Material properties from acoustic radiation force step response

Abstract

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.

Dispersion and Shear Modulus Measurements of Porcine Liver

“…Time-varying torque mea sure ments were an a lyzed to es ti mate re lax ation moduli through a 3rd-or der gen er al ized Maxwell model as previously de scribed. 21 No pre con di tion ing was ap plied to liver sam ples.…”

Optical coherence elastography for tissue characterization: a review

“…Taking the Kelvin-Voigt body as an example, the biological tissue can be modelled as a parallel combination of a linear spring and a dashpot that are representing the elastic and the viscous properties of the tissue sample, respectively. For an underdamped harmonic oscillator [101], the relationship between the loading force F ( t ) and the resulted displacement x ( t ) of the sample can be written as a second order differential equation, $$m\frac{d^{2}x\left(t\right)}{d{t}^2}+R\frac{dx\left(t\right)}{dt}+kx\left(t\right)=F\left(t\right),$$ where m is the mass of the sample, R is the coefficient of viscosity, and k is the spring constant. By solving this equation, one can obtain the displacement profile x ( t ) and the natural fluency f as $$x\left(t\right)=B{e}^{-\frac{R}{2m}t}\cos (2\pi ft+\phi )$$ $$\text{and}f=\frac{1}{2\pi }\sqrt{\frac{k}{m}-\frac{R^2}{4m^2}},$$ where B is the amplitude of displacement and φ is the phase factor of the oscillation.…”

Acoustic radiation force-based elasticity imaging methods

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