On the complexity of signal propagation in nerve fibres

Engelbrecht, Jüri; Peets, Tanel; Tamm, Kert; Laasmaa, Martin; Vendelin, Marko

doi:10.3176/proc.2017.4.28

Cited by 43 publications

(47 citation statements)

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“…Note that heat energy is proportional to the negative temperature gradient. Combining (5) and (6), we obtain…”

Section: Model Equationsmentioning

confidence: 99%

“…The coupled system of model equations has been previously proposed by the authors for describing the nerve pulse (action potential (AP)) propagation including the accompanying mechanical effects (pressure wave (PW) and longitudinal density change in the lipide bi-layer (LW)) [4][5][6][7]14]. In this paper, the temperature effects which accompany the propagation of an AP in the axoplasm, are also described.…”

Section: Model Equationsmentioning

confidence: 99%

“…In this paper, the temperature effects which accompany the propagation of an AP in the axoplasm, are also described. The dimensionless 1D model used so far [4][5][6][7]14] is the following:…”

Section: Model Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Temperature changes accompanying signal propagation in axons

Tamm

Engelbrecht

Peets

2019

Journal of Non-Equilibrium Thermodynamics

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In this paper mathematical models are formulated in order to simulate heat production and corresponding temperature changes which accompany the propagation of an axon potential. Based on earlier experimental results, several models are proposed. Together with the earlier system of coupled differential equations derived by the authors for describing the electrical and mechanical components of signalling in nerve fibres, the novel results permit to cast the whole process of signalling into one system. The emphasis is on the mathematical description of coupling forces. The numerical results are qualitatively similar to experiments.

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“…Note that heat energy is proportional to the negative temperature gradient. Combining (5) and (6), we obtain…”

Section: Model Equationsmentioning

confidence: 99%

Section: Model Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Temperature changes accompanying signal propagation in axons

Tamm

Engelbrecht

Peets

2019

Journal of Non-Equilibrium Thermodynamics

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“…Although the various mechanisms of transduction between fields are analyzed (Gross et al, 1983;Gonzalez-Perez et al, 2016), there is still no widely accepted understanding about the character of this process. Here we follow an assumption that the mechanical waves are generated by two changes in electrical pulses: either in the AP or in the ion current (Engelbrecht et al, 2018) and by the changes in pressure in the axoplasm. In more general terms this means that the dynamical processes are not generated by values of the fields but by changes in the field.…”

Section: A Model Involving An Ensemble Of Wavesmentioning

confidence: 99%

Electromechanical coupling of waves in nerve fibres

Engelbrecht

Peets

Tamm

2018

Biomech Model Mechanobiol

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The propagation of an action potential (AP) in a nerve fibre is accompanied by mechanical and thermal effects. In this paper, an attempt is made to build up a mathematical model which couples the AP with a possible pressure wave (PW) in the axoplasm and waves in the nerve fibre wall (longitudinal-LW and transverse-TW) made of a lipid bilayer (biomembrane). A system of differential equations includes the governing equations of single waves with coupling forces between them. The single equations are kept as simple as possible in order to carry out the proof of concept. An assumption based on earlier studies is made that the coupling forces depend on changes (the gradient, time derivative) of the voltage. In addition, it is assumed that the transverse displacement of the biomembrane can be calculated from the gradient of the LW in the biomembrane. The computational simulation is focused to determining the influence of possible coupling forces on the emergence of mechanical waves from the AP. As a result, an ensemble of waves (AP, PW, LW, TW) emerges. The further experiments should verify assumptions about coupling forces.

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“…Most prominent nonelectrical effects are a mechanical wave (swelling) [16][17][18][19] and a pressure wave [20] that propagate along the nerve fibre together with the action potential. It is clear that for a complete understanding of nerve function, a model describing all processes in a joint framework is needed [21,22]. However, the models describing single waves should be well understood.…”

Section: Mathematical Modelmentioning

confidence: 99%

On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: A soliton doublet

et al. 2019

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In this paper the permanent profile waves governed by a Boussinesq-type wave equation are analysed. The model involves displacement-type nonlinearities and dispersion terms. Physically such a model equation describes longitudinal waves (density change) in biomembranes which have an internal structure composed by lipid molecules. The possible solutions are constructed and analysed. The phase plane analysis and numerical simulation reveal a novel phenomenon: the possible existence of a soliton doublet.

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On the complexity of signal propagation in nerve fibres

Cited by 43 publications

References 0 publications

Temperature changes accompanying signal propagation in axons

Temperature changes accompanying signal propagation in axons

Electromechanical coupling of waves in nerve fibres

On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: A soliton doublet

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