Mechanical Properties of White Matter Tracts in Aging Assessed via Anisotropic MR Elastography.

Magnetic resonance elastography (MRE) is a promising neuroimaging technique to probe tissue microstructure, which has revealed widespread softening with loss of structural integrity in the aging brain. Traditional MRE approaches assume mechanical isotropy. However, white matter is known to be anisotropic from aligned, myelinated axonal bundles, which can lead to uncertainty in mechanical property estimates in these areas when using isotropic MRE. Recent advances in anisotropic MRE now allow for estimation of shear and tensile anisotropy, along with substrate shear modulus, in white matter tracts. The objective of this study was to investigate age-related differences in anisotropic mechanical properties in human brain white matter tracts for the first time. Anisotropic mechanical properties in all tracts were found to be significantly lower in older adults compared to young adults, with average property differences ranging between 0.028-0.107 for shear anisotropy and between 0.139-0.347 for tensile anisotropy. Stiffness perpendicular to the axonal fiber direction was also significantly lower in older age, but only in certain tracts. When compared with fractional anisotropy measures from diffusion tensor imaging, we found that anisotropic MRE measures provided additional, complementary information in describing differences between the white matter integrity of young and older populations. Anisotropic MRE provides a new tool for studying white matter structural integrity in aging and neurodegeneration.

Magnetic resonance elastography captures a transient benefit of exercise intervention on forebrain stiffness in a rat model of fetal alcohol spectrum disorders.

BACKGROUND: Fetal alcohol spectrum disorders (FASD), a group of prevalent conditions resulting from prenatal alcohol exposure, affect the maturation of cerebral white matter as first identified with neuroimaging. However, traditional methods are unable to track subtle microstructural alterations to white matter. This preliminary study uses a highly sensitive and clinically translatable magnetic resonance elastography (MRE) protocol to assess brain tissue microstructure through its mechanical properties following an exercise intervention in a rat model of FASD. METHODS: Female rat pups were either alcohol-exposed (AE) via intragastric intubation of alcohol in milk substitute (5.25 g/kg/day) or sham-intubated (SI) on postnatal days (PD) four through nine to model alcohol exposure during the brain growth spurt. On PD 30, half of AE and SI rats were randomly assigned to either a wheel-running or standard cage for 12 days. Magnetic resonance elastography was used to measure whole brain and callosal mechanical properties at the end of the intervention (around PD 42) and at 1 month post-intervention, and findings were validated with histological quantification of oligoglia. RESULTS: Alcohol exposure reduced forebrain stiffness (p = 0.02) in standard-housed rats. The adolescent exercise intervention mitigated this effect, confirming that increased aerobic activity supports proper neurodevelopmental trajectories. Forebrain damping ratio was lowest in standard-housed AE rats (p < 0.01), but this effect was not mitigated by intervention exposure. At 1 month post-intervention, all rats exhibited comparable forebrain stiffness and damping ratio (p > 0.05). Callosal stiffness and damping ratio increased with age. With cessation of exercise, there was a negative rebound effect on the quantity of callosal oligodendrocytes, irrespective of treatment group, which diverged from our MRE results. CONCLUSIONS: This is the first application of MRE to measure the brain's mechanical properties in a rodent model of FASD. MRE successfully captured alcohol-related changes in forebrain stiffness and damping ratio. Additionally, MRE identified an exercise-related increase to forebrain stiffness in AE rats.

Characterizing the Myoarchitecture of the Supraspinatus and Infraspinatus Muscles With MRI Using Diffusion Tensor Imaging.

BACKGROUND: The societal cost of shoulder disabilities in our aging society keeps rising. Providing biomarkers of early changes in the microstructure of rotator cuff (RC) muscles might improve surgical planning. Elevation angle (E1A) and pennation angle (PA) assessed by ultrasound change with RC tears. Furthermore, ultrasounds lack repeatability. PURPOSE: To propose a repeatable framework to quantify the myocyte angulation in RC muscles. STUDY TYPE: Prospective. SUBJECTS: Six asymptomatic healthy volunteers (1 female aged 30 years; 5 males, mean age 35 years, range 25-49 years), who underwent three repositioned scanning sessions (10 minutes apart) of the right infraspinatus muscle (ISPM) and supraspinatus muscle (SSPM). FIELD STRENGTH/SEQUENCE: 3-T, T1-weighted and diffusion tensor imaging (DTI; 12 gradient encoding directions, b-values of 500 and 800 s/mm2 ). ASSESSMENT: Each voxel was binned in percentage of depth defined by the shortest distance in the antero-posterior direction (manual delineation), i.e. the radial axis. A second order polynomial fit for PA across the muscle depth was used, while E1A described a sigmoid across depth: E 1 A sig = E 1 A range × sigmf 1 : 100 % depth , - EA 1 grad   ,   E 1 A asym + E 1 A shift . STATISTICAL TESTS: Repeatability was assessed with the nonparametric Wilcoxon's rank-sum test for paired comparisons across repeated scans in each volunteer for each anatomical muscle region and across repeated measures of the radial axis. A P-value <0.05 was considered statistically significant. RESULTS: In the ISPM, E1A was constantly negative, became helicoidal, then mainly positive across the antero-posterior depth, respective at the caudal, central and cranial regions. In the SSPM, posterior myocytes ran more parallel to the intramuscular tendon ( PA ≈ 0 ° ), while anterior myocytes inserted with a pennation angle ( PA ≈ - 20 ° ). E1A and PA were repeatable in each volunteer (error < 10%). Intra-repeatability of the radial axis was achieved (error < 5%). DATA CONCLUSION: ElA and PA in the proposed framework of the ISPM and SSPM are repeatable with DTI. Variations of myocyte angulation in the ISPM and SSPM can be quantified across volunteers. EVIDENCE LEVEL: 2 TECHNICAL EFFICACY: Stage 2.

Minimizing Measurement-Induced Errors in Viscoelastic MR Elastography.

The inverse problem that underlies Magnetic Resonance Elastography (MRE) is sensitive to the measurement data and the quality of the results of this tissue elasticity imaging process can be influenced both directly and indirectly by measurement noise. In this work, we apply a coupled adjoint field formulation of the viscoelastic constitutive parameter identification problem, where the indirect influence of noise through applied boundary conditions is avoided. A well-posed formulation of the coupled field problem is obtained through conditions applied to the adjoint field, relieving the computed displacement field from kinematic errors on the boundary. The theoretical framework for this formulation via a nearly incompressible, parallel subdomain-decomposition approach is presented, along with verification and a detailed exploration of the performance of the methods via a numerical simulation study. In addition, the advantages of this novel approach are demonstrated in-vivo in the human brain, showing the ability of the method to obtain viable tissue property maps in difficult configurations, enhancing the accuracy of the method.

Estimating the viscoelastic properties of the human brain at 7 T MRI using intrinsic MRE and nonlinear inversion.

Intrinsic actuation magnetic resonance elastography (MRE) is a phase-contrast MRI technique that allows for in vivo quantification of mechanical properties of the brain by exploiting brain motion that arise naturally due to the cardiac pulse. The mechanical properties of the brain reflect its tissue microstructure, making it a potentially valuable parameter in studying brain disease. The main purpose of this study was to assess the feasibility of reconstructing the viscoelastic properties of the brain using high-quality 7 T MRI displacement measurements, obtained using displacement encoding with stimulated echoes (DENSE) and intrinsic actuation. The repeatability and sensitivity of the method for detecting normal regional variation in brain tissue properties was assessed as secondary goal. The displacement measurements used in this analysis were previously acquired for a separate study, where eight healthy subjects (27 ± 7 years) were imaged with repeated scans (spatial resolution approx. 2 mm isotropic, temporal resolution 75 ms, motion sensitivity 0.35 mm/2π for displacements in anterior-posterior and left-right directions, and 0.7 mm/2π for feet-head displacements). The viscoelastic properties of the brain were estimated using a subzone based non-linear inversion scheme. The results show comparable consistency to that of extrinsic MRE between the viscoelastic property maps obtained from repeated displacement measurements. The shear stiffness maps showed fairly consistent spatial patterns. The whole-brain repeatability coefficient (RC) for shear stiffness was (mean ± standard deviation) 8 ± 8% relative to the mean whole-brain stiffness, and the damping ratio RC was 28 ± 17% relative to the whole-brain damping ratio. The shear stiffness maps showed similar statistically significant regional trends as demonstrated in a publicly available atlas of viscoelastic properties obtained with extrinsic actuation MRE at 50 Hz. The damping ratio maps showed less consistency, likely due to data-model mismatch of describing the brain as a viscoelastic material under low frequencies. While artifacts induced by fluid flow within the brain remain a limitation of the technique in its current state, intrinsic actuation based MRE allow for consistent and repeatable estimation of the mechanical properties of the brain. The method provides enough sensitivity to investigate regional variation in such properties in the normal brain, which is likely sufficient to also investigate pathological changes.

Monitoring lasting changes to brain tissue integrity through mechanical properties following adolescent exercise intervention in a rat model of Fetal Alcohol Spectrum Disorders.

Background: Fetal Alcohol Spectrum Disorders (FASD) encompass a group of highly prevalent conditions resulting from prenatal alcohol exposure. Alcohol exposure during the third trimester of pregnancy overlapping with the brain growth spurt is detrimental to white matter growth and myelination, particularly in the corpus callosum, ultimately affecting tissue integrity in adolescence. Traditional neuroimaging techniques have been essential for assessing neurodevelopment in affected youth; however, these methods are limited in their capacity to track subtle microstructural alterations to white matter, thus restricting their effectiveness in monitoring therapeutic intervention. In this preliminary study we use a highly sensitive and clinically translatable Magnetic Resonance Elastography (MRE) protocol for assessing brain tissue microstructure through its mechanical properties following an exercise intervention in a rat model of FASD. Methods: Rat pups were divided into two groups: alcohol-exposed (AE) pups which received alcohol in milk substitute (5.25 g/kg/day) via intragastric intubation on postnatal days (PD) four through nine during the rat brain growth spurt (Dobbing and Sands, 1979), or sham-intubated (SI) controls. In adolescence, on PD 30, half AE and SI rats were randomly assigned to either a modified home cage with free access to a running wheel or to a new home cage for 12 days (Gursky and Klintsova, 2017). Previous studies conducted in the lab have shown that 12 days of voluntary exercise intervention in adolescence immediately ameliorated callosal myelination in AE rats (Milbocker et al., 2022, 2023). MRE was used to measure longitudinal changes to mechanical properties of the whole brain and the corpus callosum at intervention termination and one-month post-intervention. Histological quantification of precursor and myelinating oligoglia in corpus callosum was performed one-month post-intervention. Results: Prior to intervention, AE rats had lower forebrain stiffness in adolescence compared to SI controls ( p = 0.02). Exercise intervention immediately mitigated this effect in AE rats, resulting in higher forebrain stiffness post-intervention in adolescence. Similarly, we discovered that forebrain damping ratio was lowest in AE rats in adolescence ( p < 0.01), irrespective of intervention exposure. One-month post-intervention in adulthood, AE and SI rats exhibited comparable forebrain stiffness and damping ratio (p > 0.05). Taken together, these MRE data suggest that adolescent exercise intervention supports neurodevelopmental "catch-up" in AE rats. Analysis of the stiffness and damping ratio of the body of corpus callosum revealed that these measures increased with age. Finally, histological quantification of myelinating oligodendrocytes one-month post-intervention revealed a negative rebound effect of exercise cessation on the total estimate of these cells in the body of corpus callosum, irrespective of treatment group which was not convergent with noninvasive MRE measures. Conclusions: This is the first application of MRE to measure changes in brain mechanical properties in a rodent model of FASD. MRE successfully captured alcohol-related changes to forebrain stiffness and damping ratio in adolescence. These preliminary findings expand upon results from previous studies which used traditional diffusion neuroimaging to identify structural changes to the adolescent brain in rodent models of FASD (Milbocker et al., 2022; Newville et al., 2017). Additionally, in vivo MRE identified an exercise-related alteration to forebrain stiffness that occurred in adolescence, immediately post-intervention.

General guidelines for the performance of viscoelastic property identification in elastography: A Monte-Carlo analysis from a closed-form solution.

Identification of the mechanical properties of a viscoelastic material depends on characteristics of the observed motion field within the object in question. For certain physical and experimental configurations and certain resolutions and variance within the measurement data, the viscoelastic properties of an object may become non-identifiable. Elastographic imaging methods seek to provide maps of these viscoelastic properties based on displacement data measured by traditional imaging techniques, such as magnetic resonance and ultrasound. Here, 1D analytic solutions of the viscoelastic wave equation are used to generate displacement fields over wave conditions representative of diverse time-harmonic elastography applications. These solutions are tested through the minimization of a least squares objective function suitable for framing the elastography inverse calculation. Analysis shows that the damping ratio and the ratio of the viscoelastic wavelength to the size of the domain play critical roles in the form of this least squares objective function. In addition, it can be shown analytically that this objective function will contain local minima, which hinder discovery of the global minima via gradient descent methods.

Imaging the subcellular viscoelastic properties of mouse oocytes.

In recent years, cellular biomechanical properties have been investigated as an alternative to morphological assessments for oocyte selection in reproductive science. Despite the high relevance of cell viscoelasticity characterization, the reconstruction of spatially distributed viscoelastic parameter images in such materials remains a major challenge. Here, a framework for mapping viscoelasticity at the subcellular scale is proposed and applied to live mouse oocytes. The strategy relies on the principles of optical microelastography for imaging in combination with the overlapping subzone nonlinear inversion technique for complex-valued shear modulus reconstruction. The three-dimensional nature of the viscoelasticity equations was accommodated by applying an oocyte geometry-based 3D mechanical motion model to the measured wave field. Five domains-nucleolus, nucleus, cytoplasm, perivitelline space, and zona pellucida-could be visually differentiated in both oocyte storage and loss modulus maps, and statistically significant differences were observed between most of these domains in either property reconstruction. The method proposed herein presents excellent potential for biomechanical-based monitoring of oocyte health and complex transformations across lifespan. It also shows appreciable latitude for generalization to cells of arbitrary shape using conventional microscopy equipment.

Transversely-isotropic brain in vivo MR elastography with anisotropic damping.

Measuring tissue parameters from increasingly sophisticated mechanical property models may uncover new contrast mechanisms with clinical utility. Building on previous work on in vivo brain MR elastography (MRE) with a transversely-isotropic with isotropic damping (TI-ID) model, we explore a new transversely-isotropic with anisotropic damping (TI-AD) model that involves six independent parameters describing direction-dependent behavior for both stiffness and damping. The direction of mechanical anisotropy is determined by diffusion tensor imaging and we fit three complex-valued moduli distributions across the full brain volume to minimize differences between measured and modeled displacements. We demonstrate spatially accurate property reconstruction in an idealized shell phantom simulation, as well as an ensemble of 20 realistic, randomly-generated simulated brains. We characterize the simulated precisions of all six parameters across major white matter tracts to be high, suggesting that they can be measured independently with acceptable accuracy from MRE data. Finally, we present in vivo anisotropic damping MRE reconstruction data. We perform t-tests on eight repeated MRE brain exams on a single-subject, and find that the three damping parameters are statistically distinct for most tracts, lobes and the whole brain. We also show that population variations in a 17-subject cohort exceed single-subject measurement repeatability for most tracts, lobes and whole brain, for all six parameters. These results suggest that the TI-AD model offers new information that may support differential diagnosis of brain diseases.

In vivoestimation of anisotropic mechanical properties of the gastrocnemius during functional loading with MR elastography.

Objective.In vivoimaging assessments of skeletal muscle structure and function allow for longitudinal quantification of tissue health. Magnetic resonance elastography (MRE) non-invasively quantifies tissue mechanical properties, allowing for evaluation of skeletal muscle biomechanics in response to loading, creating a better understanding of muscle functional health.Approach. In this study, we analyze the anisotropic mechanical response of calf muscles using MRE with a transversely isotropic, nonlinear inversion algorithm (TI-NLI) to investigate the role of muscle fiber stiffening under load. We estimate anisotropic material parameters including fiber shear stiffness (µ1), substrate shear stiffness (µ2), shear anisotropy (ϕ), and tensile anisotropy (ζ) of the gastrocnemius muscle in response to both passive and active tension.Main results. In passive tension, we found a significant increase inµ1,ϕ,andζwith increasing muscle length. While in active tension, we observed increasingµ2and decreasingϕandζduring active dorsiflexion and plantarflexion-indicating less anisotropy-with greater effects when the muscles act as agonist.Significance. The study demonstrates the ability of this anisotropic MRE method to capture the multifaceted mechanical response of skeletal muscle to tissue loading from muscle lengthening and contraction.

Intersession Repeatability of Diffusion-Tensor Imaging in the Supraspinatus and the Infraspinatus Muscles of Volunteers.

BACKGROUND: Quantifying the rotator cuff (RC) muscles' viscoelasticity could provide outcome relevant information in patients with RC tears. MR-elastography requires robust diffusion-tensor imaging (DTI) to account for tissue anisotropy in muscles stiffness computation. PURPOSE: To assess the repeatability of DTI parameters in the supraspinatus and infraspinatus muscles and to explore DTI tractography conformity with the muscles' anatomy. STUDY TYPE: Prospective. SUBJECTS: Six healthy volunteers underwent three consecutive shoulder MRI sessions about 10 minutes apart. FIELD STRENGTH/SEQUENCE: 3T/T1-vibe Dixon and Spin echo EPI DTI (12 gradient encoding directions, b-values 500 and 800 sec/mm2 ). ASSESSMENT: Supraspinatus and infraspinatus muscles were segmented on the T1-vibe Dixon sequence. DTI image quality was assessed using a quantitative threshold based on the signal-to-noise ratio (SNR). The eigenvalues ( λ 1 , λ 2 , λ 3 ), fractional anisotropy (FA) and mean diffusivity were calculated. DTI tractography was visually assessed. STATISTICAL TESTS: DTI parameters within-subject intersession repeatability was assessed with Bland-Altman analysis and the coefficient of variation (CV). Repeatability was considered good for CV < 10%. RESULTS: The SNR between diffusion-weighted and non-diffusion-weighted images was greater than 3, which aligns with standards for estimating DTI parameters. The FA showed the lowest mean bias (-0.007; 95% confidence interval [CI] -0.031 to 0.018) whereas the λ1 had the highest mean bias (0.146 × 10-3  mm2 /sec; CI -0.034 to 0.326 × 10-3  mm2 /sec). CVs of the DTI parameters varied between 3.5% (FA) and 8.4% (λ3 ) for the supraspinatus and between 3.2% (λ1 ) and 6.8% (λ3 ) for the infraspinatus. Tractography provided muscle fiber representations in three-dimensional space concordant with RC anatomy. DATA CONCLUSION: DTI of the supraspinatus and infraspinatus muscles achieved an adequate SNR, allowing the measurement of the DTI metrics with good repeatability, and thus can be used for optimizing stiffness estimation in these anisotropic tissues. EVIDENCE LEVEL: 2 TECHNICAL EFFICACY: Stage 2.

Anisotropic mechanical properties in the healthy human brain estimated with multi-excitation transversely isotropic MR elastography.

Magnetic resonance elastography (MRE) is an MRI technique for imaging the mechanical properties of brain in vivo, and has shown differences in properties between neuroanatomical regions and sensitivity to aging, neurological disorders, and normal brain function. Past MRE studies investigating these properties have typically assumed the brain is mechanically isotropic, though the aligned fibers of white matter suggest an anisotropic material model should be considered for more accurate parameter estimation. Here we used a transversely isotropic, nonlinear inversion algorithm (TI-NLI) and multiexcitation MRE to estimate the anisotropic material parameters of individual white matter tracts in healthy young adults. We found significant differences between individual tracts for three recovered anisotropic parameters: substrate shear stiffness, µ (range: 2.57 - 3.02 kPa), shear anisotropy, ϕ (range: -0.026 - 0.164), and tensile anisotropy, ζ (range: 0.559 - 1.049). Additionally, we demonstrated the repeatability of these parameter estimates in terms of lower variability of repeated measures in a single subject relative to variability in our sample population. Further, we observed significant differences in anisotropic mechanical properties between segments of the corpus callosum (genu, body, and splenium), which is expected based on differences in axonal microstructure. This study shows the ability of MRE with TI-NLI to estimate anisotropic mechanical properties of white matter and presents reference properties for tracts throughout the healthy brain.

Mapping heterogenous anisotropic tissue mechanical properties with transverse isotropic nonlinear inversion MR elastography.

The white matter tracts of brain tissue consist of highly-aligned, myelinated fibers; white matter is structurally anisotropic and is expected to exhibit anisotropic mechanical behavior. In vivo mechanical properties of tissue can be imaged using magnetic resonance elastography (MRE). MRE can detect and monitor natural and disease processes that affect tissue structure; however, most MRE inversion algorithms assume locally homogenous properties and/or isotropic behavior, which can cause artifacts in white matter regions. A heterogeneous, model-based transverse isotropic implementation of a subzone-based nonlinear inversion (TI-NLI) is demonstrated. TI-NLI reconstructs accurate maps of the shear modulus, damping ratio, shear anisotropy, and tensile anisotropy of in vivo brain tissue using standard MRE motion measurements and fiber directions estimated from diffusion tensor imaging (DTI). TI-NLI accuracy was investigated with using synthetic data in both controlled and realistic settings: excellent quantitative and spatial accuracy was observed and cross-talk between estimated parameters was minimal. Ten repeated, in vivo, MRE scans acquired from a healthy subject were co-registered to demonstrate repeatability of the technique. Good resolution of anatomical structures and bilateral symmetry were evident in MRE images of all mechanical property types. Repeatability was similar to isotropic MRE methods and well within the limits required for clinical success. TI-NLI MRE is a promising new technique for clinical research into anisotropic tissues such as the brain and muscle.

Quantifying stability of parameter estimates forin vivonearly incompressible transversely-isotropic brain MR elastography.

Easily computable quality metrics for measured medical data at point-of-care are important for imaging technologies involving offline reconstruction. Accordingly, we developed a new data quality metric forin vivotransversely-isotropic (TI) magnetic resonance elastography (MRE) based on a generalization of the widely accepted octahedral shear-strain calculation. The metric uses MRE displacement data and an estimate of the TI property field to yield a 'stability map' which predicts regions of low versus high accuracy in the resulting material property reconstructions. We can also calculate an average TI parameter stability (TIPS) score over all voxels in a region of interest for a given measurement to indicate how reliable the recovered mechanical property estimate for the region is expected to be. The calculation is rapid and places little demand on computing resources compared to the computationally intensive material property reconstruction from non-linear inversion (TI-NLI) of displacement fields, making it ideal for point-of-care evaluation of data quality. We test the predictions of the stability map for both simulated phantoms andin vivohuman brain data. We used a range of different displacement datasets from vibrations applied in the anterior-posterior (AP), left-right (LR) and combined AP + LR directions. The TIPS and variability maps (noise sensitivity or variation from the mean of repeated MRE scans) were consistently anti-correlated. Notably, Spearman correlation coefficients ∣R∣>0.6 were found between variability and TIPS score for individual white matter tracts within vivodata. These observations demonstrate the reliability and promise of this data quality metric to screen data rapidly in realistic clinical MRE applications.

Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico.

Magnetic Resonance Elastography allows noninvasive visualization of tissue mechanical properties by measuring the displacements resulting from applied stresses, and fitting a mechanical model. Poroelasticity naturally lends itself to describing tissue - a biphasic medium, consisting of both solid and fluid components. This article reviews the theory of poroelasticity, and shows that the spatial distribution of hydraulic permeability, the ease with which the solid matrix permits the flow of fluid under a pressure gradient, can be faithfully reconstructed without spatial priors in simulated environments. The paper describes an in-house MRE computational platform - a multi-mesh, finite element poroelastic solver coupled to an artificial epistemic agent capable of running Bayesian inference to reconstruct inhomogenous model mechanical property images from measured displacement fields. Building on prior work, the domain of convergence for inference is explored, showing that hydraulic permeabilities over several orders of magnitude can be reconstructed given very little prior knowledge of the true spatial distribution.

Standard-space atlas of the viscoelastic properties of the human brain.

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 symmetrized anatomical detail. Leveraging the substantial amount of data assembled, we illustrate that subcortical gray matter structures, white matter tracts, and regions of the cerebral cortex exhibit differing mechanical characteristics. Moreover, we report sex differences in viscoelasticity for specific neuroanatomical structures, which has implications for understanding patterns of individual differences in health and disease. These atlases provide reference values for clinical investigations as well as novel biophysical signatures of neuroanatomy. The templates are made openly available (github.com/mechneurolab/mre134) to foster collaboration across research institutions and to support robust cross-center comparisons.

Uniqueness of poroelastic and viscoelastic nonlinear inversion MR elastography at low frequencies.

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.

A numerical framework for interstitial fluid pressure imaging in poroelastic MRE.

A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed.

Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography.

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.

Observation of direction-dependent mechanical properties in the human brain with multi-excitation MR elastography.

Magnetic resonance elastography (MRE) has shown promise in noninvasively capturing changes in mechanical properties of the human brain caused by neurodegenerative conditions. MRE involves vibrating the brain to generate shear waves, imaging those waves with MRI, and solving an inverse problem to determine mechanical properties. Despite the known anisotropic nature of brain tissue, the inverse problem in brain MRE is based on an isotropic mechanical model. In this study, distinct wave patterns are generated in the brain through the use of multiple excitation directions in order to characterize the potential impact of anisotropic tissue mechanics on isotropic inversion methods. Isotropic inversions of two unique displacement fields result in mechanical property maps that vary locally in areas of highly aligned white matter. Investigation of the corpus callosum, corona radiata, and superior longitudinal fasciculus, three highly ordered white matter tracts, revealed differences in estimated properties between excitations of up to 33%. Using diffusion tensor imaging to identify dominant fiber orientation of bundles, relationships between estimated isotropic properties and shear asymmetry are revealed. This study has implications for future isotropic and anisotropic MRE studies of white matter tracts in the human brain.