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Super-Resolution Hyperpolarized 13C Imaging of Human Brain Using Patch-Based Algorithm

Spatial resolution of metabolic imaging with hyperpolarized 13C-labeled substrates is limited owing to the multidimensional nature of spectroscopic imaging and the transient characteristics of dissolution dynamic nuclear polarization. In this study, a patch-based algorithm (PA) is proposed to enhance spatial resolution of hyperpolarized 13C human brain images by exploiting compartmental information from the corresponding high-resolution 1H images. PA was validated in simulation and phantom studies. Effects of signal-to-noise ratio, upsampling factor, segmentation, and slice thickness on reconstructing 13C images were evaluated in simulation. PA was further applied to low-resolution human brain metabolite maps of hyperpolarized [1-13C] pyruvate and [1-13C] lactate with 3 compartment segmentations (gray matter, white matter, and cerebrospinal fluid). The performance of PA was compared with other conventional interpolation methods (sinc, nearest-neighbor, bilinear, and spline interpolations). The simulation and the phantom tests showed that PA improved spatial resolution by up to 8 times and enhanced the image contrast without compromising quantification accuracy or losing the intracompartment signal inhomogeneity, even in the case of low signal-to-noise ratio or inaccurate segmentation. PA also improved spatial resolution and image contrast of human 13C brain images. Dynamic analysis showed consistent performance of the proposed method even with the signal decay along time. In conclusion, PA can enhance low-resolution hyperpolarized 13C images in terms of spatial resolution and contrast by using a priori knowledge from high-resolution 1H magnetic resonance imaging while preserving quantification accuracy and intracompartment signal inhomogeneity.

INTRODUCTION Hyperpolarized 13 C magnetic resonance (MR) is an emerging imaging method that can assess in vivo metabolism (1). [1-13 C] pyruvate is currently the most widely used substrate for hyperpolarization and has proven its utility in exploring both normal and altered metabolism of multiple diseases with a series of successful translation to humans (2)(3)(4)(5). Despite the relatively long spin-lattice relaxation time (T1) of [1-13 C] pyruvate, data acquisition with an adequate sampling rate is challenging for hyperpolarized 13 C imaging owing to the multidimensional nature of magnetic resonance spectroscopic imaging (MRSI) and the transient characteristics of hyperpolarized signals. Sufficient spectral bandwidth and resolution are needed to resolve 13 C-labeled products such as [1-13 C] lactate, [1-13 C] alanine, and [ 13 C] bicarbonate from hyperpolarized [1-13 C] pyruvate, and spatial encoding with proper k-space sampling is necessary to capture spatial distribution of the metabolites. In general, optimal acquisition strategies depend on the applications and adjust the tradeoffs between spectral, spatial, and time domains. In particular, compromised spatial resolution is inevitable owing to the limited signal-to-noise ratio (SNR) of hyperpolarized 13 C-labeled products, long acquisition time, and hardware performance. For instance, in-plane spatial resolution of cerebral metabolite maps in humans using hyperpolarized [1-13 C] pyruvate ranges from 1 cm to 2 cm (2,3,6,7). The suboptimal resolution of hyperpolarized 13 C images usually results in large partial volume effects, hampering accurate assessment of the hyperpolarized metabolites. Exploiting the coregistered high-resolution structural 1 H magnetic resonance imaging (MRI) for the reconstruction of hyperpolarized 13 C images may improve the spatial resolution, identifying the originated anatomical compartments of the hyperpolarized 13 C signal.
Several acquisition strategies have been suggested to improve spatial resolution of hyperpolarized 13 C images in the aspect of radiofrequency (RF) excitation and data sampling. A common approach is to omit the spectral sampling by applying a spectrally selective RF pulse, allowing more efficient utilization of hyperpolarized signals and longer acquisition time to cover larger k-space than conventional chemical shift imaging (CSI) methods (8). However, RF excitation with spectrally selective pulses is susceptible to potential contamination of other large hyperpolarized peaks, especially when imaging low-concentrated metabolites. Spectroscopic imaging sequences such as echo-planar spectroscopic imaging (9) or spiral CSI (10) can be also used to improve the spatial resolution at the expense of reduced spectral bandwidth. Besides, other conventional acceleration techniques such as parallel imaging (11) and compressed sensing (12) can be used in hyperpolarized 13 C imaging. Previous studies have shown 3-fold acceleration with 4-channel array coils using sensitivity encoding (SENSE) for hyperpolarized 13 C pyruvate spectroscopic imaging (13) and up to 3Â acceleration using a volumetric echo-planar imaging in combination with compressed sensing for hyperpolarized [1-13 C] pyruvate and [1-13 C] lactate images (14). However, SNR penalty and possible artifacts exist when using these acceleration methods. Even with these techniques, the enhancement of spatial resolution for hyperpolarized 13 C images is still limited.
Spatial resolution can be also improved at the postprocessing level by the so-called super-resolution reconstruction methods (15). By definition, super-resolution methods reconstruct low-resolution images toward a higher spatial resolution under the guidance of a priori knowledge from other high-resolution imaging modalities without having any SNR penalty. For MRI, 2 types of super-resolution algorithms exist, namely, k-spacebased and image-based methods (16). One type of k-space-based super-resolution method uses linear regression with an assumption of signal uniformity within each compartment, which is segmented by other high-resolution images. This type of method describes MR data as a linear combination of independent variables and solves the optimal weighting coefficients for the variables. For instance, spectral localization by imaging is a linear regressionbased super-resolution method that uses structural information of 1 H spin-echo image to guide the reconstruction of MR spectroscopic data (17), allowing significant enhancement of spatial resolution of the spectroscopic image. The linear regression method can be further improved by adding a regularization function that constraints anatomical consistency (18). Recently, Farkash et al. (19) applied a modified linear algebraic model to hyperpolarized 13 C MRSI to enhance the spatial resolution of 13 C images with the assumption of spectra similarity within each compartment. Another type of kspace-based super-resolution method is Bayesian super-resolution method that formularizes the reconstruction as a likelihood function from the a priori structural information. The Bayesian method was used to reconstruct 1 H brain MRSI data by incorporating anatomical information from high-resolution magnetization-prepared rapid acquisition gradient-echo images (20). Although more accurate regional metabolite levels are quantifiable with the Bayesian-based method, often locally optimal solutions are found owing to the reconstruction complexity.
Image-based super-resolution method is a relatively simple alternative of k-space-based methods. In particular, patch-based algorithm (PA) is an image-based method that reconstructs a high-resolution image using the similarity of the adjacent voxels to the central voxel. The similarity is defined by the matching high-resolution reference images. As PA specifies only similarity of signal distribution, it still allows signal variability within the same compartment. Previously, PA was applied to reconstruct MRSI of patients with multiple sclerosis (16). In the study, low-resolution N-acetylaspartate and myo-inositol maps were upsampled under the guidance of 1 H T1-weighted and fluid-attenuated inversion recovery (FLAIR) images, which outperformed other conventional upsampling methods in preserving the structural information and the tissue contrasts.
One major challenge of implementing super-resolution methods is the choice of appropriate a priori knowledge; this usually comes from attendant high-resolution acquisition, physical principles related to the measurement process, or precepts from previous experience (15). Jain et al. (16) acquired a priori information from high-resolution 1 H T1-weighted and FLAIR images, which share the same brain tissue boundaries with the low-resolution MRSI. Previous healthy human brain imaging studies (2,6) showed compartmentalized spatial distribution of hyperpolarized 13 C metabolites between gray matter (GM) and white matter (WM) even though the distribution of 13 C signals according to anatomic segmentation needs further investigation.
In this study, we propose a modified PA for enhancing the spatial resolution of hyperpolarized 13 C human brain images by using the brain tissue boundaries' information from high-resolution 1 H T1-weighted MRI. The effect of SNR, upsampling factor, segmentation, and slice thickness on the performance of PA is evaluated with digital phantoms, and the feasibility of the proposed method for reconstructing high-resolution 13 C images is shown in phantom studies and in vivo hyperpolarized [1-13 C] pyruvate images of healthy human brain.

Patch-Based Super-Resolution Algorithm
For a low-resolution hyperpolarized 13 C image y, the corresponding to-be-reconstructed high-resolution image x can be described as follows: where H is the blurring and downsampling operator, and g is the acquisition noise. To reconstruct x, a classical smoothness constraint can be applied to the high-resolution image as follows: x where UðxÞ is the regularization term that maintains the geometric consistency of x, and k controls the level of the regularization. The regularization term is determined by the nonlocal patchbased method (21,22) in the high-resolution space, X: Þis the estimated value of x i , calculated from the neighboring voxels within the volume, V i . For 13 C MRSI, patches from different metabolites are assumed to be similar. Moreover, as the spatial resolution increases, the similarities between neighboring patches are expected to decrease. Under these assumptions, the 2 terms in equation [2] can be decoupled and separately calculated during the mean correction and reconstruction steps, respectively (16), and k can be ignored, as the 2 terms are asymptotically approximated. w x i jV i ð Þis defined as follows: The weighting factor, w x i ; x j ð Þ , quantifies the contribution of voxel, x j , to the reconstruction of x i based on a priori knowledge (23): Z i is the normalization constant that satisfies 1 are the intensity matrices of the neighborhood voxels around voxel i and j, respectively. r 2 i is the variance of the neighborhood voxel intensities inN i . In this study,N i andN j are both 5 Â 5 matrices.
A previous study (24) proposed a PA that conducts nonlocal means reconstruction iteratively using equation [4] (reconstruction step). For each iteration, the offset between the reconstructed values and the acquired low-resolution data is adjusted (mean correction step). The corrected signal intensity of voxel i is as follows: where U is an upsampling operator. In this study, the downsampling operation, H, is conducted by averaging signal from corresponding voxels at high resolution. As an extension of equation [5], the weighting factors can include tissue compartmentalization, estimated from other types of images (16): Here, k specifies individual tissue compartment (k 2 K), and p i;k is the probability that voxel i belongs to compartment k. In this preliminary study, we considered 3 compartments in the brain: K = (GM, WM, cerebrospinal fluid [CSF]) using a high-resolution T1-weighted 1 H MRI. Figure 1 shows the schematic diagram of PA for reconstructing high-resolution hyperpolarized 13 C images. High-resolution 1 H MRI (eg, T1-weighted 1 H MRI) and low-resolution hyperpolarized 13 C MRI, acquired from the same subject, are used as input. Then, 3 compartments (WM, GM, CSF) are segmented from the T1-weighted 1 H image to get the possibility maps and the 1 H MRI weights. As an initial step, the low-resolution hyperpolarized 13 C image is upsampled to the targeted spatial resolution.
Using the 1 H MRI weights, the previously estimated high-resolution 13 C image is updated, followed by a mean correction step. These iterative steps continue until the maximum signal difference of all voxels between the previous iteration and current iteration is smaller than a threshold. The final super-resolution hyperpolarized 13 C MRI is used to evaluate the proposed PA.

Hardware and Hyperpolarization
All the MR studies were performed using a clinical 3 T 750w widebore MRI scanner (diameter 1 = 70 cm; GE Healthcare, Waukesha, WI). A 1 H/ 13 C dual-tuned quadrature transmit/receive birdcage RF coil (1 inner = 60 mm; GE Healthcare) was used for phantom studies. Human brain imaging was performed using a dual-frequency human head RF coil (nested-design of a quadrature transmit/receive 1 H coil, quadrature 13 C transmit coil, and 8-channel 13 C array receive coils) (25). For in vivo studies, [1-13 C] pyruvic acid samples (Sigma Aldrich, St. Louis, MO) were prepared in clinical fluid paths and polarized using a SPINlab TM clinical dynamic nuclear polarization system (GE Healthcare) as described previously (5). The imaging protocol was approved by the local institutional review board (IRB#: STU 072017-009).

Simulation
A series of simulations were performed using digital phantoms to evaluate the effects of SNR, upsampling factor, segmentation, and slice thickness on the performance of the proposed algorithm. All the digital phantoms were generated using MATLAB (MathWorks, Natick, MA). A 2-dimensional (2D) phantom image consisting of 3 compartments (matrix size = 64 Â 64) was used as a high-resolution 1 H MRI (Figure 2A), and the possibility map of each compartment was calculated. Similarly, 2 low-resolution images were created for 13 C MRI with peak SNRs (SNR peak ) of 10 and 100 (matrix size = 16 Â 16; Figure 2B). The mean 13 C signal intensities of compartments 1, 2, and 3 were assigned to 1000, 750, and 250, respectively. From the high-resolution 1 H image and the low-resolution 13 C images, high-resolution 13 C images were reconstructed using PA. For comparison, conventional interpolation methods, including sinc interpolation (SI), nearest-neighbor interpolation (NI), bilinear interpolation (BLI), and spline interpolation (SP), were applied to the low-resolution 13 C images. The SI method interpolates the image data by zerofilling the high spatial-frequency components of the k-space data. The NI method assigns the query point to the value of the nearest sample grid point. The BLI method linearly interpolates the new point based on the nearest 2-by-2 neighborhood. For SP, a cubic spline method was used to interpolate the new point with 4 old points in the neighborhood. The mean signal intensities from 4 region of interests (ROIs), drawn in different compartments of the low-resolution 13 C images, were used as ground truth.
To consider the cases of inaccurate segmentation from highresolution 1 H MRI, 2 additional low-resolution 13 C images were generated (matrix size = 16 Â 16, SNR peak = 10): one with an extra 13 C signal source in a segmented compartment ( Figure 3) and the other with missing 13 C signal in a compartment ( Figure  4). The signal intensities of these 2 images were maintained the same as before (1000, 750, and 250).
The effect of slice thickness on the performance of PA was determined using a 3D digital phantom with 3 compartments. Six slices were generated for 1 H MRI (simulated slice thickness = 5 mm, matrix size = 64 Â 64). For 13 C images, 2 cases of slice thicknesses were simulated (2, 3, 6, 7). In the first case, 2-slice low-resolution 13 C MRIs were generated with SNR peak = 6.67 and SNR peak = 10 (simulated slice thickness = 1.5 cm, matrix size = 16 Â 16; Figure  5B). In the second case, single-slice low-resolution 13 C image was generated (simulated slice thickness = 3.0 cm, matrix size = 16 Â 16; Figure 5C). The SNR peak of the single slice was 16.67. For each 5-mm slice, the 13 C signal intensities in compartments 1, 2, and 3 were assigned as 1000, 750, and 250, respectively.

Phantom Validation
Four cylindrical phantoms ( Figure 6; 1 = 1 cm, length = 5 cm) were prepared for performance evaluation of PA at the scanner. Phantoms #1-#3 were filled with pure ethylene glycol (not 13  . The hyperpolarized [1-13 C] pyruvate solution passed the quality control before the injection. In total, 80 seconds after the dissolution, a dose of 0.1 mmol/kg of hyperpolarized pyruvate solution was administered intravenously to the subject, followed by a 25-mL saline flush (injection rate = 5 mL/s). The 13 C acquisition began 3 seconds after the start of injection, and the center frequency was set to the in vivo hyperpolarized [1-13 C] pyruvate resonance. The acquired 1 H images were used for brain skull-stripping and brain segmentation with FSL package (FMRIB, Oxford, UK) (28,29), from which the possibility maps of GM, WM, and CSF were produced. The 13 C data were reconstructed using MATLAB, and the time-averaged images of hyperpolarized [1-13 C] pyruvate and [1-13 C] lactate were upsampled by 2 and 4 times using the 5 interpolation methods (SI, NI, BLI, SP, and PA). Besides, the kinetic results of [1-13 C] pyruvate and [1-13 C] lactate from different reconstruction methods were compared.

RESULTS
When the 1 H-based segmentation was correctly assigned to the 13 C signal distribution, PA reconstructed high-resolution 13 C images with enhanced spatial resolution and contrast (Figure 2).
The high-resolution 13 C images that were reconstructed using PA outperformed those reconstructed by SI, NI, BLI, and SP methods ( Figure 2B) with respect to the contrast at the edge of each compartment. Both low-and high-SNR 13 C images (SNR peak = 10 and  100) confirmed the sharper transition of signal intensity between compartments and more consistent signal profiles within each compartment, as shown by the cross-sectional profiles along the reference lines ( Figure 2C). The peak SNRs from the reconstructed images were quantified and summarized in Figure 2D. Along with BLI and SP, PA moderately improved the SNR. The mean signal intensities calculated from the 4 ROIs (SNR peak = 10) showed that PA maintains the quantification accuracy in the reconstructed high-resolution 13 C images for upsampling factors of 2-8 ( Figure 2E). Moreover, signal variation within each compartment was preserved by PA for the tested upsampling factors, particularly for ROI (a) and (b). The simulation validated reliability of the proposed method when the compartments were properly segmented to the 13 C distribution.
Performance of PA was further tested when 13 C signal distribution and segmentation were mismatched. First, the case when an additional 13 C signal source presents within one of the 1 Hdefined possibility maps was examined. When compartment #3 of the simulated low-resolution 13 C image was not identified by the 1 H image ( Figure 3A), compartment #3 was treated as a part of compartment #2 in the possibility maps, although the compartments showed distinct 13 C signal intensities. In this case, all the conventional methods (SI, NI, BLI, and SP) retained the structural information of the 3 compartments in the interpolated images ( Figure 3B). The reconstructed image by PA also showed comparable signal distribution in the unsegmented compartment (compartment #3) while achieving enhanced contrasts compared with other interpolation methods in the properly segmented compartments (compartments #1 and #2) as shown in the cross-sectional profile ( Figure 3C) along the reference line (white dotted line in Figure 3B). PA was able to maintain the quantification accuracy in the missing compartment ( Figure 3D). Second, PA was tested for the case when a compartment in the 13 C map is partially lost (eg, signal contamination owing to noise, shading, or artifacts). To show the case, a low-resolution 13 C phantom image with partially lost signal from the upper part of compartment #3 was generated ( Figure 4), whereas the 1 H image showed homogeneous signal distribution within the compartment. All the interpolation methods, including PA, showed clear boundaries between upper and lower parts of the compartment #3 ( Figure 4B), and the signal distribution along the reference line x was at the noise level ( Figure 4C). Meanwhile, PA still outperformed the conventional interpolation methods in terms of contrast (Figure 4, B and D).
The effect of relative 13 C/ 1 H slice thickness on PA reconstruction was also evaluated. A 3D 3-compartment digital phantom was created for high-resolution 1 H MRI (6 slices, simulated slice thickness = 0.5 cm; Figure 5A). From the corresponding thicker low-resolution 13 C images (2 slices, simulated slice thickness = 1.5 cm), the matching 2-slice possibility maps were calculated ( Figure 5B). When PA was applied to the low-resolution 13 C images with the possibility maps and an upsampling factor of 4, enhanced contrast across the compartments was observed in both slices. Quantification accuracy was also comparable to that from other interpolation methods for both slices. Similarly, the reconstructed high-resolution images from a thicker 13 C image (single slice, simulated slice thickness = 3.0 cm; Figure 5C) also showed moderately enhanced contrast and comparable signal distribution when PA was applied as compared with the other Super-Resolution Hyperpolarized 13 C Imaging of Human Brain methods. It was noted that the contrast enhancement in reconstructed image by PA was reduced when the 13 C slice thickened. Figure 6 shows the phantom test results at the scanner. A lowresolution 13 C image was obtained from the 4 cylindrical tubes that contain incremental concentrations of ethylene glycol (spatial resolution = 5 Â 5mm 2 ; Figure 6B). High-resolution 13 C images were reconstructed using SI, NI, BLI, SP, and PA with upsampling factors of 2, 4, 6, and 8, respectively. Figure 6, B and C, shows the reconstructed high-resolution 13 C images and the signal change along the reference lines x, y, and z with an upsampling factor of 4 (spatial resolution= 1:25 Â 1:25 mm 2 ). The high-resolution image from PA showed significantly enhanced contrast as compared with the results from the other interpolation methods. In all of the upsampled images, no obvious 13 C signal was detected from the water phantom (phantom #4). The mean signal intensities calculated from 3 ROIs of the reconstructed high-resolution images are summarized in Figure  6D, which shows accurate quantification results from PA compared with the ground truth.
Finally, the proposed super-resolution method was tested with hyperpolarized 13 C human brain images. After skull-stripping from the T1-weighted 1 H image, the possibility maps of GM, WM, and CSF were calculated ( Figure 7A). The time-averaged low-resolution hyperpolarized 13 C images of [1-13 C] pyruvate and [1-13 C] lactate (spatial resolution = 1:5 Â 1:5cm 2 ) were upsampled by 2 and 4 times using SI, NI, BLI, SP, and PA. Peak SNR was measured as 32.4 and 20.9 from the pyruvate and lactate images, respectively. Figure 7B shows the 4-fold upsampled hyperpolarized 13 C images, overlaid over the corresponding 1 H MRI (spatial resolution = 0:375 Â 0:375cm 2 ). Compared with the upsampled images using SI, NI, BLI, and SP, the results from PA showed clearer boundaries for each compartment. In particular, the edge of brain and the boundary across CSF and WM showed significant contrast enhancement. The signal changes along the reference lines (dotted lines in Figure 7B) are shown in Figure 7D, and again, the upsampled images from PA showed the highest contrast at the edge and similar intracompartment signal profile as other images. Moreover, signal increased at the edge of the brain in PA-reconstructed 13 C images, especially in the pyruvate map. The mean signal intensities from ROIs in CSF (ROI 1), GM (ROI 2), and WM (ROI 3) are summarized in Figure 7F. For all 3 ROIs, the quantification accuracy of mean signal intensities was comparable between PA and the other methods for both 2-and 4-time upsampled cases. Figure 8 shows the time-resolved low-resolution images of hyperpolarized [1-13 C] pyruvate and [1-13 C] lactate at selected time points and the interpolated high-resolution images. Similar to the time-averaged images, increased contrast was consistently observed after applying PA even with the decaying 13 C SNRs over time. Temporal changes in 3 representative ROIs of CSF (#1), GM (#2), and WM (#3) were comparable to those from other interpolation methods ( Figure 8C). For full 13 C images of pyruvate and lactate at all time points and the averaged spectrum, see online supplemental Material.

DISCUSSION
In this study, we showed that the patch-based reconstruction algorithm improves spatial resolution and image contrast of 13 C images by using a priori information obtained from high-resolution 1 H MRI. Simulation, phantom, and in vivo studies showed that signal intensity and spatial variation within each compartment were preserved in PA-reconstructed 13 C images even when the 1 H-based segmentation was suboptimal or Figure 5. Effect of relative 13 C slice thickness to 1 H slice on the performance of the PA. A 6-slice 3D digital phantom was generated to represent high-resolution axial multislice 1 H images (eg, 0.5-cm slices) (A). To show the case that hyperpolarized 13 C images are 3 and 6 times thicker than those of 1 H MRI, 2 and 1 low-resolution 13 C images were created, respectively, over the slab (eg, 1.5-and 3.0cm slices). For both cases, the low-resolution 13 C images were reconstructed using SI, NI, BLI, SP, and PA. The reconstructed high-resolution 13 C images, the signal profiles along the reference lines, and the quantification results are summarized for the 13 C images when the slice thickness is 3 (B) and 6 (C) times larger than the 1 H slice.
Super-Resolution Hyperpolarized 13 C Imaging of Human Brain contaminated to represent the actual 13 C distribution. Moreover, the time-resolved dynamic hyperpolarized 13 C human brain images showed a consistent performance of PA over temporal changes of the 13 C signals.

Consideration of Reconstruction Parameters for Patch-Based Algorithm
The potential mismatch between segmentation and upsampled 13 C image increased in proportion to the upsampling factor. Because of the large partial volume effect, the high-resolution segmentation information did not fit into the upsampled image. The impact of this misalignment can be more severe for organs with complex structures and multiple compartments (eg, brain). To maintain the reconstruction accuracy, the upsampling factor was limited to 4 for reconstructing the human brain images (16). However, higher upsampling factors might be eligible for organs with simpler structures without compromising quantification accuracy as the simulation and phantom studies have shown (Figures 2 and 6).
Partial volume effect along the slice thickness on PA performance was also determined. In the simulation, we considered 2 slice thicknesses for 13 C images (1.5 and 3.0 cm), considering those reported in the literature (2,3,6,7). The quantification accuracy was not compromised in both cases. With increased slice thickness of 13 C image, the calculated possibility maps were exposed to larger potential partial volume effects along the slice direction and blurred edges of compartments, which resulted in limited contrast enhancement in the high-resolution 13 C images ( Figures 5B and 5C). Nonetheless, the high-resolution images reconstructed from hyperpolarized 13 C brain images by using PA showed clear contrast enhancement across CSF and WM, especially for lactate ( Figure 8).

Segmentation Strategies for Tissue Compartments
Translation of hyperpolarized 13 C technology is still in early stage, and metabolic profiles measured by hyperpolarized 13 Cpyruvate in the human brain have not been fully established. As  this study focused on the verification of PA for hyperpolarized 13 C images, a simple model was tested by segmenting the brain tissue to GM, WM, and CSF. Indeed, recent human brain imaging studies using hyperpolarized [1-13 C] pyruvate (2, 6) showed larger [1-13 C] pyruvate, [1-13 C] lactate, and [ 13 C] bicarbonate signals in GM than WM. Although the reconstructed images from PA showed improved intercompartmental contrast and reliable intracompartmental signal distribution, this overly simplified segmentation strategy needs to be further verified and, perhaps, more detailed segmentation models will be required. For instance, Lee et al. (6) reported that the distribution of hyperpolarized [1-13 C] lactate, produced from [1-13 C] pyruvate, exhibited a consistent pattern when registered to the LPBA40 (LONI Probabilistic Brain Atlas) atlas. Vasculature is another potential compartment, as a large portion of hyperpolarized [1-13 C] pyruvate and [1-13 C] lactate is preserved in the vasculature. Thus, possibility maps calculated from perfusion images (eg, ASL [Arterial Spin Labeling]) would provide additional detail for reconstructing high-resolution pyruvate and lactate images by PA. If necessary, multimodal imaging-based segmentation strategies can be considered for the optimal PA-based reconstruction (16).
Elevated signals, appearing in the peripherals of PA-reconstructed 13 C brain maps (Figure 7, B and D), are likely because of the PA corrected partial volume effect by incorporating the 1 Hbased segmented information during the reconstruction. This phenomenon was also reported in a previous study (16) and is more noticeable in the pyruvate map. Besides, brighter 13 C regions adjacent to dark rims outside of the brain were observed, Figure 7. Reconstruction of high-resolution hyperpolarized 13 C images of human brain using PA. From the skull-striped T1-weighted 1 H image, possibility maps of GM, WM, and CSF were calculated (A). Low-resolution brain images of hyperpolarized [1-13 C] pyruvate and [1-13 C] lactate were acquired from a healthy subject, then 2-and 4-fold upsampled using SI, NI, BLI, SP, and PA. The images shown are 4-fold upsampled (B). Three distinct ROIs (dotted circles in B) of the brain showed that the signal intensities were reliable for all the 13 C-metabolites when reconstructed with upsampling factors of 2 and 4 (C). The signal changes along the reference lines marked in (B) are shown in (D).
implying a misalignment between the segmentation (especially for CSF) and actual 13 C signal distribution. In addition to partial volume effect of the low-resolution 13 C maps, the mismatch is contributed by insufficient a priori knowledge of cerebral compartments. Probability maps with more detailed segmentation strategies may improve the performance of PA at the edges. In particular, inclusion of perfusion map in segmentation will better describe the distribution of pyruvate and lactate in vasculature.

Other Limitations, Potential Improvements, and Future Applications
Because of the characteristics of hyperpolarized 13 C molecules and the limited hardware performance used for this study, highresolution 13 C metabolite maps of the human brain could not be acquired. Instead, we compared PA with several other conventional interpolation methods to show the feasibility of PA for reconstructing super-resolution in vivo hyperpolarized 13 C images. Potentially, high-resolution in vivo 13 C images measured  by accelerated acquisition strategies (eg, parallel imaging, denoising schemes) may be used as ground truth for further evaluation.
Our study shows that proposed PA mainly improves marginal information of the 13 C image where segmentation is applied. Within each segmentation, PA shows comparable performance as other interpolation methods. The influence of this limitation could be minor when the 13 C images have less complicated segmentation, as shown in simulation and phantom studies. However, for images with intricate compartments such as brain maps, the segmentation strategy should be carefully chosen for optimal performance of PA.
In this study, we assessed PA's performance for improving spatial resolution of single-slice dynamic 2D 13 C images. PA can be further developed as a 3D super-resolution method for improving the spatial resolution of volumetric data along the slice-encoding domain as well.
As long as proper segmentations that delineate pathological regions are available, PA can be applied to images with lesions. Indeed, Jain et al. (16) achieved super-resolution spectroscopic 1 H brain imaging of patients with multiple sclerosis using PA under the guidance of segmented information from 1 H T 1weighted FLAIR images. Besides, PA is applicable to enhance the hyperpolarized 13 C imaging of other organs (such as heart, kidney, and skeletal muscle) with appropriate segmentation strategies. For instance, a compartment for bones would be appropriate when applying PA to hyperpolarized 13 C skeletal muscle images, as they do not contain any 13 C signal (30).
In conclusion, we proposed a patch-based super-resolution algorithm that exploited high-resolution 1 H MRI for reconstructing hyperpolarized 13 C images and showed the performance in simulations, phantoms, and hyperpolarized [1-13 C] pyruvate images of healthy human brain. Effects of SNR, upsampling factor, segmentation, and slice thickness on the performance of PA were assessed. In addition to improving spatial resolution, the proposed algorithm also enhanced image contrast of 13 C images while maintaining the quantification accuracy and intracompartmental signal inhomogeneity.