In this study, we describe numerical implementation of a heterogenous, nearly incompressible, transverse isotropic (NITI) finite element (FE) model with key advantages for use in MR elastography of fibrous soft tissue. MR elastography (MRE) estimates heterogenous property distributions from MR-measured harmonic motion fields based on assumed mechanical models of tissue response. Current MRE property estimation methods usually assume isotropic properties, which cause inconsistencies arising from model-data mismatch when anisotropy is present. In this study, we use a NITI model parameterized by a base shear modulus, shear anisotropy, tensile anisotropy, and an isotropic bulk modulus, which describes the mechanical behavior of tissues with aligned fiber structures well. Property and fiber direction heterogeneity are implemented at the level of FE Gauss points, which allows high-resolution diffusion tensor imaging (DTI) data to be incorporated easily into the model. The resulting code was validated against analytical solutions and a commercial FEM package, and is suitable for incorporation into nonlinear inversion MRE algorithms. Simulations of MRE in brain tissue with heterogeneous properties and anisotropic fiber tracts, which produced wavefields similar to experimental MRE, were generated from anatomical, DTI and MRE image data, allowing investigation of MRE inversion performance in a realistic setting where the ground truth and underlying mechanical behavior are known. Two established isotropic inversion algorithms—nonlinear inversion (NLI) and local direct inversion (LDI)—were applied to simulated MRE data. Both algorithms performed well in simple isotropic homogenous cases; however, heterogeneity cased substantial artifacts in LDI arising from violation of local homogeneity assumptions. NLI was able to recover accurate heterogenous displacement fields in the presence of measurement noise. Isotropic NLI inversion of simulated anisotropic data (generated using the NITI model) produced maps of isotropic mechanical properties with undesirable dependence on the wavefield. Local anisotropy also caused wavefield-dependent errors of 7% in nearby isotropic structures, compared to 10% in the anisotropic structures.

在这项研究中，我们描述了一种异质、几乎不可压缩、横向各向同性 (NITI) 有限元 (FE) 模型的数值实现，该模型具有用于纤维软组织 MR 弹性成像的关键优势。MR 弹性成像 (MRE) 根据假定的组织响应力学模型从 MR 测量的谐波运动场中估计异质特性分布。当前的 MRE 特性估计方法通常假设各向同性特性，当存在各向异性时，这会导致模型数据不匹配而导致不一致。在这项研究中，我们使用由基本剪切模量、剪切各向异性、拉伸各向异性和各向同性体积模量参数化的 NITI 模型，该模型很好地描述了具有对齐纤维结构的组织的机械行为。属性和纤维方向异质性在 FE 高斯点级别实现，这允许将高分辨率扩散张量成像 (DTI) 数据轻松合并到模型中。生成的代码已针对分析解决方案和商业 FEM 包进行了验证，适用于并入非线性反演 MRE 算法。从解剖学、DTI 和 MRE 图像数据生成具有异质特性和各向异性纤维束的脑组织中的 MRE 模拟，产生类似于实验 MRE 的波场，从而可以在真实环境中研究 MRE 反演性能，其中地面实况和潜在的机械行为是已知的。两种已建立的各向同性反演算法——非线性反演（NLI）和局部直接反演（LDI）——被应用于模拟的 MRE 数据。两种算法在简单的各向同性同质情况下都表现良好；然而，由于违反局部同质性假设，异质性会导致 LDI 中的大量伪影。NLI 能够在存在测量噪声的情况下恢复准确的异质位移场。模拟各向异性数据（使用 NITI 模型生成）的各向同性 NLI 反演生成了各向同性力学性能图，这些图对波场具有不良依赖性。局部各向异性还导致附近各向同性结构中的波场相关误差为 7%，而各向异性结构中为 10%。NLI 能够在存在测量噪声的情况下恢复准确的异质位移场。模拟各向异性数据（使用 NITI 模型生成）的各向同性 NLI 反演生成了各向同性力学性能图，这些图对波场具有不良依赖性。局部各向异性还导致附近各向同性结构中的波场相关误差为 7%，而各向异性结构中为 10%。NLI 能够在存在测量噪声的情况下恢复准确的异质位移场。模拟各向异性数据（使用 NITI 模型生成）的各向同性 NLI 反演生成了各向同性力学性能图，这些图对波场具有不良依赖性。局部各向异性还导致附近各向同性结构中的波场相关误差为 7%，而各向异性结构中为 10%。