Analysis of heat-aided membrane-controlled drug release from a process control perspective

Analytical solutions were derived for the time lag and steady-state transdermal flux of drugs across a heat-aided drug-delivery device. The expressions incorporate thermodynamic and physical properties of the solvent/medicament and membrane system, making the approach amenable to in silico evaluation of process performance in a spreadsheet-like environment. Methods and concepts from classical control theory were applied to predict the onset of the steady-state flux. The methodology was based on the system's time constant, computed by taking the inverse of the first eigenvalue of a Sturm-Liouville problem. This framework does not require a solution to the transient heat-enhanced diffusion problem and relaxes the assumption of a constant diffusion coefficient throughout the membrane. The results match published data, partially explain some clinical trial observations, and suggest a novel method to control the plasma drug concentration. An optimal control strategy was proposed to keep the delivery rate as close as possible to 9.07 μg cm^-2 h^-1 over a 30-min period by adjusting the skin surface temperature. The integral of the absolute value of the error was 1138.19 compared to 1217.08 when the surface temperature was fixed at 37 °C.