On sampling spatially-correlated random fields for complex geometries.
Extracting spatial heterogeneities from patient-specific data is challenging. In most cases, it is unfeasible to achieve an arbitrary level of detail and accuracy. This lack of perfect knowledge can be treated as an uncertainty associated with the estimated parameters and thus be modeled as a spatially-correlated random field superimposed to them. In order to quantify the effect of this uncertainty on the simulation outputs, it is necessary to generate several realizations of these random fields. This task is far from trivial, particularly in the case of complex geometries. Here, we present two different approaches to achieve this. In the first method, we use a stochastic partial differential equation, yielding a method which is general and fast, but whose underlying correlation function is not readily available. In the second method, we propose a geodesic-based modification of correlation kernels used in the truncated Karhunen-Loève expansion with pivoted Cholesky factorization, which renders the method efficient even for complex geometries, provided that the correlation length is not too small. Both methods are tested on a few examples and cardiac applications.
The authors acknowledge financial support by the Theo Rossi di Montelera Foundation, the Metis Foundation Sergio Mantegazza, the Fidinam Foundation, and the Horten Foundation to the Center for Computational Medicine in Cardiology. This work was also supported by grants from the Swiss National Supercomputing Centre (CSCS) under project ID s778. Finally, we would like to thank Prof. Michael Multerer for the fruitful discussion.
This paper was presented as a poster at the 10th international meeting Functional Imaging and Modeling of the Heart, which was held at the Victoire Campus of the University of Bordeaux in June 2019. The meeting was organized by Yves Coudière, Valéry Ozenne, Edward Vigmond, and Nejib Zemzemi, and was attended by about 120 scientists.
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