Simulating multiple scattering inside a population of nonlinearly oscillating microbubbles using the Iterative Nonlinear Contrast Source method

Abstract

For several decades, microbubbles have been the primary choice for ultrasound contrast agents both for efficiency and safety reasons. To optimize their performance in various applications e.g. proton therapy, it is important to understand the dynamics of populations of nonlinearly oscillating microbubbles. Especially for high concentration clouds, multiple scattering can significantly influence the propagation of medical ultrasound. To numerically study the higher-order interaction between nonlinear microbubbles, we present a modified version of the Iterative Nonlinear Contrast Source (INCS) method. Based on a Neumann iterative scheme, the acoustic pressure is obtained by treating the nonlinearly scattering bubbles as individual contrast sources in a “linearized” background medium. In each iteration, the full nonlinear pressure field is updated by applying the 4D spatiotemporal convolution between the background Green’s function and the contrast sources obtained from the previous iteration. In this study, all microbubbles may exhibit an individual behavior. To accommodate this, in each iteration the solution of the Marmottant equation for each microbubble is obtained and used as the temporal signature of the respective contrast source. Using this scheme, each iteration adds an order of multiple scattering. The accuracy and the efficiency of INCS results will be demonstrated for monodisperse and polydisperse concentrations.

Nonlinear sound-sheet microscopy: imaging opaque organs at the capillary and cellular scale

“…In practice, these two transmissions generate non-diffractive beams with main-lobes separated by a distance of . The thickness of the sound sheet was estimated using INCS simulations (25), the Full Width at Half Maximum (FWHM) of the main-lobe of the non-diffractive beam can be approximated with the following relation:…”

“…1C and Fig. 1E were computed with the Iterative Nonlinear Contrast Source (INCS) method (25). Briefly, INCS was developed to solve the four-dimensional spatiotemporal Westervelt equation describing nonlinear sound wave propagation.…”

“…Image reconstruction relies on a delay-and-sum beamforming algorithm with the assumption that ultrasound backscattering only arises from the sound-sheet plane. For beamforming delay laws, see the image reconstruction paragraph and reference (25).…”

“…Here we introduce nonlinear sound-sheet microscopy (NSSM), a method to image targeted biological functions across cm 3 of opaque living tissue. NSSM relies on a large field-of-view, high-frequency row-column addressed transducer array (RCA) (21)(22)(23) and the transmission of non-diffracting ultrasound beams to detect cells labelled with GVs (24) or vessels labelled with microbubbles (MBs) (25). NSSM expands the field of view of biomolecular ultrasound at 15 MHz from ~3.5 x 64 x 100 λ 3 to 80 x 80 x 100 λ 3 , λ denoting the ultrasound wavelength, the upper bound 2D imaging speed from 400 Hz to 25.6 kHz, and spatial resolution from 1 x 1 x 3.5 λ 3 to 1 x 1 x 0.6 λ 3 .…”