Standard anatomical atlases are common in neuroimaging because they facilitate data analyses and comparisons across subjects and studies. The purpose of this study was to develop a standardized human brain atlas based on the physical mechanical properties (i.e., tissue viscoelasticity) of brain tissue using magnetic resonance elastography (MRE). MRE is a phase contrast-based MRI method that quantifies tissue viscoelasticity noninvasively and in vivo thus providing a macroscopic representation of the microstructural constituents of soft biological tissue. The development of standardized brain MRE atlases are therefore beneficial for comparing neural tissue integrity across populations. Data from a large number of healthy, young adults from multiple studies collected using common MRE acquisition and analysis protocols were assembled (N = 134; 78F/ 56 M; 18-35 years). Nonlinear image registration methods were applied to normalize viscoelastic property maps (shear stiffness, μ, and damping ratio, ξ) to the MNI152 standard structural template within the spatial coordinates of the ICBM-152. We find that average MRE brain templates contain emerging and

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.

Intrinsic actuation MR elastography (IA-MRE) exploits natural pulsations of the brain as a motion source to estimate mechanical property maps. The low frequency motion of IA-MRE introduces new considerations for inversion algorithms relative to traditional external actuation MRE. Specifically, inertial forces become very small, which leaves low frequency viscoelastic inversions with a non-unique scalar multiplier. Biphasic poroelastic inversions include additional fluid–solid interaction forces to balance the elastic forces, which avoids the non-uniqueness. Analyzing the convergence behavior from different starting values using 1 Hz simulated data, IA-MRE data from a gelatin phantom and in vivo brain IA-MRE data reveal that higher frequency (50 Hz) viscoelastic inversion reaches the correct, unique solution regardless of initial property estimate; whereas, low frequency viscoelastic inversion recovers relative values of shear modulus. In the presence of measurement noise, the non-unique scalar multiplier is determined by the softest material reaching the prescribed lower bound on shear modulus. Poroelastic inversion produces a unique solution at both 50 Hz and 1 Hz; however, hydraulic conductivity must be known or accurately estimated in order to recover quantitatively accurate shear modulus maps at low frequency.

River bed topography is of paramount importance for the study of fluvial hydraulics, flood prediction and river flow monitoring. It is therefore important to develop fast, easy-to-implement and cost-effective methods to determine underwater river topography. This paper presents a new one-step approach for reconstructing the river bed topography from known free surface data. This problem corresponds to the inverse of the classical hydrodynamic problem where the shallow water equations provide the free surface profile for a given river bed. We show in this work that instead of treating this inverse problem in the traditional partial differential equation (PDE)-constrained optimization framework, we can conveniently rearrange the governing equations for the direct problem to obtain an explicit PDE for the inverse problem. This leads to a direct solution of the inverse problem. An interesting consequence of the analysis is that the equations governing the forward and inverse problems have a very similar form, and the same discretization technique, based on an upwind conservative numerical scheme, can be used. The proposed methodology is successfully tested on a range of benchmark problems for noisy and noiseless free surface data. It was found that this solution approach creates very little amplification of noise.

Digital Image-based Elasto-Tomography (DIET) is a novel surface-based elasticity reconstruction method for determining the elastic property distribution within the breast. Following on from proof of concept simulation studies, this research considers the motion evaluation and stiffness reconstruction of a soft tissue approximating gelatine phantom. This initial phantom work provides an intermediate stage between prior simulation studies more detailed phantom studies to follow. Reference points on the surface of a cylindrical phantom were successfully tracked and converted into a steady-state motion description. Motion error based mechanical property reconstruction allowed an estimation of the stiffness of the gelatine when actuated at 50 Hz. The reconstructed stiffness compared favorably with independently measured stiffness properties of the gelatine material when experimental assumptions were considered. An experimental noise estimate of 50% was confirmed accurate by comparing experimental motions to simulated motion data with added noise.