Estimating BrAC from Transdermal Alcohol Concentration Data Using the BrAC Estimator Software Program

Estimating BrAC from Transdermal Alcohol Concentration

Data Using the BrAC Estimator Software Program

Susan E. Luczak and I. Gary Rosen

Background: Transdermal alcohol sensor (TAS) devices have the potential to allow researchers andclinicians to unobtrusively collect naturalistic drinking data for weeks at a time, but the transdermalalcohol concentration (TAC) data these devices produce do not consistently correspond with breathalcohol concentration (BrAC) data. We present and test the BrAC Estimator software, a programdesigned to produce individualized estimates of BrAC from TAC data by fitting mathematical modelsto a specific person wearing a specific TAS device.

Methods: Two TAS devices were worn simultaneously by 1 participant for 18 days. The trial beganwith a laboratory alcohol session to calibrate the model and was followed by a field trial with 10 drink-ing episodes. Model parameter estimates and fit indices were compared across drinking episodes toexamine the calibration phase of the software. Software-generated estimates of peak BrAC, time ofpeak BrAC, and area under the BrAC curve were compared with breath analyzer data to examine theestimation phase of the software.

Results: In this single-subject design with breath analyzer peak BrAC scores ranging from 0.013 to0.057, the software created consistent models for the 2 TAS devices, despite differences in raw TACdata, and was able to compensate for the attenuation of peak BrAC and latency of the time of peakBrAC that are typically observed in TAC data.

Conclusions: This software program represents an important initial step for making it possible fornon mathematician researchers and clinicians to obtain estimates of BrAC from TAC data in naturalis-tic drinking environments. Future research with more participants and greater variation in alcohol con-sumption levels and patterns, as well as examination of gain scheduling calibration procedures andnonlinear models of diffusion, will help to determine how precise these software models can become.

Key Words: Transdermal Alcohol Sensor, Transdermal Alcohol Concentration, Real-TimeAssessment, Ecological Momentary Assessment, BrAC Estimation.

RESEARCHERS AND CLINICIANS who wish tocapture real-time levels of alcohol consumption cur-

rently have limited data collection method options. The useof a breath analyzer or a drinking diary during drinking epi-sodes requires continuous active participation that increasesparticipant burden and decreases the naturalism of the drink-ing environment. In addition, these methods are not appro-priate for monitoring individuals who may not be motivatedto give accurate accounts of their drinking. Even in moti-vated participants, such methods have the potential to pro-duce inaccurate results, with breath analyzer readings beingtoo high due to mouth alcohol, being too low due to not tak-ing deep lung breaths, and failing to capture peak breathalcohol concentration (BrAC) due to the time between mea-

surements. Drinking diary inaccuracies are likely in thosewho are drinking in a manner where they cannot gauge theamount of alcohol they have consumed (e.g., mixed drinks,sharing pitchers, playing drinking games).Transdermal alcohol sensor (TAS) devices, including the

WrisTASTM (Giner, Inc., Newton, MA), TAC� (BI, Inc.,Boulder, CO), and SCRAM© (Alcohol Monitoring Systems,Inc., Denver, CO), offer a promising method for unobtru-sively collecting continuous alcohol levels in naturalistic set-tings over long periods of time (see Swift, 2003). Until now,however, these TAS devices have been used almost exclu-sively as abstinence monitors (see Marques and McKnight,2009; Sakai et al., 2006). This is primarily for 2 reasons: first,the alcohol community, which has traditionally relied uponblood alcohol concentration (BAC) and BrAC as the stan-dard quantitative indices of intoxication, has no experiencein, or benchmarks for, interpreting or analyzing the transder-mal alcohol concentration (TAC) data that TAS devices pro-duce; and second, evidence has shown that, unlike the breathanalyzer, there is significant variation from individual toindividual and device to device when correlating TAC withBAC or BrAC (Dumett et al., 2008).If BAC or BrAC estimates could be reliably derived from

TAC data, researchers and clinicians would be able to pas-sively and unobtrusively obtain weeks of easily interpreted,

From the Department of Psychology (SEL), University of SouthernCalifornia, Los Angeles, California; Department of Psychiatry (SEL),University of California, San Diego, California; and Department ofMathematics (IGR), University of Southern California, Los Angeles,California.

Received for publication November 22, 2013; accepted April 23, 2014.Reprint requests: Susan E. Luczak, PhD, Department of Psychology,

SGM 501, Los Angeles, CA 90089-1061; Tel.: 213-740-4872;Fax: 213-746-9082; E-mail: [email protected]

Copyright© 2014 by the Research Society on Alcoholism.

DOI: 10.1111/acer.12478

Alcohol Clin Exp Res,Vol 38, No 8, 2014: pp 2243–2252 2243

ALCOHOLISM: CLINICAL AND EXPERIMENTAL RESEARCH Vol. 38, No. 8August 2014

detailed data on an individual’s naturalistic alcohol con-sumption (see Dougherty et al., 2012). Fundamental infor-mation on the time-varying patterns of consumption couldprove useful in studies of differences between social andproblem drinkers, cognition and behavior while intoxicated,symptomatology (e.g., sensitization, tolerance, withdrawal,craving, relapse), and clinical intervention and preventionefforts.

The purpose of this study is to present and test a softwareprogram, the BrAC Estimator, that uses a comprehensivemathematical data analysis system to produce estimates ofBrAC from TAC data. (Note that from here on we refer toBrAC only, but that either BAC or BrAC estimates can beproduced from the software depending upon which type ofdata are input into the calibration models; for differencesbetween BAC and BrAC, see Hustad and Carey, 2005).Packaging these mathematical advancements in a softwareprogram intended for nonmathematicians makes these mod-els readily available for use by researchers, clinicians, andmedical professionals. The anticipated result of this softwareis the capability to analyze BrAC levels at the required reso-lution and finesse for a great variety of experimental andanalytic studies of alcohol-related phenomena.

Mathematical Models of the BrAC Estimator SoftwareProgram

The BrAC Estimator software program is based upon amathematically sophisticated first principles forward modelfor the transport of alcohol from the blood through the skinto the TAS sensor and its oxidation by the TAS sensor (fordetails on the mathematical models, see Dumett et al., 2008;Luczak et al., 2013; Rosen et al., 2013, 2014). Unlike abreath analyzer, which relies on a relatively simple modelfrom elementary chemistry (i.e., Henry’s Law) for theexchange of gases between circulating pulmonary blood andalveolar air that has been observed to be reasonably robustacross people, the transport and filtering of alcohol by theskin is more appropriately modeled (to be consistent withhuman physiology and physics) as a diffusion equation (i.e.,the standard linear Fick’s law of diffusion; see Okubo, 1980).The parameters for modeling and measuring this diffusionprocess vary based on a number of factors (e.g., skin layerthicknesses, TAS device anomalies) and thus need to be indi-vidually determined for each person wearing each device inorder to convert TAC output into more interpretable BrACvalues. Four parameters are needed to model this system,which can be obtained during an alcohol administration ses-sion where the individual wears a particular device and ismonitored for both TAC (via the TAS device) and BrAC(via a breath analyzer device) throughout the course of thesession. Once this calibration session is conducted and theparameters are determined for this individual and device, theparticipant can then wear the device in the field and the indi-vidualized model parameters can be used to convert theTAC data into estimates of BrAC for all subsequent drinking

episodes (without requiring any additional BrAC readingsbeyond those obtained during the initial calibration session).

The first 2 of the 4 model parameters are q1, whichdescribes the rate at which alcohol diffuses through the vari-ous layers of the skin, and q2, which describes the effectivenet rate at which alcohol enters and leaves the skin and isprocessed by the transdermal sensor. The software programuses the TAC and BrAC data from the alcohol calibrationsession to optimally choose values for the 2 parameters(denoted by q1* and q2*) and to produce a model of TACthat closely approximates the TAC data generated by theTAS device. As a result of filtering effects in this forward pro-cess model, however, the estimated BrAC signal can exhibitexcessive magnitude and/or oscillations that are nonphysical.To remedy this, 2 additional parameters (i.e., penalty terms)are required to regularize the problem and make the resultingsolutions more physically reasonable (Banks and Kunish,1989; Bertsekas, 1999; Bradley et al., 1977). These penalty,or regularization, parameters are r1 and r2. The software pro-gram uses the laboratory calibration data to optimallychoose r1 and r2 (denoted by r1* and r2*) so that the inver-sion or deconvolution process provides an optimal estimateof BrAC. All 4 parameters are combined in an impulseresponse function (a curve that represent the individualizedoutput response of the entire skin-TAC-TAS system to aninput consisting of an impulse of instantaneous durationwith BrAC of 0.001% alcohol), which represents the modelused to correctly transform the TAC data obtained fromthe TAS device into meaningful BrAC data (accurate interms of both magnitude and time) for that person wearingthat device.

It is important to note that, because this system modelsalcohol from the blood through the skin and TAS device(using BrAC and TAC data) back only to BrAC (not back toingestion or metabolism through the stomach, gut, or liver),that individual characteristics (e.g., gender, age, height,weight) and drinking episode characteristics (e.g., rate ofconsumption, stomach contents) that affect BrAC levels (seeWatson et al., 1980, 1981) do not change the parameters.This means that only the 1 set of individualized modelparameters is needed per person-device pair to model all sub-sequent drinking episodes.

User Interface of the BrAC Estimator Software Program

The BrAC Estimator software is run in Matlab on eitherApple or PC computers. It uses the Excel output file of TACdata from the TAS device software, adding the BrAC dataobtained by the breath analyzer during the calibration ses-sion into this file in a new column. The BrAC Estimator soft-ware can be run in either “auto” or “interactive” mode. Automode, which would most likely be used by a nonmathemati-cian, only requires the user to input time ranges for the startand stop of the baseline signal (the low-level noise signal thatis recorded by the TAS device when worn), alcohol calibra-tion session, and each drinking episode.

2244 LUCZAK AND ROSEN

The program output produces a BrAC estimate for everyTAC data point (depending on the TAS device, ranging fromevery 10 seconds to every 30 minutes) and writes these esti-mates into the original Excel file as a new column of data.The software also computes the peak BrAC (% alcohol),time of peak BrAC (hours), and area under the estimatedBrAC curve (% alcohol 9 hours) for each drinking episode,and plots the estimated BrACs and TACs as predicted by themodel; the raw BrAC from the breath analyzer and rawTAC from the TAS device are also included in these plots toallow for visual comparison.

Current Study

In this study, we examine the accuracy of the models cre-ated in both the calibration and estimation phases of theBrAC Estimator software. First, we test the accuracy of thecalibration phase by using different drinking episodes from asingle subject wearing 2 TAS devices to calibrate the models.If the models were fully accurate, the 4 model parameters(q1*, q2*, r1*, r2*) together would yield equivalent impulseresponse curves, regardless of which drinking episode wasused to calibrate the model. Additionally, the differencesbetween the raw (TAS device) and software-estimated TACdata and between the raw (breath analyzer) and software-estimated BrAC data as assessed by the indices of relativeerror and by BrAC summary scores (i.e., peak BrAC, time ofpeak BrAC, and area under the BrAC curve) would be small.Second, we test the accuracy of the estimation phase by com-paring the program’s output of BrAC summary scores withthose calculated from breath analyzer data.

MATERIALS ANDMETHODS

Procedure

All data were collected by 1 participant, the first author, whichwas not considered human subjects research by the University ofSouthern California Institutional Review Board. For 18 days, theparticipant wore 2 WrisTASTM 7 devices that were set to recordTAC measurements at 5-minute intervals and collected BrAC mea-surements every 15 to 30 minutes during drinking episodes with theAlco-Sensor IV (Intoximeters, Inc., St. Louis, MO).

In the laboratory calibration session (see Luczak et al., 2002), theparticipant consumed an alcoholic beverage evenly over 15 minutesto reach a peak BrAC of approximately 0.050 mg% as determinedby body water weight (Watson et al., 1980, 1981). BrAC wasrecorded every 15 minutes from the start of the session until return-ing to 0.000.

The participant continued to wear the TAS devices for the next17 days in the field trial. During each drinking episode, the partici-pant took BrAC readings every 30 minutes until the level returnedto 0.000 or in 1 episode until she went to sleep; in another episodewhere alcohol quantity was low, she took BrAC readings every15 minutes.

The breath analyzer is considered valid (�0.005) with deep lungbreaths taken after 15 minutes of not drinking alcohol, due tomouth alcohol affecting BrAC readings. To reduce this time periodin the field, the participant rinsed her mouth twice and refrainedfrom consuming alcohol for at least 5 minutes before taking eachBrAC reading. In 2 instances where the BrAC reading appeared to

be too high, she rinsed her mouth again, waited an additional5 minutes, and re-tested her BrAC; the initial BrAC value was thenomitted. Note that BrAC measurements would not be required fortypical study participants during the field trial (just during the labo-ratory calibration session where they would be obtained by trainedresearch staff), but to test the accuracy of the software program out-put, BrAC data were required for all drinking episodes in this study.

Data Analysis

At the end of the 18 days, the TAC data from the 2 devices weredownloaded into 2 Excel data files. BrAC data from the breath ana-lyzer were added to these files. The researcher (second author) ranthe software in auto mode.

We used 2 indices of model fit: (i) the relative L2 error, which isthe square root of the sum of squares of the difference between the 2signals being compared, and (ii) the relative L∞ error, which is themaximum absolute value of the difference between the 2 signalsbeing compared. The L2 error is a measure of the area between the 2curves whereas the L∞ error provides a uniform or upper bound forthe distance between the 2 curves. If the L∞ error is small, then theL2 error must be small as well. However, the converse is not neces-sarily true; it is possible for 2 signals to be close in an L2 sense (i.e.,they are close on average over that time interval) and still be farapart in the L∞ sense (i.e., the distance is far between the predictedand actual curve at a specific time or times in that interval).

We also evaluated the performance of the BrAC Estimator soft-ware using the 3 BrAC summary scores. We compared these scoresfrom the BrAC software (which we denote as the “Est BrAC”method) with the TAC data (“Raw TAC”), BrAC from a breathanalyzer (“Raw BrAC”), and Raw BrAC fit to a smooth piecewisepolynomial curve (“Spline BrAC”; Schultz, 1973).

RESULTS

Table 1 summarizes the 11 drinking episodes recordedover the 18 days. Figure 1 shows the 2 sets of TAC datafrom each TAS device along with the contemporaneousBrAC data from the breath analyzer (Datasets 1 and 2).From visual inspection of these 2 graphs, the general patternof TAC measurements is similar across the 2 TAS devices,although the TAC peak for the calibration episode is lowerin Dataset 2 than in Dataset 1.

Calibration Phase

Tables 2a,b present tabular calibration results for Data-sets 1 and 2, respectively, using each of the 11 drinking epi-sodes as the calibration session. The results of the calibrationphase using Episode 1 as the calibration session are displayedgraphically in Fig. 2 and are representative of the calibrationresults for each of the 11 drinking episodes (all plots avail-able upon request). From Fig. 2, it can be seen that the esti-mated TAC closely approximates the Raw TAC throughoutthe drinking episode and the estimated BrAC approximatesthe Raw BrAC closely for much of the drinking episode.

Model Parameters Across Devices and Episodes. The val-ues of the 4 optimal model parameters in the 2 datasets(shown in the top 4 rows of Tables 2a,b) indicate the calibra-tion results were consistent across the 2 TAS devices, despite

ESTIMATING BRAC FROMTRANSDERMAL ALCOHOL DATA 2245

the devices producing different TAC values. The relative L2

and L∞ error fit indices (shown in the middle 4 rows ofTables 2a,b) were also similar across the 2 datasets using anyof the 11 drinking episodes.

The models estimating TAC had an average relative L2

error (RETAC,2) of 14 to 15% (SD = 9%) and an average rel-ative L∞ error (RETAC,∞) of 18 to 20% (SD = 7%). Themodels estimating BrAC had an average relative L2 error(REBrAC,2) of 27% (SD = 9 to 11%) and an average relativeL∞ error in BrAC (REBrAC,∞) of 33 to 39% (SD = 12 to19%). It is clear, however, that there is variance among thecalibration models when created using TAC data from the11 different drinking episodes. This is illustrated in Fig. 3,which shows the variability of the impulse response functionswhen using each of the 11 drinking episodes to calibrate themodel.

Model Estimates of BrAC. The bottom half of Table 2shows the Est BrAC scores compared with those obtainedfrom Raw BrAC and Spline BrAC. Plots of all 11 episodesindicated Est BrAC matched well to the Raw BrAC. Onaverage, peak of Est BrAC (PeakEst), was within 0.004 (12%)of PeakSpline in both datasets. PeakEst only differed fromPeakSpline by more than 0.005 in Episodes 2 and 11. Notethat Episode 11 was one of the longer drinking sessions with3 drinks consumed over 2 hours. For time of peak BrAC,TimeEst differed from TimeSpline on average by 18 minutes(33 to 34%) in both datasets. TimeEst differed by <15 min-utes from TimeSpline for 5 episodes in each dataset, and by<30 minutes for all episodes except for Episode 4 (40 min-utes). In Episode 4, PeakEst only differed by 0.001 in Dataset1 and by 0.002 in Dataset 2 from PeakSpline, with the RawBrACs being 0.054, 0.057, and 0.055 over the hour that con-tained both TimeEst and TimeSpline, indicating little BrACvariation over this time. For the area under the BrAC curve,AUCEst was within 0.010 of AUCSpline for all episodes exceptfor Episode 5, which differed by 0.021 in both datasets.Episode 5 was the longest drinking episode, with 3 drinks

Table 1. Summary Data for the 11 Drinking Episodes

Drinkingepisode

BrACinterval(minutes) Alcohol type

Totaldrinks

Minutesof

drinking

Number ofBrAC

readings

Minutesof BrACreadings Comments

1 15 95% ethanol in 1:4 mixer 2 15 15 225 BrAC omitted at 90 minutes2 15 Bottle of beer 1 45 7 90 None3 30 Bottles of beer 2 75 8 150 None4 30 Pitchers of beer 3.5 150 9 225 Went to sleep at 225 minutes

when BrAC was 0.0365 30 Margaritas, bottle of beer, wine 3 300 14 420 BrAC omitted at 310 minutes6 30 Margarita 1 30 5 120 None7 30 Wine 1.5 90 6 150 Redid 2 BrACs that were high8 30 Bottle of beer 1 30 5 105 BrAC omitted at 30 minutes9 30 Bottle of beer, wine 2.5 120 9 250 Transdermal alcohol sensor off

from 235 to 245 minutes10 30 Wine 1 60 5 120 None11 30 Margaritas, wine 3 120 10 270 None

BrAC, breath alcohol concentration.

A

B

Fig. 1. Transdermal alcohol concentration (TAC; crosses) and breathalcohol concentration (BrAC) (dots) data for (A) Dataset 1 and (B) Data-set 2 . These 2 datasets were collected by the same participant over thesame 18 days using 2 transdermal alcohol sensor devices and a breathanalyzer.


consumed over 5 hours with intervals between drinks andmultiple BrAC peaks and declines. In summary, Est BrACsummary scores were similar to the Spline BrAC summaryscores across episodes. The episodes that had the largest dis-crepancy between the Est BrAC and Spline BrAC scoreswere different for each of the BrAC summary variables, butwere logical when examining both the drinking patterns andthe output differences.

Estimation Phase

We then used the model calibrated with Episode 1 todeconvolve the BrAC signal from the TAC signal for each ofthe subsequent 10 drinking episodes in each dataset (as

would be done in the usual protocol). The results are tabu-lated in Tables 3a,b, with the last 2 columns showing themean absolute difference and standard deviation of EstBrAC compared with the Spline BrACmodels. Figure 4 pro-vides graphic displays of some of the data summarized inTable 3. In Fig. 4A, we show the estimated BrAC curves forEpisode 7 from Dataset 2 where the BrAC Estimatorsoftware performed relatively well. In Fig. 4B, we show theresults of Episode 5 from Dataset 1 where the methodperformed less well.

Peak BrAC. For all 10 episodes, PeakEst had a meandifference from PeakSpline of 0.011 (�0.011) in Dataset 1and 0.006 (�0.006) in Dataset 2. The misfit for Episode 5

Table 2. Calibration Results Using Each of the 11 Drinking Episodes as the Calibration Session for (a) Dataset 1 and (b) Dataset 2

Drinking episode

M SD1 2 3 4 5 6 7 8 9 10 11

(a) Dataset 1Parameterq1* 0.93 0.47 1.55 0.29 2.35 0.46 0.82 0.53 1.11 2.27 0.63 1.04 0.721q2* 1.24 1.17 1.77 1.20 1.47 1.04 0.83 0.20 1.53 1.76 0.97 1.20 0.452r1* 0.10 0.10 0.10 0.21 0.16 0.11 0.11 0.10 0.19 0.14 0.10 0.13 0.040r2* 0.10 0.10 0.11 0.90 0.37 0.25 0.20 0.10 1.08 0.28 0.11 0.33 0.342

Relative errorRETAC,2 0.06 0.21 0.05 0.18 0.06 0.33 0.27 0.10 0.17 0.15 0.10 15% 9%RETAC,∞ 0.17 0.22 0.20 0.18 0.13 0.26 0.29 0.12 0.32 0.20 0.11 20% 7%REBrAC,2 0.24 0.38 0.20 0.18 0.19 0.37 0.17 0.35 0.19 0.17 0.49 27% 11%REBrAC,∞ 0.77 0.45 0.54 0.29 0.19 0.49 0.17 0.39 0.21 0.24 0.61 39% 19%

Peak BrACPeakRaw 0.052 0.023 0.036 0.057 0.052 0.023 0.018 0.017 0.026 0.013 0.048 – –PeakSpline 0.052 0.023 0.036 0.057 0.052 0.023 0.018 0.019 0.026 0.013 0.050 – –PeakEst 0.049 0.017 0.032 0.058 0.055 0.020 0.018 0.014 0.024 0.014 0.068 12% 12%

Time of peakTimeRaw 0.75 0.50 1.50 2.00 3.00 0.58 1.58 0.83 2.08 1.08 0.92 – –TimeSpline 0.75 0.50 1.50 1.83 2.92 0.67 1.50 0.58 2.08 0.92 1.17 – –TimeEst 0.67 0.83 1.00 2.50 2.50 1.08 1.50 0.67 2.25 1.00 1.67 33% 30%

Area under curveAUCSpline 0.110 0.016 0.077 0.168 0.201 0.029 0.027 0.020 0.055 0.018 0.120 – –AUCEst 0.110 0.016 0.087 0.167 0.222 0.026 0.026 0.017 0.057 0.017 0.111 6% 5%

(b) Dataset 2Parameterq1* 1.30 0.32 0.52 0.32 1.53 0.44 0.53 0.54 0.63 1.24 0.87 0.75 0.424q2* 1.63 2.32 2.19 1.15 1.56 1.21 1.29 2.13 1.56 2.07 0.87 1.64 0.484r1* 0.10 0.12 0.10 0.19 0.15 0.12 0.16 0.11 0.21 0.11 0.10 0.23 0.039r2* 0.10 0.08 0.11 1.08 0.48 0.29 0.37 0.09 0.90 0.20 0.11 0.35 0.346

Relative errorRETAC,2 0.07 0.15 0.04 0.19 0.06 0.34 0.24 0.10 0.17 0.12 0.07 14% 9%RETAC,∞ 0.16 0.24 0.07 0.18 0.17 0.27 0.23 0.13 0.31 0.16 0.09 18% 7%REBrAC,2 0.23 0.41 0.23 0.18 0.19 0.38 0.21 0.35 0.18 0.16 0.41 26% 9%REBrAC,∞ 0.41 0.44 0.27 0.27 0.20 0.49 0.23 0.44 0.20 0.21 0.49 33% 12%

Peak BrACPeakRaw 0.052 0.023 0.036 0.057 0.052 0.023 0.018 0.017 0.026 0.013 0.048 – –PeakSpline 0.052 0.023 0.036 0.057 0.052 0.023 0.018 0.019 0.026 0.013 0.050 – –PeakEst 0.057 0.015 0.037 0.059 0.057 0.021 0.018 0.014 0.025 0.014 0.063 11% 11%

Time of peakTimeRaw 0.75 0.50 1.50 2.00 3.00 0.58 1.58 0.83 2.00 1.08 0.92 – –TimeSpline 0.75 0.50 1.50 1.83 2.92 0.67 1.50 0.58 2.08 0.92 1.17 – –TimeEst 0.83 0.83 1.00 2.42 2.50 1.17 1.50 0.75 2.17 0.83 1.67 34% 33%

Area under curveAUCSpline 0.106 0.016 0.077 0.168 0.201 0.029 0.027 0.020 0.055 0.018 0.120 – –AUCEst 0.109 0.016 0.081 0.166 0.222 0.026 0.026 0.016 0.054 0.018 0.111 6% 6%

q1* and q2*, optimal parameter estimates; r1* and r2*, optimal regularization parameter estimates; RE, relative error; TAC, transdermal alcohol concen-tration; 2, L2 error; ∞, L∞ error; Peak, peak breath alcohol concentration (BrAC) score (% alcohol); Time, time of peak BrAC (hours); AUC, area under theBrAC curve (% alcohol 9 hours); Raw, breath analyzer BrAC; Spline, spline curve fit to the breath analyzer BrAC; Est, BrAC Estimator software.


using the Est BrAC was larger in Dataset 1 (0.038) than inDataset 2 (0.022), which contributed to the difference inaverage peak differences across datasets. Peak values werewithin 0.005 of PeakSpline for half of the episodes and onlyabove 0.020 for Episode 5. Raw TAC provided similar esti-mates of peak BrAC in both datasets, with PeakTAC differ-ing from PeakSpline on average by 0.007 (�0.007) in Dataset1 and 0.006 (�0.006) in Dataset 2.

Time of Peak BrAC. TimeEst differed on average fromTimeSpline by 30 (�20) minutes, the typical interval betweenRaw BrAC readings. When examined for each episode,TimeEst was within 15 minutes of TimeSpline for 9 (41%) epi-sodes and within 30 minutes for all episodes except Episode

4 (65 minutes), which was the second longest drinking epi-sode at 150 minutes of drinking with the steady BrAC level(within 0.003) for over an hour. TimeTAC was on averageover an hour (70 � 29 minutes) later than TimeSpline, beingover an hour later in 17 (77%) episodes and not within15 minutes of TimeSpline for any episode.

Area Under BrAC Curve. AUCEst differed fromAUCSpline on average 0.024 for Dataset 1 and 0.014 forDataset 2. AUCEst was within 0.010 for 11 (50%) episodes,but above 0.025 for 5 (23%) episodes. The variability acrossdatasets is likely due in part to the software program select-ing slightly different start and stop points for the drinkingepisode given the baseline level of noise of the individual sen-sors. AUCTAC differed on average from AUCSpline by 0.024

A

B

Fig. 2. Transdermal alcohol concentration (TAC) and breath alcoholconcentration (BrAC) calibration results for Drinking Episode 1 for (A)Dataset 1 and (B) Dataset 2. The upper panels show the Raw TAC(crosses) along with the Est TAC (solid line). The lower panels show theRaw BrAC (dots) along with the Est BrAC (solid line) obtained by using theoptimal values of the model (q1*, q2*) and regularization (r1*, r2*) parame-ters to deconvolve the TAC data shown in the upper panels.

A

B

Fig. 3. Calibrated impulse response functions for all 11 drinking epi-sodes for (A) Dataset 1 and (B) Dataset 2. Each line labeled Event No. 1 to11 represents the impulse response function determined by drinkingEpisodes 1 to 11, respectively. These functions indicate the BrAC Estima-tor software calibration results were consistent across the 2 datasets, butthat there is a substantial variance among the models created using the 11different drinking episodes.


in Dataset 1 and 0.028 in Dataset 2 and was within 0.010 for12 (55%) episodes, but above 0.025 for 7 (31%) episodes.Thus, the AUCEst and AUCTAC were similar.

DISCUSSION

Calibration Phase

The BrAC Estimator software was able to fit each individ-ual drinking episode well (based on fit indices, BrAC sum-mary scores, and visual comparison of TAC and BrACplots), suggesting that diffusion as modeled by 4 parametersis an appropriate paradigm to describe the transdermaltransport of alcohol from the blood through the skin to theTAS device. Our results also indicate that there was variancein the values of the optimal model parameters across the 2TAS devices, highlighting the need to calibrate the model notjust to the individual, but also to the device. Despite the dif-ferences in the raw TACs across devices, the BrAC Estimatorsoftware created consistent models for the 2 TAS devices thatyielded similar BrAC estimates.We also found variation in BrAC Estimator software

models when the calibration was conducted using differentdrinking episodes. There are a number of mathematical

approaches that might improve the performance of theBrAC Estimator method. One such technique is a fre-quency domain analysis of the different drinking episodes,which could potentially help us to identify drinking pat-terns that could then be correlated with the different val-ues of the parameters. It is possible that the values of theparameters themselves may serve to characterize differentdrinking patterns or profiles. To explore this, we recali-brated the model using Episodes 3 and 8 from Dataset 2,which produced similar parameter values, and theninverted the other episode. With the model calibratedusing Episode 3 instead of Episode 1, BrAC software esti-mates for Episode 8 improved for peak BrAC from 0.019to 0.017 (peak Raw BrAC was 0.017), relative L2 errorimproved from 0.004 to 0.003, and relative L∞ errorimproved from 0.008 to 0.005 (see Fig. 5). With the modelcalibrated using Episode 8 instead of Episode 1, softwareestimates for Episode 3 improved for peak BrAC from0.043 to 0.039 (peak Raw BrAC was 0.036), relative L2

error improved from 0.017 to 0.009, and relative L∞ errorimproved from 0.015 to 0.008 (see Fig. 6). Thus, a moreintricate alcohol calibration protocol yielding a richer cali-bration dataset and a procedure involving gain schedulingmay improve the accuracy of the model estimates.

Table 3. Inversion Results for the 11 Drinking EpisodesWith Model Calibrated on Drinking Episode 1 for (a) Dataset 1 and (b) Dataset 2

Drinking episode

M diff SD1 2 3 4 5 6 7 8 9 10 11

(a) Dataset 1PeakPeakRaw 0.052 0.023 0.036 0.057 0.052 0.023 0.018 0.017 0.026 0.013 0.048 – –PeakSpline 0.052 0.023 0.036 0.057 0.052 0.024 0.018 0.017 0.026 0.014 0.049 – –PeakTAC 0.035 0.017 0.050 0.057 0.074 0.022 0.018 0.017 0.036 0.020 0.044 0.0074 0.00747PeakEst 0.050 0.022 0.056 0.066 0.090 0.029 0.019 0.024 0.041 0.030 0.057 0.0114 0.01094

Time of peakTimeRaw 0.75 75.00 95.75 123.25 144.00 166.08 192.08 217.17 240.67 265.08 335.75 – –TimeSpline 0.75 75.00 95.75 123.08 143.92 166.25 192.00 217.17 240.75 264.83 336.00 – –TimeTAC 1.17 76.17 96.25 125.17 145.50 167.42 193.25 217.67 242.33 265.67 337.17 1.108 0.5221TimeEst 0.67 75.50 95.17 124.17 143.25 166.83 192.25 217.17 241.25 264.75 336.50 0.492 0.3185

Area under curveAUCSpline 0.106 0.016 0.076 0.156 0.200 0.027 0.027 0.016 0.056 0.018 0.119AUCTAC 0.092 0.014 0.131 0.094 0.329 0.026 0.028 0.017 0.087 0.027 0.123 0.0282 0.04011AUCEst 0.101 0.022 0.128 0.134 0.292 0.039 0.036 0.027 0.088 0.038 0.120 0.0241 0.02691

(b) Dataset 2PeakPeakRaw 0.052 0.023 0.036 0.057 0.052 0.023 0.018 0.017 0.026 0.013 0.048 – –PeakSpline 0.052 0.023 0.036 0.057 0.052 0.024 0.018 0.017 0.026 0.014 0.049 – –PeakTAC 0.052 0.017 0.052 0.061 0.072 0.022 0.017 0.014 0.033 0.017 0.040 0.0064 0.00634PeakEst 0.057 0.018 0.043 0.051 0.074 0.023 0.017 0.016 0.030 0.020 0.037 0.0063 0.00610

Time of peakTimeRaw 0.75 75.00 95.75 123.25 144.00 166.08 192.08 217.17 240.67 265.08 335.75 – –TimeSpline 0.75 75.00 95.75 123.08 143.92 166.25 192.00 217.17 240.75 264.83 336.00 – –TimeTAC 1.25 76.25 97.17 125.17 144.92 167.67 193.42 217.83 242.17 265.85 337.49 1.2209 0.43640TimeEst 0.83 75.60 95.58 124.17 143.42 166.92 192.25 217.25 241.33 264.85 336.65 0.4682 0.33329

Area under curveAUCSpline 0.106 0.016 0.076 0.156 0.200 0.027 0.027 0.016 0.056 0.018 0.119 – –AUCTAC 0.123 0.012 0.115 0.105 0.322 0.019 0.019 0.009 0.072 0.020 0.111 0.0236 0.03547AUCEst 0.101 0.016 0.097 0.108 0.222 0.027 0.025 0.017 0.058 0.025 0.078 0.0138 0.02725

Diff, difference; Peak, peak breath alcohol concentration (BrAC) or transdermal alcohol concentration (TAC) score (% alcohol); Time, time of peak(hours); AUC, area under the curve (% alcohol 9 hours); Raw, breath analyzer BrAC; Spline, spline curve fit to the breath analyzer BrAC; Est, BrACEstimator software.


Another mathematical approach that might improve theperformance of the BrAC Estimator software would be toreplace the linear diffusion model with a more sophisticatednonlinear paradigm. This technique would allow the diffusiv-ity constant q1 to depend on the alcohol concentration and/or the gradient of alcohol concentration at that depth in theskin. Such a modification would add a significant level ofcomplexity to both the mathematical analyses and computa-tions that may improve model fit.

Estimation Phase

In the estimation phase, the BrAC Estimator softwaremodels were able to compensate for the attenuation of peakBrAC and the latency of the time of peak BrAC typicallyobserved in TAC data, as well as the variation in TAC data

across devices, to produce consistent measures of BrAC. Thesoftware modeling did not appear to be affected by eating(e.g., empty stomach in Episode 6, eating while drinking inEpisode 10, and drinking after eating in Episode 4), whichwas expected given the mathematical models in the softwareuse BrAC data, an indicator of alcohol in the bloodstream(alcohol that has already passed through the gut). The BrACEstimator software was better (in terms of BrAC summaryscores) at estimating drinking episodes that had clear ascend-ing and descending limbs (e.g., Episodes 2 and 7). The soft-ware models performed less well for drinking sessions whenalcohol was consumed sporadically over a longer periods oftime, resulting in relatively even levels of BrAC for long timeperiods or multiple ups and downs in BrAC levels (e.g., Epi-sodes 5 and 11). In addition, less distinct start and stop timepoints for these drinking episodes also likely contributed tothe relatively poorer estimate of the area under the curve.The plots of BrAC modeled by the software for the moreplateaued drinking episode curves, however, still mappedonto the raw TAC and raw BrAC values relatively well.Thus, it appears the fit of the BrAC Estimator modeling maybe more affected by the shape of the drinking curve and dis-cernable start and stop points than by level of peak BrAC orstomach content, although additional modeling of the shapeof the curve using signal processing tools and frequencydomain analysis are needed to mathematically support theseobservations.

The software estimates of peak BrACmeasure were withinthe�0.005 reported error range of the breath analyzer for allbut 2 drinking episodes, and were within 0.020 (the equiva-lent of approximately 1 standard drink) for all episodes. Theraw TAC peak estimates, however, had similar accuracy lev-els as the software models, as did the area under the curvefor most episodes. The most noteworthy improvement pro-duced by the BrAC Estimator software compared with theraw TAC data was for time of peak BrAC. These estimateswere improved by over 30 minutes on average, being within20 to 30 minutes of the breath analyzer peak (obtained at 30-minute intervals) as compared with being on average over anhour delayed for the raw TAC data. The raw TAC techniqueis attractive in that it requires no active participation by thesubject in collecting the data with the exception of having toproperly wear the TAS sensor. The BrAC Estimator soft-ware method requires a laboratory calibration session priorto the field trial, but no active participation by the subjectduring naturalistic drinking episodes. Thus, if it is appropri-ate to administer alcohol to an individual in the laboratory,the BrAC Estimator software can improve accuracy of BrACestimates in the field, particularly the time displacement,without incurring real-time subject burden.

Limitations and Future Directions

Our findings should be viewed within the limitations ofthis study. First, this dataset only contained 11 drinking epi-sodes over 18 days, although it did include 93 BrAC readings

A

B

Fig. 4. Drinking episode results: (A) Episode 7 in Dataset 2 on whichthe method performed well, and (B) Episode 5 in Dataset 1 on which themethod performed less well. These panels show results of calculating esti-mated breath alcohol concentration (BrAC) with the software (Est BrAC;dashed line) compared with a breath analyzer (Raw BrAC, crosses) and atransdermal alcohol sensor device (Raw transdermal alcohol concentration[TAC]; dots).


taken over 35 hours (10 hours of drinking) with very fewmissing data points and data from 2 TAS devices; thus, itwas relatively comprehensive for each drinking episode. Sec-ond, how our findings from a single subject fit with differenttypes of subjects and higher alcohol quantities needs to bedetermined. The model, however, was able to fit all 22 epi-sodes in the 2 datasets. Furthermore, we do not expect differ-ences in model fit based on individual characteristics thataffect BrAC levels (e.g., age, gender, height, weight), giventhe BrAC scores already account for these, or that affectmodel parameters (e.g., skin thickness), given the model iscalibrated to the individual and device. Finally, we used thebreath analyzer data to compare with software results, butrecognize that raw BrAC data are also subject to error andare only recorded at 30-minute intervals. Thus, the rawBrAC peak levels and times likely missed higher BrAC levelsthat occurred between data collection time points, which

could underestimate the accuracy of the software BrAC sum-mary scores.These limitations can be addressed in future research that

tests the BrAC Estimator modeling program across a varietyof consumption patterns and a range of peak BrACs in boththe calibration session and field trial and with additional par-ticipants. More varied alcohol administration protocols forthe calibration session(s), together with gain scheduling andnonlinear models, may also improve model fit.In conclusion, this research provides information for

understanding how the TAS device, while currently in rela-tively early stages of development, may be used to generatequantitative measures of BrAC in real-time drinking epi-sodes. With the development the BrAC Estimator softwareprogram to calculate these models for nonmathematicians,the TAS technology becomes a more informative tool foralcohol researchers and clinicians.

A

B

Fig. 6. Model results for Episode 3 in Dataset 2 when calibrated by Epi-sode 1 (A) and Episode 8 (B). These graphs indicate improvement inmodel fit when calibrating the model with a drinking episode that more clo-sely matched the episode being inverted.

A

B

Fig. 5. Model results for Episode 8 in Dataset 2 when calibrated by Epi-sode 1 (A) and Episode 3 (B). These graphs indicate improvement inmodel fit when calibrating the model with a drinking episode that more clo-sely matches the episode being inverted.


ACKNOWLEDGMENTS

This study was funded by National Institutes of Healthgrant R21AA17711 and a grant from the Alcoholic BeverageMedical Research Foundation. These funding sources hadno other role other than financial support.

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Estimating BrAC from Transdermal Alcohol Concentration Data Using the BrAC Estimator Software Program