Pathmanathan, P. and Chapman, S. J. and Gavaghan, D. J. and Whiteley, J. P. (2010) Cardiac Electromechanics: The effect of contraction model on the mathematical problem and accuracy of the numerical scheme. Quaterly Journal of Mechanics and Applied Mathematics . (Submitted)

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Abstract
Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level, and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electrophysiology, but can also be dependent on
the stretch and stretchrate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing PDEs, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretchrateindependent contraction models; whereas for stretchratedependent contraction models we introduce a corresponding thirdorder problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the timestep prior to the bulk deformation being computed) is: (i) appropriate for stretchindependent contraction models; (ii) only conditionallystable, with the stability criterion independent of timestep, for contractions models which just depend on stretch (but not stretchrate), and (iii) inappropriate for stretchratedependent models.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  992 
Deposited By:  Peter Hudston 
Deposited On:  26 Oct 2010 09:24 
Last Modified:  29 May 2015 18:40 
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