Assessment of shear modulus of tissue using ultrasound radiation force acting on a spherical acoustic inhomogeneity

Abstract

An ultrasound-based method to locally assess the shear modulus of a medium is reported. The proposed approach is based on the application of an impulse acoustic radiation force to an inhomogeneity in the medium and subsequent monitoring of the spatio-temporal response. In our experimental studies, a short pulse produced by a 1.5-MHz highly focused ultrasound transducer was used to initiate the motion of a rigid sphere embedded into an elastic medium. Another 25 MHz focused ultrasound transducer operating in pulse-echo mode was used to track the displacement of the sphere. The experiments were performed in gel phantoms with varying shear modulus to demonstrate the relationship between the displacement of the sphere and shear modulus of the surrounding medium. Because the magnitude of acoustic force applied to sphere depends on the acoustic material properties and, therefore, cannot be used to assess the absolute value of shear modulus, the temporal behavior of the displacement of the sphere was analyzed. The results of this study indicate that there is a strong correlation between the shear modulus of a medium and spatio-temporal characteristics of the motion of the rigid sphere embedded in this medium.

Fig. 1

The photograph of the experimental setup. The excitation transducer was attached at the bottom of a tank while the imaging transducer was located on the top.

Fig. 2

The experimental dependence of the shear elastic modulus on the temperature measured with In-Spec 2200 benchtop portable tester (Instron, Inc., Norwood, MA). The error bars represent ±1 standard deviation.

Fig. 3

The experimentally measured (a) and theoretically calculated (b) displacement of the sphere embedded in phantom with the varying shear elasticity.

Fig. 4

Experimental (points) and theoretical (solid line) dependences of maximum displacement of solid sphere under applied radiation force on shear modulus of surrounding tissue.

Fig. 5

The displacements of the solid sphere in response to applied acoustic radiation forces of different magnitude. The vertical line highlights the fact that the sphere reaches its maximum displacement at exactly the same time regardless of the amplitude of applied force.

Fig. 6

The experimental (points) and theoretical (solid line) relationship between shear modulus and the τ_max defined as a time required for the solid sphere to reach the maximum displacement.

Fig. 7

The calculated displacements of the solid sphere in response to applied acoustic radiation force. The sphere was embedded in the phantom with shear modulus of 1000 Pa. Note that the sphere reaches its maximum displacement at approximately the same time (as highlighted by vertical line) regardless of the shear viscosity of the phantom material.

Fig. 8

Comparison of shear moduli obtained from uniaxial test and radiation force measurements. Points represent experimental points while the solid line indicates the ideal coincident between these 2 methods. The horizontal error bars in Fig. 8 correspond to the vertical error bars in Fig. 2.