Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography

The Networking Brain: How Extracellular Matrix, Cellular Networks, and Vasculature Shape the In Vivo Mechanical Properties of the Brain

Mechanically, the brain is characterized by both solid and fluid properties. The resulting unique material behavior fosters proliferation, differentiation, and repair of cellular and vascular networks, and optimally protects them from damaging shear forces. Magnetic resonance elastography (MRE) is a noninvasive imaging technique that maps the mechanical properties of the brain in vivo. MRE studies have shown that abnormal processes such as neuronal degeneration, demyelination, inflammation, and vascular leakage lead to tissue softening. In contrast, neuronal proliferation, cellular network formation, and higher vascular pressure result in brain stiffening. In addition, brain viscosity has been reported to change with normal blood perfusion variability and brain maturation as well as disease conditions such as tumor invasion. In this article, the contributions of the neuronal, glial, extracellular, and vascular networks are discussed to the coarse-grained parameters determined by MRE. This reductionist multi-network model of brain mechanics helps to explain many MRE observations in terms of microanatomical changes and suggests that cerebral viscoelasticity is a suitable imaging marker for brain disease.

Effect of polymerization on free water in polyacrylamide hydrogels observed with Brillouin spectroscopy

Brillouin spectroscopy is used to determine the effects of polymer concentration, crosslinking density, and polymerization on the longitudinal storage and loss moduli of polyacrylamide hydrogels. The model established by Chiarelli et al. is implemented to calculate the speed of sound in the free water [Chiarelli et al., The Journal of the Acoustical Society of America, 2010, 127(3), 1197-1207]. The polymer concentration has the greatest effect on the moduli of the polymer matrix. We determined that the crosslink density has no measurable effect on the logitudinal storage or loss modulus of polyacrylamide hydrogels when measurements are made at GHz frequencies, in contrast to measurements made at kHz frequencies as documented by other studies. However, the moduli are independent of monomer concentration if the acrylamide is not polymerized. We show at the GHz frequency that the incorporation of acrylamide polymer chains affects the mechanical properties of the free water. The speed of sound in the free water is reduced by the introduction of polymerized acrylamide. The long polymer chains and their interactions with the bounded water disrupt the bonding organization of the unbound water, causing a reduction of the average hydrogen bond strength between free water molecules. This results in a decreased speed of sound in the free water and an increase in the longitudinal storage modulus of the hydrogel.

Feasibility of assessing non-invasive intracranial compliance using FSI simulation-based and MR elastography-based brain stiffness

Intracranial compliance (ICC) refers to the change in intracranial volume per unit change in intracranial pressure (ICP). Magnetic resonance elastography (MRE) quantifies brain stiffness by measuring the shear modulus. Our objective is to investigate the relationship between ICC and brain stiffness through fluid-structure interaction (FSI) simulation, and to explore the feasibility of using MRE to assess ICC based on brain stiffness. This is invaluable due to the clinical importance of ICC, as well as the fast and non-invasive nature of the MRE procedure. We employed FSI simulation in hydrocephalus patients with aqueductal stenosis to non-invasively calculate ICP which is the basis of the calculation of ICC and FSI-based brain stiffness. The FSI simulated parameters used have been validated with experimental data. Our results showed that there is no relationship between FSI simulated-based brain stiffness and ICC in hydrocephalus patients. However, MRE-based brain stiffness may be sensitive to changes in intracranial fluid dynamic parameters such as cerebral perfusion pressure (CPP), cerebral blood flow (CBF), and ICP, as well as to mechano-vascular changes in the brain, which are determining parameters in ICC assessment. Although optimism has been found regarding the assessment of ICC using MRE-based brain stiffness, especially for acute-onset brain disorders, further studies are necessary to clarify their direct relationship.

Magnetic resonance elastography resolving all gross anatomical segments of the kidney during controlled hydration

Introduction: Magnetic resonance elastography (MRE) is a non-invasive method to quantify biomechanical properties of human tissues. It has potential in diagnosis and monitoring of kidney disease, if established in clinical practice. The interplay of flow and volume changes in renal vessels, tubule, urinary collection system and interstitium is complex, but physiological ranges of in vivo viscoelastic properties during fasting and hydration have never been investigated in all gross anatomical segments simultaneously. Method: Ten healthy volunteers underwent two imaging sessions, one following a 12-hour fasting period and the second after a drinking challenge of >10 mL per kg body weight (60-75 min before the second examination). High-resolution renal MRE was performed using a novel driver with rotating eccentric mass placed at the posterior-lateral wall to couple waves (50 Hz) to the kidney. The biomechanical parameters, shear wave speed (cs in m/s), storage modulus (Gd in kPa), loss modulus (Gl in kPa), phase angle ( Υ = 2 π atan G l G d ) and attenuation (α in 1/mm) were derived. Accurate separation of gross anatomical segments was applied in post-processing (whole kidney, cortex, medulla, sinus, vessel). Results: High-quality shear waves coupled into all gross anatomical segments of the kidney (mean shear wave displacement: 163 ± 47 μm, mean contamination of second upper harmonics <23%, curl/divergence: 4.3 ± 0.8). Regardless of the hydration state, median Gd of the cortex and medulla (0.68 ± 0.11 kPa) was significantly higher than that of the sinus and vessels (0.48 ± 0.06 kPa), and consistently, significant differences were found in cs, Υ , and Gl (all p < 0.001). The viscoelastic parameters of cortex and medulla were not significantly different. After hydration sinus exhibited a small but significant reduction in median Gd by -0.02 ± 0.04 kPa (p = 0.01), and, consequently, the cortico-sinusoidal-difference in Gd increased by 0.04 ± 0.07 kPa (p = 0.05). Only upon hydration, the attenuation in vessels became lower (0.084 ± 0.013 1/mm) and differed significantly from the whole kidney (0.095 ± 0.007 1/mm, p = 0.01). Conclusion: High-resolution renal MRE with an innovative driver and well-defined 3D segmentation can resolve all renal segments, especially when including the sinus in the analysis. Even after a prolonged hydration period the approach is sensitive to small hydration-related changes in the sinus and in the cortico-sinusoidal-difference.

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.

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.

Valsalva Maneuver Decreases Liver and Spleen Stiffness Measured by Time-Harmonic Ultrasound Elastography

Ultrasound elastography quantitatively measures tissue stiffness and is widely used in clinical practice to diagnose various diseases including liver fibrosis and portal hypertension. The stiffness of soft organs has been shown to be sensitive to blood flow and pressure-related diseases such as portal hypertension. Because of the intricate coupling between tissue stiffness of abdominal organs and perfusion-related factors such as vascular stiffness or blood volume, simple breathing maneuvers have altered the results of liver elastography, while other organs such as the spleen are understudied. Therefore, we investigated the effect of a standardized Valsalva maneuver on liver stiffness and, for the first time, on spleen stiffness using time-harmonic elastography (THE). THE acquires full-field-of-view stiffness maps based on shear wave speed (SWS), covers deep tissues, and is potentially sensitive to SWS changes induced by altered abdominal pressure in the hepatosplenic system. SWS of the liver and the spleen was measured in 17 healthy volunteers under baseline conditions and during the Valsalva maneuver. With the Valsalva maneuver, SWS in the liver decreased by 2.2% (from a median of 1.36 m/s to 1.32 m/s; p = 0.021), while SWS in the spleen decreased by 5.2% (from a median of 1.63 m/s to 1.51 m/s; p = 0.00059). Furthermore, we observed that the decrease was more pronounced the higher the baseline SWS values were. In conclusion, the results confirm our hypothesis that the Valsalva maneuver decreases liver and spleen stiffness, showing that THE is sensitive to perfusion pressure-related changes in tissue stiffness. With its extensive organ coverage and high penetration depth, THE may facilitate translation of pressure-sensitive ultrasound elastography into clinical routine.

Evaluation of cerebral cortex viscoelastic property estimation with nonlinear inversion magnetic resonance elastography

Objective. Magnetic resonance elastography (MRE) of the brain has shown promise as a sensitive neuroimaging biomarker for neurodegenerative disorders; however, the accuracy of performing MRE of the cerebral cortex warrants investigation due to the unique challenges of studying thinner and more complex geometries.Approach. A series of realistic, whole-brain simulation experiments are performed to examine the accuracy of MRE to measure the viscoelasticity (shear stiffness,μ, and damping ratio, ξ) of cortical structures predominantly effected in aging and neurodegeneration. Variations to MRE spatial resolution and the regularization of a nonlinear inversion (NLI) approach are examined.Main results. Higher-resolution MRE displacement data (1.25 mm isotropic resolution) and NLI with a low soft prior regularization weighting provided minimal measurement error compared to other studied protocols. With the optimized protocol, an average error inμand ξ was 3% and 11%, respectively, when compared with the known ground truth. Mid-line structures, as opposed to those on the cortical surface, generally display greater error. Varying model boundary conditions and reducing the thickness of the cortex by up to 0.67 mm (which is a realistic portrayal of neurodegenerative pathology) results in no loss in reconstruction accuracy.Significance. These experiments establish quantitative guidelines for the accuracy expected ofin vivoMRE of the cortex, with the proposed method providing valid MRE measures for future investigations into cortical viscoelasticity and relationships with health, cognition, and behavior.

Magnetic resonance elastography in normal pressure hydrocephalus-a scoping review

BACKGROUND

Magnetic resonance elastography (MRE) of the brain allows quantitative measurement of tissue mechanics. Multiple studies are exploring possible applications in normal pressure hydrocephalus (NPH) in clinical and paraclinical contexts. This is of great interest in neurological surgery due to challenges related to diagnosis and prediction of treatment effects. In this scoping review, we present a topical overview and discuss the current literature, with particular attention to clinical implications and current challenges.

METHODS

The protocol was based on the PRISMA extension for scoping reviews. After a systematic database search (PubMed, Embase, and Web of Science), the articles were screened for relevance. Thirty articles were subject to detailed screening, and key technical and clinical data items were extracted. The inclusion criteria included the use of MRE on human subjects with NPH.

RESULTS

Seven articles were included in the final study. These studies had various objectives including the role of MRE in the assessment of regional elastic changes in NPH, shunt effect, and evaluation of NPH symptoms. MRE revealed patterns of mechanical changes in NPH that differed from other dementias. Regional MRE changes were associated with specific NPH signs and symptoms. Neurosurgical shunting caused partial normalization in tissue scaffold parameters. The studies were highly heterogeneous in technical aspects and design.

CONCLUSION

MRE studies in NPH are still limited by few participants, variable cohorts, inconsistent methodologies, and technical challenges, but the approach shows great potential for future clinical application.

Quantitative effects of off-resonance related distortion on brain mechanical property estimation with magnetic resonance elastography

Off-resonance related geometric distortion can impact quantitative MRI techniques, such as magnetic resonance elastography (MRE), and result in errors to these otherwise sensitive metrics of brain health. MRE is a phase contrast technique to determine the mechanical properties of tissue by imaging shear wave displacements and estimating tissue stiffness through inverse solution of Navier's equation. In this study, we systematically examined the quantitative effects of distortion and corresponding correction approaches on MRE measurements through a series of simulations, phantom models, and in vivo brain experiments. We studied two different k-space trajectories, echo-planar imaging and spiral, and we determined that readout time, off-resonance gradient strength, and the combination of readout direction and off-resonance gradient direction, impact the estimated mechanical properties. Images were also processed through traditional distortion correction pipelines, and we found that each of the correction mechanisms works well for reducing stiffness errors, but are limited in cases of very large distortion. The ability of MRE to detect subtle changes to neural tissue health relies on accurate, artifact-free imaging, and thus off-resonance related geometric distortion must be considered when designing sequences and protocols by limiting readout time and applying correction where appropriate.

Adipose Tissue-Derived Stromal Cells Alter the Mechanical Stability and Viscoelastic Properties of Gelatine Methacryloyl Hydrogels

The extracellular matrix provides mechanical cues to cells within it, not just in terms of stiffness (elasticity) but also time-dependent responses to deformation (viscoelasticity). In this work, we determined the viscoelastic transformation of gelatine methacryloyl (GelMA) hydrogels caused by adipose tissue-derived stromal cells (ASCs) through mathematical modelling. GelMA-ASCs combination is of interest to model stem cell-driven repair and to understand cell-biomaterial interactions in 3D environments. Immortalised human ASCs were embedded in 5%, 10%, and 15% (w/v) GelMA hydrogels and evaluated for 14 d. GelMA had a concentration-dependent increase in stiffness, but cells decreased this stiffness over time, across concentrations. Viscoelastic changes in terms of stress relaxation increased progressively in 5% GelMA, while mathematical Maxwell analysis showed that the relative importance (R_i) of the fastest Maxwell elements increased proportionally. The 10% GelMA only showed differences at 7 d. In contrast, ASCs in 15% GelMA caused slower stress relaxation, increasing the R_i of the slowest Maxwell element. We conclude that GelMA concentration influenced the stiffness and number of Maxwell elements. ASCs changed the percentage stress relaxation and R_i of Maxwell elements transforming hydrogel viscoelasticity into a more fluid environment over time. Overall, 5% GelMA induced the most favourable ASC response.

Brain-mimicking phantom for biomechanical validation of motion sensitive MR imaging techniques

Motion sensitive MR imaging techniques allow for the non-invasive evaluation of biological tissues by using different excitation schemes, including physiological/intrinsic motions caused by cardiac pulsation or respiration, and vibrations caused by an external actuator. The mechanical biomarkers extracted through these imaging techniques have been shown to hold diagnostic value for various neurological disorders and conditions. Amplified MRI (aMRI), a cardiac gated imaging technique, can help track and quantify low frequency intrinsic motion of the brain. As for high frequency actuation, the mechanical response of brain tissue can be measured by applying external high frequency actuation in combination with a motion sensitive MR imaging sequence called Magnetic Resonance Elastography (MRE). Due to the frequency-dependent behavior of brain mechanics, there is a need to develop brain phantom models that can mimic the broadband mechanical response of the brain in order to validate motion-sensitive MR imaging techniques. Here, we have designed a novel phantom test setup that enables both the low and high frequency responses of a brain-mimicking phantom to be captured, allowing for both aMRI and MRE imaging techniques to be applied on the same phantom model. This setup combines two different vibration sources: a pneumatic actuator, for low frequency/intrinsic motion (1 Hz) for use in aMRI, and a piezoelectric actuator for high frequency actuation (30-60 Hz) for use in MRE. Our results show that in MRE experiments performed from 30 Hz through 60 Hz, propagating shear waves attenuate faster at higher driving frequencies, consistent with results in the literature. Furthermore, actuator coupling has a substantial effect on wave amplitude, with weaker coupling causing lower amplitude wave field images, specifically shown in the top-surface shear loading configuration. For intrinsic actuation, our results indicate that aMRI linearly amplifies motion up to at least an amplification factor of 9 for instances of both visible and sub-voxel motion, validated by varying power levels of pneumatic actuation (40%-80% power) under MR, and through video analysis outside the MRI scanner room. While this investigation used a homogeneous brain-mimicking phantom, our setup can be used to study the mechanics of non-homogeneous phantom configurations with bio-interfaces in the future.

Aging brain mechanics: Progress and promise of magnetic resonance elastography

Neuroimaging techniques that can sensitivity characterize healthy brain aging and detect subtle neuropathologies have enormous potential to assist in the early detection of neurodegenerative conditions such as Alzheimer's disease. Magnetic resonance elastography (MRE) has recently emerged as a reliable, high-resolution, and especially sensitive technique that can noninvasively characterize tissue biomechanical properties (i.e., viscoelasticity) in vivo in the living human brain. Brain tissue viscoelasticity provides a unique biophysical signature of neuroanatomy that are representative of the composition and organization of the complex tissue microstructure. In this article, we detail how progress in brain MRE technology has provided unique insights into healthy brain aging, neurodegeneration, and structure-function relationships. We further discuss additional promising technical innovations that will enhance the specificity and sensitivity for brain MRE to reveal considerably more about brain aging as well as its potentially valuable role as an imaging biomarker of neurodegeneration. MRE sensitivity may be particularly useful for assessing the efficacy of rehabilitation strategies, assisting in differentiating between dementia subtypes, and in understanding the causal mechanisms of disease which may lead to eventual pharmacotherapeutic development.

Real-Time Multifrequency MR Elastography of the Human Brain Reveals Rapid Changes in Viscoelasticity in Response to the Valsalva Maneuver

Modulation of cerebral blood flow and vascular compliance plays an important role in the regulation of intracranial pressure (ICP) and also influences the viscoelastic properties of brain tissue. Therefore, magnetic resonance elastography (MRE), the gold standard for measuring in vivo viscoelasticity of brain tissue, is potentially sensitive to cerebral autoregulation. In this study, we developed a multifrequency MMRE technique that provides serial maps of viscoelasticity at a frame rate of nearly 6 Hz without gating, i.e., in quasi-real time (rt-MMRE). This novel method was used to monitor rapid changes in the viscoelastic properties of the brains of 17 volunteers performing the Valsalva maneuver (VM). rt-MMRE continuously sampled externally induced vibrations comprising three frequencies of 30.03, 30.91, and 31.8 Hz were over 90 s using a steady-state, spiral-readout gradient-echo sequence. Data were processed by multifrequency dual elasto-visco (MDEV) inversion to generate maps of magnitude shear modulus | G^∗| (stiffness) and loss angle φ at a frame rate of 5.4 Hz. As controls, the volunteers were examined to study the effects of breath-hold following deep inspiration and breath-hold following expiration. We observed that | G^∗| increased while φ decreased due to VM and, less markedly, due to breath-hold in inspiration. Group mean VM values showed an early overshoot of | G^∗| 2.4 ± 1.2 s after the onset of the maneuver with peak values of 6.7 ± 4.1% above baseline, followed by a continuous increase in stiffness during VM. A second overshoot of | G^∗| occurred 5.5 ± 2.0 s after the end of VM with peak values of 7.4 ± 2.8% above baseline, followed by 25-s sustained recovery until the end of image acquisition. φ was constantly reduced by approximately 2% during the entire VM without noticeable peak values. This is the first report of viscoelasticity changes in brain tissue induced by physiological maneuvers known to alter ICP and detected by clinically applicable rt-MMRE. Our results show that apnea and VM slightly alter brain properties toward a more rigid-solid behavior. Overshooting stiffening reactions seconds after onset and end of VM reveal rapid autoregulatory processes of brain tissue viscoelasticity.

Poroelastic Mechanical Properties of the Brain Tissue of Normal Pressure Hydrocephalus Patients During Lumbar Drain Treatment Using Intrinsic Actuation MR Elastography

RATIONALE AND OBJECTIVES

Hydrocephalus (HC) is caused by accumulating cerebrospinal fluid resulting in enlarged ventricles and neurological symptoms. HC can be treated via a shunt in a subset of patients; identifying which individuals will respond through noninvasive imaging would avoid complications from unsuccessful treatments. This preliminary work is a longitudinal study applying MR Elastography (MRE) to HC patients with a focus on normal pressure hydrocephalus (NPH).

MATERIALS AND METHODS

Twenty-two ventriculomegaly patients were imaged and subsequently received a lumbar drain placement for cerebrospinal fluid (CSF) drainage. NPH lumbar drain responders and NPH syndrome nonresponders were categorized by clinical presentation. Displacement images were acquired using intrinsic activation (IA) MRE and poroelastic inversion recovered shear stiffness and hydraulic conductivity values. A stable IA-MRE inversion protocol was developed to produce unique solutions for both recovered properties, independent of initial estimates.

RESULTS

Property images showed significantly increased shear modulus (p = 0.003 in periventricular region, p = 0.005 in remaining cerebral tissue) and hydraulic conductivity (p = 0.04 in periventricular region) in ventriculomegaly patients compared to healthy volunteers. Baseline MRE imaging did not detect significant differences between NPH lumbar drain responders and NPH syndrome nonresponders; however, MRE time series analysis demonstrated consistent trends in average poroelastic shear modulus values over the course of the lumbar drain process in responders (initial increase, followed by a later decrease) which did not occur in nonresponders.

CONCLUSION

These findings are indicative of acute mechanical changes in the brain resulting from CSF drainage in NPH patients.

Quantitative Evaluation of Neonatal Brain Elasticity Using Shear Wave Elastography

OBJECTIVES

To demonstrate the feasibility of 2-dimensional brain ultrasound shear wave elastography (SWE) and to define the average elasticity values of the gray and white matter in term neonates.

METHODS

This work was a prospective observational single-center study including 55 healthy term neonates consecutively recruited in the maternity ward between the second and third postnatal days. All were successfully evaluated with a cerebral SWE examination performed with a multifrequency 4-9-MHz transducer. Bilateral sagittal planes of the thalamus and corona radiata were used to measure stiffness using a quantitative SWE method. Several elastograms with 5 to 15 nonoverlapping areas were obtained from the 2 different anatomic locations. The 5 most central measurements were averaged as representative values.

RESULTS

The 55 neonates ranged from 37 to 40 weeks' gestation. The estimated mean velocity values of the thalamus (1.17 m/s; 95% confidence interval, 1.13, 1.22 m/s) and corona radiata (1.60 m/s; 95% confidence interval, 1.57, 1.64 m/s) were statistically different (P < .001). There was no significant influence of laterality, gestational age, cephalic perimeter, sex, length, or type of delivery on the stiffness measurements.

CONCLUSIONS

Brain ultrasound SWE is feasible and allows measurements of neonatal brain elasticity. The elasticity of the thalamus and corona radiata at the frontal white matter in healthy term neonates is different. The knowledge of normal SWE ranges in term neonates allows comparative studies under pathologic conditions.

Superviscous properties of the in vivo brain at large scales

There is growing awareness that brain mechanical properties are important for neural development and health. However, published values of brain stiffness differ by orders of magnitude between static measurements and in vivo magnetic resonance elastography (MRE), which covers a dynamic range over several frequency decades. We here show that there is no fundamental disparity between static mechanical tests and in vivo MRE when considering large-scale properties, which encompass the entire brain including fluid filled compartments. Using gradient echo real-time MRE, we investigated the viscoelastic dispersion of the human brain in, so far, unexplored dynamic ranges from intrinsic brain pulsations at 1 Hz to ultralow-frequency vibrations at 5, 6.25, 7.8 and 10 Hz to the normal frequency range of MRE of 40 Hz. Surprisingly, we observed variations in brain stiffness over more than two orders of magnitude, suggesting that the in vivo human brain is superviscous on large scales with very low shear modulus of 42±13 Pa and relatively high viscosity of 6.6±0.3 Pa∙s according to the two-parameter solid model. Our data shed light on the crucial role of fluid compartments including blood vessels and cerebrospinal fluid (CSF) for whole brain properties and provide, for the first time, an explanation for the variability of the mechanical brain responses to manual palpation, local indentation, and high-dynamic tissue stimulation as used in elastography.

Sensitivity analysis of effective transverse shear viscoelastic and diffusional properties of myelinated white matter

Motivated by the need to interpret the results from a combined use of in vivo brain Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI), we developed a computational framework to study the sensitivity of single-frequency MRE and DTI metrics to white matter microstructure and cell-level mechanical and diffusional properties. White matter was modeled as a triphasic unidirectional composite, consisting of parallel cylindrical inclusions (axons) surrounded by sheaths (myelin), and embedded in a matrix (glial cells plus extracellular matrix). Only 2D mechanics and diffusion in the transverse plane (perpendicular to the axon direction) was considered, and homogenized (effective) properties were derived for a periodic domain containing a single axon. The numerical solutions of the MRE problem were performed with ABAQUS and by employing a sophisticated boundary-conforming grid generation scheme. Based on the linear viscoelastic response to harmonic shear excitation and steady-state diffusion in the transverse plane, a systematic sensitivity analysis of MRE metrics (effective transverse shear storage and loss moduli) and DTI metric (effective radial diffusivity) was performed for a wide range of microstructural and intrinsic (phase-based) physical properties. The microstructural properties considered were fiber volume fraction, and the myelin sheath/axon diameter ratio. The MRE and DTI metrics are very sensitive to the fiber volume fraction, and the intrinsic viscoelastic moduli of the glial phase. The MRE metrics are nonlinear functions of the fiber volume fraction, but the effective diffusion coefficient varies linearly with it. Finally, the transverse metrics of both MRE and DTI are insensitive to the axon diameter in steady state. Our results are consistent with the limited anisotropic MRE and co-registered DTI measurements, mainly in the corpus callosum, available in the literature. We conclude that isotropic MRE and DTI constitutive models are good approximations for myelinated white matter in the transverse plane. The unidirectional composite model presented here is used for the first time to model harmonic shear stress under MRE-relevant frequency on the cell level. This model can be extended to 3D in order to inform the solution of the inverse problem in MRE, establish the biological basis of MRE metrics, and integrate MRE/DTI with other modalities towards increasing the specificity of neuroimaging.

Cerebral Ultrasound Time-Harmonic Elastography Reveals Softening of the Human Brain Due to Dehydration

Hydration influences blood volume, blood viscosity, and water content in soft tissues - variables that determine the biophysical properties of biological tissues including their stiffness. In the brain, the relationship between hydration and stiffness is largely unknown despite the increasing importance of stiffness as a quantitative imaging marker. In this study, we investigated cerebral stiffness (CS) in 12 healthy volunteers using ultrasound time-harmonic elastography (THE) in different hydration states: (i) during normal hydration, (ii) after overnight fasting, and (iii) within 1 h of drinking 12 ml of water per kg body weight. In addition, we correlated shear wave speed (SWS) with urine osmolality and hematocrit. SWS at normal hydration was 1.64 ± 0.02 m/s and decreased to 1.57 ± 0.04 m/s (p < 0.001) after overnight fasting. SWS increased again to 1.63 ± 0.01 m/s within 30 min of water drinking, returning to values measured during normal hydration (p = 0.85). Urine osmolality at normal hydration (324 ± 148 mOsm/kg) increased to 784 ± 107 mOsm/kg (p < 0.001) after fasting and returned to normal (288 ± 128 mOsm/kg, p = 0.83) after water drinking. SWS and urine osmolality correlated linearly (r = -0.68, p < 0.001), while SWS and hematocrit did not correlate (p = 0.31). Our results suggest that mild dehydration in the range of diurnal fluctuations is associated with significant softening of brain tissue, possibly due to reduced cerebral perfusion. To ensure consistency of results, it is important that cerebral elastography with a standardized protocol is performed during normal hydration.

An analytical model of full-field displacement and strain induced by amplitude-modulated focused ultrasound in harmonic motion imaging

The majority of disease processes involves changes in the micro-structure of the affected tissue, which can translate to changes in the mechanical properties of the corresponding tissue. Harmonic motion imaging (HMI) is an elasticity imaging technique that allows the study of the mechanical parameters of tissue by detecting the tissue response by a harmonic motion field, which is generated by oscillatory acoustic radiation force (ARF). HMI has been demonstrated in tumor detection and characterization as well as monitoring of ablation procedures. In this study, an analytical HMI model is demonstrated and compared with a finite element model (FEM), allowing rapid and accurate computation of the displacement, strain, and shear wave velocity (SWV) at any location in a homogeneous linear elastic material. Average absolute differences between the analytical model and the FEM were respectively 1.2 % for the displacements and 0.5 % for the strains for 41940 force voxels at 0.22 seconds per displacement evaluation. A convergence study showed that the average difference could be further decreased to 1.0 % and 0.15 % for the displacements and strains, respectively, if force resolution is increased. SWV fields, as calculated with the FEM and the analytical model, have regional differences in velocities up to 0.57 m/s with an average absolute difference of 0.11±0.07 m/s, primarily due to imperfections in the non-reflecting FEM boundary conditions. The apparent SWV differed from the commonly used plane-wave approximation by up to 1.2 m/s due to near and intermediate field effects. Maximum displacement amplitudes for a model with an inclusion stabilize within 10 % of the homogeneous model at an inclusion radius of 10 mm while the maximum strain reacts faster, stabilizing at an inclusion radius of 3 mm. In conclusion, an analytical model for HMI stiffness estimation is presented in this paper. The analytical model has advantages over FEM as the full-field displacements do not need to be calculated to evaluate the model at a single measurement point. This advantage, together with the computational speed, makes the analytical model useful for real-time imaging applications. However, the analytical model was found to have restrictive assumptions on tissue homogeneity and infinite dimensions, while the FEM approaches were shown adaptable to variable geometry and non-homogeneous properties.

Effect of Aging on the Viscoelastic Properties of Hippocampal Subfields Assessed with High-Resolution MR Elastography

Age-related memory impairments have been linked to differences in structural brain parameters, including the integrity of the hippocampus (HC) and its distinct hippocampal subfields (HCsf). Imaging methods sensitive to the underlying tissue microstructure are valuable in characterizing age-related HCsf structural changes that may relate to cognitive function. Magnetic resonance elastography (MRE) is a noninvasive MRI technique that can quantify tissue viscoelasticity and may provide additional information about aging effects on HCsf health. Here, we report a high-resolution MRE protocol to quantify HCsf viscoelasticity through shear stiffness, μ, and damping ratio, ξ, which reflect the integrity of tissue composition and organization. HCsf exhibit distinct mechanical properties-the subiculum had the lowest μ and both subiculum and entorhinal cortex had the lowest ξ. Both measures correlated with age: HCsf μ was lower with age (P < 0.001) whereas ξ was higher (P = 0.002). The magnitude of age-related differences in ξ varied across HCsf (P = 0.011), suggesting differential patterns of brain aging. This study demonstrates the feasibility of using MRE to assess HCsf microstructural integrity and suggests incorporation of these metrics to evaluate HC health in neurocognitive disorders.

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.

MR elastography: Principles, guidelines, and terminology

Magnetic resonance elastography (MRE) is a phase contrast-based MRI technique that can measure displacement due to propagating mechanical waves, from which material properties such as shear modulus can be calculated. Magnetic resonance elastography can be thought of as quantitative, noninvasive palpation. It is increasing in clinical importance, has become widespread in the diagnosis and staging of liver fibrosis, and additional clinical applications are being explored. However, publications have reported MRE results using many different parameters, acquisition techniques, processing methods, and varied nomenclature. The diversity of terminology can lead to confusion (particularly among clinicians) about the meaning of and interpretation of MRE results. This paper was written by the MRE Guidelines Committee, a group formalized at the first meeting of the ISMRM MRE Study Group, to clarify and move toward standardization of MRE nomenclature. The purpose of this paper is to (1) explain MRE terminology and concepts to those not familiar with them, (2) define "good practices" for practitioners of MRE, and (3) identify opportunities to standardize terminology, to avoid confusion.

A medical percussion instrument using a wavelet-based method for archivable output and automatic classification

There is no standard instrument for carrying out medical percussion even though the procedure has been in continuous use since 1761. This study developed one such instrument. It generates medical percussion sounds in a reproducible manner and accurately classifies them into one of three classes. Percussion signals were generated using a push-pull solenoid plessor applying mechanical impulses through a polyvinyl chloride plessimeter. Signals were acquired using a National Instruments USB 6251 data acquisition card at a rate of 8.192 kHz through an air-coupled omnidirectional electret microphone located 60 mm from the impact site. Signal acquisition, processing, and classification were controlled by an NVIDIA Jetson TX2 computational device. A complex Morlet wavelet was selected as the base wavelet for the wavelet decomposition using the maximum wavelet energy method. It was also used to generate a scalogram suitable for manual or automatic classification. Automatic classification was achieved using a MobileNetv2 convolutional neural network with 17 inverted residual layers on the basis of 224 × 224 x 1 images generated by downsampling each scalogram. Testing was carried out using five human subjects with impulses applied at three thoracic sites each to elicit dull, resonant, and tympanic signals respectively. Classifier training utilized the Adam algorithm with a learning rate of 0.001, and first and second moments of 0.9 and 0.999 respectively for 100 epochs, with early stopping. Mean subject-specific validation and test accuracies of 95.9±1.6% and 93.8±2.3% respectively were obtained, along with cross-subject validation and test accuracies of 94.9% and 94.0% respectively. These results compare very favorably with previously-reported systems for automatic generation and classification of percussion sounds.

Separation of fluid and solid shear wave fields and quantification of coupling density by magnetic resonance poroelastography

PURPOSE

Biological soft tissues often have a porous architecture comprising fluid and solid compartments. Upon displacement through physiological or externally induced motion, the relative motion of these compartments depends on poroelastic parameters, such as coupling density ( ρ 12 ) and tissue porosity. This study introduces inversion recovery MR elastography (IR-MRE) (1) to quantify porosity defined as fluid volume over total volume, (2) to separate externally induced shear strain fields of fluid and solid compartments, and (3) to quantify coupling density assuming a biphasic behavior of in vivo brain tissue.

THEORY AND METHODS

Porosity was measured in eight tofu phantoms and gray matter (GM) and white matter (WM) of 21 healthy volunteers. Porosity of tofu was compared to values obtained by fluid draining and microscopy. Solid and fluid shear-strain amplitudes and ρ 12 were estimated both in phantoms and in in vivo brain.

RESULTS

T₁ -based measurement of tofu porosity agreed well with reference values (R = 0.99, P < .01). Brain tissue porosity was 0.14 ± 0.02 in GM and 0.05 ± 0.01 in WM (P < .001). Fluid shear strain was found to be phase-locked with solid shear strain but had lower amplitudes in both tofu phantoms and brain tissue (P < .05). In accordance with theory, tofu and brain ρ 12 were negative.

CONCLUSION

IR-MRE allowed for the first time separation of shear strain fields of solid and fluid compartments for measuring coupling density according to the biphasic theory of poroelasticity. Thus, IR-MRE opens horizons for poroelastography-derived imaging markers that can be used in basic research and diagnostic applications.

Advances in Magnetic Resonance Elastography of Liver

Magnetic resonance elastography (MRE) is the most accurate noninvasive technique in diagnosing fibrosis and cirrhosis in patients with chronic liver disease (CLD). The accuracy of hepatic MRE in distinguishing the severity of disease has been validated in studies of patients with various CLDs. Advanced hepatic MRE is a reliable, comfortable, and inexpensive alternative to liver biopsy for disease diagnosing, progression monitoring, and clinical decision making in patients with CLDs. This article summarizes current knowledge of the technical advances and innovations in hepatic MRE, and the clinical applications in various hepatic diseases.

Cardiac-gated steady-state multifrequency magnetic resonance elastography of the brain: Effect of cerebral arterial pulsation on brain viscoelasticity

In-vivo brain viscoelasticity measured by magnetic resonance elastography (MRE) is a sensitive imaging marker for long-term biophysical changes in brain tissue due to aging and disease; however, it is still unknown whether MRE can reveal short-term periodic alterations of brain viscoelasticity related to cerebral arterial pulsation (CAP). We developed cardiac-gated steady-state MRE (ssMRE) with spiral readout and stroboscopic sampling of continuously induced mechanical vibrations in the brain at 20, 31.25, and 40 Hz frequencies. Maps of magnitude |G*| and phase ϕ of the complex shear modulus were generated by multifrequency dual visco-elasto inversion with a temporal resolution of 40 ms over 4 s. The method was tested in 12 healthy volunteers. During cerebral systole, |G*| decreased by 6.6 ± 1.9% (56 ± 22 Pa, p < 0.001, mean ± SD), whereas ϕ increased by 0.5 ± 0.5% (0.006 ± 0.005 rad, p = 0.002). The effect size of CAP-induced softening slightly decreased with age by 0.10 ± 0.05% per year (p = 0.04), indicating lower cerebral vascular compliance in older individuals. Our data show for the first time that the brain softens and becomes more viscous during systole, possibly due to an effect of CAP-induced arterial expansion and increased blood volume on effective-medium tissue properties. This sensitivity to vascular-solid tissue interactions makes ssMRE potentially useful for detection of cerebral vascular disease.

Nonlinear Inversion MR Elastography With Low-Frequency Actuation

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.

Hypercapnia increases brain viscoelasticity

Brain function, the brain's metabolic activity, cerebral blood flow (CBF), and intracranial pressure are intimately linked within the tightly autoregulated regime of intracranial physiology in which the role of tissue viscoelasticity remains elusive. We applied multifrequency magnetic resonance elastography (MRE) paired with CBF measurements in 14 healthy subjects exposed to 5-min carbon dioxide-enriched breathing air to induce cerebral vasodilatation by hypercapnia. Stiffness and viscosity as quantified by the magnitude and phase angle of the complex shear modulus, |G*| and ϕ, as well as CBF of the whole brain and 25 gray matter sub-regions were analyzed prior to, during, and after hypercapnia. In all subjects, whole-brain stiffness and viscosity increased due to hypercapnia by 3.3 ± 1.9% and 2.0 ± 1.1% which was accompanied by a CBF increase of 36 ± 15%. Post-hypercapnia, |G*| and ϕ reduced to normal values while CBF decreased by 13 ± 15% below baseline. Hypercapnia-induced viscosity changes correlated with CBF changes, whereas stiffness changes did not. The MRE-measured viscosity changes correlated with blood viscosity changes predicted by the Fåhræus-Lindqvist model and microvessel diameter changes from the literature. Our results suggest that brain viscoelastic properties are influenced by microvessel blood flow and blood viscosity: vasodilatation and increased blood viscosity due to hypercapnia result in an increase in MRE values related to viscosity.

A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues

In this paper, the dynamic behavior of bovine brain tissue, measured from in-vitro unconfined compression tests, is examined and represented through a viscoelastic biphasic model. The experiments have been carried out under three compression speeds of 10, 100, and 1000 mm/s. The results exhibited significant rate-dependent behavior. The brain tissue is modeled as a biphasic continuum consisting of a compressible solid matrix, fully saturated with an incompressible interstitial fluid. The governing equations based on conservation of mass and momentum are used to describe the solid-fluid interactions. An inverse scheme is employed in which a finite element model runs iteratively to optimize constitutive constants. The obtained material parameters of the proposed biphasic model show relatively good agreement (R² ≥ 0.96) with the experimental tissue mechanical responses at different rates. The model can successfully capture the key aspects of the rate-dependency for both solid and fluid phases under large strain deformation. This poro-hyper viscoelastic model can effectively estimate the global and local rate-dependent tissue deformations, the spatial variations in pore spaces, hydrostatic pressure as well as fluid diffusion through the tissue.

Statistical Characterization of Human Brain Deformation During Mild Angular Acceleration Measured In Vivo by Tagged Magnetic Resonance Imaging

Understanding of in vivo brain biomechanical behavior is critical in the study of traumatic brain injury (TBI) mechanisms and prevention. Using tagged magnetic resonance imaging, we measured spatiotemporal brain deformations in 34 healthy human volunteers under mild angular accelerations of the head. Two-dimensional (2D) Lagrangian strains were examined throughout the brain in each subject. Strain metrics peaked shortly after contact with a padded stop, corresponding to the inertial response of the brain after head deceleration. Maximum shear strain of at least 3% was experienced at peak deformation by an area fraction (median±standard error) of 23.5±1.8% of cortical gray matter, 15.9±1.4% of white matter, and 4.0±1.5% of deep gray matter. Cortical gray matter strains were greater in the temporal cortex on the side of the initial contact with the padded stop and also in the contralateral temporal, frontal, and parietal cortex. These tissue-level deformations from a population of healthy volunteers provide the first in vivo measurements of full-volume brain deformation in response to known kinematics. Although strains differed in different tissue type and cortical lobes, no significant differences between male and female head accelerations or strain metrics were found. These cumulative results highlight important kinematic features of the brain's mechanical response and can be used to facilitate the evaluation of computational simulations of TBI.

Dilatational and shear waves in poro-vioscoelastic media

Dynamic elastography methods are being developed for quantitatively and noninvasively mapping the viscoelastic properties of biological tissue that are often altered by disease and injury, as well as response to treatment. This involves inducing mechanical wave motion that also can be affected by the multiphase porous nature of the tissue, whether it be consideration of blood perfusion in the vascular network found in many regions of interest, or consideration of air movement in the complex bronchial tree within the lungs. Elastographic mapping requires reconstructing material properties based on interpretation of the measured wave motion. Reconstruction methods that explicitly incorporate poroelastic behavior are an active area of development. In the present article the equivalence of two theoretical approaches to modeling poroelastic behavior is demonstrated specifically in the frequency domain using parameter values that span the range expected in vivo for analysis of blood and air-infused regions. The two methods are known as (1) the mixture or biphasic formulation and (2) the poroelastic approach. The case of acoustic wave propagation in the lungs is specifically addressed by comparison of analytical predictions to recently reported experimental measurements. Establishing and validating this equivalence of theoretical approaches not only strengthens our fundamental understanding of the relevant physics, but also may lead to improved numerical methods for simulation and elastography reconstruction.

In vivo time-harmonic ultrasound elastography of the human brain detects acute cerebral stiffness changes induced by intracranial pressure variations

Cerebral stiffness (CS) reflects the biophysical environment in which neurons grow and function. While long-term CS changes can occur in the course of chronic neurological disorders and aging, little is known about acute variations of CS induced by intracranial pressure variations. Current gold standard methods for CS and intracranial pressure such as magnetic resonance elastography and direct pressure recordings are either expensive and slow or invasive. The study objective was to develop a real-time method for in vivo CS measurement and to demonstrate its sensitivity to physiological aging and intracranial pressure variations induced by the Valsalva maneuver in healthy volunteers. We used trans-temporal ultrasound time-harmonic elastography (THE) with external shear-wave stimulation by continuous and superimposed vibrations in the frequency range from 27 to 56 Hz. Multifrequency wave inversion generated maps of shear wave speed (SWS) as a surrogate maker of CS. On average, cerebral SWS was 1.56 ± 0.08 m/s with a tendency to reduce with age (R = -0.76, p < 0.0001) while Valsalva maneuver induced an immediate stiffening of the brain as reflected by a 10.8 ± 2.5% increase (p < 0.0001) in SWS. Our results suggest that CS is tightly linked to intracranial pressure and might be used in the future as non-invasive surrogate marker for intracranial pressure, which otherwise requires invasive measurements.

Soft tissue rheology and its implications for elastography: Challenges and opportunities

Magnetic resonance elastography and related shear wave ultrasound elastography techniques can be used to estimate the mechanical properties of soft tissues in vivo by using the relationships between wave propagation and the elastic properties of materials. These techniques have found numerous clinical and research applications, tracking changes in tissue properties as a result of disease or other interventions. Most dynamic elastography approaches estimate tissue elastic (or viscoelastic) properties from a simplified version of the equations for the propagation of acoustic waves through a homogeneous linear (visco)elastic medium. However, soft tissue rheology is complex and departs significantly from this idealized picture. In particular, soft tissues are nonlinearly viscoelastic, inhomogeneous and often anisotropic, and their apparent stiffness can vary with the current loading state. All of these features have implications for the reliability and reproducibility of elastography measurements, from data acquisition to analysis and interpretation. New developments in inversion algorithms for elastography are beginning to offer solutions to account for the complex rheology of tissues, including inhomogeneity and anisotropy. There remains considerable potential to further refine elastography to capture the full spectrum of tissue rheology, and thus to better understand the underlying tissue microstructural changes in a broad range of clinical disorders.

Spring-damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography

In MR elastography, it is common to use an elastic model for the tissue's response in order to interpret the results properly. More complex models, such as viscoelastic, fractional viscoelastic, poroelastic, or poroviscoelastic ones, are also used. These models appear at first sight to be very different, but here it is shown that they may all be expressed in terms of elementary viscoelastic models. For a medium expressed with fractional models, many elementary spring-damper combinations are added, each of them weighted according to a long-tailed distribution of time constants or relaxation frequencies. This may open up a more physical interpretation of fractional models. The shear-wave component of the poroelastic model is shown to be modeled exactly by a three-component Zener model. The extended poroviscoelastic model is found to be equivalent to what is called a non-standard four-parameter model. Accordingly, the large number of parameters in the porous models can be reduced to the same number as in their viscoelastic equivalents. While the individual displacements from the solid and fluid parts cannot be measured individually, the main use of the poro(visco)elastic models is therefore as a physics-based method for determining parameters in a viscoelastic model.

Stiffness and Beyond: What MR Elastography Can Tell Us About Brain Structure and Function Under Physiologic and Pathologic Conditions

Brain magnetic resonance elastography (MRE) was developed on the basis of a desire to "palpate by imaging" and is becoming a powerful tool in the investigation of neurophysiological and neuropathological states. Measurements are acquired with a specialized MR phase-contrast pulse sequence that can detect tissue motion in response to an applied external or internal excitation. The tissue viscoelasticity is then reconstructed from the measured displacement. Quantitative characterization of brain viscoelastic behaviors provides us an insight into the brain structure and function by assessing the mechanical rigidity, viscosity, friction, and connectivity of brain tissues. Changes in these features are associated with inflammation, demyelination, and neurodegeneration that contribute to brain disease onset and progression. Here, we review the basic principles and limitations of brain MRE and summarize its current neuroanatomical studies and clinical applications to the most common neurosurgical and neurodegenerative disorders, including intracranial tumors, dementia, multiple sclerosis, amyotrophic lateral sclerosis, and traumatic brain injury. Going forward, further improvement in acquisition techniques, stable inverse reconstruction algorithms, and advanced numerical, physical, and preclinical validation models is needed to increase the utility of brain MRE in both research and clinical applications.

Mechanical properties of porcine brain tissue in vivo and ex vivo estimated by MR elastography

The mechanical properties of brain tissue in vivo determine the response of the brain to rapid skull acceleration. These properties are thus of great interest to the developers of mathematical models of traumatic brain injury (TBI) or neurosurgical simulations. Animal models provide valuable insight that can improve TBI modeling. In this study we compare estimates of mechanical properties of the Yucatan mini-pig brain in vivo and ex vivo using magnetic resonance elastography (MRE) at multiple frequencies. MRE allows estimations of properties in soft tissue, either in vivo or ex vivo, by imaging harmonic shear wave propagation. Most direct measurements of brain mechanical properties have been performed using samples of brain tissue ex vivo. It has been observed that direct estimates of brain mechanical properties depend on the frequency and amplitude of loading, as well as the time post-mortem and condition of the sample. Using MRE in the same animals at overlapping frequencies, we observe that porcine brain tissue in vivo appears stiffer than porcine brain tissue samples ex vivo at frequencies of 100 Hz and 125 Hz, but measurements show closer agreement at lower frequencies.

Perfusion alters stiffness of deep gray matter

Viscoelastic properties of the brain reflect tissue architecture at multiple length scales. However, little is known about the relation between vital tissue functions, such as perfusion, and the macroscopic mechanical properties of cerebral tissue. In this study, arterial spin labelling is paired with magnetic resonance elastography to investigate the relationship between tissue stiffness and cerebral blood flow (CBF) in the in vivo human brain. The viscoelastic modulus, | G*|, and CBF were studied in deep gray matter (DGM) of 14 healthy male volunteers in the following sub-regions: putamen, nucleus accumbens, hippocampus, thalamus, globus pallidus, and amygdala. CBF was further normalized by vessel area data to obtain the flux rate q which is proportional to the perfusion pressure gradient. The striatum (represented by putamen and nucleus accumbens) was distinct from the other DGM regions by displaying markedly higher stiffness and perfusion values. q was a predictive marker for DGM stiffness as analyzed by linear regression | G*| =  q·(4.2 ± 0.6)kPa·s + (0.80 ± 0.06)kPa ( R²= 0.92, P = 0.006). These results suggest a high sensitivity of MRE in DGM to perfusion pressure. The distinct mechano-vascular properties of striatum tissue, as compared to the rest of DGM, may reflect elevated perfusion pressure, which could explain the well-known susceptibility of the putamen to hemorrhages.

Automated In Vivo Sub-Hertz Analysis of Viscoelasticity (SAVE) for Evaluation of Breast Lesions

We present an automated method for acquiring images and contrast parameters based on mechanical properties of breast lesions and surrounding tissue at load frequencies less than 1 Hz. The method called sub-Hertz analysis of viscoelasticity (SAVE) uses a compression device integrated with ultrasound imaging to perform in vivo ramp-and-hold uniaxial creep-like test on human breast in vivo. It models the internal deformations of tissues under constant surface stress as a linear viscoelastic response. We first discuss different aspects of our unique measurement approach and the expected variability of the viscoelastic parameters estimated based on a simplified one-dimensional reconstruction model. Finite-element numerical analysis is used to justify the advantages of using imaging contrast over viscoelasticity values. We then present the results of SAVE applied to a group of patients with breast masses undergoing biopsy.

Models and tissue mimics for brain shift simulations

Capturing the deformation of human brain during neurosurgical operations is an extremely important task to improve the accuracy or surgical procedure and minimize permanent damage in patients. This study focuses on the development of an accurate numerical model for the prediction of brain shift during surgical procedures and employs a tissue mimic recently developed to capture the complexity of the human tissue. The phantom, made of a composite hydrogel, was designed to reproduce the dynamic mechanical behaviour of the brain tissue in a range of strain rates suitable for surgical procedures. The use of a well-controlled, accessible and MRI compatible alternative to real brain tissue allows us to rule out spurious effects due to patient geometry and tissue properties variability, CSF amount uncertainties, and head orientation. The performance of different constitutive descriptions is evaluated using a brain-skull mimic, which enables 3D deformation measurements by means of MRI scans. Our combined experimental and numerical investigation demonstrates the importance of using accurate constitutive laws when approaching the modelling of this complex organic tissue and supports the proposal of a hybrid poro-hyper-viscoelastic material formulation for the simulation of brain shift.

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.

Fatigue responses of the human cervical spine intervertebral discs

Numerous studies have been conducted since more than fifty years to understand the behavior of the human lumbar spine under fatigue loading. Applications have been largely driven by low back pain and human body vibration problems. The human neck also sustains fatigue loading in certain type of civilian occupational and military operational activities, and research is very limited in this area. Being a visco-elastic structure, it is important to determine the stress-relaxation properties of the human cervical spine intervertebral discs to enable accurate simulations of these structures in stress-analysis models. While finite element models have the ability to incorporate viscoelastic material definitions, data specific to the cervical spine are limited. The present study was conducted to determine these properties and understand the responses of the human lower cervical spine discs under large number of cyclic loads in the axial compression mode. Eight disc segments consisting of the adjacent vertebral bodies along with the longitudinal ligaments were subjected to compression, followed by 10,000 cycles of loading at 2 or 4Hz frequency by limiting the axial load to approximately 150 N, and subsequent to resting period, subjected to compression to extract the stress-relaxation properties using the quasi-linear viscoelastic (QLV) material model. The coefficients of the model and disc displacements as a function of cycles and loading frequency are presented. The disc responses demonstrated a plateauing effect after the first 2000 to 4000 cycles, which were highly nonlinear. The paper compares these responses with the "work hardening" phenomenon proposed in clinical literature for the lumbar spine to explain the fatigue behavior of the discs. The quantitative results in terms of QLV coefficients can serve as inputs to complex finite element models of the cervical spine to delineate the local and internal load-sharing responses of the disc segment.