Modeling Mass Transport in Axonal Transport Drug Delivery

This paper presents a model of targeted drug delivery. The model is based on recent experimental results that reported synthesis and pharmacological efficiency tests of a tri-partite complex designed for axonal transport drug delivery. The developed model accounts for two populations of pharmaceutical agent complexes (PACs). The first population of PACs includes those that are transported retrogradely by dynein motors and the second population of PACs includes those that are accumulated in the axon at the Nodes of Ranvier. The transitions between these two populations of PACs are described by first-order reactions. Laplace transform is utilized to obtain an analytical solution of the coupled system of transient equations describing conservations of these two populations of PACs. Results for various combinations of parameter values are presented and their physical significance is discussed.