磁共振弹性成像图像的位移和压力重建：应用于计算机脑模型
Displacement and pressure reconstruction from magnetic resonance elastography images: application to an in silico brain model
摘要：
磁共振弹性成像是一种运动敏感的图像模式，允许测量体内组织位移场响应于机械激励。本文研究了一种从部分弹性成像数据中重建计算机脑模型中组织位移场和压力场的数据同化方法。数据同化是基于参数化的背景数据弱的方法，其中的物理系统的状态-组织位移和压力场-是重建从现有的数据假设一个基本的多孔弹性生物力学模型。为此，通过对描述接近其生理范围的组织模型的参数空间进行采样以模拟相应的多孔弹性问题，并通过适当的正交分解计算简化的基础，来构建物理学通知的流形。位移和压力重建寻求在一个减少的空间后，解决一个最小化问题，包括降阶模型的结构和可用的测量。所提出的管道使用模拟生理大脑的多孔弹性力学后获得的合成数据进行验证。数值实验表明，该框架能够实现位移场和压力场的精确联合重建。该方法可以制定为一个任意分辨率的可用位移数据从相关的图像。
英文摘要：
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.
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