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

Investigation of hepatic inflammation via viscoelasticity at low and high mechanical frequencies - A magnetic resonance elastography study

PURPOSE

To study the potential of viscoelastic parameters such as liver stiffness, loss tangent (marker of viscous properties) and viscoelastic dispersion to detect hepatic inflammation by in-vivo and ex-vivo MR elastography (MRE) at low and high vibration frequencies.

METHODS

15 patients scheduled for liver tumor resection surgery were prospectively enrolled in this IRB-approved study and underwent multifrequency in-vivo MRE (30-60Hz) at 1.5-T prior to surgery. Immediately after liver resection, tumor-free tissue specimens were examined with ex-vivo MRE (0.8-2.8 kHz) at 0.5-T and histopathologic analysis including NAFLD activity score (NAS) and inflammation score (I-score) as sum of histological sub-features of inflammation.

RESULTS

In-vivo, in regions where tissue samples were obtained, the loss tangent correlated with the I-score (R = 0.728; p = 0.002) and c-dispersion (stiffness dispersion over frequency) correlated with lobular inflammation (R = -0.559; p = 0.030). In a subgroup of patients without prior chemotherapy, c-dispersion correlated with I-score also in the whole liver (R = -0.682; p = 0.043). ROC analysis of the loss tangent for predicting the I-score showed a high AUC for I ≥ 1 (0.944; p = 0.021), I ≥ 2 (0.804; p = 0.049) and I ≥ 3 (0.944; p = 0.021). Ex-vivo MRE was not sensitive to inflammation, whereas strong correlations were observed between fibrosis and stiffness (R = 0.589; p = 0.021), penetration rate (R = 0.589; p = 0.021), loss tangent (R = -0.629; p = 0.012), and viscoelastic model parameters (spring-pot powerlaw exponent, R = -0.528; p = 0.043; spring-pot shear modulus, R = 0.589; p = 0.021).

CONCLUSION

Our results suggest that c-dispersion of the liver is sensitive to inflammation when measured in-vivo in the low dynamic range (30-60Hz), while at higher frequencies (0.8-2.8 kHz) viscoelastic parameters are dominated by fibrosis.

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.

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.

MR Elastography With Optimization-Based Phase Unwrapping and Traveling Wave Expansion-Based Neural Network (TWENN)

Magnetic Resonance Elastography (MRE) can characterize biomechanical properties of soft tissue for disease diagnosis and treatment planning. However, complicated wavefields acquired from MRE coupled with noise pose challenges for accurate displacement extraction and modulus estimation. Using optimization-based displacement extraction and Traveling Wave Expansion-based Neural Network (TWENN) modulus estimation, we propose a new pipeline for processing MRE images. An objective function with Dual Data Consistency (Dual-DC) has been used to ensure accurate phase unwrapping and displacement extraction. For the estimation of complex wavenumbers, a complex-valued neural network with displacement covariance as an input has been developed. A model of traveling wave expansion is used to generate training datasets for the network with varying levels of noise. The complex shear modulus map is obtained through fusion of multifrequency and multidirectional data. Validation using brain and liver simulation images demonstrates the practical value of the proposed pipeline, which can estimate the biomechanical properties with minimal root-mean-square errors when compared to state-of-the-art methods. Applications of the proposed method for processing MRE images of phantom, brain, and liver reveal clear anatomical features, robustness to noise, and good generalizability of the pipeline.

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.

Ensemble Kalman inversion for magnetic resonance elastography

Magnetic resonance elastography (MRE) is an MRI-based diagnostic method for measuring mechanical properties of biological tissues. MRE measurements are processed by an inversion algorithm to produce a map of the biomechanical properties. In this paper a new and powerful method (ensemble Kalman inversion with level sets (EKI)) of MRE inversion is proposed and tested. The method has critical advantages: material property variation at disease boundaries can be accurately identified, and uncertainty of the reconstructed material properties can be evaluated by consequence of the probabilistic nature of the method. EKI is tested in 2D and 3D experiments with synthetic MRE data of the human kidney. It is demonstrated that the proposed inversion method is accurate and fast.

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.

Fast magnetic resonance elastography with multiphase radial encoding and harmonic motion sparsity based reconstruction

Objective. To achieve fast magnetic resonance elastography (MRE) at a low frequency for better shear modulus estimation of the brain. Approach. We proposed a multiphase radial DENSE MRE (MRD-MRE) sequence and an improved GRASP algorithm utilizing the sparsity of the harmonic motion (SH-GRASP) for fast MRE at 20 Hz. For the MRD-MRE sequence, the initial position encoded by spatial modulation of magnetization (SPAMM) was decoded by an arbitrary number of readout blocks without increasing the number of phase offsets. Based on the harmonic motion, a modified total variation and temporal Fourier transform were introduced to utilize the sparsity in the temporal domain. Both phantom and brain experiments were carried out and compared with that from multiphase Cartesian DENSE-MRE (MCD-MRE), and conventional gradient echo sequence (GRE-MRE). Reconstruction performance was also compared with GRASP and compressed sensing. Main results. Results showed the scanning time of a fully sampled image with four phase offsets for MRD-MRE was only 1/5 of that from GRE-MRE. The wave patterns and estimated stiffness maps were similar to those from MCD-MRE and GRE-MRE. With SH-GRASP, the total scan time could be shortened by additional 4 folds, achieving a total acceleration factor of 20. Better metric values were also obtained using SH-GRASP for reconstruction compared with other algorithms. Significance. The MRD-MRE sequence and SH-GRASP algorithm can be used either in combination or independently to accelerate MRE, showing the potentials for imaging the brain as well as other organs.

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.

Inversion-recovery MR elastography of the human brain for improved stiffness quantification near fluid-solid boundaries

PURPOSE

In vivo MR elastography (MRE) holds promise as a neuroimaging marker. In cerebral MRE, shear waves are introduced into the brain, which also stimulate vibrations in adjacent CSF, resulting in blurring and biased stiffness values near brain surfaces. We here propose inversion-recovery MRE (IR-MRE) to suppress CSF signal and improve stiffness quantification in brain surface areas.

METHODS

Inversion-recovery MRE was demonstrated in agar-based phantoms with solid-fluid interfaces and 11 healthy volunteers using 31.25-Hz harmonic vibrations. It was performed by standard single-shot, spin-echo EPI MRE following 2800-ms IR preparation. Wave fields were acquired in 10 axial slices and analyzed for shear wave speed (SWS) as a surrogate marker of tissue stiffness by wavenumber-based multicomponent inversion.

RESULTS

Phantom SWS values near fluid interfaces were 7.5 ± 3.0% higher in IR-MRE than MRE (P = .01). In the brain, IR-MRE SNR was 17% lower than in MRE, without influencing parenchymal SWS (MRE: 1.38 ± 0.02 m/s; IR-MRE: 1.39 ± 0.03 m/s; P = .18). The IR-MRE tissue-CSF interfaces appeared sharper, showing 10% higher SWS near brain surfaces (MRE: 1.01 ± 0.03 m/s; IR-MRE: 1.11 ± 0.01 m/s; P < .001) and 39% smaller ventricle sizes than MRE (P < .001).

CONCLUSIONS

Our results show that brain MRE is affected by fluid oscillations that can be suppressed by IR-MRE, which improves the depiction of anatomy in stiffness maps and the quantification of stiffness values in brain surface areas. Moreover, we measured similar stiffness values in brain parenchyma with and without fluid suppression, which indicates that shear wavelengths in solid and fluid compartments are identical, consistent with the theory of biphasic poroelastic media.

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.

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.

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.

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.

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.

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.