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Computing the Electrical Activity in the Heart by Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Frederik

By Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Frederik Nielsen, Kent-Andre Mardal, Aslak Tveito

This ebook describes mathematical types and numerical options for simulating task within the middle. The booklet offers an creation to an important versions of the sector, via an in depth description of numerical recommendations for the versions. specific concentration is on effective numerical tools for giant scale simulations on either scalar and parallel pcs. the consequences offered within the e-book might be of specific curiosity to researchers in bioengineering and computational biology, who face the problem of fixing those advanced mathematical types successfully. The booklet also will function a beneficial creation to a brand new and fascinating box for computational scientists and utilized mathematicians.

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40 20 0 −20 −40 −60 −80 −100 0 200 400 600 800 Fig. 8. Action potential for a Purkinje fibre cell, computed with the Noble model. The Noble model was a successful attempt to simulate the action potential of Purkinje fibres with a simple model of Hodgkin-Huxley type. However, because the model was created before detailed data on ionic currents in cardiac cells became available, the underlying physiology is incorrect. An improvement of the model was presented by McAllister, Noble and Tsien [102] in 1975.

Several variations have been derived to address various limitations of the original model. One detail of the original formulation that does not match well with physiological data is that the cell hyperpolarizes in the repolarization phase. 3. The values of the parameters used in the original formulation of the FitzHughNagumo model. 4. 5 0 100 200 300 400 Fig. 2. Plots of v (solid) and w (dashed) for the original and modified FitzHugh-Nagumo model. 2, where v reaches values significantly below the resting potential before returning to the resting state.

5. The ionic currents in the Hodgkin-Huxley model. is time independent and formulated as a simple linear function of the transmembrane potential. The currents are given by ¯ Na m3 h(ν − νNa ), INa = G ¯ K n4 (ν − νK ), IK = G IL = GL (ν − νL ). Here, ν is the deviation from the resting potential, defined as ν = v − veq . Similarly νNa , νK , and νL are shifted equilibrium potentials for each current, defined by νNa = vNa − veq , νK = vK − veq , νL = vL − veq , where vNa , vK , and vL are the true equilibrium potentials for the three currents.

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