Displacement and Pressure Reconstruction from Magnetic Resonance Elastography Images: Application to an In Silico Brain Model

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 pres-sure 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 poro-elastic 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 mechan-ics 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.