nonlinear elasticity, non-nested meshes, cardiac electromechanics, parallel computing, electrophysiology, cardiac mechanics, partial differential equations
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Heart failure is one of the most common cardiovascular diseases in western countries. Being the result of different heart diseases, by which the complex interplay of electrical activation and mechanical contraction within the heart is severely affected, heart failure leads to a progressive reduction in exercise capabilities and quality of life. Due to the ongoing demographic changes in our societies the incidence of heart failure will increase further.
Clearly, the understanding, diagnosis, and treatment of heart failure is of major importance for our societies and has a strong impact on economic and social life. The mechanisms of development of heart failure are complex and differ substantially between patients. This is especially true when it comes to the interaction of electrical and mechanical activity, which is a central and crucial aspect for heart function. In fact, despite intense and active research, significant parts of the electromechanical interplay in the heart muscle are still not understood
satisfactorily, posing a major obstacle towards diagnostic and therapeutic progress.
Fortunately, during the last decades the ever growing capacities of modern supercomputers and advancement of high performance computing have allowed for the realization of more and more detailed “in-silico models” of the heart: Mathematical modeling and numerical simulation have turned out to be an indispensable tool to understand and describe the different mechanisms within the heart muscle. However, most of the widely used simulation tools are based on models, discretizations, and solution methods that focus primarily on either mechanics or electrophysiology.
Electromechanical models, which incorporate both aspects, are available, but the numerical methods and tools employed for the numerical treatment of these coupled systems are not yet as efficient and elaborate as it is the case for the respective “mono-physics models.” This obviously is a clear disadvantage for research and clinical application. The number of potential applications for detailed coupled electromechanical models is vast, as they allow for, e.g., linking cellular electrophysiology and tissue mechanics across spatial scales to pump
function of the heart as a whole, relating abnormalities in ion channels and calcium handling to abnormalilites in the electrocardiogram, or linking regional infarction to aberrant wall motion.
A first reason for the “progress gap” of the coupled models can be found in the adequate and efficient coupling of the different temporal and spatial scales at which electrophysiology and mechanics take place. Whereas the electrophysiology can be considered as meso- (activation potential) and micro-effect (ion channels), the mechanical deformation is related more to the macro-scale. Nevertheless, most state-of-the art approaches employ a single spatial discretization for both displacements and activation potentials, thereby leading to one of the scales being
either under- or overresolved. Coupled approaches, in which an independent choice of discretizations for the different variables is possible, are not available.
A second reason is that the ever-increasing performance of modern supercomputers comes at the price of massive parallelism, which requires many simulation methods and the corresponding scientific software to be redesigned in order to be able to deal with the upcoming generations of supercomputers. This is especially true when it comes to the parallel solution of coupled systems of partial differential equations (PDEs) that arise from the electromechanical models, as new developments usually are first realized for “mono-physics” models.
The aim of this proposal is therefore to close this “progress gap” by 1) developing a novel coupled multiscale simulation framework which allows to fully exploit the difference in required spatiotemporal resolution of the electrophysiological and mechanical components by allowing different (finite-element) discretizations on the different scales; 2) developing implicit and monolithic solution techniques for the arising coupled multiscale-systems based on state-of-the-art discretization and solution approaches, and; 3) implementing the newly developed methods within a user-friendly software library, featuring capabilities for flexible choices of models as well as discretizations and solution methods.