received April 1 I, 1986; revised June IO, 1986

In NMR imaging, there exist two principal methods of image formation: namely, the projection reconstruction method (I) and the Fourier zeugmatographic method (2). In both methods the basic principle of measurementis to project a spin distribution in a direction in real space. In other words, the direction of a field gradient is fixed during signal measurement. Here, a new imaging method will be demonstrated in which the direction of a field gradient is rotated during the measurement.Preliminary experimental results will be reported together with some unusual aspectsof the present method. Consider a two-dimensional (x, y) imaging experiment, for simplicity, and assume that the transversemagnetization of a liquid-like object immersed in a homogeneous static field is prepared at t = 0. No chemical-shift dispersion is assumed. If a vector field gradient rotating in the xy plane at an angular frequency, WG,i.e., G ,(t) = iG, + jG, = G(i cos uGt + i sin co&), is imposed on the object, the phase of the NMR signal traces a circle in the so-called k space,(k,, kJ (3, 4). The center and the radius of the circle are given by (k, = 0, ky = -rG/w,) and yG/wG, respectively. Signals thus measuredprovide no useful data that can undergo systematic data processingto yield a spin image. However, if the center of the circle is appropriately transferred to the phase origin, useful data can be obtained: The resultant signal directly provides symmetric circular phase information about the phase origin. A pulse sequencefor the symmetric circular measurement is shown in Fig. 1. After rf excitation, only the field gradient, G ,,, is applied. The direction of the vector field gradient, G ,, is fixed along the y axis. This leads to the signal phase being transferred to a preparatory phase location, (kx = 0, k,, = -yG/w& along the simplest of many possible pathways. Thus, the signal measured during the following field-gradient rotation traces a circle that is symmetric about the phase origin. Continuous measurement, as shown by dotted lines in Fig. 1, allows signal accumulation since the signal is periodic. The k spacerepresentation of the measurement is shown in Fig. 2. Taking measurementsafter changing either the amplitude, G , or the angular frequency, wG, (or a combination of both) permits a concentric set of circular signals to be obtained (Fig. 2). Such a set of signalscan be shown to be identical to that obtained by the usual projection-reconstruction method (3). Therefore, Fourier transformations ofthe circular signals along diameters and back projections of the transformed signals can yield a spin image. 157

0022-2364186 $3.00 Copyright 0 1986 by Academic Press,Inc. All rights of reproduction in any form reserved.

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excitation

,

signal sampling

I

’

. . . . . .. . . . . . . . . . .

R

IT (7tr! $-q

g

R

..

..,...,: ,.........

I

-y

FIG. 1. Pulse sequence for symmetric circular measurement in two dimensions (x, y). The application of GY shown by the shaded area results in the transfer (T) of the signal phase to a preparatory location. Signals are acquired during the following field gradient rotation (R).

Experiments were performed at 0.5 T operating an NMR imager (5) for protons. Two-dimensional (x, y) measurements were taken using a phantom consisting of two water-filled tubes, as shown in Fig. 3. The field inhomogeneity within the field of view (94 mm) was approximately 5 ppm. The pulse sequence in Fig. 1 was modified as shown in Fig. 4 to meet current capability of the imager. Sinusoidal waveforms of the field gradients were produced simply by converting computer-controlled rectangular waveforms using Bessel low-pass filters (24 dB/oct). For excitation, a 90°-7-180’

FIG.

2. Phase space representation of symmetric circular measurement shown in Fig. 1.

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FIG. 3. Two-dimensional phantom consisting of two water-filled tubes.

spin-echo sequence(Hi = 4 G) was employed instead of a 90” pulse to avoid signal detection under initial transients of the filtered gradient waveforms. Suitable adjustments of the gradient application tim ings allowed us to carry out effectively the same experiment as depicted in Fig. 1. The rotation frequency, wG/(27r),was set at 2 17 Hz and the amplitude, G, was incremented measurementby measurement from 0 to G,, = 10.9 mT/m by steps of AG = G&31 N 0.035 mT/m (32 steps). Signalswere sampled at a rate of 4.5 ps using 1024 points and are displayed in Fig. 5a. It can be seen that each signal is nearly symmetrical about t = rr/oG, and each half signal about t = 7r/(2wG)or t = 3~/(2w~). This is consistent with the fact that projections are the same when projection angle 0 = 0”, 180”, and 360”. The small asymmetry is likely to be due mainly to nonideal sinusoidal waveforms of the gradients and partly to static field inhomogeneity. Although transverserelaxation also contributes to the asymmetry, the effect is negligibly small in the present experiment becausethe proton T, of the phantom was about 100 ms. Note that the signals traced along the gradient amplitude axis correspond to the usual FIDs. Representative Fourier transformed signals,i.e., projections, are shown in Fig. 5b. A phantom image reconstructed from 5 11 projections (uGt = 0 - a) is shown in Fig. 6. Although the image quality is lesssatisfactory at the present stage,it can be improved by better shaping of the gradient waveforms. +--15ms

-

15ms +

excitation

Gx

GY

FIG. 4. Actual pulse sequence for preliminary experiments. Broken lines indicate computer-controlled rectangular waveforms of field gradients which were converted to sinusoidal waveforms using Bessel lowpass filters.

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(a)

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i%-FIG. 5. (a) Measured circular signals. (b) Representative projections obtained from data in (a) through Fourier transformation with respect to gradient amplitude axis.

The most interesting feature of the present method is the fact that portions of FIDs can be measured separately. Long-diameter circular signals correspond to a set of FID tails measured using the usual projection-reconstruction method, and short-diameter signals correspond to the heads (Fig. 2). This fact leads to some unusual aspects of the present method.

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FIG. 6. Phantom image reconstructed from 5 11 projections as shown in Fig. 5b.

First, the number of projections obtainable is determined by the number of signal sampling points. The image matrix depends on the number of measurements.These aspectsare in contrast to the usual projection-reconstruction method, where the measurement number determines the projection number and the number of sampling points defines the image matrix. The view width and theoretical spatial resolution in the present method are given by U&TAG) and o~/(YG~~), respectively. Second, it is noted that for each FID obtained with the present method the phase development (G development in this experiment) may be determined by the field gradient effect only, provided that the amplitude is varied as a parameter while the rotation frequency is fixed. Namely, as long as motional effects such as flow and diffusion can be neglected, it is possible to obtain an FID shape which is unaffected by field inhomogeneity and transverse relaxation. (Of course, if T2 is much shorter than the signal detection period, no FID can be obtained.) As a result, spatial resolution of a projection obtained from the FID is not directly degradedby the two effects. This is in contrast to the usual methods (1, 2) where a projection is directly distorted and broadened by them. Third, the circular signal can be expressedas (3, 4) s(t) = J dxdyp(x,y)exp iPT7

[

1

E COS(C@),

[II

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which can be rewritten as (6) s(f) = s dxdyp(-W’) 5

%z(i)"Jn(R)COs(~w~t).

n=O

PI

Here, p(x,y) represents the spin distribution, J,, is the nth order Bessel function of the first kind, R = m yG/wc, and E, is the Neumann factor (i.e., E, = 1 when r? = 0 and t, = 2 when IZ> 0). Equation [2] indicates that the signal is a superposition of frequency components over an infinitely wide frequency range. Their frequencies consist of integer multiples of the rotation frequency, n&(2?r), and their amplitudes depend on the Bessel functions and the spin distribution. As a result, to correctly detect the signal, the bandwidth for receiver filters must be set infinitely wide. However, a property of the Bessel functions relaxes the unrealizable requirement for the bandwidth: The range ofR is defined by the view width, the gradient amplitude, and the rotation frequency. Therefore, once the range is fixed in an experiment, the highest order of the Bessel functions that contribute to the summation in Eq. [2] with a contribution more than l/10000 can be estimated as 12N l.lR + 8.0 (6). Thus, in practice, a narrower bandwidth, (1 . 1R + 8.0)~&2?r), can be used with negligible loss of information. This reduces noise in signal detection. Nevertheless, it should be noted that usual filters which cause frequency dependent phase shifts are unsuitable for this type of experiments. This is because such phase shifts give rise to blurring with respect to projection angles. In the present experiment, the range of R was between 0 and 15.5. As a result, detection of up to the 25th order is sufficient, which corresponds to a bandwidth of 5.4 kHz. However, since a suitable filter that causes no frequency dependent phase shifts was not available yet, a crystal filter having a bandwidth of 25 kHz was tentatively used. No remarkable blurring is observed in the image shown in Fig. 6. Finally, it should be added that since it is essential for spatial selectivity that the vector field gradient is rotated relative to the object, the present method permits imaging of rotating objects if the field gradient is spatially fixed. A more detailed account of the present method will be reported later together with refined experimental results. ACKNOWLEDGMENT We thank K. Sekihara for some helpful discussions. REFERENCES 1. P. C. LAUTERBUR, Nature (London) 242, 190 (1973). 2. A. KUMAR, D. WELTI, AND R. R. ERNST, J. Map. Reson. 18,69 (1975). 3. S. JJUNOOREN, J. Magn. Reson. 54,338 (1983). 4. D. B. TH’IEG, Med. Phys. 10,610 (1983). 5. S. MATSUI, K. SEKIHARA, AND H. KOHNO, J. Magn. Reson. 67,476 (1986).

6. P. M. MORSEAND H. FESIBACH, “Methods of Theoretical Physics,” p. 1322, McGraw-Hill, New York, 1953.