title: One-way blocks in cardiac tissue: a mechanism for propagation failure in Purkinje fibres.
abstract: The concept of a one-way block, arising from a region of depressed tissue, has remained central to theories for cardiac arrhythmias. We show that both the geometry of a depressed region and spatial heterogeneities in depression are key factors for inducing such a block. By using an asymptotic approximation, known as the eikonal equation, to model qualitatively the movement of a depolarization wave-front down a Purkinje fibre bundle, we show how a one-way block in conduction may result from asymmetric constriction in the width of a depressed bundle. We demonstrate that this theory is valid for biologically relevant parameters and simulate a one-way block by numerically solving the eikonal approximation. We consider the case of non-uniform depression, where the planar travelling wave speed is spatially dependent. Here, numerical simulations indicate that such a spatial dependency may, in itself, be sufficient to produce a one-way block.
authors.affiliation: Centre for Mathematical Biology, Mathematical Institute, Oxford, U.K.
authors.forename: M A
authors.initials: MA
authors.lastname: Lewis
authors.forename: P
authors.initials: P
authors.lastname: Grindrod
mesh_terms: D000818:Animals; D001145:Arrhythmias, Cardiac / Q000503:physiopathology*; D006321:Heart / Q000502:physiology* / Q000503:physiopathology; D006801:Humans; D008433:Mathematics; D008955:Models, Cardiovascular; D011690:Purkinje Fibers / Q000502:physiology*