Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2020 Dec;19(6):2491-2498.
doi: 10.1007/s10237-020-01350-3. Epub 2020 Jun 4.

Modelling of processes in nerve fibres at the interface of physiology and mathematics

Jüri Engelbrecht  1 , Kert Tamm  2 , Tanel Peets  2
Affiliations

Modelling of processes in nerve fibres at the interface of physiology and mathematics

Jüri Engelbrecht et al. Biomech Model Mechanobiol. 2020 Dec.

Abstract

The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal effects. This calls for an analysis at the interface of physics, physiology and mathematics. In this paper, the background of the model equations governing the effects in nerve fibres is analysed from a physical viewpoint and then discussed how to unite them into a system by using the coupling forces. The leading hypothesis associates the coupling to the changes of variables, not to their values or amplitudes. This hypothesis models actually the physiological mechanisms of energy transductions in a fibre. The general assumptions in modelling the processes and the properties of the coupled system of equations are described. The dimensionless mathematical model which couples the action potential with mechanical waves together with temperature effects is presented in "Appendix". This model generates an ensemble of waves including the electrical signal and mechanical and thermal effects.

Keywords: Action potential; Interdisciplinarity; Mathematical modelling.

PubMed Disclaimer

References

    1. Abbott BC, Hill AV, Howarth JV (1958) The positive and negative heat production associated with a nerve impulse. Proc R Soc B Biol Sci 148(931):149–187. https://doi.org/10.1098/rspb.1958.0012 - DOI
    1. Andersen SS, Jackson AD, Heimburg T (2009) Towards a thermodynamic theory of nerve pulse propagation. Prog Neurobiol. https://doi.org/10.1016/j.pneurobio.2009.03.002 - DOI
    1. Barz H, Barz U (2014) Pressure waves in neurons and their relationship to tangled neurons and plaques. Med Hypotheses 82(5):563–566. https://doi.org/10.1016/j.mehy.2014.02.012 - DOI
    1. Barz H, Schreiber A, Barz U (2013) Impulses and pressure waves cause excitement and conduction in the nervous system. Med Hypotheses 81(5):768–772. https://doi.org/10.1016/j.mehy.2013.07.049 - DOI
    1. Bennett MV (2000) Electrical synapses, a personal perspective (or history). Brain Res Rev 32(1):16–28. https://doi.org/10.1016/S0165-0173(99)00065-X - DOI

LinkOut - more resources