# Initial nucleation of nanodroplets in viscoelastic tissue driven by ultrasound: A theoretical simulation

## TL;DR

This paper explores how nanodroplets nucleate in tissue under ultrasound, using a theoretical model to better understand and optimize their use in medical treatments.

## Contribution

A modified classical nucleation theory is proposed to describe nanodroplet nucleation in viscoelastic tissue, incorporating compressibility and elasticity effects.

## Key findings

- A stable critical radius for nanodroplet nucleation is achievable when considering tissue elasticity and nanodroplet compressibility.
- The initial nucleation threshold increases with higher tissue bulk modulus, especially for smaller nanodroplets.
- Lower ultrasound frequencies expand the achievable nucleation area in tissue.

## Abstract

Phase-change nanodroplets hold promising potential for theranostic applications in tumor tissue. However, the initial nucleation of nanodroplets in tissue—a critical stage for subsequent vapor bubble dynamics and theranostic efficacy—remains unexplored. This work, accounting for nanodroplets and tissue as compressible mediums, was represented by two springs in series: one for nanodroplet compressibility and the other for tissue elasticity. By analyzing the linear relationship between internal nanodroplet pressure and volume changes in nanodroplets and tissue, the classical nucleation theory (CNT) was modified to describe the initial nucleation of perfluoropentane (PFP) nanodroplets in tissue. The key nucleation conditions, such as the stable critical radius and initial nucleation threshold (INT) were investigated based on the modified CNT. Results revealed that introducing the nanodroplet compressibility and tissue elasticity allows the existence of a stable critical radius—which is more physically meaningful, highlighting their important effects on nucleation. Additionally, the INT increased significantly with the increase in tissue bulk modulus. For example, with an increase in bulk modulus from 0.03 MPa to 0.67 MPa, the INT increased by about 1.1 MPa. The increased behavior was more obvious for smaller nanodroplets in higher bulk modulus. The presence of dissolved gases, increasing nanodroplet surface tension, and decreasing nanodroplet radius and ultrasound frequency reduced the INT. Further analysis of the achievable nucleation area in tissue, which was expanded significantly at lower frequencies. Overall, this study enhances the understanding of initial nanodroplet nucleation in tissue, offering insights into designing and optimizing nanodroplet-based theranostic strategies.