The combined importance of finite dimensions, anisotropy, and pre-stress in acoustoelastography

Test-retest reliability and follow-up of muscle magnetic resonance elastography in adults with and without muscle diseases

BACKGROUND

We investigated the potential of magnetic resonance elastography (MRE) stiffness measurements in skeletal muscles as an outcome measure, by determining its test-retest reliability, as well as its sensitivity to change in a longitudinal follow-up study.

METHODS

We assessed test-retest reliability of muscle MRE in 20 subjects with (n = 5) and without (n = 15) muscle diseases and compared this to Dixon proton density fat fraction (PDFF) and volume measurements. Next, we measured MRE muscle stiffness in 21 adults with Becker muscular dystrophy (BMD) and 21 age-matched healthy controls at baseline, and after 9 and 18 months. We compared two different methods of analysing MRE data in this study: 'Method A' used the stiffness maps generated by the Philips MRE software, and 'Method B' applied a custom-made procedure based on wavelength measurements on the MRE images.

RESULTS

Intraclass correlation coefficients (ICC) of muscle stiffness ranged from good (0.83 for left vastus medialis, P < 0.001) to poor (0.19 for right rectus femoris, P = 0.212) for the examined thigh muscles with Method A, but we did not find a significant test-retest reliability with Method B (P > 0.050 for all). The ICC of muscle PDFF and volume measurements was excellent (>0.90; P < 0.001) for all muscles. At baseline, the average stiffness of all thigh muscles was significantly lower in adults with BMD than in controls for both Method A (-0.2 kPa, P = 0.025) and Method B (-0.6 kPa, P < 0.001). Regardless of which method was used, there was no significant difference in the evolution of muscle stiffness in patients and controls over 18 months.

CONCLUSIONS

Test-retest reliability of muscle MRE using a simple 2D technique was suboptimal, and did not reliably measure muscle stiffness changes in adults with BMD as compared with controls over 18 months. While the results provide motivation for testing more advanced 3D MRE methods, we conclude that the simple 2D MRE implementation used in this study is not suitable as an outcome measure for characterizing thigh muscle in clinical trials.

Shear wave speeds in a nearly incompressible fibrous material with two unequal fiber families

The mechanical properties of soft biological tissues can be characterized non-invasively by magnetic resonance elastography (MRE). In MRE, shear wave fields are induced by vibration, imaged by magnetic resonance imaging, and inverted to estimate tissue properties in terms of the parameters of an underlying material model. Most MRE studies assume an isotropic material model; however, biological tissue is often anisotropic with a fibrous structure, and some tissues contain two or more families of fibers-each with different orientations and properties. Motivated by the prospect of using MRE to characterize such tissues, this paper describes the propagation of shear waves in soft fibrous material with two unequal fiber families. Shear wave speeds are expressed in terms of material parameters, and the effect of each parameter on the shear wave speeds is investigated. Analytical expressions of wave speeds are confirmed by finite element simulations of shear wave transmission with various polarization directions. This study supports the feasibility of estimating parameters of soft fibrous tissues with two unequal fiber families in vivo from local shear wave speeds and advances the prospects for the mechanical characterization of such biological tissues by MRE.

Full-field noise-correlation elastography for in-plane mechanical anisotropy imaging

Elastography contrast imaging has great potential for the detection and characterization of abnormalities in soft biological tissues to help physicians in diagnosis. Transient shear-waves elastography has notably shown promising results for a range of clinical applications. In biological soft tissues such as muscle, high mechanical anisotropy implies different stiffness estimations depending on the direction of the measurement. In this study, we propose the evolution of a noise-correlation elastography approach for in-plane anisotropy mapping. This method is shown to retrieve anisotropy from simulation images before being validated on agarose anisotropic tissue-mimicking phantoms, and the first results on in-vivo biological fibrous tissues are presented.

Explorative study using ultrasound time-harmonic elastography for stiffness-based quantification of skeletal muscle function

Time-harmonic elastography (THE) is an emerging ultrasound imaging technique that allows full-field mapping of the stiffness of deep biological tissues. THE's unique ability to rapidly capture stiffness in multiple tissues has never been applied for imaging skeletal muscle. Therefore, we addressed the lack of data on temporal changes in skeletal muscle stiffness while simultaneously covering stiffness of different muscles. Acquiring repeated THE scans every five seconds we quantified shear-wave speed (SWS) as a marker of stiffness of the long head (LHB) and short head (SHB) of biceps brachii and of the brachialis muscle (B) in ten healthy volunteers. SWS was continuously acquired during a 3-min isometric preloading phase, a 3-min loading phase with different weights (4, 8, and 12 kg), and a 9-min postloading phase. In addition, we analyzed temporal SWS standard deviation (SD) as a marker of muscle contraction regulation. Our results (median [min, max]) showed both SWS at preloading (LHB: 1.04 [0.94, 1.12] m/s, SHB: 0.86 [0.78, 0.94] m/s, B: 0.96 [0.87, 1.09] m/s, p < 0.001) and the increase in SWS with loading weight to be muscle-specific (LHB: 0.010 [0.002, 0.019] m/s/kg, SHB: 0.022 [0.017, 0.042] m/s/kg, B: 0.039 [0.019, 0.062] m/s/kg, p < 0.001). Additionally, SWS during loading increased continuously over time by 0.022 [0.004, 0.051] m/s/min (p < 0.01). Using an exponential decay model, we found an average relaxation time of 27 seconds during postloading. Analogously, SWS SD at preloading was also muscle-specific (LHB: 0.018 [0.011, 0.029] m/s, SHB: 0.021 [0.015, 0.027] m/s, B: 0.024 [0.018, 0.037] m/s, p < 0.05) and increased by 0.005 [0.003, 0.008] m/s/kg (p < 0.01) with loading. SWS SD did not change over loading time and decreased immediately in the postloading phase. Taken together, THE of skeletal muscle is a promising imaging technique for in vivo quantification of stiffness and stiffness changes in multiple muscle groups within seconds. Both the magnitude of stiffness changes and their temporal variation during isometric exercise may reflect the functional status of skeletal muscle and provide additional information to the morphological measures obtained by conventional imaging modalities.

Viscoelastic dynamics of a soft strip subject to a large deformation

To produce sounds, we adjust the tension of our vocal folds to shape their properties and control the pitch. This efficient mechanism offers inspiration for designing reconfigurable materials and adaptable soft robots. However, understanding how flexible structures respond to a significant static strain is not straightforward. This complexity also limits the precision of medical imaging when applied to tensioned organs like muscles, tendons, ligaments and blood vessels among others. In this article, we experimentally and theoretically explore the dynamics of a soft strip subject to a substantial static extension, up to 180%. Our observations reveal a few intriguing effects, such as the resilience of certain vibrational modes to a static deformation. These observations are supported by a model based on the incremental displacement theory. This has promising practical implications for characterizing soft materials but also for scenarios where external actions can be used to tune properties.

Quantifying uniaxial prestress and waveguide effects on dynamic elastography estimates for a cylindrical rod

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of materials by noninvasively measuring mechanical wave motion in them. The target motion is typically transversely-polarized relative to the wave propagation direction, such as bulk shear wave motion. In addition to neglecting waveguide effects caused by small lengths in one dimension or more, many reconstruction strategies also ignore nonzero, non-isotropic static preloads. Significant anisotropic prestress is inherent to the functional role of some biological materials of interest, which also are small in size relative to shear wavelengths in one or more dimensions. A cylindrically shaped polymer structure with isotropic material properties is statically elongated along its axis while its response to circumferentially-, axially-, and radially-polarized vibratory excitation is measured using optical or magnetic resonance elastography. Computational finite element simulations augment and aid in the interpretation of experimental measurements. We examine the interplay between uniaxial prestress and waveguide effects. A coordinate transformation approach previously used to simplify the reconstruction of un-prestressed transversely isotropic material properties based on elastography measurements is adapted with partial success to estimate material viscoelastic properties and prestress conditions without requiring advanced knowledge of either.

In Vivo Assessment of Shear Wave Propagation in Pennate Muscles Using an Automatic Ultrasound Probe Alignment System

Goal: Skeletal muscle mechanics can be assessed in vivo using shear wave elastography. However, the impact of pennation angle on shear wave velocity (SWV) remains unclear. This study aims to quantify the effect by automatically aligning the ultrasound probe with muscle fiber orientation. Methods: We propose an automatic ultrasound probe alignment system and compare it to manual and no alignment. SWV of the gastrocnemius medialis muscle of ten volunteers was measured during rest and isometric contractions. Results: The SWV was different between the conditions (p = 0.008). The highest SWV was obtained during the automatic alignment and differences between the conditions were most pronounced during high-level contractions. The automatic system yielded more accurate alignment compared to a manual operator (p = 0.05). Conclusions: The present study indicates that pennation angle affects SWV, hence muscle fiber orientation must be considered to reliably interpret SWV. Using automatic alignment systems allows for more accurate alignment, improving the methodology of ultrasound elastography in skeletal muscles.

Detecting age-related changes in skeletal muscle mechanics using ultrasound shear wave elastography

Aging leads to a decline in muscle mass and force-generating capacity. Ultrasound shear wave elastography (SWE) is a non-invasive method to capture age-related muscular adaptation. This study assessed biceps brachii muscle (BB) mechanics, hypothesizing that shear elastic modulus reflects (i) passive muscle force increase imposed by length change, (ii) activation-dependent mechanical changes, and (iii) differences between older and younger individuals. Fourteen healthy volunteers aged 60-80 participated. Shear elastic modulus, surface electromyography, and elbow torque were measured at five elbow positions in passive and active states. Data collected from young adults aged 20-40 were compared. The BB passive shear elastic modulus increased from flexion to extension, with the older group exhibiting up to 52.58% higher values. Maximum elbow flexion torque decreased in extended positions, with the older group 23.67% weaker. Significant effects of elbow angle, activity level, and age on total and active shear elastic modulus were found during submaximal contractions. The older group had 20.25% lower active shear elastic modulus at 25% maximum voluntary contraction. SWE effectively quantified passive and activation-dependent BB mechanics, detecting age-related alterations at rest and during low-level activities. These findings suggest shear elastic modulus as a promising biomarker for identifying altered muscle mechanics in aging.

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.

Non-invasive Measurement of the Viscoelasticity of the Optic Nerve and Sclera for Assessing Papilledema: A Pilot Clinical Study

OBJECTIVE

The purpose of this study was to evaluate our novel ultrasound vibro-elastography (UVE) technique for assessing patients with papilledema by non-invasively measuring shear wave speed (SWS), elasticity and viscosity properties of the optic nerve and sclera.

METHODS

Shear wave speeds were measured at three frequencies-100, 150 and 200 Hz-on the optic nerve and sclera tissues for assessing patients with papilledema resulting from idiopathic intracranial hypertension (IIH). The method was evaluated in six papilledema patients and six controls on two separate locations for each participant (i.e., optic nerve and posterior sclera). SWSs of the optic nerve and sclera were analyzed by using a 2-D speed map technique within a circular region of interest (ROI) (i.e., the diameter of the ROI was 1.5 mm × 3.0 mm at the optic nerve and sclera, respectively). Elasticity and viscosity were then analyzed using the wave speed dispersion over the three frequencies.

RESULTS

We measured values of SWS at both locations, optic nerve and sclera, of the right eye and left eye at three different frequencies in IIH patients and controls. The SWS (mean ± standard deviation [m/s]) of the right eye was significantly higher at the sclera in IIH patients compared with controls (i.e., patients vs. controls: 5.91 ± 0.54 vs. 3.86 ± 0.56, p < 0.0001 at 100 Hz), but there was no significant difference at the optic nerve (i.e., patients vs. controls: 3.62 ± 0.39 vs. 3.36 ± 0.35, p = 0.1100 at 100Hz). We observed increased elasticity (kPa) in IIH patients, indicating there are significant differences in elasticity between patients and controls at the optic nerve and sclera (i.e., right eye [patients vs. controls]: 14.42 ± 6.59 vs. 6.5 ± 5.71, p = 0.0065 [optic nerve]; 33.04 ± 10.62 vs. 9.16 ± 7.15, p < 0.0001 [sclera]). Viscosity was also (Pa·s) higher in the sclera and optic nerve of the left eye (i.e., left eye [patient vs. control]: 8.89 ± 4.37 vs. 7.27 ± 5.01, p = 0.3790 (optic nerve); 16.05 ± 10.79 vs. 8.49 ± 6.09, p < 0.0194 [sclera]).

CONCLUSION

This research illustrates the feasibility of using our UVE system to evaluate stiffness of different tissues in the eye non-invasively. It suggests that the viscoelasticity of the posterior sclera is higher than that of the optic nerve. We found that the posterior sclera is stiffer than the optic nerve in patients with papilledema resulting from IIH, making UVE a potential non-invasive technique for assessing papilledema.

Decoupling Uniaxial Tensile Prestress and Waveguide Effects From Estimates of the Complex Shear Modulus in a Cylindrical Structure Using Transverse-Polarized Dynamic Elastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a configuration, inspired by muscle elastography but generalizable to other applications, is analytically and experimentally studied. A hyperelastic polymer phantom cylinder is statically elongated in the axial direction while its response to transverse-polarized vibratory excitation is measured. We examine the interplay between uniaxial prestress and waveguide effects in this muscle-like tissue phantom using computational finite element simulations and magnetic resonance elastography measurements. Finite deformations caused by prestress coupled with waveguide effects lead to results that are predicted by a coordinate transformation approach that has been previously used to simplify reconstruction of anisotropic properties using elastography. Here, the approach estimates material viscoelastic properties that are independent of the nonhomogeneous prestress conditions without requiring advanced knowledge of those stress conditions.

Characterization of Muscle Weakness Due to Myasthenia Gravis Using Shear Wave Elastography

Myasthenia gravis (MG) is often accompanied with muscle weakness; however, little is known about mechanical adaptions of the affected muscles. As the latter can be assessed using ultrasound shear wave elastography (SWE), this study characterizes the biceps brachii muscle of 11 patients with MG and compares them with that of 14 healthy volunteers. Simultaneous SWE, elbow torque and surface electromyography measurements were performed during rest, maximal voluntary contraction (MVC) and submaximal isometric contractions (up to 25%, 50% and 75% MVC) at different elbow angles from flexion to extension. We found that, with increasing elbow angle, maximum elbow torque decreased (p < 0.001), whereas muscle stiffness increased during rest (p = 0.001), MVC (p = 0.004) and submaximal contractions (p < 0.001). Muscle stiffness increased with increasing contraction intensities during submaximal contractions (p < 0.001). In comparison to the healthy cohort, muscle stiffness of MG patients was 2.1 times higher at rest (p < 0.001) but 8.93% lower in active state (75% MVC, p = 0.044). We conclude that (i) increased muscle stiffness shown by SWE during rest might be an indicator of MG, (ii) SWE reflects muscle weakness and (iii) SWE can be used to characterize MG muscle.

Noncontact Acoustic Micro-Tapping Optical Coherence Elastography for Quantification of Corneal Anisotropic Elasticity: In Vivo Rabbit Study

Purpose

The purpose of this study was to demonstrate accurate measurement of corneal elastic moduli in vivo with noncontact and noninvasive optical coherence elastography.

Methods

Elastic properties (in-plane Young's modulus, E, and both in-plane, μ, and out-of-plane, G, shear moduli) of rabbit cornea were quantified in vivo using noncontact dynamic acoustic micro-tapping optical coherence elastography (AµT-OCE). The intraocular pressure (IOP)-dependence of measured mechanical properties was explored in extracted whole globes following in vivo measurement. A nearly incompressible transverse isotropic (NITI) model was used to reconstruct moduli from AµT-OCE data. Independently, cornea elastic moduli were also measured ex vivo with traditional, destructive mechanical tests (tensile extensometry and shear rheometry).

Results

Our study demonstrates strong anisotropy of corneal elasticity in rabbits. The in-plane Young's modulus, computed as E = 3μ, was in the range of 20 MPa to 44 MPa, whereas the out-of-plane shear modulus was in the range of 34 kPa to 261 kPa. Both pressure-dependent ex vivo OCE and destructive mechanical tests performed on the same samples within an hour of euthanasia strongly support the results of AµT-OCE measurements.

Conclusions

Noncontact AµT-OCE can noninvasively quantify cornea anisotropic elastic properties in vivo.

Translational Relevance

As optical coherence tomography (OCT) is broadly accepted in ophthalmology, these results suggest the potential for rapid translation of AµT-OCE into clinical practice. In addition, AµT-OCE can likely improve diagnostic criteria of ectatic corneal diseases, leading to early diagnosis, reduced complications, customized surgical treatment, and personalized biomechanical models of the eye.

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.

Biaxial Tensile Prestress and Waveguide Effects on Estimates of the Complex Shear Modulus Using Optical-Based Dynamic Elastography in Plate-Like Soft Tissue Phantoms

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a novel configuration, inspired by corneal elastography but generalizable to other applications, is studied. A polymer phantom layer is statically elongated via an in-plane biaxial normal stress while the phantom's response to transverse vibratory excitation is measured. We examine the interplay between biaxial prestress and waveguide effects in this plate-like tissue phantom. Finite static deformations caused by prestressing coupled with waveguide effects lead to results that are predicted by a novel coordinate transformation approach previously used to simplify reconstruction of anisotropic properties. Here, the approach estimates material viscoelastic properties independent of the nonzero prestress conditions without requiring advanced knowledge of those stress conditions.

Non-contact acoustic micro-tapping optical coherence elastography for quantification of corneal anisotropic elasticity: in vivo rabbit study

PURPOSE

To demonstrate accurate measurement of corneal elastic moduli in vivo with non-contact and non-invasive optical coherence elastography.

METHODS

Elastic properties (in-plane Young's modulus E and both in-plane, u, and out-of-plane, G, shear moduli) of rabbit cornea were quantified in vivo using non-contact dynamic Acoustic micro-Tapping Optical Coherence Elastography (AuT-OCE). The IOP-dependence of measured mechanical properties was explored in extracted whole globes following in vivo measurement. A nearly-incompressible transverse isotropic (NITI) model was used to reconstruct moduli from AuT-OCE data. Independently, cornea elastic moduli were also measured ex vivo with traditional, destructive mechanical tests (tensile extensometry and shear rheometry).

RESULTS

Our study demonstrates strong anisotropy of corneal elasticity in rabbits. The in-plane Young's modulus, computer as E=3u, was in the range of 20-44 MPa, whereas the out-of-plane shear modulus was in the range of 34-261 kPa. Both pressure-dependent ex vivo OCE and destructive mechanical tests performed on the same samples within an hour of euthanasia strongly support the results of AuT-OCE measurements.

CONCLUSIONS

Non-contact AuT-OCE can non-invasively quantify cornea anisotropic elastic properties in vivo.

TRANSLATIONAL RELEVANCE

As OCT is broadly accepted in Ophthalmology, these results suggest the potential for rapid translation of AuT-OCE into clinical practice. In addition, AuT-OCE can likely improve diagnostic criteria of ectatic corneal diseases, leading to early diagnosis, reduced complications, customized surgical treatment, and personalized biomechanical models of the eye.