The\
\ aim of this tutorial is to study the effect of changes in fiber orientation on\
\ the electrical behavior of cardiac tissue. Generally, electrical properties of\
\ the myocardial tissue can be described by the bidomain model accounting for the\
\ intracellular and extracellular domain. The domains are of anisotropic nature,\
\ the intracellular domain even more so than the extracellular domain resulting\
\ in ''unequal anisotropy ratios'' affecting the heart's electrical behavior causing\
\ two effects ''rotation'' and ''distribution''. This tutorial focuses on the ''distribution''\
\ effect, which refers to the relative conductivity of the intracellular and extracellular\
\ domains. As current takes the path of least resistance more current will flow\
\ in the domain where conductivity is the highest. The relative amount of current\
\ in the two spaces is defined by their respective anisotropy ratios.<a href=\"\
The setup is identical\
\ to the setup in the ''Fiber Angle Stimulation I - rotation'' tutorial, except\
\ a gradual change in fiber orientation along x is implemented.
\n
A 2D strip\
\ of infinite length of width <span class=\"math inline\">\(W=10\) mm is\
\ given. The fiber angle varies from <span class=\"math inline\">\(\alpha = 90^{\\
circ}\) to <span class=\"math inline\">\(\alpha = 0^{\circ}\)\
\ over the length of the strip. (marked as dotted gray lines in Fig. below). Conductivities\
\ are given as <span class=\"math inline\">\(g{iL} = 0.2\) S/m, <span\
\ class=\"math inline\">\(g{iT} = 0.02\) S/m, <span class=\"math inline\"\
\(g{eL} = 0.2\) S/m and <span class=\"math inline\">\(g{eT} = 0.08\\
) S/m where L and T indicate directions along and transverse to the fiber\
\ orientation, respectively (Anisotropy ratios are unequal!). The tissues membrane\
\ surface-to-volume ratio and the resistance are given as <span class=\"math inline\"\
\(\beta = 0.14\mu m^{-1}\) and <span class=\"math inline\">\(R_{m}\
\ = 0.91 \Omega m^{2}\).
For numerical analysis we assume that the length L\
\ of the strip is not infinite, but <span class=\"math inline\">\(L\gg\lambda\\
). For the data given choosing L=60mm should suffice. The spatial resolution\
\ should be used as height of the strip (only one layer of 3D elements). Thus, a\
\ hexahedral FE model with dimensions of 60mm x 10mm x 1mm is generated functioning\
\ as cardiac tissue strip. An orthotropic fiber setup may be used if the sheet angle\
\ differs from <span class=\"math inline\">\(0^\circ\). As passive ionic\
\ model the modified Beeler-Router Druhard-Roberge model as implemented in LIMPET\
\ is used with <span class=\"math inline\">\(R{m}\) set to <span class=\"\
math inline\">\(0.91 \Omega m^{2}\) and <span class=\"math inline\">\\
(\beta = 0.14\mu m^{-1}\). Current <span class=\"math inline\">\(\mathbf{J}\\
) is injected by Electrode A at x=-L/2 in x-direction and withdrawn by electrode\
\ B at x=+L/2. Electrode C is located at x=0 and can be gounded or not.
\n
Unequal\
\ anisotropy is assigned using the following values: