Estimation of the complex shear modulus in tissue-mimicking materials from optical vibrometry measurements

Abstract

This study deals with the development of an optimization-based technique for the identification of viscoelastic shear modulus in soft tissue specimens using ultrasound radiation force and optical vibrometry measurements. In the experiment, a tissue-mimicking phantom is submerged in water and excited harmonically via radiation force of modulated ultrasound, while the gel's response is monitored (in terms of particle velocity) by a laser vibrometer targeting the exposed surface of the specimen. For a systematic approach to the problem, the tissue's viscoelastic modulus is sought via gradient-based minimization of a Bayesian cost function, aided by a boundary integral equation treatment of the solid–fluid vibration problem and semi-analytical computation of the material sensitivities of the misfit function. Through an independent motion tracking of the load transferring component, the proposed technique also allows (by way of the reconstructed shear modulus) for an independent estimation of the acoustic radiation force acting on a target that, depending on a situation, may be difficult to measure directly. Beyond their immediate application, the proposed developments may also provide an impetus for extensions of the material characterization methodology that may involve internal application of the acoustic radiation force, vibro-acoustography (as opposed to laser vibrometry) observations of the tissue's response and in-vivo estimation of tissue viscoelasticity.