Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator


Advanced Numerical Methods for Scientific Computing
Computational Medicine for the Cardiocirculatory System
Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator
Friday 4th June 2021
Regazzoni, F.; Quarteroni, A.
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The results of numerical simulations of 3D cardiac electromechanical models are typically characterized by a long transient before reaching a periodic solution known as limit cycle. Since the only clinically relevant output is the one associated with such limit cycle, a long transient translates into a serious computational overhead. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator. This emulator is built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated through the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, allows to accurately detect the location of the limit cycle in less than one minute on a standard laptop. Then, using as an initial guess for the 3D model the solution obtained with its 0D surrogate, it is possible to reach in just two heartbeats a solution that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the full-order 3D model. In this manner, the proposed approach achieves an overall speedup in the simulation of about an order of magnitude. In practical applications, an electromechanical model needs to be coupled with a model for the external circulation. The latter is typically represented by either a Windkessel-type preload-afterload model, emulating the boundary conditions, or by a closed-loop model of the entire circulatory network. The closed-loop model provides higher quality results in terms of physiological soundness; however, reaching a limit cycle is more challenging in this setting. It is in this context that our 0D emulator turns out to be particularly effective. The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. As a matter of fact, the emulator does not depend on the circulation model to which it is coupled, hence its construction does not have to be repeated when the parameters of the circulation model vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. In all these cases, our numerical results show that the emulator is able to provide the 3D model with an initial guess such that, after only two heartbeats, the solution is very close to the limit cycle. This paper is accompanied by a Python library implementing the proposed algorithm, open to the integration with existing cardiac solvers.