Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac conductivities in models of potential propagation is crucial, since they have major quantitative impact on the solution. Available estimates of cardiac conductivities are significantly diverse in the literature and the definition of experimental/mathematical estimation techniques is an open problem with important practical implications in clinics. We have recently proposed a methodology based on a variational procedure, where the reliability is confirmed by numerical experiments. In this paper we explore model-order-reduction techniques to fit the estimation procedure into timelines of clinical interest. Specifically we consider the Monodomain model and resort to Proper Orthogonal Decomposition (POD) techniques to take advantage of an off-line step when solving iteratively the electrocardiological forward model online. In addition, we perform the Discrete Empirical Interpolation Method (DEIM) to tackle the nonlinearity of the model. While standard POD techniques usually fail in this kind of problems, due to the wave-front propagation dynamics, an educated novel sampling of the parameter space based on the concept of Domain of Effectiveness introduced here dramatically reduces the computational cost of the inverse solver by at least 95%.

The bidomain model is the current standard model to simulate cardiac potential propagation. The numerical solution of this system of partial differential equations strongly depends on the model parameters and in particular on the cardiac conductivities. Unfortunately, it is quite problematic to measure these parameters in vivo and even more so in clinical practice, resulting in no common agreement in the literature. In this paper we consider a variational data assimilation approach to estimating those parameters. We consider the parameters as control variables to minimize the mismatch between the computed and the measured potentials under the constraint of the bidomain system. The existence of a minimizer of the misfit function is proved with the phenomenological Rogers-McCulloch ionic model, that completes the bidomain system. We significantly improve the numerical approaches in the literature by resorting to a derivative-based optimization method with settlement of some challenges due to discontinuity. The improvement in computational efficiency is confirmed by a 2D test as a direct comparison with approaches in the literature. The core of our numerical results is in 3D, on both idealized and real geometries, with the minimal ionic model. We demonstrate the reliability and the stability of the conductivity estimation approach in the presence of noise and with an imperfect knowledge of other model parameters.

This paper presents a novel commutation failure (CF) assessment method considering the influences of voltage magnitude drop, phase shift, and spatial-temporal discreteness of AC system faults. The commutating voltage-time area is employed to analyze the spatial-temporal discreteness of AC system faults causing CF in high-voltage direct current systems, and the influences of fault position and fault time on CF are revealed. Based on this, a novel CF criterion is proposed, further considering the influence of voltage phase shift and the spatial-temporal discreteness. Then this research develops a new CF assessment method, which does not rely on electromagnetic transient simulations. A real case from the China Southern Power Grid is used to verify the practicability of the proposed method by comparing with simulation results obtained using PSCAD/EMTDC.

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Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design process, a stochastic optimization algorithm is posed based on the conditional value-at-risk measure so that an ideal acoustic liner impedance is determined that is robust in the presence of uncertainties. A parallel reduced-order modeling framework is developed that dramatically improves the computational efficiency of the stochastic optimization solver for a realistic nacelle geometry. The reduced stochastic optimization solver takes less than 500 seconds to execute. In addition, well-posedness and finite element error analyses of the state system and optimization problem are provided.