Integrating experiments, numerical simulations and Bayesian optimisation to maximise drug permeability of hollow pyramidal microneedle arrays

This study presents an experimental–numerical framework integrated with Bayesian optimisation (BO) for the design of hollow pyramidal microneedle (MN) arrays to enhance transdermal drug permeability across the skin. Finite element (FE) simulations have been carried out to model coupled fluid flow and drug delivery in multilayered skin, including convection–diffusion of the drug in HMN and fluid slip condition at fluid (MN tip)–skin (porous) interfaces. The geometric design parameters, including lumen diameter, array pitch, and needle count, have been optimised using a Gaussian process–based BO (GP-BO) framework implemented in Python via the scikit-learn library. Experimental validation has been performed using hollow microneedle (HMN) arrays loaded with ibuprofen (IBU) sodium, applied to ex vivo neonatal porcine skin in Franz diffusion cell setups. Drug permeation has been subsequently quantified using high-performance liquid chromatography (HPLC) analysis. The results revealed that approximately 150 μg (≈3%) of the administered drug permeated into the receptor compartment after 24-h, whereas 295.79 ± 148.95 μg remained within the dermal layers, indicating prolonged drug retention and effective localised delivery. The integrated BO methodology significantly improved permeability predictions while minimising computational costs, resulting in optimal HMN geometries that maximised both volumetric flow rate and transdermal permeability. The improvement in performance represents around 5% enhancement over the previously optimised configuration, demonstrating both the effectiveness and robustness of the BO framework.