Informatica

In this work the analytical expressions of half-time T1/2 and its derivatives in respect to distance ∂T1/2/∂ R in a one-dimensional RC medium (a current electrode has a shape of the segment) and in a two-dimensional RC medium (a current electrode has a shape of the circle) were received. First, by using a well-known in electrostatics a superposition principle, the current's electrodes were divided into elementary point sources by positioning them on the perimeter or the surface of the electrode. Second, with the help of the computer-simulation, the dependencies of T1/2 and ∂T1/2/∂ R on the current electrode dimensions, the degree of electrotonic anisotropy, and the distance between the current electrode and the potential measurement place were calculated. Our calculations demonstrate that the slope of the function T1/2=f(R) depends both on the distance between the potential measurement place and the current electrode, as well as the measurement direction in respect to the fibers' direction. Furthermore, the slope value can be less or greater to 0.5.

Laplace equations were used for modeling of electrotonic potential in three-dimensional isotropic double-space RC medium. Solutions of Laplace equations for the case of rectangular current pulse stimulation using spherical electrode we obtain using Laplace transforms in imaginary space. Solutions in original space we got using numerical invert Laplace transform. It showed that the rising front of the transmembrane potential becomes less steep in regard to rising radius of the stimulating electrode and asymptotically reaches single-dimensional cable case (evenly distributed RC-circuit). The steady state value of transmembrane potential decreases with the increasing distance from stimulating electrode. It remains always positive when stimulus current is negative.