Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes

We demonstrate a simple and computationally efficient method to recover the shear modulus pertaining to the focal volume of an ultrasound transducer from the measured vibro-acoustic spectral peaks. A model that explains the transport of local deformation information with the acoustic wave acting as a carrier is put forth. It is also shown that the peaks correspond to the natural frequencies of vibration of the focal volume, which may be readily computed by solving an eigenvalue problem associated with the vibrating region. Having measured the first natural frequency with a fibre Bragg grating sensor, and armed with an expedient means of computing the same, we demonstrate a simple procedure, based on the method of bisection, to recover the average shear modulus of the object in the ultrasound focal volume. We demonstrate this recovery for four homogeneous agarose slabs of different stiffness and verify the accuracy of the recovery using independent rheometer-based measurements. Extension of the method to anisotropic samples through the measurement of a more complete set of resonant modes and the recovery of an elasticity tensor distribution, as is done in resonant ultrasound spectroscopy, is suggested.