Mathematical Modelling of Composite Phantoms for the Calibration of Ultrasound Devices

We propose a methodology to narrow down the selection of design parameters of phantoms for calibrating ultrasound devices. For doing so, we model the phantoms as composite materials. Through a mathematical homogenization technique, the global properties of the phantom are given in terms of the volume fractions of its components, their geometric shapes and physical properties. We explore these parameters to determine ranges that yield the desirable values of acoustic impedance and attenuation. The procedure is illustrated for a class of sandwich-like phantoms made of layers of agar of different concentrations with complex elastic moduli. In this example, homogenization provides analytical formulae of the global properties that can be used to identify the layers’ thicknesses and concentrations that yield a low impedance and an average attenuation coefficient. These analytical results are compared with a numerical homogenization method, showing excellent agreement.