The role of the dendritic tree and the way it functions within a neuron has been of interest to neurologists for over a century. As investigative techniques have become more sophisticated and thus revealing, our perception of the dendrites as being purely an information gathering component has changed to one where the dendritic tree may be viewed as a highly complex, nonlinear information processor. In spite of this most mathematical studies of the dynamical behaviour of neural populations have neglected the influence of the dendritic tree. The aim of this thesis is to address this imbalance.

In this thesis we developed the Green's Function for a tapered equivalent cylinder model of dendritic electrical propagation. We then use the Green's Function to develop a Carleman linear embedding scheme which is used to estimate the effects of a nonlinear ion channel hot-spot on the tapered cylinder solution. Mathematica© was used to implement the Carleman embedding scheme.

The work deals with the foundations of bioelectric phenomena cardiomyocyte, then it is also part of this description of the heart conduction system and method of distribution in this system The next section is a description of the spread in the system, the very essence of the spread. In the last chapter analyzes the theory for the creation of computational models, which extend in one dimension or two dimensions

Coordinated electrical activation of the heart is essential for the maintenance of a regular cardiac rhythm and effective contractions. Action potentials spread from one cell to the next via gap junction channels. Because of the elongated shape of cardiomyocytes, longitudinal resistivity is lower than transverse resistivity causing electrical anisotropy. Moreover, non-uniformity is created by clustering of gap junction channels at cell poles and by non-excitable structures such as collagenous strands, vessels or fibroblasts. Structural changes in cardiac disease often affect passive electrical properties by increasing non-uniformity and altering anisotropy. This disturbs normal electrical impulse propagation and is, consequently, a substrate for arrhythmia. However, to investigate how these structural changes lead to arrhythmias remains a challenge. One important mechanism, which may both cause and prevent arrhythmia, is the mismatch between current sources and sinks. Propagation of the electrical impulse requires a sufficient source of depolarizing current. In the case of a mismatch, the activated tissue (source) is not able to deliver enough depolarizing current to trigger an action potential in the non-activated tissue (sink). This eventually leads to conduction block. It has been suggested that in this situation a balanced geometrical distribution of gap junctions and reduced gap junction conductance may allow successful propagation. In contrast, source-sink mismatch can prevent spontaneous arrhythmogenic activity in a small number of cells from spreading over the ventricle, especially if gap junction conductance is enhanced. Beside gap junctions, cell geometry and non-cellular structures strongly modulate arrhythmogenic mechanisms. The present review elucidates these and other implications of passive electrical properties for cardiac rhythm and arrhythmogenesis.

Rapporten behandlar simuleringar, beräkningar och mätningar av HVAC-kablar. En genomgång presenteras av kabelteori samt de olika magnetiska och elektriska effekterna som påverkar skärmströmmarnas storlek. / This report comprises simulations, calculations and measurements of HVAC cables. An introduction to cable theory and a review of the different magnetic and electric effects that has an impact on the amplitude of the screen currents in these cables.