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Computation 2016, 4(4), 42;

A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology

Department of Mathematical Modeling in Cardiology, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences (IMM UB RAS), 16 S. Kovalevskoy Street, 620990 Ekaterinburg, Russia
Mathematical Modeling in Physiology and Medicine with Use of Supercomputer Technologies, Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia
This paper is an extended version of our paper published in Pravdin, S. A mathematical model of cardiacleft ventricle anatomy and morphology. In Proceedings of the Experimental and Computational Biomedicine: Russian Conference with International Participation in Memory of Professor Vladimir S. Markhasin, Ekaterinburg, Russia, 10–12 April 2016; p. 25.
Academic Editors: Gennady Bocharov, Olga Solovyova and Vitaly Volpert
Received: 25 June 2016 / Revised: 19 October 2016 / Accepted: 21 October 2016 / Published: 27 October 2016
(This article belongs to the Special Issue Multiscale and Hybrid Modeling of the Living Systems)
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Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibers. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualization, such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously-made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilize finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation. View Full-Text
Keywords: left ventricle; myofiber; myocardium structure; rule-based model; mathematical anatomy left ventricle; myofiber; myocardium structure; rule-based model; mathematical anatomy

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Pravdin, S. A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology. Computation 2016, 4, 42.

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