Multifrequency inversion in magnetic resonance elastography

Multifrequency time-harmonic elastography for the measurement of liver viscoelasticity in large tissue windows

Elastography of the liver for the non-invasive diagnosis of hepatic fibrosis is an established method. However, investigations of obese patients or patients with ascites are often limited by small and superficial elastographic windows. Therefore, multifrequency time-harmonic elastography (THE) based on time-resolved A-line ultrasound has recently been developed for measuring liver viscoelasticity in wide soft tissue windows and at greater depths. In this study, THE was integrated into a clinical B-mode scanner connected to a dedicated actuator bed driven by superimposed vibrations of 30- to 60-Hz frequencies. The resulting shear waves in the liver were captured along multiple profiles 7 to 14 cm in width and automatically processed for reconstruction of mean efficient shear wave speed and shear wave dispersion slope. This new modality was tested in healthy volunteers and 22 patients with clinically proven cirrhosis. Patients could be separated from controls by higher shear wave speeds (3.11 ± 0.64 m/s, 2.14-4.81 m/s, vs. 1.74 ± 0.10 m/s, 1.60-1.91 m/s) without significant degradation of data by high body mass index or ascites. Furthermore, the wave speed dispersion slope was significantly (p = 0.0025) lower in controls (5.2 ± 1.8 m/s/kHz) than in patients (39.1 ± 32.2 m/s/kHz). In conclusion, THE is useful for the diagnosis of cirrhosis in large tissue windows.

Simultaneous, multidirectional acquisition of displacement fields in magnetic resonance elastography of the in vivo human brain

BACKGROUND

To implement a multidirectional motion encoding scheme for magnetic resonance elastography (MRE) of the human brain with reduced acquisition time, and investigate its performance relative to a conventional MRE scheme.

METHODS

The sample interval modulation (SLIM) scheme was implemented in a multishot, variable density spiral MRE sequence. The brains of seven healthy volunteers were investigated with both SLIM-MRE and conventional MRE acquisitions in a single imaging session on a clinical 3 Tesla MRI scanner with 50 Hz vibration. Following extraction of displacement fields, complex shear modulus property maps were estimated for each encoding concept.

RESULTS

The SLIM-MRE and conventional MRE acquisitions produced deformation fields that were nearly identical and exhibited an average correlation coefficient of 0.95 (all p < 0.05). Average properties of white matter differed between the two acquisitions by less than 5% for all volunteers, which is better than reproducibility estimates for conventional MRE alone.

CONCLUSION

The use of SLIM provides very similar quantitative property estimates compared with the conventional MRE encoding scheme. The SLIM acquisition is 2.5 times faster than the conventional acquisition, and may speed the adoption of MRE in clinical settings.

Sensitization of a stray-field NMR to vibrations: a potential for MR elastometry with a portable NMR sensor

An NMR signal from a sample in a constant stray field of a portable NMR sensor is sensitized to vibrations. The CPMG sequence is synchronized to vibrations so that the constant gradient becomes an "effective" square-wave gradient, leading to the vibration-induced phase accumulation. The integrating nature of the spot measurement, combined with the phase distribution due to a non-uniform gradient and/or a wave field, leads to a destructive interference, the drop in the signal intensity and changes in the echo train shape. Vibrations with amplitudes as small as 140 nm were reliably detected with the permanent gradient of 12.4 T/m. The signal intensity depends on the phase offset between the vibrations and the pulse sequence. This approach opens the way for performing elastometry and micro-rheology measurements with portable NMR devices beyond the walls of a laboratory. Even without synchronization, if a vibration frequency is comparable to 1/2TE of the CPMG sequence, the signal can be severely affected, making it important for potential industrial applications of stray-field NMR.

High-resolution mechanical imaging of glioblastoma by multifrequency magnetic resonance elastography

Objective

To generate high-resolution maps of the viscoelastic properties of human brain parenchyma for presurgical quantitative assessment in glioblastoma (GB).

Methods

Twenty-two GB patients underwent routine presurgical work-up supplemented by additional multifrequency magnetic resonance elastography. Two three-dimensional viscoelastic parameter maps, magnitude |G*|, and phase angle φ of the complex shear modulus were reconstructed by inversion of full wave field data in 2-mm isotropic resolution at seven harmonic drive frequencies ranging from 30 to 60 Hz.

Results

Mechanical brain maps confirmed that GB are composed of stiff and soft compartments, resulting in high intratumor heterogeneity. GB could be easily differentiated from healthy reference tissue by their reduced viscous behavior quantified by φ (0.37±0.08 vs. 0.58±0.07). |G*|, which in solids more relates to the material's stiffness, was significantly reduced in GB with a mean value of 1.32±0.26 kPa compared to 1.54±0.27 kPa in healthy tissue (P = 0.001). However, some GB (5 of 22) showed increased stiffness.

Conclusion

GB are generally less viscous and softer than healthy brain parenchyma. Unrelated to the morphology-based contrast of standard magnetic resonance imaging, elastography provides an entirely new neuroradiological marker and contrast related to the biomechanical properties of tumors.

Parametric-based brain Magnetic Resonance Elastography using a Rayleigh damping material model

The three-parameter Rayleigh damping (RD) model applied to time-harmonic Magnetic Resonance Elastography (MRE) has potential to better characterise fluid-saturated tissue systems. However, it is not uniquely identifiable at a single frequency. One solution to this problem involves simultaneous inverse problem solution of multiple input frequencies over a broad range. As data is often limited, an alternative elegant solution is a parametric RD reconstruction, where one of the RD parameters (μI or ρI) is globally constrained allowing accurate identification of the remaining two RD parameters. This research examines this parametric inversion approach as applied to in vivo brain imaging. Overall, success was achieved in reconstruction of the real shear modulus (μR) that showed good correlation with brain anatomical structures. The mean and standard deviation shear stiffness values of the white and gray matter were found to be 3±0.11kPa and 2.2±0.11kPa, respectively, which are in good agreement with values established in the literature or measured by mechanical testing. Parametric results with globally constrained μI indicate that selecting a reasonable value for the μI distribution has a major effect on the reconstructed ρI image and concomitant damping ratio (ξd). More specifically, the reconstructed ρI image using a realistic μI=333Pa value representative of a greater portion of the brain tissue showed more accurate differentiation of the ventricles within the intracranial matter compared to μI=1000Pa, and ξd reconstruction with μI=333Pa accurately captured the higher damping levels expected within the vicinity of the ventricles. Parametric RD reconstruction shows potential for accurate recovery of the stiffness characteristics and overall damping profile of the in vivo living brain despite its underlying limitations. Hence, a parametric approach could be valuable with RD models for diagnostic MRE imaging with single frequency data.

High Resolution Imaging of Viscoelastic Properties of Intracranial Tumours by Multi-Frequency Magnetic Resonance Elastography

PURPOSE

In recent years Magnetic Resonance Elastography (MRE) emerged into a clinically applicable imaging technique. It has been shown that MRE is capable of measuring global changes of the viscoelastic properties of cerebral tissue. The purpose of our study was to evaluate a spatially resolved three-dimensional multi-frequent MRE (3DMMRE) for assessment of the viscoelastic properties of intracranial tumours.

METHODS

A total of 27 patients (63 ± 13 years) were included. All examinations were performed on a 3.0 T scanner, using a modified phase-contrast echo planar imaging sequence. We used 7 vibration frequencies in the low acoustic range with a temporal resolution of 8 dynamics per wave cycle. Post-processing included multi-frequency dual elasto-visco (MDEV) inversion to generate high-resolution maps of the magnitude |G*| and the phase angle φ of the complex valued shear modulus.

RESULTS

The tumour entities included in this study were: glioblastoma (n = 11), anaplastic astrocytoma (n = 3), meningioma (n = 7), cerebral metastasis (n = 5) and intracerebral abscess formation (n = 1). Primary brain tumours and cerebral metastases were not distinguishable in terms of |G*| and φ. Glioblastoma presented the largest range of |G*| values and a trend was delineable that glioblastoma were slightly softer than WHO grade III tumours. In terms of φ, meningiomas were clearly distinguishable from all other entities.

CONCLUSIONS

In this pilot study, while analysing the viscoelastic constants of various intracranial tumour entities with an improved spatial resolution, it was possible to characterize intracranial tumours by their mechanical properties. We were able to clearly delineate meningiomas from intraaxial tumours, while for the latter group an overlap remains in viscoelastic terms.

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

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

High-resolution mechanical imaging of the kidney

The objective of this study was to test the feasibility and reproducibility of in vivo high-resolution mechanical imaging of the asymptomatic human kidney. Hereby nine volunteers were examined at three different physiological states of urinary bladder filling (a normal state, urinary urgency, and immediately after urinary relief). Mechanical imaging was performed of the in vivo kidney using three-dimensional multifrequency magnetic resonance elastography combined with multifrequency dual elastovisco inversion. Other than in classical elastography, where the storage and loss shear moduli are evaluated, we analyzed the magnitude |G(⁎)| and the phase angle φ of the complex shear modulus reconstructed by simultaneous inversion of full wave field data corresponding to 7 harmonic drive frequencies from 30 to 60Hz and a resolution of 2.5mm cubic voxel size. Mechanical parameter maps were derived with a spatial resolution superior to that in previous work. The group-averaged values of |G(⁎)| were 2.67±0.52kPa in the renal medulla, 1.64±0.17kPa in the cortex, and 1.17±0.21kPa in the hilus. The phase angle φ (in radians) was 0.89±0.12 in the medulla, 0.83±0.09 in the cortex, and 0.72±0.06 in the hilus. All regional differences were significant (P<0.001), while no significant variation was found in relation to different stages of bladder filling. In summary our study provides first high-resolution maps of viscoelastic parameters of the three anatomical regions of the kidney. |G(⁎)| and φ provide novel information on the viscoelastic properties of the kidney, which is potentially useful for the detection of renal lesions or fibrosis.

Curl-Based Finite Element Reconstruction of the Shear Modulus Without Assuming Local Homogeneity: Time Harmonic Case

In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2-D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.

Sample interval modulation for the simultaneous acquisition of displacement vector data in magnetic resonance elastography: theory and application

SampLe Interval Modulation-magnetic resonance elastography (SLIM-MRE) is introduced for simultaneously encoding all three displacement projections of a monofrequency vibration into the MR signal phase. In SLIM-MRE, the individual displacement components are observed using different sample intervals. In doing so, the components are modulated with different apparent frequencies in the MR signal phase expressed as a harmonic function of the start time of the motion encoding gradients and can thus be decomposed by applying a Fourier transform to the sampled multidirectional MR phases. In this work, the theoretical foundations of SLIM-MRE are presented and the new idea is implemented using a high field (11.7 T) vertical bore magnetic resonance imaging system on an inhomogeneous agarose gel phantom sample. The local frequency estimation-derived stiffness values were the same within the error margins for both the new SLIM-MRE method and for conventional MRE, while the number of temporally-resolved MRE experiments needed for each study was reduced from three to one. In this work, we present for the first time, monofrequency displacement data along three sensitization directions that were acquired simultaneously and stored in the same k-space.

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

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

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

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

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

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

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

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

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

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.

Selective spectral displacement projection for multifrequency MRE

We introduce a new motion encoding concept for the displacement vector in multifrequency magnetic resonance elastography (MRE). Selective spectral displacement projection (SDP)-MRE can be applied to a vibration spectrum composed of three frequencies and exploits the filter condition of MRE for selecting one frequency each per spatial motion encoding direction. The selected components are simultaneously encoded in the phase of the MR signal. Therefore, the total MR phase is represented by a sum of phase portions, each corresponding to a distinct spatial projection and vibration frequency. The individual components can be obtained by applying a Fourier-transform to the temporally resolved phase images. SDP-MRE reduces the number of temporally resolved MRE experiments for data acquisition by a factor of 3, while providing similar wave images as found using conventional monofrequency MRE.

Local mechanical properties of white matter structures in the human brain

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

[Magnetic resonance elastography of the liver]

CLINICAL/METHODICAL ISSUE

The early detection of liver fibrosis remains a major challenge in medical imaging.

STANDARD RADIOLOGICAL METHODS

Nowadays staging of liver fibrosis is not a task for radiological examinations and the gold standard is liver puncture.

METHODICAL INNOVATIONS

Elastography is sensitive to the mechanical properties of soft tissues and in the liver stiffness is highly correlated to the degree of fibrosis. In magnetic resonance imaging elastography (MRE) time-harmonic vibrations are induced in the liver and encoded by motion-sensitive phase-contrast sequences. Viscoelastic constants are recovered from the obtained wave images and displayed by so-called elastograms.

PERFORMANCE

The MRE procedure is able to discriminate low grades of fibrosis (F0-F1) from medium and severe fibrosis (F2-F4) with a diagnostic accuracy (AUROC) of 0.92.

ACHIEVEMENTS

Currently, MRE is the most sensitive imaging modality for the noninvasive staging of liver fibrosis.

PRACTICAL RECOMMENDATIONS

Current technical developments of MRE may further improve the accuracy of the method towards a new gold standard for noninvasive staging of fibrosis by radiologists.

Magnetic resonance elastography of the brain using multishot spiral readouts with self-navigated motion correction

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

Magnetic resonance elastography reveals altered brain viscoelasticity in experimental autoimmune encephalomyelitis

Cerebral magnetic resonance elastography (MRE) measures the viscoelastic properties of brain tissues in vivo. It was recently shown that brain viscoelasticity is reduced in patients with multiple sclerosis (MS), highlighting the potential of cerebral MRE to detect tissue pathology during neuroinflammation. To further investigate the relationship between inflammation and brain viscoelasticity, we applied MRE to a mouse model of MS, experimental autoimmune encephalomyelitis (EAE). EAE was induced and monitored by MRE in a 7-tesla animal MRI scanner over 4 weeks. At the peak of the disease (day 14 after immunization), we detected a significant decrease in both the storage modulus (G′) and the loss modulus (G″), indicating that both the elasticity and the viscosity of the brain are reduced during acute inflammation. Interestingly, these parameters normalized at a later time point (day 28) corresponding to the clinical recovery phase. Consistent with this, we observed a clear correlation between viscoelastic tissue alteration and the magnitude of perivascular T cell infiltration at both day 14 and day 28. Hence, acute neuroinflammation is associated with reduced mechanical cohesion of brain tissues. Moreover, the reduction of brain viscoelasticity appears to be a reversible process, which is restored when inflammation resolves. For the first time, our study has demonstrated the applicability of cerebral MRE in EAE, and showed that this novel imaging technology is highly sensitive to early tissue alterations resulting from the inflammatory processes. Thus, MRE may serve to monitor early stages of perivascular immune infiltration during neuroinflammation.