Virtual ultrasound machine operating in a GHz to MHz frequency range for particle-based biomedical simulations

TL;DR

A particle-based virtual ultrasound machine that uses a novel smoothed dissipative particle dynamics variant with an implicit pressure solver and a negative-pressure stabilization scheme, required to mimic acoustic propagation across MHz-GHz frequencies is introduced.

Abstract

Ultrasound-matter interactions underpin numerous biomedical and soft-matter applications, yet simulating these phenomena is challenging due to the large separation of viscous and sonic time scales. Continuum methods capture large-scale wave propagation but cannot resolve microscale interactions, while particle-based approaches offer molecular resolution but struggle with efficiency and stability at larger scales. We introduce a particle-based virtual ultrasound machine that uses a novel smoothed dissipative particle dynamics variant with an implicit pressure solver and a negative-pressure stabilization scheme, required to mimic acoustic propagation across MHz-GHz frequencies. We demonstrate its capabilities by modeling the acoustophoresis of encapsulated microbubbles, a key mechanism in ultrasound-mediated drug delivery. Beyond this application, the approach establishes a generalizable platform for simulating wave-matter interactions in soft and biological materials, opening new directions for computational studies of acoustics-driven phenomena in science and engineering.

Figures (16)

• Figure 1: Overview of spatiotemporal scales, simulation methods and systems, studied with US. Top: commonly used methods for US simulations and the length- and frequency-scales they typically describe. Boundaries between methods are approximate, as the applicable range depends on computational resources, geometry, and optimizations. Representative systems are shown below the frequencies: molecular dynamics (MD) for all-atom simulations of water, DPD for THz excitations in proteins, and hybrid frameworks for large-scale biological tissue simulations (such as capillary flow) and EMB dynamics. Our method, usSDPD, fits on the medically-relevant scale of EMBs. This figure shows the ranges, where the viscosity and compressibility match those of water. For example, the DPD method might be used also at larger scales, but either the compressibility and viscosity of water would not be correct, or a liquid with lower compressibility and/or higher viscosity would be used. Bottom: schematic representations of structures that can be coupled with usSDPD, including (from left to right) hydrogel microspheres, biofilms Huang2025, red blood cell microrobots with magnetic nanoparticles Huang2023, scattering EMBs, tubular microrobots Lu2020, red blood cells, interacting oscillating EMBs, tumor spheroids, and others.
• Figure 2: Response of (a) standard (vanilla) SDPD and (b) usSDPD fluids to bulk volume oscillation. Both simulations are done at 0.1 granularity with both speed of sound and viscosity matched to those of water. usSDPD shows more stable behavior than vanilla SDPD at negative pressures. The pressure amplitude is large compared to the density amplitude, which is characteristic of water with low compressibility. In vanilla SDPD simulations, 10 times smaller timestep is used for stability.
• Figure 3: Schematic of a virtual US machine. The machine consists of two US sources positioned at the left and right boundaries of the open simulation box (buffers), as well as the region of interest, where the immersed structure is located. By imposing oscillations of the same frequency in the left and right buffers, a standing wave field is generated in the region of interest (dark and light regions correspond to low and high density, respectively).
• Figure 4: Interactions in the acoustophoresis simulation system. Red circles represent external fluid particles, yellow circles represent membrane particles, and blue circles represent internal fluid particles. The arrows denote interactions between particle types.
• Figure 5: Acoustophoresis simulation in a $2.4\um \times 0.63\um \times 0.63\um$ cell. (a) snapshot of the acoustophoresis simulation at the beginning and (b) the end of the simulation (the system is sliced in half along the page plane to improve visibility). Buffer regions are shown in red and the yellow shading schematically illustrates the pressure field of the standing wave. (c) Trajectories of the EMB center-of-mass for input viscosities ranging uniformly from $\eta = 8.9e-4Pa s$ to $\eta = 1.0e-4Pa s$ with pressure amplitude $\Delta p_0 = 9bar$ in all cases. Frequency is 178MHz and EMB diameter is 0.24 in all cases. (d) EMB center-of-mass velocity for largest and smallest viscosity. (e) Time required for a EMB to reach the position $x = 1.4\um$ as a function of the simulated viscosity $\eta'$. As explained in the main text, simulated viscosity differs slightly from the input viscosity due to additional LJ contribution.