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Computerorientierte Elektromechanik des Herzens: Entwicklung FE-basierter verlässlicher Simulationsansätze für die patientenspezifische Analyse

Fachliche Zuordnung Angewandte Mechanik, Statik und Dynamik
Förderung Förderung von 2012 bis 2022
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 217579293
 
Erstellungsjahr 2021

Zusammenfassung der Projektergebnisse

This research project aims at paving a stepping stone towards realistic, efficient and robust predictive computer simulations in cardiology that will provide a beneficial support for successful patient-specific treatment methods. The main motivation of this endeavor lies in the fact that heart related diseases have the highest morbidity and mortality rate and comprise a significantly high financial burden with an increasing tendency over the next decades. In this research, we adopted a continuum based approach and the well-established finite element method was used to model the problem of electrophysiology, mechanics and electromechanical coupling in the heart tissue. One of the crucial aspects of this study was the development of a novel constitutive model incorporating the viscous features of the myocardium, which are mainly neglected in computer models of excitation-contraction problem in the heart tissue. First of all, the myocardium is considered as a passive material and a rheological model consisting of two branches connected in parallel is proposed. One branch is related to the equilibrium response through an elastic spring and the other branch represents the non-equilibrium response through a spring+dashpot element. Regarding the orthotropic viscous properties of the myocardial tissue, the non-equilibrium part of the free energy function is additively decomposed into fibre, sheet and normal directions and each orientation is associated with distinct material parameters. Furthermore, this rheology is furnished with a contractile element along the fibre direction in order to describe the influence of the electrical excitation on the mechanical field. The resulting setting can be also considered as the extension of the classical Hill model to the viscosity in three-dimensional space. The suggested rheological model demonstrates an outstanding agreement with the experimental data for passive and active response of the myocardial tissue. Besides, extensive comparative analysis between the viscoelastic and elastic cases indicated that viscous effects significantly alter the electromechanical response of the cardiac tissue and is thought to be crucial in the virtual assessment of the cardiac function. As another important advancement, a phenomenological model for the intracellular calcium concentration and the active stretch was proposed. The model is capable of producing realistic intracellular calcium concentration and myocyte shortening graphs, can be easily calibrated to capture different intracellular calcium concentration and contraction characteristics and, at the same time, is easy to implement and ensures efficient computer simulations. This study was inspired by the fact that existing models in this context either contain a number of complex equations and material parameters, which reduce their feasibility, or are very simple and cannot accurately mimic reality, which eventually influences the realm of computer simulations. It was shown that the model can be accurately fitted to the experimental data and can easily capture heterogeneous myocardial shortening characteristics throughout the ventricles. Apart from the improvements at material level, a surface element formulation was developed in order to mimic the presence of blood pressure within the ventricles, where an implicit time integration scheme was applied to the evolution equations in the name of an efficient and a stable framework. To this end, a uniform traction load applying perpendicularly to the whole endocardial surface was considered and its evolution was formulated in terms of the ventricle cavity volume at constitutive level. Since the ventricle cavity volume explicitly depends on the current configuration of the endocardial surface, consistent linearization of the deformation dependent pressure load leads to non-local entries in the global stiffness matrix as opposed to standard finite element formulations. Another important focus of this research project was on developing efficient simulation methods for the problem of excitation and excitation-contraction coupling of the cardiac tissue. In this regard, we inquired into different integration methods, linearization techniques and solution procedures of the coupled balance equations. We found that the fully implicit staggered solution algorithm achieves the most efficient solution of the bidomain equations and excitation-contraction coupling in terms of computational time and memory without any stability and accuracy issue. The possible future application areas of the developed numerical framework was presented through various initial-boundary value problems. For this purpose, scroll wave, pressure-volume and volume-time relation, electrocardiogram, basic characteristics of left ventricle motion, arrhythmia, defibrillation, cardiac resynchronization therapy, drug application, commotio cordis, precordial thump and premature ventricular contraction, which can be considered as clinically relevant and interesting problems, were demonstrated. The results were evaluated together with cardiologists from the Department of Cardiology, Technische Universität Dresden. In several examples, personalized ventricle geometries generated from medical imaging tools were used.

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