Computational Framework for Nonlinear Viscoelasticity: A Continuum Electromechanical Model of Heart Myocardium Tissue

Abstract

Computational modelling of cardiac function have gradually progressed during past 4 decades and now beginning to translate toward clinical applications. To accrue maximum bene t from predictions of cardiac computational models, it is essential that the underlying assump- tions and mathematical models are based on a faithful representation of actual physiological function. In the past, computational studies have mostly modeled heart myocardium as isotropic, transversely isotropic and lately as an orthotropic elastic material. Despite re- ported viscoelastic behavior of both canine (1983) and porcine (2002) myocardium, the rate dependance and viscoelasticity of myocardium tissue remained an inactive research area. After three decades, the rst experimental study on human heart samples have now con- rmed the heart myocardium tissue as orthotropic, rate dependent and viscoelastic material. Further numerical investigations have also suggested an important role of tissue viscoelas- ticity on electromechanics of the heart, still no study to date have attempted to quantify these effects on cardiac function. Considering recent experimental evidence and the need of further investigations on myocardium viscoelasticity, we have modeled left ventricle (LV) myocardium using an orthotropic viscoelastic constitutive relation. To this end we used con- tinuum balance law to capture physiological function of LV cardiac cycle using an idealized geometry and solved resulting equations using Python based Finite Element(FE) platform. Furthermore, viscoelastic model was compared with an elastic LV model so as to quantify the effects of myocardium viscoelasticity. The numerical investigations in this thesis yielded a difference of 4.2 ml end diastolic volume between elastic and viscoelastic tissue deforma- tion with 2.8 percent difference in ber strain. The viscoelastic deformation resulted in a variation of 7.8 percent in conduction velocity which caused reduction in Action Potential Duration (APD). These results show that viscoelastic behavior of myocardium tissue has an important role in cardiac electromechanics and future investigations can help to re ne these observations for further clinical predictions.