When and How Ultrasound Enhances Nanoparticle Diffusion in Hydrogels: A Stick-and-Release Mechanism

TL;DR

This study probes when ultrasound enhances nanoparticle diffusion in hydrogel-like extracellular matrices using a coarse-grained Langevin Dynamics framework. By validating in dilute buffer and then varying NP–network attraction, it reveals a stick-and-release mechanism: US reduces transient NP–matrix contacts only when attractive interactions are sufficiently strong and US pulses extend over multiple cycles. The findings reconcile divergent experimental results, showing strong acoustic diffusion only in sticky networks and under appropriate pulse durations, and they provide molecular-level design principles for ultrasound-assisted drug delivery in hydrogels. Together, the work clarifies how NP–ECM interactions and US parameters govern diffusion, with implications for optimizing therapies that rely on hydrogel-like tumor matrices.

Abstract

Nanoparticles (NPs) are widely used as drug carriers in cancer therapy due to their ability to accumulate in tumor tissue via the enhanced permeability and retention effect. However, their transport within tumors is often hindered by the dense extracellular matrix, where diffusion dominates. Several studies suggest that ultrasound (US) irradiation can enhance NP diffusion in ECM-mimicking hydrogels, yet the underlying molecular mechanisms remain unclear, and experimental findings are often contradictory. Here, we use coarse-grained Langevin Dynamics simulations to investigate the conditions under which US can enhance NP diffusion in hydrogels. After validating our simulation framework against an exact analytical solution for NP motion under US in dilute buffer, we systematically explore NP diffusion in hydrogels with varying degrees of NP-network attraction. Our results reveal that acoustic enhancement arises from reduced contact time between NPs and the hydrogel matrix. This effect becomes significant only when NP-hydrogel interactions are sufficiently strong and US pulses are long enough to disrupt these interactions, following a "stick-and-release" mechanism. These findings reconcile previously conflicting experimental observations and explain why acoustic enhancement is observed in some studies but not others. Overall, our study provides a molecular-level explanation for US-enhanced NP diffusion in hydrogels and establishes design principles for optimizing therapeutic US protocols in drug delivery applications.

Figures (24)

• Figure 1: Simulation snapshot of nanoparticles (NPs) diffusing in a hydrogel with a polymer volume fraction of $0.86\%$. The system is subjected to an ultrasound (US) wave propagating along the long axis $L_\parallel$ of the simulation box (a square prism with shorter edges $L_\perp = 1/3L_\parallel$), schematically illustrated by a speaker in the left corner of the box (created in https://BioRender.com). This snapshot corresponds to the “steric network” scenario, where NP-hydrogel interactions are purely steric. Color code: hydrogel fibril beads (orange), hydrogel node beads (red), NPs (purple, pink, cyan, brown, green), periodic images (gray).
• Figure 2: Mean squared displacement ($\langle R(\tau)^{2}\rangle$, panel A) and diffusion coefficient at zero US amplitude ($D$, panel B) of NPs as a function of lag time $\tau$ obtained from LD simulations in a buffer (markers) for two input US peak pressures $P_{\textrm{max}}$. Panel A includes the analytical solutions for $\langle R(\tau)^{2}\rangle$ from the Einstein–Smoluchowski equation (Eq. \ref{['eq:einstein_smo']}, labeled ES) and for the US-modified model (Eq. \ref{['eq:msd_osc']}, labeled ES-US). The lower sub-panel of A shows the relative error between simulation results and the ES-US prediction, calculated as $(\langle R(\tau)^{2}\rangle_{\textrm{LD}}-\langle R(\tau)^{2}\rangle_{\textrm{ES-US}})/\langle R(\tau)^{2}\rangle_{\textrm{ES-US}}$. In panel A, data points used to calculate $D$ are highlighted in darker shades. In panel B, the input Stokes–Einstein diffusion coefficient $D_0$ (Eq. \ref{['eq:stokes_einstein']}) is shown as a reference (solid line).
• Figure 3: Probability density of pore radius in hydrogel networks with varying polymer volume fractions ($\phi$). The NP radius is indicated by a vertical line for reference. Dashed lines represent bimodal Gaussian fits to the distributions and are included as visual guides.
• Figure 4: Mean squared displacement ($\langle R(\tau)^{2}\rangle$, panel A) and diffusion coefficient at zero US amplitude ($D$, panel B) of NPs in a steric network of volume fraction $\phi = 0.86 \%$, under varying US peak pressures $P_{\textrm{max}}$. Panel A includes the analytical solution from the Einstein–Smoluchowski equation (Eq. \ref{['eq:einstein_smo']}, labeled ES). In panel B, the input Stokes–Einstein diffusion coefficient $D_0$ (Eq. \ref{['eq:stokes_einstein']}) is shown as a reference (solid line).
• Figure 5: Diffusion coefficient at long lag times ($D^\mathrm{long}$) as a function of US peak pressure ($P_{\textrm{max}}$) for steric networks with varying polymer volume fractions ($\phi$). The Stokes–Einstein diffusion coefficient $D_0$ (see Eq. \ref{['eq:stokes_einstein']}) is shown as a reference (solid line).