Abstract

The use of nanoparticle-based drug delivery systems (DDS) has revolutionized biomedical engineering by enabling the targeted delivery of therapeutic agents. The DDS minimizing systemic toxicity and side effects, and improving the efficiency of therapy in complex diseases such as cancer, cardiovascular disorders, and inflammatory disorders. In this study, a stochastic mathematical model for the biodistribution of nanoparticles in heterogeneous biological tissues is presented, based on probabilistic transport phenomena and diffusion-reaction processes. Monte Carlo and finite-difference numerical simulations are carried out to analyze the transport behaviour of nanoparticles under different physiological conditions (e.g., particle size, diffusion coefficient, permeability constant). Results show that stochastic modelling can make more realistic predictions of nanoparticle accumulation and retention than deterministic modelling, especially in highly heterogeneous tumour tissue. The different tissue heterogeneities investigated in the simulations are found to have a significant effect on the penetration depth, gradient distribution and therapeutic efficacy of nanoparticles in the tissue. According to the overall research a sensitivity analysis also shows that vessel permeability and diffusion intensity are the most influential factors affecting the biodistribution dynamics. Another aspect of the framework is the role of random fluctuations in cellular uptake in creating non-uniform nanoparticle deposition patterns within tissues. The stochastic framework provides a powerful computational model for devising optimal therapeutic strategies and precision medicine applications based on nanoparticles. The model can accurately simulate transport behaviour in realistic biological systems and aid in the design of advanced nanomedicine systems.