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.

翻译：磁共振弹性成像是运动敏感成像模态，可测量生物组织在机械激励下的体内位移场。本文研究了一种数据同化方法，利用部分弹性成像数据在计算机模拟脑模型中重建组织位移场和压力场。该数据同化方法基于参数化背景数据弱方法，通过假定的孔隙弹性生物力学模型，从可用数据重建物理系统状态——组织位移与压力场。为此，通过采样组织模型参数空间中接近其生理范围的参数值来模拟相应孔隙弹性问题，并利用本征正交分解计算简化基，构建物理信息流形。在求解包含降阶模型结构和可用测量数据的最小化问题后，在降阶空间中寻求位移与压力重建。利用模拟生理脑孔隙弹性力学获得的合成数据对提出的流程进行验证。数值实验表明，该框架能够实现位移场与压力场的精确联合重建。该方法可针对相关图像中任意分辨率的可用位移数据进行公式化表述。