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The in silico simulations are widely used in contemporary systems biologyincluding the analysis of nerve pulse propagation. As known from numerousexperiments, the propagation of an action potential is accompanied bymechanical and thermal effects. This calls for an analysis at the interface ofphysics, physiology and mathematics. In this paper, the background of the modelequations governing the effects in nerve fibres is analysed from a physicalviewpoint and then discussed how to unite them into a system by using thecoupling forces. The leading hypothesis associates the coupling to the changesof variables, not to their values or amplitudes. This hypothesis modelsactually the physiological mechanisms of energy transductions in a fibre. Thegeneral assumptions in modelling the processes and the properties of thecoupled system of equations are described. The dimensionless mathematical modelwhich couples the action potential with mechanical waves together withtemperature effects is presented in the Appendix. This model generates anensemble of waves including the electrical signal and mechanical and thermaleffects.

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