Rapid in vivo proton shimming

MAGNETIC RESONANCE IN MEDICINE 18, 335-347 ( 1991 )

Rapid in Vivo Proton Shimming

ERIKA SCHNEIDER AND GARY GLOVER*

GE Medical Systems, PO Box 414, Milwaukee, Wisconsin 53201

Received April 2, 1990

A rapid and completely automated method of adjusting the magnetic field (Bo) homogeneity for in vivo proton spectroscopy and imaging is described. Bo inhomogeneity maps are generated by a gradient-recalled echo pulse sequence in which the frequency dispersion is chosen to eliminate the effects of the fat/water chemical shift. Low-order shim values are derived by magnitude-weighted least-squares fits to the Bo maps and automatically applied as DC offsets to the X , Y , and Z gradient amplifiers. Imaging with chemical shift selective saturation is used as a measure of the efficacy of the technique. Results indicate that AUTOSHIM improves the overall homogeneity; however, local high- order field distortions which cannot be corrected by linear gradients are generated by certain air/tissue and bone/tissue morphology. In such cases a “ZOOM SHIM” may be applied over a limited region of interest for local homogeneity improvement at the expense of other regions. It is suggested that such scans are a necessity for recording the homogeneity during clinical MR spectroscopy. 0 1991 Academic Press, Inc.

INTRODUCTION

With conventional spin-echo imaging, it is not necessary to perform in vivo shimming for each patient. However, certain sequences require more stringent homogeneity for proper operation, such as chemical shift imaging (CSI) spectroscopy ( I ) , other sequences with chemical shift selectivity (e.g., fat suppression by RF saturation) ( 2 ) , Dixon/Sepponen methods of fat/water decomposition (3, 4) , and ultrarapid scanning ( 5 ). Inasmuch as irregularly shaped subjects such as humans can have demagnetizing effects (6) which distort the field in the several parts per million range, such scan techniques may require in vivo shimming to make adaptive corrections.

Several methods have been developed for shimming large-bore imaging magnets. One approach uses CSI to derive a field map from which shim corrections can be obtained ( 7). A second technique, long used in classical spectroscopy, is to maximize the energy of the FID signal from some localized region of the subject by iteratively altering shim currents according to a simplex (8) or other feedback approaches. Other techniques use phase-sensitized imaging sequences to derive field maps ( 9, 10).

Two problems arise when applying the above techniques to in vivo shimming. The first is that the field of view over which it is desired to correct the shim often contains more than one chemical shift component (e.g., both water and lipid signals may be

* Present address: Dept. of Diagnostic Radiology, Stanford University School of Medicine, Stanford, CA 94305.

335 0740-3194/91 $3.00 Copynghl 0 1991 by Academic Press, Inc All nghts ofreproduction in any funn reserved.

336 SCHNEIDER AND GLOVER

present). If there is only a single component, the measurement is straightforward since the peak position in the spectrum provides the Bo information directly. Two components, however, can cause the correction algorithm to misinterpret the off-resonance of the signal from the shifted component as being due to shim or susceptibility error. The second problem with the previous techniques is that the procedures are generally lengthy and could cause unacceptable prolongation of the MR exam.

The conceptual solution proposed here to the problem of the two-component spectrum is to configure the measurement process such that the two components are rendered indistinguishably from each other. This can be done in a Fourier method by choosing the sampling frequency equal to the chemical shift. In this way the two lines are “aliased” on top of each other and background resonance offsets will show up identically in the fat and water species.

The aliasing method above thus solves the first problem. In order to address the second problem, i.e., the desire to obtain the BO information rapidly, we propose that the spectral information be obtained in just two acquisitions per phase encoding. This is possible for proton imaging since there are only two components of the spectrum to be aliased. The acquisitions are gathered as gradient-recalled echoes with small flip angles so that the TR can be minimized. While the aliasing method solves the problem of the chemical shift, as will be shown, it necessarily constrains the spectral frequency range of the measurements or dispersion to be exactly the chemical shift frequency (-3.2 ppm or -203 Hz at 1.5 T). Spectral components beyond this range are not unambiguously resolved. Thus the difficulty of extending the useful dispersion beyond the chemical shift range must be addressed.

In the following section we develop the theory for the new technique which is called AUTOSHIM. It is based on a gradient-recalled proton imaging sequence having two interleaved acquisitions with different echo times chosen such that the frequency range spanned by the measurement is equal to the fat/water chemical shift. Aliasing of components larger than the chemical shift is handled by fitting a low-order two-dimensional function to the derivative of the wraparound (aliasing) regions. Once the fit is obtained, coefficients for the integrated low-order polynomial are used to adjust the shim currents.

MEASUREMENT THEORY

Bo Measurement

results for echo time T , The gradient-recalled echo sequence used is shown in Fig. 1. The following signal

[I1 s(t, T ) = [ p(x , W ) e m G , ~ t e i 4 t + T ) e in(r + ?3e-(t+T)/T2dxdW,

where p is the effective (relaxation-weighted) density of spins in the selected plane and projected onto the G, gradient axis, o is a resonance offset due to chemical shift,

is a shim-induced offset, T2 is the spin-spin relaxation time, and the other symbols are defined in Fig. 1. We need only consider the x (readout) axis explicitly since the other directions play no part in the off-resonance phase encoding, and they may be buried within p .

RAPID IN VIVO PROTON SHIMMING 337

RF

I ...-_. , i.....'. I .

Gy I i.....:; . .. _.

s2 ; 0 '

(B 1 0 position, x

FIG. 1. Pulse sequence using gradient-recalled echoes.

FIG. 2. ( A ) One-dimensional Bo(x) plot showing arctangent aliasing for offsets + u F / 2 . (B) Spikes in 8Bo/8x at boundaries are easily removed during least-squares curve fit (shown dashed).

The general case of spatially distributed spectra is difficult to solve unless many measurements are obtained as a function of echo time, T ( 4 ) . However, water and lipid are the only two significant proton species in human subjects. Although in reality each component has a finite-width spectrum, a reasonable approximation is to consider the total spectrum to be composed of two delta functions. Therefore, we consider the density function to be

where p , and p2 are real-valued distributions of the two components, and wF is the chemical shift of p2 relative to p l . If the T2 apodization during the readout may be ignored, [ 11 becomes


where

x' = x + Q f y G , , [41

X" = X + ( W F + Q ) / y G x . P I Reconstruction of S( t ) contains two components:

[61 p ( x > = S( t)e-'yG*x'dt

p2 ( ,IQ ( x") T e l w ~ T e -T/TZ(x") s

- - (Xr)e~L2(~')Te-T/T2(~') +

The components are pixel-displaced according to [ 41 because of the resonance offsets due to Q and wF. Under typical imaging conditions, these displacements may be of the order of 1-2 pixels, and are therefore small enough to ignore for low spatial frequency shimming. Then the reconstruction is

p(x) = [ p l ( x ) + p2(~)e'WFT]e(1"(X)-'/T2(x))T [71 It is seen that the image P is complex because of the known phase factor from the chemical shift and the unknown phase shift from the background Bo off-resonance.

We now consider an experiment in which two data sets are collected with different echo times as shown in Fig. 1. For echo time T ,

PI = + p2e'W~T]e('"-'/T2)T [81 while for time T + AT,

p2 = + p2e'odT+AT)]e(ln-1/T2)(T+AT) [91 For this application, we are only interested in finding Q ( x ) . If we choose the echo time difference AT such that

wFAT = 2 ~ , [lo1

9 [ I 1 1

1121 Thus the difference in phase between the two reconstructions is directly proportional to the shim offset, Q. The densities of both chemical species and phase modulations due to chemical shift, etc., are common to both acquisitions and disappear in the phase difference image because of the judicious choice of echo time shift. Note that the T2 relaxation effect does not alter the field determination. Finally, the measured field, expressed in Hertz offset, is

then we have p2 = + p 2 e ~ ~ ~ T ] e ( ~ " ~ 1 / T 2 ) ( T + A T ) = p 1RATe-AT/T2 le

so that a phase difference image is generated as

A$ = arg(P2) - arg(P1) = G A T .

Bo(x, v) = A d x , v)w/2a, ~ 3 1 where UF = w F / 2 r ,

The time shift AT is dictated by the chemical shift frequency, u F . This frequency is also the maximum range of the phase difference image, since A$ = +a corresponds to +vF/2 . Thus if there are offset frequencies which exceed +vF/2, they will "alias"

RAPID I N VIVO PROTON SHIMMING 339

due to the 2a periodicity of the arctangent function, as shown in Fig. 2a. At 1.5 T, uF = 203 Hz, which makes AT = 4.9 ms.

One solution for resolving the aliasing is to unwrap the phase, keeping track of additive 2ir components. While this is reasonably simple in cases where the object being imaged is continuous, in practice the field of view may include regions with few protons or protons which yield little NMR signal. In such cases keeping track of the unwrap components becomes a difficult, two-dimensional topological problem.

A second solution, and the one employed here, is to eliminate the aliasing issue by realizing that the end result of the measurement process is to calculate gradients in magnetic fields. This calculation need only preserve the local differential character, and not the absolute field values, so that additive factors of 27r are unimportant. Accordingly, the curve fitting process described next uses derivatives of the field image, instead of the field image itself.

Curve Fitting

The phase difference image formed after reconstruction is an in vivo homogeneity map Bo(x, y ) . For AUTOSHIM applications, only linear field gradients are internally adjustable through the shim and gradient hardware. Thus if there were no aliasing discontinuities present as in Fig. 2a, a simple low-order polynomial least-squares fit would serve to provide shim correction coefficients. Note, however, that the equivalent information is available in the gradient image (dBo/dx, for one dimension) as shown in Fig. 2b, at all points except near the discontinuities. At such points the derivative is very large ( -vF Hz/pixel) and accordingly may be easily recognized and discarded in the curve fitting process. Thus by utilizing the derivative of the field it is straightforward to remove the arctangent aliasing and thus extend the shim correction range beyond +uP/2.

The assumed form of the inhomogeneity is a biquadratic function of the form

Bo(x, Y ) = a 2 ( ~ - xoI2 + ai(x - X O ) + ~ Z ( Y - YO)’ + ~ I ( Y - Y O ) + C. [I41

The actual fitting process is described in the Appendix. Its implementation allows a limited region of interest (ROI) to be selected for “ZOOM SHIMMING.”

Shim Adjustment

cancelled out. Thus we apply constant correction gradients, The terms al and 6, determined above represent linear gradients which are to be

AGx = - ~ I / ( T P )

AG,, = -h / (W) , ~ 5 1 where p is the pixel size. Similarly, the quadratic terms are

AG, = -a*/(-Yp2)

AG,, = - b z / ( - Y P 2 ) . [I61

Higher-order terms can be easily included by straightforward extension.


IMPLEMENTATION

The technique was developed on a 1.5-T system (GE SIGNA), and consists of the pulse sequence and a reconstruction / correction program.

Pulse Sequence

Figure I shows a diagram of the pulse sequence used. Two interleaved acquisitions are obtained with echo times T and T + A T . The resulting data set resembles a two- echo scan to the reconstruction algorithm. The two echoes correspond to PI (Eq. [ 81) and P2 (Eq. [ 91 ), respectively. The gradient axes shown correspond to an axial slice. In practice one or two additional planes can also be scanned in a continuous sequence by appropriate changes in the pulse program. The first moments of the gradient distributions in x and z are nulled (“flow compensation”) to reduce ghosting artifacts from moving blood. The TR used is 28 ms, so a one-slice scan (e.g., x y ) requires about 7 s with spatial resolution 128 X 256. If desired, the phase-encoding resolution (and scan time) could be cut by a factor of 4 and still maintain adequate fidelity for low-order shimming.

Analysis Algorithm

A reconstruction program was written to perform the magnitude and phase reconstructions, curve fitting, and shim download. The magnitude and normalized Bo images can be displayed and stored in the original image files. The Bo images are scaled so that one pixel intensity unit corresponds to I Hz (Eq. [ 131).

Once the curve fit is obtained and the linear shim corrections are calculated, the values are automatically downloaded as offsets to the x, y , and z gradient amplifiers. Present hardware implementation does not allow higher-order correction automatically.

EXPERIMENTAL RESULTS/DISCUSSION

AUTOSHIM was tested by performing a fat suppression imaging sequence using a selective rf saturation pulse, before and after an in vivo shim. Figures 3A and 3B show fat saturation images before and after the application of AUTOSHIM, respectively. The corresponding Bo images from AUTOSHIM are shown in Figs. 3C and 3D. After the shim procedure, the suppression in the posterior regions and near the eyes is improved, despite the fact that the shim and imaging planes are different. The increased homogeneity is also apparent in the Bo image.

The head image of a second volunteer indicates more substantial Bo inhomogeneity (Fig. 4A). After AUTOSHIM was applied, the Bo homogeneity map (Fig. 4B) was globally improved, although local inhomogeneities remained. Likewise, the fat saturation algorithm was somewhat more successful after AUTOSHIM removed the linear magnetic field homogeneities (Fig. 4C) than with the original shim values (Fig. 4D).

As seen in Fig. 4, local field inhomogeneities resulting from differences in magnetic susceptibilities have strong geometric dependencies and can cause saturation methods to fail. These local Bo inhomogeneities occur over a few centimeters, and because of

RAPID IN V l VO PROTON SHIMMING 34 1

FIG. 3. (A, B) Fat-suppressed images before and after AUTOSHIM on volunteer 1 . (C, D) Corresponding Bo field maps. Incomplete suppression noted in A (arrows) is improved by shim.

their high spatial frequency, cannot be completely corrected by linear gradients (Fig. 4B).

When a region of interest contains such local field inhomogeneities (an eye, or ear, for example), a “ZOOM SHIM” can be applied. An example is shown in Fig. 5 , where the global and ZOOM SHIM results are displayed. After AUTOSHIM was applied over the entire head (Fig. 5B), incomplete saturation of fat magnetization was measured (Fig. 5A). Since linear field adjustment did not provide adequate homogeneity over the regions of interest, local shim values were derived for a small region about the ear. Successful local field adjustment is possible (Fig. 5C, 5D); however, adequate homogeneity for fat suppression was only obtained for the slice on which the shim was performed (Fig. 6 ) . The large linear gradients required to ZOOM SHIM the ear resulted in water saturation occurring in the right posterior region. This is evidenced in both the magnitude (Figs. 5C, 5D) and the Bo (Fig. 5D) images. If images of multiple regions of local inhomogeneity are required, the Bo map resulting from the head shim can provide many ZOOM SHIM settings.


FIG. 4. (A, B) B, field map before and after AUTOSHIM was applied to volunteer 2, respectively. (C, D) Corresponding fat-suppressed images on volunteer 2 before and after AUTOSHIM. Note that little shim improvement was observed.


FIG. 4-Continued


FIG. 5 . ( A ) Fat-suppressed images after global AUTOSHIM for volunteer 2. (B) B,, map corresponding to A. (C) Fat-suppressed images for ZOOM SHIM near ear. (D) Bo map corresponding to C. Note that suppression is good in target ROI, but that water is saturated in the right posterior region of the brain due to severe inhomogeneity created there.

CONCLUSION

A rapid and completely automated low-order shim program has been demonstrated which solves the problem of in vivo shimming on water/lipid proton fields. The growing interest in fat-suppressed imaging, spectroscopy, and “instant” scanning should be well serviced by this technique. While the present implementation only adjusts linear shim components, the method could be readily extended to any order desired.

The chemical shift selective saturation and AUTOSHIM studies on two volunteers indicate that linear gradient correction of field inhomogeneity is not sufficient for all regions. Owing to surprisingly large geometric demagnetization effects, highly nonlinear gradients in field can occur. In the volunteers examined, AUTOSHIM improved the Bo homogeneity and chemical shift selectively over the default shim obtained with phantoms. Since regions of high local susceptibility cannot be globally removed by


FIG. 6. Fat suppression sequence with ZOOM SHIM, as in Fig. 5 , showing other slices. Only two slices received adequate fat suppression.

linear gradients, localized gradient shimming (ZOOM SHIM) is necessary to correct within a sub-volume of interest, perhaps at the expense of other regions within the same slice. Alternative fat suppression methods are being explored which use pixel- dependent phase corrections to the imaging data.

The Bo maps typically show substantial variations even in relatively homogeneous fields of view. In the axial Bo map shown in Fig. 4A, for example, the field variation from center to edge of the head was >3 ppm, while in the sagittal view more than 4 ppm was observed across the image. In abdominal and thoracic scans, as much as 7 ppm has been measured.

These results suggest that great care must be exercised when performing in vivo MR spectroscopy (MRS ) experiments, because the homogeneity can be severely compro- mised by certain tissue morphology. Therefore, it is suggested that MRS examinations or other sequences for which resonance integrity is important should include a map of the Bo homogeneity as a matter of course.


APPENDIX: CURVE FIT

The phase difference image formed after reconstruction is an in vivo homogeneity map Bo(x , y ) . For AUTOSHIM applications, only low-order gradients are readily adjustable through the shim and gradient hardware. Thus only linear and quadratic amplitudes are computed here from the measured field image, although extension to higher order is straightforward. Because of the 2a ambiguities, the fit is actually made with the spatial derivatives of the field, as explained in the text. We ultimately want the coefficients a;, and b, in

Bo(x, v ) = a2(x - xo)2 + ar(x - XO) + b2(Y - + h ( Y - Yo) + c, [ A l l where (xg, yo) is the center about which the field is expanded, and c is a constant offset of no importance to the shimming process.

Now define gradient functions B, and By

dB0 ax

B,(x, y ) = - = 2a2x + a, - 2a2xo,

and

These partial derivatives will contain delta functions at +vF/2 boundaries in the direction of the derivative (see Fig. 2b). Note that the constant term in the least-squares fit to aBo/ax contains a contribution from the parabolic component of Bo whenever the expansion is not centered at the origin. This contribution must be removed in order to make a linear correction without altering the parabolic term. The origin ( xo, yo) of the fit may be taken to be the center of gravity of the object, since the values chosen are of only second-order importance to the final result. This, in turn, may be obtained from the magnitude image A ( x , y ) . We have

We now perform a weighted least-squares fit to the function B J x , y ) and B y ( x , y ) separately. For the x direction, e.g., one has

aBo/ax = al + a 2 x , ~ 4 . 5 1 using A ( x , y ) for the weighted integration over y . This guarantees that only Bo values which are within the object are used. During this fit, the ROI can be chosen to be any subset of the imaging field of view if it is desired to shim over a limited portion of the subject. This is referred to as ZOOM SHIM.

With a, determined from the fit, the coefficients a, are obtained from equations [A.l] through [ A S ] ,

a2 = a 2 / 2 ,

a, = a2xO + a ] .

RAPID I N VIVO PROTON SHIMMING 347

These coefficients define the desired expansion for the field. Similar expressions hold for the y direction.

ACKNOWLEDGMENTS

The authors are grateful to Harry Profio for writing the gradient shim download subroutine and to Ann Shimakawa for supplying the chemical shift selective saturation pulse sequence. Bob Vavrek and Joe Maier have given useful feedback during trials of this technique.

REFERENCES

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8. W. W. CONOVER, in “Topics in C13 NMR Spectroscopy” (G. Levy, Ed.), Vol. 4, Chap. 2, Wiley, New

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Rapid in vivo proton shimming

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