THE NEUMANN PROBLEM ON ELLIPSOIDS.

The Neumann problem on an ellipsoid in Rn asks for a function harmonic inside the ellipsoid whose normal derivative is some specified function on the ellipsoid. We solve this problem when the specified function on the ellipsoid is a normalized polynomial (a polynomial divided by the norm of the normal vector arising from the definition of the ellipsoid). Specifically, we give a necessary and sufficient condition for a solution to exist, and we show that if a solution exists then it is a polynomial whose degree is at most the degree of the polynomial giving the specified function. Furthermore, we give an algorithm for computing this solution. We also solve the corresponding generalized Neumann problem and give an algorithm for computing its solution.

Accelerated high-bandwidth MR spectroscopic imaging using compressed sensing.

PURPOSE: To develop a compressed sensing (CS) acceleration method with a high spectral bandwidth exploiting the spatial-spectral sparsity of MR spectroscopic imaging (MRSI). METHODS: Accelerations were achieved using blip gradients during the readout to perform nonoverlapped and stochastically delayed random walks in kx -ky -t space, combined with block-Hankel matrix completion for efficient reconstruction. Both retrospective and prospective CS accelerations were applied to (13) C MRSI experiments, including in vivo rodent brain and liver studies with administrations of hyperpolarized [1-(13) C] pyruvate at 7.0 Tesla (T) and [2-(13) C] dihydroxyacetone at 3.0 T, respectively. RESULTS: In retrospective undersampling experiments using in vivo 7.0 T data, the proposed method preserved spectral, spatial, and dynamic fidelities with R(2) ≥ 0.96 and ≥ 0.87 for pyruvate and lactate signals, respectively, 750-Hz spectral separation, and up to 6.6-fold accelerations. In prospective in vivo experiments, with 3.8-fold acceleration, the proposed method exhibited excellent spatial localization of metabolites and peak recovery for pyruvate and lactate at 7.0 T as well as for dihydroxyacetone and its metabolic products with a 4.5-kHz spectral span (140 ppm at 3.0 T). CONCLUSIONS: This study demonstrated the feasibility of a new CS approach to accelerate high spectral bandwidth MRSI experiments. Magn Reson Med 76:369-379, 2016. © 2016 Wiley Periodicals, Inc.

Chemical shift separation with controlled aliasing for hyperpolarized (13) C metabolic imaging.

PURPOSE: A chemical shift separation technique for hyperpolarized (13) C metabolic imaging with high spatial and temporal resolution was developed. Specifically, a fast three-dimensional pulse sequence and a reconstruction method were implemented to acquire signals from multiple (13) C species simultaneously with subsequent separation into individual images. THEORY AND METHODS: A stack of flyback echo-planar imaging readouts and a set of multiband excitation radiofrequency pulses were designed to spatially modulate aliasing patterns of the acquired metabolite images, which translated the chemical shift separation problem into parallel imaging reconstruction problem. An eight-channel coil array was used for data acquisition and a parallel imaging method based on nonlinear inversion was developed to separate the aliased images. RESULTS: Simultaneous acquisitions of pyruvate and lactate in a phantom study and in vivo rat experiments were performed. The results demonstrated successful separation of the metabolite distributions into individual images having high spatial resolution. CONCLUSION: This method demonstrated the ability to provide accelerated metabolite imaging in hyperpolarized (13) C MR using multichannel coils, tailored readout, and specialized RF pulses.

Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion.

PURPOSE: A calibrationless parallel imaging reconstruction method, termed simultaneous autocalibrating and k-space estimation (SAKE), is presented. It is a data-driven, coil-by-coil reconstruction method that does not require a separate calibration step for estimating coil sensitivity information. METHODS: In SAKE, an undersampled, multichannel dataset is structured into a single data matrix. The reconstruction is then formulated as a structured low-rank matrix completion problem. An iterative solution that implements a projection-onto-sets algorithm with singular value thresholding is described. RESULTS: Reconstruction results are demonstrated for retrospectively and prospectively undersampled, multichannel Cartesian data having no calibration signals. Additionally, non-Cartesian data reconstruction is presented. Finally, improved image quality is demonstrated by combining SAKE with wavelet-based compressed sensing. CONCLUSION: Because estimation of coil sensitivity information is not needed, the proposed method could potentially benefit MR applications where acquiring accurate calibration data is limiting or not possible at all.

3D hyperpolarized C-13 EPI with calibrationless parallel imaging.

With the translation of metabolic MRI with hyperpolarized 13C agents into the clinic, imaging approaches will require large volumetric FOVs to support clinical applications. Parallel imaging techniques will be crucial to increasing volumetric scan coverage while minimizing RF requirements and temporal resolution. Calibrationless parallel imaging approaches are well-suited for this application because they eliminate the need to acquire coil profile maps or auto-calibration data. In this work, we explored the utility of a calibrationless parallel imaging method (SAKE) and corresponding sampling strategies to accelerate and undersample hyperpolarized 13C data using 3D blipped EPI acquisitions and multichannel receive coils, and demonstrated its application in a human study of [1-13C]pyruvate metabolism.

Using a local low rank plus sparse reconstruction to accelerate dynamic hyperpolarized 13C imaging using the bSSFP sequence.

Acceleration of dynamic 2D (T2 Mapping) and 3D hyperpolarized 13C MRI acquisitions using the balanced steady-state free precession sequence was achieved with a specialized reconstruction method, based on the combination of low rank plus sparse and local low rank reconstructions. Methods were validated using both retrospectively and prospectively undersampled in vivo data from normal rats and tumor-bearing mice. Four-fold acceleration of 1-2 mm isotropic 3D dynamic acquisitions with 2-5 s temporal resolution and two-fold acceleration of 0.25-1 mm2 2D dynamic acquisitions was achieved. This enabled visualization of the biodistribution of [2-13C]pyruvate, [1-13C]lactate, [13C, 15N2]urea, and HP001 within heart, kidneys, vasculature, and tumor, as well as calculation of high resolution T2 maps.

Cancer recurrence monitoring using hyperpolarized [1-13C]pyruvate metabolic imaging in murine breast cancer model.

The purpose of this work was to study the anatomic and metabolic changes that occur with tumor progression, regression and recurrence in a switchable MYC-driven murine breast cancer model. Serial 1H MRI and hyperpolarized [1-13C]pyruvate metabolic imaging were used to investigate the changes in tumor volume and glycolytic metabolism over time during the multistage tumorigenesis. We show that acute de-induction of MYC expression in established tumors results in rapid tumor regression and significantly reduced glycolytic metabolism as measured by pyruvate-to-lactate conversion. Moreover, cancer recurrences occurring at the tumor sites independently of MYC expression were observed to accompany markedly increased lactate production.

Development of high resolution 3D hyperpolarized carbon-13 MR molecular imaging techniques.

The goal of this project was to develop and apply techniques for T2 mapping and 3D high resolution (1.5mm isotropic; 0.003cm3) 13C imaging of hyperpolarized (HP) probes [1-13C]lactate, [1-13C]pyruvate, [2-13C]pyruvate, and [13C,15N2]urea in vivo. A specialized 2D bSSFP sequence was implemented on a clinical 3T scanner and used to obtain the first high resolution T2 maps of these different hyperpolarized compounds in both rats and tumor-bearing mice. These maps were first used to optimize timings for highest SNR for single time-point 3D bSSFP acquisitions with a 1.5mm isotropic spatial resolution of normal rats. This 3D acquisition approach was extended to serial dynamic imaging with 2-fold compressed sensing acceleration without changing spatial resolution. The T2 mapping experiments yielded measurements of T2 values of >1s for all compounds within rat kidneys/vasculature and TRAMP tumors, except for [2-13C]pyruvate which was ~730ms and ~320ms, respectively. The high resolution 3D imaging enabled visualization the biodistribution of [1-13C]lactate, [1-13C]pyruvate, and [2-13C]pyruvate within different kidney compartments as well as in the vasculature. While the mouse anatomy is smaller, the resolution was also sufficient to image the distribution of all compounds within kidney, vasculature, and tumor. The development of the specialized 3D sequence with compressed sensing provided improved structural and functional assessments at a high (0.003cm3) spatial and 2s temporal resolution in vivo utilizing HP 13C substrates by exploiting their long T2 values. This 1.5mm isotropic resolution is comparable to 1H imaging and application of this approach could be extended to future studies of uptake, metabolism, and perfusion in cancer and other disease models and may ultimately be of value for clinical imaging.

Screen-printed flexible MRI receive coils.

Magnetic resonance imaging is an inherently signal-to-noise-starved technique that limits the spatial resolution, diagnostic image quality and results in typically long acquisition times that are prone to motion artefacts. This limitation is exacerbated when receive coils have poor fit due to lack of flexibility or need for padding for patient comfort. Here, we report a new approach that uses printing for fabricating receive coils. Our approach enables highly flexible, extremely lightweight conforming devices. We show that these devices exhibit similar to higher signal-to-noise ratio than conventional ones, in clinical scenarios when coils could be displaced more than 18 mm away from the body. In addition, we provide detailed material properties and components performance analysis. Prototype arrays are incorporated within infant blankets for in vivo studies. This work presents the first fully functional, printed coils for 1.5- and 3-T clinical scanners.

Development and testing of hyperpolarized (13)C MR calibrationless parallel imaging.

A calibrationless parallel imaging technique developed previously for (1)H MRI was modified and tested for hyperpolarized (13)C MRI for applications requiring large FOV and high spatial resolution. The technique was demonstrated with both retrospective and prospective under-sampled data acquired in phantom and in vivo rat studies. A 2-fold acceleration was achieved using a 2D symmetric EPI readout equipped with random blips on the phase encode dimension. Reconstructed images showed excellent qualitative agreement with fully sampled data. Further acceleration can be achieved using acquisition schemes that incorporate multi-dimensional under-sampling.

Rapid sequential injections of hyperpolarized [1-¹³C]pyruvate in vivo using a sub-kelvin, multi-sample DNP polarizer.

The development of hyperpolarized technology utilizing dynamic nuclear polarization (DNP) has enabled the rapid measurement of (13)C metabolism in vivo with very high SNR. However, with traditional DNP equipment, consecutive injections of a hyperpolarized compound in an animal have been subject to a practical minimum time between injections governed by the polarization build-up time, which is on the order of an hour for [1-(13)C]pyruvate. This has precluded the monitoring of metabolic changes occurring on a faster time scale. In this study, we demonstrated the ability to acquire in vivo dynamic magnetic resonance spectroscopy (MRS) and 3D magnetic resonance spectroscopic imaging (MRSI) data in normal rats with a 5 min interval between injections of hyperpolarized [1-(13)C]pyruvate using a prototype, sub-Kelvin dynamic nuclear polarizer with the capability to simultaneously polarize up to 4 samples and dissolve them in rapid succession. There were minimal perturbations in the hyperpolarized spectra as a result of the multiple injections, suggesting that such an approach would not confound the investigation of metabolism occurring on this time scale. As an initial demonstration of the application of this technology and approach for monitoring rapid changes in metabolism as a result of a physiological intervention, we investigated the pharmacodynamics of the anti-cancer agent dichloroacetate (DCA), collecting hyperpolarized data before administration of DCA, 1 min after administration, and 6 min after administration. Dramatic increases in (13)C-bicarbonate were detected just 1 min (as well as 6 min) after DCA administration.