Anisotropic composite material phantom to improve skeletal muscle characterization using magnetic resonance elastography

Mechanically anisotropic phantoms for magnetic resonance elastography

PURPOSE

Imaging phantoms with known anisotropic mechanical properties are needed to evaluate magnetic resonance elastography (MRE) methods to estimate anisotropic parameters. The aims of this study were to fabricate mechanically anisotropic MRE phantoms, characterize their mechanical behavior by direct testing, then assess the accuracy of MRE estimates of anisotropic properties using a transversely isotropic nonlinear inversion (TI-NLI) algorithm.

METHODS

Directionally scaled and unscaled lattices were designed to exhibit anisotropic or isotropic mechanical properties. Lattices were three-dimensionally printed in poly(ethelyne glycol) diacrylate using a commercial digital light processing printer, then infilled with gelatin to form a composite material. Benchtop testing determined two shear stiffnesses,μ 1 $$ {\mu}_1 $$ andμ 2 $$ {\mu}_2 $$ , governing loading parallel and perpendicular to the symmetry axis, and two analogous Young's moduliE 1 $$ {E}_1 $$ andE 2 $$ {E}_2 $$ . From these measures, shear anisotropyϕ $$ \phi $$ =μ 1 / μ 2 - 1 $$ {\mu}_1/{\mu}_2-1 $$ and tensile anisotropyζ $$ \zeta $$ =E 1 / E 2 - 1 $$ {E}_1/{E}_2-1 $$ were calculated. Three phantoms were driven by a central actuator and imaged with MRE at frequencies from 300 to 500 Hz. From MRE data, the TI-NLI algorithm estimated maps ofμ 2 $$ {\mu}_2 $$ ,ϕ $$ \phi $$ , andζ $$ \zeta $$ .

RESULTS

In benchtop tests, geometrically scaled lattice composites exhibited the following anisotropic properties:{ μ 2 $$ \Big\{{\mu}_2 $$ = 6.1 ± 0.7 kPa,ϕ $$ \phi $$ = 0.83 ± 0.13,ζ $$ \zeta $$ = 0.78 ± 0.09} (mean ± standard deviation). MRE of scaled lattice composites revealed elliptical wavefields; TI-NLI analysis identified the following median property ranges:{ μ 2 $$ \Big\{{\mu}_2 $$ = 11-19 kPa,ϕ $$ \phi $$ = 0.6-1.0,ζ $$ \zeta $$ = 0.8-1.6}.

CONCLUSION

Anisotropic MRE phantoms are created by embedding anisotropic three-dimensionally printed lattices into a softer matrix. The TI-NLI algorithm accurately estimates spatial contrast in anisotropic properties.

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.

Nondestructive ultrasound evaluation of microstructure-related material parameters of skeletal muscle: An in silico and in vitro study

Direct and nondestructive assessment of material properties of skeletal muscle in vivo shall advance our understanding of intact muscle mechanics and facilitate personalized interventions. However, this is challenged by intricate hierarchical microstructure of the skeletal muscle. We have previously regarded the skeletal muscle as a composite of myofibers and extracellular matrix (ECM), formulated shear wave propagation in the undeformed muscle using the acoustoelastic theory, and preliminarily demonstrated that ultrasound-based shear wave elastography (SWE) could estimate microstructure-related material parameters (MRMPs): myofiber stiffness μ_f, ECM stiffness μ_m, and myofiber volume ratio V_f. The proposed method warrants further validation but is hampered by the lack of ground truth values of MRMPs. In this study, we presented analytical and experimental validations of the proposed method using finite-element (FE) simulations and 3D-printed hydrogel phantoms, respectively. Three combinations of different physiologically relevant MRMPs were used in the FE simulations where shear wave propagations in the corresponding composite media were simulated. Two 3D-printed hydrogel phantoms with the MRMPs close to those of a real skeletal muscle (i.e., μ_f=2.02kPa, μ_m=52.42kPa, and V_f=0.675,0.832) for ultrasound imaging were fabricated by an alginate-based hydrogel printing protocol that we modified and optimized from the freeform reversible embedding of suspended hydrogels (FRESH) method in literature. Average percent errors of (μ_f,μ_m,V_f) estimates were found to be (2.7%,7.3%,2.4%)in silico and (3.0%,8.0%,9.9%)in vitro. This quantitative study corroborated the potential of our proposed theoretical model along with ultrasound SWE for uncovering microstructural characteristics of the skeletal muscle in an entirely nondestructive way.

In vivoestimation of anisotropic mechanical properties of the gastrocnemius during functional loading with MR elastography

Objective.In vivoimaging assessments of skeletal muscle structure and function allow for longitudinal quantification of tissue health. Magnetic resonance elastography (MRE) non-invasively quantifies tissue mechanical properties, allowing for evaluation of skeletal muscle biomechanics in response to loading, creating a better understanding of muscle functional health.Approach. In this study, we analyze the anisotropic mechanical response of calf muscles using MRE with a transversely isotropic, nonlinear inversion algorithm (TI-NLI) to investigate the role of muscle fiber stiffening under load. We estimate anisotropic material parameters including fiber shear stiffness (μ1), substrate shear stiffness (μ2), shear anisotropy (ϕ), and tensile anisotropy (ζ) of the gastrocnemius muscle in response to both passive and active tension.Main results. In passive tension, we found a significant increase inμ1,ϕ,andζwith increasing muscle length. While in active tension, we observed increasingμ2and decreasingϕandζduring active dorsiflexion and plantarflexion-indicating less anisotropy-with greater effects when the muscles act as agonist.Significance. The study demonstrates the ability of this anisotropic MRE method to capture the multifaceted mechanical response of skeletal muscle to tissue loading from muscle lengthening and contraction.

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.

Vascular elasticity measurement of the great saphenous vein based on optical coherence elastography

Vascular elasticity is important in physiological and clinical problems. The mechanical properties of the great saphenous vein (GSV) deserve attention. This research aims to measure the radial elasticity of ex vivo GSV using the optical coherence elasticity (OCE). The finite element model of the phantom is established, the displacement field is calculated, the radial mechanical characteristics of the simulation body are obtained. Furthermore, we performed OCE on seven isolated GSVs. The strain field is obtained by combining the relationship between strain and displacement to obtain the radial elastic modulus of GSVs. In the phantom experiment, the strain of the experimental region of interest is mainly between 0.1 and 0.4, while the simulation result is between 0.06 and 0.40. The radial elastic modulus of GSVs ranged from 3.83 kPa to 7.74 kPa. This study verifies the feasibility of the OCE method for measuring the radial elastic modulus of blood vessels.

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.

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.

Axially- and torsionally-polarized radially converging shear wave MRE in an anisotropic phantom made via Embedded Direct Ink Writing

Magnetic Resonance Elastography (MRE) is a non-invasive imaging method to quantitatively map the shear viscoelastic properties of soft tissues. In this study, Embedded Direct Ink Writing is used to fabricate a muscle mimicking anisotropic phantom that may serve as a standard for imaging studies of anisotropic materials. The technique allowed us to obtain a long shelf life silicone-based phantom expressing transverse isotropic mechanical properties. Another goal of the present investigation is to introduce a torsionally-polarized, radially-converging shear wave actuation method for MRE. The implemented design for this novel setup was first validated via its application to isotropic and homogeneous gelatin phantoms. Then, a comparison of the resulting complex wave images from axially- and torsionally-polarized MRE on the developed anisotropic phantom and on a skeletal muscle murine sample is presented, highlighting the value of using multiple actuation and motion encoding polarization directions when studying anisotropic materials.

Micro Air-Pulse Spatial Deformation Spreading Characterizes Degree of Anisotropy in Tissues

In optical coherence elastography (OCE), air-pulse stimulation has been widely used to produce propagation of mechanical waves for elastic characterization of tissues. In this paper, we propose the use of spatial deformation spreading (SDS) on the surface of samples produced by air-pulse stimulation for the OCE of transverse isotropic tissues. Experiments in isotropic tissue-mimicking phantoms and anisotropic chicken tibialis muscle were conducted using a spectral-domain optical coherence tomography system synchronized with a confocal air-pulse stimulation. SDS measurements were compared with wave speeds values calculated at different propagation angles. We found an approximately linear relationship between shear wave speed and SDS in isotropic phantoms, which was confirmed with predictions made by the numerical integration of a wave propagation model. Experimental measurements in chicken muscle show a good agreement between SDS and surface wave speed taken along and across the axis of symmetry of the tissues, also called degree of anisotropy. In summary, these results demonstrated the capabilities of SDS produced by the air-pulse technique in measuring the shear elastic anisotropy of transverse isotropic tissues.

Influence of fibrosis progression on the viscous properties of in vivo liver tissue elucidated by shear wave dispersion in multifrequency MR elastography

PURPOSE

Many elastography studies have shown that liver stiffness increases with fibrosis and thus can be used as a reliable marker for noninvasively staging fibrosis. However, the sensitivity of viscosity-related mechanical parameters, such as shear wave dispersion, to liver fibrosis is less well understood.

METHODS

In this proof-of-concept study, 15 healthy volunteers and 37 patients with chronic liver disease and biopsy-proven fibrosis were prospectively investigated by MR elastography at six drive frequencies of 35-60 Hz. Maps of shear wave speed (SWS, in m/s) and loss angle (φ, in rad), as a marker of stiffness and viscous properties, respectively, were generated using tomoelastography data processing. The Child-Pugh score was used to assess cirrhosis severity.

RESULTS

While SWS increased with fibrosis (F0: 1.53 ± 0.11 m/s, F1-F3: 1.71 ± 0.17 m/s, F4: 2.50 ± 0.39 m/s; P < 0.001), φ remained unchanged during mild to severe fibrosis (F0: 0.63 ± 0.05 rad, F1-F3: 0.60 ± 0.05 rad, P = 0.21) but increased in cirrhosis (F4: 0.81 ± 0.16 rad; P < 0.001). Correspondingly, the slope of SWS-dispersion within the investigated range of vibration frequencies increased from insignificant (F0-F3: 0.010 ± 0.007 m/s/Hz) to significant (F4: 0.038 ± 0.025 m/s/Hz; P = 0.005). Significant correlation with the Child-Pugh score was found for φ (R = 0.60, P = 0.01) but not for SWS.

CONCLUSION

Although cirrhosis is associated with liver stiffening and, intuitively, transition towards more rigid material properties, the observed increases in φ and slope of SWS-dispersion indicate abnormally high mechanical friction in cirrhotic livers. This biophysical signature might provide a prognostic imaging marker for the detection of pathological processes associated with fibrosis independent of stiffness.

Measuring viscoelastic parameters in Magnetic Resonance Elastography: a comparison at high and low magnetic field intensity

Magnetic Resonance Elastography (MRE) is a non-invasive imaging technique which involves motion-encoding MRI for the estimation of the shear viscoelastic properties of soft tissues through the study of shear wave propagation. The technique has been found informative for disease diagnosis, as well as for monitoring of the effects of therapies. The development of MRE and its validation have been supported by the use of tissue-mimicking phantoms. In this paper we present our new MRE protocol using a low magnetic field tabletop MRI device at 0.5 T and sinusoidal uniaxial excitation in a geometrical focusing condition. Results obtained for gelatin are compared to those previously obtained using high magnetic field MRE at 11.7 T. A multi-frequency investigation is also provided via a comparison of commonly used rheological models: Maxwell, Springpot, Voigt, Zener, Jeffrey, fractional Voigt and fractional Zener. Complex shear modulus values were comparable when processed from images acquired with the tabletop low field scanner and the high field scanner. This study serves as a validation of the presented tabletop MRE protocol and paves the way for MRE experiments on ex-vivo tissue samples in both normal and pathological conditions.

Ultrasound Shear Wave Velocity Varies Across Anatomical Region in Ex Vivo Bovine Ovaries

The physical properties of the ovarian extracellular matrix (ECM) regulate the function of ovarian cells, specifically the ability of the ovary to maintain a quiescent primordial follicle pool while allowing a subset of follicles to grow and mature in the estrous cycle. Design of a long-term, cycling artificial ovary has been hindered by the limited information regarding the mechanical properties of the ovary. In particular, differences in the mechanical properties of the two ovarian compartments, the cortex and medulla, have never been quantified. Shear wave (SW) ultrasound elastography is an imaging modality that enables assessment of material properties, such as the mechanical properties, based on the velocity of SWs, and visualization of internal anatomy, when coupled with B-mode ultrasound. We used SW ultrasound elastography to assess whole, ex vivo bovine ovaries. We demonstrated, for the first time, a difference in mechanical properties, as inferred from SW velocity, between the cortex and medulla, as measured along the length (cortex: 2.57 ± 0.53 m/s, medulla: 2.87 ± 0.77 m/s, p < 0.0001) and width (cortex: 2.99 ± 0.81 m/s, medulla: 3.24 ± 0.97 m/s, p < 0.05) and that the spatial distribution and magnitude of SW velocity vary between these two anatomical planes. This work contributes to a larger body of literature assessing the mechanical properties of the ovary and related cells and specialized ECMs and will enable the rational design of biomimetic tissue engineered models and durable bioprostheses. Impact Statement Shear wave (SW) ultrasound elastography can be used to simultaneously assess the material properties and tissue structures when accompanied with B-mode ultrasound. We report a quantitative difference in mechanical properties, as inferred from SW velocity, between the cortex and medulla, with SW velocity being 11.4% and 8.4% higher in the medulla than the cortex when measured along the length and width, respectively. This investigation into the spatial and temporal variation in SW velocity in bovine ovaries will encourage and improve design of more biomimetic scaffolds for ovarian tissue engineering.

Physical imaging phantoms for simulation of tumor heterogeneity in PET, CT, and MRI: An overview of existing designs

BACKGROUND

In oncology, lesion characterization is essential for tumor grading, treatment planning, and follow-up of cancer patients. Hybrid imaging systems, such as Single Photon Emission Computed Tomography (SPECT)/CT, Positron Emission Tomography (PET)/CT, or PET/magnetic resonance imaging (MRI), play an essential role for the noninvasive quantification of tumor characteristics. However, most of the existing approaches are challenged by intra- and intertumor heterogeneity. Novel quantitative imaging parameters that can be derived from textural feature analysis (as part of radiomics) are promising complements for improved characterization of tumor heterogeneity, thus, supporting clinically relevant implementations of personalized medicine concepts. Nevertheless, establishing new quantitative parameters for tumor characterization requires the use of standardized imaging objects to test the reliability of results prior to their implementation in patient studies.

METHODS

In this review, we summarize existing reports on heterogeneous phantoms with a focus on simulating tumor heterogeneity. We discuss the techniques, materials, advantages, and limitations of the existing phantoms for PET, CT, and MR imaging modalities.

CONCLUSIONS

Finally, we outline the future directions and requirements for the design of cross modality imaging phantoms.

Which Confounders Have the Largest Impact in Shear Wave Elastography of Muscle and How Can They be Minimized? An Elasticity Phantom, Ex Vivo Porcine Muscle and Volunteer Study Using a Commercially Available System

The goal of the study was to investigate the quantitative impact of region of interest (ROI), software choice, muscle fiber orientation and preload tension on shear wave velocity (SWV). First, SWV was assessed in an isotropic elasticity phantom and ex vivo porcine muscle using a commercially available clinical ultrasound system. Secondly, SWV was acquired in relaxed and stretched calf muscles of healthy volunteers (dorsal extension of the talocrural joint), for both parallel and transverse probe direction to the fibers, as well as for different ROIs and software versions. The effect of intermediate probe-fiber alignments was also analyzed. Finally, the impact of confounding factors on SWV reproducibility was minimized with a second force-controlled volunteer study, in which the calf was isometrically loaded, and fiber orientation and ROI were well-defined. 2046 in vivoSWE images were acquired to analyze SWV reproducibility with different confounder settings. In healthy volunteers, the main variance-contributing factors were in order of importance muscle tension, fiber orientation, horizontal ROI size and insertion depth. Regression analysis showed significantly reduced SWV with increasing insertion depth for each study material. Parallel probe-fiber orientation, muscle stretch and increasing horizontal ROI size led to significantly higher SWV. Based on the results of the study, we provide recommendations to minimize the impact of confounders in musculoskeletal elastography and discuss the main confounding mechanisms and trade-offs between confounding variables. Coefficients of variation can be significantly reduced with a controlled protocol, if the confounders are clinically taken into account.

An investigation into the relationship between inhomogeneity and wave shapes in phantoms and ex vivo skeletal muscle using Magnetic Resonance Elastography and finite element analysis

Soft biological tissues such as skeletal muscle and brain white matter can be inhomogeneous and anisotropic due to the presence of fibers. Unlike biological tissue, phantoms with known microstructure and defined mechanical properties enable a quantitative assessment and systematic investigation of the influence of inhomogeneities on the nature of shear wave propagation. This study introduces a mathematical measure for the wave shape, which the authors call as the 1-Norm, to determine the conditions under which homogenization may be a valid approach. This is achieved through experimentation using the Magnetic Resonance Elastography technique on 3D printed inhomogeneous fiber phantoms as well as on ex-vivo porcine lumbus muscle. In addition, Finite Element Analysis is used as a tool to decouple the effects of directional anisotropy from those of inhomogeneity. A correlation is then established between the values of 1-Norm derived from the wave front geometry, and the spacing (d) between neighboring inhomogeneities (spherical inclusions or fibers and fiber intersections in phantoms and muscle). Smaller values of 1-Norm indicate less wave scattering at the locations of fiber intersections, which implies that the wave propagation may be approximated to that of a homogeneous medium; homogenization may not be a valid approximation when significant scattering occurs at the locations of inhomogeneities. In conclusion, the current study proposes 1-Norm as a quantitative measure of the magnitude of wave scattering in a medium, which can potentially be used as a homogeneity index of a biological tissue.

Dilatational and shear waves in poro-vioscoelastic media

Dynamic elastography methods are being developed for quantitatively and noninvasively mapping the viscoelastic properties of biological tissue that are often altered by disease and injury, as well as response to treatment. This involves inducing mechanical wave motion that also can be affected by the multiphase porous nature of the tissue, whether it be consideration of blood perfusion in the vascular network found in many regions of interest, or consideration of air movement in the complex bronchial tree within the lungs. Elastographic mapping requires reconstructing material properties based on interpretation of the measured wave motion. Reconstruction methods that explicitly incorporate poroelastic behavior are an active area of development. In the present article the equivalence of two theoretical approaches to modeling poroelastic behavior is demonstrated specifically in the frequency domain using parameter values that span the range expected in vivo for analysis of blood and air-infused regions. The two methods are known as (1) the mixture or biphasic formulation and (2) the poroelastic approach. The case of acoustic wave propagation in the lungs is specifically addressed by comparison of analytical predictions to recently reported experimental measurements. Establishing and validating this equivalence of theoretical approaches not only strengthens our fundamental understanding of the relevant physics, but also may lead to improved numerical methods for simulation and elastography reconstruction.