An investigation into therapies for atrial arrythmias using a biophysical model of the human atria

Lam Dang
EPFL, 2006
Thèse EPFL

The most common type of sustained arrhythmia is atrial fibrillation (AF), affecting about 2% of the general population and 8% to 11% of the elderly, more than 65 years of age. The treatment of atrial arrythmia is still based on empirical considerations and is usually evaluated in clinical studies or in animal experiments. The main drawbacks of animal experiments lie in the difficulty of technically accessing the whole atria and in the differences between animal and human anatomy. In the last years, ever-increasing computer power has permitted the development of biophysical models of the human atria. It has become possible to simulate cellular electrical propagation in the whole human heart. Compared to clinical and animal studies, an in silico approach has the advantages of repeatability and reproducibility under controlled conditions. In this thesis, a biophysical model of the human atria has been used to investigate therapies of atrial arrhythmias: surgical ablation and therapeutic pacing. First, a brief review of the concepts of biophysical modeling of human atria developed until now is presented, as well as a brief description of several types of arrhythmia that can be simulated with the biophysical model. Second, measures of organization are considered to quantify and classify the different types of AF. With these measures, AF organization is evaluated at the electrogram signals level as well as at the cellular level. Four types of atrial arrhythmia are differentiated with the use of the biophysical model: atrial flutter, chronic AF, meandering AF and cholinergic AF. Finally, simulations of atrial therapies are investigated. The biophysical model has been used to test the efficacy of ablation lines. The surgical Maze-III procedure has proven to be highly effective in treating chronic AF. However, due to the technical difficulty and the risk of the procedure, less invasive ablation techniques have been investigated. The results confirm the superiority of aggressive surgical procedures in the termination of AF, as described in the clinical studies. Furthermore, an ideal ablation pattern has been proposed using the biophysical model. The ideal pattern should be able to prevent AF with a limited number of ablation lines of minimal length, while allowing for the maintenance or recovery of mechanical activity of both atria during sinus rhythm. The second therapeutic approach investigated is that of pacing. An algorithm of pacing and different pacing sites are investigated during this research. Antitachycardia pacing on different types of AF are carried out. The simulations showed that more organized arrhythmia such as atrial flutter can be pace-terminated. On the other hand, only local capture is possible on more complex AF. The results obtained with the biophysical model are in agreement with the clinical studies. The results of the present research prove that atrial therapies can be approached by means of a biophysical model of the human atria. This tool can be used to investigate further therapeutic techniques and thus, improve the quality of life of patients.

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Lam Dang
EPFL, 2006
Thèse EPFL

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https://infoscience.epfl.ch/record/56032?ln=fr

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Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the partial differential equation that one wants to solve in the geometrical model of interest, removing some important geometrical features may greatly impact the solution accuracy. For instance, in solid mechanics simulations, such features can be holes or fillets near stress concentration regions. Unfortunately, the effect of geometrical simplification on the accuracy of the problem solution is often neglected, because its analysis is a time-consuming task that is often performed manually, based on the expertise of engineers. It is therefore important to have a better understanding of the effect of geometrical model simplification, also called defeaturing, to improve our control on the simulation accuracy along the design and analysis phase.In this thesis, we formalize the process of defeaturing, and we analyze its impact on the accuracy of solutions of some partial differential problems. To achieve this goal, we first precisely define the error between the problem solution defined in the exact geometry, and the one defined in the simplified geometry. Then, we introduce an a posteriori estimator of the energy norm of this error. This allows us to reliably and efficiently control the error coming from the addition or the removal of geometrical features. We subsequently consider a finite element approximation of the defeatured problem, and the induced numerical error is integrated to the proposed defeaturing error estimator. In particular, we address the special case of isogeometric analysis based on (truncated) hierarchical B-splines, in possibly trimmed and multipatch geometries. In this framework, we derive a reliable a posteriori estimator of the overall error, i.e., of the error between the exact solution defined in the exact geometry, and the numerical solution defined in the defeatured geometry.We then propose a two-fold adaptive strategy for analysis-aware defeaturing, which starts by considering a coarse mesh on a fully-defeatured computational domain. On the one hand, the algorithm performs classical finite element mesh refinements in a (partially) defeatured geometry. On the other hand, the strategy also allows for geometrical refinement. That is, at each iteration, the algorithm is able to choose which missing geometrical features should be added to the simplified geometrical model, in order to obtain a more accurate solution.Throughout the thesis, we validate the presented theory, the properties of the aforementioned estimators and the proposed adaptive strategies, thanks to an extensive set of numerical experiments.

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