Skip to main content
SpringerLink
Log in

Modeling electromagnetic fields detectability in a HH-like neuronal system: stochastic resonance and window behavior

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

Noise has already been shown to play a constructive role in neuronal processing and reliability, according to stochastic resonance (SR). Here another issue is addressed, concerning noise role in the detectability of an exogenous signal, here representing an electromagnetic (EM) field. A Hodgkin–Huxley like neuronal model describing a myelinated nerve fiber is proposed and validated, excited with a suprathreshold stimulation. EM field is introduced as an additive voltage input and its detectability in neuronal response is evaluated in terms of the output signal-to-noise ratio. Noise intensities maximizing spiking activity coherence with the exogenous EM signal are clearly shown, indicating a stochastic resonant behavior, strictly connected to the model frequency sensitivity. In this study SR exhibits a window of occurrence in the values of field frequency and intensity, which is a kind of effect long reported in bioelectromagnetic experimental studies. The spatial distribution of the modeled structure also allows to investigate possible effects on action potentials saltatory propagation, which results to be reliable and robust over the presence of an exogenous EM field and biological noise. The proposed approach can be seen as assessing biophysical bases of medical applications funded on electric and magnetic stimulation where the role of noise as a cooperative factor has recently gained growing attention.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adair RK (2001) Simple neural networks for the amplification and utilization of small changes in neuron firing rates. Proc Natl Acad Sci USA 98:7253–7258

    Article  PubMed  CAS  Google Scholar 

  • Apollonio F, Liberti M, D’Inzeo G, Tarricone L (2000) Integrated models for the analysis of biological effects of EM fields used for mobile communications. IEEE Trans Microw Theory Tech 48:2082–2093

    Article  Google Scholar 

  • Astumian RD, Adair RK, Weaver JC (1997) Stochastic resonance at the single-cell level. Nature 388:632–633

    Article  PubMed  CAS  Google Scholar 

  • Astumian RD, Weaver JC, Adair RK (1995) Rectification and signal averaging of weak electric fields by biological cells. Proc Natl Acad Sci USA 92:3740–3743

    Article  PubMed  CAS  Google Scholar 

  • Baker M, Bostock H, Grafe P, Martius P (1987) Function and distribution of three types of rectifying channel in rat spinal root myelinated axons. J Physiol 383:45–67

    PubMed  CAS  Google Scholar 

  • BeMent SL, Ranck JB Jr (1969) A quantitative study of electrical stimulation of central myelinated fibers. Exp Neurol 24:147–170

    Article  PubMed  CAS  Google Scholar 

  • Benzi R, Sutera A, Vulpiani A (1981) The mechanism of stochastic resonance. J Phys A 14L:453

    Article  Google Scholar 

  • Bernardi P, D’Inzeo G, Pisa S (1994) A generalized ionic model of the neuronal membrane electrical activity. IEEE Trans Biomed Eng 41:125–133

    Article  PubMed  CAS  Google Scholar 

  • Bezrukov SM, Vodyanoy I (1997) Stochastic resonance in non-dynamical systems without response thresholds. Nature 385:319–321

    Article  PubMed  CAS  Google Scholar 

  • Bryant P, Wiesenfeld K, McNamara B (1987) Noise rise in parametric amplifiers. Phys Rev B 36:752–755

    Article  Google Scholar 

  • Fauve S, Heslot H (1983) stochastic resonance in a bistable system. Phys Lett A 97:5–7

    Article  Google Scholar 

  • Foster KR, Schwan HP (1986) CRC Handbook of biological effects of electromagnetic fields. CRC, Boca Raton

    Google Scholar 

  • Gluckman BJ, Netoff TI, Neel EJ, Ditto WL, Spano ML, Schiff SJ (1996) Stochastic resonance in a neuronal network from mammalian brain. Phys Rev Lett 77:4098–4101

    Article  PubMed  CAS  Google Scholar 

  • Hibbs A, Jacobs E, Beckedahl J, Bulsara A, Moss F (1995) Signal enhancement in a rf SQUID using stochastic resonance. Il Nuovo Cimento 17D:811–817

    Article  CAS  Google Scholar 

  • Holden AV (1976) Lecture notes in biomathematics 12. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Jia Y, Yu S, Li J Jr (2000) Stochastic resonance in a bistable system subject to multiplicative and additive noise. Phys Rev E 62:1869–1878

    Article  CAS  Google Scholar 

  • Levin JE, Miller JP (1996) Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance. Nature 380:165–168

    Article  PubMed  CAS  Google Scholar 

  • Lin VW, Hsiao IN, Dhaka V (2000) Magnetic coil design considerations for functional magnetic stimulation. IEEE Trans Biomed Eng 47:600–610

    Article  PubMed  CAS  Google Scholar 

  • Lindner B, Schimansky-Geier L, Longtin A (2002) Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. Phys Rev E 66:031916

    Article  CAS  Google Scholar 

  • Liu F, Hu B, Wang W (2001a) Effects of correlated and independent noise on signal processing in neuronal systems. Phys Rev E 63:031907

    Article  CAS  Google Scholar 

  • Liu F, Yu Y, Wang W (2001b) Signal-to-noise ratio gain in neuronal systems. Phys Rev E 63:051912

    Article  CAS  Google Scholar 

  • Liu F, Wang J, Wang W (1999) Frequency sensitivity in weak signal detection. Phys Rev E 59:3453–3460

    Article  CAS  Google Scholar 

  • Markin VS, Liu D, Gimsa J, Strobel R, Rosenberg MD, Tsong TY (1992) Ion channel enzyme in an oscillating electric field. J Membr Biol 126:137–145

    PubMed  CAS  Google Scholar 

  • Masuda N, Aihara K (2002) Bridging rate coding and temporal spike coding by effect of noise. Phys Rev Lett 88:248101

    Article  PubMed  CAS  Google Scholar 

  • McIntyre CC, Richardson AG, Grill WM (2002) Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle. J Neurophysiol 87:995–1006

    PubMed  Google Scholar 

  • McNamara B, Wiesenfeld K, Roy R (1988) Observation of stochastic resonance in a ring laser. Phys Rev Lett 60:2626–2629

    Article  PubMed  Google Scholar 

  • McNeal DR (1976) Analysis of a model for excitation of myelinated nerve. IEEE Trans Biomed Eng 23:329–337

    Article  PubMed  CAS  Google Scholar 

  • Mino H, Grill WM Jr (2002) Effects of stochastic sodium channels on extracellular excitation of myelinated nerve fibers. IEEE Trans Biomed Eng 49:527–532

    Article  PubMed  Google Scholar 

  • Mino H, Rubinstein JT, Miller CA, Abbas PJ (2004) Effects of electrode-to-fiber distance on temporal neural response with electrical stimulation. IEEE Trans Biomed Eng 51:13–20

    Article  PubMed  Google Scholar 

  • Morse RP, Roper P (2000) Enhanced coding in a cochlear-implant model using additive noise: aperiodic stochastic resonance with tuning. Phys Rev E 61:5683–5692

    Article  CAS  Google Scholar 

  • Moss F, Ward LM, Sannita WG (2004) Stochastic resonance and sensory information processing: a tutorial and review of application. Clin Neurophysiol 115:267–281

    Article  PubMed  Google Scholar 

  • Panizza M, Nilsson J, Roth BJ, Grill SE, Demirci M, Hallett M (1998) Differences between the time constant of sensory and motor peripheral nerve fibers: further studies and considerations. Muscle Nerve 21:48–54

    Article  PubMed  CAS  Google Scholar 

  • Panizza M, Nilsson J, Roth BJ, Rothwell J, Hallett M (1994) The time constants of motor and sensory peripheral nerve fibers measured with the method of latent addition. Electroencephalogr Clin Neurophysiol 93:147–154

    Article  PubMed  CAS  Google Scholar 

  • Plesser HE, Geisel T (2001) Signal processing by means of noise. Neurocomputing 38–40:307–312

    Article  Google Scholar 

  • Postow E, Swicord ML (1996) CRC Handbook of biological effects of electromagnetic fields (II edition). CRC, Boca Raton

    Google Scholar 

  • Roberts WJ, Smith DO (1973) Analysis of threshold currents during microstimulation of fibres in the spinal cord. Acta Physiol Scand 89:384–394

    PubMed  CAS  Google Scholar 

  • Ross, SM (1988) A first course in probability. MacMillan, New York

    Google Scholar 

  • Ruohonen J, Ravazzani P, Grandori F, Ilmoniemi RJ (1999) Theory of multichannel magnetic stimulation: toward functional neuromuscular rehabilitation. IEEE Trans Biomed Eng 46:646–651

    Article  PubMed  CAS  Google Scholar 

  • Rushton DN (1997) Functional electrical stimulation. Physiol Meas 18:241–275

    Article  PubMed  CAS  Google Scholar 

  • Scherer SS (1999) Nodes, paranodes, and incisures: from form to function. Ann N Y Acad Sci 883:131–142

    Article  PubMed  CAS  Google Scholar 

  • Schneidman E, Freedman B, Segev I (1998) Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput 10:1679–1703

    Article  PubMed  CAS  Google Scholar 

  • Schwarz JR, Reid G, Bostock H (1995) Action potentials and membrane currents in the human node of Ranvier. Pflugers Arch 430:283–292

    Article  PubMed  CAS  Google Scholar 

  • Stephanova DI, Mileva K (2000) Different effects of blocked potassium channels on action potentials, accommodation, adaptation and anode break excitation in human motor and sensory myelinated nerve fibres: computer simulations. Biol Cybern 83:161–167

    Article  PubMed  CAS  Google Scholar 

  • Tanabe S, Pakdaman K (2001) Noise-enhanced neuronal reliability. Phys Rev E 64:041904

    Article  CAS  Google Scholar 

  • Tsong TY, Astumian RD (1987) Electroconformational coupling and membrane protein function. Prog Biophys Mol Biol 50:1–45

    Article  PubMed  CAS  Google Scholar 

  • Wang S, Liu F, Wang W, Yu Y (2004) Impact of spatially correlated noise on neuronal firing. Phys Rev E 69:011909

    Article  CAS  Google Scholar 

  • Weaver JC, Astumian RD (1992) Estimates for ELF effects: noise-based thresholds and the number of experimental conditions required for empirical searches. Bioelectromagnetics Suppl 1:119–138

    Article  Google Scholar 

  • Weaver JC, Vaughan TE, Adair RK, Astumian RD (1998) Theoretical limits on the threshold for the response of long cells to weak extremely low frequency electric fields due to ionic and molecular flux rectification. Biophys J 75:2251–2254

    Article  PubMed  CAS  Google Scholar 

  • Wenning G, Obermayer K (2002) Adjusting stochastic resonance in a leaky integrate and fire neuron to sub-threshold stimulus distributions. Neurocomputing 44–46:325–331

    Google Scholar 

  • Wenning G, Obermayer K (2003) Activity driven adaptive stochastic resonance. Phys Rev Lett 90:120602

    Article  PubMed  CAS  Google Scholar 

  • White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:131–137

    Article  PubMed  CAS  Google Scholar 

  • Wiesenfeld K, Jaramillo F (1998) Minireview of stochastic resonance. Chaos 8:539–548

    Article  PubMed  Google Scholar 

  • Yamada WM, Koch C, Adams PR (1998) Methods in neuronal modeling. MIT, London

    Google Scholar 

  • Yamanishi T, Sakakibara R, Uchiyama T, Suda S, Hattori T, Ito H, Yasuda K (2000) Comparative study of the effects of magnetic versus electrical stimulation on inhibition of detrusor overactivity. Urology 56:777–781

    Article  PubMed  CAS  Google Scholar 

  • Yu Y, Liu F, Wang W (2001a) Frequency sensitivity in Hodgkin-Huxley systems. Biol Cybern 84:227–235

    Article  CAS  Google Scholar 

  • Yu Y, Wang W, Wang J, Liu F (2001b) Resonance-enhanced signal detection and transduction in the Hodgkin-Huxley neuronal systems. Phys Rev E 63:021907

    Article  CAS  Google Scholar 

  • Zeng FG, Fu QJ, Morse R (2000) Human hearing enhanced by noise. Brain Res 869:251–255

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ICEmB at Department of Electronic Engineering, “La Sapienza” University of Rome, 00184, Rome, Italy

    Matteo Giannì, Micaela Liberti, Francesca Apollonio & Guglielmo D’Inzeo

Authors
  1. Matteo Giannì
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Micaela Liberti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francesca Apollonio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guglielmo D’Inzeo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matteo Giannì.

Additional information

This work investigates the role of noise as a cooperative factor for the detection of an exogenous electromagnetic field in a compartimental model of a myelinated nerve fiber. The occurrence of stochastic resonance is discussed in relation to neuronal frequency sensitivity.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Giannì, M., Liberti, M., Apollonio, F. et al. Modeling electromagnetic fields detectability in a HH-like neuronal system: stochastic resonance and window behavior. Biol Cybern 94, 118–127 (2006). https://doi.org/10.1007/s00422-005-0029-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-005-0029-5

Keywords

Search

Navigation