An analytical solution to the dispersion‐by‐inversion problem in magnetic resonance elastography

Purpose: Magnetic resonance elastography (MRE) measures stiffness of soft tissues by analyzing their spatial harmonic response to externally induced shear vibrations. Many MRE methods use inversion-based reconstruction approaches, which invoke first- or second-order derivatives by finite difference operators (first- and second-FDOs) and thus give rise to a biased frequency dispersion of stiffness estimates. Methods: We here demonstrate analytically, numerically, and experimentally that FDO-based stiffness estimates are affected by (1) noise-related underestimation of values in the range of high spatial wave support, that is, at lower vibration frequencies, and (2) overestimation of values due to wave discretization at low spatial support, that is, at higher vibration frequencies. Results: Our results further demonstrate that second-FDOs are more susceptible to noise than first-FDOs and that FDO dispersion depends both on signal-to-noise ratio (SNR) and on a lumped parameter A, which is defined as wavelength over pixel size and over a number of pixels per stencil of the FDO. Analytical FDO dispersion functions are derived for optimizing A parameters at a given SNR. As a simple rule of thumb, we show that FDO artifacts are minimized when A/2 is in the range of the square root of 2SNR for the first-FDO or cubic root of 5SNR for the second-FDO. Conclusions: Taken together, the results of our study provide an analytical solution to a long-standing, well-recognized, yet unsolved problem in MRE postprocessing and might thus contribute to the ongoing quest for minimizing inversion artifacts in MRE

Elasticity-based determination of isovolumetric phases in the human heart

<p>Abstract</p> <p>Background/Motivation</p> <p>To directly determine isovolumetric cardiac time intervals by magnetic resonance elastography (MRE) using the magnitude of the complex signal for deducing morphological information combined with the phase of the complex signal for tension-relaxation measurements.</p> <p>Methods</p> <p>Thirty-five healthy volunteers and 11 patients with relaxation abnormalities were subjected to transthoracic wave stimulation using vibrations of approximately 25 Hz. A <it>k</it>-space-segmented, ECG-gated gradient-recalled echo steady-state sequence with a 500-Hz bipolar motion-encoding gradient was used for acquiring a series of 360 complex images of a short-axis view of the heart at a frame rate of less than 5.2 ms. Magnitude images were employed for measuring the cross-sectional area of the left ventricle, while phase images were used for analyzing the amplitudes of the externally induced waves. The delay between the decrease in amplitude and onset of ventricular contraction was determined in all subjects and assigned to the time of isovolumetric tension. Conversely, the delay between the increase in wave amplitude and ventricular dilatation was used for measuring the time of isovolumetric elasticity relaxation.</p> <p>Results</p> <p>Wave amplitudes decreased during systole and increased during diastole. The variation in wave amplitude occurred ahead of morphological changes. In healthy volunteers the time of isovolumetric elasticity relaxation was 75 ± 31 ms, which is significantly shorter than the time of isovolumetric tension of 136 ± 36 ms (<it>P </it>< 0.01). In patients with relaxation abnormalities (mild diastolic dysfunction, <it>n </it>= 11) isovolumetric elasticity relaxation was significantly prolonged, with 133 ± 57 ms (<it>P </it>< 0.01), whereas isovolumetric tension time was in the range of healthy controls (161 ± 45 ms; <it>P </it>= 0.053).</p> <p>Conclusion</p> <p>The complex MRE signal conveys complementary information on cardiac morphology and elasticity, which can be combined for directly measuring isovolumetric tension and elasticity relaxation in the human heart.</p

Valsalva maneuver decreases liver and spleen stiffness measured by time-harmonic ultrasound elastography

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

The MRE inverse problem for the elastic shear modulus

Magnetic resonance elastography (MRE) is a powerful technique for noninvasive determination of the biomechanical properties of tissue, with important applications in disease diagnosis. A typical experimental scenario is to induce waves in the tissue by time-harmonic external mechanical oscillation and then measure the tissue's displacement at fixed spatial positions 8 times during a complete time-period, extracting the dominant frequency signal from the discrete Fourier transform in time. Accurate reconstruction of the tissue's elastic moduli from MRE data is a challenging inverse problem, and we derive and analyze two new methods which address different aspects. The first of these concerns the time signal: using only the dominant frequency component loses information for noisy data and typically gives a complex value for the (real) shear modulus, which is then hard to interpret. Our new reconstruction method is based on the Fourier time-interpolant of the displacement: it uses all the measured information and automatically gives a real value of shear modulus up to rounding error. This derivation is for homogeneous materials, and our second new method (stacked frequency wave inversion, SFWI) concerns the inhomogeneous shear modulus in the time-harmonic case. The underlying problem is ill-conditioned because the coefficient of the shear modulus in the governing equations can be zero or small, and the SFWI approach overcomes this by combining approximations at different frequencies into a single overdetermined matrix--vector equation. Careful numerical tests confirm that both these new algorithms perform well

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

Purpose: Biological soft tissues often have a porous architecture comprising fluid and solid compartments. Upon displacement through physiological or externally induced motion, the relative motion of these compartments depends on poroelastic parameters, such as coupling density (rho 12) and tissue porosity. This study introduces inversion recovery MR elastography (IR-MRE) (1) to quantify porosity defined as fluid volume over total volume, (2) to separate externally induced shear strain fields of fluid and solid compartments, and (3) to quantify coupling density assuming a biphasic behavior of in vivo brain tissue. Theory and Methods: Porosity was measured in eight tofu phantoms and gray matter (GM) and white matter (WM) of 21 healthy volunteers. Porosity of tofu was compared to values obtained by fluid draining and microscopy. Solid and fluid shear-strain amplitudes and rho 12were estimated both in phantoms and in in vivo brain. Results T-1-based measurement of tofu porosity agreed well with reference values (R = 0.99,P < .01). Brain tissue porosity was 0.14 ± 0.02 in GM and 0.05 ± 0.01 in WM (P < .001). Fluid shear strain was found to be phase-locked with solid shear strain but had lower amplitudes in both tofu phantoms and brain tissue (P < .05). In accordance with theory, tofu and brain rho 12were negative. Conclusion: IR-MRE allowed for the first time separation of shear strain fields of solid and fluid compartments for measuring coupling density according to the biphasic theory of poroelasticity. Thus, IR-MRE opens horizons for poroelastography-derived imaging markers that can be used in basic research and diagnostic applications

Multiple motion encoding in Phase-Contrast MRI:A general theory and application to elastography imaging

While MRI allows to encode the motion of tissue in the magnetization’s phase, it remains yet a challenge to obtain high fidelity motion images due to wraps in the phase for high encoding efficiencies. Therefore, we propose an optimal multiple motion encoding method (OMME) and exemplify it in Magnetic Resonance Elastography (MRE) data. OMME is formulated as a non-convex least-squares problem for the motion using an arbitrary number of phase-contrast measurements with different motion encoding gradients (MEGs). The mathematical properties of OMME are proved in terms of standard deviation and dynamic range of the motion’s estimate for arbitrary MEGs combination which are confirmed using synthetically generated data. OMME’s performance is assessed on MRE data from in vivo human brain experiments and compared to dual encoding strategies. The unwrapped images are further used to reconstruct stiffness maps and compared to the ones obtained using conventional unwrapping methods. OMME allowed to successfully combine several MRE phase images with different MEGs, outperforming dual encoding strategies in either motion-to-noise ratio (MNR) or number of successfully reconstructed voxels with good noise stability. This lead to stiffness maps with greater resolution of details than obtained with conventional unwrapping methods. The proposed OMME method allows for a flexible and noise robust increase in the dynamic range and thus provides wrap-free phase images with high MNR. In MRE, the method may be especially suitable when high resolution images with high MNR are needed

Brain Viscoelasticity Alteration in Chronic-Progressive Multiple Sclerosis

Introduction: Viscoelastic properties indicate structural alterations in biological tissues at multiple scales with high sensitivity. Magnetic Resonance Elastography (MRE) is a novel technique that directly visualizes and quantitatively measures biomechanical tissue properties in vivo. MRE recently revealed that early relapsing-remitting multiple sclerosis (MS) is associated with a global decrease of the cerebral mechanical integrity. This study addresses MRE and MR volumetry in chronic-progressive disease courses of MS

MR Elastography-Based Assessment of Matrix Remodeling at Lesion Sites Associated With Clinical Severity in a Model of Multiple Sclerosis

Magnetic resonance imaging (MRI) with gadolinium based contrast agents (GBCA) is routinely used in the clinic to visualize lesions in multiple sclerosis (MS). Although GBCA reveal endothelial permeability, they fail to expose other aspects of lesion formation such as the magnitude of inflammation or tissue changes occurring at sites of blood-brain barrier (BBB) disruption. Moreover, evidence pointing to potential side effects of GBCA has been increasing. Thus, there is an urgent need to develop GBCA-independent imaging tools to monitor pathology in MS. Using MR-elastography (MRE), we previously demonstrated in both MS and the animal model experimental autoimmune encephalomyelitis (EAE) that inflammation was associated with a reduction of brain stiffness. Now, using the relapsing-remitting EAE model, we show that the cerebellum-a region with predominant inflammation in this model-is especially prone to loss of stiffness. We also demonstrate that, contrary to GBCA-MRI, reduction of brain stiffness correlates with clinical disability and is associated with enhanced expression of the extracellular matrix protein fibronectin (FN). Further, we show that FN is largely expressed by activated astrocytes at acute lesions, and reflects the magnitude of tissue remodeling at sites of BBB breakdown. Therefore, MRE could emerge as a safe tool suitable to monitor disease activity in MS

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

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