Characterization of Viscoelastic Media Combining Ultrasound and Magnetic-Force Induced Vibrations on an Embedded Soft Magnetic Sphere

We report a method to locally assess the complex shear modulus of a viscoelastic medium. The proposed approach is based on the application of a magnetic force to a millimeter-sized steel sphere embedded in the medium and the subsequent monitoring of its dynamical response. A coil is used to create a magnetic field inducing the displacement of the sphere located inside a gelatin phantom. Then, a phased-array system using 3 MHz ultrasound probe operating in pulse-echo mode is used to track the displacement of the sphere. Experiments were conducted on several samples and repeated as a function of phantom temperature. The dynamic response of the sphere measured experimentally is in good agreement with Kelvin–Voigt theory. Since the magnetic force is not affected by weak diamagnetic media, our proposal results in an accurate estimation of the force acting on the inclusion. Consequently, the estimated viscoelastic parameters show excellent robustness and the elastic modulus agrees with the measurements using a quasi-static indentation method, obtaining errors below 10% in the whole temperature range. The use of the macroscopic inclusion limits the direct application of this method in a biomedical context, but it provides a robust estimation of the elastic modulus that can be used for material characterization in industrial applications.