Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 495-507. doi: 10.3934/mbe.2016003
Previous Article Next Article

Successive spike times predicted by a stochastic neuronal model with a variable input signal

  • 1.
    Dipartimento di Matematica e Applicazioni, Università degli studi di Napoli, FEDERICO II, Via Cinthia, Monte S.Angelo, Napoli, 80126
  • 2.
    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 January 2016

  • MSC : Primary: 60G20, 60J70; Secondary: 65C30.

  • 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.

    Citation: Giuseppe D'Onofrio, Enrica Pirozzi. Successive spike times predicted by a stochastic neuronal model with a variable input signal[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 495-507. doi: 10.3934/mbe.2016003

    Related Papers:

    [1] Lernik Asserian, Susan E. Luczak, I. G. Rosen . Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol. Mathematical Biosciences and Engineering, 2023, 20(11): 20345-20377. doi: 10.3934/mbe.2023900
    [2] Kimberlyn Roosa, Ruiyan Luo, Gerardo Chowell . Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study. Mathematical Biosciences and Engineering, 2019, 16(5): 4299-4313. doi: 10.3934/mbe.2019214
    [3] Celia Schacht, Annabel Meade, H.T. Banks, Heiko Enderling, Daniel Abate-Daga . Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model. Mathematical Biosciences and Engineering, 2019, 16(6): 7299-7326. doi: 10.3934/mbe.2019365
    [4] Walid Emam, Khalaf S. Sultan . Bayesian and maximum likelihood estimations of the Dagum parameters under combined-unified hybrid censoring. Mathematical Biosciences and Engineering, 2021, 18(3): 2930-2951. doi: 10.3934/mbe.2021148
    [5] Kamil Rajdl, Petr Lansky . Fano factor estimation. Mathematical Biosciences and Engineering, 2014, 11(1): 105-123. doi: 10.3934/mbe.2014.11.105
    [6] H. T. Banks, R. A. Everett, Neha Murad, R. D. White, J. E. Banks, Bodil N. Cass, Jay A. Rosenheim . Optimal design for dynamical modeling of pest populations. Mathematical Biosciences and Engineering, 2018, 15(4): 993-1010. doi: 10.3934/mbe.2018044
    [7] Walid Emam, Ghadah Alomani . Predictive modeling of reliability engineering data using a new version of the flexible Weibull model. Mathematical Biosciences and Engineering, 2023, 20(6): 9948-9964. doi: 10.3934/mbe.2023436
    [8] P. van den Driessche, Lin Wang, Xingfu Zou . Modeling diseases with latency and relapse. Mathematical Biosciences and Engineering, 2007, 4(2): 205-219. doi: 10.3934/mbe.2007.4.205
    [9] H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Carola Kruse, Simon Shaw, John Whiteman, Mark P. Brewin, Stephen E. Greenwald, Malcolm J. Birch . Model validation for a noninvasive arterial stenosis detection problem. Mathematical Biosciences and Engineering, 2014, 11(3): 427-448. doi: 10.3934/mbe.2014.11.427
    [10] Azmy S. Ackleh, H.T. Banks, Keng Deng, Shuhua Hu . Parameter Estimation in a Coupled System of Nonlinear Size-Structured Populations. Mathematical Biosciences and Engineering, 2005, 2(2): 289-315. doi: 10.3934/mbe.2005.2.289
  • 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.


    [1] Biological Cybernetics, 95 (2006), 1-19.
    [2] Methodol. Comput. Appl. Prob., 13 (2011), 29-57.
    [3] Neural Computation, 22 (2010), 2558-2585.
    [4] Math. Biosci. Eng., 11 (2014), 189-201.
    [5] Applied Mathematics and Computation, 232 (2014), 799-809.
    [6] Journal of Computational and Applied Mathematics, 285 (2015), 59-71.
    [7] Advances in Cognitive Neurodynamics (IV), 11 (2015), 299-305.
    [8] Neural Computation, 15 (2003), 253-276.
    [9] Adv. Appl. Prob., 33 (2001), 453-482.
    [10] The Journal of Neuroscience, 24 (2004), 2989-3001.
    [11] Math. Bios. Eng., 11 (2014), 285-302.
    [12] Math. Bios. Eng., 11 (2014), 49-62.
    [13] Biol. Cybern., 99 (2008), 253-262.
    [14] Physical Review E, 55 (1997), 2040-2043.
    [15] Physical Review E, 69 (2004), 022901-1-022901-4.
    [16] Biological Cybernetics, 35 (1979), 1-9.
    [17] Mathematica Japonica, 50 (1999), 247-322.
    [18] Journal of Computational Neuroscience, 39 (2015), 29-51.
    [19] Academic Press, Boston (USA), 1994.
    [20] Neural Computation, 11 (1997), 935-951.
    [21] PNAS, 110 (2013), E1438-E1443.
    [22] Neural Computation, 26 (2014), 819-859.
    [23] J. Stat. Phys., 140 (2010), 1130-1156.
    [24] J. Appl. Probab., 48 (2011), 420-434.
    [25] PLoS Comput. Biol., 8 (2012), e1002615, 1-19.
    [26] SIAM, 1989.
    [27] J. Stat. Phys., 140 (2010), 1130-1156.

  • This article has been cited by:

    1. H. T. Banks, J. E. Banks, S. L. Joyner, Estimation in time-delay modeling of insecticide-induced mortality, 2009, 17, 0928-0219, 10.1515/JIIP.2009.012
    2. H. T. Banks, Jimena L. Davis, Shuhua Hu, 2010, Chapter 2, 978-3-642-11277-5, 19, 10.1007/978-3-642-11278-2_2
    3. H T Banks, Jimena L Davis, Stacey L Ernstberger, Shuhua Hu, Elena Artimovich, Arun K Dhar, Experimental design and estimation of growth rate distributions in size-structured shrimp populations, 2009, 25, 0266-5611, 095003, 10.1088/0266-5611/25/9/095003
    4. H. T. Banks, John E. Banks, Natalie G. Cody, Mark S. Hoddle, Annabel E. Meade, Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period, 2019, 13, 1751-3758, 422, 10.1080/17513758.2019.1616839
    5. Nonlinear stochastic Markov processes and modeling uncertainty in populations, 2012, 9, 1551-0018, 1, 10.3934/mbe.2012.9.1
    6. 2012, 978-1-4398-8083-8, 241, 10.1201/b12209-19
    7. E. M. Rutter, H. T. Banks, K. B. Flores, Estimating intratumoral heterogeneity from spatiotemporal data, 2018, 77, 0303-6812, 1999, 10.1007/s00285-018-1238-6
    8. K. Wendelsdorf, G. Dean, Shuhua Hu, S. Nordone, H.T. Banks, Host immune responses that promote initial HIV spread, 2011, 289, 00225193, 17, 10.1016/j.jtbi.2011.08.012
  • Reader Comments
  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(3052) PDF downloads(549) Cited by(18)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog