Mathematics of Nerve Signals

  title={Mathematics of Nerve Signals},
  author={J. Engelbrecht and Kert Tamm and Tanel Peets},
  journal={Applied Wave Mathematics II},
Since the classical works of Hodgkin and Huxley (J. Physiol. 117(4), 500–544 (1952)), it has become evident that the nerve function is a richer phenomenon than a set of electrical action potentials (AP ) alone. The propagation of an AP is accompanied by mechanical and thermal effects. These include the pressure wave (PW) in axoplasm , the longitudinal wave (LW) in a biomembrane , the transverse displacement (TW) of a biomembrane and temperature changes (Θ). The whole nerve signal is, therefore… 

Nerve Impulses Have Three Interdependent Functions: Communication, Modulation, and Computation

Nerve impulses appear to be an ensemble of three inseparable, interdependent, concurrent states: the physiological action potential, the APPulse and the computational action potential (CAP), whose temporal fixed point is threshold, rather than the rather plastic action potential peak used in other models.

Mechanical waves in myelinated axons.

The deformation of the myelinated axon wall is studied using a mathematical model inspired by the mechanics of microstructured materials with multiple scales that describes the process in the myelin sheath.

Signals in nerves from the philosophical viewpoint

The signals in nerve include electrical, mechanical and thermal components and are characterized by the complexity of processes. The modelling of these signals is analyzed from the viewpoint of

Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity



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.

Axonal excitability revisited.

  • J. Clay
  • Biology
    Progress in biophysics and molecular biology
  • 2005

Modeling of complex signals in nerve fibers.

On the complexity of signal propagation in nerve fibres

It is proposed that three processes – the propagation of an action potential and mechanical waves in the biomembrane and in the axoplasmatic fluid – be united into a general model with additional interaction forces for reflecting coupling, which results in the emerging of a mutually interacting ensemble of waves.

Primary and secondary components of nerve signals

The action potential propagating in a nerve fibre generates accompanying mechanical and thermal effects. The whole signal is therefore an ensemble which includes primary and secondary components. The

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.

Impulses and Physiological States in Theoretical Models of Nerve Membrane.

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.

Towards a thermodynamic theory of nerve pulse propagation