Displacement and pressure reconstruction from magnetic resonance elastography images: application to an in silico brain model

TL;DR

This paper presents a data assimilation framework for reconstructing tissue displacement and pressure fields in the brain using magnetic resonance elastography data, leveraging a physics-informed reduced-order model for accurate joint reconstructions.

Contribution

It introduces a novel methodology combining parametrized-background data weak approach with reduced basis techniques for in silico brain tissue reconstruction.

Findings

Accurate joint reconstruction of displacement and pressure fields demonstrated.

Framework effective with synthetic brain elastography data.

Method adaptable to various image resolutions.

Abstract

Magnetic resonance elastography is a motion-sensitive image modality that allows to measure in vivo tissue displacement fields in response to mechanical excitations. This paper investigates a data assimilation approach for reconstructing tissue displacement and pressure fields in an in silico brain model from partial elastography data. The data assimilation is based on a parametrized-background data weak methodology, in which the state of the physical system -- tissue displacements and pressure fields -- is reconstructed from the available data assuming an underlying poroelastic biomechanics model. For this purpose, a physics-informed manifold is built by sampling the space of parameters describing the tissue model close to their physiological ranges to simulate the corresponding poroelastic problem, and computing a reduced basis via Proper Orthogonal Decomposition. Displacements and pressure reconstruction is sought in a reduced space after solving a minimization problem that encompasses both the structure of the reduced-order model and the available measurements. The proposed pipeline is validated using synthetic data obtained after simulating the poroelastic mechanics of a physiological brain. The numerical experiments demonstrate that the framework can exhibit accurate joint reconstructions of both displacement and pressure fields. The methodology can be formulated for an arbitrary resolution of available displacement data from pertinent images.