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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Magn Reson. Author manuscript; available in PMC 2012 August 1.
Published in final edited form as:
PMCID: PMC3143308

Multi-band Frequency Encoding Method for Metabolic Imaging with Hyperpolarized [1-13C]Pyruvate

Cornelius von Morze, Ph.D.,* Galen Reed, B.S.,* Peter Shin, B.S.,* Peder E.Z. Larson, Ph.D.,* Simon Hu, Ph.D.,* Robert Bok, M.D. Ph.D.,* and Daniel B. Vigneron, Ph.D.*


We describe a new method for simultaneous spatial localization and spectral separation of multiple compounds based on a single echo, by designing the acquisition to place individual compounds in separate frequency encoding bands. This method was specially designed for rapid and robust metabolic imaging of hyperpolarized 13C substrates and their metabolic products, and was investigated in phantom studies and studies in normal mice and transgenic models of prostate cancer to provide rapid metabolic imaging of hyperpolarized [1-13C]pyruvate and its metabolic products [1-13C]lactate and [1-13C]alanine at spatial resolutions up to 3 mm in-plane. Elevated pyruvate and lactate signals in the vicinity of prostatic tissues were observed in transgenic tumor mice. The multi-band frequency encoding technique enabled rapid metabolic imaging of hyperpolarized 13C compounds with important advantages over prior approaches, including less complicated acquisition and reconstruction methods.


Hyperpolarized 13C imaging provides >10,000 fold signal enhancement for detecting uptake of endogenous, nontoxic 13C-labeled probes such as pyruvate, and their enzymatic conversion through key biochemical pathways (14). Hyperpolarization lifts the prior constraint of poor sensitivity in MR metabolic imaging, but challenges the design of optimal acquisition strategies by requiring rapid sampling of spatial and chemical shift information of multiple 13C resonances. To address these requirements for hyperpolarized MR, specialized pulse sequences have been developed with the capability to image multiple compounds rapidly, in order to track the metabolism of hyperpolarized substrates in vivo. Prior approaches include “spectroscopic imaging” (MRSI) methods, characterized by high spectral resolution, such as chemical shift imaging (CSI) (3), echo planar spectroscopic imaging (EPSI) (5), and spiral CSI (6), as well as “imaging” approaches like multi-echo methods (7,8), and interleaved acquisition of individual metabolites by frequency-specific excitation (9). In this project, we have developed an "imaging" method called multi-band frequency encoding (FE), which uses a single gradient echo for both localization and spectral separation. The method relies on wide spectral separation and is thus well suited for hyperpolarized 13C applications.

By leveraging the large chemical shift between hyperpolarized 13C resonances, this method allows metabolic imaging with comparable or faster speeds than prior fast MRSI approaches. At the same time, it avoids the complexity of fast MRSI acquisition schemes involving rapidly switching gradients and/or non-Cartesian k-space trajectories, and their associated reconstruction steps, without sacrificing readout efficiency (2,6). In comparison to the interleaved frequency-specific approach, images are truly acquired simultaneously, which provides an important advantage for multi-compound studies (10). This new imaging technique was tested through imaging of a multi-chamber 13C phantom, and in vivo imaging of hyperpolarized [1-13C]pyruvate and its metabolic products [1-13C]lactate and [1-13C]alanine in normal mice and transgenic models of prostate cancer. This work is a novel implementation of the same basic idea recently described by Mugler et al. for separating hyperpolarized 129Xe images of gas and dissolved phases (11), and is conceptually similar to previous work by Weaver et al. for simultaneous multislice 1H imaging (12), in this case applied to metabolic imaging of distinct 13C labeled metabolites. A full development of the theory of the technique is also presented in this work.


In spectroscopic imaging, spin frequency in the rotating frame (ω) is modulated by a magnetic field gradient and chemical shift:

Eq. 1

where γ is the gyromagnetic ratio, δi is the chemical shift of species i, B0 is the main magnetic field strength, G is the gradient strength and x is the spin position In the multi-band frequency encoding technique, the readout gradient amplitude is set such that the minimum chemical shift separation among species present (Δδmin) exceeds the gradient field difference across the FOV (i.e. ΔδminB0 > G · FOV), whereby unique modulation occurs for all species at all locations, allowing determination of all spectral-spatial components by FE. The FOV here is defined only as the true object FOV, not an extended version containing the entire frequency range. Following Fourier transformation, images corresponding to each spectral component appear side-by-side within different FE bands (Figure 1). To measure all of these components, the readout filter is opened wider than the conventional imaging setting of γG · FOV ; instead, the minimum setting is

Eq. 2

where δmin and δmax are the minimum and maximum chemical shifts among the chemical species present. Due to practical sequence considerations, the readout bandwidth is likely to be the smallest multiple of ΔδminγB0 exceeding this minimum. During the reconstruction procedure, metabolite images are shifted along x to their proper locations, based on known chemical shift differences. For example, if the maximum value of G is used, the reconstruction shift for metabolite i is (δi − δmin)N / Δδmin pixels (where N= number of pixels across the FOV).

Figure 1
Schematic representation of multi-band frequency encoding method, showing spread of metabolite signals into adjacent, non-overlapping frequency bands used for spatial encoding, when a correctly chosen frequency encoding gradient is activated. All quantities ...

While in conventional imaging the readout gradient strength is usually maximized in order to minimize distortion (and also, to maximize imaging speed), in this method it is typically much lower than maximum. This is acceptable as long as the degree of misregistration and blurring remain small, and the imaging time remains sufficiently short.

The maximum FE bandwidth per pixel depends on the resolution and the minimum chemical shift separation:

Eq. 3

which is also equal to the inverse of the minimum readout time for full Fourier sampling, determining the minimum TE and TR (and thus total scan time). B0 misregistration (i.e. in mm per ppm inhomogeneity) scales with FOV /Δδmin. In this initial implementation for animal experiments as detailed below, the maximum misregistration due to a typical inhomogeneity of ±0.25 ppm is ±1 mm or one-third of a voxel.

If the T2* relaxation time is on the order of or less than the duration of the readout window, T2* blurring may occur along the readout direction, which could reduce the true spatial resolution in this dimension, and there could also be degradation of SNR. The corresponding k-space filter, which combines this asymmetric exponential decay filter with symmetric windowed sampling of the Fourier data (13), is

Eq. 4

where W is the width of the spatial frequency sampling window, and the function “rect” is defined as a boxcar function equal to 1 when the argument lies between −1/2 and 1/2, and 0 otherwise. After inverse Fourier transformation (see Appendix), the point spread function is

Eq. 5

where Δx is the nominal spatial resolution (equal to 1 / W), and τread is the readout time (equal to W / γG). To assess the extent of this effect on the experiments described in this study, this function was computed (Methods) over a range of reasonable representative values of T2*, and resultant loss of spatial resolution and SNR were estimated.

This method has not been applied for 1H spectroscopic imaging because it would result in excessive distortion due to low FE bandwidth in the presence of B0 inhomogeneity. Much larger minimum chemical shift separation in many 13C applications should allow much higher spatial resolution, pixel bandwidth, and imaging speed with this method for 13C. Comparing the minimum spectral separation for 1H MRSI of the brain (choline-creatine, 0.2 ppm) to hyperpolarized 13C studies of [1-13C]pyruvate (pyruvate- alanine, 5.7 ppm), pixel misregistration due to a fixed ppm difference in B0 would be 28× lower for 13C (e.g. for a 4 cm FOV, misregistration due to 0.1 ppm inhomogeneity is 20 mm for 1H vs. just 0.7 mm for 13C), and the scan time is also 7 times faster.


Phantom experiments

A cylindrical multi-chamber phantom (d= 5.6 cm) containing [1-13C]pyruvate, [1-13C]alanine, and [1-13C]lacate in three separate internal spheres, respectively, was scanned in a 3T GE human scanner equipped with a custom built transmit-receive dual-tuned 1H / 13C coil designed for imaging rats (d= 8 cm, length= 9 cm, 13C channel- quadrature, 1H channel- linear only). The pulse sequence was a single slice axial 2D spoiled gradient echo (SPGR) acquisition designed for resolution of pyruvate and its metabolic products lactate and alanine. The chemical shifts were determined from a separate non-localized MRS scan. A 32-point readout of total bandwidth = 0.74 kHz was used. The first two eight-point bands represented pyruvate and alanine, with lactate extending into the remaining two bands. The spatial resolution was 7.5 mm in-plane by 20 mm slice (1.13 cm3). The other parameters were: flip angle= 20°, TE / TR = 26ms / 58 ms (τread= 44ms with Gread= 0.029 G/cm, Gslice select= 0.58 G/cm), FOV= 6 cm (AP, frequency) × 12 cm (RL, phase), acquisition matrix= 32 × 16, NEX= 160, scan time per NEX= 928 ms.

Animal experiments

The distribution and metabolism of hyperpolarized [1-13C]pyruvate was imaged in one normal mouse and two transgenic mice with prostate cancer (transgenic adenocarcinoma of the mouse prostate, or TRAMP) (14). Each sample (24 µL or ~ 30 mg) of 99% [1-13C]pyruvate mixed with trityl radical OX063 (GE Healthcare, Oslo, Norway) was loaded into the 3.35T magnet of the HyperSense polarizer (Oxford Instruments Biotools, Oxford, UK), where it was cooled to 1.3 K and irradiated by microwaves @ 94.117 GHz for approximately one hour. The sample was then removed from the magnet and rapidly dissolved in a heated solution of 4.6 mL TRIS/NaOH buffer, resulting in a ~ 80 mM solution of pH ~ 7.5. After rapidly transporting the solution to the scanner room, the mice were intravenously injected with a bolus of 350 µL over 12 sec, followed by a 150 µL saline flush. The polarization of an aliquot taken from the dissolved sample was measured in a low field spectrometer.

A single stack of eight axial slices extending from the prostate to the liver was acquired at 35 sec after the start of the injection. In vivo chemical shifts differed slightly from the phantom in their absolute values, and were determined from previously acquired MRS data (ωpyr= 32,131,400 * 2π rad / sec, Δδpyr-ala= 5.7 ppm, Δδala-lac= 6.6 ppm). The spatial resolution was 3 mm in-plane by 5 mm slice (0.045 cm3). The imaging parameters were as described above except: FOV= 2.4cm (AP, frequency) × 4.8 cm (RL, phase), Gread= 0.072 G/cm, Gslice select= 2.34 G/cm, acquisition matrix= 32 × 16, scan time= 7.4 sec. To maintain nearly constant transverse magnetization following each RF pulse, the flip angle was increased over the phase encoding steps for each slice according to θ(n) = arctan(sin(θ(n+1)), with the last pulse being 9° (15). A syringe containing a solution of enriched [13C]lactate (1.77M) was placed in the coil along with each mouse in order to calibrate the transmit gain prior to the experiment. In this case the RF coil was a quadrature transmit-receive dual-tuned 1H / 13C coil designed for imaging mice (d= 5 cm, length= 8 cm).


The transmit RF pulse was centered on the pyruvate frequency. For relatively thin 2D slices, some small chemical shift misregistration of the RF pulse profiles occurs. The RF pulse bandwidth was 1250 Hz, resulting in shifted transmit profiles for alanine (shifted by ~ 0.7mm) and lactate (~ 1.6mm). In post-processing, the alanine and lactate data were interpolated, shifted, and resampled to realign the data along z. Even after correction, a consequence of the misregistration is that one edge slice has incomplete alanine and lactate signal.

A small signal from pyruvate hydrate, centered between the alanine and lactate bands, resulted in slight contamination of the alanine band, and to a lesser extent, the lactate band. The contamination was reduced by applying knowledge of the pyruvate signal to estimate a minimum pyruvate hydrate signal level at physiological pH (5% of the pyruvate signal, based on previous MRSI studies), which was subtracted from the appropriate locations in the alanine and lactate bands. Finally, interpolated metabolite images (64 × 64 for each metabolite) were overlaid onto standard axial multi-slice T2-weighted 1H FSE images acquired with identical graphic prescription.


Simulations were conducted to assess the potential extent of T2* blurring and loss of SNR. The T2 relaxation times of the 13C nuclei of interest are relatively long, in the hundreds of milliseconds. We derived T2* relaxation times from a previous study in which T2 relaxation times were measured (16), taking the shortest T2 value measured (380 ms for alanine in normal rat liver) and adjusting downward up to a factor of 10 for varying levels of intravoxel inhomogeneity (T2*= 380 ms, 125 ms, 38 ms, and for comparison, infinite). The point spread function (Eq. 5) was calculated for each of these T2* values, and the FWHM of each function was measured and compared to the ideal value for infinite relaxation time to determine degradation of spatial resolution, and the integral of each function in the FWHM portion was taken as an estimate of the relative SNR.


Shifting the lactate and alanine sub-images by amounts corresponding to their in vivo chemical shifts as measured in previous MRSI studies resulted in excellent co-registration of all image sets (Figure 2- multi-chamber phantom, Figure 3- in vivo). For each metabolite, exactly the same shift was applied across all slices in the data sets. The small pyruvate hydrate signal was effectively filtered from the alanine and lactate bands by the described method. The polarization of the injected pyruvate was ~ 25%, as measured by the spectrometer.

Figure 2
Axial imaging of a cylindrical multi-chamber 13C phantom (d= 5.6 cm) with internal spheres (d= 2.3 cm) containing enriched 13C-pyruvate, -alanine, and -lactate. Nominal spatial resolution of 13C image acquisition was 7.5 mm in-plane. Top row: Individual ...
Figure 3
Separation of pyruvate, alanine, and lactate images in a normal mouse by multi-band frequency encoding method. Nominal resolution was 3 mm in-plane by 5 mm slice. Liver slice was selected for high concentration of all three metabolites. Pyruvate image ...

In all three animals (Figure 4 & 5), the largest hyperpolarized signals were observed in the kidneys and liver, with alanine mostly localized to the liver. Both transgenic prostate cancer mice had regions of T2-weighted signal changes in the anatomic region just surrounding and superior to the urethra, which is the site of early tumor development in the TRAMP model (17). The mean tumor lactate-to-pyruvate ratios in both mice, 1.32 for one mouse with a large periurethral gross tumor (dmax = 1.5 cm), and 0.64 for the other mouse with a smaller tumor (dmax = 1.0 cm), were elevated over the ratio in the prostatic region of the normal mouse (0.49). In the smaller tumor, pyruvate was largest in the periphery, around a centralized region of lower pyruvate and high lactate.

Figure 4
Axial imaging of hyperpolarized [1-13C]pyruvate and its metabolic products by multiband frequency encoding in a normal mouse. All individual metabolite images from stack are shown, overlaid on co-registered T2w 1H images, with anatomic landmarks. Alanine ...
Figure 5
Pelvic / abdominal metabolite distribution from two transgenic prostate cancer (TRAMP) mice imaged using multi-band frequency encoding. (left-to-right = inferior-to-superior). In the mouse at top, lactate is well localized to the region of gross tumor ...

The qualitative appearance of the results in Figures 2 & 3 indicate that the resolution of the acquisitions were not seriously degraded by T2* blurring. It is important to note that although the resolution of the phantom scan was lower than the animal scans due to much lower SNR, the readout duration was the same, so the percent degradation of spatial resolution from the nominal value due to T2* blurring would be the same (from Eq. 5). Results of the simulations of T2* blurring and SNR loss are shown in Figure 6 in the plots of the point spread function. Increases in the FWHM of the point spread function from its ideal value (for infinite T2*, FWHM= 3.616 mm) were negligible for T2* values of 380 ms (3.622 mm) and 125 ms (3.638 mm). The expected degradation in spatial resolution was 5.4% for T2*= 38 ms (3.810 mm), based on comparing the FWHM values. The relative SNR values measured by integrating under the FWHM area were 94% (380 ms), 82% (125 ms) and 56% (38 ms).

Figure 6
Plots of point spread function for MBFE imaging method (Eq. 5) as described for animal experiments, including effects of T2* blurring and symmetric windowed Fourier sampling, computed for various possible T2* values to reflect different levels of intravoxel ...


In this project we developed a new, robust method for imaging of multiple 13C compounds widely separated in chemical shift and demonstrated its application for imaging hyperpolarized [1-13C]pyruvate and its metabolic products in vivo. In phantom scans and animal scans of normal mice and transgenic models of prostate cancer, identical shifts were applicable to all of the data (i.e. in all slices of all exams). This was expected due to the fact that very consistent chemical shifts have been robustly observed through prior in vivo MRSI studies. We successfully implemented a method for removing signal contamination resulting from overlap of a small pyruvate hydrate signal into the alanine and lactate bands. This method assumes that pyruvate hydrate signal adds in phase with lactate and alanine signals, which should be a reasonable assumption. A situation could arise where a small difference in the B0 field between the aliased spatial positions may put the signals out of phase. In any case, the levels of pyruvate hydrate are quite small in comparison to lactate at 35 seconds after injection, but this could be a problem for dynamic studies. B0 misregistration was estimated to be minor for the described application, and this was corroborated by good alignment of the experimental data with 1H images. If misregistration were increased in a different application or experimental conditions of poor shim, misregistration could also be corrected based on a B0 map, and the same correction could be applied to all images as they all have the same misregistration.

Higher spatial resolution and faster acquisition times are facilitated by larger minimum chemical shift separation. Another application that could benefit is imaging of pH using hyperpolarized [13C]bicarbonate (18), in which bicarbonate and CO2 are separated by 36 ppm. Similarly, more advanced RF methods such as suppression pulses for alanine or multi-band excitation of pyruvate and lactate could be utilized to localize just these components for better performance than demonstrated in this study.


Derivation of point spread function Eq. 5 from Eq. 4:


And since τread = 1/(γGΔx),



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