The theory of finite dose absorption of pharmaceutical compounds following solvent deposition on skin has been addressed multiple times dating back to early experimental work and analysis thereof by Scheuplein and Ross [1]. For low doses that dissolve into the upper stratum corneum (SC) or for compounds that are either liquid at skin temperature or dissolve rapidly into the skin, elegant analytical solutions to this problem have been found [[2], [3], [4], [5], [6]]. Anissimov and Roberts provide an excellent summary up to 2001 as well as impressive fits to Scheuplein's data [4]. The matter becomes thornier when the solute precipitates on the skin surface or in the upper SC. Delivery in this case may become dissolution-limited, and dissolution kinetics can be complex [7,8]. We recently addressed this problem in order to model the finite dose absorption of two small nonelectrolytes, niacinamide and methyl nicotinate [9]. A dissolution-limitation was proposed for niacinamide, whereas methyl nicotinate appeared to dissolve rapidly on the skin, or perhaps never even crystallized.

An extension to the above problem is presented by the case in which the dissolved solute is a weak electrolyte, and the composition of the deposited solute is governed by the ionization state of the solute in the formulation. This case is of practical interest for dermatological drugs such as diclofenac and lidocaine, which are commonly formulated at a neutral pH in which the bulk of the active agent is ionized. The magnitude of the dose and the rate at which the pH of the SC returns to its natural value of 5.0–5.5 presumably govern the delivery rate of the drug to the lower skin layers and beyond. A second case of interest is the finite dose testing of cosmetic ingredients for their dermal absorption characteristics, either to assess their potential for delivering skin benefits or systemic absorption. Toxicologists often eschew the addition of extra excipients to test formulations and may recommend compositions that mimic internal body conditions. Interpreting absorption of weak electrolytes tested under these conditions can be challenging [10]. Some guidance is offered by steady state analyses of weak electrolyte absorption from aqueous solutions as a function of pH [[11], [12], [13], [14]], which have shown that the skin permeability of weak acids and especially weak bases do not conform to the pH-partition hypothesis for lipid membrane permeability. However, these analyses apply to dilute solutions and do not involve a dissolution step, so they are not directly applicable to the solvent deposition scenario. Particularly detailed, mechanistic finite dose simulations of topical application of two weak acids, diclofenac and benzoic acid have been recently published by FDA and Certara scientists [15,16]. These simulations were conducted on Certara's Symcyp platform with the MPML MechDermA™ extension, a modeling framework that has the capability of modeling precipitation and redissolution of dissolved and potentially ionizable solutes. The issues of formulation and SC pH and their respective buffer capacities were clearly recognized by these authors. Patel et al. write “It is unclear whether the skin surface pH or the formulation pH are responsible for the fraction nonionized at the skin surface, therefore the simulator allows the user to select which of these values is used for the calculation. Currently, the interplay between these two and their buffering capacities is not modeled,” later adding “The interplay between buffering capacities of the skin and formulations is still largely unknown.” The research reported here addresses this issue.

In this report we discuss the underlying mechanisms that drive cutaneous permeation of finite dose applications of weak electrolytes dissolved in volatile solvents and provide an update to the model developed within our group [9,10]. The resulting model describes the percutaneous absorption of weak electrolytes over the full range of ionization states and skin loads that might be encountered in topical products. The model, which we term Model 4.1 following the nomenclature introduced in [10], is calibrated for in vitro exposures by analyzing a previously published experimental study from our group involving benzoic acid (BA, a weak acid) and propranolol (PR, a weak base) [17]. New features not incorporated in our previous analyses nor, to our knowledge, reported elsewhere include (1) an exponential return of SC pH to its natural value following topical application, with a time constant proportional to the buffer capacity of the dose solution; (2) a load-dependent fractional contact area of the deposited solid with the skin; and (3) a slow transfer of protons across the lipid dissolution layer that allows gradual conversion of precipitated salt to free acid or base, enabling continuous permeation of the deposited solute. We acknowledge that application of the developed model to in vivo exposures will likely involve substitution of a skin surface lipid film for the SC lipid film as discussed by Yu et al. [9] and also an upward adjustment of the skin buffer capacity as discussed by Miller and Kasting [17]. Nomenclature associated with the analysis is summarized in Table S1 of the Supplementary Information (SI).

The solvent-deposited solid problem is a subset of the more general problem of the dry down of semisolid products on skin, a field that has recently been dignified by substitution of the word “metamorphosis” for “dry down”. Aspects of this process have been studied for many years, as recently reviewed by Jin et al. [18]. The area has received considerable attention in recent years due to the interest from the US FDA and dermatological drug manufacturers in facilitating generic topical drug approvals by establishing robust in vitro bioequivalence measures. A series of FDA workshops have been held on this subject, e.g. [[19], [20], [21]] and successful examples of generic approvals are now available [15,16]. Research continues in both experimental method development and simulation and modeling of the dry down process.