Abstract. The transition between Sinoatrial cells and Atrial cells in the Heart is not fully understood. Here we focus in cell-to-cell mathematical models involving typical Sinoatrial cells and Atrial cells connected with experimentally observed conductance values exclusively. We are interested mainly in the geometry of the microstructure of the conduction paths in the Sinoatrial Node. We show with some models that appropriate source-sink relationships between Atrial and Sinoatrial cells may occur according to certain geometric arrangements. Inter-phase between Atrial and Sinoatrial cellsIt has been observed in different species that going from the center of the sinoatrial node (SAN) in the heart toward the atrium, there is a transitional zone of cells having morphological and electrophysiological properties in-between to that of typical sinoatrial (SA) and atrial (A) cells [16]. The transitional cells have an aspect intermediate between that of typical nodal cells and that of the common atrial cells. Typical nodal cells have poor development of the contractile system and is assumed in general that they do not contract, moreover the existence of connexin43 is undetectable in the SA node center (see [3] and references therein), but posses automaticity in firing its action potential. On the contrary, atrial cells do contract themselves, but they require of an stimulus in order to contract, and they contain mainly connexin-43. This characteristics are included in the cells models used in this paper. A whole range of intermediate cells have been reported, but more important to the models in this paper, cells with one end connected to SA cells and the other end with A cells have been found [16]. The basic structure conforming the cytoarchitecture of this groups of cells consists of interdigitations of nodal and atrial bundles forming histological connections between nodal and atrial myocytes at regular distances [18].In [29] the authors, introduce a model of strands of atrial cells penetrating the SA node observed in the Pig. The model was constructed with 101 × 101 atrial and SA cells modeled with Oxsoft HEART V4.5. The lattice so constructed has a center of SA cells forming a circle of 30 cells of radius with twelve atrial interdigitations positioned at 30 deg intervals, where interdigitations are defined as sets of atrial cells at least ten cells distant from the node centre, and which are subtended by an angle of 15 deg. In that paper SA to SA conductance is g SA = 10 nS and the A to A conductance g A , varies from 10 nS to 250 nS.

With the aim to model the propagation of sound pressure emitted by a source, based on the postulates of Far from equilibrium thermodynamics theory, a wave equation was constructed. The equation obtained is a classic generalized wave equation adding dissipative behavior as a function of the media in which wave propagates. The new equation is of Maxwell-Cattaneo-Vernotte type. Also, an experimental activity was realized and the results were in accordance with theoretical solution of the new differential equation.

Abstract. In [24] we studied the transitional zone between Sinoatrial cells and Atrial cells in the Heart. The present paper study the mechanisms underlying the dynamics of the modeled nets in that paper.