Differential effects of pre-tension on shear wave propagation in elastic media with different boundary conditions as measured by magnetic resonance elastography and finite element modeling

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,μ0US= 12.3 ± 0.3 kPa andμ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

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

Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues

In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment.

Rescaled Local Interaction Simulation Approach for Shear Wave Propagation Modelling in Magnetic Resonance Elastography

Properties of soft biological tissues are increasingly used in medical diagnosis to detect various abnormalities, for example, in liver fibrosis or breast tumors. It is well known that mechanical stiffness of human organs can be obtained from organ responses to shear stress waves through Magnetic Resonance Elastography. The Local Interaction Simulation Approach is proposed for effective modelling of shear wave propagation in soft tissues. The results are validated using experimental data from Magnetic Resonance Elastography. These results show the potential of the method for shear wave propagation modelling in soft tissues. The major advantage of the proposed approach is a significant reduction of computational effort.

Magnetic resonance elastography of abdomen

Many diseases cause substantial changes in the mechanical properties of tissue, and this provides motivation for developing methods to noninvasively assess the stiffness of tissue using imaging technology. Magnetic resonance elastography (MRE) has emerged as a versatile MRI-based technique, based on direct visualization of propagating shear waves in the tissues. The most established clinical application of MRE in the abdomen is in chronic liver disease. MRE is currently regarded as the most accurate noninvasive technique for detection and staging of liver fibrosis. Increasing experience and ongoing research is leading to exploration of applications in other abdominal organs. In this review article, the current use of MRE in liver disease and the potential future applications of this technology in other parts of the abdomen are surveyed.

Acoustic radiation force beam sequence performance for detection and material characterization of atherosclerotic plaques: preclinical, ex vivo results

This work presents preclinical data demonstrating performance of acoustic radiation force (ARF)-based elasticity imaging with five different beam sequences for atherosclerotic plaque detection and material characterization. Twelve trained, blinded readers evaluated parametric images taken ex vivo under simulated in vivo conditions of 22 porcine femoral arterial segments. Receiver operating characteristic (ROC) curve analysis was carried out to quantify reader performance using spatially-matched immunohistochemistry for validation. The beam sequences employed had high sensitivity (sens) and specificity (spec) for detecting Type III+ plaques (sens: 85%, spec: 79%), lipid pools (sens: 80%, spec: 86%), fibrous caps (sens: 86%, spec: 82%), calcium (sens: 96%, spec: 85%), collagen (sens: 78%, spec: 77%), and disrupted internal elastic lamina (sens: 92%, spec: 75%). 1:1 single-receive tracking yielded the highest median areas under the ROC curve (AUC), but was not statistically significantly higher than 4:1 parallel-receive tracking. Excitation focal configuration did not result in statistically different AUCs. Overall, these results suggest ARF-based imaging is relevant to detecting and characterizing plaques and support its use for diagnosing and monitoring atherosclerosis.

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.

Characterization of a hyper-viscoelastic phantom mimicking biological soft tissue using an abdominal pneumatic driver with magnetic resonance elastography (MRE)

The purpose of this study was to create a polymer phantom mimicking the mechanical properties of soft tissues using experimental tests and rheological models. Multifrequency Magnetic Resonance Elastography (MMRE) tests were performed on the present phantom with a pneumatic driver to characterize the viscoelastic (μ, η) properties using Voigt, Maxwell, Zener and Springpot models. To optimize the MMRE protocol, the driver behavior was analyzed with a vibrometer. Moreover, the hyperelastic properties of the phantom were determined using compressive tests and Mooney-Rivlin model. The range of frequency to be used with the round driver was found between 60 Hz and 100 Hz as it exhibits one type of vibration mode for the membrane. MRE analysis revealed an increase in the shear modulus with frequency reflecting the viscoelastic properties of the phantom showing similar characteristic of soft tissues. Rheological results demonstrated that Springpot model better revealed the viscoelastic properties (μ=3.45 kPa, η=6.17 Pas) of the phantom and the Mooney-Rivlin coefficients were C(10)=1.09.10(-2) MPa and C(01)=-8.96.10(-3) MPa corresponding to μ=3.95 kPa. These studies suggest that the phantom, mimicking soft tissue, could be used for preliminary MRE tests to identify the optimal parameters necessary for in vivo investigations. Further developments of the phantom may allow clinicians to more accurately mimic healthy and pathological soft tissues using MRE.

Assessment of stiffness changes in the ex vivo porcine aortic wall using magnetic resonance elastography

Magnetic resonance elastography (MRE) is a noninvasive phase-contrast technique for estimating the mechanical properties of tissues by imaging propagating mechanical waves within the tissue. In this study, we hypothesize that changes in arterial wall stiffness, experimentally induced by formalin fixation, can be measured using MRE in ex vivo porcine aortas. In agreement with our hypothesis, the significant stiffness increase after sample fixation was clearly demonstrated by MRE and confirmed by mechanical testing. The results indicate that MRE can be used to examine the stiffness changes of the aorta. This study has provided evidence of the effectiveness of using MRE to directly assess the stiffness change in aortic wall. The results offer motivation to pursue MRE as a noninvasive method for the evaluation of arterial wall mechanical properties.

Abdominal magnetic resonance elastography

Magnetic resonance elastography (MRE) is a magnetic resonance imaging-based technique for quantitatively assessing the mechanical properties of tissues based on the propagation of shear waves. Multiple studies have described many potential applications of MRE, from characterizing tumors to detecting diffuse disease processes. Studies have shown that MRE can be successfully implemented to assess abdominal organs. The first clinical application of MRE to be well documented is the detection and characterization of hepatic fibrosis, which systematically increases the stiffness of liver tissue. In this diagnostic role, it offers a safer, less expensive, and potentially more accurate alternative to invasive liver biopsy. Emerging results suggest that measurements of liver and spleen stiffness may provide an indirect way to assess portal hypertension. Preliminary studies have demonstrated that it is possible to use MRE to evaluate the mechanical properties of other abdominal structures, such as the pancreas and kidneys. Steady technical progress in developing practical protocols for applying MRE in the abdomen and the pelvis provides opportunities to explore many other potential applications of this emerging technology.

Magnetic resonance elastography: Inversions in bounded media

Magnetic resonance elastography is a noninvasive imaging technique capable of quantifying and spatially resolving the shear stiffness of soft tissues by visualization of synchronized mechanical wave displacement fields. However, magnetic resonance elastography inversions generally assume that the measured tissue motion consists primarily of shear waves propagating in a uniform, infinite medium. This assumption is not valid in organs such as the heart, eye, bladder, skin, fascia, bone and spinal cord, in which the shear wavelength approaches the geometric dimensions of the object. The aim of this study was to develop and test mathematical inversion algorithms capable of resolving shear stiffness from displacement maps of flexural waves propagating in bounded media such as beams, plates, and spherical shells, using geometry-specific equations of motion. Magnetic resonance elastography and finite element modeling of beam, plate, and spherical shell phantoms of various geometries were performed. Mechanical testing of the phantoms agreed with the stiffness values obtained from finite element modeling and magnetic resonance elastography data, and a linear correlation of r(2) >or= 0.99 was observed between the stiffness values obtained using magnetic resonance elastography and finite element modeling data. In conclusion, we have demonstrated new inversion methods for calculating shear stiffness that may be more appropriate for waves propagating in bounded media.

Identification and quantification of myofascial taut bands with magnetic resonance elastography

OBJECTIVE

To explore the feasibility of using a new magnetic resonance imaging (MRI) technique--magnetic resonance elastography (MRE)--to identify and quantitate the nature of myofascial taut bands.

DESIGN

This investigation consisted of 3 steps. The first involved proof of concept on gel phantoms, the second involved numeric modeling, and the third involved a pilot trial on 2 subjects. Imaging was performed with a 1.5 T MRI machine. Shear waves were produced with a custom-developed acoustically driven pneumatic transducer with gradient-echo image collection gated to the transducer's motion. Shear wave propagation were imaged by MRE.

SETTING

An MRI research laboratory.

PARTICIPANTS

Two women, one with a 3-year history of myofascial pain and the other serving as the control.

INTERVENTIONS

Not applicable.

MAIN OUTCOME MEASURES

MRE images, finite element analysis calculations, and tissue and phantom stiffness determinations.

RESULTS

Results of the phantom measurements, finite element calculations, and study patients were all consistent with the concept that taut bands are detectable and quantifiable with MRE imaging. The findings in the subjects suggest that the stiffness of the taut bands (9.0+/-0.9 KPa) in patients with myofascial pain may be 50% greater than that of the surrounding muscle tissue.

CONCLUSIONS

Our findings suggest that MRE can quantitate asymmetries in muscle tone that could previously only be identified subjectively by examination.

Developments in dynamic MR elastography for in vitro biomechanical assessment of hyaline cartilage under high-frequency cyclical shear

The design, construction, and evaluation of a customized dynamic magnetic resonance elastography (MRE) technique for biomechanical assessment of hyaline cartilage in vitro are described. For quantification of the dynamic shear properties of hyaline cartilage by dynamic MRE, mechanical excitation and motion sensitization were performed at frequencies in the kilohertz range. A custom electromechanical actuator and a z-axis gradient coil were used to generate and image shear waves throughout cartilage at 1000-10,000 Hz. A radiofrequency (RF) coil was also constructed for high-resolution imaging. The technique was validated at 4000 and 6000 Hz by quantifying differences in shear stiffness between soft ( approximately 200 kPa) and stiff ( approximately 300 kPa) layers of 5-mm-thick bilayered phantoms. The technique was then used to quantify the dynamic shear properties of bovine and shark hyaline cartilage samples at frequencies up to 9000 Hz. The results demonstrate that one can obtain high-resolution shear stiffness measurements of hyaline cartilage and small, stiff, multilayered phantoms at high frequencies by generating robust mechanical excitations and using large magnetic field gradients. Dynamic MRE can potentially be used to directly quantify the dynamic shear properties of hyaline and articular cartilage, as well as other cartilaginous materials and engineered constructs.