Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface

• We derive an analytical solution for a percutaneous drug absorption model in two dimensions.
• The time necessary to reach 98% of the steady-state delivery rate can be computed.
• Closed-from expressions can be used for design purposes and parameter estimations.
• The methodology can be extended to other transdermal delivery systems.

A transient percutaneous drug absorption model was solved in two dimensions. Clearance of the topically-applied pharmaceutical occured at the skin-capillary boundary. Timolol penetration profiles in the dermal tissue were produced revealing concentration gradients in the directions normal and parallel to the skin surface. Ninety-eight percent of the steady-state flux was reached after 85 h or four time constants. The analytical solution procedure agreed with published results. As the clearance rate increased relative to diffusion, the delivery rate and amount of drug absorbed into the bloodstream increased while the time to reach the equilibrium flux decreased. Researchers can apply the closed-form expressions to simulate the process, estimate key parameters and design devices that meet specific performance requirements.