On Aspects of Cardiac and Artificial Muscle Modelling – Insights into Orthotropic Tissue Structure and Dielectric Elastomer Actuators

Document Type
Doctoral Thesis
Granting Institution
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Technische Fakultät
Issue Date
Holz, David

The heart is a fascinating organ whose seemingly simple function of mechanically pumping blood throughout the body is ensured by a complex interaction of mechanical, electrical, chemical and biological mechanisms. However, complex systems inherently bear the risk of disruptions, causing a variety of cardiovascular diseases (CVD) such as myocardial infarction, heart failure, arrhythmia, and hypertension. The field of biomechanics is playing a key role in the fundamental research concerning CVDs. In this context, computational modelling and simulation of the cardiovascular system are crucial in furthering the understanding of CVDs, enhancing diagnostic capabilities, and developing patient-specific therapeutic interventions. Moreover, computer models can facilitate the development of novel medical devices, such as cardiac assist devices (CaAD) comprised of dielectric materials. In this thesis, the focus is on the development of two types of computational muscle models, specifically a cardiac muscle model based on biological tissue and an artificial muscle model based on dielectric materials. The work on the cardiac muscle model primarily focuses on the modelling of the orthotropic cardiac tissue structure. The developed tissue structure model (TSM) is based on a discontinuous Galerkin framework to accurately assess the transmural path and thickness in the myocardial wall. The framework enables more accurate modelling of the orthotropic tissue structure compared to established methods. Moreover, due to the modularity, the framework can be easily integrated into other TSMs. In this regard, transmural fibre and sheet angle rules are proposed for the left ventricle based on diffusion tensor magnetic resonance imaging (DT-MRI) data and demonstrate enhanced fidelity in representing the measurement data compared to existing rules. A study about the influence of different TSMs on important characteristics of cardiac function, based on an electromechanical model of the cardiac tissue, underscores the significant influence of the TSM. The artificial muscle model is inspired by the idea of an innovative concept for cardiac assist devices (CaAD) based on dielectric elastomers. However, there is a dearth of computational models that are able to simulate the complex electromechanical, dynamic, and viscoelastic behaviour of such a dielectric elastomer actuator-based CaAD. In this thesis, the computational model of the artificial muscle is based on an electromechanical shell formulation, including dynamics and viscoelasticity. The variational formulation of the dynamic, viscoelastic, and electromechanical shell is derived from the Lagrange-d’Alembert principle. A variational time integration ensures a good long-term energy behaviour. To demonstrate the potential of the model, numerical examples, including different geometries as well as deformation states, are presented. Overall, the proposed TSM, in conjunction with the improved transmural fibre and sheet angle rules, is a robust, efficient and accurate method by which to compute the orthotropic tissue structure for finite element models of the cardiac tissue. Furthermore, the significant influence of different TSMs on important characteristics of cardiac function is demonstrated. The electromechanical shell model proves to be a promising approach towards the development of patient-specific CaADs based on dielectric elastomer actuators (DEA).

Schriftenreihe Technische Dynamik
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