Exposed faces of semidefinitely representable sets

A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set of an LMI is called a spectrahedron. Linear images of spectrahedra are called semidefinite representable sets. Part of the interest in spectrahedra and semidefinite representable sets arises from the fact that one can efficiently optimize linear functions on them by semidefinite programming, like one can do on polyhedra by linear programming. It is known that every face of a spectrahedron is exposed. This is also true in the general context of rigidly convex sets. We study the same question for semidefinite representable sets. Lasserre proposed a moment matrix method to construct semidefinite representations for certain sets. Our main result is that this method can only work if all faces of the considered set are exposed. This necessary condition complements sufficient conditions recently proved by Lasserre, Helton and Nie

Temperature Sensitive 19F-Substituted Molecules for Combined Proton-/Fluorine-Imaging in a 7 T Whole-Body MRI System

¹⁹F MR spectroscopy and imaging represent important tools for the development of new MR contrast agents and pharmaceutics. Until now, there are only a few published data that described the influence of temperature changes to the ¹⁹F chemical shifts in aqueous solutions. Temperature coefficients up to ~ 8.7Hz/K were determined. Thermoresponsive agents are of high interest in, e.g. hyperthermia studies. Changes in signal intensity and chemical shift give information of the local temperature. Here, we present novel MR spectroscopic and imaging data, which describe the ¹⁹F MR signal temperature dependency of different fluorinated organic substrates in isotonic saline solution and their temperature calculation methods

LED-based photo-CIDNP hyperpolarization enables 19F MR imaging and 19F NMR spectroscopy of 3-fluoro-DL-tyrosine at 0.6 T

Although 19F has high potential to serve as a background-free molecular marker in bioimaging, the molar amount of marker substance is often too small to enable 19F MR imaging or 19F NMR spectroscopy with a sufficiently high signal-to-noise ratio (SNR). Hyperpolarization methods such as parahydrogen-based hyperpolarization or dynamic nuclear polarization (DNP) can significantly improve the SNR, but require expensive and complex sample preparation and the removal of toxic catalysts and solvents. Therefore, we used the biologically compatible model of the fluorinated amino acid 3-fluoro-DL-tyrosine with riboflavin 5'-monophosphate (FMN) as a chromophore dissolved in D2O with 3.4% H2Odest. allowing to transform light energy into hyperpolarization of the 19F nucleus via photo-chemically induced dynamic nuclear polarization (photo-CIDNP). We used a low-cost high-power blue LED to illuminate the sample replacing traditionally used laser excitation, which is both potentially harmful and costly. For the first time, we present results of hyperpolarized 19F MRI and 19F NMR performed with a low-cost 0.6 T benchtop MRI system. The device allowed simultaneous dual channel 1H/19F NMR. 19F imaging was performed with a (0.94 mm)2 in-plane resolution. This enabled the spatial resolution of different degrees of hyperpolarization within the sample. We estimated the photo-CIDNP-based 19F signal enhancement at 0.6 T to be approximately 465. FMN did not bleach out even after multiple excitations, so that the signal-to-noise ratio could be further improved by averaging hyperpolarized signals. The results show that the easy-to-use experimental setup has a high potential to serve as an efficient preclinical tool for hyperpolarization studies in bioimaging.Comment: 16 pages, 5 figures, supplementary information (4pages, 4 figures

The Travelling-Wave Primate System: A New Solution for Magnetic Resonance Imaging of Macaque Monkeys at 7 Tesla Ultra-High Field

INTRODUCTION: Neuroimaging of macaques at ultra-high field (UHF) is usually conducted by combining a volume coil for transmit (Tx) and a phased array coil for receive (Rx) tightly enclosing the monkey's head. Good results have been achieved using vertical or horizontal magnets with implanted or near-surface coils. An alternative and less costly approach, the travelling-wave (TW) excitation concept, may offer more flexible experimental setups on human whole-body UHF magnetic resonance imaging (MRI) systems, which are now more widely available. Goal of the study was developing and validating the TW concept for in vivo primate MRI. METHODS: The TW Primate System (TWPS) uses the radio frequency shield of the gradient system of a human whole-body 7 T MRI system as a waveguide to propagate a circularly polarized B1 field represented by the TE11 mode. This mode is excited by a specifically designed 2-port patch antenna. For receive, a customized neuroimaging monkey head receive-only coil was designed. Field simulation was used for development and evaluation. Signal-to-noise ratio (SNR) was compared with data acquired with a conventional monkey volume head coil consisting of a homogeneous transmit coil and a 12-element receive coil. RESULTS: The TWPS offered good image homogeneity in the volume-of-interest Turbo spin echo images exhibited a high contrast, allowing a clear depiction of the cerebral anatomy. As a prerequisite for functional MRI, whole brain ultrafast echo planar images were successfully acquired. CONCLUSION: The TWPS presents a promising new approach to fMRI of macaques for research groups with access to a horizontal UHF MRI system

The application of novel Ir-NHC polarization transfer complexes by SABRE

In recent years, the hyperpolarization method Signal Amplification By Reversible Exchange (SABRE) has developed into a powerful technique to enhance Nuclear Magnetic Resonance (NMR) signals of organic substrates in solution (mostly via binding to the nitrogen lone pair of N-heterocyclic compounds) by several orders of magnitude. In order to establish the application and development of SABRE as a hyperpolarization method for medical imaging, the separation of the Ir-N-Heterocyclic Carbene (Ir-NHC) complex, which facilitates the hyperpolarization of the substrates in solution, is indispensable. Here, we report for the first time the use of novel Ir-NHC complexes with a polymer unit substitution in the backbone of N-Heterocyclic Carbenes (NHC) for SABRE hyperpolarization, which permits the removal of the complexes from solution after the hyperpolarization of a target substrate has been generated

13C MRI of hyperpolarized pyruvate at 120 µT

Abstract Nuclear spin hyperpolarization increases the sensitivity of magnetic resonance dramatically, enabling many new applications, including real-time metabolic imaging. Parahydrogen-based signal amplification by reversible exchange (SABRE) was employed to hyperpolarize [1-13C]pyruvate and demonstrate 13C imaging in situ at 120 µT, about twice Earth’s magnetic field, with two different signal amplification by reversible exchange variants: SABRE in shield enables alignment transfer to heteronuclei (SABRE-SHEATH), where hyperpolarization is transferred from parahydrogen to [1-13C]pyruvate at a magnetic field below 1 µT, and low-irradiation generates high tesla (LIGHT-SABRE), where hyperpolarization was prepared at 120 µT, avoiding magnetic field cycling. The 3-dimensional images of a phantom were obtained using a superconducting quantum interference device (SQUID) based magnetic field detector with submillimeter resolution. These 13C images demonstrate the feasibility of low-field 13C metabolic magnetic resonance imaging (MRI) of 50 mM [1-13C]pyruvate hyperpolarized by parahydrogen in reversible exchange imaged at about twice Earth’s magnetic field. Using thermal 13C polarization available at 120 µT, the same experiment would have taken about 300 billion years

Metabolic and Molecular Imaging with Hyperpolarised Tracers.

Since reaching the clinic, magnetic resonance imaging (MRI) has become an irreplaceable radiological tool because of the macroscopic information it provides across almost all organs and soft tissues within the human body, all without the need for ionising radiation. The sensitivity of MR, however, is too low to take full advantage of the rich chemical information contained in the MR signal. Hyperpolarisation techniques have recently emerged as methods to overcome the sensitivity limitations by enhancing the MR signal by many orders of magnitude compared to the thermal equilibrium, enabling a new class of metabolic and molecular X-nuclei based MR tracers capable of reporting on metabolic processes at the cellular level. These hyperpolarised (HP) tracers have the potential to elucidate the complex metabolic processes of many organs and pathologies, with studies so far focusing on the fields of oncology and cardiology. This review presents an overview of hyperpolarisation techniques that appear most promising for clinical use today, such as dissolution dynamic nuclear polarisation (d-DNP), parahydrogen-induced hyperpolarisation (PHIP), Brute force hyperpolarisation and spin-exchange optical pumping (SEOP), before discussing methods for tracer detection, emerging metabolic tracers and applications and progress in preclinical and clinical application