Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells and the extracellular space. Given the complexity of brain's structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A non-local model of the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non-locality on the distribution of the membrane potential are investigated using numerical simulations.
{"title":"A Non-local Model of the Propagation of Action Potentials in Myelinated Neurons","authors":"C. Drapaca, S. Ozdemir, E. Proctor","doi":"10.28991/esj-2020-01219","DOIUrl":"https://doi.org/10.28991/esj-2020-01219","url":null,"abstract":"Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells and the extracellular space. Given the complexity of brain's structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A non-local model of the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non-locality on the distribution of the membrane potential are investigated using numerical simulations.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122602123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-05DOI: 10.1016/b978-0-12-801238-3.11588-0
KongFatt Wong-Lin, J. Sanchez-Bornot, N. Mccombe, D. Kaur, P. McClean, Xin Zou, V. Youssofzadeh, X. Ding, M. Bucholc, Su Yang, G. Prasad, D. Coyle, Liam P. Maguire, Haiying Wang, Hui Wang, Nadim A. A. Atiya, Alok Joshi
{"title":"Computational Neurology: Computational Modeling Approaches in Dementia","authors":"KongFatt Wong-Lin, J. Sanchez-Bornot, N. Mccombe, D. Kaur, P. McClean, Xin Zou, V. Youssofzadeh, X. Ding, M. Bucholc, Su Yang, G. Prasad, D. Coyle, Liam P. Maguire, Haiying Wang, Hui Wang, Nadim A. A. Atiya, Alok Joshi","doi":"10.1016/b978-0-12-801238-3.11588-0","DOIUrl":"https://doi.org/10.1016/b978-0-12-801238-3.11588-0","url":null,"abstract":"","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126676166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-09DOI: 10.1103/physrevresearch.2.023289
Chun-Wang Su, Liang Zheng, Youjun Li, Haijun Zhou, Jue Wang, Zi-Gang Huang, Y. Lai
The dynamical mechanism underlying the processes of anesthesia-induced loss of consciousness and recovery is key to gaining insights into the working of the nervous system. Previous experiments revealed an asymmetry between neural signals during the anesthesia and recovery processes. Here we obtain experimental evidence for the hysteresis loop and articulate the dynamical mechanism based on percolation on multilayer complex networks with self-similarity. Model analysis reveals that, during anesthesia, the network is able to maintain its neural pathways despite the loss of a substantial fraction of the edges. A predictive and potentially testable result is that, in the forward process of anesthesia, the average shortest path and the clustering coefficient of the neural network are markedly smaller than those associated with the recovery process. This suggests that the network strives to maintain certain neurological functions by adapting to a relatively more compact structure in response to anesthesia.
{"title":"Hysteresis in anesthesia and recovery: Experimental observation and dynamical mechanism","authors":"Chun-Wang Su, Liang Zheng, Youjun Li, Haijun Zhou, Jue Wang, Zi-Gang Huang, Y. Lai","doi":"10.1103/physrevresearch.2.023289","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.023289","url":null,"abstract":"The dynamical mechanism underlying the processes of anesthesia-induced loss of consciousness and recovery is key to gaining insights into the working of the nervous system. Previous experiments revealed an asymmetry between neural signals during the anesthesia and recovery processes. Here we obtain experimental evidence for the hysteresis loop and articulate the dynamical mechanism based on percolation on multilayer complex networks with self-similarity. Model analysis reveals that, during anesthesia, the network is able to maintain its neural pathways despite the loss of a substantial fraction of the edges. A predictive and potentially testable result is that, in the forward process of anesthesia, the average shortest path and the clustering coefficient of the neural network are markedly smaller than those associated with the recovery process. This suggests that the network strives to maintain certain neurological functions by adapting to a relatively more compact structure in response to anesthesia.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124555157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-25DOI: 10.1016/j.carbon.2020.02.0430008-6223/2020
M. L. DiFrancesco, E. Colombo, E. D. Papaleo, J. F. Maya-Vetencourt, G. Manfredi, G. Lanzani, F. Benfenati
{"title":"A hybrid P3HT-Graphene interface for efficient photostimulation of neurons.","authors":"M. L. DiFrancesco, E. Colombo, E. D. Papaleo, J. F. Maya-Vetencourt, G. Manfredi, G. Lanzani, F. Benfenati","doi":"10.1016/j.carbon.2020.02.0430008-6223/2020","DOIUrl":"https://doi.org/10.1016/j.carbon.2020.02.0430008-6223/2020","url":null,"abstract":"","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130713599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-24DOI: 10.20944/preprints201912.0333.v1
Shen Ning, Mehdi Jorfi
In recent years, many molecular and environmental factors have been studied to understand how synaptic plasticity is modulated. Sleep, as an evolutionary conserved biological function, has shown to be a critical player for the consolidation and filtering of synaptic circuitry underlying memory traces. Although sleep disturbances do not alter normal memory consolidation, they may reflect fundamental circuit malfunctions that can play a significant role in exacerbating diseases, such as autism and Alzheimer’s disease. Very recently, scientists sought to answer part of this enigma and they identified p75 neurotrophic receptor (p75NTR) as a critical player in mediating impairments in hippocampal-dependent associative plasticity upon sleep deprivation. This paper will review the role of the p75NTR, critically discuss the impact and implications of this research as the bridge for sleep research and neurological diseases.
{"title":"p75NTR as a Molecular Memory Switch","authors":"Shen Ning, Mehdi Jorfi","doi":"10.20944/preprints201912.0333.v1","DOIUrl":"https://doi.org/10.20944/preprints201912.0333.v1","url":null,"abstract":"In recent years, many molecular and environmental factors have been studied to understand how synaptic plasticity is modulated. Sleep, as an evolutionary conserved biological function, has shown to be a critical player for the consolidation and filtering of synaptic circuitry underlying memory traces. Although sleep disturbances do not alter normal memory consolidation, they may reflect fundamental circuit malfunctions that can play a significant role in exacerbating diseases, such as autism and Alzheimer’s disease. Very recently, scientists sought to answer part of this enigma and they identified p75 neurotrophic receptor (p75NTR) as a critical player in mediating impairments in hippocampal-dependent associative plasticity upon sleep deprivation. This paper will review the role of the p75NTR, critically discuss the impact and implications of this research as the bridge for sleep research and neurological diseases.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130209181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1103/physrevresearch.2.013111
Friedrich Schuessler, A. Dubreuil, F. Mastrogiuseppe, S. Ostojic, O. Barak
A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be considered random. Understanding the interplay between the structured and random components, and their effect on network dynamics and functionality is an important open question. Recent studies addressed the co-existence of random and structured connectivity, but considered the two parts to be uncorrelated. This constraint limits the dynamics and leaves the random connectivity non-functional. Algorithms that train networks to perform specific tasks typically generate correlations between structure and random connectivity. Here we study nonlinear networks with correlated structured and random components, assuming the structure to have a low rank. We develop an analytic framework to establish the precise effect of the correlations on the eigenvalue spectrum of the joint connectivity. We find that the spectrum consists of a bulk and multiple outliers, whose location is predicted by our theory. Using mean-field theory, we show that these outliers directly determine both the fixed points of the system and their stability. Taken together, our analysis elucidates how correlations allow structured and random connectivity to synergistically extend the range of computations available to networks.
{"title":"Dynamics of random recurrent networks with correlated low-rank structure","authors":"Friedrich Schuessler, A. Dubreuil, F. Mastrogiuseppe, S. Ostojic, O. Barak","doi":"10.1103/physrevresearch.2.013111","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.013111","url":null,"abstract":"A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be considered random. Understanding the interplay between the structured and random components, and their effect on network dynamics and functionality is an important open question. Recent studies addressed the co-existence of random and structured connectivity, but considered the two parts to be uncorrelated. This constraint limits the dynamics and leaves the random connectivity non-functional. Algorithms that train networks to perform specific tasks typically generate correlations between structure and random connectivity. Here we study nonlinear networks with correlated structured and random components, assuming the structure to have a low rank. We develop an analytic framework to establish the precise effect of the correlations on the eigenvalue spectrum of the joint connectivity. We find that the spectrum consists of a bulk and multiple outliers, whose location is predicted by our theory. Using mean-field theory, we show that these outliers directly determine both the fixed points of the system and their stability. Taken together, our analysis elucidates how correlations allow structured and random connectivity to synergistically extend the range of computations available to networks.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122811652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The ability to reuse lessons from past experiences is one of the most critical abilities for intelligent behavior. In this paper, we introduce three terms: kernel, kernel dimension, and kernelization. The first to describe what is being reused, the second to describe the size of what is being reused, and the last to describe the process of seeking past experience from present input. Based on the abnormalities of two psychiatric disorders, autism and schizophrenia, we hypothesize that the structure of the pyramidal neurons of the Prefrontal Cortex determines the dimension and we make two demonstrations with artificial intelligence - one to show that certain a structural property of influences the kernel dimension and the other to show that cognitive functioning is effected by the dimension of the kernel.
{"title":"Dimensions of Kernel Abstractions","authors":"Prashant C. Raju","doi":"10.31234/osf.io/d8qvy","DOIUrl":"https://doi.org/10.31234/osf.io/d8qvy","url":null,"abstract":"The ability to reuse lessons from past experiences is one of the most critical abilities for intelligent behavior. In this paper, we introduce three terms: kernel, kernel dimension, and kernelization. The first to describe what is being reused, the second to describe the size of what is being reused, and the last to describe the process of seeking past experience from present input. Based on the abnormalities of two psychiatric disorders, autism and schizophrenia, we hypothesize that the structure of the pyramidal neurons of the Prefrontal Cortex determines the dimension and we make two demonstrations with artificial intelligence - one to show that certain a structural property of influences the kernel dimension and the other to show that cognitive functioning is effected by the dimension of the kernel.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130525166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There is an increasing interest in the systematic disagreement about profoundly ambiguous stimuli in the color domain. However, this research has been hobbled by the fact that we could not create such stimuli at will. Here, we describe a design principle that allows the creation of such stimuli and apply this principle to create one such stimulus set - “the crocs and socks”. Using this set, we probed the color perception of a large sample of observers, showing that these stimuli are indeed categorically ambiguous and that we can predict the percept from fabric priors resulting from experience. We also relate the perception of these crocs to other color-ambiguous stimuli - “the dress” and “the sneaker” and conclude that differential priors likely underlie polarized disagreement in cognition more generally.
{"title":"Disagreeing about Crocs and socks: Creating profoundly ambiguous color displays","authors":"P. Wallisch, M. Karlovich","doi":"10.31234/osf.io/zpqnv","DOIUrl":"https://doi.org/10.31234/osf.io/zpqnv","url":null,"abstract":"There is an increasing interest in the systematic disagreement about profoundly ambiguous stimuli in the color domain. However, this research has been hobbled by the fact that we could not create such stimuli at will. Here, we describe a design principle that allows the creation of such stimuli and apply this principle to create one such stimulus set - “the crocs and socks”. Using this set, we probed the color perception of a large sample of observers, showing that these stimuli are indeed categorically ambiguous and that we can predict the percept from fabric priors resulting from experience. We also relate the perception of these crocs to other color-ambiguous stimuli - “the dress” and “the sneaker” and conclude that differential priors likely underlie polarized disagreement in cognition more generally.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121012026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-02DOI: 10.32470/CCN.2018.1037-0
E. Arani, Sofia Triantafillou, Konrad Paul Kording
Much of neuroscience aims at reverse engineering the brain, but we only record a small number of neurons at a time. We do not currently know if reverse engineering the brain requires us to simultaneously record most neurons or if multiple recordings from smaller subsets suffice. This is made even more important by the development of novel techniques that allow recording from selected subsets of neurons, e.g. using optical techniques. To get at this question, we analyze a neural network, trained on the MNIST dataset, using only partial recordings and characterize the dependency of the quality of our reverse engineering on the number of simultaneously recorded "neurons". We find that reverse engineering of the nonlinear neural network is meaningfully possible if a sufficiently large number of neurons is simultaneously recorded but that this number can be considerably smaller than the number of neurons. Moreover, recording many times from small random subsets of neurons yields surprisingly good performance. Application in neuroscience suggests to approximate the I/O function of an actual neural system, we need to record from a much larger number of neurons. The kind of scaling analysis we perform here can, and arguably should be used to calibrate approaches that can dramatically scale up the size of recorded data sets in neuroscience.
{"title":"Reverse engineering neural networks from many partial recordings","authors":"E. Arani, Sofia Triantafillou, Konrad Paul Kording","doi":"10.32470/CCN.2018.1037-0","DOIUrl":"https://doi.org/10.32470/CCN.2018.1037-0","url":null,"abstract":"Much of neuroscience aims at reverse engineering the brain, but we only record a small number of neurons at a time. We do not currently know if reverse engineering the brain requires us to simultaneously record most neurons or if multiple recordings from smaller subsets suffice. This is made even more important by the development of novel techniques that allow recording from selected subsets of neurons, e.g. using optical techniques. To get at this question, we analyze a neural network, trained on the MNIST dataset, using only partial recordings and characterize the dependency of the quality of our reverse engineering on the number of simultaneously recorded \"neurons\". We find that reverse engineering of the nonlinear neural network is meaningfully possible if a sufficiently large number of neurons is simultaneously recorded but that this number can be considerably smaller than the number of neurons. Moreover, recording many times from small random subsets of neurons yields surprisingly good performance. Application in neuroscience suggests to approximate the I/O function of an actual neural system, we need to record from a much larger number of neurons. The kind of scaling analysis we perform here can, and arguably should be used to calibrate approaches that can dramatically scale up the size of recorded data sets in neuroscience.","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133744067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-07DOI: 10.11588/HEIDOK.00017128
Jurgis Pods
In studies of the brain and the nervous system, extracellular signals – as measured by local field potentials (LFPs) or electroencephalography (EEG) – are of capital importance, as they allow to simultaneously obtain data from multiple neurons. The exact biophysical basis of these signals is, however, still not fully understood. Most models for the extracellular potential today are based on volume conductor theory, which assumes that the extracellular fluid is electroneutral and that the only contributions to the electric field are given by membrane currents, which can be imposed as boundary conditions in the mathematical model. This neglects a second, possibly important contributor to the extracellular field: the time- and position-dependent concentrations of ions in the intra- and extracellular fluids. In this thesis, a 3D model of a single axon in extracellular fluid is presented based on the Poisson-Nernst-Planck (PNP) equations of electrodiffusion. This fundamental model includes not only the potential, but also the concentrations of all participating ion concentrations in a self-consistent way. This enables us to study the propagation of an action potential (AP) along the axonal membrane based on first principles by means of numerical simulations. By exploiting the cylinder symmetry of this geometry, the problem can be reduced to two dimensions. The numerical solution is implemented in a flexible and efficient way, using the DUNE framework. A suitable mesh generation strategy and a parallelization of the algorithm allow to solve the problem in reasonable time, with a high spatial and temporal resolution. The methods and programming techniques used to deal with the numerical challenges of this multi-scale problem are presented in detail. Special attention is paid to the Debye layer, the region with strong concentration gradients close to the membrane, which is explicitly resolved by the computational mesh. The focus lies on the evolution of the extracellular electric potential at different membrane distances. Roughly, the extracellular space can be divided into three distinct regions: first, the distant farfield, which exhibits a characteristic triphasic waveform in response to an action potential traveling along the membrane. This is consistent with previous modeling efforts and experiments. Secondly, the Debye layer close to the membrane, which shows a completely different extracellular response in the form of an “AP echo”, which is also observed in juxtacellular recordings. Finally, there is the intermediate or diffusion layer located in between, which shows a gradual transition from the Debye layer potential towards the farfield potential. Both of these potentialregions show marked deviations from volume conductor models, which can be attributed to the redistribution of concentrations and associated ion fluxes. These differences are explained by analyzing the capacitive and ionic components of the potential. In an exten
{"title":"Electrodiffusion Models of Axon and Extracellular Space Using the Poisson-Nernst-Planck Equations","authors":"Jurgis Pods","doi":"10.11588/HEIDOK.00017128","DOIUrl":"https://doi.org/10.11588/HEIDOK.00017128","url":null,"abstract":"In studies of the brain and the nervous system, extracellular signals – as measured by local field potentials (LFPs) or electroencephalography (EEG) – are of capital importance, as they allow to simultaneously obtain data from multiple neurons. The exact biophysical basis of these signals is, however, still not fully understood. Most models for the extracellular potential today are based on volume conductor theory, which assumes that the extracellular fluid is electroneutral and that the \u0000only contributions to the electric field are given by membrane currents, which can be imposed as boundary conditions in the mathematical model. This neglects a \u0000second, possibly important contributor to the extracellular field: the time- and position-dependent concentrations of ions in the intra- and extracellular fluids. \u0000 \u0000In this thesis, a 3D model of a single axon in extracellular fluid is presented based on the Poisson-Nernst-Planck (PNP) equations of electrodiffusion. This \u0000fundamental model includes not only the potential, but also the concentrations of all participating ion concentrations in a self-consistent way. This enables us to study the propagation of an action potential (AP) along the axonal membrane based on first principles by means of numerical simulations. By exploiting the cylinder symmetry of this geometry, the problem can be reduced to two dimensions. The numerical solution is implemented in a flexible and efficient way, using the DUNE framework. A suitable mesh generation strategy and a parallelization of the algorithm allow to solve the problem in reasonable time, with a high spatial and temporal resolution. The methods and programming \u0000techniques used to deal with the numerical challenges of this multi-scale problem are presented in detail. \u0000 \u0000Special attention is paid to the Debye layer, the region with strong concentration gradients close to the membrane, which is explicitly resolved by the computational mesh. The focus lies on the evolution of the extracellular electric \u0000potential at different membrane distances. Roughly, the extracellular space can be divided into three distinct regions: first, the distant farfield, which exhibits \u0000a characteristic triphasic waveform in response to an action potential traveling along the membrane. This is consistent with previous modeling efforts and \u0000experiments. Secondly, the Debye layer close to the membrane, which shows a completely different extracellular response in the form of an “AP echo”, which \u0000is also observed in juxtacellular recordings. Finally, there is the intermediate or diffusion layer located in between, which shows a gradual transition from the \u0000Debye layer potential towards the farfield potential. Both of these potentialregions show marked deviations from volume conductor models, which can be attributed to the redistribution of concentrations and associated ion fluxes. These differences are explained by analyzing the capacitive and ionic components of the potential. \u0000 \u0000In an exten","PeriodicalId":298664,"journal":{"name":"arXiv: Neurons and Cognition","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132474224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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