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.

Thermodynamic Stability of Volatile Droplets and Thin Films Governed by Disjoining Pressure in Open and Closed Containers.

Distributed thin films of water and their coexistence with droplets are investigated using a capillary description based on a thermodynamic fundamental relation for the film Helmholtz energy, derived from disjoining pressure isotherms and an accurate equation of state. Gas-film and film-solid interfacial tensions are derived, and the latter has a dependence on film thickness. The resulting energy functionals from the capillary description are discretized, and stationary states are identified. The thermodynamic stability of configurations with thin films in systems that are closed (canonical ensemble) or connected to a particle reservoir (grand canonical ensemble) is evaluated by considering the eigenvalues of the corresponding Hessian matrices. The conventional stability criterion from the literature states that thin flat films are stable when the derivative of the disjoining pressure with respect to the film thickness is negative. This criterion is found to apply only in open systems. A closer inspection of the eigenvectors of the negative eigenvalues shows that condensation/evaporation destabilizes the film in an open system. In closed systems, thin films can be stable even though the disjoining pressure derivative is positive, and their stability is governed by mechanical instabilities of a similar kind to those responsible for spinodal dewetting in nonvolatile systems. The films are stabilized when their thickness and disjoining pressure derivative are such that the minimum unstable wavelength is larger than the container diameter. Droplets in coexistence with thin films are found to be unstable for all considered examples in open systems. In closed systems, they are found to be stable under certain conditions. The unstable droplets in both open and closed systems are saddle points in their respective energy landscapes. In the closed system, they represent the activation barrier for the transition between a stable film and a stable droplet. In the open system, the unstable droplets represent the activation barrier for the transition from a film into a bulk liquid phase. Thin films are found to be the equilibrium configuration up to a certain value of the total density in a closed system. Beyond this value, there is a morphological phase transition to stable droplet configurations.