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State Estimation with Model Reduction and Shape Variability. Application to biomedical problems

Galarce, Felipe; Lombardi, Damiano; Mula, Olga (2021), State Estimation with Model Reduction and Shape Variability. Application to biomedical problems. https://basepub.dauphine.psl.eu/handle/123456789/22105

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163525226587433.pdf (1.075Mb)
Type
Document de travail / Working paper
External document link
https://hal.inria.fr/hal-03264205
Date
2021
Series title
Cahier de recherche du CEREMADE
Pages
26
Metadata
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Author(s)
Galarce, Felipe
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Lombardi, Damiano
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Mula, Olga cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems are posed on certain organs or portions of the body which inevitably involve morphological variations. If one wants to provide fast reconstruction methods, the algorithms must take into account the geometric variability. We develop and analyze a method which allows to take this variability into account without needing any a priori knowledge on a parametrization of the geometrical variations. For this, we rely on morphometric techniques involving Multidimensional Scaling, and couple them with reconstruction algorithms that make use of reduced model spaces pre-computed on a database of geometries. We prove the potential of the method on a synthetic test problem inspired from the reconstruction of blood flows and quantities of medical interest with Doppler ultrasound imaging.
Subjects / Keywords
Model Reduction; Shape Variability

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