A proposed mathematical description of in vivo nanoparticle delivery

• Transport processes that distribute nanoparticles within a biological system can be described by rate constants. • Nano-bio interactions modify these rate constants, which ultimately determine the final delivery efficiency. Nanoparticles are promising vehicles for the precise delivery of molecular therapies to diseased sites. Nanoparticles interact with a series of tissues and cells before they reach their target, which causes less than 1% of administered nanoparticles to be delivered to these target sites. Researchers have been studying the nano-bio interactions that mediate nanoparticle delivery to develop guidelines for designing nanoparticles with enhanced delivery properties. In this review article, we define these nano-bio interactions as a series of mathematical equations that quantitatively describe the nanoparticle delivery process. We employ a compartment model framework to describe delivery where nanoparticles are either (1) at the site of administration, (2) in the vicinity of target cells, (3) internalized by the target cells, or (4) sequestered away in off-target sites or eliminated from the body. This framework explains how different biological processes govern nanoparticle transport between these compartments, and the role of intercompartmental transport rates in determining the final nanoparticle delivery efficiency. Our framework provides guiding principles to engineer nanoparticles for improved targeted delivery.