Frequency dependence of signal power and spatial reach of the local field potential

The first recording of electrical potential from brain activity was reported already in 1875, but still the interpretation of the signal is debated. To take full advantage of the new generation of microelectrodes with hundreds or even thousands of electrode contacts, an accurate quantitative link between what is measured and the underlying neural circuit activity is needed. Here we address the question of how the observed frequency dependence of recorded local field potentials (LFPs) should be interpreted. By use of a well-established biophysical modeling scheme, combined with detailed reconstructed neuronal morphologies, we find that correlations in the synaptic inputs onto a population of pyramidal cells may significantly boost the low-frequency components of the generated LFP. We further find that these low-frequency components may be less `local' than the high-frequency LFP components in the sense that (1) the size of signal-generation region of the LFP recorded at an electrode is larger and (2) that the LFP generated by a synaptically activated population spreads further outside the population edge due to volume conduction

A thermodynamic framework for modelling membrane transporters

Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of thermodynamics. However, many mathematical models of transporters, especially those incorporated into whole-cell models, are not thermodynamically consistent, leading to unrealistic behaviour. In this paper we use a physics-based modelling framework, in which the transfer of energy is explicitly accounted for, to develop thermodynamically consistent models of transporters. We then apply this methodology to model two specific transporters: the cardiac sarcoplasmic/endoplasmic Ca$^{2+}$ ATPase (SERCA) and the cardiac Na$^+$/K$^+$ ATPase

Dynamic Moment Analysis of the Extracellular Electric Field of a Biologically Realistic Spiking Neuron

Based upon the membrane currents generated by an action potential in a biologically realistic model of a pyramidal, hippocampal cell within rat CA1, we perform a moment expansion of the extracellular field potential. We decompose the potential into both inverse and classical moments and show that this method is a rapid and efficient way to calculate the extracellular field both near and far from the cell body. The action potential gives rise to a large quadrupole moment that contributes to the extracellular field up to distances of almost 1 cm. This method will serve as a starting point in connecting the microscopic generation of electric fields at the level of neurons to macroscopic observables such as the local field potential

A geographically distributed bio-hybrid neural network with memristive plasticity

Throughout evolution the brain has mastered the art of processing real-world inputs through networks of interlinked spiking neurons. Synapses have emerged as key elements that, owing to their plasticity, are merging neuron-to-neuron signalling with memory storage and computation. Electronics has made important steps in emulating neurons through neuromorphic circuits and synapses with nanoscale memristors, yet novel applications that interlink them in heterogeneous bio-inspired and bio-hybrid architectures are just beginning to materialise. The use of memristive technologies in brain-inspired architectures for computing or for sensing spiking activity of biological neurons8 are only recent examples, however interlinking brain and electronic neurons through plasticity-driven synaptic elements has remained so far in the realm of the imagination. Here, we demonstrate a bio-hybrid neural network (bNN) where memristors work as "synaptors" between rat neural circuits and VLSI neurons. The two fundamental synaptors, from artificial-to-biological (ABsyn) and from biological-to- artificial (BAsyn), are interconnected over the Internet. The bNN extends across Europe, collapsing spatial boundaries existing in natural brain networks and laying the foundations of a new geographically distributed and evolving architecture: the Internet of Neuro-electronics (IoN).Comment: 16 pages, 10 figure

Advances in surface EMG signal simulation with analytical and numerical descriptions of the volume conductor

Surface electromyographic (EMG) signal modeling is important for signal interpretation, testing of processing algorithms, detection system design, and didactic purposes. Various surface EMG signal models have been proposed in the literature. In this study we focus on 1) the proposal of a method for modeling surface EMG signals by either analytical or numerical descriptions of the volume conductor for space-invariant systems, and 2) the development of advanced models of the volume conductor by numerical approaches, accurately describing not only the volume conductor geometry, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function is derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fiber orientation. In some cases (e.g., multi-pinnate muscles) accurate description of the conductivity tensor may be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibers is presented and applied to representatively investigate a bi-pinnate muscle with rectilinear and curvilinear fibers. The study thus propose an approach for surface EMG signal simulation in space invariant systems as well as new models of the volume conductor using numerical methods

Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

Extracellular local field potentials (LFP) are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of LFPs, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is non-homogeneous, there is induction of non-homogeneous charge densities which may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically-symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na$^+$-mediated action potentials) attenuate very steeply with distance, while slower (K$^+$-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.Comment: text (LaTeX), 6 figs. (ps