Sensitivity of the Shear Wave Speed-Stress Relationship to Soft Tissue Material Properties and Fiber Alignment

2021 ◽  
Author(s):  
Jonathon Blank ◽  
Darryl Thelen ◽  
Matthew S. Allen ◽  
Joshua Roth
Keyword(s):  
Wave Propagation ◽  
Shear Modulus ◽  
Shear Wave ◽  
Wave Speed ◽  
Axial Stress ◽  
Beam Model ◽  
Fiber Alignment ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Constitutive Properties

The use of shear wave propagation to noninvasively gauge material properties and loading in tendons and ligaments is a growing area of interest in biomechanics. Prior models and experiments suggest that shear wave speed primarily depends on the apparent shear modulus (i.e., shear modulus accounting for contributions from all constituents) at low loads, and then increases with axial stress when axially loaded. However, differences in the magnitudes of shear wave speeds between ligaments and tendons, which have different substructures, suggest that the tissue’s composition and fiber alignment may also affect shear wave propagation. Accordingly, the objectives of this study were to (1) characterize changes in the apparent shear modulus induced by variations in constitutive properties and fiber alignment, and (2) determine the sensitivity of the shear wave speed-stress relationship to variations in constitutive properties and fiber alignment. To enable systematic variations of both constitutive properties and fiber alignment, we developed a finite element model that represented an isotropic ground matrix with an embedded fiber distribution. Using this model, we performed dynamic simulations of shear wave propagation at axial strains from 0% to 10%. We characterized the shear wave speed-stress relationship using a simple linear regression between shear wave speed squared and axial stress, which is based on an analytical relationship derived from a tensioned beam model. We found that predicted shear wave speeds were both in-range with shear wave speeds in previous in vivo and ex vivo studies, and strongly correlated with the axial stress (R2 = 0.99). The slope of the squared shear wave speed-axial stress relationship was highly sensitive to changes in tissue density. Both the intercept of this relationship and the apparent shear modulus were sensitive to both the shear modulus of the ground matrix and the stiffness of the fibers’ toe-region when the fibers were less well-aligned to the loading direction. We also determined that the tensioned beam model overpredicted the axial tissue stress with increasing load when the model had less well-aligned fibers. This indicates that the shear wave speed increases likely in response to a load-dependent increase in the apparent shear modulus. Our findings suggest that researchers may need to consider both the material and structural properties (i.e., fiber alignment) of tendon and ligament when measuring shear wave speeds in pathological tissues or tissues with less well-aligned fibers.

Shear Wave Speeds Track Axial Stress in Porcine Collateral Ligaments

2019 ◽  
Author(s):  
Jonathon Blank ◽  
Darryl Thelen ◽  
Joshua Roth
Keyword(s):  
Shear Wave ◽  
Wave Speed ◽  
Ex Vivo ◽  
Axial Stress ◽  
Axial Loading ◽  
Orthopedic Procedures ◽  
Stress Distributions ◽  
Collateral Ligaments ◽  
Wave Speeds ◽  
Shear Wave Speed

Ligament tension is an important factor that can affect the success of total knee arthroplasty (TKA) procedures. However, surgeons currently lack objective approaches for assessing tension in a particular ligament intraoperatively. The purpose of this study was to investigate the use of noninvasive shear wave tensiometry to characterize stress in medial and lateral collateral ligaments (MCLs and LCLs) ex vivo. Nine porcine MCL and LCL specimens were subjected to cyclic axial loading while wave speeds were measured using laser vibrometry. We found that squared shear wave speed increased linearly with stress in both the MCL (r2avg = 0.94) and LCL (r2avg = 0.98). Wave speeds were slightly lower in the MCL than the LCL when subjected to comparable axial stress (p < 0.001). Ligament-specific wave speeds may arise from differences in geometry and stress distributions between ligaments. These observations suggest it may be feasible to use noninvasive shear wave speed measures as a proxy of ligament loading during orthopedic procedures such as TKA.

scholarly journals The influence of hemodialysis-induced preload changes on the propagation speed of natural shear waves

2021 ◽  
Vol 22 (Supplement_1) ◽  
Author(s):  
S Bezy ◽  
M Orlowska ◽  
A Van Craenenbroeck ◽  
M Cvijic ◽  
J Duchenne ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Wave Speed ◽  
Shear Waves ◽  
Propagation Speed ◽  
Left Ventricular ◽  
Frame Rate ◽  
High Frame Rate ◽  
Shear Wave Speed ◽  
Wave Propagation Speed

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Research Foundation - Flanders (FWO) Background Shear wave elastography (SWE) is a novel ultrasound technique based on the detection of transverse waves travelling through the myocardium using high frame rate echocardiography. The propagation speed of these shear waves is dependent on the stiffness of the myocardium. Previous studies have shown the potential of SWE for the non-invasive assessment of myocardial stiffness. It is unclear, however, if preload changes lead to measurable changes in the shear wave propagation speed in the left ventricle. In patients undergoing hemodialysis, the volume status is acutely changed. In this way, the effect of preload changes on shear wave speed can be assessed. Purpose The aim of this study was to explore the influence of preload changes on end-diastolic shear wave propagation speed. Methods Until now, 6 patients (age: 80[53-85] years; female: n = 2) receiving hemodialysis treatment were included. Echocardiographic images were taken before and every hour during a 4 hour hemodialysis session. Left ventricular parasternal long-axis views were acquired with an experimental high frame rate ultrasound scanner (average frame rate: 1016[941-1310] Hz). Standard echocardiography was performed with a conventional ultrasound machine. Shear waves were visualized on tissue acceleration maps by drawing an M-mode line along the interventricular septum. Shear wave propagation speed after mitral valve closure (MVC) was calculated by measuring the slope of the wave pattern on the acceleration maps (Figure A). Results Over the course of hemodialysis, the systolic (141[135-156] mmHg vs. 165[105-176] mmHg; p = 0.35 among groups) and diastolic blood pressure (70[66-75] mmHg vs. 82[63-84] mmHg; p = 0.21 among groups), heart rate (56[54-73] bmp vs. 57[50-67] bpm; p = 0.76 among groups), E/A ratio (1.6[0.7-1.8] vs. 1.2[0.6-1.4]; p = 0.43 among groups) and E/e’ (14[9-15] vs. 9[8-13]; p = 0.24 among groups ) remained the same. The ultra-filtrated volumes are shown in Figure B. The shear wave propagation speed after MVC gradually decreased during hemodialysis (6.7[5.4-9.7] m/s vs. 4.4[3.6-9.0] m/s; p = 0.04 among groups) (Figure C). There was a moderate negative correlation between shear wave speed and the ultra-filtrated volume (r=-0.63; p < 0.01) (Figure D). Conclusion The shear wave propagation speed at MVC significantly decreased over the course of hemodialysis and correlated to the ultra-filtrated volume. These results indicate that alterations in left ventricular preload affect the speed of shear waves at end-diastole. End-diastolic shear wave speed might therefore be a potential novel parameter for the evaluation of the left ventricular filling state. More patients will be included in the future to further explore these findings. Abstract Figure.

scholarly journals Shear wave cardiovascular MR elastography using intrinsic cardiac motion for transducer-free non-invasive evaluation of myocardial shear wave velocity

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marian Amber Troelstra ◽  
Jurgen Henk Runge ◽  
Emma Burnhope ◽  
Alessandro Polcaro ◽  
Christian Guenthner ◽  
...  
Keyword(s):  
Healthy Volunteers ◽  
Shear Wave ◽  
Wave Speed ◽  
Shear Waves ◽  
Valve Closure ◽  
Limits Of Agreement ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Non Invasive ◽  
Aortic Valve Closure

AbstractChanges in myocardial stiffness may represent a valuable biomarker for early tissue injury or adverse remodeling. In this study, we developed and validated a novel transducer-free magnetic resonance elastography (MRE) approach for quantifying myocardial biomechanics using aortic valve closure-induced shear waves. Using motion-sensitized two-dimensional pencil beams, septal shear waves were imaged at high temporal resolution. Shear wave speed was measured using time-of-flight of waves travelling between two pencil beams and corrected for geometrical biases. After validation in phantoms, results from twelve healthy volunteers and five cardiac patients (two left ventricular hypertrophy, two myocardial infarcts, and one without confirmed pathology) were obtained. Torsional shear wave speed in the phantom was 3.0 ± 0.1 m/s, corresponding with reference speeds of 2.8 ± 0.1 m/s. Geometrically-biased flexural shear wave speed was 1.9 ± 0.1 m/s, corresponding with simulation values of 2.0 m/s. Corrected septal shear wave speeds were significantly higher in patients than healthy volunteers [14.1 (11.0–15.8) m/s versus 3.6 (2.7–4.3) m/s, p = 0.001]. The interobserver 95%-limits-of-agreement in healthy volunteers were ± 1.3 m/s and interstudy 95%-limits-of-agreement − 0.7 to 1.2 m/s. In conclusion, myocardial shear wave speed can be measured using aortic valve closure-induced shear waves, with cardiac patients showing significantly higher shear wave speeds than healthy volunteers. This non-invasive measure may provide valuable insights into the pathophysiology of heart failure.

Reconciling elasticity tensor constraints from mineral physics and seismological observations: applications to the Earth’s inner core

2020 ◽  
Vol 222 (2) ◽  
pp. 1135-1145
Author(s):  
Brent G Delbridge ◽  
Miaki Ishii
Keyword(s):  
Shear Wave ◽  
Elastic Constants ◽  
Wave Speed ◽  
Inner Core ◽  
Body Wave ◽  
Elasticity Tensor ◽  
The Body ◽  
Wave Speeds ◽  
Mineral Physics ◽  
Shear Wave Speed

SUMMARY This study establishes the proper framework in which to compare seismic observations with mineral physics constraints for studies of the inner core by determining how the elements of the elasticity tensor are sampled by the normal modes of the Earth. The obtained mapping between the elements of the elasticity tensor and the seismic wave speeds shows that the choice of averaging scheme used to calculate isotropic properties is crucial to understand the composition of the inner core, especially for comparison with the shear wave speed such as that provided in PREM. For example, the appropriate shear wave speed calculated for an Fe-Ni-Si hcp alloy at inner-core conditions differs from the shear wave speed obtained by taking a Reuss average by as much as $27\, {\rm per\, cent}$. It is also shown for the first time that by combining the isotropic observations based upon normal-mode characteristic frequencies and anisotropic parameters from their splitting, the five independent elastic parameters (A, C, F, L and N) that fully describe a transversely isotropic inner core can be uniquely constrained. The elastic values based upon a variety of mode-splitting studies are reported, and the differences between models from various research groups are shown to be relatively small ($\lt 10\, {\rm per\, cent}$). Additionally, an analogous body-wave methodology is developed to approximately estimate the five independent elastic constants from observations of compressional wave traveltime anomalies. The body-wave observations are utilized to consider the depth dependence of inner-core anisotropy, in particular, the structure of the innermost inner core. Finally, we demonstrate that substantial errors may result when attempting to relate seismically observed P and S wave speeds from Debye velocities obtained through nuclear resonant inelastic X-ray scattering. The results of these experiments should be compared directly with the Debye velocity calculated from seismically constrained elastic constants. This manuscript provides a new set of formulae and values of seismic observations of the inner core that can be easily compared against mineral physics constraints for better understanding of the inner-core composition.

Antiplane Slip and Bonded Contact Waves at a Planar Interface Between Two Elastic Layers

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
K. Ranjith
Keyword(s):  
Phase Velocity ◽  
Shear Wave ◽  
Wave Speed ◽  
Planar Interface ◽  
Interfacial Wave ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Antiplane Elasticity ◽  
Elasticity Solutions ◽  
Elastic Layers

Interfacial wave solutions for a planar interface between two finite layers have been obtained within the framework of antiplane elasticity. Solutions are found to exist both for slipping contact and for bonded contact at the interface. Both the slip and bonded contact waves are found to be dispersive and multivalued. One family of slip and bonded contact waves is found with phase velocity in between the shear wave speeds of the two solids. It is also found that two families of slip and bonded contact waves exist with phase velocity greater than the shear wave speed of both solids.

scholarly journals Fluid effects on shear waves in finely layered porous media

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. N1-N15 ◽  
Author(s):  
James G. Berryman
Keyword(s):  
Shear Modulus ◽  
Shear Wave ◽  
Wave Speed ◽  
Shear Waves ◽  
Ultrasonic Waves ◽  
Layered System ◽  
Pore Fluids ◽  
Shear Moduli ◽  
Shear Wave Speed ◽  
Shear Energy

Although there are five effective shear moduli for any layered transversely isotropic with a vertical symmetry axis (VTI) medium, one and only one effective shear modulus of the layered system (namely, the uniaxial shear) contains all the dependence of pore fluids on the elastic or poroelastic constants that can be observed in vertically polarized shear waves. Pore fluids can increase the magnitude of shear energy stored in this modulus by an amount that ranges from the smallest to the largest effective shear moduli of the VTI system. But since there are five shear moduli in play, the overall increase in shear energy due to fluids is reduced by a factor of about five in general. We can, therefore, give definite bounds on the maximum increase of overall shear modulus — about 20% of the allowed range as liquid is fully substituted for gas. An attendant increase of density (depending on porosity and fluid density) by approximately 5–10% decreases the shear-wave speed and thereby partially offsets the effect of this shear modulus increase. The final result is an increase of shear-wave speed on the order of 5–10%. This increase is shown to be possible under most favorable circumstances, that is, when the shear modulus fluctuations are large (resulting in strong anisotropy) and the medium behaves in an undrained fashion due to fluid trapping. At frequencies higher than seismic (such as sonic and ultrasonic waves for well logging or laboratory experiments), resulting short response times also produce the requisite undrained behavior; therefore, fluids also affect shear waves at high frequencies by increasing rigidity.

scholarly journals Shear Wave Tensiometry Tracks Reductions in Collateral Ligament Tension Due to Incremental Releases

2021 ◽  
Author(s):  
Matthew Blomquist ◽  
Jonathon Blank ◽  
Dylan Schmitz ◽  
Darryl Thelen ◽  
Joshua Roth
Keyword(s):  
Shear Wave ◽  
Wave Speed ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Ligament Tension ◽  
Before And After ◽  
Total Knee ◽  
Novel Method ◽  
Poor Outcomes ◽  
Implant Alignment

Surgeons routinely perform incremental releases on overly tight ligaments during total knee arthroplasty (TKA) to reduce ligament tension and achieve their desired implant alignment. However, current methods to assess whether the surgeon achieved their desired reduction in the tension of a released ligament are subjective and/or do not provide a quantitative metric of tension in an individual ligament. Accordingly, the purpose of this study was to determine whether shear wave tensiometry, a novel method to assess tension in individual ligaments based on the speed of shear wave propagation, can detect changes in ligament tension following incremental releases. In seven medial and eight lateral collateral porcine ligaments (MCL and LCL, respectively), we measured shear wave speeds and ligament tension before and after incremental releases consisting of punctures with an 18-gauge needle. We found that shear wave speed squared decreased linearly with decreasing tension in both the MCL (r^2 avg = 0.76) and LCL (r^2 avg = 0.94). We determined that errors in predicting tension following incremental releases were 24.5 N and 12.2 N in the MCL and LCL, respectively, using specimen-specific calibrations. These results suggest shear wave tensiometry is a promising method to objectively measure the tension reduction in released structures. Clinical Significance: Direct, objective measurements of the tension changes in individual ligaments following release could enhance surgical precision during soft tissue balancing in TKA. Thus, shear wave tensiometry could help surgeons reduce the risk of poor outcomes associated with overly tight ligaments, including residual knee pain and stiffness.

Spatial Variations in Achilles Tendon Shear Wave Speed Using a Cost-Effective Method of Accelerometers

2019 ◽  
Author(s):  
Muhammad Salman ◽  
Conghui Ge ◽  
Clint Morris
Keyword(s):  
Mechanical Properties ◽  
Signal Processing ◽  
Wave Propagation ◽  
Achilles Tendon ◽  
Shear Wave ◽  
Wave Speed ◽  
Cost Effective ◽  
Complex Signal ◽  
Signal Processing Technique ◽  
Shear Wave Speed

Abstract Currently there are no cost-effective ways to quantitatively measure the in-vivo mechanical properties of the Achilles tendon. Stiffness can be used as a measure of tone and mechanical integrity of both muscles and tendons. Stiffness of the Achilles tendon (AT) can be quantified by the speed of shear wave propagation. The speed of propagation can then be used to find the instantaneous shear modulus. Currently there are other methods such as Ultrasound (US) imaging and Magnetic Resonance Imaging (MRI) which are used clinically to determine the variations in stiffness of the AT. However, these methods require complex signal processing and experienced technicians. Moreover, US imaging technique is limited in measuring high shear wave speed values which are greater than 17 m/s. In this research, one-dimensional accelerometers were used to measure acceleration through the AT. Then a cross-correlation signal processing technique was used to convert acceleration to the velocity of shear wave propagation across the AT. This method could potentially evaluate the mechanical properties of both normal and damaged tendons. This process has proven to be a cost-effective and simple way to assess the stiffness of the AT. The modulus of elasticity (E) was found using the following relation: E = 3ρV2.

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