Viscoelastic FitzHugh-Nagumo models

An extended Fitzhugh-Nagumo model including linear viscoelasticity is derived in general and studied indetail in the one-dimensional case. The equations of the theory are numerically integrated in two situations: ia free insulated fiber activated by an initial Gaussian distribution of action potential, and ii a clamped fiberstimulated by two counter phased currents, located at both ends of the space domain. The former case accountsfor a description of the physiological experiments on biological samples in which a fiber contracts because ofthe spread of action potential, and then relaxes. The latter case, instead, is introduced to extend recent modelsdiscussing a strongly electrically stimulated fiber so that nodal structures associated on quasistanding waves areproduced. Results are qualitatively in agreement with physiological behavior of cardiac fibers. Modificationsinduced on the action potential of a standard Fitzhugh-Nagumo model appear to be very small even whenstrong external electric stimulations are activated. On the other hand, elastic backreaction is evident in themodel.