145 research outputs found
Exploring the effect of ionic diffusion on extracellular potentials in the brain
No full textIonic concentration gradients can exist in the extracellular space (ECS) due to neuronal activity that can change the local ionic composition. Diffusion and electrical drift are two processes that move ions around in the extracellular space. These processes can be described by the Nernst-Planck equation. Ions diffuse along concentration gradients. Since ions carry charge, this process can give rise to electric currents, which, in turn, can result in a diffusion potential.
The question under investigation is if diffusion potentials in ECS are large enough to affect the measurements of local field potentials (LFPs) in the brain? Diffusion potentials are slow-changing potentials, so its possible contributions to the LFPs would be for low frequencies [1]. To explore the effect of diffusion potentials, I compared power spectrum densities (PSDs) of diffusion potentials to PSDs of LFPs recordings.
I estimated the diffusion potentials from extracellular concentration data collected from various articles. The concentration data were obtained from different experiments. Instead of numerically simulating how the diffusion potential changed, I approximated the diffusion potential by an exponentially decaying function. For more realistic estimates, I used time constants from temporal concentration data. Then, I estimated the PSDs of the diffusion potentials from each data set.
For LFP data, I found and used data files with LFP recordings. For these data files, I calculated average PSDs. In addition, I collected LFP data represented as PSDs from figures in articles,
At low frequencies (< 1 Hz), I found that PSD of the highest diffusion potentials had similar powers as the lowest PSDs of LFP measurements. Therefore, there may be a slight possibility that diffusion potentials can contribute to the LFP at the lowest frequencies.
I also estimated diffusion potentials at pathological conditions, such as spreading depression (SD), where concentration gradients are extremely large. I used the same approach and found that the diffusion potentials in these cases could be up to 10 times larger. The PSDs of the pathological diffusion potentials had similar powers as the LFP recordings.M-M
Exploring the electric diffusion potential in the extracellular space of the brain
No full textIntense neuronal signalling may locally change the ionic composition of the extracellular space, and produce ionic concentration gradients. The ionic concentration gradients causes an electric diffusion potential, described by the Nernst--Planck equation. I have modelled this diffusion potential, by combining the Nernst--Planck equation with Kirchoff's law of current conservation, this is what is called the Kirchoff--Nernst--Planck-formalism \cite{Halnes2013}\cite{Halnes2016}. By assuming a laminar structure of the cortex, I made a one-dimensional model of the diffusion potential. The potential was simulated by implementing a numerical scheme in Python. I have found recorded concentration profiles from previously published experiments, where the extracellular concentration gradients were high, but not pathologically high. I used these concentration profiles as initial conditions. The aim of this project has been to investigate whether the diffusion potential makes up a measurable part of the extracellular potential. From previous studies \cite{Halnes2016}\cite{Gratiy2017}, I know that the diffusion potential has low frequencies, and its effect would be in the low-frequency part of the extracellular potential -- the local field potential. The the frequencies of the local field potential were analyzed by computing the power spectrum density. I found that for recordable frequencies (from 0.3 Hz and above) and non-pathological ion concentration gradients, the diffusion potential was much smaller than measured local field potential.
The concentration gradients are transient, and the baseline concentrations are re-established approximately hundred times faster than what diffusion accounts for \cite{CordingleySomjen}. I simulated a diffusion potential caused by exponentially decaying concentration gradients, with typical half-lives from previous experiments. This produced a diffusion potential with higher powers in the range of the recordable frequencies, but still not at the level of the recorded local field potential.
Some pathological conditions are associated with extreme concentration gradients. I have used a recorded concentration profile where the deviations from baseline concentrations were approximately ten times higher than the non-pathological concentration deviations. I saw that in this case, the diffusion potential was of the same magnitude as the local field potential, and even larger, for frequencies lower than approximately 2 Hz. I also tried this extreme scenario with exponentially decaying concentration gradients. This resulted in a diffusion potential which was larger than the local field potential for almost all frequencies in the range of the simulation.M-LU
Comparing different techniques for stimulating neurons - a computational study
No full textA comparison of different techniques for stimulating neurons using a computational model. The computational model is an expanded version of the electrodiffusive Pinsky-Rinzel model from Sætra et al. (2020) referenced in the thesis. The explicit modeling of ion concentrations allows for comparison of which ions are used for stimulation. The expansion of the model allows for comparison of stimulation currents coming from inside and outside the system. In conclusion, both the ion mix in the stimulation current and the stimulation technique can have an effect on the response of the model. In particular, there is an effect of potassium ions in the stimulation current
Biological network modelling
No full textThis study takes a network approach to understanding complex biological systems. The overall objective is to explore how the stability and flexibility of biological networks emerge from underlying structural and dynamical characteristics. The thesis is arranged as a journey into the complexity of biological network models. The starting point is qualitative structural network descriptions. The level of detail in the dynamical description of node properties is then gradually increased. Along this journey, new features, both structural and dynamical, are revealed as crucial for the function of biological networks. A set of constructional properties are defined: structural principles, structural complexity, interaction diversity, node diversity and network density. These constructional properties capture important aspects of the structural organization and dynamic mechanisms in biological networks. A set of functional properties are defined: structural robustness, structural cyclicity, dynamic stability and dynamic flexibility. These functional properties are systemic properties that are all related to the stability of biological networks. These two sets of properties are used to demonstrate how the construction of biological networks is crucial for their function. The general theory is applied to food web and neural network models, where the general network properties are given specific biological meanings. The studies within both fields have their system specific objectives. A simple food web model is developed for explicitly including a compartment for dead organic material (detritus). Several constructional properties are revealed as crucial for the structural robustness, the structural cyclicity and the dynamic stability of food webs. The pathways due to decomposing and recycling of detritus alter the constructional properties, and are crucial for food web function. Computational neural network models are developed for clinical applications. Possible mechanisms behind electroconvulsive treatment (ECT) and anaesthetics are modelled. Clinical observations are qualitatively reproduced. Several aspects of the constructional properties of neural networks are revealed as crucial for optimal stability and flexibility of neurodynamics
An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms
No full textIn most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na+, K+, Ca2+, and Cl−), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy
Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience
No full textpublishedVersio
An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain
No full textWithin the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate
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