Solving Maxwell’s equations in singular domains with a Nitsche type method

In this paper, we propose and analyze a method derived from a Nitsche approach for handling boundary conditions in the Maxwell equations. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. Then, it has been worked out more generally and transferred to continuity conditions. We propose here an extension to vector div–curl problems. This allows us to solve the Maxwell equations, particularly in domains with reentrant corners, where the solution can be singular. We formulate the method for both the electric and magnetic fields and report some numerical experiments.     

Magnetization transfer using inversion recovery during off-resonance irradiation

Estimation of magnetization transfer (MT) parameters in vivo can be compromised by an inability to drive the magnetization to a steady state using allowable levels of radiofrequency (RF) irradiation, due to safety concerns (tissue heating and specific absorption rate (SAR)). Rather than increasing the RF duration or amplitude, here we propose to circumvent the SAR limitation by sampling the formation of the steady state in separate measurements made with the magnetization initially along the -z and +z axis of the laboratory frame, i.e. with or without an on-resonance inversion pulse prior to the off-resonance irradiation. Results from human brain imaging demonstrate that this choice provides a tremendous benefit in the fitting procedure used to estimate MT parameters. The resulting parametric maps are characterized by notably increased tissue specificity as compared to those obtained with the standard MT acquisition in which magnetization is initially along the +z axis only.     

Rotating frame relaxation during adiabatic pulses vs. conventional spin lock: simulations and experimental results at 4 T

Spin relaxation taking place during radiofrequency (RF) irradiation can be assessed by measuring the longitudinal and transverse rotating frame relaxation rate constants (R_1ρ and R_2ρ). These relaxation parameters can be altered by utilizing different settings of the RF irradiation, thus providing a useful tool to generate contrast in MRI. In this work, we investigate the dependencies of R_1ρ and R_2ρ due to dipolar interactions and anisochronous exchange (i.e., exchange between spins with different chemical shift δω≠0) on the properties of conventional spin-lock and adiabatic pulses, with particular emphasis on the latter ones which were not fully described previously. The results of simulations based on relaxation theory provide a foundation for formulating practical considerations for in vivo applications of rotating frame relaxation methods. Rotating frame relaxation measurements obtained from phantoms and from the human brain at 4 T are presented to confirm the theoretical predictions.     

Transverse relaxation in the rotating frame induced by chemical exchange

In the presence of radiofrequency irradiation, relaxation of magnetization aligned with the effective magnetic field is characterized by the time constant T1rho. On the other hand, the time constant T2rho characterizes the relaxation of magnetization that is perpendicular to the effective field. Here, it is shown that T2rho can be measured directly with Carr-Purcell sequences composed of a train of adiabatic full-passage (AFP) pulses. During adiabatic rotation, T2rho characterizes the relaxation of the magnetization, which under adiabatic conditions remains approximately perpendicular to the time-dependent effective field. Theory is derived to describe the influence of chemical exchange on T2rho relaxation in the fast-exchange regime, with time constant defined as T2rho,ex. The derived theory predicts the rate constant R2rho,ex (= 1/T2rho,ex) to be dependent on the choice of amplitude- and frequency-modulation functions used in the AFP pulses. Measurements of R2rho,ex of the water/ethanol exchanging system confirm the predicted dependence on modulation functions. The described theoretical framework and adiabatic methods represent new tools to probe exchanging systems.     

REACTIVITY OF SINGLET OXYGEN TOWARD AMINO ACIDS AND PEPTIDES

Quenching of singlet oxygen (¹O₂) in D₂O-ethanol by the amino acids tryptophan, tyrosine, histidine, methionine, cysteine and their derivatives was measured by exciting the sensitizers rose bengal or meso-tetra (N-methyl-4-pyridyl)porphyrin tetratosylate in the presence of oxygen and the above quenchers in solution. In our polar solvent, containing 75% D₂O on a molar basis it was found that (1) substitution of the aromatic ring in indole, phenol and imidazole by the electron-donating methyl group increases the total (i.e. nonreactive and reactive) quenching rate constant by a factor of five to eight. Free or blocked amino and carboxyl groups removed by two methylene groups from the ring counteract the above increase in the rate constant. The reactive quenching of singlet oxygen, which leads to oxidative destruction of the aromatic ring, correlates with the above substitution effects. It has been proposed that the quenching process takes place by formation of an exciplex between ¹O₂ and the quencher. Thus our results indicate that the better an electron donor the amino acid residue is the more pronounced is the charge transfer contribution in the exciplex formed with ¹O₂ and the more likely it is to lead to charge separation and hence to a chemical reaction. (2) Oligopeptides in solution or peptide bonds linked to the amino acid residue have only a minor effect on singlet oxygen. It can therefore be expected that the polypeptide chains per se in the protein network will not interact significantly with the single oxygen molecules present. The quenching of the latter should, to a first approximation, depend only on the presence of the above reactive amino acid residues and to their accessibility to ¹O₂ as well as on the effective dielectric constant within the protein structure.     

Synchronous Chemoradiation Nanovesicles by X‐Ray Triggered Cascade of Drug Release

The approach of concurrent‐to‐synchronous chemoradiation has now been advanced by well‐designed nanovesicles that permit X‐ray irradiation‐triggered instant drug release. The nanovesicles consist of Au nanoparticles tethered with irradiation labile linoleic acid hydroperoxide (LAHP) molecules and oxidation‐responsive poly(propylene sulfide)‐poly(ethylene glycol) (PPS‐PEG) polymers, where DOX were loaded in the inner core of the vesicles (Au‐LAHP‐vDOX). Upon irradiation, the in situ formation of hydroxyl radicals from LAHP molecules triggers the internal oxidation of PPS from being hydrophobic to hydrophilic, leading to degradation of the vesicles and burst release of cargo drugs. In this manner, synchronous chemoradiation showed impressive anticancer efficacy both in vitro and in a subcutaneous mouse tumor model by one‐dose injection and one‐time irradiation.     

Greedy maximal independent sets via local limits

The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent to any previously added vertex. In this paper, we present a general framework for computing the asymptotic density of the random greedy independent set for sequences of (possibly random) graphs by employing a notion of local convergence. We use this framework to give straightforward proofs for results on previously studied families of graphs, like paths and binomial random graphs, and to study new ones, like random trees and sparse random planar graphs. We conclude by analysing the random greedy algorithm more closely when the base graph is a tree.     

Phenols-useful templates for the synthesis of bi-functional orthogonally protected dendron building blocks via solid phase Mitsunobu reaction

Bi-functional dendritic building blocks for convergent dendrimer growth were successfully synthesized from phenolic templates in the solid phase via a Mitsunobu reaction. Each arm of the dendron building block carries an orthogonally protected secondary amine along the arm, and a peripheral primary amine or phenol group (building block type 1) or a tertiary amine junction with orthogonally protected peripheral primary amine or carboxyl groups (building block type 2). The synthetic routes reported in this work are general and applicable for the preparation of diverse building blocks, controlling protection, arm length, and peripheral moieties. These novel dendron units can form unusual dendritic architectures by solid-phase chemistry, which may be incorporated into specific complex structures expanding the scope of dendrimer science.