R. W. Joyner, F. Ramon, and J. W. Moore, "Simulation of action potential propagation in an inhomogeneous sheet of coupled excitable cells," Circulation Research, vol. 36, pp. 654--661, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....A to be symmetric and positive definite, as this narrows the choice of iterative solvers. Diagonalization of PC Q Gamma1 is only necessary if an explicit integration method is to be used. The semi implicit form of the Crank Nicolson method, which is widelyused for monodomain problems (e.g. [26, 27, 28]) does not have this limitation. It treats the linear diffusive part of the charge conservation equations implicitly and the nonlinear transmembrane part explicitly. This can be applied to equation (17) requiring solution of the linear system P 2 Deltat C G Q Gamma1 w k 1 = F ....

R. W. Joyner, F. Ramon, and J. W. Moore, "Simulation of action potential propagation in an inhomogeneous sheet of coupled excitable cells," Circulation Research, vol. 36, pp. 654--661, 1975.

....of the simulation parameters. Many models utilize membrane current models such as Beeler Reuter, Ebihara Johnson, or Luo Rudy to represent the cellular membrane dynamics. These models represent the cardiac muscle as individual cells coupled to each other by resistive connections between cells [4, 5, 6, 7, 8]. To capture the electrophysiological dynamics with sufficient spatial and temporal fidelity, cellular membrane models must use a finely resolved spatial grid, and simultaneously, need to take small temporal steps. Fine grid resolution means that a large number of elements are required to simulate ....

....per time step would be enormous. Hence it is obvious that the problem, as posed for a 1 mm cube, is large enough to overwhelm most desktop computers. As a result, models based on microscopic scale membrane kinetics have been limited to propagation in 2 D sheets or small 3 D blocks of tissue [4, 9, 8]. Bidomain models, represent heart tissue as two continuous, intertwined spaces, the extracellular and the intracellular, separated from each other all throughout by a thin membrane. The electrical properties of this membrane are modeled using the membrane models mentioned above. Due to the ....

R.W. Joyner, R. Ramon, and J.W. Moore. Simulation of action potential propagation in an inhomogenous sheet of coupled excitable cells. Circulation Research, 36:654--661, 1975.

....not be significant, but in two and three dimensional space a potentially greater loss occurs, as described below. The cable equation has been used extensively to analyze and describe the one dimensional behaviour of cardiac tissue[107, 116] It has also been extended to two and three dimensions[52, 58, 87, 91], usually with the assumption that interstitial resistance is negligible, as in equation (2.8) The resulting equation gives a monodomain description of electrical behaviour. For modelling situations where oe i and oe e are diagonal and the anisotropy ratios are equal, the bidomain model reduces ....

....2 : 2:26) 5 Where non uniform conductivity is used, the appropriate first order accurate variant of this is used instead. Figure 2.4: Network representation of 2 D sheet al..though less accurate, approximation (2. 25) is useful because it corresponds to the discrete electrical network model[52, 59, 91] that has frequently been used in simulation studies. When used with the centered, second order approximation for 2 OE= x 2 it also results in a symmetric conductance matrix, which can be advantageous. The electrical network representation of a two dimensional sheet is shown in Figure 2.4, ....

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R. W. Joyner, F. Ramon, and J. W. Moore. Simulation of action potential propagation in an inhomogeneous sheet of coupled excitable cells. Circulation Research, 36:654--661, 1975.

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