Title : Nanotechnology in pharmaceutics and drug delivery systems: A medicinal mathematics perspective
Abstract:
Nanotechnology has emerged as a transformative approach in pharmaceutics and drug delivery systems, enabling precise targeting, controlled drug release, and improved bioavailability of therapeutic agents. This presentation explores recent advancements in nanoparticle-based drug delivery through the analytical lens of medicinal mathematics, emphasizing the role of mathematical modeling, optimization, and data-driven methodologies in enhancing therapeutic outcomes. Nanoparticles such as lipid-based carriers, polymeric systems, dendrimers, and inorganic nanostructures exhibit unique physicochemical properties that significantly influence drug transport and cellular interactions. Mathematical frameworks, including convection–diffusion equations, kinetic modeling, and stochastic processes, are employed to describe nanoparticle transport, distribution, and degradation within biological systems. These models facilitate the optimization of particle size, surface charge, and ligand density for improved targeting efficiency and reduced toxicity. The presentation further examines nanoparticulate drug delivery systems for controlled and sustained release using models such as the Korsmeyer–Peppas equation, alongside multi-compartment pharmacokinetic models. Special focus is given to nanoparticle-mediated delivery of non-coding RNAs (ncRNAs), where mathematical formulations assist in optimizing gene silencing efficiency and therapeutic dosing. Advancements in nanoparticle fabrication techniques, including microfluidics and nanoprecipitation, are analyzed through population balance equations and fluid dynamic models to ensure precise control over particle characteristics. Additionally, the integration of big data analytics and machine learning is highlighted as a powerful tool for predicting nanoparticle behavior, toxicity, and clinical efficacy. The clinical translation of nanotechnology remains a critical challenge due to biological variability and regulatory constraints. Mathematical approaches such as Bayesian inference and sensitivity analysis are discussed as essential tools for bridging preclinical and clinical studies. Furthermore, the role of nanoparticles in immuno-oncology is explored through tumor–immune interaction models, supporting the development of targeted cancer therapies. Overall, this work underscores the importance of medicinal mathematics in advancing nanotechnology-based drug delivery systems, offering a pathway toward personalized, efficient, and safe therapeutic solutions.
