Internal gradient distributions: A susceptibility-derived tensor delivering morphologies by magnetic resonance | Scientific Reports
Gonzalo A. Álvarez, Noam Shemesh & Lucio Frydman
Scientific Reports 7, 3311 (2017)
Nuclear magnetic resonance is a powerful tool for probing the structures of chemical and biological systems. Combined with field gradients it leads to NMR imaging (MRI), a widespread tool in non-invasive examinations. Sensitivity usually limits MRI’s spatial resolution to tens of micrometers, but other sources of information like those delivered by constrained diffusion processes, enable one extract morphological information down to micron and sub-micron scales. We report here on a new method that also exploits diffusion – isotropic or anisotropic– to sense morphological parameters in the nm-mm range, based on distributions of susceptibility-induced magnetic field gradients. A theoretical framework is developed to define this source of information, leading to the proposition of internal gradient-distribution tensors. Gradient-based spin-echo sequences are designed to measure these new observables. These methods can be used to map orientations even when dealing with unconstrained diffusion, as is here demonstrated with studies of structured systems, including tissues.
Noam Shemesh, Gonzalo A. Álvarez, Lucio Frydman
Published: July 21, 2015
Objects making up complex porous systems in Nature usually span a range of sizes. These size distributions play fundamental roles in defining the physicochemical, biophysical and physiological properties of a wide variety of systems – ranging from advanced catalytic materials to Central Nervous System diseases. Accurate and noninvasive measurements of size distributions in opaque, three-dimensional objects, have thus remained long-standing and important challenges. Herein we describe how a recently introduced diffusion-based magnetic resonance methodology, Non-Uniform-Oscillating-Gradient-Spin-Echo(NOGSE), can determine such distributions noninvasively. The method relies on its ability to probe confining lengths with a (length)^6 parametric sensitivity, in a constant-time, constant-number-of-gradients fashion; combined, these attributes provide sufficient sensitivity for characterizing the underlying distributions in μm-scaled cellular systems. Theoretical derivations and simulations are presented to verify NOGSE’s ability to faithfully reconstruct size distributions through suitable modeling of their distribution parameters. Experiments in yeast cell suspensions – where the ground truth can be determined from ancillary microscopy – corroborate these trends experimentally. Finally, by appending to the NOGSE protocol an imaging acquisition, novel MRI maps of cellular size distributions were collected from a mouse brain. The ensuing micro-architectural contrasts successfully delineated distinctive hallmark anatomical sub-structures, in both white matter and gray matter tissues, in a non-invasive manner. Such findings highlight NOGSE’s potential for characterizing aberrations in cellular size distributions upon disease, or during normal processes such as development.
Editor: Ichio Aoki, National Institute of Radiological Sciences, JAPAN
Received: November 25, 2014; Accepted: June 24, 2015; Published: July 21, 2015
Copyright: © 2015 Shemesh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance | J. Chem. Phys. (2014)
Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance
Gonzalo A. Álvarez, Noam Shemesh and Lucio Frydman
J. Chem. Phys. 140, 084205 (2014); http://dx.doi.org/10.1063/1.4865335
Dynamical decoupling, a generalization of the original NMR spin-echo sequence, is becoming increasingly relevant as a tool for reducing decoherence in quantum systems. Such sequences apply non-equidistant refocusing pulses for optimizing the coupling between systems, and environmental fluctuations characterized by a given noise spectrum. One such sequence, dubbed Selective Dynamical Recoupling SDR [P. E. S. Smith, G. Bensky, G. A. Álvarez, G. Kurizki, and L. Frydman, Proc. Natl. Acad. Sci. 109, 5958 (2012)], allows one to coherently reintroduce diffusion decoherence effects driven by fluctuations arising from restricted molecular diffusion [G. A. Álvarez, N. Shemesh, and L. Frydman, Phys. Rev. Lett. 111, 080404 (2013)]. The fully-refocused, constant-time, and constant-number-of-pulses nature of SDR also allows one to filter out “intrinsic” T1 and T2 weightings, as well as pulse errors acting as additional sources of decoherence. This article explores such features when the fluctuations are now driven by unrestricted molecular diffusion. In particular, we show that diffusion-driven SDR can be exploited to investigate the decoherence arising from the frequency fluctuations imposed by internal gradients. As a result, SDR presents a unique way of probing and characterizing these internal magnetic fields, given an a priori known free diffusion coefficient. This has important implications in studies of structured systems, including porous media and live tissues, where the internal gradients may serve as fingerprints for the systems composition or structure. The principles of this method, along with full analytical solutions for the unrestricted diffusion-driven modulation of the SDR signal, are presented. The potential of this approach is demonstrated with the generation of a novel source of MRI contrast, based on the background gradients active in an ex vivo mouse brain. Additional features and limitations of this new method are discussed.
© 2014 AIP Publishing LLC
Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo NOGSE NMR | J. Magn. Reson. (2013)
Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo NOGSE NMR
Noam Shemesh, Gonzalo A. Álvarez, Lucio Frydman.
Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
•NOGSE, a novel diffusion MR approach for measuring pore sizes, is presented and analyzed.
•NOGSE is based on a constant time and a constant number of oscillating gradients.
•Experiments on microstructural phantoms, spinal cords and brains, validate NOGSE.
Noninvasive measurements of microstructure in materials, cells, and in biological tissues, constitute a unique capability of gradient-assisted NMR. Diffusion–diffraction MR approaches pioneered by Callaghan demonstrated this ability; Oscillating-Gradient Spin-Echo OGSE methodologies tackle the demanding gradient amplitudes required for observing diffraction patterns by utilizing constant-frequency oscillating gradient pairs that probe the diffusion spectrum, Dω. Here we present a new class of diffusion MR experiments, termed Non-uniform Oscillating-Gradient Spin-Echo NOGSE, which dynamically probe multiple frequencies of the diffusion spectral density at once, thus affording direct microstructural information on the compartment’s dimension. The NOGSE methodology applies N constant-amplitude gradient oscillations; N − 1 of these oscillations are spaced by a characteristic time x, followed by a single gradient oscillation characterized by a time y, such that the diffusion dynamics is probed while keeping N − 1x + y ≡ TNOGSE constant. These constant-time, fixed-gradient-amplitude, multi-frequency attributes render NOGSE particularly useful for probing small compartment dimensions with relatively weak gradients – alleviating difficulties associated with probing Dω frequency-by-frequency or with varying relaxation weightings, as in other diffusion-monitoring experiments. Analytical descriptions of the NOGSE signal are given, and the sequence’s ability to extract small compartment sizes with a sensitivity towards length to the sixth power, is demonstrated using a microstructural phantom. Excellent agreement between theory and experiments was evidenced even upon applying weak gradient amplitudes. An MR imaging version of NOGSE was also implemented in ex vivo pig spinal cords and mouse brains, affording maps based on compartment sizes. The effects of size distributions on NOGSE are also briefly analyzed.
Restricted diffusion; Oscillating gradients; OGSE; Microstructure; Magnetic resonance imaging; CNS; Gradient echoes; Selective dynamical recoupling