Release Rate Optimization Based on M/M/c/c Queue in Local Nanomachine-Based Targeted Drug Delivery

As the basis for the modern medical therapeutics, targeted drug delivery is one of the most important topics in nanomedicine. In nanomachine-based targeted drug delivery, it should be taken into consideration that nanomachines have limited resources and drug molecules are expensive and lost molecules may cause undesired side effect. This paper aims to optimize drug release rate of nanomachine and is expected to pave a way for designing a drug delivery system. To this end, we proposed a method to calculate the optimized drug release rate producing a full drug response in local targeted drug delivery. In the method: first, a drug reception model based on M/M/c/c queue to simulate the interactions between ligands and receptors is established; second, the least effective concentration of drug molecules is derived from the least ratio of receptors occupied by drug molecules to produce full drug response according to the drug response theory named occupancy theory; finally, the optimized release rate is derived from the least concentration of drug molecules according to molecular diffusion law. Simulations reflecting diffusion of drug molecules and occupancy of receptors are established. The obtained simulation results match well with the results derived from the proposed analytical method.