International audienceThe complex transverse water proton magnetization subject to diffusion-encoding magneticfield gradient pulses in a heterogeneous medium can be modeled by themultiple compartment Bloch-Torrey partial differential equation (PDE).In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristicsof the medium in the long time limit.In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces.To solve these PDEs, we implemented a finite elements method thatallows jumps in the solution at the cell interfaces by using doublenodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementationof the boundary conditions. The spatial discretizationwas then coupled to the adaptive explict Runge-Kutta-Chebychev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time.We implemented this method on the FEniCSC++ platform and show time and spatial convergence results.Finally, this method is applied to study some relevant questions in diffusionMRI

We present a unified multidimensional variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. Based on an elastic wave oriented formulation and using a tensorial formalism, the proposed framework allows a better understanding of the physical meaning of the terms involved in the discontinuous Galerkin method. The unified variational framework is written for first-order velocity-stress wave equations. An uncoupled upwind numerical flux and two coupled upwind numerical fluxes using respectively the Voigt and the Reuss averages of elastic moduli are defined. Two numerical fluxes that are exact solutions of the Riemann problem on physical interfaces are also developed and analyzed in the 1D case. The implemented solvers are then applied to different elastic media, especially to polycrystalline materials that present a particular case of piecewise homogeneous media. The use of the three upwind numerical fluxes, which only solve approximately the Riemann problem at element interfaces, is investigated.

The human insular cortex is a heterogeneous brain structure which plays an integrative role in guiding behavior. The cytoarchitectonic organization of the human insula has been investigated over the last century using postmortem brains but there has been little progress in noninvasive in vivo mapping of its microstructure and large-scale functional circuitry. Quantitative modeling of multi-shell diffusion MRI data from 413 participants revealed that human insula microstructure differs significantly across subdivisions that serve distinct cognitive and affective functions. Insular microstructural organization was mirrored in its functionally interconnected circuits with the anterior cingulate cortex that anchors the salience network, a system important for adaptive switching of cognitive control systems. Furthermore, insular microstructural features, confirmed in Macaca mulatta, were linked to behavior and predicted individual differences in cognitive control ability. Our findings open new possibilities for probing psychiatric and neurological disorders impacted by insular cortex dysfunction, including autism, schizophrenia, and fronto-temporal dementia.

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation. Under the assumption of negligible water exchange between compartments, the time-dependent apparent diffusion coefficient can be directly computed from the solution of a diffusion equation subject to a time-dependent Neumann boundary condition.

Calcium carbonate (CaCO 3)-enriched biomaterial derived from freshwater mussel shells (FMS) was used as a non-porous biosorbent to explore the characteristics and mechanisms of cadmium adsorption in aqueous solution. The adsorption mechanism was proposed by comparing the FMS properties before and after adsorption alongside various adsorption studies. The FMS biosorbent was characterized using nitrogen adsorption/desorption isotherm, X-ray diffraction, scanning electron microscopy with energy dispersive spectroscopy, Fourier-transform infrared spectroscopy, and point of zero charge. The results of batch experiments indicated that FMS possessed an excellent affinity to Cd(II) ions within solutions pH higher than 4.0. An increase in ionic strength resulted in a significant decrease in the amount of Cd(II) adsorbed onto FMS. Kinetic study demonstrated that the adsorption process quickly reached equilibrium at approximately 60 min. The FMS biosorbent exhibited the Langmuir maximum adsorption capacity as follows: 18.2 mg/g at 10 °C < 26.0 mg/g at 30 °C < 28.6 mg/g at 50 °C. The Cd(II) adsorption process was irreversible, spontaneous (−∆G°), endothermic (+∆H°), and more random (+∆S°). Selective order (mmol/g) of metal cations followed as Pb 2+ > Cd 2+ > Cu 2+ > Cr 3+ > Zn 2+. For column experiments, the highest Thomas adsorption capacity (7.86 mg/g) was achieved at a flow rate (9 mL/min), initial Cd(II) concentration (10 mg/L), and bed height (5 cm). The Cd(II) removal by FMS was regarded as non-activated chemisorption that occurred very rapidly (even at a low temperature) with a low magnitude of activation energy. Primary adsorption mechanism was surface precipitation. Cadmium precipitated in the primary (Cd,Ca)CO 3 form with a calcite-type structure on the FMS surface. A crust of rhombohedral crystals on the substrate was observed by SEM. Freshwater mussel shells have the potential as a renewable adsorbent to remove cadmium from water.

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