A V Holden, M J Poole, and J V Tucker. Reconstructing the heart. Chaos, Solitons and Fractals, 5:691--704, 1995. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Hierarchical Reconstructions of Cardiac Tissue - Holden, Poole, Tucker (1998) (1 citation) Self-citation (Tucker) (Correct)
....form of model. In order to construct meaningful multi level models, concepts of abstraction and approximation between single level models needs to be clarified and validated. Thus we require a framework within which di#erent component models can be specified, compared and integrated. In [17] [13], 15] and [14] we have argued that the theory of synchronous concurrent algorithms (SCAs) provides a common framework for specifying models of excitable tissues. Here we will extend SCA theory to accommodate concepts of abstraction and approximation for models of cardiac tissue, and for building ....
....32] Thus SCAs provide us with a mathematically rigorous framework for the investigation of disparate models of cardiac tissue in a unified way. Specifically, SCAs are suited to (i) the comparison, composition and decomposition of models, including the construction of hybrid and multilevel models [13, 16, 27]; ii) experimental work with simulation software [20, 5] and (iii) the classification of the computational behaviour of models of parallel deterministic systems, including the limits of computation [21, 18] In the present paper, we use the theory of SCAs as a framework and toolset for ....
A V Holden, M J Poole, and J V Tucker. Reconstructing the heart. Chaos, Solitons and Fractals, 5:691--704, 1995.
Spatio-Temporal Irregularity in an Excitable Medium .. - Biktashev.. (1999) Self-citation (Biktashev Holden) (Correct)
....wave trains. This paradox is easily explained. The presence of a shear flow breaks the spatial reflection symmetry of the reaction diffusion system. As a result, the angular velocity of a spiral wave in the shear flow now depends on the direction of rotation. The general perturbation theory [6] predicts only that the angular velocity is = 0 mff O(ff 2 ) 9) where 0 is the angular velocity in a quiescent medium, m is direction of rotation, say m = 1 for clockwise rotating spirals and m = Gamma1 for counterclockwise, and coefficient depends on the particular model. In our ....
V. N. Biktashev and A. V. Holden, Chaos, Solitons and Fractals 5, 575 (1995).
Hierarchies of Spatially Extended Systems and Synchronous.. - Poole, Tucker, Holden (1998) Self-citation (Holden Poole Tucker) (Correct)
.... models for some time to come; recent computations using a supercomputer were limited to modelling the behaviour in a tiny twodimensional portion of tissue [WKVN93] Phenomenological PDE models such as the one defined here are commonly used for simulations of wholeheart behaviour [AP96,PH97] In [HPT95,HPT98] the concepts of hierarchy for SCAs discussed in this paper are extended to allow multi level, hybrid models of cardiac activity to be defined, where different regions of tissue are modelled using different, interacting, SCAs. Modelling small regions of tissue with biophysically derived, but ....
....systems. For example, the methods for the study of microprocessors, started in [HT93] has been applied to complex examples in [Fox98] and [FH99] and to the JAVA virtual machine in [Ste99] The methods for the study of biological excitable media have been used in our programme on heart simulation [HPT95,HPT96a]. Acknowledgements We thank W Dosch, M Holcombe and A Stumpel for many helpful comments made on a draft of this paper. ....
A V Holden, M J Poole, and J V Tucker. Reconstructing the heart. Chaos, Solitons and Fractals, 5:691--704, 1995.
Hierarchical Reconstructions of Cardiac Tissue - Holden, Poole, Tucker (1998) (1 citation) Self-citation (Holden Poole Tucker) (Correct)
....form of model. In order to construct meaningful multi level models, concepts of abstraction and approximation between single level models needs to be clarified and validated. Thus we require a framework within which different component models can be specified, compared and integrated. In [17] [13], 15] and [14] we have argued that the theory of synchronous concurrent algorithms (SCAs) provides a common framework for specifying models of excitable tissues. Here we will extend SCA theory to accommodate concepts of abstraction and approximation for models of cardiac tissue, and for building ....
....32] Thus SCAs provide us with a mathematically rigorous framework for the investigation of disparate models of cardiac tissue in a unified way. Specifically, SCAs are suited to (i) the comparison, composition and decomposition of models, including the construction of hybrid and multilevel models [13, 16, 27]; ii) experimental work with simulation software [20, 5] and (iii) the classification of the computational behaviour of models of parallel deterministic systems, including the limits of computation [21, 18] In the present paper, we use the theory of SCAs as a framework and toolset for ....
A V Holden, M J Poole, and J V Tucker. Reconstructing the heart. Chaos, Solitons and Fractals, 5:691--704, 1995.
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