Successive spike times predicted by a stochastic neuronal model with a variable input signal
Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike ti...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016003 |
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| _version_ | 1832590122257743872 |
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| author | Giuseppe D'Onofrio Enrica Pirozzi |
| author_facet | Giuseppe D'Onofrio Enrica Pirozzi |
| author_sort | Giuseppe D'Onofrio |
| collection | DOAJ |
| description | Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike time after the signal onset. The second process is a Gauss-Markov process identified by a particular mean function dependent on the first passage time of the first process. It is shown that the second process is also of a diffusion type. The probability density function of the maximum between the first passage time of the first and the second process is considered to approximate the distribution of the second spike time. Results obtained by simulations are compared with those following the numerical and asymptotic approximations. A general equation to model successive spike times is given. Finally, examples with specific input signals are provided. |
| format | Article |
| id | doaj-art-6c8a5be96b0a4461981df3616b3f1872 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6c8a5be96b0a4461981df3616b3f18722025-01-24T02:35:23ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-12-0113349550710.3934/mbe.2016003Successive spike times predicted by a stochastic neuronal model with a variable input signalGiuseppe D'Onofrio0Enrica Pirozzi1Dipartimento di Matematica e Applicazioni, Università degli studi di Napoli, FEDERICO II, Via Cinthia, Monte S.Angelo, Napoli, 80126Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 NapoliTwo different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike time after the signal onset. The second process is a Gauss-Markov process identified by a particular mean function dependent on the first passage time of the first process. It is shown that the second process is also of a diffusion type. The probability density function of the maximum between the first passage time of the first and the second process is considered to approximate the distribution of the second spike time. Results obtained by simulations are compared with those following the numerical and asymptotic approximations. A general equation to model successive spike times is given. Finally, examples with specific input signals are provided.https://www.aimspress.com/article/doi/10.3934/mbe.2016003lif neuronal modelgauss-markov processesfirst passage time. |
| spellingShingle | Giuseppe D'Onofrio Enrica Pirozzi Successive spike times predicted by a stochastic neuronal model with a variable input signal Mathematical Biosciences and Engineering lif neuronal model gauss-markov processes first passage time. |
| title | Successive spike times predicted by a stochastic neuronal model with a variable input signal |
| title_full | Successive spike times predicted by a stochastic neuronal model with a variable input signal |
| title_fullStr | Successive spike times predicted by a stochastic neuronal model with a variable input signal |
| title_full_unstemmed | Successive spike times predicted by a stochastic neuronal model with a variable input signal |
| title_short | Successive spike times predicted by a stochastic neuronal model with a variable input signal |
| title_sort | successive spike times predicted by a stochastic neuronal model with a variable input signal |
| topic | lif neuronal model gauss-markov processes first passage time. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016003 |
| work_keys_str_mv | AT giuseppedonofrio successivespiketimespredictedbyastochasticneuronalmodelwithavariableinputsignal AT enricapirozzi successivespiketimespredictedbyastochasticneuronalmodelwithavariableinputsignal |