A compartment model to predict in vitro finite dose absorption of chemicals by human skin

Abstract

Dermal uptake is an important and complex exposure route for a wide range of chemicals. Dermal exposure can occur due to occupational settings, pharmaceutical applications, environmental contamination, or consumer product use. The large range of both chemicals and scenarios of interest makes it difficult to perform generalizable experiments, creating a need for a generic model to simulate various scenarios. In this study, a model consisting of a series of four well-mixed compartments, representing the source solution (vehicle), stratum corneum, viable tissue, and receptor fluid, was developed for predicting dermal absorption. The model considers experimental conditions including small applied doses as well as evaporation of the vehicle and chemical. To evaluate the model assumptions, we compare model predictions for a set of 26 chemicals to finite dose in-vitro experiments from a single laboratory using steady-state permeability coefficient and equilibrium partition coefficient data derived from in-vitro experiments of infinite dose exposures to these same chemicals from a different laboratory. We find that the model accurately predicts, to within an order of magnitude, total absorption after 24 hours for 19 of these chemicals. In combination with key information on experimental conditions, the model is generalizable and can advance efficient assessment of dermal exposure for chemical risk assessment.

1). Introduction

Skin maintains a barrier between external and internal exposure. Undamaged skin consists of three main layers: epidermis, dermis, and hypodermis. The epidermis is divided into the stratum corneum (SC) and the viable epidermis (Kolarsick et al., 2011). The skin contains additional structures that traverse the epidermis into the dermis, e.g. hair follicles and sweat glands. Dermal exposure is an important pathway for many chemical compounds and reliable information about the movement of these compounds through the skin is a key part of human risk assessments (U.S. Environmental Protection Agency, 1992, 2015; OECD, 2019). Chemical exposure often occurs when a chemical compound is applied to the skin directly or in a carrier vehicle like water, other liquids, or semisolids (Barnes et al., 2021). This allows contact with the surface of the SC through which it then absorbs.

The study presented here builds upon dermal absorption modeling concepts developed over recent decades (Mitragotri et al., 2011; Jepps et al., 2013; Pecoraro et al., 2019). Dermal absorption has often been modeled by treating the skin layers as idealized, pseudo-homogeneous membranes through which chemicals diffuse passively according to Fick’s principles (Anissimov et al., 2013). In these models, time-dependent skin permeation is described by partial differential equations that include changes in time and the spatial concentration gradient. The SC has also been represented in more complex models as a composite membrane consisting of brick-and-mortar layers where the corneocytes (bricks) are surrounded by lipid lamellae (mortar) (Wang et al., 2006; Chen et al., 2008). An alternative modeling approach treats the skin layers as a series of compartments with uniform concentration and first-order transfer rates between them. An ordinary differential equation in time describes changes in the average concentration within each compartment. In some models, each compartment represents an entire skin layer: for example, one compartment for the SC and another compartment for the viable epidermis, either alone or in combination with the dermis (McCarley and Bunge, 2000). Other models depict a skin layer with a series of multiple compartments (Amarah et al., 2022), which allows the calculation of the concentration variation with depth within the skin layer. Single skin layers represented by multiple compartments are essentially finite difference or finite volume numerical solutions of the pseudo-homogeneous partial differential membrane equation for that layer (Amarah et al., 2018). The main advantage of compartment models is that their simpler mathematical description (i.e., first-order differential equations) are readily solved for the various exposure scenarios of interest in risk assessment.

Models need to be parameterized using measurement data, which are generated experimentally (Moya et al., 2011). This commonly requires extrapolations from measurement data associated with data-rich compounds to those of data-poor compounds. For example, dermal exposure conditions for cosmetic ingredients are often better studied and well documented compared to most chemical compounds (Safford et al., 2015). Dermal absorption depends on both chemical-specific and non-chemical-specific variables. Important variables include vehicle parameters, such as the initial concentration of the chemical, and the type of vehicle and its volume, as well as details on the exposure, such as duration of the exposure and exposed skin area. Depending on the experimental design and conditions, the dermal exposure may be considered infinite dose, meaning the chemical concentration in the vehicle remains constant, or finite dose, because the chemical concentration changes due to absorption into the skin and/or evaporation of either the chemical or vehicle (Kasting and Miller, 2006; Frasch, 2012; Frasch et al., 2014). Also, after the exposure ends, previously absorbed chemical can leave the skin by evaporation or washing (Frasch and Bunge, 2015).

In the European Union, a concerted effort to reduce, restrict, or replace animals used for scientific testing was enacted with the Registration, Evaluation, Authorisation, and Restriction of Chemicals (REACH) regulation (European Union, 2006). In addition, the Cosmetics Products Regulation implemented this effort to reduce the number of animals used for dermal testing (Pistollato, 2021). The European Centre for the Validation of Alternative Methods (ECVAM) has validated one process used for the calculation of dermal absorption, distribution, metabolism, and excretion (ADME) for cosmetics (Almeida, 2017). This process uses standardized in vitro diffusion cell measurements that mimic human exposure as specified in the Organisation for Economic Co-operation and Development (OECD) and Scientific Committee on Consumer Safety (SCCS) guidelines (OECD, 2004; SCCS, 2023). However, in vitro experiments for many chemicals have only been performed at infinite dose conditions (i.e., constant concentration of the absorbing chemical) from water, which often do not match realistic in vivo exposure scenarios. As a result, there is a need for mathematical models that can extrapolate from these in vitro results to make predictions for a range of exposure scenarios, such as for small doses applied within vehicles that can evaporate on the timescale of the exposure. Additionally, for compounds without available in vitro measurements, mathematical models are needed that can be applied to extrapolate quantitative structure activity relationship (QSAR) predictions of in vitro steady-state absorption to realistic in vivo scenarios.

To address this need, we have designed a compartment model based on mass balance and diffusion principles for four compartments: unoccluded vehicle, SC, viable tissue (VT; includes viable epidermis and dermis), and receptor fluid (RF). Evaporation rates of both the vehicle and chemical from the unoccluded applied solution are included in the model. The model also considers whether the chemical left as a residue on the skin surface is in a solid or liquid phase after the vehicle evaporates. The goal is a generic, user-friendly dermal absorption model that can predict chemical dermal absorption following an unoccluded chemical exposure to the skin. This necessarily requires consideration of changing chemical concentrations in the vehicle along with evaporation of both the vehicle and chemical from the exposed dose.

We evaluated the model by comparing dermal absorption predictions with experimental measurements for unoccluded finite dose exposures of 26 chemicals reported by Hewitt et al. (2020). The model requires steady-state permeability coefficient and partition coefficient parameters, which could be estimated using predictive QSAR. However, to avoid the uncertainties associated with QSAR estimates, we used steady-state permeability coefficient and partition coefficient data reported by Ellison et al. (2020) for the same 26 chemicals derived from infinite dose experiments that closely matched those from Hewitt et al. (2020).

2). Methods

2.1). Compartment Model

A compartment model was developed to simulate dermal uptake from a finite source and implemented in R (v4.1.3). The model consists of four well-mixed compartments in series that are each represented by an ordinary differential equation (ODE) with rate constants defining chemical mass transfer between adjacent compartments (Figure 1).

Figure 1.

A: General schematic of the compartment model. Each of the four compartments is assumed to be well mixed with bidirectional chemical transfer as indicated by the blue arrows. Evaporation of chemical and vehicle from the source compartment is allowed. (Left) Source thickness decreases from its initial value until the vehicle has fully evaporated. (Middle) Skin absorption after the vehicle evaporates. Scenario 1 is used when the chemical remaining on the skin surface is a liquid; chemical transfer and evaporation proceed as if the chemical is in a saturated vehicle. Scenario 2 is used when the remaining chemical is solid; chemical transfer from the source to the SC stops but evaporation continues. (Right) After chemical on the skin surface is gone, it can evaporate from the SC.

B: Definitions of the forward and reverse rate constants, $k_{i,j}$ (cm³ s⁻¹), describing mass transfer between adjacent compartments $i$ and $j$, and the permeability coefficients in the SC and VT compartments. In these equations, $A_{sk}$ is the exposed skin area (cm²),$L_j$ is the thickness (cm) of compartment j, ${\mathrm{D}}_{\mathrm{j}}$ is the effective diffusivity (cm² s⁻¹) of the absorbing chemical in compartment j, $K_{j/S}$ is the partition coefficient of the absorbing chemical between compartment j and the source solution (j is either the SC, VT, or RF), and $k_p^j$ is the permeability coefficient (cm s⁻¹) for compartment j (j is either the SC or VT). $B=k_p^{SC}/k_p^{VT}$. Because the mass transfer rate from the RF to the VT is the product of $k_{RF,VT}$ and the concentration in the RF, $k_{RF,VT}$ does not need to be calculated if sink conditions are maintained in the RF (i.e., concentration in the RF is zero), even though $k_{RF,VT}$ is not zero (see Eqs. (2) and (3)).

The source compartment accounts for the chemical mass on the skin surface, which can be either in a vehicle or alone after the vehicle evaporates. From the source compartment, chemical absorbs into the SC and evaporates into air. We assume that the vehicle evaporates into air but absorbs insignificantly into SC. The exposed area of the skin is assumed to be constant, meaning that decreases in the vehicle volume due to evaporation result only in decreased thickness of the vehicle.

Skin is modeled as two compartments representing the SC and VT, in which the latter includes the viable epidermis (VE) and some dermis. The VE and dermis are combined into a single compartment because, in the absence of a functional microcirculation in the dermis of the in vitro experiment, they have similar properties and permeability coefficients (Reddy et al., 2000; McCarley and Bunge, 2001). The final compartment represents the receptor fluid in the experimental system and is assumed in the analysis presented here to maintain sink conditions. Rate constants between each compartment are estimated from permeability coefficients, partition coefficients, and thicknesses for the SC and VT (McCarley and Bunge, 2000). Vehicle and chemical evaporation from the source compartment are represented by gas phase mass transfer that depends on molecular weight, vapor pressure, and the velocity of ambient air (Frasch and Bunge, 2015). The governing equations are solved numerically using the deSolve package in R assuming the initial concentrations in the skin and receptor fluid are zero.

2.2). Governing Equations

All compartments in the model are assumed to be well-mixed, meaning that concentration variation with position is neglected. The governing equations describe the mass of the chemical flowing into and out of each compartment, allowing the model to track the mass in each compartment over time. For example, the rate of change of the chemical concentration in the SC ($d〈C_{SC}〉/dt$) is described by:

$$V_{SC}\frac{d〈C_{SC}〉}{dt}=k_{S,SC}〈C_S〉-k_{SC,S}〈C_{SC}〉+k_{VT,SC}〈C_{VT}〉-k_{SC,VT}〈C_{SC}〉$$ #(Eq. 1)

in which $V_{SC}$ is the volume (cm³) of the SC compartment, $〈C_i〉$ is the average concentration (μg cm⁻³) of the absorbing chemical in compartment $i$, and $k_{i,j}$ is the rate constant (cm³ s⁻¹) for chemical transfer from compartment $i$ to compartment $j$ where $i$ and $j$ designate the SC, source (S), or VT compartments. Volume for each compartment is calculated as the product of the exposure area ($A_{sk}$; cm²) and the thickness of the compartment ($L_i$; cm).

Similarly, the rate of change in the VT is:

$$V_{VT}\frac{d〈C_{VT}〉}{dt}=k_{SC,VT}〈C_{SC}〉-k_{VT,SC}〈C_{VT}〉-k_{VT,RF}〈C_{VT}〉+k_{RF,VT}〈C_{RF}〉$$ #(Eq. 2)

where subscript RF designates the receptor fluid compartment, which is maintained at sink conditions (i.e., $〈C_{RF}〉=0$) for the in vitro scenario considered in the analysis presented here. In writing Eqs. (1) and (2), chemical reactions within either the SC or VT, such as metabolism or binding, are not considered. This restriction can be removed by adding rate expressions representing these chemical reactions. If needed, skin can be depicted by more than two compartments. For example, if a chemical’s behavior is significantly different in the VE and the dermis, it may be necessary to divide the VT compartment into two separate VE and dermis compartments. Also, for some chemicals, a single compartment representing only the SC may be sufficient.

The mass balance for the RF in a flow-through diffusion cell is

$$\frac{d{M}_{RF}}{dt}=V_{RF}\frac{d〈C_{RF}〉}{dt}=k_{VT,RF}〈C_{VT}〉-k_{RF,VT}〈C_{RF}〉-F_{RF}〈C_{RF}〉$$ #(Eq. 3)

where $M_{RF}$ is the chemical mass (μg) in the RF, $V_{RF}$ is the volume (cm³) of the RF, and $F_{RF}$ is the volumetric flow rate (cm³ s⁻¹) of the RF into (absent any chemical) and out of the diffusion cell receptor chamber. For a static diffusion cell configuration, $F_{RF}=0$ and $M_{RF}$ is the cumulative mass transferred from the skin to the RF. It is apparent from Eq. (3) that sink conditions in the RF are satisfied (i.e., $〈C_{RF}〉0$) if either $V_{RF}$ is large, thereby diluting the chemical concentration, or $F_{RF}$ is large, thereby flushing the chemical out of the RF rapidly. In either of these cases, Eq. (3) simplifies to give

$$\frac{d{M}_{RF}}{dt}=k_{VT,RF}〈C_{VT}〉$$ #(Eq. 4)

In modeling the in vivo scenario, the receptor fluid compartment is replaced with one or more compartments describing systemic absorption, distribution, metabolism, and elimination of the absorbing chemical. The governing equations for added compartments would follow a similar format: the rate of change in the amount of chemical in a compartment is calculated from the difference in the rate that chemical transfers into and out of the compartment from neighboring compartments minus the rate of chemical metabolism or other consumptive reaction of the chemical within the compartment.

Lastly, the mass balance for the source compartment is included to track the dynamics of unoccluded and/or finite chemical dosing. The governing equation for chemical mass in the source compartment ($M_S$) accounts for chemical evaporation as well as chemical exchange between the source and SC compartments:

$$\frac{d{M}_S}{dt}=k_{SC,S}〈C_{SC}〉-k_{S,SC}〈C_S〉-A_{sk}{k}_g{K}_{a/S}〈C_S〉$$ #(Eq. 5)

In this equation, the rate of evaporation from a constant area ($A_{sk}$; cm²) is expressed in terms of a chemical-specific gas phase mass transfer coefficient ($k_g$; cm h⁻¹), and the equilibrium chemical concentration in air, which is the product of the chemical’s partition coefficient between air and the source ($K_{a/S}$) and its average concentration in the source solution, $〈C_S〉$. This concentration is defined as the dissolved mass of the absorbing chemical per volume of the source solution, which is the sum of the vehicle (e.g., water in the calculations presented below) volume ($V_V$; cm³) and the chemical volume ($V_c$; cm³) for solutions with a zero-volume change of mixing. That is,

$$〈C_S〉=\frac{M_S}{V_S}=\frac{M_S}{V_V+V_c}=\frac{M_S}{V_V+M_S/{\rho }_c}$$ #(Eq. 6)

where ${\rho }_c$ is the density (μg cm⁻³) of the pure absorbing chemical.

When the source is unoccluded, the vehicle can evaporate causing $V_V$ to change as described by the mass balance,

$${\rho }_V\frac{d{V}_V}{dt}=-A_{sk}{k}_g{K}_{a/V}〈C_V〉$$ #(Eq. 7)

where ${\rho }_V$ is the vehicle density (μg cm⁻³). Eq. (7) is written with three simplifying assumptions: (a) the vehicle is (or behaves as) a single component (e.g., water) and not a chemical mixture, (b) it does not absorb into the skin, and (c) it evaporates from a constant surface area. As a result, only the thickness of the vehicle film changes over time and only due to evaporation. If the vehicle evaporates faster than skin absorption and evaporation of the chemical, then $〈C_S〉$ can increase above its initial value and perhaps even reach its solubility limit in the source solution $C_{S,sat}$, causing the chemical to precipitate (assuming supersaturation does not occur) so that $〈C_S〉$ never surpasses $C_{S,sat}$. $〈C_S〉$ is then the concentration of the dissolved portion of chemical mass, which is equal to $M_S-M_P$, where $M_P$ is the mass of precipitated chemical

$$〈C_S〉=\frac{M_S-M_P}{V_V+\left(M_S-M_P\right)/{\rho }_c}$$ #(Eq. 8)

The chemical will phase separate as either a liquid or a solid depending on whether the temperature of the source solution, which for a thin film will be approximately the surface temperature of the SC (i.e., 32 °C), is above or below the chemical’s melting point. Theoretically, the precipitate or separate phase liquid can redissolve if $〈C_S〉$ drops below $C_{S,sat}$, but this situation is uncommon.

It is often the case that the dissolved chemical concentration in the source solution is small, which means that $V_S\approx V_V$ until the vehicle is almost completely gone, allowing thereby a simpler expression for $〈C_S〉$

$$〈C_S〉=\frac{M_S-M_P}{V_V}$$ #(Eq. 9)

Also, $V_S{V}_V$ means that the source solution is an almost pure vehicle, and thus, the air concentration of the vehicle, $K_{a/V}〈C_V〉$ in Eq. (7), is equivalent to its saturated value, $C_{sat,V\left(air\right)}$. The saturated air concentration (in μg mL⁻¹) of the vehicle (or a pure chemical), assuming an ideal gas, is readily estimated from its vapor pressure ($P_{vap};$ atm) at the absolute air temperature ($T$; K):

$$C_{sat\left(air\right)}=\frac{MW{P}_{vap}}{RT}\left(\frac{{10}^3\mathrm{\mu }\mathrm{g}{\mathrm{m}\mathrm{L}}^{-1}}{\mathrm{g}{\mathrm{L}}^{-1}}\right)$$ #(Eq. 10)

where $MW$ is molecular weight (g mol⁻¹) and R is the real gas constant in consistent units (0.08206 L atm mol⁻¹ K⁻¹). Source solutions containing absorbing chemicals that are fully miscible (or nearly fully miscible) in the vehicle do not satisfy the assumptions that $〈C_S〉$ is always small, $V_S$ ≈ $V_V$, and the vehicle evaporates at the same rate as when the chemical is absent. Modeling absorption of chemicals with large or no solubility limit requires that the source concentrations of both the vehicle and chemical be considered.

If the vehicle volume reaches zero over the course of the simulation, then we model the disposition of chemical that remains on the skin surface using one of two limiting scenarios, chosen to simulate either a liquid or a solid at the skin surface temperature. In the first scenario, the residual neat liquid chemical continues to evaporate and transfer to the SC compartment at rates corresponding to its concentration being at the maximum thermodynamic activity, which is equivalent to $〈C_S〉=C_{S,sat}$ in the vehicle. Once all residual chemical on the skin surface is gone, then $〈C_S〉$ is zero and chemical can transfer directly from the SC to air, i.e., $k_{SC,S}$ in Eq. (1) is replaced with $A_{sk}{k}_g{K}_{a/S}/K_{SC/S}$.

In the second scenario, the residual neat solid chemical continues to evaporate at its maximum thermodynamic activity (i.e., $〈C_S〉$ is set equal to $C_{S,sat}$ in the vehicle so that $K_{a/S}〈C_S〉=C_{sat\left(air\right)}$) but transfer to the SC stops. Transfer from the SC to the source (i.e., $k_{SC,S}=k_{S,SC}=0$) also stops until the residual chemical is gone and direct transfer from the SC to air occurs as in scenario 1. Scenario 2 reflects the view that transfer to the SC from solids is much slower than from a liquid (Akhter and Barry, 1985; Chia-Ming et al., 1989; Oliveira et al., 2012). That said, scenario 1 might be a better model choice than scenario 2 for a solid chemical that has a large vapor pressure (e.g., naphthalene) and, therefore, significant evaporation and gas phase mass transfer to the SC. In both scenarios, the residual chemical is assumed to completely cover the original skin area ($A_{sk}$) over the time of the experiment or until the chemical is fully depleted, if this occurs before the experiment ends. Other scenarios may be needed to acceptably model the range of possible exposure dynamics. For example, the two scenarios just described ignore complications such as precipitation into different solid phases (e.g., a crystalline or an amorphous) or into a solid phase with a different vapor pressure than the saturated chemical dissolved in the vehicle, as well as possible dissolution into sweat or sebum.

The cumulative mass of chemical that evaporates into air ($M_a$) is calculated from the time integration of Eq. (11), which is consistent with Eq. (5) and the assumed evaporating conditions of the two scenarios.

$$\frac{d{M}_a}{dt}=A_{sk}{k}_g{K}_{a/S}{C}_S$$ #(Eq. 11)

where

$$\begin{gathered} C_S=⟨C_S⟩\le C_{S,sat}\mathrm{f}\mathrm{o}\mathrm{r}t<t_e \\ =C_{sat}\left(S\right)\mathrm{f}\mathrm{o}\mathrm{r}{t}_e\le t<t_c \\ =⟨C_{SC}⟩/K_{SC/S}\mathrm{f}\mathrm{o}\mathrm{r}t\ge t_c \end{gathered}$$

and $t_e$ and $t_c$ designate the times (h) at which the vehicle has fully evaporated and at which the chemical is depleted, respectively. The relative fractional mass balance error (${RM}_{err}$) for chemical in all compartments and air compared to the initial concentration of chemical in the source compartment $〈C_{S,0}〉$

$${RM}_{err}=\left(M_a+M_S+A_{sk}{L}_{SC}〈C_{SC}〉+A_{sk}{L}_{VT}〈C_{VT}〉+M_{RF}-V_S〈C_{S,0}〉\right)/V_S〈C_{S,0}〉$$ #(Eq. 12)

was confirmed to be essentially zero (absolute value less than 10⁻¹⁰).

2.3). Rate Constants for Mass Transfer Between Compartments

Chemicals permeate across the skin by partitioning into and then diffusing through the SC and then VE in series to reach, in the in vivo scenario, the highly vascularized dermis, which provides access to the systemic circulation and the rest of the body. For in vitro, if the skin sample includes some or all the dermis, partitioning into and diffusion through the dermis layer will also occur before the chemical reaches the receptor solution. Well-mixed compartment models provide a simpler-to-solve approximation of this membrane diffusion process when the rate constants describing transfer between the compartments are related to partitioning, diffusion, and permeability coefficients that define a chemical’s transport through the skin membranes (Reddy et al., 1998; McCarley and Bunge, 2000).

In this study, we used the rate constant equations presented in McCarley and Bunge (2000), which were derived by matching conditions of the two-compartment and two-membrane models for skin. Because the number of conditions that define a two-membrane model (i.e., steady-state and equilibrium concentrations and fluxes, lead and lag times) exceed the number of rate constants in a two-compartment model, two-compartment models cannot match the two-membrane model behavior in all respects. In the analysis presented here, we used rate constant expressions for the two-compartment skin model (identified as version B1) from McCarley and Bunge (2000), which were derived by matching the membrane model for steady-state and equilibrium concentrations of the SC and VT, with the added assumption of no mass transfer resistance in the vehicle or the receptor fluid. These constants can be defined in terms of effective diffusivities, partition coefficients, and thicknesses or in terms of permeability and partition coefficients. Both definitions are listed in Figure 1. Compartment models using the B1 model rate constants should provide reasonable estimates of the concentrations in the SC and VT compartments, but with potentially reduced accuracy in the time course because the characteristic times of the membrane model (i.e., the lag and lead times) were not included in the derivation of the B1 model rate constants. For modeling dermal absorption over times that are not long relative to the lag time, B2 model rate constants (also from McCarley and Bunge (2000)), which were derived by matching characteristic times along with steady-state concentrations and fluxes of the membrane model, may provide better predictions.

Evaporation of both the chemical and the vehicle from the source solution is represented by the chemical-specific gas phase mass transfer coefficient ($k_g$) calculated in cm h⁻¹ as (Frasch and Bunge, 2015; Frasch et al., 2018):

$$k_g=3260D^{2/3}{\begin{array}{c}\left(v/h\right)\end{array}}^{0.5}$$ #(Eq. 13)

where $v$ is the air velocity in cm s⁻¹, $h$ is the length in cm of the air flow across the exposed skin area, estimated as $A_{sk}^{0.5}$, and $D$ is the diffusivity in cm² s⁻¹ of the chemical or vehicle in air at a specified temperature and pressure. The derivation of Eq. (13) assumes air is in laminar flow parallel to the skin surface; see section S1.1 in the Supplementary Information (SI) for more details including a method for estimating $D$. An air velocity of 10 cm s⁻¹ has been recommended for typical residential room conditions (Frasch and Bunge, 2015). Section S1.2 in the SI shows example calculations for an evaporating water vehicle, which can also be applied to an evaporating chemical.

Some dermal absorption models (Kasting and Miller, 2006; Tonnis et al., 2022; Verma et al., 2023) have calculated $k_g$ values using an alternative equation that assumes a stronger dependence on the air velocity; specifically $k_g$ is proportional to $v^{0.78}$ instead of $v^{0.5}$. We choose to use Eq. (13) because it shows excellent agreement, including the square-root dependence on $v$, with experimental evaporation rates from liquid films of comparable size to those that occur on human skin measured at a range of air velocities (12 to 178 cm s⁻¹) (Frasch et al., 2018). In contrast, the alternative equation underestimates experimental rates by almost an order of magnitude while overestimating the air velocity dependence (Frasch et al., 2018); see S1.1 in the SI for additional details.

2.4). Model Parameterization

The model was parameterized to simulate important experimental system characteristics including the thicknesses of the SC and VT layers, exposure area, exposure concentration, vehicle volume, and chemical and vehicle volatility. Model rate constants require permeability and partition coefficient data for the SC and dermis (assumed to represent the VT), which could be measured or estimated using QSAR expressions derived from experimental measurements (e.g., as described in Cleek and Bunge (1993) among others) with adjustment for the vehicle if it is different from the vehicle (typically water) in the experiments used to develop the QSAR (Zhang, 2013). However, reasonable extrapolations of QSAR-predicted parameters to another vehicle, calculated using the ratio of the measured (or estimated) chemical solubility in the two vehicles, are not assured if the vehicle significantly alters the skin or enhances chemical permeation.

In the model calculations presented below, we used experimental data reported by Ellison et al. (2020) for human cadaver skin from backs or thighs, frozen at -20 °C in a proprietary freezing media of glycerin, buffer, and dimethyl sulfoxide (DMSO) until thawed and soaked for 0.5 h in phosphate buffered saline (PBS) to remove the freezing media prior to sample preparation. Ellison et al. (2020) measured equilibrium partition coefficients and steady-state permeability coefficients at 32 °C for 50 chemicals in PBS, including the 26 chemicals considered here, in dermatomed skin (~500 ± ~140 μm, median ± 25% centile, as measured by the authors; C. Ellison, personal communication, email 2 March 2022), and separately in epidermis and dermis (prepared by heat separating the dermatomed skin), and in isolated SC (prepared by trypsin digestion of the epidermis). Partition coefficients were calculated as the ratio of the equilibrium chemical concentrations in the skin layer and vehicle. SC partition coefficients were measured using dried tissue and adjusted using equations from Wang et al. (2006) to give values representing partitioning in partial or fully hydrated tissue. Fully hydrated partition coefficients were used in this analysis to be consistent with the permeability coefficients data, which were measured across fully hydrated skin samples. Specifically, Ellison et al. (2020) calculated permeability coefficients from the cumulative mass of chemical in the RF over 22 h after infinite dosing for each chemical in a flow-through Franz diffusion cell. Table S1 lists the experimental permeability and partition coefficient values used in the model calculations.

The air-source partition coefficient, $K_{a/S}$, was estimated from the ratio of the chemical saturation concentrations in air ($C_{sat\left(air\right)}$) and the source vehicle, which in the experiments modeled here was water ($C_{sat\left(water\right)}$) in consistent units:

$$K_{a/S}=K_{a/w}=\frac{C_{sat\left(air\right)}}{C_{sat\left(water\right)}}.$$ #(Eq. 14)

Estimates of $C_{sat\left(air\right)}$ were calculated using Eq. (10) and $P_{vap}$ calculated at 25 °C using OPERA (from CompTox Chemicals Dashboard: https://comptox.epa.gov/dashboard/) because experimental values were not available for several chemicals. Experimental values of $C_{sat\left(water\right)}$ were obtained from a study of cosmetic-relevant chemicals (Grégoire et al., 2017); see Table S2. Table S2 lists $C_{sat\left(water\right)}$, $MW$, and $P_{vap}$ values for the modeled chemicals; diffusivity in air ($D$), $k_g$, $C_{sat\left(air\right)}$, and $K_{a/S}$ are listed in Table S3. Table S4 lists the compartment model rate constants.

2.5). Model Evaluation

To evaluate the model’s ability to represent dermal absorption from exposure to a small applied dose of chemical, model results were compared with human skin in vitro permeation test (IVPT) data for 26 chemicals in the study of 56 chemicals from Hewitt et al. (2020). This data set provides a consistent set of skin penetration results for a large set of chemicals. Thirty of the 56 chemicals were excluded from this evaluation because (a) the chemical was not measured in the Ellison et al. (2020) infinite dose dermal absorption study, (b) the vehicle was 100% ethanol instead of an aqueous (PBS) solution, or (c) the experiment was conducted in a fume hood. The bases for the latter two criteria were that ethanol can, as Hewitt et al. (2020) observed, significantly affect skin uptake and permeation, and that the fume hood may have altered the ambient air velocity, and therefore the evaporation rate, by an unknown amount compared with measurements performed outside the hood. The selected 26 chemicals represent a range in physical property values that are pertinent to dermal absorption (Table S2): molecular weight (92 to 372 Da), logarithm of the octanol-water partition coefficient (−0.32 to 3.97), water saturation concentration (207 to 504000 mg mL⁻¹), vapor pressure (~0 to 0.08 mm Hg), melting point (−16 to 238 °C), and pK_a (2.1 to 12.7). Because Hewitt et al. (2020) studied the more volatile chemicals in the fume hood, only two of the 26 chemicals are liquids at skin temperature.

Hewitt et al. (2020) measured absorption into human abdominal skin from surgical waste frozen within 24 h without any freezing media and stored at −20 °C until thawed and dermatomed to 400 ± 50 μm (mean ± standard deviation) for use. Three skin samples from each of 4 donors were used for each chemical. Chemical was applied to the skin at selected concentrations, which varied by chemical, in 10 μL cm⁻² of PBS to 1 cm² without occlusion. The temperature was maintained at 32 °C throughout the experiment. The experiment lasted 24 h and data were collected from the accumulated receptor fluid at 0, 0.5, 1, 2, 4, 8, 16, and 24 h after application. The percent of the applied dose collected in the RF over 24 h (Tables S5) was calculated for each chemical and used to evaluate our model. In addition to the input data described above, the model required values for the thicknesses of the SC and VT layers (assumed to be 25 μm and 375 μm, respectively), exposure area (1 cm²), vehicle volume (10 μL), applied chemical concentration (Table S5), and the chemical’s melting point (Table S2). Chemical structure is also required for calculating chemical diffusivity in air (see section S1.1 in the SI). Consistent with the assumption of a constant exposed surface area, the aqueous vehicle evaporates at a constant rate, calculated from Eqs. (7) and (10) for water (see section S1.2 in the SI), until it is gone at 0.11 h for the default air velocity of 10 cm s⁻¹. In general, chemical ionization in the vehicle affects its permeability through and partitioning into the skin layers and adjustments of the parameter values for the fraction of the non-ionized species are needed (e.g., see Vecchia and Bunge (2002) and Parry et al. (1990)). However, because PBS (pH ~ 7.4) was the vehicle in both the Ellison et al. (2020) and Hewitt et al. (2020) studies, ionization adjustments of the Ellison et al. data for predicting the Hewitt et al. results were considered unnecessary.

3). Results and Discussion

Model predictions for the cumulative mass of chemical in the RF at the end of the experiment (24 h) relative to the experimental measurements are presented in Figure 2A. For the 26 chemicals modeled, predictions at 24 h ranged from 0.1% to 99.8% with an average of 42.1% of the applied dose compared with 0.1% to 93.9% with an average of 40.7% in the experiments. All but seven chemicals are within a factor of ten of the measured mass fraction in the RF. A further 5 fell outside of a factor of five; 7 of the 12 chemicals not within a factor of five were overestimated. Of the remaining 14 chemicals, 5 were overestimated. For dermal absorption modeling, predictions within an order of magnitude are generally considered reasonable given the order of magnitude variability commonly observed in the permeability measurements used in the models (Vecchia and Bunge, 2002; Alinaghi et al., 2022; Cheruvu et al., 2022), which lead to a similar variability in the absorption predictions. Other comparisons of the model predictions and experimental results for the cumulative mass fraction in the RF are provided in the SI, including the differences at 24 h relative to the experimental standard deviation of each chemical (Table S5) and detailed time course results (Figure S1).

Figure 2:

A: Ratio of model predictions to experimental observations from Hewitt et al. (2020) of the cumulative mass of chemical in the RF at 24 h for the 26 chemicals listed in Table S5 by number. Model results were calculated at the default air velocity of 10 cm s⁻¹. Horizontal lines represent perfect model predictions (solid) and over or underestimates by factors of five (dotted) and ten (dashed). Circles denote chemicals that are solids at skin temperature and triangles those that are liquids. The four chemicals selected as case studies are denoted with red symbols. Chemicals used in the case study, chemicals that were over or underestimated by a factor larger than ten, and propylparaben, which was measured twice by Hewitt et al., have been labeled.

B: Predicted fraction of the applied mass in each compartment, and air, during the first hour of exposure to example chemicals. Vertical dotted lines identify the time at which the vehicle has fully evaporated. Compartments are labeled and designated by color: Source (blue; solid), SC (green; dashed), VT (orange; dashed), RF (black; solid), and evaporated (purple; solid).

The predicted chemical distributions among the model’s four compartments and air for the first hour are illustrated in Figure 2B for four example chemicals, three of which are solids at skin temperature (caffeine, resorcinol, and benzoic acid) and one, thioglycolic acid, is a liquid. Figures S2 and S3 show compartment distribution plots for all 26 chemicals for the first hour and the entire 24-h exposure, respectively. Over time chemical transfers first into the SC, then to the VT, and finally to the RF. If the aqueous vehicle evaporates faster than the dissolved chemical, as it does for each of the 4 example chemicals, chemical concentration in the source compartment increases, producing a noticeable increase in the transfer rate to the SC (indicated by the increased slope of the SC mass fraction versus time). By the time the vehicle has completely evaporated, most of the applied dose for some chemicals is depleted. This can be due to a combination of absorption into the skin (the primary reason for caffeine) and evaporation (as seen for thioglycolic acid).

For other chemicals, a significant fraction of the applied dose remains as a solid residue to subsequently evaporate but not absorb into the skin, such as for resorcinol (66%) and benzoic acid (18%). Unlike the other three example chemicals, thioglycolic acid, because it is a liquid at skin temperature, would have continued to absorb into the skin after the vehicle had evaporated, had any chemical mass been left over. Regardless, once the source has been depleted of both vehicle and chemical, thioglycolic acid is volatile enough that chemical in the SC does evaporate. Absorption into and through the SC to the VT is noticeably slower for resorcinol compared with the other three chemicals, which is consistent with its smaller SC permeability coefficient (~ 0.004 cm h⁻¹ compared to ~ 0.025 cm h⁻¹ for the others). At the end of the first hour, permeation into the RF is complete (benzoic acid) or nearly complete (caffeine and thioglycolic acid) as indicated by zero or small mass fractions in the SC and VT. In contrast, most of the resorcinol absorbed into the SC still must transfer through the VT and into the RF.

Deviations of model predictions from experimental data can be caused by poor input parameter estimates or failings in the model structure or assumptions. Predictions by the model presented here for unoccluded finite dose experiments with volatile vehicles are particularly sensitive to two factors: (a) the SC permeability coefficients, which largely control the rate of SC absorption and transfer to the VT and RF, and (b) the time for the vehicle to evaporate, which limits the time for chemicals that are solids at skin temperature to absorb into skin. We consider each of these factors in turn.

Due to the overlap in studied chemicals, including many that had not been previously measured, Ellison et al. (2020) was a natural source for permeability and partition coefficients when evaluating the model presented here against the Hewitt et al. (2020) dataset. However, comparisons of the permeability coefficient values with measurements available from other sources suggest that permeability measurements from Ellison et al. (2020) for six chemicals may be too high by an order of magnitude or more (see data compilations in Alinaghi et al. (2022), Cheruvu (2022), and Vecchia and Bunge (2002)). These chemicals are 1,4 phenylenediamine, benzoic acid (which because it was mostly ionized in the Ellison et al. (2020) and Hewitt et al. (2020) studies should have been lower than the non-ionized values from other sources), caffeine (also see Barbero and Frasch (2016) and Rothe et al. (2017)), hydrocortisone, hydroquinone, and resorcinol (also see Rothe et al. (2017)). High permeability coefficient values can, depending on other contributing factors, lead to overestimates of the measured mass fraction in the RF (see Figure S4 for examples of sensitivity), which is observed for each of these chemicals aside from resorcinol and ibuprofen, which are both underestimated by the model (Table S5 and Figure S1).

The vehicle’s evaporation time (see section S1.2) depends on the inverse of $k_g$, which is estimated to vary with the square-root of the ambient air velocity (Eq. 13). Depending on the situation, skin could be exposed to air velocities that deviate from the recommended default of 10 cm s⁻¹ for standard residential room conditions (Frasch and Bunge, 2015) to as low as 1.1 cm s⁻¹ (Matthews et al., 1989), or even zero (for a stagnant air film), or as high as 80 cm s⁻¹ (ASHRAE, 2010). The impact of changes in vehicle evaporation times varies. For example, model predictions of the cumulative mass fraction of caffeine in the RF for air velocities of 10 and 1.1 cm ⁻¹, corresponding to estimated water evaporation times of 6.6 and 19 min, are unchanged because caffeine is almost completely absorbed into the skin within 6.6 min (Figure S5). Increasing the air velocity to 80 cm s⁻¹ decreases the water evaporation time to 2.2 min, which reduces the caffeine mass fraction in the RF at 24 by about 28%. For resorcinol, the predicted cumulative mass fraction in the RF increases by 2.6-fold as the evaporation time increases from 2.2 min to 6.6 min with a further 2.2-fold increase for the 19 min evaporation time (Figure S5). Vehicle evaporation times in an in vitro diffusion cell experiment might be even longer than 19 min due to the formation of a stagnant air layer, perhaps as large as 1.4 cm in the Hewitt et al. experiments, created by the donor chamber holding the applied vehicle dose onto the skin surface (see section S1.3 for the potential effect on vehicle evaporation times).

Other factors that can affect predictions of some chemicals include variation in vapor pressure estimates if chemical evaporation is significant and lower evaporation rates for chemicals that are ionized in the vehicle. As examples for vapor pressure, the 45-fold larger value calculated using OPERA compared with EPIsuite for ibuprofen (110 x 10⁻⁷ and 2.45 x 10⁻⁷ atm, respectively) increased the estimated ibuprofen evaporation, which decreased the predicted mass fraction in the RF at 24 h from 7.8% to 0.1%; however, the thousand-fold variation in the low vapor pressure values estimated by OPERA and EPIsuite does not affect the predicted dermal absorption of hydrocortisone.

As explained previously, ionization adjustments of the permeability coefficients and partition coefficients from Ellison et al. (2020) were considered unnecessary when modeling the Hewitt et al. (2020) data because the pH control at approximately 7.4 in the PBS vehicle used by both the Ellison and Hewitt studies probably produced similar chemical ionization. However, ionization might affect evaporation while the water vehicle is present, and thereby dermal absorption of some chemicals such as thioglycolic acid, which has the highest vapor pressure of the 26 chemicals (Table S2) and is estimated to be mostly ionized at pH 7.4 (Hewitt et al., 2020). In fact, the effect of neglecting ionization on thioglycolic evaporation is at most small. As shown in Figure 2B, the model predicts that more than 90% of the applied thioglycolic acid absorbed into the skin while the water vehicle evaporated, which limited evaporation during this time to less than 10%.

Ionization would significantly decrease the evaporation estimate (and increase the dermal absorption estimate) of ibuprofen when calculated using the OPERA vapor pressure, but only minimally when using the lower value from EPIsuite (see section S5 in the SI), which is still 20-fold larger than the experimental value (1.2 x 10⁻⁸ atm from Ertel et al. (1990)). At the experimental vapor pressure, almost no ibuprofen evaporates while water is still present. All other chemicals that evaporated significantly before water evaporated (i.e., 6-methylcoumarin, benzophenone, benzylidene acetone, cinnamyl alcohol, and trans-cinnamaldehyde; see Figure S2) were not ionizable. A more general application of the model would use permeability and partition coefficient values that represent the behaviors of the non-ionized fraction of ionizable chemicals. Model calculations for these chemicals should use parameters that have been adjusted for the fraction of chemical ionized.

With respect to the model structure itself, we are unable to evaluate the dynamics of the scenario 1 assumption because neither of the two chemicals that are liquids at skin temperature are predicted to leave a residue on the skin surface after the vehicle has evaporated. Expanding the model to describe the increased ambient air velocity in a fume hood could enlarge the number of liquid chemicals in the database. Also related to model structure, the rate constants for the SC and VT compartments were chosen by prioritizing matching membrane models for concentrations in the SC and VT at steady state and equilibrium rather than the characteristic times (e.g., the lag time). It is therefore expected that the lag times and intermediary concentrations, particularly those in the SC at shorter times, may be less accurate than those calculated at longer times. This will have the largest effect when absorption times are short; i.e., for exposures to chemicals that are solids at skin temperature in small vehicle volumes with shorter evaporation times. Upgrading these rate constants to more complex versions that consider lag times (i.e., the B2 model from McCarley and Bunge (2000)) might improve estimates, although perhaps not significantly. Based on one-compartment models (consisting of an SC but no VT), the B2 model rate constants are likely to predict slightly larger dermal absorption (Reddy et al., 1998).

4). Conclusion

In this study, we have developed and evaluated a flexible mathematical model that can be parameterized to simulate dermal uptake for a large range of chemicals and exposure scenarios. Our modeling approach is novel in that it incorporates vehicle evaporation and makes use of experimental measurements for permeability coefficients and partition coefficients from infinite dose studies (Ellison et al., 2020) that were mostly harmonized with finite dose measurements for the same 26 chemicals (Hewitt et al., 2020). Model predictions are within an order of magnitude of the experimental results for all but seven of the 26 chemicals. Uncertainties associated with chemical parameters and experimental conditions require further investigation to explain dermal absorption of the chemicals that were not well predicted. For example, comparisons with other available permeability coefficient measurements suggest that some of the permeability measurements used from Ellison et al. (2020) are too high, which would lead the model to overpredict the absorption of these chemicals. The time for the vehicle to evaporate is an important factor in the model, which assumes chemicals that are solid at skin temperature stop absorbing into skin once the vehicle is gone. It may be less important for chemicals that are liquid at skin temperature, as these will continue to absorb even after the vehicle has evaporated away, but more data will be needed to evaluate such chemicals. New modeling scenarios may need to be developed to better handle absorption dynamics in the absence of the vehicle for some chemicals; for example, chemicals with significant volatility that are solids at skin temperature.

Finally, certain mechanisms that are currently neglected by the model may be required to simulate certain groups of chemicals. For example, ionization is not considered. While the effects of ionization on the permeability are partially accounted for, since the steady-state values were, like the finite dose data, measured using PBS, changes in the pH of the vehicle during the dry-down process could cause the fraction of chemical that is ionized to change over time. Furthermore, the model does not yet account for any changes to chemical evaporation that could be associated with ionization.