Displacement and pressure reconstruction from magnetic resonance elastography images: Application to an in silico brain model
- Galarce Marín, Felipe
- Tabelow, Karsten
- Polzehl, Jörg
- Papanikas, Christos Panagiotis
- Vavourakis, Vasileios
- Lilaj, Ledia
- Sack, Ingolf
- Caiazzo, Alfonso
2020 Mathematics Subject Classification
- 35R30 65N21 74L15 92-08
- data assimilation, state estimation, finite element method, poroelasticity, reduced-order modeling
This paper investigates a data assimilation approach for non-invasive quantification of intracranial pressure from partial displacement data, acquired through magnetic resonance elastography. 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 partially 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 compute a reduced basis. 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 on 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. It can also inherently handle uncertainty on the physical parameters of the mechanical model by enlarging the physics-informed manifold accordingly. Moreover, the framework can be used to characterize, in silico, biomarkers for pathological conditions, by appropriately training the reduced-order model. A first application for the estimation of ventricular pressure as an indicator of abnormal intracranial pressure is shown in this contribution.
- SIAM J. Imaging Sci., 16 (2023), pp. 996--1027, DOI 10.1137/22M149363X .