Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology.

A proposed model consisting of two coupled models (Hodgkin-Huxley and Yanagihara-Noma-Irisawa model) is considered as a description of the heart's action potential. System of ordinary differential equations is used to recreate pathological behaviour in the conducting heart's system such as double fire and the most common tachycardia: atrioventricular nodal reentrant tachycardia (AVNRT). Part of the population has an abnormal accessory pathways: fast and slow (Fujiki, 2008). These pathways in the atrioventricular node (AV node) are anatomical and functional contributions of supraventricular tachycardia. However, the appearance of two pathways in the AV node may be a contribution of arrhythmia, which is caused by coexistent conduction by two pathways (called double fire). The difference in the conduction time between these pathways is the most important factor. This is the reason to introduce three types of couplings and delay to our system in order to reproduce various types of the AVNRT. In our research, introducing the feedback loops and couplings entails the creation of waves which can correspond to the re-entry waves occurring in the AVNRT. Our main aim is to study solutions of the given equations and take into consideration the influence of feedback and delays which occur in these pathological modes. We also present stability analysis for both components, that is Hodgkin-Huxley and Yanagihara-Noma-Irisawa models, as well as for the final double-fire model.

Shapes of leaves with parallel venation. Modelling of the Epipactis sp. (Orchidaceae) leaves with the help of a system of coupled elastic beams.

Static properties of leaves with parallel venation, with particular emphasis on the genus EpipactisZinn, 1757 (Orchidaceae, Neottieae) have been modelled with coupled quasi-parallel elastic "beams." The non-linear theory of strongly bended beams have been employed. The resulting boundary-value problem has been solved numerically with the help of the finite-difference method. Possible dislocations resulting in additional Dirac-delta like forces have been take into account. Morphological similarity of the model and real leaves has been obtained. In particular, the concentrated forces have been shown to cause undulation in the leaves.