Nowadays, carbon nano (CN) structures and specifically carbon nanotubes (CNTs), because of the nanotube's nanoscale shape, are widely used in carrier and separation applications. The conjugation of CNTs with polysaccharide, proteins, drugs, and magnetic nanoparticles provides a chance for smart targeting and trajectory manipulation, which are used in the crucial field of life science applications, including for cancer disease diagnostics and treatments. Providing an optimal procedure for delivering a drug to a specific area based on mathematical criteria is key in systemic delivery design. Trajectory guidance and applied force control are the main parameters affected by systemic delivery. Moreover, a better understanding of the tissue parameters and cell membrane molecular behaviour are other factors that can be indirectly affected by the targeted delivery. Both sides are an essential part of successful targeting. The lung is one of the challenging organs for drug delivery inside the human body. It has a large surface area with a thin epithelium layer. A few severe diseases directly involve human lung cells, and optimal and successful drug delivery to the lung for the treatment procedure is vital. In this paper, we studied functionalized CNTs' targeted delivery via crossing through the lung cell membrane. Molecular dynamics (MD) software simulated all the interaction forces. Mathematical modelling of the cell membrane and proposed delivery system based on the relation of velocity and force has been considered. Dynamics equations for CNTs were defined in the time and frequency domain using control theory methods. The proposed delivery system consists of two main parts: crossing through the cell membrane and targeting inside the cell. For both steps, a mathematical model and a proper magnetic field profile have been proposed. The designed system provides criteria for crossing through the cell membrane within 30 s to 5 min and a translocation profile of 1 to 100 Å.
Keywords: carbon nanotube (CNTs); cell membrane; dynamic system modeling; molecular dynamics simulation.