Dynamic Elastography Research Articles

Shear wave induced resonance elastography of spherical masses with polarized torsional waves

Shear Wave Induced Resonance (SWIR) is a technique for dynamic ultrasound elastography of confined mechanical inclusions. It was developed for breast tumor imaging and tissue characterization. This method relies on the polarization of torsional shear waves modeled with the Helmholtz equation in spherical coordinates. To validate modeling, an in vitro set-up was used to measure and image the first three eigenfrequencies and eigenmodes of a soft sphere. A preliminary in vivo SWIR measurement on a breast fibroadenoma is also reported. Results revealed the potential of SWIR elastography to detect and mechanically characterize breast lesions for early cancer detection.

Bandpass sampling of high-frequency tissue motion

The characterization of tissue viscoelastic properties requires the measurement of tissue motion over a region of interest at frequencies that significantly exceed the frame rates of conventional ultrasound systems. In this paper, we propose that the bandpass sampling technique be applied to tissue motion sampling. With this approach, high-frequency signals limited to a frequency band can be sampled and reconstructed without aliasing at a sampling frequency that is lower than the Nyquist rate. We first review this approach and discuss the selection of the tissue excitation frequency band and of the feasible sampling frequencies that allow signal reconstruction without aliasing. We then demonstrate the approach using simulations based on the finite element method and ultrasound simulations. Finally, we perform experiments on tissue-mimicking materials and demonstrate accurate motion estimation using a lower sampling rate than that required by the conventional sampling theorem. The estimated displacements were used to measure the elasticity and viscosity in a phantom in which an inclusion has been correctly delineated. Thus, with bandpass sampling, it is feasible to use conventional beamforming on diagnostic ultrasound systems to perform high-frequency dynamic elastography. The method is simple to implement because it does not require beam interleaving, additional hardware, or synchronization.

Wide-range dynamic magnetic resonance elastography

Tissue mechanical parameters have been shown to be highly sensitive to disease by elastography. Magnetic resonance elastography (MRE) in the human body relies on the low-dynamic range of tissue mechanics <100 Hz. In contrast, MRE suited for investigations of mice or small tissue samples requires vibration frequencies 10–20 times higher than those used in human MRE. The dispersion of the complex shear modulus ( G ⁎) prevents direct comparison of elastography data at different frequency bands and, consequently, frequency-independent viscoelastic models that fit to G * over a wide dynamic range have to be employed. This study presents data of G * of samples of agarose gel, liver, brain, and muscle measured by high-resolution MRE in a 7T-animal scanner at 200–800 Hz vibration frequency. Material constants μ and α according to the springpot model and related to shear elasticity and slope of the G *-dispersion were determined. Both μ and α of calf brain and bovine liver were found to be similar, while a sample of fibrotic human liver (METAVIR score of 3) displayed about fifteen times higher shear elasticity, similar to μ of bovine muscle measured in muscle fiber direction. α was the highest in fibrotic liver, followed by normal brain and liver, while muscle had the lowest α-values of all biological samples investigated in this study. As expected, the least G *-dispersion was seen in soft gel. The proposed technique of wide-range dynamic MRE can provide baseline data for both human MRE and high-dynamic MRE for better understanding tissue mechanics of different tissue structures.

Characterization of blood clot viscoelasticity by dynamic ultrasound elastography and modeling of the rheological behavior

Dynamic elastography (DE) is a new tool to study mechanical behavior of soft tissues via their motion response to propagating shear waves. This technique characterized viscoelasticity of 9 porcine whole blood samples (3 animals) during coagulation for a shearing frequency of 70Hz, and after complete clot formation between 50 and 160Hz. Clot storage (G′) and loss (G″) moduli were calculated from shear wave velocity and attenuation. Temporal evolutions of G′ and G″ during coagulation were typified with 4 parameters: maximum change in elasticity (G′ slopemax), elasticity after 120min of coagulation (G′max), time occurrence of G″ maximum (te) and G″ at the plateau (G″plateau). G′ and G″ frequency dependence of completely formed blood clots was fitted with 5 standard rheological models: Maxwell, Kelvin–Voigt, Jeffrey, Zener and third-order generalized Maxwell. DE had sufficient sensitivity to follow the coagulation kinetics described by a progressive increase in G′, while G″ transitory increased followed by a rapid stabilization. Inter- and intra-animal dispersions (InterAD and IntraAD) of G′max (InterAD=15.9%, IntraAD=9.1%) showed better reproducibility than G′ slopemax (InterAD=40.4%, IntraAD=21.9%), te (InterAD=27.4%, IntraAD=18.7%) and G″plateau (InterAD=58.6%, IntraAD=40.2%). G′ evolution within the considered range of frequency exhibited an increase, followed by stabilization to a plateau, whereas G″ presented little variations with convergence at a quasi-constant value at highest frequencies. Residues χ⁎, describing the goodness of fit between models and experimental data, showed statistically (p<0.05) that the Kelvin–Voigt model was less in agreement with experimental data than other models. The Zener model is recommended to predict G′ and G″ dispersion of coagulated blood over the explored frequency range.

2-D high-frame-rate dynamic elastography using delay compensated and angularly compounded motion vectors: Preliminary results

This paper describes a new ultrasound-based system for high-frame-rate measurement of periodic motion in 2-D for tissue elasticity imaging. Similarly to conventional 2-D flow vector imaging, the system acquires the RF signals from the region of interest at multiple steering angles. A custom sector subdivision technique is used to increase the temporal resolution while keeping the total acquisition time within the range suitable for real-time applications. Within each sector, 1-D motion is estimated along the beam direction. The intra- and inter-sector delays are compensated using our recently introduced delay compensation algorithm. In-plane 2-D motion vectors are then reconstructed from these delay-compensated 1-D motions. We show that Young's modulus images can be reconstructed from these 2-D motion vectors using local inversion algorithms. The performance of the system is validated quantitatively using a commercial flow phantom and a commercial elasticity phantom. At the frame rate of 1667 Hz, the estimated flow velocities with the system are in agreement with the velocity measured with a pulsed-wave Doppler imaging mode of a commercial ultrasound machine with manual angle correction. At the frame rate of 1250 Hz, phantom Young's moduli of 29, 6, and 54 kPa for the background, the soft inclusion, and the hard inclusion, are estimated to be 30, 11, and 53 kPa, respectively.

Anderson localization of shear waves observed by magnetic resonance imaging

In this letter we present for the first time an experimental investigation of shear wave localization using motion-sensitive magnetic resonance imaging (MRI). Shear wave localization was studied in gel phantoms containing arrays of randomly positioned parallel glass rods. The phantoms were exposed to continuous harmonic vibrations in a frequency range from 25 to 175 Hz, yielding wavelengths on the order of the elastic mean free path, i.e. the Ioffe-Regel criterion of Anderson localization was satisfied. The experimental setup was further chosen such that purely shear horizontal waves were induced to avoid effects due to mode conversion and pressure waves. Analysis of the distribution of shear wave intensity in experiments and simulations revealed a significant deviation from Rayleigh statistics indicating that shear wave energy is localized. This observation is further supported by experiments on weakly scattering samples exhibiting Rayleigh statistics and an analysis of the multifractality of wave functions. Our results suggest that motion-sensitive MRI is a promising tool for studying Anderson localization of time-harmonic shear waves, which are increasingly used in dynamic elastography.

Dynamic spectral-domain optical coherence elastography for tissue characterization

A dynamic spectral-domain optical coherence elastography (OCE) imaging technique is reported. In this technique, audio-frequency compressive vibrations are generated by a piezoelectric stack as external excitation, and strain rates in the sample are calculated and mapped quantitatively using phase-sensitive spectral-domain optical coherence tomography. At different driving frequencies, this technique provides contrast between sample regions with different mechanical properties, and thus is used to mechanically characterize tissue. We present images of a three-layer silicone tissue phantom and rat tumor tissue ex vivo, based on quantitative strain rate. Both acquisition speed and processing speed are improved dramatically compared with previous OCE imaging techniques. With high resolution, high acquisition speed, and the ability to characterize the mechanical properties of tissue, this OCE technique has potential use in non-destructive volumetric imaging and clinical applications.

Fractional wave equation for compressional and shear waves.

This study has been motivated by the observed difference in the range of the power law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is generalized Hooke’s law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo (1967) and Wismer (2006). In the low ωτ (low‐frequency) case, this equation has an attenuation with a power law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high ωτ (high‐frequency) case, it describes attenuation with a power law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases. Recent results on fractional random media will also be discussed as they give similar characteristics from a microperspective.

Shear wave induced resonance elastography of soft heterogeneous media

In the context of ultrasound dynamic elastography imaging and characterization of venous thrombosis, we propose a method to induce mechanical resonance of confined soft heterogeneities embedded in homogenous media. Resonances are produced by the interaction of horizontally polarized shear (SH) waves with the mechanical heterogeneity. Due to such resonance phenomenon, which amplifies displacements up to 10 times compared to non-resonant condition, displacement images of the underlying structures are greatly contrasted allowing direct segmentation of the heterogeneity and a more precise measurement of displacements since the signal-to-noise ratio is enhanced. Coupled to an analytical model of wave scattering, the feasibility of shear wave induced resonance (SWIR) elastography to characterize the viscoelasticity of a mimicked venous thrombosis is demonstrated (with a maximum variability of 3% and 11% for elasticity and viscosity, respectively). More generally, the proposed method has the potential to characterize the viscoelastic properties of a variety of soft biological and industrial materials.

Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography

We present a new method for performing dynamic elastography of soft tissue samples. By sensing nanoscale displacements with optical coherence tomography, a chirped, modulated force is applied to acquire the mechanical spectrum of a tissue sample within a few seconds. This modulated force is applied via magnetic nanoparticles, named ‘nanotransducers’, which are diffused into the tissue, and which contribute negligible inertia to the soft tissue mechanical system. Using this novel system, we observed that excised tissues exhibit mechanical resonance modes which are well described by a linear damped harmonic oscillator. Results are validated by using cylindrical tissue phantoms of agarose in which resonant frequencies (30–400 Hz) are consistent with longitudinal modes and the sample boundary conditions. We furthermore show that the Young's modulus can be computed from their measured resonance frequencies, analogous to resonant ultrasound spectroscopy for stiff material analysis. Using this new technique, named magnetomotive resonant acoustic spectroscopy (MRAS), we monitored the relative stiffening of an excised rat liver during a chemical fixation process.

A unifying fractional wave equation for compressional and shear waves

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Fifty years of brain tissue mechanical testing: From in vitro to in vivo investigations

Beginning in the 1960s many studies have been performed to investigate the mechanical properties of brain. In this paper we point out the difficulties linked with in vitro experimental protocols as well as the advantages of using recently developed non-invasive in vivo techniques, such as magnetic resonance elastography. Results of in vitro and in vivo work are compared, emphasizing the specificities and disparities of the in vitro as well as the in vivo results. In particular, a detailed discussion of the results obtained from dynamic shear experiments and magnetic resonance elastography is given before arriving at a tentative conclusion on the state of knowledge of the mechanical properties of brain.

Measurements of Biomechanics by Dynamic Optical Coherence Elastography

Researchers have developed techniques for using light to probe sub-wavelength dimensions.

In vivo dynamic optical coherence elastography using a ring actuator

We present a novel sample arm arrangement for dynamic optical coherence elastography based on excitation by a ring actuator. The actuator enables coincident excitation and imaging to be performed on a sample, facilitating in vivo operation. Sub-micrometer vibrations in the audio frequency range were coupled to samples that were imaged using optical coherence tomography. The resulting vibration amplitude and microstrain maps are presented for bilayer silicone phantoms and multiple skin sites on a human subject. Contrast based on the differing elastic properties is shown, notably between the epidermis and dermis. The results constitute the first demonstration of a practical means of performing in vivo dynamic optical coherence elastography on a human subject.

Biomechanical properties of in vivo human skin from dynamic optical coherence elastography.

Dynamic optical coherence elastography is used to determine in vivo skin biomechanical properties based on mechanical surface wave propagation. Quantitative Young's moduli are measured on human skin from different sites, orientations, and frequencies. Skin thicknesses, including measurements from different layers, are also measured simultaneously. Experimental results show significant differences among measurements from different skin sites, between directions parallel and orthogonal to Langer's lines, and under different skin hydration states. Results also suggest surface waves with different driving frequencies represent skin biomechanical properties from different layers in depth. With features such as micrometer-scale resolution, noninvasive imaging, and real-time processing from the optical coherence tomography technology, this optical measurement technique has great potential for measuring skin biomechanical properties in dermatology.

Acoustomotive optical coherence elastography for measuring material mechanical properties

Acoustomotive optical coherence elastography (AM-OCE), a dynamic and internal excitation optical coherence elastography technique, is reported. Acoustic radiation force was used for internal mechanical excitation, and spectral-domain optical coherence tomography was used for detection. Mechanical properties of gelatin tissue phantoms were measured by AM-OCE and verified using rheometry results. Measured mechanical properties including shear moduli and shear damping parameters of the gelatin samples double when their polymer concentration increases from 3% to 4%. Spectral analysis was also performed on the acquired data, which improved the processing speed by a factor of 5 compared with a least-square fitting approach. Quantitative measurement, microscale resolution, and remote excitation are the main features of AM-OCE, which make the technique promising for measuring biomechanical properties.

Experimental Evaluation of the High-Speed Motion Vector Measurement by Combining Synthetic Aperture Array Processing with Constrained Least Square Method

Ultrahigh speed dynamic elastography has promising potential capabilities in applying clinical diagnosis and therapy of living soft tissues. In order to realize the ultrahigh speed motion tracking at speeds of over thousand frames per second, synthetic aperture (SA) array signal processing technology must be introduced. Furthermore, the overall system performance should overcome the fine quantitative evaluation in accuracy and variance of echo phase changes distributed across a tissue medium. On spatial evaluation of local phase changes caused by pulsed excitation on a tissue phantom, investigation was made with the proposed SA signal system utilizing different virtual point sources that were generated by an array transducer to probe each component of local tissue displacement vectors. The final results derived from the cross-correlation method (CCM) brought about almost the same performance as obtained by the constrained least square method (LSM) extended to successive echo frames. These frames were reconstructed by SA processing after the real-time acquisition triggered by the pulsed irradiation from a point source. The continuous behavior of spatial motion vectors demonstrated the dynamic generation and traveling of the pulsed shear wave at a speed of one thousand frames per second.

Magnetic resonance elastography with a phased‐array acoustic driver system

Dynamic MR elastography (MRE) quantitatively maps the stiffness of tissues by imaging propagating shear waves in the tissue. These waves can be produced from intrinsic motion sources (e.g., due to cardiac motion), from external motion sources that produce motion directly at depth in tissue (e.g., amplitude-modulated focused ultrasound), and from external actuators that produce motion at the tissue surface that propagates into the tissue. With external actuator setups, typically only a single transducer is used to create the shear waves, which in some applications might have limitations due to shadowing and attenuation of the waves. To address these limitations, a phased-array acoustic driver system capable of applying independently controlled waveforms to each channel was developed and tested. It was found that the system produced much more uniform illumination of the object, improving the quality of the elastogram. It was also found that the accuracy of the stiffness value of any arbitrary region of interest could be improved by obtaining maximal shear wave illumination with the phased array capability of the system.

Three-dimensional transient and harmonic shear-wave scattering by a soft cylinder for dynamic vascular elastography

With the objective of characterizing biological soft tissues with dynamic elastography, a three-dimensional (3D) analytical model is proposed to simulate the scattering of plane shear waves by a soft cylinder embedded in an infinite soft medium. The 3D problem of harmonic plane shear-wave scattering is first formulated and solved, and the monochromatic solution is employed to simulate transient wave scattering. Both harmonic and transient simulations are compared with experimental 3D acquisitions. The good agreements obtained between measured and calculated displacement fields allowed to conclude on the validity of the proposed 3D harmonic and transient models. The spatial distribution of displacements (diffraction lobes, displacement oscillations, wave diffraction angles, etc.) and their relative amplitudes in both inclusion and surrounding materials depended on the contrast between the viscoelastic properties of the different media. The possibility of solving an inverse problem to assess soft heterogeneous medium viscoelasticity is discussed and some future theoretical and experimental developments are proposed.

Characterization of the dynamic shear properties of hyaline cartilage using high‐frequency dynamic MR elastography

This work evaluated the feasibility of dynamic MR Elastography (MRE) to quantify structural changes in bovine hyaline cartilage induced by selective enzymatic degradation. The ability of the technique to quantify the frequency-dependent response of normal cartilage to shear in the kilohertz range was also explored. Bovine cartilage plugs of 8 mm in diameter were used for this study. The shear stiffness (mu(s)) of each cartilage plug was measured before and after 16 hr of enzymatic treatments by dynamic MRE at 5000 Hz of shear excitation. Collagenase and trypsin were used to selectively affect the collagen and proteoglycans contents of the matrix. Additionally, normal cartilage plugs were tested by dynamic MRE at shear-excitations of 3000-7000 Hz. Measured micro(s) of cartilage plugs showed a significant decrease (-37%, P < 0.05) after collagenase treatment and a significant decrease (-28%, P < 0.05) after trypsin treatment. Furthermore, a near-linear increase (R(2) = 0.9141) in the speed of shear wave propagation with shear-excitation frequency was observed in cartilage, indicating that wave speed is dominated by viscoelastic effects. These experiments suggest that dynamic MRE can provide a sensitive quantitative tool to characterize the degradation process and viscoelastic behavior of cartilage.