Single ventricle hearts have only one ventricle that can pump blood effectively and the treatment requires three stages of operations to reconfigure the heart and circulatory system. At the second stage, Glenn procedure is performed to connect Superior Vena Cava (SVC) to the Pulmonary Arteries (PA). For the third and most complex operation, called Fontan, an extracardiac conduit is used to connect Inferior Vena Cava (IVC) to the PL and there after no deoxygenated blood goes to the heart.

This paper explores cardiac electrophysiological simulations of the monodomain equations and introduces a novel subcycling time integration algorithm to exploit the structure of the ionic model. The aim of this work is to improve upon the efficiency of parallel cardiac monodomain simulations by using our subcycling algorithm in the computation of the ionic model to handle the local sharp changes of the solution. This will reduce the turnaround time for the simulation of basic cardiac electrical function on both idealized and patient-specific geometry. Numerical experiments show that the proposed approach is accurate and also has close to linear parallel scalability on a computer with more than 1000 processor cores. Ultimately, the reduction in simulation time can be beneficial in clinical applications, where multiple simulations are often required to tune a model to match clinical measurements.cardiac electrophysiology, finite element on unstructured meshes, parallel processing, patient-specific cardiac geometry, time integration with subcycling | INTRODUCTIONThe prevalence of cardiovascular disease 1 gives cardiac research a sense of great importance, because advancements in cardiac research could ultimately lead to a reduction in deaths related to cardiovascular disease. One crucial area of cardiac research is cardiac electrophysiology, which investigates the electrical propagation that drives a heartbeat in the human heart. In a clinical setting, this can be studied, for example, with magnetic resonance imaging (MRI) and electrocardiograms (ECG) in order to monitor and detect irregularities in the electrical activity. A different approach is to simulate the electrical activity in the heart using cardiac models. [2][3][4][5] Cardiac electrophysiology simulations at the tissue level can often be modeled by either the bidomain or the monodomain equations, and incorporate a cellular model to deal with the intracellular currents. In this paper, we utilize the monodomain equations. This is a tradeoff between complexity and accuracy, as the bidomain equations more accurately describe cardiac electrical activity, but are also more expensive to solve computationally. 6,7 The monodomain equations are solved via the finite element method (FEM) on a variety of meshes, ranging from simple slabs for benchmarking to meshes generated from actual MRI data. In order to generate patient-specific meshes from MRI data, we developed a semi-automatic mesh generation pipeline, which utilizes user-guided segmentation and automatic model creation from segmentation. This pipeline uses a variety of open source software, and allows for flexibility in mesh generation, including mesh size and quality.

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