Quantification of kinetic rate constants for transcytosis of polymeric nanoparticle through blood-brain barrier

Background: Polymeric nanoparticles (PNP) have received significant amount of interests for targeted drug delivery across the blood-brain barrier (BBB). Experimental studies have revealed that PNP can transport drug molecules from microvascular blood vessels to brain parenchyma in an efficient and non-invasive way. Despite that, very little attention has been paid to theoretically quantify the transport of such nanoparticles across BBB. Methods: In this study, for the first time, we developed a mathematical model for PNP transport through BBB endothelial cells. The mathematical model is developed based on mass-action laws, where kinetic rate parameters are determined by an artificial neural network (ANN) model using experimental data from in-vitro BBB experiments. Results: The presented ANN model provides a much simpler way to solve the parameter estimation problem by avoiding integration scheme for ordinary differential equations associated with the mass-action laws. Furthermore, this method can efficiently deal with both small and large data set and can approximate highly nonlinear functions. Our results show that the mass-action model, constructed with ANN based rate parameters, can successfully predict the characteristics of the polymeric nanoparticle transport across the BBB. Conclusions: Our model results indicate that exocytosis of nanoparticles is seven fold slower to endocytosis suggesting that future studies should focus on enhancing the exocytosis process. General significance: This mathematical study will assist in designing new drug carriers to overcome the drug delivery problems in brain. Furthermore, we anticipate that this model will form the basis of future comprehensive models for drug transport across BBB.