Extracellular and intracellular components of the impedance of neural tissue

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depend on the electric structure and properties of extracellular media, but the measurements of these electric properties are subject to controversy. Some measurements point to a model where the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements in various preparations, for acute brain slices and primary cell cultures, and we compare to measurements using the same setup in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated to Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity, that should be taken into account to correctly interpret extracellular potentials generated by neurons.

Double-diffusive depletion of layers in hydrothermal systems

<p>In hydrothermal systems, the circulation of water through the porous matrix is strongly influenced by the joint effects of heat and salinity. Because of phase separation, layers of different salinities and temperature are thought to form, but their stability or their typical lifetime remains unclear. Moreover, the dynamics of heat transport across such a layered system is considerably enriched by double diffusive effects due to the slower diffusion of salinity relative to heat. Here, we study numerically the time evolution of an ideal two-layer configuration where a heavy layer of warm and salty water is overlain by a light layer of cold and fresh water. Thermal convection quickly develops in each layer and maintains a thin diffusive interface between the layers. There is long-standing controversy on the temporal evolution of such a system. Although Griffiths (1981) found experimentally that the sharp interface seemed to persist indefinitely, Schoofs & Hansen (2000) reported via numerical simulations systematic depletion and vanishing of the layers. We resolve this apparently inconsistency. In our simulations, we find systematic depletion of the two-layer initial condition in all cases. However, the timescale over which it occurs depends strongly on the ratio between salinity and temperature contributions to density. When salinity is weakly stabilising, thermal convection and layers are maintained over (very long) diffusive timescales. When salt is strongly stabilising, however, convection becomes quiescent over much shorter times and the sharp interface between layers is quickly diffused away. We determine scalings on the lifetime of the layers in both regimes as a function of the governing parameters.</p>

On a role of anisotropy and nonlinear diffusive effects during the construction of waveguides in the lithium niobate

Direct numerical simulation of a process of hydrogen diffusive intrusion into the lithium niobate monocrystal is fulfilled with reference to the manufacturing two-channel system of waveguides. The calculations were carried out according to the technology of waveguides production, taking into account the presence of several stages, which at first include the material saturation with the protons by treating the working surface with the melt of benzoic acid, and then annealing the sample. The contribution of the nonlinear diffusion to the process of the waveguide shaping is analyzed. It is shown that the formation of a stepped waveguide boundary is significantly influenced by the procedure of monocrystal annealing. Heretofore, the annealing stage was not quantitatively investigated. It can be emphasized that the attention has not been paid to the possible role of the annealing on formation of the sharper boundary between the waveguide and its mother substrate. A theoretical model of anisotropic diffusion in a solid material is constructed on the basis of experimental data, which indicate the presence of a transitional surface layer with pronounced regular mesostructural directions in the polished lithium niobate monocrystal. Based on the derived equations, the waveguides shape in a cross-section was simulated numerically for different values of inclination angle of the main axes with respect to the cut lines of the crystal. It is demonstrated that in the region of the waveguide bifurcation, when at the stage of protons intrusion the interaction of diffusive fluxes is possible, the diffusion anisotropy can lead to a breakdown of the waveguides symmetry, which can affect their optical properties.

Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods

We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the spatial movement and interactions of a population of susceptible, infected and recovered individuals. Thanks to this, the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models, is removed. In particular, we formally show how such reaction-diffusion models are recovered in an appropriate diffusive limit. The kinetic transport model is therefore considered within a spatial network, characterizing different places such as villages, cities, countries, etc. The transmission conditions in the nodes are analyzed and defined. Finally, the model is solved numerically on the network through a finite-volume IMEX method able to maintain the consistency with the diffusive limit without restrictions due to the scaling parameters. Several numerical tests for simple epidemic network structures are reported and confirm the ability of the model to correctly describe the spread of an epidemic.

Mathematical Modeling and Simulation of a Gas Emission Source Using the Network Simulation Method

A mathematical model for the simulation of the diffusion of the pollutants released from a point source is presented. All phenomena have been included, such as thermal and wind gradients, turbulence, fumigation, convective and diffusive effects, and atmospheric stabilities. To better understand the dynamics of these occurrences, the Network Simulation Method was used to provide the concentration of pollutants in three spatial coordinates. The model was simulated in open source software and validated with experimental data, satisfying the Hanna criteria. Additionally, this model selects for the appropriate expressions based on the physical phenomena that govern each case and allows for time-dependent data entry. The cases studied show the great coupling that exists between the variables of wind velocity and atmospheric stability for the pollutant diffusion. The model can be used for two important aims, to identify the behavior of the emission of pollutants, and to determine the concentration of a pollutant at various points, through an inverse problem, locating the source of the emission.

Successive waves in pandemic infections: physical diffusion theory and data comparisons

We establish the principal that the prediction, timing and magnitude of second and more distinct waves of infection can be based on the well - known physics and assumptions of classical diffusion theory. This model is fundamentally different from the commonly used SEIR and R0 fitting methods. Driven by data, we seek a working approximation for the observed orders of magnitude for the timing and rate of second and more waves. The dynamic results and characteristics are compared to the data and enable predictions of timescales and maximum expected rates where diffusive effects dominate.The important point is this simple physical model allows understanding of the dominant processes, provides prediction estimates, and is based the solutions derived from existing, consistent and well-known physical principles. The medical system and health policy implications of such inexorable diffusive spread are that any NPI and other countermeasures deployed for and after the rapid first peak must recognize that large residual infection waves will then likely occur.

Combining Electrostatic, Hindrance and Diffusive Effects for Predicting Particle Transport and Separation Efficiency in Deterministic Lateral Displacement Microfluidic Devices

Microfluidic separators based on Deterministic Lateral Displacement (DLD) constitute a promising technique for the label-free detection and separation of mesoscopic objects of biological interest, ranging from cells to exosomes. Owing to the simultaneous presence of different forces contributing to particle motion, a feasible theoretical approach for interpreting and anticipating the performance of DLD devices is yet to be developed. By combining the results of a recent study on electrostatic effects in DLD devices with an advection–diffusion model previously developed by our group, we here propose a fully predictive approach (i.e., ideally devoid of adjustable parameters) that includes the main physically relevant effects governing particle transport on the one hand, and that is amenable to numerical treatment at affordable computational expenses on the other. The approach proposed, based on ensemble statistics of stochastic particle trajectories, is validated by comparing/contrasting model predictions to available experimental data encompassing different particle dimensions. The comparison suggests that at low/moderate values of the flowrate the approach can yield an accurate prediction of the separation performance, thus making it a promising tool for designing device geometries and operating conditions in nanoscale applications of the DLD technique.