Spectral Localization by Imaging Using Multi-Element Receiver Coils

Abstract

A new spectral localization technique for in vivo magnetic resonance spectroscopy (MRS) is introduced. Structural information extracted from anatomical imaging is utilized for defining compartments which provide the basis for spectral localization. Inherent spatial heterogeneity of multiple receiver coil elements is used along with optional phase encoding to resolve signals from different compartments. This technique allows a few compartmental spectra to be reconstructed from multi-channel data acquired with no or very few phase encoding steps, resulting in short scan time and high efficiency. Alternatively, this technique also allows a significant number of compartmental spectra to be reconstructed if sufficient phase encoding steps are used. A procedure is developed to semi-automatically generate a significant number of compartments of comparable sizes, which allows one to obtain spectra from small regions of interest with curvilinear shapes. This may be useful for obtaining spectra from relatively small stroke lesions or tumors. Phantom experiments and in vivo MRS of stroke patients have been performed to demonstrate this technique.

INTRODUCTION

Magnetic resonance spectroscopy (MRS) allows non-invasive investigation of metabolites in humans and has become increasingly useful in the study of several diseases, including cancer, stroke, multiple sclerosis, and Alzheimer’s disease. Localized single-voxel spectroscopy is still the best choice when quality of spectrum is the highest concern. Fourier-based chemical shift imaging (CSI) comes in handy when spatial variations of metabolites need to be investigated as it can obtain spectra from a rectangular array of voxels in a single study (1–3). In conventional Fourier CSI, spatial resolution is achieved by performing phase encodings in all spatial dimensions and spectral information is obtained by acquiring time-domain signal without any field gradient.

Multi-dimensional phase encodings are time consuming. The scan time limitation and signal-to-noise ratio (SNR) requirement limit the spatial resolution of conventional Fourier CSI to the order of 1 cm in most clinical studies. A direct consequence of coarse spatial resolution is the partial volume effect which affects a significant percentage of the CSI voxels in a study. It is also well known that discrete and finite sampling in the k-space leads to cross-voxel contamination in the image domain. For a two-dimensional (2D) CSI of a uniform object, about 24% signal in each voxel comes from its neighbors (4). Various techniques have been proposed to reduce the partial volume effect and cross-voxel contamination (4–9). One of these techniques, spectral localization by imaging (SLIM), makes it possible to reduce the partial volume effect, cross contamination, and scan time at the same time (5). In SLIM, an anatomical image of the subject is used to divide the subject into several compartments, each of which is assumed to have a spatially uniform spectrum. Spectra of these compartments may be resolved from data collected with a small number of phase encoding steps (e.g. 16 steps). In another technique (4), a hypothetical two-compartment phantom is numerically simulated. The square CSI voxels are redefined such that each redefined voxel is uniform inside. Numerical simulation shows that this redefinition of the voxel shapes reduces the partial volume effect and cross-voxel contamination.

Sensitivity encoded spectroscopic imaging (SENSE-SI) makes it possible to perform accelerated CSI using a multi-element receiver coil (10). In SENSE-SI, scan time can be shortened by reducing the number of phase encoding steps in each dimension. The spatial encoding information lost by under-sampling is recovered by exploiting the distinct spatial sensitivity of each coil element. Similar to other Fourier CSI techniques, SENSE-SI suffers from the partial volume effect and cross-voxel contamination.

In this work, we introduce a new technique (11) for performing MRS using a multi-element receiver coil. Similar to SLIM, the proposed technique uses structural information extracted from anatomical imaging to define compartments which provide the basis for spectral localization. Different from SLIM, the proposed technique uses inherent spatial heterogeneity of multiple receiver coil elements along with optional phase encoding to resolve signals from different compartments. The first goal of this work is to achieve short scan time and high efficiency by reconstructing compartmental spectra from data acquired with no or very few phase encoding steps. The second goal of this work is to achieve spatial resolutions comparable to conventional Fourier CSI but with much reduced partial volume effect and less cross contamination when a significant number of phase encoding steps are used. Since multi-element receiver coils are now routinely used in clinical MRS studies, it is natural to use the proposed technique to improve sensitivity and shorten scan time by taking advantage of the intrinsic high sensitivity and spatial heterogeneity of multiple small coil elements. The cross contamination originated from B₁ inhomogeneity is also eliminated without extra effort as coil sensitivity heterogeneity is naturally incorporated into the reconstruction. A fundamental limitation for the proposed technique is the assumption that each compartment has a spatially uniform spectrum. This assumption is often violated to some degree because uniform anatomical image intensity within each compartment does not guarantee a uniform distribution of metabolites within each compartment. Intra-compartment inhomogeneity will result in cross-compartment contamination. This problem could be alleviated in the future by using optimized phase encoding gradients as described in SLOOP (15) (spectral localization with optimal pointspread function).

THEORY

Experiments using the proposed technique can be performed with or without conventional volume localization. When no conventional volume localization is used, the entire volume of tissue is measured. In this work, PRESS (Point RESolved Spectroscopy) volume localization (12,13) was used. Because of volume localization, only spins inside the VOI contribute to the detected MR signal. The pulse sequence for the proposed technique without phase encodings is basically a single-voxel PRESS sequence except that the VOI covers a larger volume and a multi-element receiver coil is used to resolve smaller compartments within the excited VOI. In post-processing, the VOI is divided into curvilinear compartments based on anatomical images and other a priori information. Each of the compartments is assumed to have a spatially uniform spectrum. The time-domain MR signal D_m(t), received by the mth coil element, is given by

$$D_m(t)=\sum _{n=1}^N{S}_{m,n}{C}_n(t),m=1,2,\dots ,M,$$ [1]

where N is the total number of compartments and M the total number of coil elements; C_n(t) is the magnetization vector of the nth compartment; S_m,n is the integrated sensitivity of the mth coil element over the nth compartment,

$$S_{m,n}={\int }_{\text{compartment}n}{s}_m(\mathit{r})d^3\mathit{r},$$ [2]

with s_m(r) being the sensitivity of the mth coil element at location r. Eq. [1] can be expressed in a matrix form,

$$\mathit{D}=\mathit{SC}.$$ [3]

The dimensions of the matrices are M × P for D, M × N for S, and N × P for C, where P is the number of time domain data points for D_m(t) and C_n(t). In Eq. [3], D is the MR signal detected by each coil element, S can be computed from coil sensitivity maps, and C is the only unknown. The weighted least square solution of matrix C is given by

$$\mathit{C}=\mathit{FD},$$ [4]

where the unfolding matrix F is expressed as (14)

$$\mathit{F}={({\mathit{S}}^{†}{\mathit{\Psi }}^{-1}\mathit{S})}^{-1}{\mathit{S}}^{†}{\mathit{\Psi }}^{-1}.$$ [5]

In Eq. [5], Ψ is the noise covariance matrix of the coil elements and ‘†’ denotes conjugate transpose. The spectrum for each compartment is the Fourier transform of each row of C. Noise in C_n(t) can be computed by (14)

$${\sigma }_n=\sqrt{{[{({\mathit{S}}^{†}{\mathit{\Psi }}^{-1}\mathit{S})}^{-1}]}_{n,n}},n=1,2,\dots ,N.$$ [6]

If H phase encoding gradients are used, Eq. [1] becomes

$$D_{m,h}(t)=\sum _{n=1}^N{\stackrel{\sim }{S}}_{(m,h),n}{C}_n(t),m=1,2,\dots ,M,\text{and}h=1,2,\dots ,H,$$ [1a]

where D_m,h(t) is the MR signal received by the mth coil element at phase encoding step h; The integrated sensitivity S̃_(m,h),n is defined as

$${\stackrel{\sim }{S}}_{(m,h),n}={\int }_{\text{compartment}n}{s}_m(\mathit{r})exp(-i2\pi {\mathit{k}}_h•\mathit{r})d^3\mathit{r},$$ [2a]

where k_h is the k-vector due to the hth phase encoding gradient. The dimensions of D and S̃ are MH × P and MH × N, respectively. Correspondingly, Eqs. [3–6] becomes

$$\mathit{D}=\stackrel{\sim }{\mathit{S}}\mathit{C},$$ [3a]

$$\mathit{C}=\stackrel{\sim }{\mathit{F}}\mathit{D},$$ [4a]

$$\stackrel{\sim }{\mathit{F}}={({\stackrel{\sim }{\mathit{S}}}^{†}{\stackrel{\sim }{\mathit{\psi }}}^{-1}\stackrel{\sim }{\mathit{S}})}^{-1}{\stackrel{\sim }{\mathit{S}}}^{†}{\stackrel{\sim }{\mathit{\psi }}}^{-1},$$ [5a]

$${\sigma }_n=\sqrt{{[{({\stackrel{\sim }{\mathit{S}}}^{†}{\stackrel{\sim }{\mathit{\psi }}}^{-1}\stackrel{\sim }{\mathit{S}})}^{-1}]}_{n,n}},n=1,2,\dots ,N.$$ [6a]

In Eqs. [5a] and [6a], Ψ̃ is the expanded noise covariance matrix which is given by Ψ̃ = I_H ⊗ Ψ where I_H is an H × H identity matrix and ‘⊗’ denotes tensor product.

In order to evaluate signal-to-noise (SNR) performances, a sensitivity parameter “efficiency ” (15) is defined as

[7]

where ${\mathit{SNR}}_n^{\text{actual}}$ is the SNR of the nth compartment when the compartmental spectra are reconstructed using the proposed method; ${\mathit{SNR}}_n^{\text{ideal}}$ is the best-possible SNR of the nth compartment, which is computed as if the nth compartment was isolated from the rest of the sample and its entire magnetization was detected by the multi-element coil in H acquisitions without any phase encoding. The SNR ratio is inversely proportional to the noise ratio. Therefore, the efficiency parameter is also an indicator of noise amplification. Similar to the derivations of the SNR ratio in SENSE (14), efficiency is found to be

[8]

where [(S̃^†Ψ̃⁻¹S̃)⁻¹]_n,n is the actual noise variance and (S^†Ψ⁻¹S)_n,n is the inverse of the ideal noise variance with H = 1. If the number of compartments is greater than 1, the efficiency is always smaller than 1. Similar to SLOOP, when multiple compartmental spectra need to be acquired, an experiment using the proposed technique could be more efficient than the ideal experiment where the spectra of the hypothetically isolated compartments are acquired one by one.

As described by von Kienlin and Mejia (15) and Dydak et. al. (10), a “spatial response function (SRF)” can be used to better understand the mechanism of localization. The SRF for each compartment describes how each point in space contributes in magnitude and phase to the reconstructed compartmental spectrum. The SRF for the nth compartment is defined as

$${\mathit{SRF}}_n(\mathit{r})=\sum _{m=1}^M\sum _{h=1}^H{\stackrel{\sim }{F}}_{n,(m,h)}{s}_m(\mathit{r})exp(-i2\pi {\mathit{k}}_h•\mathit{r}),n=1,2,\dots ,N.$$ [9]

The signal contribution of compartment j to the spectrum of compartment n is computed as the integral of SRF_n(r) inside compartment j. Based on Eqs. [2a], [5a], and [9], it can be shown

$${\int }_{\text{compartment}j}{\mathit{SRF}}_n(\mathit{r})d^3\mathit{r}={(\stackrel{\sim }{\mathit{F}}\stackrel{\sim }{\mathit{S}})}_{n,j}={({\mathit{I}}_N)}_{n,j}={\delta }_{n,j},$$ [10]

where I_N is an N × N identity matrix and δ denotes the Kronecker delta function. Eq. [10] holds as long as the unfolding matrix F̃ can be found (15). From Eq. [5a], we can see that F̃ exists if matrix S̃^†Ψ⁻¹S̃ has N nonzero singular values, a condition that can be satisfied in almost all practical situations by choosing an appropriate phase encoding scheme in addition to utilizing the spatial heterogeneity of multiple receiver coil elements. Therefore, contamination-free localization is achieved under the assumption of uniform compartments. In practice, however, the assumption that each compartment has a spatially uniform spectrum is often violated to some degree. As a result, a localization that heavily depends on SRF signal cancellation outside the compartment of interest could be unreliable. A more robust localization will be achieved if the SRF has a low intensity outside the compartment of interest. A parameter for gauging the reliability of localization is defined as (15)

[11]

Because the integral of SRF_n(r) inside compartment n is exactly 1, the value of indicates how much signal intensity from the outside compartments, relative to the signal from inside compartment n, depends on phase cancellation to null its contribution to the spectrum of compartment n. A smaller will generally result in less cross contamination for compartment n in the presence of intra-compartment spatial inhomogeneity.

For comparison purpose, the SRF for conventional CSI using a multi-element receiver coil is also computed, which is given by (10)

$${\mathit{SRF}}_n^{\text{CSI}}(\mathit{r})=\sum _{m=1}^M[{({\mathit{S}}^{†}{\mathit{\psi }}^{-1})}_{n,m}/{({\mathit{S}}^{†}{\mathit{\psi }}^{-1}\mathit{S})}_{n,n}]s_m(\mathit{r})\frac{1}{H}\sum _{h=1}^{H}exp[-i2\pi {\mathit{k}}_{\text{h}}·(\mathit{r}-{\mathit{r}}_{\text{n}})].$$ [12]

In Eq. [12], ${\mathit{SRF}}_n^{\text{CSI}}(\mathit{r})$ (r) is the SRF for the nth CSI voxel; S is the integrated sensitivity of each coil element in each CSI voxel computed using Eq. [2]; r_n is the center location of the nth CSI voxel; (S^†Ψ⁻¹) _n,m / (S^†Ψ⁻¹S)_n,n is the optimal weighting factor for the signal contribution from the mth coil to the spectrum of the nth CSI voxel; $\frac{1}{H}{\displaystyle \sum _{h=1}^H}exp[i2\pi {\mathit{k}}_{\text{h}}·(\mathit{r}-{\mathit{r}}_{\text{n}})]$ is the discrete Fourier transform of exp(−i2π k_h· r), which results in the well-known sinc-like function.

METHODS

Phantom Experiments

Phantom experiments were performed on a Philips 3 T scanner (Achieva R2.6; Philips Healthcare, Best, The Netherlands). A two-compartment phantom consisting of 25 mM t-butanol in the inner sphere and 25 mM sodium acetate in the outer bottle was made in our lab (see Fig. 1). Two single-voxel spectra, one localized in t-butanol and the other in sodium acetate, were acquired separately using a single-channel transmit/receive head coil and a PRESS sequence (TR = 2 s, TE = 144 ms, VOI = 2 × 2 × 2 mm³, number of signal averages (NSA) = 48). These single-voxel spectra of the two solutions in the phantom are used as the standard, to which the spectra obtained using the proposed method will be compared.

Fig. 1.

Single-voxel MRS experiment of the phantom. TR = 2 s, TE = 144 ms, VOI = 2 × 2 × 2 mm³, NSA = 48.

The rest of the phantom experiments were performed using a Philips eight-channel SENSE head coil (Receive-only, coil diameter = 240 mm, foot-head coverage = 220 mm). Immediately after a localizer scan, a reference scan was performed to create the coil sensitivity maps. The reference scan used a gradient-echo sequence (TR = 4 ms, TE = 0.79 ms, FOV = 450 × 300 × 300 mm³, scan time = 30 s) to acquire data from the eight coil elements as well as the body coil. The initial coil sensitivity map for an individual coil element was computed as the ratio of the image obtained from the coil element to the image obtained from the body coil. The final sensitivity maps were created by fitting the initial coil sensitivity maps with a third order polynomial function to fill up areas where there is little or no signal.

After the reference scan, a 40-slice axial image of the phantom was acquired using a gradient-echo sequence (TR = 800 ms, TE = 10 ms, FOV = 240 × 240 mm², slice thickness = 3.5 mm). To acquire data for the proposed technique, a 2D PRESS CSI scan was prescribed based on the axial gradient-echo image. The pulse sequence parameters for the CSI scan were: TR = 2 s, TE = 144 ms, FOV = VOI = 50 × 90 × 14 mm³, NSA = 1, phase encoding matrix = 5 × 9, number of time points = 1024, and full spectral width = 2000 Hz. The 14 mm thick CSI slice covered exactly four slices of the axial image. The VOI was placed in such a way that the upper part of the VOI was in the inner sphere and the lower part of the VOI was in the outer bottle. The VOI is depicted as a green box on top of the gradient-echo image in Fig. 2. The k-vectors for the 5 × 9 phase encoding steps were given by

Fig. 2.

Compartmental spectra and SRF maps of the phantom computed using the proposed technique. The pulse sequence used TR = 2 s, TE = 144 ms, NSA = 1, VOI = 50 × 90 × 14 mm³. The VOI (green box), the user drawn compartment boundary (blue polyline), and two initial seed points (red dots) for region growing are depicted on the gradient-echo image. The compartment numbers are labeled on the compartment map beside the gradient-echo image. a: Compartmental spectra and SRF maps computed using single-shot data. Scan time = 2 s. b: Compartmental spectra and SRF maps computed using data with phase encoding matrix = 1 × 3 (h_x = 0, h_y = −1, 0, 1). Scan time = 6 s. c: Compartmental spectra and SRF maps computed using data with phase encoding matrix = 1 × 5 (h_x = 0, h_y = −2, −1, 0, 1, 2). Scan time = 10 s. d: Compartmental spectra and SRF maps computed using data with phase encoding matrix = 5 × 9 (h_x = −2, −1, 0, 1, 2, h_y = −4, −3, −2, −1, 0, 1, 2, 3, 4). Scan time = 1 min 30 s.

$${\mathit{k}}_h=(h_x\mathrm{\Delta }{k}_x,h_y\mathrm{\Delta }{k}_y),$$ [13]

where h_x = −2, −1, 0, 1, 2, h_y = −4, −3,…, 4, Δk_x = 1/FOV_x = 1/(50 mm), and Δk_y = 1/FOV_y = 1/(90 mm). Eight-channel CSI data were acquired from all 5 × 9 phase encoding steps, which gave us the flexibility to choose different number of phase encoding steps for different reconstruction schemes. Prior to the CSI scan, shim correction up to second order and chemical shift-selective (CHESS) water suppression were optimized for the selected VOI.

In Vivo Experiments

In vivo experiments were performed on the Philips 3 T scanner using the Philips eight-channel SENSE head coil. Two stroke patients were studied, both of whom were consented in accordance with procedures approved by our institutional review board. The pulse sequences for the localizer and reference scan were identical to those for the phantom experiments. A DWI sequence (TR = 4.5 s, TE = 62 ms, b-values = 0 and 1000 s/mm², number of diffusion encoding directions = 15, FOV = 240 × 240 mm², slice thickness of = 3.5 mm, number of slices = 40) was used to acquire axial images. The isotropic b = 1000 s/mm² DWI images were used to prescribe 2D PRESS CSI scans.

The first patient (male, 42 years old) had a large DWI lesion in the right middle cerebral artery (MCA) territory. The CSI scan was performed 24 hours after symptom onset. The parameters for the CSI scan were: TR = 2 s, TE = 144 ms, FOV = VOI = 110 × 50 × 14 mm³, NSA = 2, phase encoding matrix = 11 × 5, number of time points = 1024, and full spectral width = 2000 Hz. The VOI was placed in such a way that it covered both the right hemisphere lesion and the left hemisphere normal tissue. The 14 mm thick VOI covered exactly four DWI image slices. The VOI is depicted as a green box on top of one slice of the DWI image in Fig. 3.

Fig. 3.

Spectra and SRF maps computed using data from a stroke patient. The pulse sequence used TR = 2 s, TE = 144 ms, VOI = 110 × 50 × 14 mm³. a: Conventional Fourier CSI spectra for voxels 1, 2, and 3 (depicted on the DWI image), as well as SRF maps for voxel 1. Phase encoding matrix = 11 × 5, NSA = 2, scan time = 3 min 40 s. b: Compartmental spectra and SRF maps reconstructed from single-shot data using the proposed technique. Scan time = 2 s. c: Compartmental spectra reconstructed from 2 × 1 (h_x = 0, 1, h_y = 0) k-space data using the proposed technique, as well as SRF maps of compartment 1 computed using both the proposed technique and SLIM. NSA = 1, scan time = 4 s. d: Compartmental spectra and SRF maps reconstructed from 6 × 5 (h_x = −5, −3, −1, 1, 3, 5, h_y = −2, −1, 0, 1, 2) k-space data using the proposed technique. NSA = 2, scan time = 2 min.

The second patient (female, 75 years old) had a large DWI lesion in the left MCA territory. The CSI scan was performed 5 days after symptom onset. The CSI sequence had the following parameters: TR = 2 s, TE = 144 ms, FOV = VOI = 50 × 50 × 14 mm³, NSA = 2, phase encoding matrix = 3 × 1, number of time points = 1024, and full spectral width = 2000 Hz. The VOI was placed in the left hemisphere, which is depicted as a green box on top of one slice of the DWI image in Fig. 4.

Fig. 4.

Compartmental spectra and SRF maps computed using data from a different stroke patient. TR = 2 s, TE = 144 ms, phase encoding matrix = 3 × 1 (h_x = −1, 0, 1, h_y = 0), NSA = 2, scan time = 12 s. The VOI, user drawn compartment boundaries, and two initial seed points for region growing are depicted on the DWI image (b = 1000 s/mm²). The compartment numbers are labeled on the compartment map below the DWI image.

Post-Processing

Post-processing software was developed in-house using IDL (ITT Visual Information Solutions, Boulder, Colorado) and Visual C++ (Microsoft Corporation, Redmond, WA). This software provides the graphic user interface to display anatomical images with the option of overlaying the VOI box and the Fourier CSI grid on them. It also allows the user to manually draw polylines to define compartments. We will use Fig. 2 to explain how compartments are defined. After the axial gradient-echo image of the phantom and the 2D PRESS CSI data were loaded, the PRESS VOI was displayed as a green box on top of the gradient-echo image. A blue polyline was drawn by the user following the boundary between the inner sphere and outer bottle. This polyline along with the VOI box defined the boundary of the two compartments. The user had to draw a polyline to separate the two compartments on each of the four image slices covered by the 14 mm thick CSI slice. The user also picked two points (red dots), one in each compartment, to be used as initial seed points for a region growing process. In the region growing process, each compartment was grown separately starting from one initial seed point and stopping at the boundaries defined by the VOI box and the user drawn polylines. For this simple segmentation task, region growing in 2D or 3D does not make any difference to the final result. We chose the 2D approach. This 2D region growing process was performed for each of the four image slices covered by the CSI slice to generate the two compartments. The compartment map obtained from this region growing process is displayed beside the gradient-echo image in Fig. 2. Based on the compartment map and coil sensitivity maps, integrated coil sensitivity matrix S̃ was computed according to Eq. [2a]. The noise covariance matrix Ψ was computed using spectral data (Fourier transform of time-domain data D) from each coil between 8 to 11 ppm where there were no metabolite signals but only noise. After matrix C was obtained using Eq. [4a], time-domain data in each row of C were first filtered with a 3 Hz exponential function and then Fourier transformed into the frequency domain to give the spectrum for each compartment. A zero-order phase correction was applied to the complex-valued spectra to generate the final real-valued compartmental spectra.

One might want to obtain more than a few compartmental spectra when a significant number of phase encoding steps are performed. It will become time consuming to manually draw the boundaries for all compartments. Based on the idea proposed by Wang et al. (4), we developed a procedure to semi-automatically create an array of compartments that are comparable in size. In Fig. 3d, a polyline was manually drawn to separate the lesion from the normal tissue. In addition, boundaries for two small regions of interest were also drawn. Four points (red dots) in the image were selected to be used as initial seed points for the region growing process. After the region growing process was finished, the VOI was divided into four regions. Meanwhile, the software automatically divided the VOI uniformly into 11 × 5 voxels with rectangular shapes. Most of these 55 voxels located entirely in one region, which were directly assigned as compartments. Some voxels lay on the region boundaries and were split into multiple fractions by the region boundaries. These voxel fractions were combined with a neighboring voxel, or one or multiple voxel fractions in the same region, to create a compartment that was larger than a certain percentage (e.g. 80%) of the voxel volume. This task of creating compartments from the voxels and voxel fractions was automatically handled by the software. The generated compartment map is displayed beside the DWI image in Fig. 3d, in which there are a total of 46 compartments. The two small user drawn regions of interest turned out to be two compartments, each of which was the result of merging together multiple voxel fractions in the same region. Spectra of these two compartments were reconstructed using Eq. [4a], along with the other 44 compartmental spectra.

RESULTS

Phantom Experiments

Two single-voxel spectra, one for t-butanol in the inner sphere and the other for sodium acetate in the outer bottle, are displayed in Fig. 1. Similar to all other spectra presented in this work, these two spectra were apodized with Lorentzian linebroadening of 3 Hz. Next, the proposed technique was used to compute compartmental spectra and corresponding SRF maps using the 2D CSI data. In Fig. 2a, the compartmental spectra and SRF maps were computed using only the dc-component of the CSI data, which were equivalent to those of a 2 s single-shot PRESS spectroscopic scan. In Figs. 2b, 2c, and 2d, the compartmental spectra and SRF maps were computed using data with 1 × 3, 1 × 5, and 5 × 9 phase encoding steps, respectively. Using the single-voxel spectra in Fig. 1 as the standard, we can see that the compartmental spectra in Figs. 2a – 2d are correctly reconstructed and the cross-compartment contaminations are small and similar in all four experiments. The small cross-compartment contaminations were probably caused by systematic errors such as errors in the coil sensitivity maps. For the SRF maps, most of the information is in the real parts and the imaginary parts have much smaller absolute values and spatial variations compared to the real parts. When the imaginary part is small, a phase map can have many sudden near 180 degree changes when the real part crosses zero. Therefore, the real and imaginary parts of the SRF maps are displayed instead of the magnitude and phase parts. For all four experiments (Figs. 2a, 2d), the integrals of SRF₁ over compartments 1 and 2 were found to be exactly 1 and 0 (errors < 10⁻³), respectively; The integrals of SRF₂ over compartments 1 and 2 were found to be exactly 0 and 1 (errors < 10⁻³), respectively. This result agrees with our theory and means that there is no cross-compartment contamination under ideal conditions. The computed values for efficiency are similar for the first two experiments (Figs. 2a and 2b) and starts to drop when more phase encoding steps are used (Figs. 2c and 2d). This shows that a single-shot scan or a scan with very few phase encoding steps have the advantage of short scan time and high efficiency if the compartments are relatively large. On the other hand, the values of the localization parameter become smaller when more phase encoding steps are used (Figs. 2a – 2d). This indicates that cross-compartment contamination due to intra-compartment spatial inhomogeneity will become smaller in general when a larger number of phase encoding steps are used.

In Vivo Experiments

Conventional Fourier CSI spectra were first reconstructed using data acquired from the first stroke patient. All 11 × 5 k-space data points with NSA = 2 were used in the reconstruction. The spectrum for each voxel was the weighted average of spectra from eight coil elements. The total scan time was 3 min and 40 s. Spectra for three voxels near the boundary of the DWI lesion are shown in Fig. 3a. From the DWI image, we can see that voxel 2 contains both lesion and normal tissue. This partial volume effect caused the N-acetyle-aspartate (NAA) peak and lacate (Lac) peak for voxel 2 to have moderate amplitudes. Voxel 2 and all other voxels on the lesion boundary suffered from relatively large partial volume effect. The SRF maps (real and imaginary parts) for voxel 1 were computed according to Eq. [12] and are shown in Fig. 3a. The integrals of SRF₁ over voxel 1 and all other voxels were 0.76 and 0.24, respectively. This means that each CSI voxel has 24% of its signal coming from other voxels. Therefore, conventional Fourier CSI suffers from cross-voxel contamination even under ideal conditions. The localization parameter had a value of 2.3.

The proposed technique was then used to compute compartmental spectra and SRF maps using different amount of k-space data. In Fig. 3b, the compartmental spectra and SRF maps were computed using only the dc-component of the CSI data, which were equivalent to those of a 2 s single-shot PRESS spectroscopic scan. The VOI (green box), user drawn compartment boundaries (blue polylines), and two initial seed points (red dots) for the region growing process are depicted on the DWI image. Because cerebrospinal fluid (CSF) does not contain metabolites, the CSF volumes were prevented from being included into either compartment by drawing boundaries around them. The compartment map beside the DWI image shows that the ventricles (black areas) were excluded from the two compartments. In the first compartmental spectrum where the lesion is located, the NAA peak is small and a large negative lactate peak is present. In the second compartmental spectrum, the NAA peak is large and no negative lactate peak is discernible. The lack of lactate peak in the second spectrum indicates that cross-compartment contamination is small. The SRF maps (real and imaginary parts) of compartment 1 are also shown in Fig. 3b. The integrals of SRF₁ over compartments 1 and 2 were exactly 1 and 0 (errors < 10⁻³), respectively. The integrals of SRF₂ over compartments 1 and 2 were exactly 0 and 1 (errors < 10⁻³), respectively. The efficiency values for the two compartments were found to be = 0.75 and = 0.75. The localization parameters were found to be = 1.0 and = 0.18. In order to verify Eq. [6], standard deviations of noise for the two compartmental spectra were first computed using Eq. [6] and then obtained by direct measurement. The ratios of the computed noise values to the measured noise values were 1.003 and 1.002 for compartment 1 and 2, respectively. SLIM did not work using this single-shot data because two unknown spectra could not be resolved from only one equation.

The same compartment boundary definition was used in computing compartmental spectra and SRF maps shown in Fig. 3c. The phase encoding matrix was 2 × 1 (h_x = 0, 1, h_y = 0), NSA was 1, and equivalent scan time was 4 s. It can be seen that the reconstructed compartmental spectra (Fig. 3c) have less noise than the previous spectra (Fig. 3b) and the SRF maps have less intra-compartment variations than the previous ones. The efficiency and localization parameters were found to be = 0.86, = 0.69, = 0.55, and = 0.24. SLIM would also work for this phase encoding scheme. The SLIM SRF maps were computed according to Ref. (15). The SRF maps for the hypothetical SLIM reconstruction are also displayed in Fig. 3c. The efficiency and localization parameters for SLIM were found to be = 0.81, = 0.65, = 1.6, and = 0.18. Here, = 1 for SLIM represents a different SNR performance compared to = 1 for the proposed technique. For SLIM, is defined to be 1 when the compartment of interest is isolated from the rest of the sample and its entire magnetization is detected by a single-element coil (15). For the proposed technique, is defined to be 1 when the compartment of interest is isolated from the rest of the sample and its entire magnetization is detected by a multi-element coil. Because the spatially averaged SNR performance of a well-designed multi-element coil can be several times higher than that of a single-element coil (16), = 1 for the proposed technique represents a much higher spatially averaged SNR performance than = 1 for SLIM. Therefore, the actual SNR performance of the proposed technique is generally much higher than that of SLIM. In terms of localization reliability, the proposed technique has a much lower value but a slightly higher value than SLIM does.

Two compartmental spectra of interest are displayed in Fig. 3d. The phase encoding matrix was 6 × 5 (h_x = −5, −3, −1, 1, 3, 5, h_y = −2, −1, 0, 1, 2), NSA was 2, and equivalent scan time was 2 min. The compartment map in Fig. 2d verified the procedure for semi-automatically generating small compartments. In the spectrum for compartment 1 (lesion), the negative lactate peak is large and the NAA peak is very small. In the spectrum for compartment 2 (normal tissue), the NAA peak is large and there is no discernible negative lactate peak. The partial volume effect and cross contamination, which are present in the spectrum of voxel 2 in Fig. 3a, is not noticeable here. This reconstruction has a spatial resolution similar to that of conventional Fourier CSI (Fig. 3a) but with much reduced partial volume effect and reduced cross contamination. The integrals of SRF₁ over compartments 1 and 2 were exactly 1 and 0 (errors < 10⁻³), respectively. The efficiency was 0.64 and localization parameter was 3.2. This value is comparable to that of conventional Fourier CSI. Using more phase encoding steps (11 × 5), conventional Fourier CSI has an value of 2.3 while the integral of |SRF₁| inside voxel 1 is 0.76 instead of 1. SLIM did not work using this reduced k-space data because the number of unknowns (46) was more than the number of equations (30).

For the second stroke patient, compartmental spectra and SRF maps (Fig. 4) were reconstructed using data acquired with a 3 × 1 (h_x = −1, 0, 1, h_y = 0) phase encoding matrix. The NSA was 2 and scan time was 12 s. In the first compartmental spectrum (normal tissue), the NAA peak is large and there is no visible lactate peak. In the second compartmental spectrum (lesion), the NAA peak is small but there is a large negative lactate peak. Again, there is no significant cross contamination for the lactate peak in the first spectrum. The efficiencies were found to be = 0.80 and = 0.74. The localization parameters were found to be = 0.50 and = 0.10.

DISCUSSION

The SRF maps for both conventional Fourier CSI and the proposed technique (Fig. 3) are spatially slow varying and cannot represent the sharp signal changes at the compartment boundaries. However, the integral of the SRF inside any compartment is exactly one and the outside integral is zero. This means that the proposed technique does not have any cross-compartment contamination under ideal conditions. For conventional Fourier CSI, however, the integral of the SRF of a voxel within the same voxel is 0.76 and the integral over all other voxels is 0.24. So, 24 % signal comes from outside the voxel of interest under ideal conditions. In the proposed technique, structural information extracted from anatomical imaging provides the high spatial frequency information in spectral localization. The low spatial frequency coil sensitivity profiles and phase encoding functions are only used to resolve signals from different predefined compartments. Conventional Fourier CSI, on the other hand, only relies on the phase encoding functions and coil sensitivity profiles to achieve spectral localization. This is why the proposed technique is superior to conventional Fourier CSI in reducing cross contamination for spectral localization using a multi-element receiver coil. In addition to reducing cross contamination, the proposed technique can greatly reduce the partial volume effect compared to conventional Fourier CSI by allowing curvilinear compartment shapes. We can see that several CSI voxels in Fig. 3a along the DWI lesion boundary contain both lesion and normal tissue and thus suffer from large partial volume effect. This partial volume effect is greatly reduced by drawing the compartment boundary following the lesion boundary on the DWI image.

Similar to SLIM, the proposed technique uses structural information extracted from anatomical imaging to define compartments which provide the basis for spectral localization. Different from SLIM, the proposed technique is designed to be used with a multi-element receiver coil, which makes it possible to reconstruct compartmental spectra from a single-shot scan or a scan with reduced phase encoding steps. Because the spatially averaged sensitivity of a multi-element receiver coil can be much higher that of a single-element coil, the actual SNR performance of the proposed technique can be much higher than that of SLIM when similar phase encoding schemes are used. Localization reliability can also be improved using the proposed technique when very few phase encoding steps are used and the compartment sizes are relatively large compared to the size of the coils. In addition, a procedure was developed to semi-automatically generate a significant number of compartments of comparable sizes, which allows one to obtain spectra from small regions of interest with curvilinear shapes. This may be useful for obtaining spectra from relatively small stroke lesions or tumors.

A fundamental assumption for the proposed technique to work perfectly is that each compartment has a spatially uniform spectrum. Violation of this assumption will result in cross-compartment contamination. In general, uniform anatomical image intensity within each compartment does not guarantee a uniform distribution of metabolites within each compartment. In MR literature, however, there are many examples of compartmentalization of the distribution of metabolites/chemicals where intra-compartment differences in concentration is far smaller than inter-compartment differences (e.g., lactate and N-acetylaspartate in stroke tissue and normal tissue compartments; water-fat compartmentalization; lactate in muscle and tumor; and common brain metabolites and metabolic fluxes in gray matter, white mater and CSF compartments). Therefore, it is important to know where this compartmental modeling might work well and where it might break down based on a priori information. Phantom experiments (Fig. 2) have shown that the values of localization parameter become smaller when more phase encoding steps are used. This indicates that cross-compartment contamination due to intra-compartment spatial inhomogeneity will become smaller in general when a larger number of phase encoding steps are used at the expense of longer scan time and lower efficiency. In this work, only some CSI phase encoding schemes are used without a systematic optimization procedure. For future work, a numerical minimization procedure similar to the one used in SLOOP could be developed to find an optimal phase encoding scheme that offers improved efficiency and localization reliability once the compartment boundaries are defined. When the receiver coil has a large number of coil elements and the compartment sizes are relatively large, optimization of the phase encoding gradients becomes important and an optimized phase encoding scheme should be able to substantially improve localization reliability while keeping the efficiency values high.

The integrated sensitivity matrix S̃ can become ill-conditioned if too many compartments are defined for the available coil elements and phase encoding steps. This matrix ill-conditioning problem can be avoided by reducing the number of compartments, using a coil with more elements, or adding more phase encoding steps. However, reducing the number of compartments will make the compartments larger and thus might result in more intra-compartment inhomogeneity; Using a coil with more elements only provides limited help with localization when a large number of phase encoding steps are already used; Adding more phase encoding steps with optimal phase encoding gradients is most effective but at the cost of longer scan time. Matrix S̃ could also become poorly conditioned when some small compartments are encompassed by surrounding large compartments. A poorly conditioned S̃ will lower SNR and increase model errors. The procedure for semi-automatically generating small compartments of comparable sizes will help avoid this poor-conditioning problem. The computation time for solving Eq. [5a] is very short and only needs to be done once. On a 2.0 GHz personal computer, it took less than a second to solve Eq. [5a] for reconstructing 46 compartmental spectra.

It has been reported that cross contamination in SLIM experiments caused by B₁ (RF) field inhomogeneity can be corrected by incorporating a phase factor into the elements of the SLIM encoding matrix (17). The coil sensitivities used in the proposed technique are basically the ratio of B₁ of the coil elements to B₁ of the body coil. After solving Eq. [4a], the only remaining B₁ inhomogeneity effect is from the body coil, which is negligible at 3 Tesla due to the large size of the body coil. When necessary, the B₀ inhomogeneity effects can also be corrected by incorporating a B₀ field inhomogeneity map (17,18) into Eq. [2a]. This will make matrix S̃ time dependent and the unfolding matrix F̃ has to be computed for each time-point independently.

In this work, PRESS was used for volume localization. Because of volume localization, only spins inside the VOI contribute to the detected MR signal. Experiments using the proposed technique can also be performed without conventional volume localization. When no conventional volume localization is used, the entire volume of tissue is measured based on coil sensitivity profiles. In many non-proton MRS experiments (e.g., ¹³C MRS of brain in the carboxylic/amide spectral region), localization of cortical gray matter with complex geometric boundaries by proton imaging and sensitivity heterogeneity of receiver coil elements is highly desirable because it combines the short scan time achievable with the proposed technique and the intrinsic high sensitivity of multiple small coil elements (19).

CONCLUSIONS

In summary, a new technique was developed for performing MRS using a multi-element receiver coil. Structural information extracted from anatomical imaging was utilized for defining compartments which provide the basis for spectral localization. Inherent spatial heterogeneity of multiple receiver coil elements was used along with optional phase encoding to resolve signals from different compartments. Phantom experiments and in vivo MRS of stroke patients were performed to demonstrate this technique. Compartmental spectra were successfully reconstructed from data collected using an eight-element receiver coil. The compartmental spectra along with SRF analyses showed that the proposed technique effectively reduced the partial volume effect and cross contamination compared to conventional Fourier CSI performed using the same multi-element receiver coil. Compared to SLIM, this technique took advantage of the intrinsic high sensitivity and spatial heterogeneity of multiple small coil elements to further shorten scan time, increase sensitivity, and improve localization reliability. In addition, a procedure was developed to semi-automatically generate a significant number of compartments of comparable sizes, which allows one to obtain spectra from small regions of interest with curvilinear shapes. With the advent of multi-element receiver coils having a large number of coil elements, this technique has the potential to be useful in many applications including heteronuclear MRS.