Robust Control of Nanoscale Drug Delivery System in Atherosclerosis: A Mathematical Approach

Abstract: This paper proposes a mathematical approach for robust control of a nanoscale drug delivery system in treatment of atherosclerosis. First, a new nonlinear lumped model is introduced for mass transport in the arterial wall, and its accuracy is evaluated in comparison with the original distributed-parameter model. Then, based on the notion of sliding-mode control, an abstract model is designed for a smart drug delivery nanoparticle. In contrast to the competing strategies on nanorobotics, the proposed nanoparticles carry simpler hardware to penetrate the interior arterial wall and become more technologically feasible. Finally, from this lumped model and the nonlinear control theory, the overall system's stability is mathematically proven in the presence of uncertainty. Simulation results on a well-known model, and comparisons with earlier benchmark approaches, reveals that even when the LDL concentration in the lumen is high, the proposed nanoscale drug delivery system successfully reduces the drug consumption levels by as much as 16% and the LDL level in the Endothelium, Intima, Internal Elastic Layer (IEL) and Media layers of an unhealthy arterial wall by as much as 14.6%, 50.5%, 51.8%, and 64.4%, respectively.