Computational modeling of human atrial cardiomyocytes: integration of electro-mechanical & mechano-electric feedback pathways

The cardiomyocytes are very complex consisting of many interlinked non-linear regulatory mechanisms between electrical excitation and mechanical contraction. Thus given a integrated electromechanically coupled system it becomes hard to understand the individual contributor of cardiac electrics and mechanics under both physiological and pathological conditions. Hence, to identify the causal relationship or to predict the responses in a integrated system the use of computational modeling can be beneficial. Computational modeling is a powerful tool that provides complete control of parameters along with the visibility of all the individual components of the integrated system. The advancement of computational power has made it possible to simulate the models in a short timeframe, providing the possibility of increased predictive power of the integrated system. My doctoral thesis is focused on the development of electromechanically integrated human atrial cardiomyocyte model with proper consideration of feedforward and feedback pathways.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.