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J Appl Physiol 100: 649-655, 2006. First published October 20, 2005; doi:10.1152/japplphysiol.00927.2005
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The kinetics of transdermal ethanol exchange

Joseph C. Anderson1 and Michael P. Hlastala1,2

Departments of 1Medicine and 2Physiology and Biophysics, University of Washington, Seattle, Washington

Submitted 5 October 2005 ; accepted in final form 12 October 2005


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The kinetics of ethanol transport from the blood to the skin surface are incompletely understood. We present a mathematical model to predict the transient exchange of ethanol across the skin while it is being absorbed from the gut and eliminated from the body. The model simulates the behavior of a commercial device that is used to estimate the blood alcohol concentration (BAC). During the elimination phase, the stratum corneum of the skin has a higher ethanol concentration than the blood. We studied the effect of varying the maximum BAC and the absorption rate from the gut on the relationship between BAC and equivalent concentration in the gas phase above the skin. The results showed that the ethanol concentration in the gas compartment always took longer to reach its maximum, had a lower maximum, and had a slower apparent elimination rate than the BAC. These effects increased as the maximum BAC increased. Our model's predictions are consistent with experimental data from the literature. We performed a sensitivity analysis (using Latin hypercube sampling) to identify and rank the importance of parameters. The analysis showed that outputs were sensitive to solubility and diffusivity within the stratum corneum, to stratum corneum thickness, and to the volume of gas in the sampling chamber above the skin. We conclude that ethanol transport through the skin is primarily governed by the washin and washout of ethanol through the stratum corneum. The dynamics can be highly variable from subject to subject because of variability in the physical properties of the stratum corneum.

diffusion; convection; blood alcohol concentration; skin alcohol; SCRAM

ACCURATE QUANTIFICATION OF alcohol concentration in the body is important in both forensic and physiological research applications. The most accurate and reliable method is direct blood sampling and analysis by gas chromatography. The alcohol breath test is commonly used because of its noninvasive and indirect approach. The measurement is not continuous, which makes it difficult to follow the pharmacokinetics of the blood alcohol concentration (BAC) and inaccurate due to the variability in delivery of the sample in different subjects (14).

The pharmacokinetics of alcohol are complex because of the intricate nature of the distribution into the various watery tissues in the body. The kinetics are dependent on absorption from the intestine into the blood, elimination from the blood via metabolism in the liver, and transport in different tissue compartments via diffusion and convection. This balance between absorption and elimination of alcohol is reflected in the BAC. After a drink, the BAC rises until absorption is complete. After a maximum in BAC is achieved, the BAC decreases during the "burn-off" or elimination phase primarily due to metabolism in the liver.

In legal cases involving the use of alcohol, courts may require abstinence until the matter is resolved in a legal proceeding. In the past, abstinence has been monitored with random breath testing, which leaves the possibility that a drinking event might be missed. The recent development of the SCRAM device (secure continuous remote alcohol monitor; Alcohol Monitoring Systems, Highlands Ranch, CO) (12) shows promise as a means for measuring a pseudocontinuous supradermal ethanol concentration, ethanol concentration in the gas space above the skin, at multiple points in time as a means for identification of violation of abstinence from alcohol. The SCRAM device is an ankle bracelet that simultaneously measures skin temperature and ethanol vapor above the skin surface. Ethanol arrives at the skin surface via passive alcohol diffusion from blood flowing through skin capillaries (insensible perspiration) and perspiration due to secretory activity of sweat glands (sensible perspiration). The alcohol concentration in an air sample taken from just above the skin surface vs. time is analyzed as a means of estimating BAC as a function of time. Only minimal information regarding the design and functional features of the SCRAM device is available in the literature. Thus we have chosen to focus on the kinetics of alcohol diffusion from the blood, through the skin, and into a generic measurement device lying on the surface of the skin.

It has been assumed that the shape of the supradermal ethanol concentration curve mimics the shape of the BAC curve. This interpretation may fail to recognize physiological variation in the process of diffusive transport through the skin, resulting in either false positive or false negative findings of alcohol consumption. This paper seeks to define the important factors governing the relationships between the BAC vs. time curve and the supradermal ethanol concentration vs. time curve. Additionally, this paper intends to evaluate the physiological limitations to interpretation of supradermal ethanol concentration data. In the present study, we develop a mathematical model of ethanol transport through the skin. Using this model, we explore how the time-varying concentration of ethanol in the blood affects the ethanol concentration above the skin. Additionally, a sensitivity analysis using Latin hypercube sampling (LHS) is implemented to reveal how variability in tissue, blood, and gas parameters affect skin ethanol concentration. These analyses answer the following two questions. Why is the supradermal ethanol concentration delayed and attenuated relative to the ethanol concentration in the blood? What factors are most responsible for this attenuation?


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Mathematical model.   To simulate ethanol exchange across the skin surface, we chose a model consisting of four compartments: blood, epidermis, stratum corneum, and gas (Fig. 1). Dissolved ethanol in the blood) is delivered to the skin via blood flow through the capillaries. Ethanol enters and leaves the capillaries at partial pressures Pa and Pc, respectively. Ethanol diffuses through the epidermis and the stratum corneum before it reaches the gas phase, which is ventilated with fresh air. As a first approach, we focused only on diffusional transport through the tissue layers. We neglected any transport resulting from sensible perspiration (i.e., sweating). We assumed that the capillary and gas compartments were individually well mixed and that uniform diffusion occurred across the epidermis and stratum corneum.


Figure 1
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  		Fig. 1. Schematic showing a cross-section of skin next to a device for measuring supradermal ethanol concentration. Ethanol entering the system via the blood diffuses through the epidermis and stratum corneum before entering the gas compartment and is removed from the system by convective gas flow (Formula 6). A differential length (dx) was used for mathematical analysis. Pa, Pc, Pe, Pg, Ps, arterial, capillary, epidermal, gas, and stratum corneum ethanol partial pressures, respectively. See Table 1 for more definitions.

 
Similar to the model of vanLöbensels et al. (29), we used four coupled differential equations to describe mass transport between blood, epidermis, stratum corneum, and gas. Equation 1 represents the rate of change of mass of a dissolved gas in the capillary blood compartment. It is equal to the rate of gas delivery to the capillary space via blood flow, the rate of gas removal via blood flowing out of the capillary, and the rate of diffusive gas flux across the capillary membrane into the epidermis. Pe is the partial pressure of ethanol in the epidermis. See Table 1 for parameter definitions.

Formula 1(1)


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  		Table 1. Model parameters and uncertainty ranges

 
Equations 2 and 3 describe diffusion in the epidermis and stratum corneum, respectively.

Formula 2(2)

Formula 3(3)
Ps is the partial pressure of ethanol in the stratum corneum. Between the epidermis and stratum corneum, we imposed that the flow of gas between the epidermis and stratum corneum was equal.

Formula 4(4)

Equation 5 represents an enclosed air space above the skin. The rate of change of gas in this compartment is determined by addition of gas from the ambient air (PI = 0), subtraction of gas removed by fresh air ventilation, and addition of gas diffusing across the air-skin interface from the stratum corneum, adjacent to the compartment.

Formula 5(5)
where Pg is the partial pressure of ethanol in the gas compartment. The section Parameter estimates, below, defines and presents average values for all model parameters.

We solved the system of four partial differential equations numerically to determine the partial pressure profiles in the epidermis and stratum corneum and the partial pressure of ethanol in the gas compartment as a function of time given a time-varying Pa of ethanol. Spatial derivatives were solved by upwind finite difference, and time derivatives were solved using LSODE, a time-integrating algorithm developed by Hindmarsh (13). The executable program was submitted as a batch job in which each simulation was solved numerically using an Intel Pentium IV computer running Digital Visual Fortran. Pc and Pg are equal to Pe(0) and Ps(Le + Ls), respectively. To simplify the presentation of results, the partial pressures of ethanol in all model compartments were converted to equivalent BAC at 37°C using the following relationship:

Formula 6(6)
where R is the universal gas constant (62,360 Torr·cm3·mol–1·K–1), T is the temperature (K), and betag and betab represent solubility (ml ethanol·100 ml medium–1·Torr–1) of ethanol in gas and blood, respectively.

Parameter estimates.   We chose parameter values that corresponded to the average dimensions and physical characteristics of healthy skin tissue. The average values and uncertainty ranges for 11 parameters are listed in Table 1. We subjectively chose uncertainty ranges based on the methods used to select the average value. For example, little information is known about Formula 6, but betab was based on careful measurements. We assigned the former a high level of uncertainty (±50%) and the latter a small level of uncertainty (±10%). We assumed each variable to have a uniform (i.e., rectangular) probability distribution function, where the lower (upper) limit of the probability distribution function corresponded to the average value minus (plus) the uncertainty listed in Table 1. The skin tissue model has dimensions of 1 cm x 1 cm x L, where L is the thickness of each compartment. In our model, the skin tissue is composed of two compartments: the stratum corneum and the epidermis. The thickness of the stratum corneum ranges from 10 to 20 µm (3, 5, 18, 23, 24). On the basis of these data, we chose the thickness of the stratum corneum to be 15 µm (0.0015 cm). The thickness of the epidermis, the distance between the stratum corneum and the center of mass of the capillary vessels, depends on where the blood supply resides. Some investigators state the microcirculation lies at a depth of 100–300 µm (9, 16, 20). Based on this data, we chose the thickness of the epidermis to be 200 µm (0.02 cm).

The capillary volume was calculated from estimates of the capillary diameter and surface area. We assumed the thickness of a capillary to be 7 µm (0.0007 cm), the diameter of a red blood cell. We estimated that the surface area of the capillaries covered 7.5% of the 1-cm2 capillary-epidermis interface (0.075 cm2) (26). Therefore, the capillary volume was 3.5 x 10–4 ml. The values for skin Formula 6 given in the literature range from 0.0057 to 0.049 ml·min–1·cm–2 (2, 11, 25, 30). Based on these values, we assumed Formula 6s = 0.024 ml·min–1·cm–2. Therefore, Formula 6 in the model was 4.0 x 10–4 ml/s.

The volume of the gas compartment enclosed by the measurement device was estimated by assuming that the dimensions of the skin surface (A) were 1 cm x 1 cm = 1 cm2 and the distance between the surface of the skin and the bottom of the detector was 0.5 cm. The corresponding gas volume (Vg) was 0.5 ml. Additionally, we assumed that the device measures ethanol once every 30 min and that each sample required 0.1 ml of gas. On average, over an entire 1 h, the flow rate within the gas compartment of the device would be 0.2 ml/h. To approximate this flow rate, we chose Formula 6 = 5.0 x 10–5 ml/s.

The solubilities of ethanol in blood, epidermis, stratum corneum, and gas were obtained from experimental studies that reported liquid-air partition coefficients. For example, the partition coefficient of blood to air is the ratio of betab to ethanol solubility in air, betag. The "solubility" of ethanol in the gas phase, betag, is defined as 0.132 ml ethanol·100 ml gas–1·Torr–1 (17). The blood-air partition coefficient ({lambda}b:a) for ethanol is 1,756 at 37°C (15). Thus betab = 1,756 x 0.132 = 232 ml ethanol·100 ml blood–1·Torr–1. We assumed the solubility of ethanol in the epidermis to be the same as that in blood, {lambda}b:e = 1.0 (1, 25). On the basis of the stratum corneum-water partition coefficient (19, 21), {lambda}sc:w = 0.75, and the water-air partition coefficient (15), {lambda}w:a = 2,132 at 37°C, we estimated betas to be = 0.75 x 2,132 x 0.132 = 211 ml ethanol·100 ml stratum corneum–1·Torr–1.

De of ethanol has been measured and found to range between 4 x 10–6 and 5.5 x 10–6 cm2/s (10, 21). We chose De = 5 x 10–6 cm2/s. Likewise, literature values of the Ds of ethanol ranges between 6.6 x 10–10 and 3.5 x 10–11 cm2/s (21, 22). We chose Ds = 5.0 x 10–10 cm2/s.

Model simulations.   The model was used to simulate the elimination of ethanol from the blood through the skin and into the air. The time course of ethanol in the blood can be described by three parameters: absorption time, maximum BAC, and metabolic elimination rate. Ethanol was assumed to be absorbed, in a linear fashion, from the gut into the blood over a given period of time. We simulated absorption times ranging from 0.25 to 2.0 h in 0.25-h increments. At the end of the absorption phase, the concentration of ethanol in the blood reaches a peak. The maximum BAC (BACmax) values used in these simulations range from 0.02 to 0.1 g/dl in 0.02 g/dl increments. In the postabsorptive state, BAC decreases predominately as a result of metabolic breakdown. The rate of decrease in ethanol concentration in the blood (metabolic elimination rate) was assumed to be 0.018 g·dl–1·h–1 for all simulations. For the gas compartment, we assumed that convective gas flow moves ambient air into the gas compartment to replace the gas that has been removed for measurement and that this ambient air does not contain ethanol (i.e., PI = 0) for all simulations.

Using model simulations, we determined the effect of the absorption time and BACmax on ethanol levels in and above the skin as a function of time. These simulations investigated all possible combinations of absorption time and BACmax outlined above and used the average values of tissue thickness, molecular diffusivity, solubility, and flow rates provided in Table 1. Model simulations resulted in ethanol profiles in the blood, tissue, and air as a function of time. From these profiles, we calculated four quantities that describe the ethanol transport kinetics (Fig. 2): 1) maximum ethanol concentration in the gas space (Cg,max) as calculated using Eq. 6, 2) maximum decrease in ethanol concentration in the gas space with respect to time (WOmax), 3) difference in time between the maximum ethanol concentration in the gas space and that in the blood (TPD), and 4) difference in time between zero ethanol concentration in the gas space and that in the blood (TZD). "Zero ethanol concentration in the gas space" was defined as a Cg = 0.001 g/dl.


Figure 2
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  		Fig. 2. Graphical definition of critical outputs. Blood alcohol concentration (BAC) curve (thick black line) was imposed, and the equivalent ethanol concentration in the gas compartment (Cg; thin black) was calculated from the model. The delay time between peaks (TPD) is the difference in time between the maximum BAC and maximum ethanol concentration in the gas compartment (Cg,max). The maximum washout rate (WOmax) was calculated as the negative of the slope of the Cg curve. TZD, difference in time between zero ethanol concentration in the gas space and that in the blood.

 
Sensitivity analysis.   We performed a sensitivity analysis of the mathematical model of transdermal ethanol transport to determine the relative importance of model parameters on critical model predictions. For this study, the LHS sensitivity analysis was chosen to investigate the relationship between model parameters and outputs (4). We evaluated the impact of 11 model parameters (Table 1) describing gas solubility, the tissue thickness, and molecular diffusion coefficients, on four outputs (Fig. 2). The following LHS sensitivity analyses were performed nine times using all combinations of the following conditions: 1) absorption time of alcohol into the blood (0.5, 1, or 2 h) and 2) maximum blood alcohol content as measured using the Widmark (31) formula (0.02, 0.05, or 0.10 g/dl).

To perform the LHS analysis, the mathematical model simulated the kinetics of ethanol transport through the skin as ethanol is absorbed into the blood and subsequently eliminated from the body. For each LHS analysis, the model simulated the transdermal kinetics of ethanol 50 times with each simulation involving a unique set of 11 parameter values. The value of each parameter during each of the 50 simulations was chosen by using the following algorithm. First, the probability distribution function for each parameter was divided into 50 equal probability intervals, the number of simulations. Second, each probability interval was assigned a number between 1 and 50, with 1 assigned to the probability interval nearest the lower confidence limit and 50 assigned to the probability interval nearest the upper confidence limit. Third, for every simulation, each parameter was assigned a random number between 1 and 50 without replacement (each number was used only once for a given parameter) that corresponded to the defined equal probability interval. Fourth, the equal probability interval corresponding to the random number was identified. The parameter value was equal to the average of the upper and lower limits of this interval. Thus a parameter value for each model simulation was chosen completely randomly (i.e., by random selection of the probability interval) but without replacement. Examples of studies using the LHS method for sensitivity analyses can be found in the literature (4, 7).

The last step in the sensitivity analysis was to determine a quantitative sensitivity index for each of the 11 parameters and establish a threshold to identify those parameters to which a particular output was sensitive. To do this, a partial rank correlation coefficient (PRCC) was calculated for each input variable against each output variable (4). The significance of a nonzero PRCC value was tested using a two-sided Student's t-test (4) to determine whether each PRCC was statistically different from zero (P < 0.05). We studied the four outputs described in Model simulations (Cg,max, WOmax, TPD, and TZD) with the sensitivity analysis.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Solutions of the model were well behaved with no instances of negative results or mass imbalance. Partial pressures at the boundaries between compartments were continuous. The numerically integrated time- and space-dependent solutions did not change as the size of the time step or spatial grid was altered.

Figure 3 demonstrates the spatial profiles of ethanol concentration through the epidermis and stratum corneum at multiple time points. The conditions imposed on the BAC profile are BACmax = 0.05 g/dl, absorption time = 2 h, and metabolic elimination rate = 0.018 g·dl–1·h–1. For this simulation, the value for each model parameter is the average value listed in Table 1. Truncated ethanol profiles in the epidermis are presented because the equivalent BAC at the epidermis-stratum corneum interface (200 µm) is within 2% of the equivalent BAC at the blood-epidermis interface at all times. The ethanol profiles in the tissue are shown every 0.5 h. As BAC increases during absorption from the gut, the ethanol profiles (solid black line) in the stratum corneum increase as shown by the solid black arrow. Throughout the absorptive phase (solid black lines), BAC is always greater than the ethanol concentration in the gas phase because the large diffusion barrier imposed by the stratum corneum causes steep spatial gradients. After BAC reaches its peak (i.e., the rate of metabolic elimination is greater than that for absorption), the ethanol profiles in the stratum corneum (thin black line) decrease with time as shown by the thin black arrow. In the postabsorptive phase, the ethanol concentration in the blood drops below that in the gas phase because the metabolic elimination rate of ethanol in the liver is larger than the washout rate of ethanol from the stratum corneum. Therefore, the diffusion gradient reverses and ethanol diffuses from the tissue into the blood.


Figure 3
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  		Fig. 3. Ethanol washin-washout kinetics in the tissue. BAC increases during the absorptive phase (solid lines), and ethanol follows the diffusion gradient from blood to tissue, loading the epidermis and stratum corneum with ethanol. BAC decreases during the postabsorptive phase (thin lines), the diffusion gradient reverses, and ethanol diffuses from the tissue into the blood. Tracings represent equivalent BAC vs. position at 0.5-h intervals. Model parameters are listed in Table 1. BACmax = 0.05 g/dl, absorption time = 2 h, and metabolic elimination rate = 0.018 g·dl–1·h–1.

 
Devices measuring supradermal ethanol only sample ethanol in the gas space above the skin. Therefore, it is important to compare the concentration of supradermal ethanol, Cg, to the BAC at corresponding points in time. An example of a BAC and the corresponding Cg curve are presented in Fig. 2. This BAC curve (thick solid line) is a model input and has the following characteristics: a rise time of 30 min, a BACmax of 0.05 g/dl, and a metabolic elimination rate of 0.018 g·dl–1·h–1. With this BAC curve and the typical model parameters (i.e., average values) listed in Table 1, the model simulated the transport of ethanol through the tissue and generated a typical Cg curve (thin solid curve) shown in Fig. 2. Compared with the BAC trace vs. time, the Cg curve has a maximum value, Cg,max, that is smaller and is delayed in time, TPD, relative to BACmax by ~1 h in this example. The decreasing slope of the Cg curve is less than that of the BAC curve. Thus the Cg curve is shifted, attenuated, and spread relative to the BAC curve. These transformations result from the diffusion barrier imposed by the stratum corneum.

We investigated how the shape of the BAC curve affected four outputs: Cg,max, WOmax, TPD, and TZD. We imposed different BAC curves by changing BACmax and the absorption time. The metabolic elimination rate was 0.018 g·dl–1·h–1 for all simulations. We set each model parameter equal to the average value listed in Table 1. We plotted each output against BACmax for eight different absorption times beginning with 0.25 h and ending with 2 h. Intermediate curves are separated by 0.25 h. Figure 4 shows the relationship between Cg,max normalized by BACmax and BACmax for multiple absorption times. Cg,max is directly related to absorption time and BACmax. However, Cg,max is at most equal to 78% of BACmax and can be as small as 43% of BACmax for a small absorption time and BACmax. Figure 5 shows how WOmax changes with absorption time and BACmax. For none of the simulations does the washout rate calculated from the Cg curve equal the imposed metabolic elimination rate of 0.018 g·dl–1·h–1. For any given absorption time and BACmax ≥ 0.08 g/dl, WOmax equals 0.0164 g·dl–1·h–1. For BACmax ≤ 0.08 g/dl, WOmax decreases with decreasing absorption time and BACmax. For BACmax = 0.02 and 0.25 h absorption times, WOmax is ~45% of the metabolic elimination rate. Because the WOmax is generally calculated at Cg values that are small, limitations of the measurement device may increase the difference between calculated WOmax and the metabolic elimination rate. Figure 6 shows that the time delay between BACmax and Cg,max, TPD, increases with increasing BACmax and decreasing absorption time. The model predicts TPD to range from 27 min for BACmax = 0.02 and 2-h absorption time to 93 min for BACmax = 0.1 and 15-min absorption time. Figure 7 shows the delay time between zeros, TZD, as a function of BACmax and absorption time. For BACmax ≤ 0.08 g/dl, increasing BAC or absorption time increases TZD. However, for BAC ≥ 0.08 g/dl, TZD = 3.3 h independent of absorption time.


Figure 4
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  		Fig. 4. Cg,max normalized to BACmax increases with BACmax and absorption time. Cg,max never equals BACmax. Top and bottom curves represent 2- and 0.25-h absorption times, respectively, with curves interposed at 0.25-h increments.

 

Figure 5
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  		Fig. 5. WOmax increases with increases in BACmax and absorption time. When BACmax ≥ 0.08 g/dl, WOmax = 0.0164 g·dl-1·h–1. Top and bottom curves represent 0.25- and 2-h absorption times, respectively, with curves interposed at 0.25-h increments. The metabolic elimination rate of ethanol in blood was 0.018 g·dl–1·h–1.

 

Figure 6
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  		Fig. 6. TPD between BACmax and Cg,max increases as BACmax increases or the absorption time decreases. A 30- to 90-min delay exists between these 2 peaks for all cases shown. Top and bottom curves represent 0.25- and 2-h absorption times, respectively, with curves interposed at 0.25-h increments.

 

Figure 7
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  		Fig. 7. TZD increases slightly with increases in BACmax and absorption time. When BACmax ≥ 0.08 g/dl, TZD = 3.3 h. Top and bottom curves represent 2- and 0.25-h absorption times, respectively, with curves interposed at 0.25-h increments.

 
Nine sensitivity analyses were performed on the mathematical model using LHS. For a representative analysis with a 1-h absorption time and BACmax = 0.05 g/dl, we present Cg curves resulting from the 50 simulations of the LHS analysis in Fig. 8 to show the effect of parameter uncertainty on Cg. For this LHS analysis, the PRCC and their corresponding P values are summarized in Table 2. Coefficients with P < 0.05 are in bold. Although Table 2 presents sensitivity results for a representative BAC profile, this sensitivity relationship between outputs and parameters holds for all nine BAC curves studied. Additionally, three parameters (Formula 6, betae, and De) significantly affect WOmax under specific BACmax conditions. WOmax is sensitive to gas flow when BACmax is 0.1 or 0.05 g/dl and is sensitive to betae and De when BACmax is 0.05 or 0.02 g/dl.


Figure 8
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  		Fig. 8. Large variability in the supradermal ethanol curves results from relatively large uncertainty in the 11 model parameters. Fifty supradermal ethanol curves are predicted by the model. For each simulation, values for the 11 model parameters were selected using Latin hypercube sampling. BAC profile (thick black line) characteristics used for these simulations: ethanol absorption time = 1 h, BACmax = 0.05 g/dl, and metabolic elimination rate for ethanol = 0.018 g·dl–1·h–1.

 

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  		Table 2. Sensitivity coefficients (PRCC) for a representative sensitivity analysis using a 1-h absorption time and BACmax = 0.05 g/dl

 
There are four parameters to which all four outputs are statistically sensitive. One parameter defines the size of the gas compartment, Lg. The three remaining parameters, betas, Ds, and Ls, together completely define the characteristics of the stratum corneum. Of these four parameters, two (Ds and Ls) have the largest absolute PRCC values. Therefore, variations in the value of these two parameters over their uncertainty range change the outputs more than alterations in any of the other parameters. The sign in front of the PRCC value indicates the relationship between a parameter and an output. A negative PRCC value signifies an inverse relationship; that is, an increase in the parameter will cause a decrease in the output. The parameters identified by this analysis may need to be more accurately measured or can be used to fit the model predictions to measured data.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
To qualitatively validate our model, we compared our model predictions to experimental data from SCRAM-like devices in the literature that examined how changes in BACmax and absorption time from the gut affect Cg and Cg/BAC. First, the model predicted that Cg,max/BACmax was < 1 (i.e., Cg,max was always less than BACmax) and increases with absorption time and BACmax (Fig. 4). Experimental data show that Cg,max is less than BACmax (as estimated with an alcohol breath test) (6, 27), and another study stated that the two peaks were "of similar amplitude" (28). An investigation (27) found Cg,max/BACmax resided between 0.29 and 0.5, whereas, in our model study, this ratio varied between 0.43 and 0.78. Second, the model predicted the delay time between Cg,max and BACmax to be between 30 and 90 min. Three studies reported that TPD was between 30 min and 2 h (6, 27, 28). Additionally, observations showed that TPD increased from 30 to 120 min as BACmax increased from <0.1 g/dl to >0.15 g/dl (28). The model predicted the same trend between TPD and BACmax (Fig. 6). Third, the model predicted that the maximum washout rate was always less than the imposed metabolic elimination rate of 0.018 g·dl–1·h–1. Experimental results (6) agree with this model prediction showing the elimination rate of ethanol in the gas phase to be 83% of that in the blood (as estimated with an alcohol breath test). Fourth, an experimental observation showed the delay time between Cg = 0 and BAC = 0 to be >2 h (28), which is similar to the model-predicted values (~3 h).

Our model included diffusion and neglected sensible perspiration (i.e., sweating). Whereas diffusion through the skin requires a significant amount of time for ethanol to cross the tissue and reach equilibrium, sensible perspiration moves liquid with an ethanol content similar to blood quickly (relative to diffusion) to the skin surface (27). If sensible perspiration was included in the model, the Cg curve would more closely match the BAC curve, causing TPD to decrease and Cg,max to more closely resemble BACmax. However, our model results appear to underpredict TPD and overpredict Cg,max values measured experimentally and reported in the literature (see paragraph above), which indicates that perspiration is less important than diffusion and that the chosen parameter values (Table 1) are conservative estimates. A larger tissue thickness and smaller diffusion coefficients may be more appropriate. Although perspiration did not appear to impact the experimental data used for model validation, studies are needed to evaluate the effect of perspiration resulting from stressful conditions (e.g., exercise or hyperthermia) on ethanol transport through the skin.

A sensitivity analysis revealed the model to be most sensitive to parameters describing the stratum corneum (solubility, diffusivity, and thickness) and the gas compartment (thickness and convective gas flow). These parameters strongly influence the outputs for two reasons. First, the values of these parameters are less established, as reflected in their relatively large uncertainties that stem from large variability in their measurements (betas, Ds, and Ls) or a lack of information (Formula 6 and Lg). Second, these parameters significantly control the transport of ethanol or affect the measurement of ethanol. The stratum corneum provides the majority of resistance for transport of ethanol, as reflected in its large time constant. The stratum corneum has a larger time constant ({tau}s = Ls2/Ds = 3,380 s) than the epidermis ({tau}e = Le2/De = 80 s) or the blood compartment ({tau}b = capillary volume/Formula 6 = 1 s). Experimental evidence supports this calculation. In an isolated skin preparation, investigators removed the stratum corneum and found the ethanol concentration above the skin increased by a factor of four compared with the intact preparation (8). However, the time constant in the gas phase is larger than all other compartments ({tau} = Vg/Formula 6 = 10,000 s). The gas compartment's role is to collect ethanol for measurement, not to participate in ethanol transport. Thus the ideal time constant for the gas compartment would be infinity as Formula 6 approaches 0 ml/s for any finite Vg.

Our sensitivity analysis demonstrates that the supradermal ethanol concentration is governed by the three model parameters describing the stratum corneum. In turn, each of these three parameters is dependent on water content and/or temperature. The thickness of the stratum corneum can increase almost fourfold from a dehydrated state (Ls = 8.2 µm) to a well-hydrated state(Ls = 27 µm) (21, 24). The molecular diffusivity of ethanol through this tissue can change by almost an order of magnitude from a value of 3.5 x 10–11 cm2/s for a desiccated tissue to 6.6 x 10–10 cm2/s for a well-hydrated stratum corneum (21, 22). Additionally, a temperature change from 30 to 37°C increases the molecular diffusivity of ethanol through water by 20% (32). Although stratum corneum is not water, this trend may still hold true except with a different magnitude of change. The solubility of ethanol in stratum corneum is dependent on water content. The solubility of ethanol in relatively dry stratum corneum was less than that in wet tissue (19, 21). Ethanol solubility in this tissue may decrease with temperature if it follows the behavior of ethanol solubility in water and blood (i.e., decreasing ~6% per °C) (15). Because these parameters significantly impact the predicted Cg curve, it may be necessary to control the water content and temperature of the tissue during experimental investigations.

The practice of using the skin alcohol monitoring device employs a single correction factor to adjust the peak gas concentration to an equivalent alcohol concentration in breath. Further correction to an equivalent alcohol concentration in blood is then required to allow use of skin alcohol readings to be compared with BACs. This practice is inherently flawed due to the large variation in supradermal gas concentration compared with blood concentration (as illustrated in Fig. 8). The variation in peak amplitude for supradermal gas is ~2 to 1. When this variation is coupled with the variation in breath to blood correction (14), it is clear that the measure of skin alcohol diffusion is plagued with an extremely large variation if the physiological variables are not accounted for in a quantitative manner.

Our mathematical model of ethanol transport across the skin during absorption from the gut and elimination from the body predicts 1) ethanol kinetics follow classic washin-washout kinetics in the tissue, 2) the supradermal ethanol concentration is attenuated and delayed compared with the BAC, 3) ethanol transport through the skin is governed by the parameters describing the stratum corneum and the volume of gas above the skin, and 4) the kinetics of ethanol transport can be highly variable between subjects because of variability in the physical characteristics of the stratum corneum. The results of this study suggest the water content and temperature of the stratum corneum along with the volume and flow rate of gas above the skin need to be closely controlled to ensure accurate measurements. Additional experimental information concerning the solubility of ethanol, diffusivity of ethanol through, and thickness of the stratum corneum and their dependence on temperature and water content is needed.


   GRANTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This work was supported, in part, by Grant T32 EB001650 from the National Institute for Biomedical Imaging and Bioengineering and by Grants HL-24163 and HL-073598 from the National Heart, Lung, and Blood Institute.


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. C. Anderson, Division of Pulmonary and Critical Care Medicine, Box 356522, Univ. of Washington, Seattle, WA 98195-6522 (e-mail: clarkja{at}u.washington.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

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