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.

On Sampling Spatially-Correlated Random Fields for Complex Geometries / Pezzuto, S.; Quaglino, A.; Potse, M.. - STAMPA. - 11504:(2019), pp. 103-111. (Intervento presentato al convegno FIMH tenutosi a Bordeaux nel June 6-8, 2019) [10.1007/978-3-030-21949-9_12].

On Sampling Spatially-Correlated Random Fields for Complex Geometries

Pezzuto S.;
2019-01-01

Abstract

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.
2019
Functional Imaging and Modeling of the Heart: 10th International Conference, FIMH 2019, Bordeaux, France, June 6–8, 2019, Proceedings
Cham
Springer
Pezzuto, S.; Quaglino, A.; Potse, M.
On Sampling Spatially-Correlated Random Fields for Complex Geometries / Pezzuto, S.; Quaglino, A.; Potse, M.. - STAMPA. - 11504:(2019), pp. 103-111. (Intervento presentato al convegno FIMH tenutosi a Bordeaux nel June 6-8, 2019) [10.1007/978-3-030-21949-9_12].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/360552
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