We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation.

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Measuring neuronal cell activity using microelectrode arrays reveals a great variety of derived signal shapes within extracellular recordings. However, possible mechanisms responsible for this variety have not yet been entirely determined, which might hamper any subsequent analysis of the recorded neuronal data. Methods: To investigate this issue, we propose a computational model based on the finite element method describing the electrical coupling between an electrically active neuron and an extracellular recording electrode in detail. This allows for a systematic study of possible parameters that may play an essential role in defining or altering the shape of the measured electrode potential. Results: Our results indicate that neuronal geometry, neurite structure, as well as the actual pathways of input potentials that evoke action potential generation, have a significant impact on the shape of the resulting extracellular electrode recording and explain most of the known variations of signal shapes. Conclusion: The presented models offer a comprehensive insight into the effect of geometrical and morphological factors on the resulting electrode signal. Significance: Computational modeling complemented with experimental measurements shows much promise to yield meaningful insights into the electrical activity of a neuronal network.