Topical drug formulation for enhanced permeation: A comparison of Bayesian optimisation and response surface methodology with an ibuprofen-loaded poloxamer 407-based formulations case study

Abstract

Topical skin products aim to address aesthetic, protective, and/or therapeutic needs through interaction with the human epidermal system. Traditionally, formulation development relies on empirical knowledge and trial-and-error experiments. In this paper, we introduced the Bayesian optimisation method and compared it with the traditional response surface methodology (RSM) for topical drug formulation. The objective was to optimise the formulation composition of ibuprofen gel-like to achieve a maximum flux through in vitro permeation tests (IVPTs). As a model system, poloxamer 407, ethanol, and propylene glycol (PG) were selected as the key excipients, whose concentrations were optimised. Strat-M membrane, serving as a surrogate for human skin, and Franz cell diffusion were employed in IVPTs. Two sets of experiments were conducted under identical conditions for 30 h. Under the RSM approach, the optimised ibuprofen gel-like formulation was identified with a poloxamer 407: ethanol: PG ratio of 20:20:10, achieving a measured permeation flux of 11.28 ± 0.35 μg cm⁻²h⁻¹. In comparison, Bayesian optimisation, after four iterations, yielded an optimised formulation with a ratio of 20.95:19.44:12.14, resulting in a permeation flux of 14.15 ± 0.77 μg cm⁻²h⁻¹. These findings highlight the potential of Bayesian optimisation as an effective tool for improving topical drug formulations.

Introduction

Topical pharmaceutical products, such as dermatological and transdermal drugs, often need to ensure efficient penetration of the active pharmaceutical ingredient (API) into or through the skin to elicit the intended effect (Tanwar and Sachdeva, 2016). Compared to the oral delivery route, topical pharmaceutical products lead to less adverse effects (Kovács, 2024) and avoid the impact of first-pass metabolism (Shakya et al., 2018). Skin permeability of the API is one of the critical parameters in the development of topical/dermatological pharmaceutical forms (Tieppo Francio et al., 2017). A wide range of formulations can be used as topical pharmaceutical products, such as gels, lotions, creams, emulsions and dispersions. These formulations are often developed empirically by experts via a trial-and-error approach, where skin permeability is evaluated by the time-consuming and costly in vitro permeation test (IVPT) (Santos et al., 2020). In addition, the availability of human skin tissue or alternatively porcine skin for IVPT may be limited, whilst ethical considerations may further restrict such studies (Neupane et al., 2020).

To overcome these limitations, the response surface methodology (RSM) has been used to formulate topical drugs with the aim of achieving the required permeability, e.g., in the transdermal delivery of melatonin (Kandimalla et al., 1999), cellulose acetate butyrate (Vaithiyalingam and Khan, 2002), ondansetron (Obata et al., 2010), diclofenac and curcumin (Chaudhary et al., 2011). In addition to skin permeability, RSM has also been used to optimise other attributes of topical drugs, e.g. viscosity, stability and sensory characteristics (Vukašinović et al., 2023). RSM relies on the statistical design of experiments (DoE, e.g., the Box-Behnken design (Pinheiro et al., 2021, Mohammed, 2020, Aziz et al., 2022) with a data-driven model that predicts the response variable as a function of the formulation factors. This data-driven model can be a simple polynomial function or an artificial neural network (Koletti et al., 2020, Naguib et al., 2017, Zhang, 2020, Lefnaoui et al., 2020). However, the classical RSM is limited to certain DoE methods and ignores the prediction uncertainty of the data-driven model, leading to potentially suboptimal results (Yan et al., 2011).
More recently, the Bayesian optimisation approach has emerged as an alternative to RSM by using state-of-the-art machine learning algorithms and an explicit account of the prediction uncertainty when solving the optimisation problem (Sano et al., 2020); it has found extensive use in pharmaceutical formulation (Narayanan, 2021, Shields, 2021, Wang and Dowling, 2022) but not yet for topical drugs. By establishing a machine learning model that relates the design factors and response variables, Bayesian optimisation employs decision theory to recommend the next experiments in an iterative manner, culminating in the identification of optimal values.

This study investigates the potential of Bayesian optimisation as a new tool for guiding the design of topical drug formulations for maximum permeation flux. The Bayesian optimisation method is compared with the classical RSM with a case study of formulating topical ibuprofen-loaded formulations consisting of poloxamer 407, ethanol, propylene glycol (PG), medium chain triglycerides and ultrapure water. These 5-component systems might offer several benefits, such as low toxicity, high solubilisation capacity for poorly water-soluble drugs such as ibuprofen and gelation at body temperature enabling formulation to remain at the applied region (Täuber and Müller-Goymann, 2015). As a model system, the formulation space was defined by the proportion of excipients (poloxamer 407, ethanol, and PG), as the design factors, to maximise the steady-state flux (the response variable) through the Strat-M membrane as a model membrane for the skin. The comparative analysis was then conducted based on the results obtained by each method.

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Materials

Ibuprofen and medium chain triglycerides (MCTs) were purchased from Fagron (Netherlands); ethanol, PG and Kolliphor® P407 (poloxamer 407) were purchased from Sigma Aldrich (US), acetonitrile was purchased from Honeywell (Germany), phosphoric acid was purchased from Fisher chemical (U.S.A). Sodium chloride, sodium phosphate dibasic dodecahydrate and potassium phosphate monobasic were used to prepare phosphate-buffered saline (PBS) and were purchased from Sigma Aldrich (Germany).

Yongrui Xiao, Tanja Ilić, Anđela Tošić, Branka Ivković, Dimitrios Tsaoulidis, Snežana Savić, Tao Chen, Topical drug formulation for enhanced permeation: A comparison of Bayesian optimisation and response surface methodology with an ibuprofen-loaded poloxamer 407-based formulations case study, International Journal of Pharmaceutics, 2025, 125306, ISSN 0378-5173, https://doi.org/10.1016/j.ijpharm.2025.125306.

Read also our introduction article on Topical Excipients here: