Workshop on Numerical Methods and Analysis in CFD - Abstract

Galarce, Felipe

Inverse problems on non-parametric domains. Flow reconstruction from medical data using non linear dimensionality reduction

Co-authors:
D. Lombardi (Centre de Recherche INRIA de Paris & Laboratoire Jacques-Louis Lions. Sorbonne University, France)
O. Mula (Eindhoven Univerity of Technology)

Solving in real time inverse problems for biomedical applications requires learning techniques that involve simulations and databases from different patients which inevitably involve anatomical variations.
We present a state estimation method which allows to take this variability into account without needing any a priori knowledge on a parametrization of the anatomical differences. We rely on morphometric techniques involving Multidimensional Scaling and couple them with reconstruction techniques that make use of reduced modeling [1].
We prove the potential of the method on a simple application inspired from the reconstruction of blood flows and quantities of medical interest with Doppler ultrasound imaging [2, 3, 4].

References:
[1] N. Saeed, H. Nam, M. Imtiaz Ul Haq and D. Muhammad Saqib Bhatti. A Survey on Multidimensional Scaling. ACM Comput. 2018.
[2] F. Galarce, J.F. Gerbeau, D. Lombardi and O. Mula. State estimation with nonlinear reduced models. Application to the reconstruction of blood flows with Doppler ultrasound images. SIAM Journal on Scientific Computing. 2021. arXiv:1904.13367.
[3] F. Galarce, D. Lombardi, O. Mula. Reconstructing Haemodynamics Quantities of Interest from Doppler Ultrasound Imaging. International Journal for Numerical Methods in Biomedical Engineering. 2020.
arXiv:2006.04174.
[4] F. Galarce, D. Lombardi, O. Mula. Fast reconstruction of 3D blood flows from Doppler ultrasound images and reduced models. Computer Methods in Applied Mechanics and Engineering. 2021. arXiv:1904.13367.