Magnetic resonance spectroscopy with sparse spectral sampling and interleaved dynamic shimming

Abstract

The present invention relates to a magnetic resonance spectroscopic imaging (MRSI) method, specifically to a magnetic resonance spectroscopic imaging method with up to three spatial dimensions and one spectral dimension. Interleaving dynamically switched magnetic field gradients into the spectroscopic encoding scheme enables multi-region shimming in a single shot to compensate the spatially varying spectral line broadening resulting from local magnetic field gradients. The method also employs sparse spectral sampling with controlled spectral aliasing and nonlinear sampling density to maximize encoding speed, data sampling efficiency and sensitivity.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows schematically the different time domain sampling schemes with interleaved gradient encoding modules (Encod): (a) full bandwidth equidistant sampling, (b) equidistant undersampling in the time domain (c) nonlinear spectral sampling with increasing spectral dwell time. The encoding block duration in case c) may increase or decrease monotonically, or change non-monotonically. The spacing of the encoding blocks symbolizes the spectral sampling raster. The increase in the size of the gradient encoding module symbolizes the increase in k-space encoding coverage and/or encoding gradient strength. Gradients and ADC sampling may only be applied during part of the encoding blocks. Spacing between encoding blocks is a guide to the eye.

FIG. 2 illustrates examples of encoding modules but not limited to these: (a) 1D encoding (b) 2D single-shot encoding (c) 3D single shot encoding.

FIG. 3 illustrates spectral aliasing as a function of the sampled spectral width when using linear sampling.

FIG. 4 shows a simulated short TE (15 ms) in vivo 3T spectrum with 4-fold aliasing showing dominant peaks from Cho, Cr and NAA. The water peak at 0 ppm has been omitted for clarity.

FIG. 5 shows a schematic PEPSI pulse sequence with compensation gradients along X,Y and Z-axes interleaved between each readout gradient of the PEPSI sequence (T_d=dwell time after sorting of even and odd echoes).

FIG. 6 shows a simulation of a spin-echo PEPSI high speed spectroscopic imaging pulse sequence with interleaved shim gradients that was implemented on a Siemens scanner. Alternating compensation gradient blips are applied along the Y- and Z-axes. Blips are interleaved with PEPSI readout gradients that are applied along the X-axis. This example of gradient compensation corresponds to method a (linear sampling). The ADC trace shows segments of data acquisition that correspond to a single spectral acquisition point and 1-dimensional spatial encoding. Alternating gradient compensation is thus applied between each spectral acquisition point to collect two sets of data—one compensated for local gradients and one uncompensated data set.

FIG. 7 is a water line width maps at 4 Tesla in vivo without (left) and with (center) linear gradient compensation. The composite map (right) shows more uniform line width across the slice.

FIG. 8: (a) Uncompensated 4 Tesla spectra from (a) posterior brain and (b) anterior cingulate. (c) The same anterior cingulate voxel after compensation shows much reduced line width. (d) Composite NAA map shows improved sensitivity in frontal brain.

DETAILED DESCRIPTION OF THE INVENTION

In MRS and MRSI the dwell time for spectroscopic encoding depends on the nucleus. In proton spectroscopy the spectral range is rather narrow (9 ppm=380 Hz/Tesla) and the necessary dwell time to encode the entire spectral range is on the order of 1.75 ms at 1 Tesla and 0.88 ms at 3 Tesla, which are commonly used field strengths. This is sufficient time between spectral encoding points to interleave magnetic field gradient pulses (FIG. 1,2). This is now common practice for high-speed MRSI (e.g. 9,10). Sparse sampling can be implemented such that the spectral dwell time for linear time domain sampling is increased at the expense of spectral aliasing. A key element of this approach is to select the spectral dwell time such that minimal loss of spectral information is incurred in the aliased spectrum (FIG. 3,4). Aliased data may be reconstructed using constrained spectral models. Alternatively, non-uniform sampling of spectral data points in time can be used and this approach can be combined with increasing the spectral dwell time to further reduce sampling density. The preferred implementation of this case involves the use of linear or nonlinear, but not necessarily monotonous, increase in spectral dwell time. Known approaches to design the sampling raster based on the known spectral pattern and to reconstruct the data include Kernel Density Estimation (42), the chirp Z-transform (43), the interlaced chirp Z-transform (44) and the non-uniform digital Fourier transform (45). The following methods may also be used to reconstruct the data: filtered backprojection, Generalized Fourier Transform, or parametric signal modeling (1-5).

The elongated spectral dwell time enables interleaving of gradient encoding modules into the spectroscopic acquisitionto sample additional data points between spectral dwell points, which convolves spectral information and information encoded by the new gradient encoding modules. While insertion of readout gradients has been customary for high-speed MRSI (e.g. 9,10), the extra time allows interleaving of additional spatial encoding gradients (e.g. to encode a second and third spatial dimension) and/or dynamic shim gradients into the k-t space trajectory (FIG. 1). More generally, extended k-space trajectories can be designed as a function of spectral acquisition time to compensate the effects of spatially varying local magnetic field gradients by acquiring multiple data sets that are shimmed for different regions.

Interleaving a series of alternating short gradient pulses, which counteracts the dephasing effects of local intrinsic gradients, into the spectroscopic acquisition is intended to improve overall spectral resolution. The amplitude of these gradient pulses increases with time in accordance with the increase in local gradient moments and the duration of these gradient pulses is either constant or may increase in time as the gradient moments increases. These gradient pulses can be inserted at regular intervals between each of the spectroscopic data points while maintaining linear data sampling (method a) or alternatively inserted at increasing time intervals while the frequency of data acquisition is adjusted accordingly as the data acquisition progresses (method b). As a consequence two (or more) data sets (subsets) with different gradient compensation parameters can be collected in a single acquisition to compensate local gradients in one or multiple spatial locations, thus obtaining more uniform narrow line width in the reconstructed spectroscopic data set. More generally, gradient compensation vector trajectories can be designed to serially compensate within a single gradient waveform a complex distribution of local gradient vectors. Ideally, the switched compensation gradients should consist of linear and higher order spatial components (i.e. an expansion of spatial harmonics) to increase compensation efficiency for regions with spatially nonlinear local gradients. The data sets obtained with different compensation gradients can be combined by selecting the data with the smallest line width in each location or weighted averaging, to achieve maximum overall sensitivity.

For method a the sampling frequency for each data subset is constant throughout and all spectral components are encoded with equal spectral width. For method b, the sampling frequency for each data subset decreases nonlinearly during the time course of the data acquisition due to the decreasing time intervals between gradient pulses for compensation. This method is advantageous, since it can be optimized according to gradient performance and gradient stimulation constraints. A limitation of linear spectral sampling is that the gradient slew rate of the blipped compensation gradients at the end of the readout train, which may lead to peripheral nerve stimulation. In order to increase SNR per unit time and unit volume and to reduce the possibility of peripheral nerve stimulation we will be using blipped compensation gradients that increase in duration during the readout gradient train. Specifically, the duration between consecutive readout gradients will initially be very short and increase in accordance with the required gradient moment for compensation. This will ensure that the data acquisition of the spectroscopic half-echo starts with high duty cycle, which maximizes SNR. The interleaving of compensation gradients is not limited to a single set of compensation gradients. In principle, multiple sets of compensation gradients can be applied, however, at correspondingly reduced spectral width and data acquisition efficiency. The benefit of this methodology is single-shot compensation of local gradients in one or more regions of interest, which is advantageous for 3D acquisition and 2D time resolved acquisition. A disadvantage of the method is the decrease in SNR per unit time as a function of the number of separately shimmed data sets and the reduced duty cycle of the data acquisition.

Nonlinear spectral sampling has the following features: Broad spectral components are thus sampled with full spectral bandwidth, whereas narrow spectral components are sampled with reduced spectral bandwidth. Narrow spectral components may thus experience aliasing, but in vivo spectra are composed mostly of broad components and relatively few narrow peaks. By using appropriate choice of the spectroscopic sampling bandwidth the spectral overlap of narrow peaks in the aliased spectrum can be minimized and spectral information can be more evenly distributed in frequency space. More generally, the sampling intervals can be adjusted to match the expected information density based on a priori modeling of the spectra. Known approaches to design the sampling raster based on the known spectral pattern and to reconstruct the data include Kernel Density Estimation (42), the chirp Z-transform (43), the interlaced chirp Z-transform (44) and the non-uniform digital Fourier transform (45). By adding prior information about the known spectral frequencies, line widths and line shapes a complete deconvolution can be achieved. To reconstruct such nonlinearly sampled data alternative reconstruction methods, such as filtered backprojection, Generalized Fourier Transform, parametric signal modeling or maximum entropy methods, may be used (1-5). The advantage of this method is that overall sampling rate can either be (a) decreased during the data acquisition to improve signal-to-noise per unit time and unit volume (b) kept constant, thus maintaining signal-to-noise per unit time and unit volume, while compensating local gradients without increasing measurement time or (c) increased at a controlled rate to minimize the penalty in signal-to-noise per unit time and unit volume with gradient compensation.

This method can be applied to single voxel localized spectroscopy to compensate local gradients in different parts of the voxel, or to spectroscopic imaging to compensate local gradients in different parts of the spectroscopic image. This acquisition can be combined with echo-planar spectra-spatial encoding, which is particularly well suited for this type of gradient compensation. This method may also be applicable to functional magnetic resonance imaging and high resolution in vitro magnetic resonance spectroscopy. We expect that future shim designs will incorporate active shielding, which will make this approach entirely feasible and provide increased flexibility for choosing optimum gradient trajectories for compensation of local magnetic field inhomogeneities.

The spectral aliasing approach has multiplet benefits beyond interleaved shimming, such as accelerating the following two applications.

Use of longer readout gradients enables much higher spatial resolution and/or reduced ramp sampling as compared to full spectral width sampling. This is particularly advantageous at high field where gradient slew rate limitations translate into substantial time spent on ramp sampling, which is inefficient in terms of SNR per unit time and unit volume. Furthermore, with large bandwidth trajectories the readout must be along the X-direction to avoid peripheral nerve stimulation. The use of longer readout gradients reduces gradient stimulation and thus permits readout along the Y-axis, which is the long axis of the brain. The phase encoding matrix in the X-direction can thus be reduced, which accelerates spatial encoding.

Interleaving of additional spatial encoding gradients, such as alternating phase encoding gradient blips between the readout gradients as described in (16) to acquire multiple k-space line per excitation to accelerate k-space encoding. Combining this approach with parallel imaging enables single-shot 2D spectroscopic imaging.

Interleaving can be done between adjacent readout gradients, which does not allow combination of even and odd echoes and results in first order phase errors, or between pairs of readout gradient to minimize first-order phase errors. Regridding in the k-t-plane is necessary to minimize first-order phase errors.

It is now of interest to assess the feasibility of applying this approach to the measurement of short echo time spectra where spectral information is much denser and spectral overlap is therefore much stronger than at long echo times simulated in FIG. 3. Tuning the spectral width to minimize spectral interference and overlap with residual water will become more challenging. The aim is to improve the separation of dominant multiplet resonances (inositol and glutamate) with LCModel fitting. Spectral interference, which is aggravated by J-modulation, is expected to be minimized at very short echo times. FIG. 4 shows a simulated spectrum at TE 15 ms at 3 Tesla with 272 Hz spectral width, which would allow 4-fold acceleration of phase encoding as compared to the conventional PEPSI sequence. The multiplet resonances are clearly separated from the singlets. Even multiplet resonances from inositol and glutamate are clearly distinguishable. Spectral fitting of multiplets under conditions of spectral aliasing is expected to be more robust at high field strength.

However, there are two obvious limitations with this approach: (i) Spectral aliasing puts high demands on the suppression of the water signal, which would appear in the center of the spectrum and on the modeling of macromolecular spectra. (ii) The Cramer Rao Lower Bounds of the spectral fit, in particular of the multiplets, are expected to be higher than with full spectral sampling, which will vary among multiplets depending on the spectral pattern. These increases need to be characterized as a function of spectral width to find minima that are suitable for in vivo studies.

Experimental validation of Single-Shot Gradient Compensation of Susceptibility Induced Line Broadening in PEPSI.

The new method was integrated into a Proton Echo-Planar spectroscopic imaging (PEPSI) sequence (9,10,14) and uses a train of alternating gradient pulses of increasing strengths, interleaved into the spatial-spectral encoding scheme, to simultaneously collect an uncompensated and a compensated data set (FIG. 5,6). Controlled spectral aliasing was used to overcome gradient slew rate and stimulation limitations. The NAA and the choline/creatine peaks now fall on the opposite sides of the water peak and can be deconvolved by suitable techniques.

The PEPSI method acquires two data sets in a single scan, a compensated data set for local gradients GI in regions that suffer from susceptibility related spectral line broadening and a non-compensated data set from magnetically homogeneous regions. The new method uses a train of alternating compensation gradient pulses G_c of linearly increasing gradient moment along all three spatial axes, interleaved into the spatial-spectral encoding scheme (FIG. 5,6). In order to compensate the kth readout gradient we require that the gradient moments observe (2k−1)G_lT_d=G_cT_c, where T_d is the dwell time after sorting even and odd echoes and T_c is the duration of the compensation gradient. However, gradient slew rate and stimulation limitations at the end of the gradient train require decreasing the spectral width, which introduces spectral aliasing. To control spectral aliasing to avoid interference of the major metabolite peaks the spectral width was selected as a function of field strength using a minimization procedure. The NAA and the choline/creatine peaks now fall on the opposite sides of the water peak and can be deconvolved by suitable techniques (FIG. 3).

Brain scans on 5 healthy subjects were performed on a 4 Tesla Bruker MedSpec scanner equipped with a Siemens console and Sonata gradients. PEPSI data were collected with TR: 2 sec, TE: 50 ms, spatial matrix: 32×32, pixel size: 10×10 mm2, and slice thickness of 15 mm. Water-suppressed (8 averages) and non-water-suppressed (1 average) data were obtained, resulting in 10 minute scan time. The compensation gradients were calculated based on phase difference images obtained from a dual echo gradient echo sequence. For Td=1.34 ms and Tc=0.73 ms (see FIG. 3), the maximum local gradient that can be compensate is 0.0426 mT/m. The maximum gradient amplitude (40 mT/m) with 256 readout gradients inversions is reached after 686 msec, which provides adequate spectral resolution at 4 T. The maximum local gradient strength that could be compensated with this approach was 0.0426 mT/m.

FIGS. 7 and 8 show improved line width and spectral quality with gradient compensation in anterior cingulate. Applying gradient compensation incurs an SNR penalty due to the decreased sampling efficiency and splitting of even and odd echoes, which is √{square root over (2(T_d/(T_d−T_c)))}. Furthermore, the use of linear compensation gradients limits the efficiency of this approach in regions with nonlinear local gradients.

To investigate the feasibility of linear gradient compensation in different brain region we obtained whole brain gradient echo phase at 4 Tesla in 9 subjects and examined histograms of the amplitude and angular distribution of local gradients in 4 brain regions. The dispersion of local gradients angles and amplitudes was much larger in ventral prefrontal cortex and inferior temporal cortex as compared to dorsal prefrontal cortex and medial inferior temporal lobe, which will thus be the targets of our method development.

Claims

1. An MRI apparatus that permits collecting a complete spectroscopic image with one spectral dimension and up to three spatial dimensions in a single signal excitation comprising: an RF pulse transmitting device to excite nuclear spins in a circumscribed region;a gradient pulse application device to encode k-space;an NMR signal receiving device;a spatial-spectral data collection, reconstruction and storage device; anda pulse sequence control device to generate a high-speed magnetic resonance spectroscopic imaging (MRSI) pulse sequence with interleaved spatial-spectral encoding that permits uniform sampling in the spectral and spatial domains

2. An MRI apparatus according to claim 1, wherein data are encoded with controlled spectral aliasing using a correspondingly longer dwell time between spectroscopic data points and with optimal selection of the spectral width to minimize loss of spectral information due to spectral aliasing.

3. An MRI apparatus according to claim 1, wherein the choice of spectral with is such that maximum separation of the spectral lines and in the case of proton MRS/MRSI, of the residual water peak, is achieved in the aliased spectrum.

4. An MRI apparatus according to claim 1, wherein increased spatial resolution is achieved using longer and stronger readout gradients and/or additional spatial dimensions are spatially encoded using interleaved phase encoding gradient pulses.

5. An MRI apparatus that permits collecting a complete spectroscopic image with one spectral dimension and up to three spatial dimensions in a single signal excitation comprising: an RF pulse transmitting device to excite nuclear spins in a circumscribed region;a gradient pulse application device to encode k-space;an NMR signal receiving device;a spatial-spectral data collection, reconstruction and storage device; anda pulse sequence control device to generate a high-speed magnetic resonance spectroscopic imaging (MRSI) pulse sequence with interleaved spatial-spectral encoding that permits nonuniform and sparse sampling in the spectral and spatial domains.

6. An MRI apparatus according to claim 6, wherein a spectral sampling scheme is designed based on a priori spectral model of the measured data, using a design methods based on one of the following approaches but not excluding related approaches: Kernel Density Estimation, the chirp Z-transform, the interlaced chirp Z-transform and the non-uniform digital Fourier transform.

7. An MRI apparatus according to claim 6, wherein a spectral sampling scheme is designed based on a priori spectral model of the measured data and reconstruction of localized spectra is achieved using on one of the following approaches but not excluding related approaches: Kernel Density Estimation, the chirp Z-transform, the interlaced chirp Z-transform and the non-uniform digital Fourier transform.

8. An MRI apparatus according to claim 6, wherein data sampling rate in the spectral domain decreases with increasing sampling time, enabling integration of increasingly longer spatial encoding modules that provide increasingly higher spatial resolution and/or encoding of additional spatial dimensions.

9. An MRI apparatus according to claim 6, wherein data sampling rate in the spectral domain decreases with increasing sampling time, enabling integration of increasingly longer spatial encoding modules that enable tailoring of k-space encoding as a function of spectral encoding time by extending data acquisition into k-space domains that encode k-space shifted group spin echo signals originating from regions that suffer from local magnetic field distortion, thus reducing the effects of local magnetic field inhomogeneity.

10. An MRI apparatus that permits collecting a complete spectroscopic image with one spectral dimension and up to three spatial dimensions in a single signal excitation comprising: an RF pulse transmitting device to excite nuclear spins in a circumscribed region;a gradient pulse application device to encode k-space;an NMR signal receiving device;a spatial-spectral data collection, reconstruction and storage device; anda pulse sequence control device to generate a high-speed magnetic resonance spectroscopic imaging (MRSI) pulse sequence with interleaved spatial-spectral encoding that permits uniform or nonuniform sparse sampling and interleaving of linear and nonlinear shim gradient pulses into the spatial-spectral encoding scheme.

11. An MRI apparatus according to claim 10, wherein data are encoded with controlled spectral aliasing using a correspondingly longer dwell time between spectroscopic data points and interleaving of a plurality of shim gradient pulses into the spectroscopic acquisition to compensate the increasing effects of local magnetic field inhomogeneities in multiple regions in a single shot as a function of spectroscopic encoding time, the gradient moment of each shim gradient pulse is designed to cancel the effects of local magnetic field inhomogeneity at that spectroscopic encoding time, the cumulative gradient moment of the plurality of these shim gradient pulses cancels periodically in synchrony with the dwell time for the spectroscopic data acquisition, the gradient moment of each of the shim gradient pulses increases linearly with spectroscopic data acquisition time.

12. A magnetic resonance spectroscopic imaging (MRSI) method that allows collecting a complete spectroscopic image with up to three spatial dimensions and one spectral dimension in a single signal excitation, comprising the steps of: spectral sampling with controlled spectral aliasing with optimal selection of the spectral width to enable faster spatial sampling in a interleaved spatial-spectral encoding and nonlinear spatial-spectral sampling density to maximize encoding speed, data sampling efficiency and sensitivity and to interleave additional spatial-spectral encoding into the spectroscopic encoding scheme to enable sampling of additional spatial dimensions in a single shot;interleaving of dynamic shim gradients into the spectroscopic acquisition; using generalized k-t-space trajectories that expand in k-space with increasing spectral sampling time t to compensate local magnetic field inhomogeneities; nonlinear sampling of spectral information; controlling spectral aliasing with optimal selection of the spectral width to enable faster spatial sampling in a interleaved spatial-spectral encoding method; andcontrolling spectral aliasing with optimal selection of the spectral width to enable sampling of additional spatial dimensions in a single shot.