By Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Frederik Nielsen, Kent-Andre Mardal, Aslak Tveito
This e-book describes mathematical types and numerical thoughts for simulating job within the center. The booklet supplies an advent to an important types of the sector, by way of an in depth description of numerical strategies for the types. specific concentration is on effective numerical tools for giant scale simulations on either scalar and parallel desktops. the consequences awarded within the ebook could be of specific curiosity to researchers in bioengineering and computational biology, who face the problem of fixing those advanced mathematical versions successfully. The booklet also will function a precious creation to a brand new and interesting box for computational scientists and utilized mathematicians.
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Extra resources for Computing the Electrical Activity in the Heart
4) which is the relation describing the electric potential in a volume conductor with no current sources. 1. 4) is only valid for a volume conductor with no current sources. The active heart tissue does generate such sources, and to simulate this activity the equation has to be adjusted slightly. A commonly used approach is to model the current sources in the active heart as one or more dipoles. 4), and the resulting equation is valid throughout the body, including the heart muscle. It is natural to assume that the body is surrounded by air or some other electrically insulating medium.
In the physiological situation, there are a number of different ions, both in the intracellular and extracellular domains, all of which affect the transmembrane potential. 2 where we had two compartments, i and e, separated by a thin membrane. The compartments contained NaCl in different concentrations. Assume now that instead of being completely impermeable to Cl− ions, the membrane allows both ions to pass, but with different permeabilities. The difference in permeability for the two ions will cause a potential difference across the membrane, and the flux of each ion may reach an equilibrium situation where the net flux is zero.
With this kind of volume-averaging approach, a quantity at a point P is viewed as an average over a small volume around P . The chosen volume over which the quantity is averaged must be small compared to the scales of the problem under study, but large compared to the molecular size of the material. This averaging of volumes can also be used at the level of cells, to obtain a continuous description of biological tissue. The chosen volume over which the averaging is performed should now be small compared to the dimension of the problem under study, but large compared to the volume of a single cell.
Computing the Electrical Activity in the Heart by Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Frederik Nielsen, Kent-Andre Mardal, Aslak Tveito