Preprint Article Version 1 NOT YET PEER-REVIEWED

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

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 620990 Ekaterinburg, Russia
  2. Ural Federal University, 19 Mira street, 620002 Ekaterinburg, Russia
Version 1 : Received: 7 August 2016 / Approved: 8 August 2016 / Online: 8 August 2016 (12:28:29 CEST)
Version 2 : Received: 19 October 2016 / Approved: 20 October 2016 / Online: 20 October 2016 (08:22:39 CEST)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Computation 2016, 4, 42
DOI: 10.3390/computation4040042

Abstract

Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation 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 based on 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 utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.

Subject Areas

left ventricle; myofibre; myocardium structure; rule-based model; mathematical anatomy

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