A framework to reconcile frequency scaling measurements, from intracellular recordings, local-field potentials, up to EEG and MEG signals

In this viewpoint article, we discuss the electric properties of the medium around neurons, which are important to correctly interpret extracellular potentials or electric field effects in neural tissue. We focus on how these electric properties shape the frequency scaling of brain signals at different scales, such as intracellular recordings, the local field potential (LFP), the electroencephalogram (EEG) or the magnetoencephalogram (MEG). These signals display frequency-scaling properties which are not consistent with resistive media. The medium appears to exert a frequency filtering scaling as $1/\sqrt{f}$, which is the typical frequency scaling of ionic diffusion. Such a scaling was also found recently by impedance measurements in physiological conditions. Ionic diffusion appears to be the only possible explanation to reconcile these measurements and the frequency-scaling properties found in different brain signals. However, other measurements suggest that the extracellular medium is essentially resistive. To resolve this discrepancy, we show new evidence that metal-electrode measurements can be perturbed by shunt currents going through the surface of the brain. Such a shunt may explain the contradictory measurements, and together with ionic diffusion, provides a framework where all observations can be reconciled. Finally, we propose a method to perform measurements avoiding shunting effects, thus enabling to test the predictions of this framework.Comment: (in press

On the effect of temperature on the insertion of zinc into hydroxyapatite.

International audienceRietveld analysis on X-ray powder diffraction patterns recorded from 28 hydroxyapatite samples containing various amount of zinc (0, 1.6, 3.2 and 6.1 wt. Zn %) and heat treated at various temperatures (between 500°C and 1100°C) have allowed to finely characterize the Zn insertion mechanism into the HAp crystal structure. The formation of Zn-doped HAp was achieved above 900°C only. Zn-doped HAp has the Ca10Znx(PO4)6(OH)2-2xO2x (0 < x ≤ 0.25) chemical composition with a constant Ca/P ratio of 1.67 due to the insertion mechanism into the hexagonal channel (partial occupancy of the 2b Wyckoff site with formation of linear OZn- O entities). Samples heat treated at 500 °C were almost single phase, HAp did not incorporate Zn and about half of the Zn atoms incorporated during the synthesis are not observable by X-ray powder diffraction (contained in an amorphous compound or physisorbed at the HAp surface). The reversible formation of Zn-doped β-TCP phase was observed at 600°C, reached its maximum content at 900°C and almost vanished at 1100°C. The results presented here strengthen the recently described mechanism of Zn insertion in the interstitial 2b Wyckoff position of the HAp structure, and explain the origin of the contradictory reports in the corresponding literature

Differential Taxation and Occupational Choice

We study nonlinear income taxation in a Roy model in which agents' productivity is sectorspecific. We show that when income taxes can be sector-specific, the Diamond-Mirrlees theorem (according to which the second-best displays production efficiency) fails: social welfare (be it Rawlsian or Weighed Utilitarian) can be increased by assigning some agents to their least productive sector. By sacrificing production efficiency, the planner incurs second-order losses in total output, but obtains a first-order reduction in the informational costs of redistribution. The same result obtains when the government is constrained to a uniform income tax schedule, as long as sales taxes can be made sector-specific. In this latter case, our result also implies failure of the Atkinson-Stiglitz theorem (according to which, when preferences over consumption and leisure are separable, as they are in our economy, the second-best can be implemented with zero sales taxes)

Differential Taxation and Occupational Choice

We develop a framework to study optimal sector-specific taxation, where each agent chooses an occupation by comparing her skill differential with the tax burden differential across sectors. Because skills are not perfectly transferable, the Diamond-Mirrlees theorem (according to which the second-best entails production efficiency) fails: social welfare can be increased by inducing some agents to join the sector in which their productivity is not the highest. At the optimum, income taxes balance the marginal losses from inter-sector migration with the marginal gains from tailoring tax schedules to the distribution of productivities in each sector (“tagging”). A calibrated model indicates that sector-specific taxation generates substantive welfare gains when skill transferability decreases with income, as it enables the government to increase average taxes on high earners with large wage premia

Differential Taxation and Occupational Choice

We develop a framework to study optimal sector-specific taxation, where each agent chooses an occupation by comparing her skill differential with the tax burden differential across sectors. Because skills are not perfectly transferable, the Diamond-Mirrlees theorem (according to which the second-best entails production efficiency) fails: social welfare can be increased by inducing some agents to join the sector in which their productivity is not the highest. At the optimum, income taxes balance the marginal losses from inter-sector migration with the marginal gains from tailoring tax schedules to the distribution of productivities in each sector (“tagging”). A calibrated model indicates that sector-specific taxation generates substantive welfare gains when skill transferability decreases with income, as it enables the government to increase average taxes on high earners with large wage premia

Etude expérimentale et théorique de la genèse des potentiels de champs locaux par les neurones corticaux

Local field potentials (LFPs) are low-frequency (< 200-500 Hz) events resulting from brain activity. Their meaning and the mechanisms shaping them have been highly debated for decades. The existence and importance of a frequency-dependant filtering of ionic currents by brain tissue is controversial. Some authors conclude that the medium is resistive, while others suggest that brain tissue may exert significative low-pass filtering on electrical currents. A new measurement method is presented here, relying on the concept of natural impedance, which is measured using a neuron as an ''electrode''. This allows to obtain the most relevant impedance from a physiological point of view, in terms of electrode-medium interface, current intensity and spatial scale. The measured impedance is stable, reproducible, stronger than what is traditionally measured, and has a 1/\√f frequency dependance. A physical model, taking into account ionic diffusion in the medium, is able to reproduce this impedance. A similar method allows to compute the transfer function between the intra- and extracellular potentials of a neuron. Models are proposed to explain its structure, predict LFPs from cell activity and vice-versa. These results may help interpreting LFP and electroencephalography signals, yielding a deeper understanding of the physiological and pathological brain function.Les potentiels de champs locaux (LFP) sont des événements de fréquence inférieure à 200-500 Hz, résultant de l'activité cérébrale. Leur signification et les mécanismes contribuant à leur formation sont encore très débattus. Ainsi, l'existence et l'importance d'un filtrage des courants ioniques par le tissu cérébral est controversée. Certains auteurs concluent que le milieu est résistif, alors que d'autres suggèrent que le tissu cérébral pourrait exercer un filtrage passe-bas significatif sur les courants électriques. Une méthode de mesure nouvelle est présentée ici, s'appuyant sur le concept d'impédance naturelle, mesurée en utilisant un neurone comme " électrode " . Ceci permet d'obtenir l'impédance la plus pertinente d'un point de vue physiologique, en termes d'interface électrode-milieu, d'intensité des courants et d'échelle spatiale. L'impédance mesurée est stable, reproductible, plus forte que celle mesurée traditionnellement, et possède une dépendance en fréquence en 1/vf. Un modèle physique prenant en compte la diffusion ionique dans le milieu est capable de reproduire cette impédance. Une méthode similaire permet de calculer la fonction de transfert entre les potentiels intra- et extracellulaire d'un neurone. Des modèles sont proposés pour expliquer sa forme, prédire les LFP d'après l'activité cellulaire et vice-versa. Ces résultats pourraient aider à l'interprétation des signaux de LFP et d'électroencéphalographie, permettant une compréhension plus profonde du fonctionnement cérébral physiologique et pathologique

Stifness and influence of non-saturation in granitic materials

Neste artigo, apresentam-se as características de deformabilidade para dois materiais com a mesma origem geológica: um agregado granítico (0/12.5; D50=0.52mm) e uma areia siltosa designada de areia de Perafita (0/6.35; D50=0.36mm). A rigidez, dos materiais compactados, no domínio das pequenas deformações (<10-5) é estudada através de ensaios triaxiais de precisão. A influência da não saturação na deformabilidade dos materiais é estudada através de ensaios triaxiais com medição das pressões intersticiais. Tais medidas permitiram a análise do comportamento mecânico dos materiais não saturados em termos de tensões efectivas, que foram calculadas através das aproximações de Terzaghi e Bishop. Os resultados obtidos mostram para cada material uma relação única entre o módulo de deformabilidade e a tensão efectiva (para e=0.5), independentemente do grau de saturação das amostras ensaiadas.In this paper, the stiffness of two materials with the same geological origin is presented, a granite aggregate (0/12.5, D50=0.52mm) and a silty sand, called Perafita sand (0/6.35; D50=0.36mm). The stiffness in very small strains (<10-5) of the compacted materials is studied by means of precision triaxial tests. The influence of non-saturation on the stiffness is also studied through triaxial tests with measurement of negative pore water pressures. Such measurements allow the analysis of the mechanical behaviour of the unsaturated material in terms of effective stresses. For this purpose two approaches were used: the Terzaghi’s and Bishop’s approaches. The results obtained show, for each material, a unique relationship between vertical stiffness and vertical effective stress (constant void ratio=0.5), independently of the saturation degree of the studied samples.Universidade de Coimbra. Faculdade de Ciências e Tecnologia (FCT-UC)GRICES/CNRS – “Security of road and railway infrastructures versus climatic changes

Influencia de la no saturación y granulometría en la rigidez de materiales de naturaleza granítica

In this paper, the stiffness of two materials with the same geological origin is presented, a silty sand, called Perafita sand (D50=0.36mm) and a granite aggregate (0/12.5, D50=0.52mm). The stiffness in very small strains ( <10-5) of the compacted materials is studied by means of precision triaxial tests (with local strain measurements). The influence of non-saturation on the stiffness is also studied through triaxial tests with measurement of negative pore water pressures. Such measurements allow the analysis of the mechanical behaviour of the unsaturated material in terms of effective stresses. For this purpose two approaches were used: the Terzaghi’s and Bishop’s approaches. The results obtained show, for each material, a unique relationship between vertical stiffness and vertical effective stress (constant void ratio = 0.5), independently of the saturation degree of the studied samples.En este artículo se presenta la rigidez de dos materiales con el mismo origen geológico, una arena con limo, llamada arena Perafita (D50=0.36mm) y un agregado granítico (0/12.5, D50=0.52mm). La rigidez para deformaciones muy pequeñas ( <10-5) de los materiales compactados es estudiada mediante ensayos triaxiales de precisión (con medidas locales de deformación). La influencia de la no-saturación en la rigidez se ha estudiado también mediante ensayos triaxiales con medición de la presión negativa del agua en los poros. Estas medidas permiten el análisis del comportamiento mecánico de materiales no saturados por lo que se refiere a tensiones efectivas. Con este propósito fueron usados dos procedimientos: el de Terzaghi y el de Bishop. Los resultados obtenidos revelan, para cada material, una relación única entre la rigidez vertical y la tensión efectiva vertical (ratio de vacíos constante = 0.5), independientemente del grado de saturación de las muestras estudiadas

Influence of Compaction and Loading Conditions of the Dynamic Properties of a Silty Sand

Elastic properties of a compacted silty sand were measured in a precision triaxial cell at the École Centrale de Paris in the range of very small strains (between 10-6 and 10-4), using improved Hall effect-based local strain gauges and data acquisition system. The dynamic properties of the soil were also derived from resonant column tests at the IST, in Lisbon, as functions of shear strain, compaction water content and confining pressure. Elastic limits as low as 5.10-6 were found in both devices, with Poisson’s ratio from triaxial tests ranging from 0.05 at very strains (\u3c 10-4) to 0.37 at larger strains. Comparison between quasi-static and dynamic values were found to be in good agreement, with a reasonable value of Poisson’s ratio, despite the complex properties of this soil such as viscosity, ageing effects and anisotropy