Displacement and Pressure Reconstruction from Magnetic Resonance Elastography Images: Application to an In Silico Brain Model
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 are 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. 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 noninvasive estimation of ventricular pressure as an indicator of abnormal intracranial pressure is shown in this contribution.
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© 2023 Society for Industrial and Applied Mathematics.
History
Submitted: 2 May 2022
Accepted: 16 February 2023
Published online: 8 June 2023
Keywords
MSC codes
Authors
Funding Information
Deutsche Forschungsgemeinschaft (DFG): EXC-2046/1, 390685689
Cyprus Cancer Research Institute: CCRI 2020 FUN 001, CCRI_2021_FA_LE_105
Funding: The work of the authors was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy MATH+: The Berlin Mathematics Research Center EXC-2046/1, project 390685689. The work of the fifth author was supported by the Cyprus Cancer Research Institute through Bridges in Research Excellence CCRI_2020_FUN_001, project “PROTEAS,” grant CCRI_2021_FA_LE_105.
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