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

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.