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.

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.

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.

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 of the brain using multishot spiral readouts with self-navigated motion correction.

Magnetic resonance elastography (MRE) has been introduced in clinical practice as a possible surrogate for mechanical palpation, but its application to study the human brain in vivo has been limited by low spatial resolution and the complexity of the inverse problem associated with biomechanical property estimation. Here, we report significant improvements in brain MRE data acquisition by reporting images with high spatial resolution and signal-to-noise ratio as quantified by octahedral shear strain metrics. Specifically, we have developed a sequence for brain MRE based on multishot, variable-density spiral imaging, and three-dimensional displacement acquisition and implemented a correction scheme for any resulting phase errors. A Rayleigh damped model of brain tissue mechanics was adopted to represent the parenchyma and was integrated via a finite element-based iterative inversion algorithm. A multiresolution phantom study demonstrates the need for obtaining high-resolution MRE data when estimating focal mechanical properties. Measurements on three healthy volunteers demonstrate satisfactory resolution of gray and white matter, and mechanical heterogeneities correspond well with white matter histoarchitecture. Together, these advances enable MRE scans that result in high-fidelity, spatially resolved estimates of in vivo brain tissue mechanical properties, improving upon lower resolution MRE brain studies that only report volume averaged stiffness values.

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.

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.

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.

Subzone based magnetic resonance elastography using a Rayleigh damped material model.

PURPOSE: Recently, the attenuating behavior of soft tissue has been addressed in magnetic resonance elastography by the inclusion of a damping mechanism in the methods used to reconstruct the resulting mechanical property image. To date, this mechanism has been based on a viscoelastic model for material behavior. Rayleigh, or proportional, damping provides a more generalized model for elastic energy attenuation that uses two parameters to characterize contributions proportional to elastic and inertial forces. In the case of time-harmonic vibration, these two parameters lead to both the elastic modulus and the density being complex valued (as opposed to the case of pure viscoelasticity, where only the elastic modulus is complex valued). METHODS: This article presents a description of Rayleigh damping in the time-harmonic case, discussing the differences between this model and the viscoelastic damping models. In addition, the results from a subzone based Rayleigh damped elastography study of gelatin and tofu phantoms are discussed, along with preliminary results from in vivo breast data. RESULTS: Both the phantom and the tissue studies presented here indicate a change in the Rayleigh damping structure, described as Rayleigh composition, between different material types, with tofu and healthy tissue showing lower Rayleigh composition values than gelatin or cancerous tissue. CONCLUSIONS: It is possible that Rayleigh damping elastography and the concomitant Rayleigh composition images provide a mechanism for differentiating tissue structure in addition to measuring elastic stiffness and attenuation. Such information could be valuable in the use of Rayleigh damped magnetic resonance elastography as a diagnostic imaging tool.

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.

Digital image elasto-tomography: mechanical property estimation of silicone phantoms.

The application of a surface motion error based elasticity estimation method to hard and soft silicone phantom data is presented. Steady-state harmonic surface motion was measured at a limited number of measurement sites, and fitted with an ideal damped motion path. A finite element (FE) model was used to simulate phantom motion at a range of modulus and damping values. Comparing the simulated cases with the measured motion allowed estimation of the actual elastic properties of the silicone. These estimations compared favorably to static mechanical tests of the material, showing the DIET system can identify homogenous material stiffness values from surface motion measurements alone.

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.

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.

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.

A three-parameter mechanical property reconstruction method for MR-based elastic property imaging.

A reconstruction process featuring full parameterization of the three dimensional, time-harmonic equations of linear elasticity is developed and reconstructed property images are presented from simulation-based investigation. While interesting in its own right through the potential for increased adaptability of these reconstructive elastic imaging techniques, this study also presents a set of analysis tools used to study the poor convergence behavior found in the case of tissue like conditions (i.e. nearly incompressible materials). The choice of elastic properties for imaging in elastography research remains an open question at this point; the use of the stability and sensitivity-based analytical methods described here will help to predict and understand the value and reliability of different parameterizations of elasticity imaging. Additionally, though results indicate significant work needs to be done to achieve effective multiparameter reconstructive imaging, the methods detailed here offer the promise of increased flexibility and sophistication in elastographic imaging techniques.

Imaging the shear modulus of the heel fat pads.

BACKGROUND: Steady state, dynamic MR elastography provides quantitative images of the shear modulus of tissues in vivo. MR elastography was evaluated for its ability to characterize the mechanical properties of the weight bearing plantar soft tissues in vivo. METHODS: MR elastography was used to image the heel fat pad and surrounding soft tissues when the subject applied a low pressure on the foot and again when the subject applied high pressure. The placement of the foot was identical for both sets of images. FINDINGS: The results agree well with expected trends. The shear modulus of the tissue under the calcaneus increased from 8 kPa to 12 kPa with increasing pressure while that of peripheral tissues remained constant at 8 kPa which is similar to the shear modulus of fat in breast tissue. INTERPRETATION: Preliminary results from the steady state MR elastography methods being developed to measure the shear modulus of plantar soft tissues are promising. MR elastography is sufficiently accurate to observe the change in shear modulus with changes in applied pressure and is capable of characterizing the mechanical properties of the plantar soft tissues. Detailed anatomic information can be combined with co-registered mechanical properties. MR elastography could play a significant role in understanding the weight bearing functions of the plantar soft tissues and in evaluating those structures for improved diagnosis and assessment of disease progression.

Optimizing porous lattice structures for orthopaedic implants.

Porous lattice structures are increasingly used for tissue and implant device design, and require precise structural characteristics such as stiffness, porosity, volume fraction and surface area. A non-uniform distribution of these properties may be required to suit design requirements or to match in-vivo conditions. Thus, porous lattice design is complex due to competing objectives from the distributed structural properties. A lattice structural design and optimization methods is presented using global objective functions for effective stiffness, porosity, volume fraction and surface area.

Thresholds for detecting and characterizing focal lesions using steady-state MR elastography.

An objective contrast-detail analysis was performed in this study to assess the low contrast detectability of a clinical prototype harmonic magnetic resonance elastographic imaging system. Elastographic imaging was performed on gelatin phantoms containing spherical inclusions of varying size and modulus contrast. The results demonstrate that lesions as small as 5 mm can be detected with a minimum modulus contrast of 14 dB. However, the shear modulus of such small lesions was not accurately recovered. In general, the shear modulus of larger focal lesions was accurately (i.e., within 25% of the true value) recovered. The minimum modulus contrast needed to detect focal lesions was observed to decrease with increasing lesion size.

Parameter identification in a generalized time-harmonic Rayleigh damping model for elastography.

The identifiability of the two damping components of a Generalized Rayleigh Damping model is investigated through analysis of the continuum equilibrium equations as well as a simple spring-mass system. Generalized Rayleigh Damping provides a more diversified attenuation model than pure Viscoelasticity, with two parameters to describe attenuation effects and account for the complex damping behavior found in biological tissue. For heterogeneous Rayleigh Damped materials, there is no equivalent Viscoelastic system to describe the observed motions. For homogeneous systems, the inverse problem to determine the two Rayleigh Damping components is seen to be uniquely posed, in the sense that the inverse matrix for parameter identification is full rank, with certain conditions: when either multi-frequency data is available or when both shear and dilatational wave propagation is taken into account. For the multi-frequency case, the frequency dependency of the elastic parameters adds a level of complexity to the reconstruction problem that must be addressed for reasonable solutions. For the dilatational wave case, the accuracy of compressional wave measurement in fluid saturated soft tissues becomes an issue for qualitative parameter identification. These issues can be addressed with reasonable assumptions on the negligible damping levels of dilatational waves in soft tissue. In general, the parameters of a Generalized Rayleigh Damping model are identifiable for the elastography inverse problem, although with more complex conditions than the simpler Viscoelastic damping model. The value of this approach is the additional structural information provided by the Generalized Rayleigh Damping model, which can be linked to tissue composition as well as rheological interpretations.

Localization and detection of breast cancer tumors with digital image elasto-tomography.

Digital Image Elasto-Tomography (DIET) is a novel elastic contrast based breast imaging method using time-harmonic motion data obtained from a calibrated array of high resolution digital cameras scanning the tissue surface. The method is currently undergoing initial clinical testing and preliminary results in cases of malignant breast tumors are now available. The method has proved capable of detecting and localizing the stiff lesions within the heterogeneous tissue structure of the beast through the use of an evolution based optimization algorithm implemented in linear finite elements. The method has also proved successful at detecting both inclusion and non-inclusion cases in specially constructed tissue mimicking silicon phantoms.