Transmission, attenuation and reflection of shear waves in the human brain

A longitudinal magnetic resonance elastography study of murine brain tumors following radiation therapy

An accurate and noninvasive method for assessing treatment response following radiotherapy is needed for both treatment monitoring and planning. Measurement of solid tumor volume alone is not sufficient for reliable early detection of therapeutic response, since changes in physiological and/or biomechanical properties can precede tumor volume change following therapy. In this study, we use magnetic resonance elastography to evaluate the treatment effect after radiotherapy in a murine brain tumor model. Shear modulus was calculated and compared between the delineated tumor region of interest (ROI) and its contralateral, mirrored counterpart. We also compared the shear modulus from both the irradiated and non-irradiated tumor and mirror ROIs longitudinally, sampling four time points spanning 9-19 d post tumor implant. Results showed that the tumor ROI had a lower shear modulus than that of the mirror ROI, independent of radiation. The shear modulus of the tumor ROI decreased over time for both the treated and untreated groups. By contrast, the shear modulus of the mirror ROI appeared to be relatively constant for the treated group, while an increasing trend was observed for the untreated group. The results provide insights into the tumor properties after radiation treatment and demonstrate the potential of using the mechanical properties of the tumor as a biomarker. In future studies, more closely spaced time points will be employed for detailed analysis of the radiation effect.

Evaluation of wave delivery methodology for brain MRE: Insights from computational simulations

PURPOSE

MR elastography (MRE) of the brain is being explored as a biomarker of neurodegenerative disease such as dementia. However, MRE measures for healthy brain have varied widely. Differing wave delivery methodologies may have influenced this, hence finite element-based simulations were performed to explore this possibility.

METHODS

The natural frequencies of a series of cranial models were calculated, and MRE-associated vibration was simulated for different wave delivery methods at varying frequency, using simple isotropic viscoelastic material models for the brain. Displacement fields and the corresponding brain constitutive properties estimated by standard inversion techniques were compared across delivery methods and frequencies.

RESULTS

The delivery methods produced widely different MRE displacement fields and inversions. Furthermore, resonances at natural frequencies influenced the displacement patterns. Consequently, some delivery methods led to lower inversion errors than others, and the error on the storage modulus varied by up to 11% between methods.

CONCLUSION

Wave delivery has a considerable impact on brain MRE reliability. Assuming small variations in brain biomechanics, as recently reported to accompany neurodegenerative disease (e.g., 7% for Alzheimer's disease), the effect of wave delivery is important. Hence, a consensus should be established on a consistent methodology to ensure diagnostic and prognostic consistency. Magn Reson Med 78:341-356, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Viscoelasticity of subcortical gray matter structures

Viscoelastic mechanical properties of the brain assessed with magnetic resonance elastography (MRE) are sensitive measures of microstructural tissue health in neurodegenerative conditions. Recent efforts have targeted measurements localized to specific neuroanatomical regions differentially affected in disease. In this work, we present a method for measuring the viscoelasticity in subcortical gray matter (SGM) structures, including the amygdala, hippocampus, caudate, putamen, pallidum, and thalamus. The method is based on incorporating high spatial resolution MRE imaging (1.6 mm isotropic voxels) with a mechanical inversion scheme designed to improve local measures in pre-defined regions (soft prior regularization [SPR]). We find that in 21 healthy, young volunteers SGM structures differ from each other in viscoelasticity, quantified as the shear stiffness and damping ratio, but also differ from the global viscoelasticity of the cerebrum. Through repeated examinations on a single volunteer, we estimate the uncertainty to be between 3 and 7% for each SGM measure. Furthermore, we demonstrate that the use of specific methodological considerations-higher spatial resolution and SPR-both decrease uncertainty and increase sensitivity of the SGM measures. The proposed method allows for reliable MRE measures of SGM viscoelasticity for future studies of neurodegenerative conditions. Hum Brain Mapp 37:4221-4233, 2016. © 2016 Wiley Periodicals, Inc.

3D multislab, multishot acquisition for fast, whole-brain MR elastography with high signal-to-noise efficiency

PURPOSE

To develop an acquisition scheme for generating MR elastography (MRE) displacement data with whole-brain coverage, high spatial resolution, and adequate signal-to-noise ratio (SNR) in a short scan time.

THEORY AND METHODS

A 3D multislab, multishot acquisition for whole-brain MRE with 2.0 mm isotropic spatial resolution is proposed. The multislab approach allowed for the use of short repetition time to achieve very high SNR efficiency. High SNR efficiency allowed for a reduced acquisition time of only 6 min while the minimum SNR needed for inversion was maintained.

RESULTS

The mechanical property maps estimated from whole-brain displacement data with nonlinear inversion (NLI) demonstrated excellent agreement with neuroanatomical features, including the cerebellum and brainstem. A comparison with an equivalent 2D acquisition illustrated the improvement in SNR efficiency of the 3D multislab acquisition. The flexibility afforded by the high SNR efficiency allowed for higher resolution with a 1.6 mm isotropic voxel size, which generated higher estimates of brainstem stiffness compared with the 2.0 mm isotropic acquisition.

CONCLUSION

The acquisition presented allows for the capture of whole-brain MRE displacement data in a short scan time, and may be used to generate local mechanical property estimates of neuroanatomical features throughout the brain.

Cerebral multifrequency MR elastography by remote excitation of intracranial shear waves

The aim of this study was to introduce remote wave excitation for high-resolution cerebral multifrequency MR elastography (mMRE). mMRE of 25-45-Hz drive frequencies by head rocker stimulation was compared with mMRE by remote wave excitation based on a thorax mat in 12 healthy volunteers. Maps of the magnitude |G*| and phase φ of the complex shear modulus were reconstructed using multifrequency dual elasto-visco (MDEV) inversion. After the scan, the subjects and three operators assessed the comfort and convenience of cerebral mMRE using two methods of stimulating the brain. Images were acquired in a coronal view in order to identify anatomical regions along the spinothalamic pathway. In mMRE by remote actuation, all subjects and operators appreciated an increased comfort and simplified procedural set-up. The resulting strain amplitudes in the brain were sufficiently large to analyze using MDEV inversion, and yielded high-resolution viscoelasticity maps which revealed specific anatomical details of brain mechanical properties: |G*| was lowest in the pons (0.97 ± 0.08 kPa) and decreased within the corticospinal tract in the caudal-cranial direction from the crus cerebri (1.64 ± 0.26 kPa) to the capsula interna (1.29 ± 0.14 kPa). By avoiding onerous mechanical stimulation of the head, remote excitation of intracranial shear waves can be used to measure viscoelastic parameters of the brain with high spatial resolution. Therewith, the new mMRE method is suitable for neuroradiological examinations in the clinic.

Magnetic resonance elastography of the brain: An in silico study to determine the influence of cranial anatomy

PURPOSE

Magnetic resonance elastography (MRE) of the brain has demonstrated potential as a biomarker of neurodegenerative disease such as dementia but requires further evaluation. Cranial anatomical features such as the falx cerebri and tentorium cerebelli membranes may influence MRE measurements through wave reflection and interference and tissue heterogeneity at their boundaries. We sought to determine the influence of these effects via simulation.

METHODS

MRE-associated mechanical stimulation of the brain was simulated using steady state harmonic finite element analysis. Simulations of geometrical models and anthropomorphic brain models derived from anatomical MRI data of healthy individuals were compared. Constitutive parameters were taken from MRE measurements for healthy brain. Viscoelastic moduli were reconstructed from the simulated displacement fields and compared with ground truth.

RESULTS

Interference patterns from reflections and heterogeneity resulted in artifacts in the reconstructions of viscoelastic moduli. Artifacts typically occurred in the vicinity of boundaries between different tissues within the cranium, with a magnitude of 10%-20%.

CONCLUSION

Given that MRE studies for neurodegenerative disease have reported only marginal variations in brain elasticity between controls and patients (e.g., 7% for Alzheimer's disease), the predicted errors are a potential confound to the development of MRE as a biomarker of dementia and other neurodegenerative diseases. Magn Reson Med 76:645-662, 2016. © 2015 Wiley Periodicals, Inc.

Improved measurement of brain deformation during mild head acceleration using a novel tagged MRI sequence

In vivo measurements of human brain deformation during mild acceleration are needed to help validate computational models of traumatic brain injury and to understand the factors that govern the mechanical response of the brain. Tagged magnetic resonance imaging is a powerful, noninvasive technique to track tissue motion in vivo which has been used to quantify brain deformation in live human subjects. However, these prior studies required from 72 to 144 head rotations to generate deformation data for a single image slice, precluding its use to investigate the entire brain in a single subject. Here, a novel method is introduced that significantly reduces temporal variability in the acquisition and improves the accuracy of displacement estimates. Optimization of the acquisition parameters in a gelatin phantom and three human subjects leads to a reduction in the number of rotations from 72 to 144 to as few as 8 for a single image slice. The ability to estimate accurate, well-resolved, fields of displacement and strain in far fewer repetitions will enable comprehensive studies of acceleration-induced deformation throughout the human brain in vivo.

Enhanced adult neurogenesis increases brain stiffness: in vivo magnetic resonance elastography in a mouse model of dopamine depletion

The mechanical network of the brain is a major contributor to neural health and has been recognized by in vivo magnetic resonance elastography (MRE) to be highly responsive to diseases. However, until now only brain softening was observed and no mechanism was known that reverses the common decrement of neural elasticity during aging or disease. We used MRE in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine hydrochloride (MPTP) mouse model for dopaminergic neurodegeneration as observed in Parkinson's disease (PD) to study the mechanical response of the brain on adult hippocampal neurogenesis as a robust correlate of neuronal plasticity in healthy and injured brain. We observed a steep transient rise in elasticity within the hippocampal region of up to over 50% six days after MPTP treatment correlating with increased neuronal density in the dentate gyrus, which could not be detected in healthy controls. Our results provide the first indication that new neurons reactively generated following neurodegeneration substantially contribute to the mechanical scaffold of the brain. Diagnostic neuroimaging may thus target on regions of the brain displaying symptomatically elevated elasticity values for the detection of neuronal plasticity following neurodegeneration.

The mechanics of traumatic brain injury: a review of what we know and what we need to know for reducing its societal burden

Traumatic brain injury (TBI) is a significant public health problem, on pace to become the third leading cause of death worldwide by 2020. Moreover, emerging evidence linking repeated mild traumatic brain injury to long-term neurodegenerative disorders points out that TBI can be both an acute disorder and a chronic disease. We are at an important transition point in our understanding of TBI, as past work has generated significant advances in better protecting us against some forms of moderate and severe TBI. However, we still lack a clear understanding of how to study milder forms of injury, such as concussion, or new forms of TBI that can occur from primary blast loading. In this review, we highlight the major advances made in understanding the biomechanical basis of TBI. We point out opportunities to generate significant new advances in our understanding of TBI biomechanics, especially as it appears across the molecular, cellular, and whole organ scale.

Strain Localization in an Oscillating Maxwell Viscoelastic Cylinder

The transient rotation responses of simple, axisymmetric, viscoelastic structures are of interest for interpretation of experiments designed to characterize materials and closed structures such as the brain using magnetic resonance techniques. Here, we studied the response of a Maxwell viscoelastic cylinder to small, sinusoidal displacement of its outer boundary. The transient strain field can be calculated in closed form using any of several conventional approaches. The solution is surprising: the strain field develops a singularity that appears when the wavefront leaves the center of the cylinder, and persists as the wavefront reflects to the outer boundary and back to the center of the cylinder. The singularity is alternately annihilated and reinitiated upon subsequent departures of the wavefront from the center of the cylinder until it disappears in the limit of steady state oscillations. We present the solution for this strain field, characterize the nature of this singularity, and discuss its potential role in the mechanical response and evolved morphology of the brain.

MR elastography in a murine stroke model reveals correlation of macroscopic viscoelastic properties of the brain with neuronal density

The aim of this study was to investigate the influence of neuronal density on viscoelastic parameters of living brain tissue after ischemic infarction in the mouse using MR elastography (MRE). Transient middle cerebral artery occlusion (MCAO) in the left hemisphere was induced in 20 mice. In vivo 7-T MRE at a vibration frequency of 900 Hz was performed on days 3, 7, 14 and 28 (n = 5 per group) after MCAO, followed by the analysis of histological markers, such as neuron counts (NeuN). MCAO led to a significant reduction in the storage modulus in the left hemisphere relative to contralateral values (p = 0.03) without changes over time. A correlation between storage modulus and NeuN in both hemispheres was observed, with correlation coefficients of R = 0.648 (p = 0.002, left) and R = 0.622 (p = 0.003, right). The loss modulus was less sensitive to MCAO, but correlated with NeuN in the left hemisphere (R = 0.764, p = 0.0001). In agreement with the literature, these results suggest that the shear modulus in the brain is reduced after transient ischemic insult. Furthermore, our study provides evidence that the in vivo shear modulus of brain tissue correlates with neuronal density. In diagnostic applications, MRE may thus have diagnostic potential as a tool for image-based quantification of neurodegenerative processes.

Cerebral magnetic resonance elastography in supranuclear palsy and idiopathic Parkinson's disease

Detection and discrimination of neurodegenerative Parkinson syndromes are challenging clinical tasks and the use of standard T₁- and T₂-weighted cerebral magnetic resonance (MR) imaging is limited to exclude symptomatic Parkinsonism. We used a quantitative structural MR-based technique, MR-elastography (MRE), to assess viscoelastic properties of the brain, providing insights into altered tissue architecture in neurodegenerative diseases on a macroscopic level. We measured single-slice multifrequency MRE (MMRE) and three-dimensional MRE (3DMRE) in two neurodegenerative disorders with overlapping clinical presentation but different neuropathology — progressive supranuclear palsy (PSP: N = 16) and idiopathic Parkinson's disease (PD: N = 18) as well as in controls (N = 18). In PSP, both MMRE (Δμ = − 28.8%, Δα = − 4.9%) and 3DMRE (Δ|G*|: − 10.6%, Δφ: − 34.6%) were significantly reduced compared to controls, with a pronounced reduction within the lentiform nucleus (Δμ = − 34.6%, Δα = − 8.1%; Δ|G*|: − 7.8%, Δφ: − 44.8%). MRE in PD showed a comparable pattern, but overall reduction in brain elasticity was less severe reaching significance only in the lentiform nucleus (Δμ n.s., Δα = − 7.4%; Δ|G*|: − 6.9%, Δφ: n.s.). Beyond that, patients showed a close negative correlation between MRE constants and clinical severity. Our data indicate that brain viscoelasticity in PSP and PD is differently affected by the underlying neurodegeneration; whereas in PSP all MRE constants are reduced and changes in brain softness (reduced μ and |G*|) predominate those of viscosity (α and φ) in PD.

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We assessed brain viscoelasticity in neurodegenerative disorders by MR-elastography.

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Parameters of brain softness and viscosity are reduced in PSP, particularly in the lentiform nucleus.

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Reduction of viscoelasticity in Parkinson’s disease is less severe and limited to brain softness.

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Reduction of brain viscoelasticity is correlated with measures of clinical severity.

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Combination of MMRE and 3DMRE is a sensitive tool to quantify regional neurodegeneration.

Mechanical properties of viscoelastic media by local frequency estimation of divergence-free wave fields

Magnetic resonance elastography (MRE) is an imaging modality with which mechanical properties can be noninvasively measured in living tissue. Magnetic resonance elastography relies on the fact that the elastic shear modulus determines the phase velocity and, hence the wavelength, of shear waves which are visualized by motion-sensitive MR imaging. Local frequency estimation (LFE) has been used to extract the local wavenumber from displacement wave fields recorded by MRE. LFE -based inversion is attractive because it allows material parameters to be estimated without explicitly invoking the equations governing wave propagation, thus obviating the need to numerically compute the Laplacian. Nevertheless, studies using LFE have not explicitly addressed three important issues: (1) tissue viscoelasticity; (2) the effects of longitudinal waves and rigid body motion on estimates of shear modulus; and (3) mechanical anisotropy. In the current study we extend the LFE technique to (1) estimate the (complex) viscoelastic shear modulus in lossy media; (2) eliminate the effects of longitudinal waves and rigid body motion; and (3) determine two distinct shear moduli in anisotropic media. The extended LFE approach is demonstrated by analyzing experimental data from a previously-characterized, isotropic, viscoelastic, gelatin phantom and simulated data from a computer model of anisotropic (transversely isotropic) soft material.

Towards an elastographic atlas of brain anatomy

Cerebral viscoelastic constants can be measured in a noninvasive, image-based way by magnetic resonance elastography (MRE) for the detection of neurological disorders. However, MRE brain maps of viscoelastic constants are still limited by low spatial resolution. Here we introduce three-dimensional multifrequency MRE of the brain combined with a novel reconstruction algorithm based on a model-free multifrequency inversion for calculating spatially resolved viscoelastic parameter maps of the human brain corresponding to the dynamic range of shear oscillations between 30 and 60 Hz. Maps of two viscoelastic parameters, the magnitude and the phase angle of the complex shear modulus, |G*| and φ, were obtained and normalized to group templates of 23 healthy volunteers in the age range of 22 to 72 years. This atlas of the anatomy of brain mechanics reveals a significant contrast in the stiffness parameter |G*| between different anatomical regions such as white matter (WM; 1.252±0.260 kPa), the corpus callosum genu (CCG; 1.104±0.280 kPa), the thalamus (TH; 1.058±0.208 kPa) and the head of the caudate nucleus (HCN; 0.649±0.101 kPa). φ, which is sensitive to the lossy behavior of the tissue, was in the order of CCG (1.011±0.172), TH (1.037±0.173), CN (0.906±0.257) and WM (0.854±0.169). The proposed method provides the first normalized maps of brain viscoelasticity with anatomical details in subcortical regions and provides useful background data for clinical applications of cerebral MRE.

Local mechanical properties of white matter structures in the human brain

The noninvasive measurement of the mechanical properties of brain tissue using magnetic resonance elastography (MRE) has emerged as a promising method for investigating neurological disorders. To date, brain MRE investigations have been limited to reporting global mechanical properties, though quantification of the stiffness of specific structures in the white matter architecture may be valuable in assessing the localized effects of disease. This paper reports the mechanical properties of the corpus callosum and corona radiata measured in healthy volunteers using MRE and atlas-based segmentation. Both structures were found to be significantly stiffer than overall white matter, with the corpus callosum exhibiting greater stiffness and less viscous damping than the corona radiata. Reliability of both local and global measures was assessed through repeated experiments, and the coefficient of variation for each measure was less than 10%. Mechanical properties within the corpus callosum and corona radiata demonstrated correlations with measures from diffusion tensor imaging pertaining to axonal microstructure.

Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter

White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve strain energy density functions that depend on the I4 and I5 pseudo-invariants of the Cauchy-Green strain tensor to account for the effects of relatively stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I4 but not on I5. Here, we explore the small strain limits of these models in the context of experimental measurements that probe these dependencies. Models in which strain energy depends on I4 but not I5 can capture differences in Young's (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I4 and I5 strain pseudo-invariants; and (2) behavior in the small strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.

Viscoelastic properties of the ferret brain measured in vivo at multiple frequencies by magnetic resonance elastography

Characterization of the dynamic mechanical behavior of brain tissue is essential for understanding and simulating the mechanisms of traumatic brain injury (TBI). Changes in mechanical properties may also reflect changes in the brain due to aging or disease. In this study, we used magnetic resonance elastography (MRE) to measure the viscoelastic properties of ferret brain tissue in vivo. Three-dimensional (3D) displacement fields were acquired during wave propagation in the brain induced by harmonic excitation of the skull at 400 Hz, 600 Hz and 800 Hz. Shear waves with wavelengths in the order of millimeters were clearly visible in the displacement field, in strain fields, and in the curl of displacement field (which contains no contributions from longitudinal waves). Viscoelastic parameters (storage and loss moduli) governing dynamic shear deformation were estimated in gray and white matter for these excitation frequencies. To characterize the reproducibility of measurements, two ferrets were studied on three different dates each. Estimated viscoelastic properties of white matter in the ferret brain were generally similar to those of gray matter and consistent between animals and scan dates. In both tissue types G' increased from approximately 3 kPa at 400 Hz to 7 kPa at 800 Hz and G″ increased from approximately 1 kPa at 400 Hz to 2 kPa at 800 Hz. These measurements of shear wave propagation in the ferret brain can be used to both parameterize and validate finite element models of brain biomechanics.

Quantitative imaging methods for the development and validation of brain biomechanics models

Rapid deformation of brain tissue in response to head impact or acceleration can lead to numerous pathological changes, both immediate and delayed. Modeling and simulation hold promise for illuminating the mechanisms of traumatic brain injury (TBI) and for developing preventive devices and strategies. However, mathematical models have predictive value only if they satisfy two conditions. First, they must capture the biomechanics of the brain as both a material and a structure, including the mechanics of brain tissue and its interactions with the skull. Second, they must be validated by direct comparison with experimental data. Emerging imaging technologies and recent imaging studies provide important data for these purposes. This review describes these techniques and data, with an emphasis on magnetic resonance imaging approaches. In combination, these imaging tools promise to extend our understanding of brain biomechanics and improve our ability to study TBI in silico.