Mathematical Probe of Nanoparticle Aggregation in Capillary-Tissue System Applying Fractal Model

Targeted drug delivery using nanoparticle-based technology represents an advance in tumor treatment aiming to improve drug retention in tumors and minimize side effects. This study explores nanoparticle aggregation as a mechanism of enhanced retention and controlled dispersion of therapeutic agents in tumor tissues. Unlike existing models that primarily focus on single-particle diffusion, this research investigates the aggregation dynamics of nanoparticles upon diffusion from capillaries into the surrounding tissue, using a fractal-based mathematical model. By incorporating fractal geometry, this model uniquely captures the complexity of nanoparticle interactions with heterogeneous tumor environments. The equations, solved using MATLAB, reveal that nanoparticles form aggregates of approximately 75 nm in the capillary, with an optimal fractal dimension of 2.8 promoting efficient aggregation and retention. These findings provide a new perspective on aggregation-controlled drug delivery systems, offering insights for enhancing nanoparticle bioavailability and therapeutic efficacy in tumors.