# Mathematics of Nerve Signals

@article{Engelbrecht2019MathematicsON, title={Mathematics of Nerve Signals}, author={J. Engelbrecht and Kert Tamm and Tanel Peets}, journal={Applied Wave Mathematics II}, year={2019} }

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…

## 5 Citations

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

- BiologyBioelectricity
- 2021

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.

- BiologyBiomechanics and modeling in mechanobiology
- 2022

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

- Philosophy
- 2020

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

- MathematicsMathematics
- 2021

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…

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