• Corpus ID: 100813425

On modelling of physical effects accompanying the propagation of action potentials in nerve fibres

  title={On modelling of physical effects accompanying the propagation of action potentials in nerve fibres},
  author={J. Engelbrecht and Tanel Peets and Kert Tamm and Martin Laasmaa and Marko Vendelin},
  journal={arXiv: Biological Physics},
The recent theoretical and experimental studies have revealed many details of signal propagation in nervous systems. In this paper an attempt is made to unify various mathematical models which describe the signal propagation in nerve fibres. The analysis of existing single models permits to select the leading physiological effects. As a result, a more general mathematical model is described based on the coupling of action potentials with mechanical waves in a nerve fibre. The crucial issue is… 

Figures from this paper

Electromechanical coupling of waves in nerve fibres

An attempt is made to build up a mathematical model which couples the AP with a possible pressure wave in the axoplasm and waves in the nerve fibre wall made of a lipid bilayer (biomembrane) to determine the influence of possible coupling forces on the emergence of mechanical waves from the AP.

Action Potential: A Vortex Phenomena; Driving Membrane Oscillations

A novel theory is proposed here which, unravels vortex ring formation due to ion currents in the intracellular and extracellular region leading to variation of pressure causing the increment/decrement in axon diameter.

Thinking About the Nerve Impulse: The Prospects for the Development of a Comprehensive Account of Nerve Impulse Propagation

The Engelbrecht model is conceptually analyzed, finding that attempts to develop models that represent the nerve impulse accurately and completely appear unfeasible and that integrating distinct models into a general unifying model that provides a consistent picture of nerve impulse propagation is impossible.

Incorporating inductances in tissue-scale models of cardiac electrophysiology.

A hyperbolic bidomain model is developed that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes and it is shown that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic andhyperbolic models when using relatively coarse spatial discretizations.

Challenges in modeling nerve-electrode interactions of neuronal implants

This paper accompanies a tutorial on challenges in modeling of nerve-electrode interactions in the context of neurochips and cochlear implants on the importance of mathematical models in abstracting the biological phenomena of nerves.

On Nonlinear Waves in Media with Complex Properties

In nonlinear theories the axiom of equipresence requires all the effects of the same order to be taken account. In this paper the mathematical modelling of deformation waves in media is analysed



On mathematical modelling of solitary pulses in cylindrical biomembranes

The possible dispersive effects in such microstructured cylinders are analysed from the viewpoint of solid mechanics, particularly using the information from the analysis of the well-known rod models to propose a more general governing equation.

Towards a thermodynamic theory of nerve pulse propagation

A quantitative description of membrane current and its application to conduction and excitation in nerve

This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre by putting them into mathematical form and showing that they will account for conduction and excitation in quantitative terms.


It is suggested that the propagation of the action potential is accompanied by anAxoplasmic pressure pulse propagating in the axoplasm along the axon length, causing their accelerated activation and inactivation and increasing peak channel conductance.

Mechanical surface waves accompany action potential propagation.

A model for mechanical displacements as arising from the driving of surface wave modes in which potential energy is stored in elastic properties of the neuronal membrane and cytoskeleton while kinetic energy is carried by the axoplasmic fluid is presented.

On theory of pulse transmission in a nerve fibre

  • J. Engelbrecht
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1981
The ray method is used to analyse pulse propagation in a nerve fibre. The initial equations are considered to be hyperbolic, i. e. with a finite velocity of propagation, and the corresponding

Impulses and pressure waves cause excitement and conduction in the nervous system.

A macromolecular approach to excitation phenomena: mechanical and thermal changes in nerve during excitation.

  • I. Tasaki
  • Biology, Chemistry
    Physiological chemistry and physics and medical NMR
  • 1988
A physicochemical theory is described that explains macromolecular transitions between two stable states of the nerve membrane and the mechanism of nerve excitation is explained on a physicochemical basis.

A quantitative overview of biophysical forces impinging on neural function

By considering the collective actions of biophysical forces influencing neuronal activity, working models can be expanded and new paradigms can be applied to the investigation and characterization of brain function and dysfunction.

Impulses and Physiological States in Theoretical Models of Nerve Membrane.