Ultrasound enhanced diffusion in hydrogels: An experimental and non-equilibrium molecular dynamics study.

Focused ultrasound has experimentally been found to enhance the diffusion of nanoparticles; our aim with this work is to study this effect closer using both experiments and non-equilibrium molecular dynamics. Measurements from single particle tracking of 40 nm polystyrene nanoparticles in an agarose hydrogel with and without focused ultrasound are presented and compared with a previous experimental study using 100 nm polystyrene nanoparticles. In both cases, we observed an increase in the mean square displacement during focused ultrasound treatment. We developed a coarse-grained non-equilibrium molecular dynamics model with an implicit solvent to investigate the increase in the mean square displacement and its frequency and amplitude dependencies. This model consists of polymer fibers and two sizes of nanoparticles, and the effect of the focused ultrasound was modeled as an external oscillating force field. A comparison between the simulation and experimental results shows similar mean square displacement trends, suggesting that the particle velocity is a significant contributor to the observed ultrasound-enhanced mean square displacement. The resulting diffusion coefficients from the model are compared to the diffusion equation for a two-time continuous time random walk. The model is found to have the same frequency dependency. At lower particle velocity amplitude values, the model has a quadratic relation with the particle velocity amplitude as described by the two-time continuous time random walk derived diffusion equation, but at higher amplitudes, the model deviates, and its diffusion coefficient reaches the non-hindered diffusion coefficient. This observation suggests that at higher ultrasound intensities in hydrogels, the non-hindered diffusion coefficient can be used.

Nanoparticle Dynamics in Composite Hydrogels Exposed to Low-Frequency Focused Ultrasound.

Pulsed focused ultrasound (FUS) in combination with microbubbles has been shown to improve delivery and penetration of nanoparticles in tumors. To understand the mechanisms behind this treatment, it is important to evaluate the contribution of FUS without microbubbles on increased nanoparticle penetration and transport in the tumor extracellular matrix (ECM). A composite agarose hydrogel was made to model the porous structure, the acoustic attenuation and the hydraulic conductivity of the tumor ECM. Single-particle tracking was used as a novel method to monitor nanoparticle dynamics in the hydrogel during FUS exposure. FUS exposure at 1 MHz and 1 MPa was performed to detect any increase in nanoparticle diffusion or particle streaming at acoustic parameters relevant for FUS in combination with microbubbles. Results were compared to a model of acoustic streaming. The nanoparticles displayed anomalous diffusion in the hydrogel, and FUS with a duty cycle of 20% increased the nanoparticle diffusion coefficient by 23%. No increase in diffusion was found for lower duty cycles. FUS displaced the hydrogel itself at duty cycles above 10%; however, acoustic streaming was found to be negligible. In conclusion, pulsed FUS alone cannot explain the enhanced penetration of nanoparticles seen when using FUS and microbubbles for nanoparticle delivery, but it could be used as a tool to enhance diffusion of particles in the tumor ECM.

A volume-averaged model for acoustic streaming induced by focused ultrasound in soft porous media.

Equations describing acoustic streaming in soft, porous media driven by focused ultrasound are derived based on the assumption that acoustic waves pass through the porous material as if it were homogeneous. From these equations, a model that predicts the time-averaged flow on the macroscopic scale, as well as the advective transport of the trace components, is created. The model is used to perform simulations for different shapes of the focused ultrasound beam. For a given shape, and using the paraxial approximation for the ultrasound, the acoustic streaming is found to be linearly proportional to the applied ultrasound intensity, to the permeability of the porous material and to the attenuation coefficient, and inversely proportional to the liquid viscosity. Results from simulations are compared to a simplified expression stating that the dimensionless volumetric liquid flux is equal to the dimensionless acoustic radiation force. This approximation for the acoustic streaming is found to be reasonable near the beam axis for focused ultrasound beam shapes that are long in the axial direction, compared to their width. Finally, a comparison is made between the model and experimental results on acoustic streaming in a gel, and good agreement is found.