Estimation of Anisotropic Material Properties of Soft Tissue by MRI of Ultrasound-Induced Shear Waves

3D vector MR elastography applications in small organs

BACKGROUND

Magnetic resonance elastography (MRE) is a rapidly developing medical imaging technique that allows for quantitative assessment of the biomechanical properties of the tissue. MRE is now regarded as the most accurate noninvasive test for detecting and staging liver fibrosis. A two-dimensional (2D MRE) acquisition version is currently deployed at >2000 locations worldwide. 2D MRE allows for the evaluation of the magnitude of the complex shear modulus, also referred to as stiffness. The development of 3D vector MRE has enabled researchers to assess the biomechanical properties of small organs where wave propagation cannot be adequately analyzed with the 2D MRE imaging approach used in the liver. In 3D vector MRE, the shear waves are imaged and processed throughout a 3D volume and processed with an algorithm that accounts for wave propagation in any direction. Additionally, the motion is also imaged in x, y, and z directions at each voxel, allowing for more advanced processing to be applied.

PURPOSE

This review describes the technical principles of 3D vector MRE, surveys its clinical applications in small organs, and discusses potential clinical significance of 3D vector MRE.

CONCLUSION

3D vector MRE is a promising tool for characterizing the biomechanical properties of small organs such as the uterus, pancreas, thyroid, prostate, and salivary glands. However, its potential has not yet been fully explored.

Structural tuning of anisotropic mechanical properties in 3D-Printed hydrogel lattices

We investigated the ability to tune the anisotropic mechanical properties of 3D-printed hydrogel lattices by modifying their geometry (lattice strut diameter, unit cell size, and unit cell scaling factor). Many soft tissues are anisotropic and the ability to mimic natural anisotropy would be valuable for developing tissue-surrogate "phantoms" for elasticity imaging (shear wave elastography or magnetic resonance elastography). Vintile lattices were 3D-printed in polyethylene glycol di-acrylate (PEGDA) using digital light projection printing. Two mechanical benchtop tests, dynamic shear testing and unconfined compression, were used to measure the apparent shear storage moduli (G') and apparent Young's moduli (E) of lattice samples. Increasing the unit cell size from 1.25 mm to 2.00 mm reduced the Young's and shear moduli of the lattices by 91% and 85%, respectively. Decreasing the strut diameter from 300 μm to 200 μm reduced the apparent shear moduli of the lattices by 95%. Increasing the geometric scaling ratio of the lattice unit cells from 1.00 × to 2.00 × increased mechanical anisotropy in shear (by a factor of 3.1) and in compression (by a factor of 2.9). Both simulations and experiments show that the effects of unit cell size and strut diameter are consistent with power law relationships between volume fraction and apparent elastic moduli. In particular, experimental measurements of apparent Young's moduli agree well with predictions of the theoretical Gibson-Ashby model. Thus, the anisotropic mechanical properties of a lattice can be tuned by the unit cell size, the strut diameter, and scaling factors. This approach will be valuable in designing tissue-mimicking hydrogel lattice-based composite materials for elastography phantoms and tissue engineered scaffolds.

Post-mortem changes of anisotropic mechanical properties in the porcine brain assessed by MR elastography

Knowledge of the mechanical properties of brain tissue in vivo is essential to understanding the mechanisms underlying traumatic brain injury (TBI) and to creating accurate computational models of TBI and neurosurgical simulation. Brain white matter, which is composed of aligned, myelinated, axonal fibers, is structurally anisotropic. White matter in vivo also exhibits mechanical anisotropy, as measured by magnetic resonance elastography (MRE), but measurements of anisotropy obtained by mechanical testing of white matter ex vivo have been inconsistent. The minipig has a gyrencephalic brain with similar white matter and gray matter proportions to humans and therefore provides a relevant model for human brain mechanics. In this study, we compare estimates of anisotropic mechanical properties of the minipig brain obtained by identical, non-invasive methods in the live (in vivo) and dead animals (in situ). To do so, we combine wave displacement fields from MRE and fiber directions derived from diffusion tensor imaging (DTI) with a finite element-based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal alive and at specific times post-mortem. These maps show that white matter is stiffer, more dissipative, and more anisotropic than gray matter when the minipig is alive, but that these differences largely disappear post-mortem, with the exception of tensile anisotropy. Overall, brain tissue becomes stiffer, less dissipative, and less mechanically anisotropic post-mortem. These findings emphasize the importance of testing brain tissue properties in vivo.

Statement of Significance

In this study, MRE and DTI in the minipig were combined to estimate, for the first time, anisotropic mechanical properties in the living brain and in the same brain after death. Significant differences were observed in the anisotropic behavior of brain tissue post-mortem. These results demonstrate the importance of measuring brain tissue properties in vivo as well as ex vivo, and provide new quantitative data for the development of computational models of brain biomechanics.

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development.

Design and characterization of 3-D printed hydrogel lattices with anisotropic mechanical properties

The goal of this study was to design, fabricate, and characterize hydrogel lattice structures with consistent, controllable, anisotropic mechanical properties. Lattices, based on three unit-cell types (cubic, diamond, and vintile), were printed using stereolithography (SLA) of polyethylene glycol diacrylate (PEGDA). To create structural anisotropy in the lattices, unit cell design files were scaled by a factor of two in one direction in each layer and then printed. The mechanical properties of the scaled lattices were measured in shear and compression and compared to those of the unscaled lattices. Two apparent shear moduli of each lattice were measured by dynamic shear tests in two planes: (1) parallel and (2) perpendicular to the scaling direction, or cell symmetry axis. Three apparent Young's moduli of each lattice were measured by compression in three different directions: (1) the "build" direction or direction of added layers, (2) the scaling direction, and (3) the unscaled direction perpendicular to both scaling and build directions. For shear deformation in unscaled lattices, the apparent shear moduli were similar in the two perpendicular directions. In contrast, scaled lattices exhibit clear differences in apparent shear moduli. In compression of unscaled lattices, apparent Young's moduli were independent of direction in cubic and vintile lattices; in diamond lattices Young's moduli differed in the build direction, but were similar in the other two directions. Scaled lattices in compression exhibited additional differences in apparent Young's moduli in the scaled and unscaled directions. Notably, the effects of scaling on apparent modulus differed between each lattice type (cubic, diamond, or vintile) and deformation mode (shear or compression). Scaling of 3D-printed, hydrogel lattices may be harnessed to create tunable, structures of desired shape, stiffness, and mechanical anisotropy, in both shear and compression.

Constitutive parameter identification of transtibial residual limb soft tissue using ultrasound indentation and shear wave elastography

Finite element analysis (FEA) can be used to evaluate applied interface pressures and internal tissue strains for computational prosthetic socket design. This type of framework requires realistic patient-specific limb geometry and constitutive properties. In recent studies, indentations and inverse FEA with MRI-derived 3D patient geometries were used for constitutive parameter identification. However, long computational times and use of specialized equipment presents challenges for clinical, deployment. In this study, we present a novel approach for constitutive parameter identification using a combination of FEA, ultrasound indentation, and shear wave elastography. Local shear modulus measurement using elastography during an ultrasound indentation experiment has particular significance for biomechanical modeling of the residual limb since there are known regional dependencies of soft tissue properties such as varying levels of scarring and atrophy. Beyond prosthesis design, this work has broader implications to the fields of muscle health and monitoring of disease progression.

Parametric Analysis of SV Mode Shear Waves in Transversely Isotropic Materials Using Ultrasonic Rotational 3-D SWEI

Ultrasonic rotational 3-D shear wave elasticity imaging (SWEI) has been used to induce and evaluate multiple shear wave modes, including both the shear horizontal (SH) and shear vertical (SV) modes in in vivo muscle. Observations of both the SH and SV modes allow the muscle to be characterized as an elastic, incompressible, transversely isotropic (ITI) material with three parameters: the longitudinal shear modulus μL , the transverse shear modulus μT , and the tensile anisotropy χE . Measurement of the SV wave is necessary to characterize χE , but the factors that influence SV mode generation and characterization with ultrasonic SWEI are complicated. This work uses Green's function (GF) simulations to perform a parametric analysis to determine the optimal interrogation parameters to facilitate visualization and quantification of SV mode shear waves in muscle. We evaluate the impact of five factors: μL , μT , χE , fiber tilt angle [Formula: see text], and F-number of the push geometry on SV mode speed, amplitude, and rotational distribution. These analyses demonstrate that the following hold: 1) as μL increases, SV waves decrease in amplitude so are more difficult to measure in SWEI imaging; 2) as μT increases, the SV wave speeds increase; 3) as χE increases, the SV waves increase in speed and separate from the SH waves; 4) as fiber tilt angle [Formula: see text] increases, the measurable SV waves remain approximately the same speed, but change in strength and in rotational distribution; and 5) as the push beam geometry changes with F-number, the measurable SV waves remain approximately the same speed, but change in strength and rotational distribution. While specific SV mode speeds depend on the combinations of all parameters considered, measurable SV waves can be generated and characterized across the range of parameters considered. To maximize measurable SV waves separate from the SH waves, it is recommended to use an F/1 push geometry and [Formula: see text].

Tabletop MR elastography for investigating effects of the freeze-thaw cycle on the mechanical properties of biological tissues

PURPOSE

We aimed at characterizing the effects of the freeze-thaw cycle (FTC) on ex vivo specimens of porcine muscle, liver, kidney, and brain using tabletop magnetic resonance elastography (MRE) combined with rheological modeling. While frozen tissue banks potentially facilitate access to large amounts of well-preserved biospecimens, the impact of the FTC on their viscoelastic properties remains elusive.

METHODS

In this proof-of-concept study, fresh specimens from porcine lumbar muscle (n = 6), liver (n = 6), kidney (n = 6), and brain (n = 6) were examined before and after the FTC using 0.5T tabletop MRE at 500 Hz, 1000 Hz, 1500 Hz, and 2000 Hz. Seven standard rheological models (Maxwell, Springpot, Voigt, Zener, Jeffrey, fractional Voigt, fractional Zener) were employed to calculate frequency independent viscoelastic parameters.

RESULTS

The Zener rheological model showed the best fit quality for tissues before and after FTC in the investigated frequency range. Global rheological behavior after the FTC was softer for all tissues. Differences in mechanical parameters between tissues were preserved after the FTC and showed similar trends as before the FTC. Moreover, rheological fit quality improved after the FTC - a result that will be beneficial in investigating frozen tissue bank samples.

CONCLUSION

Multifrequency tabletop MRE allows rheological characterization of tissue samples before and after the FTC. Our results encourage further biomechanical characterization of frozen tissue bank samples, which may provide valuable information on the diagnostic potential of elastographic methods.

Characterizing Musculoskeletal Tissue Mechanics Based on Shear Wave Propagation: A Systematic Review of Current Methods and Reported Measurements

Developing methods for the non-invasive characterization of the mechanics of musculoskeletal tissues is an ongoing research focus in biomechanics. Often, these methods use the speed of shear wave propagation to characterize tissue mechanics (e.g., shear wave elastography and shear wave tensiometry). The primary purpose of this systematic review was to identify, compare, and contrast current methods for exciting and measuring shear wave propagation in musculoskeletal tissues. We conducted searches in the Web of Science, PubMed, and Scopus databases for studies published from January 1, 1900, to May 1, 2020. These searches targeted both shear wave excitation using acoustic pushes and mechanical taps, and shear wave speed measurement using ultrasound, magnetic resonance imaging, accelerometers, and laser Doppler vibrometers. Two reviewers independently screened and reviewed the articles, identifying 524 articles that met our search criteria. Regarding shear wave excitation, we found that acoustic pushes are useful for exciting shear waves through the thickness of the tissue of interest, and mechanical taps are useful for exciting shear waves in wearable applications. Regarding shear wave speed measurement, we found that ultrasound is used most broadly to measure shear waves due to its ability to study regional differences and target specific tissues of interest. The strengths of magnetic resonance imaging, accelerometers, and laser Doppler vibrometers make them advantageous to measure shear wave speeds for high-resolution shear wave imaging, wearable measurements, and non-contact ex vivo measurements, respectively. The advantages that each method offers for exciting and measuring shear waves indicate that a variety of systems can be assembled using currently available technologies to determine musculoskeletal tissue material behavior across a range of innovative applications.

Estimation of the mechanical properties of a transversely isotropic material from shear wave fields via artificial neural networks

Artificial neural networks (ANN), established tools in machine learning, are applied to the problem of estimating parameters of a transversely isotropic (TI) material model using data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI). We use neural networks to estimate parameters from experimental measurements of ultrasound-induced shear waves after training on analogous data from simulations of a computer model with similar loading, geometry, and boundary conditions. Strain ratios and shear-wave speeds (from MRE) and fiber direction (the direction of maximum diffusivity from diffusion tensor imaging (DTI)) are used as inputs to neural networks trained to estimate the parameters of a TI material (baseline shear modulus μ, shear anisotropy φ, and tensile anisotropy ζ). Ensembles of neural networks are applied to obtain distributions of parameter estimates. The robustness of this approach is assessed by quantifying the sensitivity of property estimates to assumptions in modeling (such as assumed loss factor) and choices in fitting (such as the size of the neural network). This study demonstrates the successful application of simulation-trained neural networks to estimate anisotropic material parameters from complementary MRE and DTI imaging data.

Full Characterization of in vivo Muscle as an Elastic, Incompressible, Transversely Isotropic Material Using Ultrasonic Rotational 3D Shear Wave Elasticity Imaging

Using a 3D rotational shear wave elasticity imaging (SWEI) setup, 3D shear wave data were acquired in the vastus lateralis of a healthy volunteer. The innate tilt between the transducer face and the muscle fibers results in the excitation of multiple shear wave modes, allowing for more complete characterization of muscle as an elastic, incompressible, transversely isotropic (ITI) material. The ability to measure both the shear vertical (SV) and shear horizontal (SH) wave speed allows for measurement of three independent parameters needed for full ITI material characterization: the longitudinal shear modulus μL , the transverse shear modulus μT , and the tensile anisotropy χE . Herein we develop and validate methodology to estimate these parameters and measure them in vivo, with μL = 5.77±1.00 kPa, μT = 1.93±0.41 kPa (giving shear anisotropy χμ = 2.11±0.92 ), and χE = 4.67±1.40 in a relaxed vastus lateralis muscle. We also demonstrate that 3D SWEI can be used to more accurately characterize muscle mechanical properties as compared to 2D SWEI.

Analytical solution based on spatial distortion for a time-harmonic Green's function in a transverse isotropic viscoelastic solid

A strategy of spatial distortion to make an anisotropic problem become isotropic has been previously validated in two-dimensional transverse isotropic (TI) viscoelastic cases. Here, the approach is extended to the three-dimensional problem by considering the time-harmonic point force response (Green's function) in a TI viscoelastic material. The resulting wave field, exactly solvable using a Radon transform with numerical integration, is approximated via spatial distortion of the closed form analytical solution to the isotropic case. Different distortions are used, depending on whether the polarization of the wave motion is orthogonal to the axis of isotropy, with the approximation yielding differing levels of accuracy.

Shear wave speeds in nearly-incompressible fibrous materials with two fiber families

An analytical and numerical investigation of shear wave behavior in nearly-incompressible soft materials with two fiber families was performed, focusing on the effects of material parameters and imposed pre-deformations on wave speed. This theoretical study is motivated by the emerging ability to image shear waves in soft biological tissues by magnetic resonance elastography (MRE). In MRE, the relationships between wave behavior and mechanical properties can be used to characterize tissue properties non-invasively. We demonstrate these principles in two material models, each with two fiber families. One model is a nearly-incompressible linear elastic model that exhibits both shear and tensile anisotropy; the other is a two-fiber-family version of the widely-used Holzapfel-Gasser-Ogden (HGO) model, which is nonlinear. Shear waves can be used to probe nonlinear material behavior using infinitesimal dynamic deformations superimposed on larger, quasi-static "pre-deformations." In this study, closed-form expressions for shear wave speeds in the HGO model are obtained in terms of the model parameters and imposed pre-deformations. Analytical expressions for wave speeds are confirmed by finite element simulations of shear waves with various polarizations and propagation directions. These studies support the feasibility of estimating the parameters of an HGO material model noninvasively from measured shear wave speeds.