MAGNETIC RESONANCE IN MEDICINE 6, 87-91 (1988)

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Fast MRI Data Acquisition Using Multiple Detectors

MICHAEL HUTCHINSON* AND ULRICH RAFF

Department of Radiological Sciences, University of Colorado Health Sciences Center, 4200 East Ninth Avenue, Denver, Colorado 80262

Received April 17, 1987; revised November 1, 1987

We present a novel imaging procedure using multiple receiver coils. This circumvents the sequential acquisition of signals required by conventional imaging strategies. The ad- vantage of this technique over existing subsecond imaging techniques is that (a) contrast can be maintained and (b) there is no magnetic field gradient switching involved. o 1988

Academic Press, Inc.

Although magnetic resonance is in wide use as an imaging technique, the time taken to construct the image is clearly an undesirable feature, although recently, considerable progress has been made in reducing imaging time (1-11). What all the current pro- cedures have in common is that they are based ultimately on two-dimensional Fourier transforms (2DFT; or the related back-projection technique) and furthermore employ only one (Helmholtz) detector. It has been shown that a reduction in imaging time using these procedures places certain restrictions on contrast (12).

In conventional 2DlT strategies, a spatial location is encoded using a magnetic field gradient in a particular direction. Thus, dipoles within the object will absorb and emit radiation at frequencies that correspond to their spatial location. However, these frequencies are not unique, and therefore entire lines of pixels within the object field are subject to the same magnetic field strength and absorb at the same frequency. Removal of this ambiguity requires the imposition of N different, and successive, field gradients. The set of N echoes then contains enough information to determine the amplitude of an emitter at a particular space-time point within the object. Comparison with a subsequent set of N echoes then leads directly to the relaxation parameters TI and T,, which are the quantities of interest. Current fast scan strategies employ es- sentially the same methodology but rely on reducing the flip angle of the dipoles in the object field (7, 8). Recently progress has been reported in shortening image ac- quisition times with partial flip angle imaging and short TR values, while maintaining the contrast obtained in longer TR sequences (10).

A novel procedure is outlined here, in which imaging time might in principle be reduced to a fraction of a second, without any change in contrast and without the need for magnetic field gradient switching. This is because all signals from the object are obtained simultaneously with a full 90" flip angle for the spin. The key innovation

* Present address: Ph.D. to M.D. Program (R-123), University of Miami School of Medicine, Miami, FL 33 136.

0740-3194/88 $3.00 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.

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is the introduction of N radio detectors arranged around the object (where N is the dimension of the image matrix). Each detector consists of a narrow loop, with a long axis parallel to the imposed fixed magnetic field Bo, and the minor axis perpendicular to the line joining the center of the array and the detector.

The procedure proposed here is as follows: there is only one magnetic field gradient, say in the x direction, g,. A given column within the object may be considered to consist of a set of pixels each experiencing the same incremental precessional frequency

with respect to Bo, where the gyromagnetic ratio, y, is defined to be 1. Different pixels may be distinguished according to their different distances from

fixed points distributed around the object. Define a point within the object field: r = (x, y), and denote the time-dependent magnetization at this point as

where p(r) is the spin density at point r in the object, and

for a conventional spin echo (13). Here TI and T2 are relaxation times, and are implicit functions of r. These quantities define the image. TR is the time between pulse se- quences. Consider a detector a located at one of the fixed points, and in particular the FID for this detector, denoted by SJt),

where FJr) is the amplitude at detector a of a source of unit amplitude located at position r within the object. Fa(r) is a "geometric factor" containing the amplitude dependence of the electromagnetic field of the emitted radiation. For a dipole source in the near-field limit (A 9 d) , this is just proportional to sin 8/d3, where 6' is the angle between the dipole source and the line joining the detector and the dipole source, and dis the distance from detector to source (14). (Note, however, that the signal is actually proportional to the line integral of the electromagnetic field around the loop of the detector. As the length of the loop tends to infinity, the signal becomes proportional to d-2 and as the geometry of the loop tends to a point the signal is proportional to d-3. For a detector of finite length and area the distance dependence of the field lies between these two limits. For computational convenience we have used the d-3 de- pendence but point out that in practice the exact line integral around the loop of finite dimensions should be calculated.) The Fourier transform of Eq. [4] is given by

S,(w) = s d 2 r L e-"'dtF,(r)M(r, t)cos(xg,t). [51

Splitting the cosine into real and imaginary parts and expanding M,

where the lower limit is taken to be 0 rather than -co, sincef(r, t ) = 0 for t < 0. Assuming that fvaries much more slowly in time than the exponentials (this is a

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U w ) = r2/2 f dYP(X, Y M X , Y , TE)FOI(X, Y ) . PI

or

We have performed a computer simulation to demonstrate the viability of this procedure. A 32 X 32 portion of a real TI-weighted image of a brain stem was used to define a matrix of TI ; i.e., T2 was taken to be long compared with T, so that Eq. [3] is a function only of Tl(r). Moreover, the spin density p(r) was taken to be consistent across the object so that the time dependence of the radio field is given byf(r, t). These values were then used to reconstruct the field radiated by the original object, i.e., &(t). The set of N matrices I;?) was constructed using the sin(6)/d3 dependence mentioned above. Here the indices (w, m) were used to determine the ( x , y ) location of the dipole, assuming a "line detector"; i.e., the width of the detector is taken to be negligible so that the electromagnetic field can be considered constant across the detector. The detectors were located along the edges of a square surrounding the object. The set of matrices A'") were then obtained by Fourier transformation of &(t), and the matrices F and A substituted into Eq. [9] to obtain p'"). This is the reconstructed image. In Fig. 1 a comparison is made between the original object and the reconstructed image. The difference matrix (1 part in 10,000) displayed in the lower part of Fig. 1 demonstrates that the reconstruction of this 32 X 32 matrix by our technique is correct. We note that the deviation from the original is greatest at the edges, but is in any case very slight.

In conclusion we have demonstrated the theoretical feasibility of fast data acquisition using multiple detectors. It has not escaped our attention, however, that at a practical level there are obstacles to be overcome concerning the arrangement of a large number of closely spaced detector loops around an object, most notably the problem of coupling between detectors, and that this problem requires imaginative solutions for its technical implementation. While it was not the purpose of this communication to suggest prac- tical implementation, we point out two possibilities. First, the coupling could be re-

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FIG. 1. A 32 X 32 matrix of a sagittal midbrain section (upper left) has been used to simulate the method. The reconstructed image obtained from the “simultaneous acquisition of 32 detectors” is shown on the upper right side. The difference matrix is displayed on the bottom: the difference matrix is scaled to 256 gray levels to emphasize the errors.

duced, using lower impedance coils by a time multiplexing procedure, in which the minimized coupling between the coils would be corrected by applying numerical methods to the approach outlined in (15). The time multiplexing would consist of sampling sequentially the N signals from the N detectors such that the Nyquist theorem is satisfied when the second sample of the first signal is obtained after completion of the first Nsample turn. Second, the coupling may be minimized using high impedance detectors (here, however, although amplification is not a significant problem at typical MRI frequencies, the low signal-to-noise ratio will limit the applicability). We point out that in both mentioned cases, low and high impedance input amplifiers (based on MOS FET, J E T , or BJT) could be used for the amplifying circuitry (16,17). However, this particular problem is beyond the scope of this paper.

Finally, we point out that if the coupling problem can be successfully overcome, it might be possible to employ a nest of large overlapping detectors, in which case the signal-to-noise ratio might be largely preserved.

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