Biological neuron model

Summary

Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system. Spiking neuron models can be divided into different categories: the most detailed mathematical models are biophysical neuron models (also called Hodgkin-Huxley models) that describe the membrane voltage as a function of the input current and the activation of ion channels. Mathematically simpler are integrate-and-fire models that describe the membrane voltage as a function of the input current and predict the spike times without a description of the biophysical processes that shape the

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An action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur

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Data-driven whole mouse brain modeling for multi-scale simulations

Dimitri Bruno Marie Rodarie

In this thesis, we present a data-driven iterative pipeline to generate, simulate and validate point-neuron models of the whole mouse brain. The ultimate goal is to replicate close loop experiments with a virtual body in a virtual world. This pipeline was origi-nally created by a PhD student of the Blue Brain Project and this pioneer work has yielded the first versions of the model and their simulations. My objective is to refine, extend and consolidate the previous version of the workflow and in particular to extend the repertoire of neuron types by integrating and consolidating available literature data.The pipeline has four main parts. First, we define a pair of reference atlases to create a spatial reference for every dataset that we want to integrate. Second, we create a cell atlas with estimates of the number and density of the major cell types in each brain region. Then, we build a connectivity atlas that describes the connections of each neuron of the mouse brain and their properties. Finally, we assign point-neuron parameters to each of the neuron types, and synaptic parameters to each of the connection types of our model to obtain a point-neuron network of the mouse brain. This network can be simulated to perform mouse brain experi-ments in-silico.In this thesis, we evaluate the quality of the different reference atlases, released by the Allen Institute for Brain Science and pro-vide methods to mitigate the impact of artifacts in the original images. We further extend the cell atlas with density estimates of more inhibitory neuron types. To do so, we introduce a new method to combine estimates of inhibitory neuron counts from the literature into a consistent framework. We also estimate inhibitory neuron density in regions where no literature data are avai-lable, using collected literature estimates and gene expression data from in situ hybridization image stacks. Our approach can be further extended to other cell types and provides a resource to build more detailed circuits of the mouse brain. Next, we refine the connectivity atlas, including literature findings on short-range connectivity. Additionally, we construct a database to store data collected on neuron types point-neuron parameters and synaptic parameters. With the results of the previous steps, we generate a new version of the whole mouse brain point-neuron network. We tested this new model against its previous version using three benchmark experiments. We explore the possibility to embed and connect detailed circuit reconstructions of the mouse brain to our point neuron model and co-simulate them. Finally, we constrain a 3D skeleton model of the mouse with joint constraints from the literature and attach muscle to its bones to create a musculoskeletal model of the mouse body that can be simulated in close-loop with our model to reproduce motor control experiments.

EPFL2022

Mathematical modeling and numerical simulation of excitation-contraction phenomena in the heart

In this Master thesis we aim at studying some physiological and computational aspects of the excitation-contraction mechanisms in the heart muscle. This phenomenon exhibits many complexities at different spatio-temporal scales. The relevance and applicability of several recent phenomenological and physiologically detailed ionic models will be assessed. The choice of the treated models is based on an equilibrium between results that manage to reproduce correctly the complexity of the cardiac electrophysiology and a weak computational cost in order to solve the large set of ODEs which describe the dynamics of that ionic model. The preferred models include a large part of the more recent electrophysiological discoveries and understandings (e.g. L-type calcium and ryanodine channels) in order to reproduce at best the electrical conduction in the human cardiac tissue based on different experimental or computational measurements. According to these previous remarks, we will perform a thorough testing and quantitative comparison of these models and mechanical activation mechanisms in the framework of the LifeV finite element library. In a second step, a recent model for the description of crossbridge dynamics will be implemented. The importance of using good ionic models makes sense to identify correctly the possible influence on the muscle mechanics activation, which enable the heart to pump blood throughout the entire circulatory system.

2013

Computational neuroscience is a branch of the neurosciences that attempts to elucidate the principles underlying the operation of neurons with the help of mathematical modeling. In contrast with a number of fields pursuing a tightly related goal, such as machine learning or statistical learning, computational neuroscience emphasizes the realistic description of neuronal function and organization, and therefore requires a collaboration with experimental research in order to design new models and test their predictions. With the growing computational power available in modern computers, the simulation of neuronal networks with realistic numbers of neurons and functional organization is becoming routinely accessible. For the accurate design of such network models, the experimental characterization of neuronal response properties is required to probe the structural layout of biological networks at the single cell level. We develop here a novel method, the dynamic I-V method, that allows for the extraction of cellular response properties, and requires only a small amount of experimental data. Using this technique a simplified model of the neuronal response is obtained that is shown to accurately fit the experimental data. We demonstrate the use of the dynamic I-V method on both cortical pyramidal cells and inhibitory interneurons, and give the distributions of cellular parameters for the studied sample of cells. We also give theoretical results on the spike-triggered average, a quantity that is easily measured experimentally, which relate the neuronal response properties to identifiable features of the spike-triggered average, and can potentially be helpful to extend the dynamic I-V method in order to derive more accurate models. Potential applications and extensions of our results are discussed.

EPFL2009

Data-driven whole mouse brain modeling for multi-scale simulations

Dimitri Bruno Marie Rodarie

EPFL2022