A bulk modulus dependent linear model for acoustical imaging

Modeling the acoustical process of soft biological tissue imaging and understanding the consequences of the approximations required by such modeling are key steps for accurately simulating ultrasonic scanning as well as estimating the scattering coefficient of the imaged matter. In this document, a linear solution to the inhomogeneous ultrasonic wave equation is proposed. The classical assumptions required for linearization are applied; however, no approximation is made in the mathematical development regarding density and speed of sound. This leads to an expression of the scattering term that establishes a correspondence between the signal measured by an ultrasound transducer and an intrinsic mechanical property of the imaged tissues. This expression shows that considering the scattering as a function of small variations in the density and speed of sound around their mean values along with classical assumptions in this domain is equivalent to associating the acoustical acquisition with a measure of the relative longitudinal bulk modulus. Comparison of the model proposed to Jensen's earlier model shows that it is also appropriate to perform accurate simulations of the acoustical imaging process.