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Register a new userParametric model order reduction and its application to inverse analysis of large nonlinear coupled cardiac problems
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Predictive high-fidelity finite element simulations of human cardiac mechanics co-mmon-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose a novel approach to reduce only the structural dimension of the monolithically coupled structure-windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. To incorporate changes in the parameter set into our reduced order model, we provide a comparison of subspace interpolation methods. We further show how projection-based model order reduction can be easily integrated into a gradient-based optimization and demonstrate its performance in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.
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We introduce a new dominance concept consisting of three new dominance metrics based on Lloyds (1967) mean crowding index. The new metrics link communities and species, whereas existing ones are applicable only to communities. Our community-level metric is a function of Simpsons diversity index. For species, our metric quantifies the difference between community dominance and the dominance of a virtual community whose mean population size (per species) equals the population size of the focal species. The new metrics have at least two immediate applications: (i) acting as proxies for diversity in diversity-stability modeling (ii) replacing population abundance in reconstructing species dominance networks. The first application is demonstrated here using data from a longitudinal study of the human vaginal microbiome, and provides new insights relevant for microbial community stability and disease etiology.
We present a novel approach aimed at high-performance uncertainty quantification for time-dependent problems governed by partial differential equations. In particular, we consider input uncertainties described by a Karhunen-Loeeve expansion and compute statistics of high-dimensional quantities-of-interest, such as the cardiac activation potential. Our methodology relies on a close integration of multilevel Monte Carlo methods, parallel iterative solvers, and a space-time discretization. This combination allows for space-time adaptivity, time-changing domains, and to take advantage of past samples to initialize the space-time solution. The resulting sequence of problems is distributed using a multilevel parallelization strategy, allocating batches of samples having different sizes to a different number of processors. We assess the performance of the proposed framework by showing in detail its application to the solution of nonlinear equations arising from cardiac electrophysiology. Specifically, we study the effect of spatially-correlated perturbations of the heart fibers conductivities on the mean and variance of the resulting activation map. As shown by the experiments, the theoretical rates of convergence of multilevel Monte Carlo are achieved. Moreover, the total computational work for a prescribed accuracy is reduced by an order of magnitude with respect to standard Monte Carlo methods.
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated as a nonlinear convex function with respect to the reconstructed image. Using the proposed framework, we put forward six specific iterative schemes, and present their detailed mathematical explanation. We also establish the relationship to existing algorithms. Moreover, under proper assumptions, we analyze the convergence of the schemes for the general model when the optimal dual variable regarding the nonlinear operator is non-vanishing. As a representative, the image reconstruction for spectral computed tomography is used to demonstrate the effectiveness of the proposed algorithm framework. By special properties of the concrete problem, we further prove the convergence of these customized schemes when the optimal dual variable regarding the nonlinear operator is vanishing. Finally, the numerical experiments show that the proposed algorithm has good performance on image reconstruction for various data with non-standard scanning configuration.
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