Modeling of soft poroelastic tissue in time-harmonic 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.

Viscoelastic polyacrylamide MR elastography phantoms with tunable damping ratio independent of shear stiffness

Physiologically modeled test samples with known properties and characteristics, or phantoms, are essential for developing sensitive, repeatable, and accurate quantitative MRI techniques. Magnetic resonance elastography (MRE) is one such technique used to estimate tissue mechanical properties, and it is advantageous to use phantoms with independently tunable mechanical properties to benchmark the accuracy of MRE methods. Phantoms with tunable shear stiffness are commonly used for MRE, but tuning the viscosity or damping ratio has proven to be difficult. A promising candidate for MRE phantoms with tunable damping ratio is polyacrylamide (PAA). While pure PAA has very low attenuation, viscoelastic hydrogels have been made by entrapping linear polyacrylamide strands (LPAA) within the PAA network. In this study, we evaluate the use of LPAA/PAA gels as physiologically accurate phantoms with tunable damping ratio, independent of shear stiffness, via MRE. Phantoms were made with 15.3 wt% PAA while the LPAA concentration ranged from 4.5 wt% to 8.0 wt%. MRE was performed at 9.4 T with 400 Hz vibration on all phantoms revealing a strong, positive correlation between damping ratio and LPAA content (p < 0.001). There was no significant correlation between shear stiffness and LPAA content, confirming a constant PAA concentration yielded constant shear stiffness. Rheometry at 10 Hz was performed to verify the damping ratio of the phantoms. Nearly identical slopes for damping ratio versus LPAA content were found from both MRE and rheometry (0.0073 and 0.0075 respectively). Ultimately, this study validates the adaptation of polyacrylamide gels into physiologically-relevant MRE phantoms to enable testing of MRE estimates of damping ratio.

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.

The influence of static portal pressure on liver biophysical properties

The liver is a highly vascularized organ where fluid properties, including vascular pressure, vessel integrity and fluid viscosity, play a critical role in gross mechanical properties. To study the effects of portal pressure, liver confinement, fluid viscosity, and tissue crosslinking on liver stiffness, water diffusion, and vessel size, we applied multiparametric magnetic resonance imaging (mpMRI), including multifrequency magnetic resonance elastography (MRE) and apparent diffusion coefficient (ADC) measurements, to ex vivo livers from healthy male rats (13.6±1.6 weeks) at room temperature. Four scenarios including altered liver confinement, tissue crosslinking, and vascular fluid viscosity were investigated with mpMRI at different portal pressure levels (0-17.5 cmH2O). Our experiments demonstrated that, with increasing portal pressure, rat livers showed higher water content, water diffusivity, and increased vessel sizes quantified by the vessel tissue volume fraction (VTVF). These effects were most pronounced in native, unconfined livers (VTVF: 300±120%, p<0.05, ADC: 88±29%, p<0.01), while still significant under confinement (confined: VTVF: 53±32%, p<0.01, ADC: 28±19%, p<0.05; confined-fixed: VTVF: 52±20%, p<0.001, ADC: 11±2%, p<0.01; confined-viscous: VTVF: 210±110%, p<0.01, ADC: 26±9%, p<0.001). Softening with elevated portal pressure (-12±5, p<0.05) occurred regardless of confinement and fixation. However, the liver stiffened when exposed to a more viscous inflow fluid (11±4%, p<0.001). Taken together, our results elucidate the complex relationship between macroscopic-biophysical parameters of liver tissue measured by mpMRI and vascular-fluid properties. Influenced by portal pressure, vascular permeability, and matrix crosslinking, liver stiffness is sensitive to intrinsic poroelastic properties, which, alongside vascular architecture and water diffusivity, may aid in the differential diagnosis of liver disease. STATEMENT OF SIGNIFICANCE: Using highly controllable ex vivo rat liver phantoms, hepatic biophysical properties such as tissue-vascular structure, stiffness, and water diffusivity were investigated using multiparametric MRI including multifrequency magnetic resonance elastography (MRE) and diffusion-weighted imaging (DWI). Through elaborate tuning of the experimental conditions such as the static portal pressure, flow viscosity, amount and distribution of fluid content in the liver, we identified the contributions of the fluid component to the overall imaging-based biophysical properties of the liver. Our finding demonstrated the sensitivity of liver stiffness to the hepatic poroelastic properties, which may aid in the differential diagnosis of liver diseases.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells’ migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.

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.

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.

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.

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.

Towards noninvasive estimation of tumour pressure by utilising MR elastography and nonlinear biomechanical models: a simulation and phantom study

The solid and fluid pressures of tumours are often elevated relative to surrounding tissue. This increased pressure is known to correlate with decreased treatment efficacy and potentially with tumour aggressiveness and therefore, accurate noninvasive estimates of tumour pressure would be of great value. We present a proof-of-concept method to infer the total tumour pressure, that is the sum of the fluid and solid parts, by examining stiffness in the peritumoural tissue with MR elastography and utilising nonlinear biomechanical models. The pressure from the tumour deforms the surrounding tissue leading to changes in stiffness. Understanding and accounting for these biases in stiffness has the potential to enable estimation of total tumour pressure. Simulations are used to validate the method with varying pressure levels, tumour shape, tumour size, and noise levels. Results show excellent matching in low noise cases and still correlate well with higher noise. Percent error remains near or below 10% for higher pressures in all noise level cases. Reconstructed pressures were also calculated from experiments with a catheter balloon embedded in a plastisol phantom at multiple inflation levels. Here the reconstructed pressures generally match the increases in pressure measured during the experiments. Percent errors between average reconstructed and measured pressures at four inflation states are 17.9%, 52%, 23.2%, and 0.9%. Future work will apply this method to in vivo data, potentially providing an important biomarker for cancer diagnosis and treatment.

Atlas registration for edema-corrected MRI lesion volume in mouse stroke models

Lesion volume measurements with magnetic resonance imaging are widely used to assess outcome in rodent models of stroke. In this study, we improved a mathematical framework to correct lesion size for edema which is based on manual delineation of the lesion and hemispheres. Furthermore, a novel MATLAB toolbox to register mouse brain MR images to the Allen brain atlas is presented. Its capability to calculate edema-corrected lesion size was compared to the manual approach. Automated image registration performed equally well in in a mouse middle cerebral artery occlusion model (Pearson r = 0.976, p = 2.265e-11). Information encapsulated in the registration was used to generate maps of edema induced tissue volume changes. These showed discrepancies to simplified tissue models underlying the manual approach. The presented techniques provide biologically more meaningful, voxel-wise biomarkers of vasogenic edema after stroke.

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.

Frequency-dependent shear properties of annulus fibrosus and nucleus pulposus by magnetic resonance elastography

Aging and degeneration are associated with changes in mechanical properties in the intervertebral disc, generating interest in the establishment of mechanical properties as early biomarkers for the degenerative cascade. Magnetic resonance elastography (MRE) of the intervertebral disc is usually limited to the nucleus pulposus, as the annulus fibrosus is stiffer and less hydrated. The objective of this work was to adapt high-frequency needle MRE to the characterization of the shear modulus of both the nucleus pulposus and annulus fibrosus. Bovine intervertebral discs were removed from fresh oxtails and characterized by needle MRE. The needle was inserted in the center of the disc and vibrations were generated by an amplified piezoelectric actuator. MRE acquisitions were performed on a 4.7-T small-animal MR scanner using a spin echo sequence with sinusoidal motion encoding gradients. Acquisitions were repeated over a frequency range of 1000-1800 Hz. The local frequency estimation inversion algorithm was used to compute the shear modulus. Stiffness maps allowed the visualization of the soft nucleus pulposus surrounded by the stiffer annulus fibrosus surrounded by the homogeneous gel. A significant difference in shear modulus between the nucleus pulposus and annulus fibrosus, and an increase in the shear modulus with excitation frequency, were observed, in agreement with the literature. This study demonstrates that global characterization of both the nucleus pulposus and annulus fibrosus of the intervertebral disc is possible with needle MRE using a preclinical magnetic resonance imaging (MRI) scanner. MRE can be a powerful method for the mapping of the complex properties of the intervertebral disc. The developed method could be adapted for in situ use by preserving adjacent vertebrae and puncturing the side of the intervertebral disc, thereby allowing an assessment of the contribution of osmotic pressure to the mechanical behavior of the intervertebral disc.

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.

Magnetic resonance elastography of liver and spleen: Methods and applications

The viscoelastic properties of the liver and spleen can be assessed with magnetic resonance elastography (MRE). Several actuators, MRI acquisition sequences and reconstruction algorithms have been proposed for this purpose. Reproducible results are obtained, especially when the examination is performed in standard conditions with the patient fasting. Accurate staging of liver fibrosis can be obtained by measuring liver stiffness or elasticity with MRE. Moreover, emerging evidence shows that assessing the tissue viscous parameters with MRE is useful for characterizing liver inflammation, non-alcoholic steatohepatitis, hepatic congestion, portal hypertension, and hepatic tumors. Further advances such as multifrequency acquisitions and compression-sensitive MRE may provide novel quantitative markers of hepatic and splenic mechanical properties that may improve the diagnosis of hepatic and splenic diseases.

Stiffness reconstruction methods for MR elastography

Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave-motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

Numerical simulations of magnetic resonance elastography using finite element analysis with a linear heterogeneous viscoelastic model

Abstract

Magnetic resonance elastography (MRE) is a technique to identify the viscoelastic moduli of biological tissues by solving the inverse problem from the displacement field of viscoelastic wave propagation in a tissue measured by MRI. Because finite element analysis (FEA) of MRE evaluates not only the viscoelastic model for a tissue but also the efficiency of the inversion algorithm, we developed FEA for MRE using commercial software called ANSYS, the Zener model for displacement field of a wave inside tissue, and an inversion algorithm called the modified integral method. The profile of the simulated displacement field by FEA agrees well with the experimental data measured by MRE for gel phantoms. Similarly, the value of storage modulus (i.e., stiffness) recovered using the modified integral method with the simulation data is consistent with the value given in FEA. Furthermore, applying the suggested FEA to a human liver demonstrates the effectiveness of the present simulation scheme.

Graphical abstract

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.

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.

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

AIM

The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elastography (MRE)-an imaging technique that allows for the noninvasive visualization of the displacement field throughout an object from externally driven harmonic motion-as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles.

METHODS

Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multistep process for which custom scaffolding was designed and built. A customized spin-echo-based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite-element method.

RESULTS

Both complex shear moduli show a significant frequency dependence (p 0.001) in keeping with previous work.

CONCLUSION

The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies.

SIGNIFICANCE

On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g., a cylinder representing a blood vessel. This study demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

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

PURPOSE

Descriptions of the structure of brain tissue as a porous cellular matrix support application of a poroelastic (PE) mechanical model which includes both solid and fluid phases. However, the majority of brain magnetic resonance elastography (MRE) studies use a single phase viscoelastic (VE) model to describe brain tissue behavior, in part due to availability of relatively simple direct inversion strategies for mechanical property estimation. A notable exception is low frequency intrinsic actuation MRE, where PE mechanical properties are imaged with a nonlinear inversion algorithm.

METHODS

This paper investigates the effect of model choice at each end of the spectrum of in vivo human brain actuation frequencies. Repeat MRE examinations of the brains of healthy volunteers were used to compare image quality and repeatability for each inversion model for both 50 Hz externally produced motion and ≈1 Hz intrinsic motions. Additionally, realistic simulated MRE data were generated with both VE and PE finite element solvers to investigate the effect of inappropriate model choice for ideal VE and PE materials.

RESULTS

In vivo, MRE data revealed that VE inversions appear more representative of anatomical structure and quantitatively repeatable for 50 Hz induced motions, whereas PE inversion produces better results at 1 Hz. Reasonable VE approximations of PE materials can be derived by equating the equivalent wave velocities for the two models, provided that the timescale of fluid equilibration is not similar to the period of actuation. An approximation of the equilibration time for human brain reveals that this condition is violated at 1 Hz but not at 50 Hz. Additionally, simulation experiments when using the "wrong" model for the inversion demonstrated reasonable shear modulus reconstructions at 50 Hz, whereas cross-model inversions at 1 Hz were poor quality. Attenuation parameters were sensitive to changes in the forward model at both frequencies, however, no spatial information was recovered because the mechanisms of VE and PE attenuation are different.

CONCLUSIONS

VE inversions are simpler with fewer unknown properties and may be sufficient to capture the mechanical behavior of PE brain tissue at higher actuation frequencies. However, accurate modeling of the fluid phase is required to produce useful mechanical property images at the lower frequencies of intrinsic brain motions.

A microchannel flow model for soft tissue elasticity

A number of advances, including imaging of tissue displacements, have increased our ability to make measurements of tissue elastic properties of animal and human tissues. Accordingly, the question is increasingly asked, 'should our data be fit to a viscoelastic model, and if so which one?' In this paper we focus solely on soft tissues in a functional (non-pathological) state, and develop a model of elastic behavior that is based on the flow of viscous fluids through the extensive network of tissue microchannels in response to applied stress. This behavior can be captured in a 2-parameter model, and the model appears to predict the stress-relaxation behavior and the dispersive shear wave behavior of bovine liver specimens and other soft tissues and phantoms. The relationship of the microchannel flow model to more traditional models is also examined.

Including spatial information in nonlinear inversion MR elastography using soft prior regularization

Tissue displacements required for mechanical property reconstruction in magnetic resonance elastography (MRE) are acquired in a magnetic resonance imaging (MRI) scanner, therefore, anatomical information is available from other imaging sequences. Despite its availability, few attempts to incorporate prior spatial information in the MRE reconstruction process have been reported. This paper implements and evaluates soft prior regularization (SPR), through which homogeneity in predefined spatial regions is enforced by a penalty term in a nonlinear inversion strategy. Phantom experiments and simulations show that when predefined regions are spatially accurate, recovered property values are stable for SPR weighting factors spanning several orders of magnitude, whereas inaccurate segmentation results in bias in the reconstructed properties that can be mitigated through proper choice of regularization weighting. The method was evaluated in vivo by estimating viscoelastic mechanical properties of frontal lobe gray and white matter for five repeated scans of a healthy volunteer. Segmentations of each tissue type were generated using automated software, and statistically significant differences between frontal lobe gray and white matter were found for both the storage modulus and loss modulus . Provided homogeneous property assumptions are reasonable, SPR produces accurate quantitative property estimates for tissue structures which are finer than the resolution currently achievable with fully distributed MRE.

Towards an elastographic atlas of brain anatomy

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

Brain mechanical property measurement using MRE with intrinsic activation

Many pathologies alter the mechanical properties of tissue. Magnetic resonance elastography (MRE) has been developed to noninvasively characterize these quantities in vivo. Typically, small vibrations are induced in the tissue of interest with an external mechanical actuator. The resulting displacements are measured with phase contrast sequences and are then used to estimate the underlying mechanical property distribution. Several MRE studies have quantified brain tissue properties. However, the cranium and meninges, especially the dura, are very effective at damping externally applied vibrations from penetrating deeply into the brain. Here, we report a method, termed 'intrinsic activation', that eliminates the requirement for external vibrations by measuring the motion generated by natural blood vessel pulsation. A retrospectively gated phase contrast MR angiography sequence was used to record the tissue velocity at eight phases of the cardiac cycle. The velocities were numerically integrated via the Fourier transform to produce the harmonic displacements at each position within the brain. The displacements were then reconstructed into images of the shear modulus based on both linear elastic and poroelastic models. The mechanical properties produced fall within the range of brain tissue estimates reported in the literature and, equally important, the technique yielded highly reproducible results. The mean shear modulus was 8.1 kPa for linear elastic reconstructions and 2.4 kPa for poroelastic reconstructions where fluid pressure carries a portion of the stress. Gross structures of the brain were visualized, particularly in the poroelastic reconstructions. Intra-subject variability was significantly less than the inter-subject variability in a study of six asymptomatic individuals. Further, larger changes in mechanical properties were observed in individuals when examined over time than when the MRE procedures were repeated on the same day. Cardiac pulsation, termed intrinsic activation, produces sufficient motion to allow mechanical properties to be recovered. The poroelastic model is more consistent with the measured data from brain at low frequencies than the linear elastic model. Intrinsic activation allows MRE to be performed without a device shaking the head so the patient notices no differences between it and the other sequences in an MR examination.

In vivo measurement of volumetric strain in the human brain induced by arterial pulsation and harmonic waves

Motion-sensitive phase contrast magnetic resonance imaging and magnetic resonance elastography are applied for the measurement of volumetric strain and tissue compressibility in human brain. Volumetric strain calculated by the divergence operator using a biphasic effective-medium model is related to dilatation and compression of fluid spaces during harmonic stimulation of the head or during intracranial passage of the arterial pulse wave. In six volunteers, phase contrast magnetic resonance imaging showed that the central cerebrum expands at arterial pulse wave to strain values of (2.8 ± 1.9)·10(-4). The evolution of volumetric strain agrees well with the magnitude of the harmonic divergence measured in eight volunteers by magnetic resonance elastography using external activation of 25 Hz vibration frequency. Intracranial volumetric strain was proven sensitive to venous pressure altered by abdominal muscle contraction. In eight volunteers, an increase in volumetric strain due to abdominal muscle contraction of approximately 45% was observed (P = 0.0001). The corresponding compression modulus in the range of 9.5-13.5 kPa demonstrated that the compressibility of brain tissue at 25 Hz stimulation is much higher than that of water. This pilot study provides the background for compression-sensitive magnetic resonance imaging with or without external head stimulation. Volumetric strain may be sensitive to fluid flow abnormalities or pressure imbalances between vasculature and parenchyma as seen in hydrocephalus.

Measurement of vibration-induced volumetric strain in the human lung

Noninvasive image-based measurement of intrinsic tissue pressure is of great interest in the diagnosis and characterization of diseases. Therefore, we propose to exploit the capability of phase-contrast MRI to measure three-dimensional vector fields of tissue motion for deriving volumetric strain induced by external vibration. Volumetric strain as given by the divergence of mechanical displacement fields is related to tissue compressibility and is thus sensitive to the state of tissue pressure. This principle is demonstrated by the measurement of three-dimensional vector fields of 50-Hz oscillations in a compressible agarose phantom and in the lungs of nine healthy volunteers. In the phantom, the magnitude of the oscillating divergence increased by about 400% with 4.8 bar excess air pressure, corresponding to an effective-medium compression modulus of 230 MPa. In lungs, the averaged divergence magnitude increased in all volunteers (N = 9) between 7 and 78% from expiration to inspiration. Measuring volumetric strain by MRI provides a compression-sensitive parameter of tissue mechanics, which varies with the respiratory state in the lungs. In future clinical applications for diagnosis and characterization of lung emphysema, fibrosis, or cancer, divergence-sensitive MRI may serve as a noninvasive marker sensitive to disease-related alterations of regional elastic recoil pressure in the lungs.

Model-based elastography: a survey of approaches to the inverse elasticity problem

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.

Model-based elastography: a survey of approaches to the inverse elasticity problem

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.

AN OVERVIEW OF ELASTOGRAPHY - AN EMERGING BRANCH OF MEDICAL IMAGING

From times immemorial manual palpation served as a source of information on the state of soft tissues and allowed detection of various diseases accompanied by changes in tissue elasticity. During the last two decades, the ancient art of palpation gained new life due to numerous emerging elasticity imaging (EI) methods. Areas of applications of EI in medical diagnostics and treatment monitoring are steadily expanding. Elasticity imaging methods are emerging as commercial applications, a true testament to the progress and importance of the field.In this paper we present a brief history and theoretical basis of EI, describe various techniques of EI and, analyze their advantages and limitations, and overview main clinical applications. We present a classification of elasticity measurement and imaging techniques based on the methods used for generating a stress in the tissue (external mechanical force, internal ultrasound radiation force, or an internal endogenous force), and measurement of the tissue response. The measurement method can be performed using differing physical principles including magnetic resonance imaging (MRI), ultrasound imaging, X-ray imaging, optical and acoustic signals.Until recently, EI was largely a research method used by a few select institutions having the special equipment needed to perform the studies. Since 2005 however, increasing numbers of mainstream manufacturers have added EI to their ultrasound systems so that today the majority of manufacturers offer some sort of Elastography or tissue stiffness imaging on their clinical systems. Now it is safe to say that some sort of elasticity imaging may be performed on virtually all types of focal and diffuse disease. Most of the new applications are still in the early stages of research, but a few are becoming common applications in clinical practice.

The influence of physiological aging and atrophy on brain viscoelastic properties in humans

Physiological aging of the brain is accompanied by ubiquitous degeneration of neurons and oligodendrocytes. An alteration of the cellular matrix of an organ impacts its macroscopic viscoelastic properties which can be detected by magnetic resonance elastography (MRE)--to date the only method for measuring brain mechanical parameters without intervention. However, the wave patterns detected by MRE are affected by atrophic changes in brain geometry occurring in an individual's life span. Moreover, regional variability in MRE-detected age effects is expected corresponding to the regional variation in atrophy. Therefore, the sensitivity of brain MRE to brain volume and aging was investigated in 66 healthy volunteers aged 18-72. A linear decline in whole-brain elasticity was observed (-0.75%/year, R-square = 0.59, p<0.001); the rate is three times that determined by volume measurements (-0.23%/year, R-square = 0.4, p<0.001). The highest decline in elasticity (-0.92%/year, R-square = 0.43, p<0.001) was observed in a region of interest placed in the frontal lobe with minimal age-related shrinkage (-0.1%, R-square = 0.06, p = 0.043). Our results suggest that cerebral MRE can measure geometry-independent viscoelastic parameters related to intrinsic tissue structure and altered by age.

An octahedral shear strain-based measure of SNR for 3D MR elastography

A signal-to-noise ratio (SNR) measure based on the octahedral shear strain (the maximum shear strain in any plane for a 3D state of strain) is presented for magnetic resonance elastography (MRE), where motion-based SNR measures are commonly used. The shear strain, γ, is directly related to the shear modulus, μ, through the definition of shear stress, τ = μγ. Therefore, noise in the strain is the important factor in determining the quality of motion data, rather than the noise in the motion. Motion and strain SNR measures were found to be correlated for MRE of gelatin phantoms and the human breast. Analysis of the stiffness distributions of phantoms reconstructed from the measured motion data revealed a threshold for both strain and motion SNR where MRE stiffness estimates match independent mechanical testing. MRE of the feline brain showed significantly less correlation between the two SNR measures. The strain SNR measure had a threshold above which the reconstructed stiffness values were consistent between cases, whereas the motion SNR measure did not provide a useful threshold, primarily due to rigid body motion effects.

Effects of frequency- and direction-dependent elastic materials on linearly elastic MRE image reconstructions

The mechanical model commonly used in magnetic resonance elastography (MRE) is linear elasticity. However, soft tissue may exhibit frequency- and direction-dependent (FDD) shear moduli in response to an induced excitation causing a purely linear elastic model to provide an inaccurate image reconstruction of its mechanical properties. The goal of this study was to characterize the effects of reconstructing FDD data using a linear elastic inversion (LEI) algorithm. Linear and FDD phantoms were manufactured and LEI images were obtained from time-harmonic MRE acquisitions with variations in frequency and driving signal amplitude. LEI responses to artificially imposed uniform phase shifts in the displacement data from both purely linear elastic and FDD phantoms were also evaluated. Of the variety of FDD phantoms considered, LEI appeared to tolerate viscoelastic data-model mismatch better than deviations caused by poroelastic and anisotropic mechanical properties in terms of visual image contrast. However, the estimated shear modulus values were substantially incorrect relative to independent mechanical measurements even in the successful viscoelastic cases and the variations in mean values with changes in experimental conditions associated with uniform phase shifts, driving signal frequency and amplitude were unpredictable. Overall, use of LEI to reconstruct data acquired in phantoms with FDD material properties provided biased results under the best conditions and significant artifacts in the worst cases. These findings suggest that the success with which LEI is applied to MRE data in tissue will depend on the underlying mechanical characteristics of the tissues and/or organs systems of clinical interest.

Contrast detection in fluid-saturated media with magnetic resonance poroelastography

PURPOSE

Recent interest in the poroelastic behavior of tissues has led to the development of magnetic resonance poroelastography (MRPE) as an alternative to single-phase MR elastographic image reconstruction. In addition to the elastic parameters (i.e., Lamé's constants) commonly associated with magnetic resonance elastography (MRE), MRPE enables estimation of the time-harmonic pore-pressure field induced by external mechanical vibration.

METHODS

This study presents numerical simulations that demonstrate the sensitivity of the computed displacement and pore-pressure fields to a priori estimates of the experimentally derived model parameters. In addition, experimental data collected in three poroelastic phantoms are used to assess the quantitative accuracy of MR poroelastographic imaging through comparisons with both quasistatic and dynamic mechanical tests.

RESULTS

The results indicate hydraulic conductivity to be the dominant parameter influencing the deformation behavior of poroelastic media under conditions applied during MRE. MRPE estimation of the matrix shear modulus was bracketed by the values determined from independent quasistatic and dynamic mechanical measurements as expected, whereas the contrast ratios for embedded inclusions were quantitatively similar (10%-15% difference between the reconstructed images and the mechanical tests).

CONCLUSIONS

The findings suggest that the addition of hydraulic conductivity and a viscoelastic solid component as parameters in the reconstruction may be warranted.

Time-harmonic magnetic resonance elastography of the normal feline brain

Imaging of the mechanical properties of in vivo brain tissue could eventually lead to non-invasive diagnosis of hydrocephalus, Alzheimer's disease and other pathologies known to alter the intracranial environment. The purpose of this work is to (1) use time-harmonic magnetic resonance elastography (MRE) to estimate the mechanical property distribution of cerebral tissue in the normal feline brain and (2) compare the recovered properties of grey and white matter. Various in vivo and ex vivo brain tissue property measurement strategies have led to the highly variable results that have been reported in the literature. MR elastography is an imaging technique that can estimate mechanical properties of tissue non-invasively and in vivo. Data was acquired in 14 felines and elastic parameters were estimated using a globo-regional nonlinear image reconstruction algorithm. Results fell within the range of values reported in the literature and showed a mean shear modulus across the subject group of 7-8 kPa with all but one animal falling within 5-15 kPa. White matter was statistically stiffer (p<0.01) than grey matter by about 1 kPa on a per subject basis. To the best of our knowledge, the results reported represent the most extensive set of estimates in the in vivo brain which have been based on MRE acquisition of the three-dimensional displacement field coupled to volumetric shear modulus image reconstruction achieved through nonlinear parameter estimation. However, the inter-subject variation in mean shear modulus indicates the need for further study, including the possibility of applying more advanced models to estimate the relevant tissue mechanical properties from the data.