Hadamard Encoding Research Articles

Fast high-resolution 2D NMR spectroscopy in inhomogeneous fields via Hadamard frequency encoding and spatial encoding

Two new pulse sequences via Hadamard frequency encoding and spatial encoding are proposed to achieve high-resolution intermolecular double-quantum coherence correlation spectroscopy (iDQC-COSY) in inhomogeneous fields within a few scans. Hadamard encoding and spatial encoding are utilized to reduce acquisition time, while iDQC is used to remove the influence of inhomogeneous fields. Two Hadamard encoded schemes, namely, solute Hadamard encoding and solvent Hadamard encoding, are different in the two sequences. Detail analyses of the advantages and disadvantages of the two sequences are carried out. Acquisition times are both shortened by orders of magnitude. Experiments are performed to show their efficiencies.

Hadamard encoded 2D correlation spectroscopy in inhomogeneous fields

In this Letter, we present a new approach to obtain two-dimensional high-resolution COSY spectra in inhomogeneous fields based on Hadamard encoding. It is an extension of one-dimensional high-resolution intermolecular double-quantum coherence Hadamard encoding approach. The approach is time-efficient and can recover useful structural information even when the inhomogeneous line broadening leads to overlap of neighboring resonances in the conventional COSY spectrum. Theoretical expression of the resulting signals was deduced based on intermolecular multiple-quantum coherence treatment in combination with distant dipolar field treatment. Experiments were performed to verify its feasibility and advantages over previous methods.

Volumetric measurement of perfusion and arterial transit delay using hadamard encoded continuous arterial spin labeling

Creating images of the transit delay from the labeling location to image tissue can aid the optimization and quantification of arterial spin labeling perfusion measurements and may provide diagnostic information independent of perfusion. Unfortunately, measuring transit delay requires acquiring a series of images with different labeling timing that adds to the time cost and increases the noise of the arterial spin labeling study. Here, we implement and evaluate a proposed Hadamard encoding of labeling that speeds the imaging and improves the signal-to-noise ratio efficiency. Volumetric images in human volunteers confirmed the theoretical advantages of Hadamard encoding over sequential acquisition of images with multiple labeling timing. Perfusion images calculated from Hadamard encoded acquisition had reduced signal-to-noise ratio relative to a dedicated perfusion acquisition with either assumed or separately measured transit delays, however.

High‐resolution NMR spectroscopy in inhomogeneous fields via Hadamard‐encoded intermolecular double‐quantum coherences

A new pulse sequence based on intermolecular double-quantum coherences was proposed to obtain one-dimensional high-resolution liquid NMR spectra in inhomogeneous magnetic fields via Hadamard encoding. In contrast with the conventional intermolecular multiple-quantum coherences method with a two-dimensional acquisition to obtain one one-dimensional high-resolution spectrum, the new method can provide relatively high-resolution spectra directly through one-dimensional acquisition, and can greatly improve the signal-to-noise ratio of the spectrum within a relatively short acquisition time. Theoretical derivation was performed and analytical expressions of the resulting signals are given. Solution samples in purposely de-shimmed magnetic fields and pig brain tissue samples were tested. The experimental results demonstrate that this sequence can retain useful structural information, even when the field inhomogeneity is sufficiently severe to erase almost all spectral information with conventional one-dimensional single-quantum coherence techniques, and good solvent suppression can be achieved. This method may provide a promising technique for applications in in vivo and in vitro NMR.

Chemical-shift imaging in micro- and nano-MRI

We demonstrate chemical-shift imaging of solids with a spatial resolution of about 1 $\ensuremath{\mu}$m using magnetic resonance force microscopy. Images with two spatial dimensions and one spectral dimension were recorded and an extension to three spatial dimensions and several spectral dimensions is possible. To reduce the measurement time multiplexing schemes are used for all dimensions (by either a Fourier or a Hadamard method) and quadrature detection is introduced for the directly acquired spatial dimension, in combination with Hadamard encoding.

Proton evolved local field solid-state nuclear magnetic resonance using Hadamard encoding: Theory and application to membrane proteins

NMR anisotropic parameters such as dipolar couplings and chemical shifts are central to structure and orientation determination of aligned membrane proteins and liquid crystals. Among the separated local field experiments, the proton evolved local field (PELF) scheme is particularly suitable to measure dynamically averaged dipolar couplings and give information on local molecular motions. However, the PELF experiment requires the acquisition of several 2D datasets at different mixing times to optimize the sensitivity for the complete range of dipolar couplings of the resonances in the spectrum. Here, we propose a new PELF experiment that takes the advantage of the Hadamard encoding (HE) to obtain higher sensitivity for a broad range of dipolar couplings using a single 2D experiment. The HE scheme is obtained by selecting the spin operators with phase switching of hard pulses. This approach enables one to detect four spin operators, simultaneously, which can be processed into two 2D spectra covering a broader range of dipolar couplings. The advantages of the new approach are illustrated for a U-(15)N NAL single crystal and the U-(15)N labeled single-pass membrane protein sarcolipin reconstituted in oriented lipid bicelles. The HE-PELF scheme can be implemented in other multidimensional experiments to speed up the characterization of the structure and dynamics of oriented membrane proteins and liquid crystalline samples.

Simultaneous two-voxel localized 1H-observed 13C-edited spectroscopy for in vivo MRS on rat brain at 9.4 T: Application to the investigation of excitotoxic lesions

13C spectroscopy combined with the injection of 13C-labeled substrates is a powerful method for the study of brain metabolism in vivo. Since highly localized measurements are required in a heterogeneous organ such as the brain, it is of interest to augment the sensitivity of 13C spectroscopy by proton acquisition. Furthermore, as focal cerebral lesions are often encountered in animal models of disorders in which the two brain hemispheres are compared, we wished to develop a bi-voxel localized sequence for the simultaneous bilateral investigation of rat brain metabolism, with no need for external additional references. Two sequences were developed at 9.4 T: a bi-voxel 1H–( 13C) STEAM-POCE (Proton Observed Carbon Edited) sequence and a bi-voxel 1H–( 13C) PRESS-POCE adiabatically decoupled sequence with Hadamard encoding. Hadamard encoding allows both voxels to be recorded simultaneously, with the same acquisition time as that required for a single voxel. The method was validated in a biological investigation into the neuronal damage and the effect on the Tri Carboxylic Acid cycle in localized excitotoxic lesions. Following an excitotoxic quinolinate-induced localized lesion in the rat cortex and the infusion of U– 13C glucose, two 1H–( 13C) spectra of distinct (4 × 4 × 4 mm 3) voxels, one centred on the injured hemisphere and the other on the contralateral hemisphere, were recorded simultaneously. Two 1H bi-voxel spectra were also recorded and showed a significant decrease in N-acetyl aspartate, and an accumulation of lactate in the ipsilateral hemisphere. The 1H–( 13C) spectra could be recorded dynamically as a function of time, and showed a fall in the glutamate/glutamine ratio and the presence of a stable glutamine pool, with a permanent increase of lactate in the ipsilateral hemisphere. This bi-voxel 1H–( 13C) method can be used to investigate simultaneously both brain hemispheres, and to perform dynamic studies. We report here the neuronal damage and the effect on the Tri Carboxylic Acid cycle in localized excitotoxic lesions.

Pulse Repetition Time and Contrast Enhancement

To investigate theoretically enhancement and optimal pulse repetition times for Gd-BOPTA and Gd-DTPA enhanced brain imaging at 0.23, 1.5, and 3.0 T. The theoretical relaxation times of unenhanced, conventional contrast agent (Gd-DTPA) and new generation contrast agent (Gd-BOPTA) enhanced glioma were calculated. Then, simulation of the signals and contrasts as a function of concentration and pulse repetition time (TR) in spin echo sequence was done at 0.23, 1.5, and 3.0 T. The effect of echo time (TE) on tumor-white matter contrast was also clarified. Three patient cases were imaged at 0.23 T as a test of principle. Gd-BOPTA may give substantially better glioma-to-white matter contrast than Gd-DTPA but is more sensitive to the length of TR. These characteristics are accentuated at 0.23 T. Optimal TR lengths are shorter for Gd-BOPTA than for Gd-DTPA enhanced imaging at all field strengths. TR optimized for Gd-DTPA may thus give suboptimal contrast in Gd-BOPTA enhanced imaging. Higher enhancement with Gd-BOPTA is further accentuated by short TE. Appropriate TRs at 0.23 T appear to be approximately 300 to 400 milliseconds and 250 to 300 milliseconds, at 1.5 T 500 to 600 milliseconds and 400 to 450 milliseconds and at 3.0 T 550 to 650 milliseconds and 475 to 525 milliseconds using Gd-DTPA and Gd-BOPTA, respectively. For Gd-BOPTA enhanced imaging, it seems justified to optimize TR according to contrast and seek options like parallel excitation (Hadamard encoding) for increasing the number of slices and SNR.

Improved 3D DOSY-TOCSY experiment for mixture analysis

With respect to best currently available pulse sequences, a 10-fold reduction in minimum experiment time together with significant resolution enhancement can be achieved in 3D DOSY homonuclear experiments by means of Hadamard encoding, as illustrated here for the 3D DOSY-TOCSY experiment.

Fast magnetic resonance force microscopy with Hadamard encoding

We present a spatial encoding technique for magnetic resonance force microscopy that allows for a much enhanced image acquisition rate. The technique uses multiplexing, based on spatial Hadamard encoding, to acquire several slices of the image simultaneously and at an undiminished signal-to-noise ratio. We demonstrate an improvement in imaging time by a factor of 7.6, and further advances can be expected.

Partial discrete Fourier transform (PDFT) multiband encoding.

For conventional multiband encoding techniques such as Hadamard encoding, scan time scales linearly with the number of slices encoded simultaneously. In this work, a new multiband encoding technique called partial discrete Fourier transform (PDFT) encoding is introduced, which overcomes this restriction. This technique incorporates the principle of partial Fourier imaging, allowing the tradeoff of SNR and imaging time without changing the number of slices. The theory behind PDFT encoding and its inherent sensitivity to phase errors are outlined. The theory was validated through simulations, showing that phase errors result in degraded slice localization. The feasibility of PDFT encoding of 12 slices was tested with experimental excitation profile measurements and heart images of a human subject using commercial MRI equipment. Imaging time was reduced to 66% with SNR reduced to 82%. Magn Reson Med 45:118-127, 2001.

Fast 3D T 2-weighted MRI with Hadamard encoding in the slice select direction

A fast method to obtain 3-dimensional (3D) magnetic resonance imaging with long repetition times is presented. It can be used to obtain fast 3D MRI with for example T 2 or diffusion weighted imaging. The method uses a 3D multiple thin slab sequence with radio frequency encoding, preferably Hadamard encoding, in the slice select direction. The point-spread function of the Hadamard-encoded slices is close to ideal even at low encoding numbers. This allows the acquisition of 3D data volumes with tolerable image quality up to four times faster than is possible using Fourier phase encoding. The scope of the method includes both longitudinal and transverse encoding. Longitudinal encoding provides a better point spread function than transverse encoding, at the expense of having to discard one slice per slab. The method is demonstrated experimentally for 4th order longitudinal Hadamard encoding to obtain 3D T 2-weighted images.

High-resolution imaging using Hadamard Encoding

High-resolution imaging techniques using noninvasive modalities such as magnetic resonance (MR) imaging are being pursued as in vivo cancer screening techniques in an attempt to eliminate the invasive nature of surgical biopsy. When acquiring high-resolution MR images for tissue screening, image fields of view have in the past been limited by the matrix sizes available in conventional MR scanners. We present here a technique that uses aliasing to produce high resolution images with larger matrix sizes than are currently available. The image is allowed to alias in both the frequency encoding and phase encoding dimensions, and the individual, aliased fields of view are recovered by Hadamard encoding methods. These fields may then be tiled to obtain a composite image with high spatial resolution and a large field of view. The technique is demonstrated using two-dimensional and three-dimensional in vivo imaging of the human brain and breast.

Multiple-voxel double-quantum lactate-edited spectroscopy using two-dimensional longitudinal Hadamard encoding

A conventional gradient-selected double-quantum lactate editing sequence was combined with fourth order two-dimensional longitudinal Hadamard encoding and slice-selective refocusing to acquire lactate-edited spectra in a 3 x 3 matrix of voxels. The performance of the sequence was verified in phantoms at 9.4 T and in focally ischemic rat brain at 7.0 T. Efficient suppression of water, lipid, and the singlet resonances of creatine, choline, and N-acetylaspartate was achieved, giving multi-voxel localized lactate-edited spectra with good signal-to-noise ratio.

Two methods for peak RF power minimization of multiple inversion-band pulses.

Two novel methods to minimize peak RF power for high order longitudinal Hadamard encoding are described and demonstrated experimentally. The first method uses the fact that the choice of a reference phase in an inversion process does not affect the final frequency response. In this method, the different single inversion-band pulses are added together, each with a different reference phase. For a proper phase choice, minimization of the peak RF power is obtained. Scaling laws are defined allowing the use of a given phase-set in multiple cases. In the second method, single inversion-band pulses are added together, each partially shifted in time. This results in a significant reduction in peak power with only a moderate increase in pulse length. Theoretical conditions outlining the optimal addition order are defined. Experimental results verify the theoretical conditions and demonstrate that the frequency response is not affected by the peak power minimization process. With the new low peak RF power, longitudinal Hadamard encoding of 8TH (or 16TH) order can be performed in any clinical setting.

Application of a Two-Dimensional Hadamard Encoding Mask for the Imaging of Thin-Layer Chromatography Plates by Laser-Induced Fluorescence or Surface-Enhanced Raman Scattering and for Use with a Photoacoustic Detector to Generate Three-Dimensional Photoacoustic Images

Spatial imaging of thin-layer chromatography plates using laser-induced fluorescence and surface-enhanced Raman scattering has been accomplished with a stationary two-dimensional Hadamard encoding mask. Detection of three nanograms of pararosaniline hydrochloride on a thin-layer chromatography plate was made possible by means of the surface-enhanced Raman phenomenon. The imaging capabilities of the stationary two-dimensional Hadamard encoding mask coupled with the depth profiling ability of photoacoustic detection allows for the three-dimensional photoacoustic imaging of a multiple analyte sample.

Simultaneous acquisition of phase‐contrast angiograms and stationary‐tissue images with Hadamard encoding of flow‐induced phase shifts

A technique for the simultaneous acquisition of three-dimensional phase-contrast angiograms and stationary-tissue images is described. Hadamard multiplexed encoding of flow information permits image acquisition times that are a third shorter than those of previous phase-contrast methods. The encoding scheme described also enables differentiation of flow-induced phase shifts from phase shifts due to resonance offset conditions such as field inhomogeneities and chemical shift. Display strategies that combine this phase information with the flow image are described.

A Visible Near-Infrared Hadamard Transform Spectrometer Based on a Liquid Crystal Spatial Light Modulator Array: A New Approach in Spectrometry

A stationary Hadamard encodement mask has been designed from a liquid crystal display. This mask, when properly installed and positioned in a dispersive instrument, allows the selected Hadamard encoded spectral elements to be focused on a single detector. Discussion of the advantages derived by this technique is presented. Several emission spectra in the visible and near-infrared region demonstrate the usefulness of the Hadamard transform technique. This novel spectrometer can provide a no-moving-parts spectroscopy for future spectral applications.