Effects of permeable boundaries on the diffusion-attenuated MR signal: insights from a one-dimensional model

The local magnetization distribution M(x,t) and the net MR signal S arising from a one-dimensional periodic structure with permeable barriers in a Tanner-Stejskal pulsed-field gradient experiment are considered. In the framework of the narrow pulse approximation, the general expressions for M(x,t) and S as functions of diffusion time and the bipolar field gradient strength are obtained and analyzed. In contrast to a system with impermeable boundaries, the signal S as a function of the b-value is modeled well as a bi-exponential decay not only in the short-time regime but also in the long-time regime. At short diffusion times, the local magnetization M(x,t) is strongly spatially inhomogeneous and the two exponential components describing S have a clear physical interpretation as two "population fractions" of the slow- and fast-diffusing quasi-compartments (pools). In the long-diffusion time regime, the two exponential components do not have clear physical meaning but rather serve to approximate a more complex functional signal form. The average diffusion propagator, obtained by means of standard q-space analysis procedures in the long-diffusion time regime is explored; its structure creates the deceiving appearance of a system with multiple compartments of different sizes, while in reality, it reflects the permeable nature of boundaries in a system with multiple compartments all of the same size.     

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities

A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant deltaR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay lnS approximately -tlnt in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.     

Polynuclear Heteroligand Yb(III)–Er(III) Complexes as Potential Upconversion Materials

Russian Journal of Coordination Chemistry - The synthesis of complexes LnI(C6F5O)2 and LnCp(L)2 (Ln = Er, Yb; L = C6F5O, SONF), which are convenient precursors for the preparation of heteroligand...     

Luminescent properties of MBE-grown Si:Er/SOI structures

Here we report on luminescent properties of multilayer Si:Er structures grown by sublimation molecular-beam epitaxy on “silicon-on-insulator” substrates. We demonstrate formation in such structures of a unique erbium-related center Er-1. This optical complex stands out among other known erbium-related centers in silicon for its record narrow luminescent line (<10 μeV) and largest absorption cross-section and, therefore, provides the best conditions to achieve practically significant amplification and stimulated emission in erbium-doped silicon structures.     

Upconversion Luminescence of Er3+ Ions from Barium Titanate Xerogel Powder and Target Fabricated by Explosive Compaction Method

Journal of Applied Spectroscopy - Photo- and cathodoluminescence in the visible range from erbium-doped barium titanate xerogels obtained in the form of a powder and a target pressed from it by...     

Protein-induced water 1H MR frequency shifts: Contributions from magnetic susceptibility and exchange effects

Defining the biophysics underlying the remarkable MRI phase contrast reported in high field MRI studies of human brain would lead to more quantitative image analysis and more informed pulse sequence development. Toward this end, the dependence of water ¹H resonance frequency on protein concentration was investigated using bovine serum albumin (BSA) as a model system. Two distinct mechanisms were found to underlie a water ¹H resonance frequency shift: (i) a protein-concentration-induced change in bulk magnetic susceptibility, causing a shift to lower frequency, and (ii) exchange of water between chemical-shift distinct environments, i.e., free (bulk water) and protein-associated (“bound”) water, including freely exchangeable ¹H sites on proteins, causing a shift to higher frequency. At 37 °C the amplitude of the exchange effect is roughly half that of the susceptibility effect.     

Lanthanide complexes with substituted naphtholate ligands: extraordinary bright near-infrared luminescence of ytterbium

A series of Pr, Nd, Ho, Er, Tm, and Yb complexes with 3-(2-benzoxazol-2-yl)-2-naphtholate and 3-(2-benzothiazol-2-yl)-2-naphtholate ligands was synthesized. The structure, as well as the photo- and electroluminescent properties of these complexes were studied. An extraordinary bright emission of Yb³⁺ was detected. To explain the phenomenon, a novel excitation mechanism involving intramolecular electron transfer was proposed.     

Quantitative phenomenological model of the BOLD contrast mechanism

Different theoretical models of the BOLD contrast mechanism are used for many applications including BOLD quantification (qBOLD) and vessel size imaging, both in health and disease. Each model simplifies the system under consideration, making approximations about the structure of the blood vessel network and diffusion of water molecules through inhomogeneities in the magnetic field created by deoxyhemoglobin-containing blood vessels. In this study, Monte-Carlo methods are used to simulate the BOLD MR signal generated by diffusing water molecules in the presence of long, cylindrical blood vessels. Using these simulations we introduce a new, phenomenological model that is far more accurate over a range of blood oxygenation levels and blood vessel radii than existing models. This model could be used to extract physiological parameters of the blood vessel network from experimental data in BOLD-based experiments. We use our model to establish ranges of validity for the existing analytical models of Yablonskiy and Haacke, Kiselev and Posse, Sukstanskii and Yablonskiy (extended to the case of arbitrary time in the spin echo sequence) and Bauer et al. (extended to the case of randomly oriented cylinders). Although these models are shown to be accurate in the limits of diffusion under which they were derived, none of them is accurate for the whole physiological range of blood vessels radii and blood oxygenation levels. We also show the extent of systematic errors that are introduced due to the approximations of these models when used for BOLD signal quantification.     

Theory of FID NMR signal dephasing induced by mesoscopic magnetic field inhomogeneities in biological systems.

A theory of the NMR signal dephasing due to the presence of tissue-specific magnetic field inhomogeneities is developed for a two-compartment model. Randomly distributed magnetized objects of finite size embedded in a given media are modeled by ellipsoids of revolution (prolate and oblate spheroids). The model can be applied for describing blood vessels in a tissue, red blood cells in the blood, marrow within trabecular bones, etc. The time dependence of the dephasing function connected with the spins inside of the objects, s(i), is shown to be expressed by Fresnel functions and creates a powder-type signal in the frequency domain. The short-time regime of the dephasing function for spins outside the objects, s(e), is always characterized by Gaussian time dependence, s(e) approximately exp[-zeta(k)(t/tc)2], with zeta being a volume fraction occupied by the objects, t(c) being a characteristic dephasing time, and the coefficient k depending on the ellipsoid's shape through the aspect ratio of its axes (a/c). The long-time asymptotic behavior of s(e) is always "quasispherical"-linear exponential in time, s(e) approximately exp(-zetaCt/tc), with the same "spherical" decay rate for any ellipsoidal shape. For long prolate spheroids (a/c)<1, there exists an intermediate characteristic regime with a linear exponential time behavior and an aspect-ratio-dependent decay rate smaller than (zetaC/tc).