Frequency Encoding Research Articles

Fast acquisition of multidimensional NMR spectra of solids and mesophases using alternative sampling methods

Unique information about the atom-level structure and dynamics of solids and mesophases can be obtained by the use of multidimensional nuclear magnetic resonance (NMR) experiments. Nevertheless, the acquisition of these experiments often requires long acquisition times. We review here alternative sampling methods, which have been proposed to circumvent this issue in the case of solids and mesophases. Compared to the spectra of solutions, those of solids and mesophases present some specificities because they usually display lower signal-to-noise ratios, non-Lorentzian line shapes, lower spectral resolutions and wider spectral widths. We highlight herein the advantages and limitations of these alternative sampling methods. A first route to accelerate the acquisition time of multidimensional NMR spectra consists in the use of sparse sampling schemes, such as truncated, radial or random sampling ones. These sparsely sampled datasets are generally processed by reconstruction methods differing from the Discrete Fourier Transform (DFT). A host of non-DFT methods have been applied for solids and mesophases, including the G-matrix Fourier transform, the linear least-square procedures, the covariance transform, the maximum entropy and the compressed sensing. A second class of alternative sampling consists in departing from the Jeener paradigm for multidimensional NMR experiments. These non-Jeener methods include Hadamard spectroscopy as well as spatial or orientational encoding of the evolution frequencies. The increasing number of high field NMR magnets and the development of techniques to enhance NMR sensitivity will contribute to widen the use of these alternative sampling methods for the study of solids and mesophases in the coming years.

Magnetic field dependence of spatial frequency encoding NMR as probed on an oligosaccharide.

The magnetic field dependence of spatial frequency encoding NMR techniques is addressed through a detailed analysis of (1)H NMR spectra acquired under spatial frequency encoding on an oligomeric saccharide sample. In particular, the influence of the strength of the static magnetic field on spectral and spatial resolutions that are key features of this method is investigated. For this purpose, we report the acquisition of correlation experiments implementing broadband homodecoupling or J-edited spin evolutions, and we discuss the resolution enhancements that are provided by these techniques at two different magnetic fields. We show that performing these experiments at higher field improves the performance of high resolution NMR techniques based on a spatial frequency encoding. The significant resolution enhancements observed on the correlation spectra acquired at very high field make them valuable analytical tools that are suitable for the assignment of (1)H chemical shifts and scalar couplings in molecules with highly crowded spectrum such as carbohydrates.

Coded excitation plane wave imaging for shear wave motion detection.

Plane wave imaging has greatly advanced the field of shear wave elastography thanks to its ultrafast imaging frame rate and the large field-of-view (FOV). However, plane wave imaging also has decreased penetration due to lack of transmit focusing, which makes it challenging to use plane waves for shear wave detection in deep tissues and in obese patients. This study investigated the feasibility of implementing coded excitation in plane wave imaging for shear wave detection, with the hypothesis that coded ultrasound signals can provide superior detection penetration and shear wave SNR compared with conventional ultrasound signals. Both phase encoding (Barker code) and frequency encoding (chirp code) methods were studied. A first phantom experiment showed an approximate penetration gain of 2 to 4 cm for the coded pulses. Two subsequent phantom studies showed that all coded pulses outperformed the conventional short imaging pulse by providing superior sensitivity to small motion and robustness to weak ultrasound signals. Finally, an in vivo liver case study on an obese subject (body mass index = 40) demonstrated the feasibility of using the proposed method for in vivo applications, and showed that all coded pulses could provide higher SNR shear wave signals than the conventional short pulse. These findings indicate that by using coded excitation shear wave detection, one can benefit from the ultrafast imaging frame rate and large FOV provided by plane wave imaging while preserving good penetration and shear wave signal quality, which is essential for obtaining robust shear elasticity measurements of tissue.

Frequency- and spectrally-encoded confocal microscopy.

We describe a three-dimensional microscopy technique based on spectral and frequency encoding. The method employs a wavelength-swept laser to illuminate a specimen with a spectrally-dispersed line focus that sweeps over the specimen in time. The spatial information along each spectral line is further mapped into different modulation frequencies. Spectrally-resolved detection and subsequent Fourier analysis of the back-scattered light from the specimen therefore enable high-speed, scanner-free imaging of the specimen with a single-element photodetector. High-contrast, three-dimensional imaging capability of this method is demonstrated by presenting images of various materials and biological specimens.

Are the visual transients from microsaccades helpful? Measuring the influences of small saccades on contrast sensitivity

Like all saccades, microsaccades cause both spatial and temporal changes in the input to the retina. In space, recent studies have shown that these small shifts precisely relocate a narrow (smaller than the foveola) high-acuity retinal locus on the stimulus. However, it has long been questioned whether the temporal modulations resulting from microsaccades are also beneficial for vision. To address this question, we combined spectral analysis of the visual input to the retina with measurements of contrast sensitivity in humans. Estimation of how different types of eye movements redistribute the power of an otherwise stationary stimulus shows that small saccades contribute more temporal power than ocular drift in the low-frequency range, suggesting a specific role for these movements in the encoding of low spatial frequencies. However, an influence on contrast sensitivity was only found for saccades with amplitudes larger than 30′. Contrast thresholds remained highly similar in the presence and absence of smaller saccades. Furthermore, saccades of all amplitudes, including microsaccades, were strongly suppressed during exposure to the stimulus. These findings do not support an important function of the visual transients caused by microsaccades.

Characterizing the limits of MRI near metallic prostheses.

To characterize the fundamental limits of MRI near metallic implants on RF excitation, frequency encoding, and chemical shift-encoding water-fat separation. Multicomponent three-dimensional (3D) digital models of a total hip and a total knee replacement were used to construct material-specific susceptibility maps. The fundamental limits and spatial relationship of imaging near metallic prostheses were investigated as a function of distance from the prosthetic surface by calculating 3D field map perturbations using a well-validated k-space based dipole kernel. Regions limited by the bandwidth of RF excitation overlap substantially with those fundamentally limited by frequency encoding. Rapid breakdown of water-fat separation occurs once the intravoxel off-resonance exceeds ∼6 ppm over a full range of fat fractions (0%-100%) and SNR (5-100). Current 3D multispectral imaging methods would not benefit greatly from exciting spins beyond ±12 kHz despite the presence of signal that lies outside of this range from tissue directly adjacent to the metallic implants. Methods such as phase encoding in all three spatial dimensions are necessary to spatially resolve spins beyond an excitation bandwidth of ±12 kHz. The approach described in this study provides a benchmark for the capabilities of current imaging techniques to guide development of new MRI methods for imaging near metal.

Neural processing of speech in children is influenced by extent of bilingual experience

Language experience fine-tunes how the auditory system processes sound. Bilinguals, relative to monolinguals, have more robust evoked responses to speech that manifest as stronger neural encoding of the fundamental frequency (F0) and greater across-trial consistency. However, it is unknown whether such enhancements increase with increasing second language experience. We predict that F0 amplitude and neural consistency scale with dual-language experience during childhood, such that more years of bilingual experience leads to more robust F0 encoding and greater neural consistency. To test this hypothesis, we recorded auditory brainstem responses to the synthesized syllables ‘ba’ and ‘ga’ in two groups of bilingual children who were matched for age at test (8.4±0.67 years) but differed in their age of second language acquisition. One group learned English and Spanish simultaneously from birth (n=13), while the second group learned the two languages sequentially (n=15), spending on average their first four years as monolingual Spanish speakers. We find that simultaneous bilinguals have a larger F0 response to ‘ba’ and ‘ga’ and a more consistent response to ‘ba’ compared to sequential bilinguals and we demonstrate that these neural enhancements track with years of bilingual experience. These findings support the notion that bilingualism enhances subcortical auditory processing.

Effect of Repetition Rate on Speech Evoked Auditory Brainstem Response in Younger and Middle Aged Individuals.

Speech evoked auditory brainstem responses depicts the neural encoding of speech at the level of brainstem. This study was designed to evaluate the neural encoding of speech at the brainstem in younger population and middle-aged population at three different repetition rates (6.9, 10.9 and 15.4). Speech evoked auditory brainstem response was recorded from 84 participants (young participants=42, middle aged participants=42) with normal hearing sensitivity. The latency of wave V and amplitude of the fundamental frequency, first formant frequency and second formant frequency was calculated. Results showed that the latency of wave V was prolonged for middle-aged individuals for all three-repetition rates compared to the younger participants. The results of the present study also revealed that there was no difference in encoding of fundamental frequency between middle aged and younger individuals at any of the repetition rates. However, increase in repetition rate did affect the encoding of the fundamental frequency in middle-aged individuals. The above results suggest a differential effect of repetition rate on wave V latency and encoding of fundamental frequency. Further, it was noticed that repetition rate did not affect the amplitude of first formant frequency or second formant frequency in middle aged participants compared to the younger participants.

Nanosensitive optical coherence tomography for the study of changes in static and dynamic structures

We briefly discuss the principle of image formation in Fourier domain optical coherence tomography (OCT). The theory of a new approach to improve dramatically the sensitivity of conventional OCT is described. The approach is based on spectral encoding of spatial frequency. Information about the spatial structure is directly translated from the Fourier domain to the image domain as different wavelengths, without compromising the accuracy. Axial spatial period profiles of the structure are reconstructed for any volume of interest within the 3D OCT image with nanoscale sensitivity. An example of application of the nanoscale OCT to probe the internal structure of medico-biological objects, the anterior chamber of an ex vivo rat eye, is demonstrated.

TH‐A‐BRF‐10: Quantification of Subject‐Specific Susceptibility‐Related Geometric Distortion in Clinical Liver MRI for Radiation Therapy

Purpose:Subject‐specific susceptibility‐induced B0 inhomogeneity affects the geometric accuracy of MRI images, with potential impact on the accuracy of treatment planning and image guidance. This study quantifies individual distortions for patients with intrahepatic tumors.Methods:Liver MRI scans of 13 patients who were enrolled in an IRB approved study were acquired on a 3T scanner (Skyra, Siemens). Clinical contrast‐enhanced images were acquired by a 3D Volume Interpolated Breath‐Hold Examination (VIBE) sequence with TE/TR =1.65/4.3ms, voxel size = 2.5×2.5×3mm (axial sets) or 3.5×3.5×5mm (coronal sets), and frequency‐encoding (FE) bandwidth of 440Hz/pixel. B0 inhomogeneity was evaluated by acquisition of dual gradient echoes (GRE) with TE1/TE2/TR =4.92/7.38/106ms, a voxel size of 3.5×3.5×3.75mm, a FE bandwidth of 290Hz/pixel and breath‐hold. The phase difference maps from the two echoes were unwrapped using a quantitative MRI analysis software package (FSL, FMRIB, Oxford, UK). The resulting calculated B0 inhomogeneity maps (ΔB0 in Hz) were converted to voxel distortion maps in the FE direction (ΔX in mm) corresponding to the VIBE images.Results:Maximum susceptibility‐induced distortions were observed in the liver dome near the diaphragm. Using results from coronal VIBE images in this study as examples, we observed clusters of voxels displaced close to or greater than ΔX=3.5mm (440 Hz in ΔB0) in the VIBE images of the liver in 3 patients, and greater than 2 mm but less than 3.5 mm in 12 patients. On average, approximately 14% of imaged liver voxels had distortions ΔX>±1mm (ΔB0>±125Hz) and 1% of the voxels had ΔX>±2mm (ΔB0>±250Hz).Conclusion:Although advanced MRI techniques, like VIBE, permit faster acquisitions allowing for breath‐held examinations with limited motion‐induced artifacts, this study suggests that localized distortions due to subject‐specific susceptibility variations can occur and require additional advanced corrections based on measuring patient‐specific B0 inhomogeneity maps.The authors would like to acknowledge funding support from NIH R01EB016079 and NIH/NCI RO1 CA132834.

CHARACTERIZATION OF SIGNAL CONDUCTION ALONG DEMYELINATED AXONS BY ACTION-POTENTIAL-ENCODED SECOND HARMONIC GENERATION

Action-potential-encoded optical second harmonic generation (SHG) has been recently proposed for use in detecting the axonal damage in patients with demyelinating diseases. In this study, the characterization of signal conduction along axons of two different levels of demyelination was studied via a modified Hodgkin–Huxley model, because some types of demyelinating disease, i.e., primary progressive and secondary progressive multiple sclerosis, are difficult to be distinguished by magnetic resonance imaging (MRI), we focused on the differences in signal conduction between two different demyelinated axons, such as the first-level demyelination and the second-level demyelination. The spatio-temporal distribution of action potentials along demyelinated axons and conduction properties including the refractory period and frequency encoding in these two patterns were investigated. The results showed that demyelination could induce the decrease both in the amplitude of action potentials and the ability of frequency coding. Furthermore, the signal conduction velocity in the second-level demyelination was about 21% slower than that in the first-level demyelination. The refractory period in the second-level demyelination was about 32% longer than the first-level. Thus, detecting the signal conduction in demyelinated axons by action-potential-encoded optical SHG could greatly improve the assessment of demyelinating disorders to classify the patients. This technique also offers a potential fast and noninvasive optical approach for monitoring membrane potential.

Simultaneous multiagent hyperpolarized 13C perfusion imaging

To demonstrate simultaneous hyperpolarization and imaging of three (13)C-labeled perfusion MRI contrast agents with dissimilar molecular structures ([(13)C]urea, [(13)C]hydroxymethyl cyclopropane, and [(13)C]t-butanol) and correspondingly variable chemical shifts and physiological characteristics, and to exploit their varying diffusibility for simultaneous measurement of vascular permeability and perfusion in initial preclinical studies. Rapid and efficient dynamic multislice imaging was enabled by a novel pulse sequence incorporating balanced steady state free precession excitation and spectral-spatial readout by multiband frequency encoding, designed for the wide, regular spectral separation of these compounds. We exploited the varying bilayer permeability of these tracers to quantify vascular permeability and perfusion parameters simultaneously, using perfusion modeling methods that were investigated in simulations. "Tripolarized" perfusion MRI methods were applied to initial preclinical studies with differential conditions of vascular permeability, in normal mouse tissues and advanced transgenic mouse prostate tumors. Dynamic imaging revealed clear differences among the individual tracer distributions. Computed permeability maps demonstrated differential permeability of brain tissue among the tracers, and tumor perfusion and permeability were both elevated over values expected for normal tissues. Tripolarized perfusion MRI provides new molecular imaging measures for specifically monitoring permeability, perfusion, and transport simultaneously in vivo.

Stability and Plasticity of Auditory Brainstem Function Across the Lifespan

The human auditory brainstem is thought to undergo rapid developmental changes early in life until age ∼2 followed by prolonged stability until aging-related changes emerge. However, earlier work on brainstem development was limited by sparse sampling across the lifespan and/or averaging across children and adults. Using a larger dataset than past investigations, we aimed to trace more subtle variations in auditory brainstem function that occur normally from infancy into the eighth decade of life. To do so, we recorded auditory brainstem responses (ABRs) to a click stimulus and a speech syllable (da) in 586 normal-hearing healthy individuals. Although each set of ABR measures (latency, frequency encoding, response consistency, nonstimulus activity) has a distinct developmental profile, across all measures developmental changes were found to continue well past age 2. In addition to an elongated developmental trajectory and evidence for multiple auditory developmental processes, we revealed a period of overshoot during childhood (5-11 years old) for latency and amplitude measures, when the latencies are earlier and the amplitudes are greater than the adult value. Our data also provide insight into the capacity for experience-dependent auditory plasticity at different stages in life and underscore the importance of using age-specific norms in clinical and experimental applications.

Radial spectroscopic MRI of hyperpolarized [1-13C] pyruvate at 7 tesla

The transient and nonrenewable signal from hyperpolarized metabolites necessitates extensive sequence optimization for encoding spatial, spectral, and dynamic information. In this work, we evaluate the utility of radial single-timepoint and cumulative spectroscopic MRI of hyperpolarized [1-(13) C] pyruvate and its metabolic products at 7 Tesla (T). Simulations of radial echo planar spectroscopic imaging (EPSI) and multiband frequency encoding (MBFE) acquisitions were performed to confirm feasibility and evaluate performance for HP (13) C imaging. Corresponding sequences were implemented on a 7T small-animal MRI system, tested in phantom, and demonstrated in a murine model of anaplastic thyroid cancer. MBFE provides excellent spectral separation but is susceptible to blurring and T2 * signal loss inherent to using low readout gradients. The higher readout gradients and more flexible spectral encoding for EPSI result in good spatial resolution and spectral separation. Radial acquisition throughout HP signal evolution offers the flexibility for reconstructing spatial maps of mean metabolite distribution and global dynamic time courses of multiple metabolites. Radial EPSI and MBFE acquisitions are well-suited for hyperpolarized (13) C MRI over short and long durations. Advantages to this approach include robustness to nonstationary magnetization, insensitivity to precise acquisition timing, and versatility for reconstructing dynamically acquired spectroscopic data.

Regularity encoding and deviance detection of frequency modulated sweeps: Human middle‐ and long‐latency auditory evoked potentials

Fast encoding of frequency modulated (FM) sweeps is crucial for communication. In humans, FM sweeps deviating from the acoustic regularity elicit the mismatch negativity (MMN) evoked potential. Yet, direction sensitivity to FM sweeps is found in animals' primary auditory cortex, upstream of MMN sources found in humans. Here, we were interested in whether direction deviants of complex FM sweeps modulated brain responses earlier than MMN. We used a controlled oddball paradigm, and measured the middle latency responses (MLRs) and the MMN. Our results showed a repetition enhancement to the standards at the Pa component of the MLR and a genuine MMN in the later response range. These results show that, early in the cortical hierarchy, the system is sensitive to the physical characteristics of the repetitive stimuli, but a higher-order mechanism is needed to detect violations of the acoustic regularity.

Combining J‐Edited and Correlation Spectroscopies Within a Multi‐dimensional Spatial Frequency Encoding: Toward Fully Resolved 1H NMR Spectra

J-resolved at a glance: Passive coupling refocusing-COSY experiments based on a frequency encoding of the sample along two directions of space are presented. It allows various spin evolutions to be triggered in different parts of the sample in a selective and fully controlled manner. This yields 2D spectra in which the whole proton network appears as a series of fully resolved and straightforwardly assignable doublets, triplets or quartets (see figure).

Influence of Internal Noise on Rhythmic Calcium Bursting

The chemical Langevin method is adopted to study effects of intrinsic noise in calcium bursting oscillations. Results show that by changing the cell volume and thus tuning the strength of internal noise the calcium oscillations show different performance. With the addition of small magnitude intrinsic noise the bursting oscillations do not appear irregular, for moderate volumes relative regular bursting oscillations are observed and internal noise shortens the period of bursting oscillations. As the volume decreases, the level of internal noise increases. Thus, for the volume small enough, the level of internal noise becomes so high that bursting behavior is disrupted, resulting in random oscillations. The most interesting phenomenon is that with the decrease of cell volume the bursting oscillations disappear entirely and only spikes remain. This will be helpful for understanding frequency encoding.

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.

Contribution of within- and cross-channel information to vibrotactile frequency discrimination

Vibrotactile stimuli normally activate multiple information-processing channels starting from different types of mechanoreceptors, and the most sensitive channel alternates depending on the range of vibration frequency. How the tactile system encodes vibration frequency using within-channel information (e.g., the temporal pattern of neural activity of each channel) and/or cross-channel information (the relationship between activities of channels) has been examined, and the usefulness of the former has been evidently shown, while that of the latter remains controversial. To see the contribution of within- and cross-channel information to vibrotactile frequency encoding, we investigated frequency discrimination for near-threshold vibration, which can activate the channels more selectively than conventional supra-threshold vibration. At near-threshold intensity, the contribution of cross-channel information, if it exists, would be observed only when two vibrations activate different channels. In the first experiment, we examined the frequency discrimination thresholds for a wide range of frequencies. The results did not show a clear contribution of the cross-channel information, though that of the within-channel information was evident. In the second experiment, we compared the signal detection threshold and the frequency identification threshold between frequency pairs. We found that for certain pairs of stimuli whose frequencies were far enough apart from each other to activate different channels, each stimulus was identified as soon as it was detected. This suggests that each channel is a labeled line as expected from cross-channel encoding of vibration frequency, but not all data were consistent with this idea. We conclude that though a labeled-line structure might exist as a basis of cross-channel encoding, the cross-channel information does not play a dominant role in frequency discrimination.

Refractoriness enhances temporal coding by auditory nerve fibers.

A universal property of spiking neurons is refractoriness, a transient decrease in discharge probability immediately following an action potential (spike). The refractory period lasts only one to a few milliseconds, but has the potential to affect temporal coding of acoustic stimuli by auditory neurons, which are capable of submillisecond spike-time precision. Here this possibility was investigated systematically by recording spike times from chicken auditory nerve fibers in vivo while stimulating with repeated pure tones at characteristic frequency. Refractory periods were tightly distributed, with a mean of 1.58 ms. A statistical model was developed to recapitulate each fiber's responses and then used to predict the effect of removing the refractory period on a cell-by-cell basis for two largely independent facets of temporal coding: faithful entrainment of interspike intervals to the stimulus frequency and precise synchronization of spike times to the stimulus phase. The ratio of the refractory period to the stimulus period predicted the impact of refractoriness on entrainment and synchronization. For ratios less than ∼0.9, refractoriness enhanced entrainment and this enhancement was often accompanied by an increase in spike-time precision. At higher ratios, little or no change in entrainment or synchronization was observed. Given the tight distribution of refractory periods, the ability of refractoriness to improve temporal coding is restricted to neurons responding to low-frequency stimuli. Enhanced encoding of low frequencies likely affects sound localization and pitch perception in the auditory system, as well as perception in nonauditory sensory modalities, because all spiking neurons exhibit refractoriness.