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.

Material properties from acoustic radiation force step response.

An ultrasonic technique for estimating viscoelastic properties of hydrogels, including engineered biological tissues, is being developed. An acoustic radiation force is applied to deform the gel locally while Doppler pulses track the induced movement. The system efficiently couples radiation force to the medium through an embedded scattering sphere. A single-element, spherically-focused, circular piston element transmits a continuous-wave burst to suddenly apply and remove a radiation force to the sphere. Simultaneously, a linear array and spectral Doppler technique are applied to track the position of the sphere over time. The complex shear modulus of the gel was estimated by applying a harmonic oscillator model to measurements of time-varying sphere displacement. Assuming that the stress-strain response of the surrounding gel is linear, this model yields an impulse response function for the gel system that may be used to estimate material properties for other load functions. The method is designed to explore the force-frequency landscape of cell-matrix viscoelasticity. Reported measurements of the shear modulus of gelatin gels at two concentrations are in close agreement with independent rheometer measurements of the same gels. Accurate modulus measurements require that the rate of Doppler-pulse transmission be matched to a priori estimates of gel properties.

3-D FDTD simulation of shear waves for evaluation of complex modulus imaging.

The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity.

Shear modulus estimation with vibrating needle stimulation.

An ultrasonic shear wave imaging technique is being developed for estimating the complex shear modulus of biphasic hydropolymers including soft biological tissues. A needle placed in the medium is vibrated along its axis to generate harmonic shear waves. Doppler pulses synchronously track particle motion to estimate shear wave propagation speed. Velocity estimation is improved by implementing a k-lag phase estimator. Fitting shear-wave speed estimates to the predicted dispersion relation curves obtained from two rheological models, we estimate the elastic and viscous components of the complex shear modulus. The dispersion equation estimated using the standard linear solid-body (Zener) model is compared with that from the Kelvin-Voigt model to estimate moduli in gelatin gels in the 50 to 450 Hz shear wave frequency bandwidth. Both models give comparable estimates that agree with independent shear rheometer measurements obtained at lower strain rates.

In vivo measurement of the complex shear modulus of rat mammary tumors using shear wave imaging techniques.

This paper summarizes dynamic measurements of shear modulus constants acquired for spontaneously growing rat mammary tumors. Measurements are compared with histology to determine tumor types. We also report on 3D shear-wave velocity fields acquired from an inhomogeneous hydrogel phantom with known mechanical properties. Phantom measurements enable us to interpret the effects of tissue structure and geometry on viscoelastic parameter estimates, and demonstrate that reproducible measurements are possible in vivo. Viscoelastic properties describe the mechano-environment of cells undergoing malignant transformation and tumor growth.

Dispersion and shear modulus measurements of porcine liver.

A narrow-band ultrasonic shear-wave imaging technique for estimating phase speed was applied to fresh and thermally damaged porcine liver in vitro. Two constitutive models were applied to the measurements to represent rheological behavior of the tissue and estimate the complex shear modulus at frequencies between 50 and 300 Hz. Our results were compared to similar values from the literature to assess how well models represent liver measurements over a range of shear-wave frequencies, experimental conditions and mammalian species. We found remarkable consistency in some parameters but not in others, suggesting that the Kelvin-Voigt model commonly applied in elasticity-imaging situations is representative of tissue dispersion but the description it offers is incomplete. Data are consistent with the theory that viscoelastic contrast is more likely due to changes in protein and other biomolecular-scale structures than from tissue anatomy larger than a cell. Dispersion measurements at frequencies between 0.5-1000 kHz are needed to more completely evaluate models for the viscoelastic behavior liver.