摘要
In this paper we introduce a new mathematical model for the active contraction of cardiac muscle,featuring different thermo-electric and nonlinear conductivity properties.The passive hyperelastic response of the tissue is described by an orthotropic exponential model,whereas the ionic activity dictates active contraction in-corporated through the concept of orthotropic active strain.We use a fully incompressible formulation,and the generated strain modifies directly the conductivity mechanisms in the medium through the pull-back transformation.We also investigate the influence of thermo-electric effects in the onset of multiphysics emergent spatiotem-poral dynamics,using nonlinear diffusion.It turns out that these ingredients have a key role in reproducing pathological chaotic dynamics such as ventricular fibrillation during inflammatory events,for instance.The specific structure of the governing equations suggests to cast the problem in mixed-primal form and we write it in terms of Kirchhoff stress,displacements,solid pressure,dimensionless electric potential,activation generation,and ionic variables.We also advance a new mixed-primal finite element method for its numerical approximation,and we use it to explore the properties of the model and to assess the importance of coupling terms,by means of a few computational experiments in 3D.
基金
supported by the Engineering and Physical Sciences Research Council(EPSRC)through the research grant EP/R00207X。
