A model for the propagation and scattering of ultrasound in tissue

Abstract

An inhomogeneous wave equation is derived describing propagation and scattering of ultrasound in an inhomogeneous medium. The scattering term is a function of density and propagation velocity perturbations. The integral solution to the wave equation is combined with a general description of the field from typical transducers used in clinical ultrasound to yield a model for the received pulse-echo pressure field. Analytic expressions are found in the literature for a number of transducers, and any transducer excitation can be incorporated into the model. An example is given for a concave, nonapodized transducer in which the predicted pressure field is compared to a measured field.

Computer Simulation of Ultrasonic Scattering and Texture in B-Mode Images

“…The time domain backscattered signal of an impulse ultrasonic wave by an inhomogeneity can be expressed as [4], and…”

Simulation of Contrast Agent Enhanced Ultrasound Imaging Based on Field II

“…If the fields p s (r, t) and p b (r, t) are weak compared to the incident field p i (r, t), the latter can replace the total pressure field p(r, t) on the right hand side of (12), what is known as Born approximation [6].…”

“…The approximation has been made by lumping the scatterer with volume V q and irradiation angle Θ q into a single point at r q [7] and using the paraxial approximation [6,8]. This is tolerable if the scatterer is small and sufficiently far away from the transducer.…”

“…Position dependency of the transducer displacement is accounted for by the surface velocity distribution function w(s). The Green's function solution to this problem is [6] …”

“…The total echo field from all Q scatterers and bubbles is thus obtained by the Green's function solution to (10) and (11) respectively [6,7]:…”