Synopsis

Keywords: Data Processing, Cardiomyopathy

The volumetric patch-based super-resolution method can reconstruct a single-slice low-resolution hyperpolarized ¹³C MRI to multiple ¹³C slices with enhanced spatial resolution by exploiting the corresponding high-resolution structural ¹H MRI. In this study, the overall performance of this method and the effects of patch size were evaluated using a simulated digital phantom and an anthropomorphic cardiac ¹³C MR phantom. The optimal patch size for this reconstruction method was also applied to in-vivo human ¹³C cardiac images acquired with an injection of hyperpolarized [1-¹³C]pyruvate.

Introduction

Carbon-13 (¹³C) MRI with hyperpolarized (HP) [1-¹³C]pyruvate captures key processes of glucose metabolism such as lactate fermentation and pyruvate oxidation of the heart^1-4. However, the rapidly varying nature of HP signals and the quarter-size gyromagnetic ratio of ¹³C as compared to ¹H restrict the spatial resolution of cardiac HP images to the order of centimeters, which is much larger than ¹H cardiac images. Previously, we developed a two-dimensional⁵ and a volumetric⁶ patch-based super-resolution (PBSR) reconstruction algorithms to enhance the spatial resolutions of HP ¹³C MRI by exploiting high-resolution compartmental information collected from ¹H patches. We noticed that the quality of the PBSR reconstructed images are sensitive to the patch size. In this study, we investigated the effects of patch size on 3D PBSR reconstruction for optimal reconstruction.

Methods

The reconstruction procedure is based on the previously presented 2D and 3D PBSR algorithms^{5, 6}. Briefly, the process is composed of three steps as summarized in Figure 1. First, a patch-based weight matrix is calculated from the high-resolution segmented ¹H MRI cardiac tissue compartments. Second, initial high-resolution multi-slice ¹³C images are estimated by interpolating the original ¹³C image. Finally, high-resolution multi-slice ¹³C images are iteratively updated by the guidance of the weight matrix and the subsequent mean correction until the incremental improvement is within a pre-determined threshold.

The range of patch sizes was investigated from 3×3×3 to 19×19×9 of neighborhood voxels with an isotropic size increment of two. A digital phantom and an anthropomorphic MR phantom that contained [¹³C]bicarbonate were examined to identify a proper patch size, which was also applied to human HP ¹³C cardiac images.

a. Digital phantom
A numerical 3D digital phantom was generated with MATLAB (MathWorks, Natick, MA, USA)⁷. The phantom depicts a cross-sectional view of the left ventricle in the heart. Three major compartments are generated, including the ventricle, cardiac skeleton (myocardium), and its surrendering area in the chest. Both ¹H (structural) and ¹³C (metabolic) images were created from this phantom.

b. ¹³C MR torso phantom
The torso phantom (Data Spectrum, Hillsborough, NC, USA) with a heart insert, filled with 0.4M [¹³C]bicarbonate. The ¹H/¹³C-integrated imaging protocol included a ¹H multi-slice 2D T1-weighted gradient echo (TE/TR=1.712/4.442ms, FOV=40×40cm², matrix size=512×512, slices=3mm×10) and a 2D ¹³C single-slice metabolite-selective multi-echo spiral imaging (TE/TR=18.42/5000ms, FOV=40×40cm², matrix=40×40, slice=30mm×1) along the short-axis view plane⁸.

c. In-vivo human HP cardiac ¹³C MRI
A set of cardiac images were acquired from a healthy volunteer (50 year old, female). For ¹H imaging, the T₁-weighted FIESTA was acquired with short-axis and long-axis views (TE/TR/IR=1.364/3.504/250ms, FOV=40×40cm², matrix=256×256, slices=5mm×6). For ¹³C images, single-slice HP images of [¹³C]bicarbonate, [1-¹³C]lactate, and [1-¹³C]pyruvate were acquired 6s after an injection of 250mM HP [1-¹³C]pyruvate solution using a multi-echo spiral imaging sequence (single shot, FOV=40×40cm², spatial resolution=1×1cm², slice=30mm×1, flip angle=90° for bicarbonate, 90° for lactate, and 5° for pyruvate) in an interleaved spiral readouts every two R-R intervals⁸.

All MR images were acquired from a clinical 3T MRI scanner (GE Healthcare, Waukesha, WI, USA). The body coil was used for ¹H RF excitation and data acquisition. A two-loop ¹³C transmit/receive Helmholtz coil was used for ¹³C (PulseTeq Limited, Chobham, Surrey, UK).

Results

In the digital phantom, the reconstruction accuracy asymptotically improved as the patch size increased and was saturated with the patch size of 17×17×9 (Figure 2). The reconstructed images were evaluated using image quality metrics (MSE, SNR_peak, and SSMI) between the ground truths and the reconstructed images. All three indices showed a similar trend of gradual changes along with the increasing patch size and reached a stable level while the patch size was larger than 17×17×9 for pyruvate, and 9×9×9 for bicarbonate images. The reconstructed images from the torso phantom showed the correct structural distribution with the patch size of 5×5×5 (Figure 3). HP [¹³C]bicarbonate, [1-¹³C]pyruvate, and [1-¹³C]lactate metabolic maps of the human heart in the short axis (Figure 4) and the long axis planes (Figure 5) were also reconstructed using the PBSR with a 5×5×5 patch. High structural similarity in reconstructed ¹³C images in torso phantom images (SSIM = 0.9943) and human cardiac images (SSIM>0.97 for all metabolites and view planes) when compared to low-resolution ¹³C images. The entropy of ¹³C images was higher in the digital phantom (6.7557) than in the torso phantom images (4.6309) and cardiac images (5.2492).

Discussion

A larger patch reconstructs more accurate images since the PBSR algorithm considers the signal continuity and redundancy between two neighboring pixels, and it includes more neighborhood information⁹. In addition, the saturating patch size depends on the dimensions of input image and reconstructed image. A large ratio of reconstruction-to-input size requires high computation complexity and therefore a large patch size¹⁰. The digital phantom required a 17×17×9 patch for the ratio of 1.6 (256/160), while a 5×5×5 patch was sufficient for the torso phantom and human cardiac images whose ratio was 1.2 (192/160). In addition, the higher entropy of the low-resolution image for the PBSR might require the larger patch because of the image complexity.

Conclusion

The current investigation demonstrated the optimal patch size to the PBSR would depend on the ratio of reconstruction-to-input size.

Acknowledgements

National Institute of Health: R01NS107409, R21EB030765, P30DK127984, P41EB015908 Department of Defense: W81XWH2210485 The Welch Foundation: I-2009-20190330.