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

TL;DR

This paper introduces a novel framework for state estimation in biomedical applications that accounts for shape variability without prior geometric parametrization, using morphometric techniques and reduced models for fast reconstruction.

Contribution

It presents a new method combining Multidimensional Scaling and reduced model spaces to handle geometric variability in inverse problems without prior shape parametrization.

Findings

Method successfully reconstructs blood flow in synthetic tests.

Framework handles shape variability without prior geometric knowledge.

Potential for real-time biomedical imaging applications.

Abstract

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.