Carcinogens for Geniusalert92 only

Risk Analysis, Vol. 29, No. 12, 2009 DOI: 10.1111/j.1539-6924.2009.01311.x

The Use of Multizone Models to Estimate an Airborne Chemical Contaminant Generation and Decay Profile: Occupational Exposures of Hairdressers to Vinyl Chloride in Hairspray During the 1960s and 1970s

Jennifer Sahmel,1,∗ Ken Unice,2 Paul Scott,2 Dallas Cowan,1 and Dennis Paustenbach3

Vinyl chloride (VC) was used as a propellant in a limited percentage of aerosol hairspray products in the United States from approximately 1967 to 1973. The question has arisen whether occupational exposures of hairdressers to VC-containing hairsprays in hair salons were sufficient to increase the risk for developing hepatic angiosarcoma (HAS). Transient two-zone and steady-state three-zone models were used to estimate the historical airborne concentration of VC for individual hairdressers using hairspray as well as estimated contri- butions from other hairdressers in the same salon. Concentrations of VC were modeled for small, medium, and large salons, as well as a representative home salon. Model inputs were determined using published literature, and variability in these inputs was also considered using Monte Carlo techniques. The 95th percentile for the daily time-weighted average expo- sure for small, medium, and large salons, assuming a market-share fraction of VC-containing hairspray use from the Monte Carlo analysis, was about 0.3 ppm, and for the home salon scenario was 0.1 ppm. The 95th percentile value for the cumulative lifetime exposure of the hairdressers was 2.8 ppm-years for the home salon scenario and 2.0 ppm-years for the small, medium, and large salon scenarios. If using the assumption that all hairsprays used in a salon contained VC, the 95th percentile of the theoretical lifetime cumulative dose was estimated to be 52–79 ppm-years. Estimated lifetime doses were all below the threshold dose for HAS of about 300 to 500 ppm-years reported in the published epidemiology literature.

KEY WORDS: Airborne contaminants; exposure modeling; hairdresser; three-zone model; two-zone model; vinyl chloride

1. INTRODUCTION

Vinyl chloride (VC) is a colorless chlorinated hydrocarbon compound with a sweet odor that ex- ists as a gas at room temperature. The primary use of VC is as a precursor to the chemical intermedi-

1ChemRisk, LLC, Boulder, CO, USA. 2ChemRisk, LLC, Pittsburgh, PA, USA. 3ChemRisk, LLC, San Francisco, CA, USA. ∗Address correspondence to Jennifer Sahmel, Supervising Health

Scientist, 4940 Pearl East Circle, Boulder, CO 80301, USA; tel: 303-417-1046; fax: 303-417-1066; [email protected].

ate polyvinyl chloride (PVC), a component of plas- tic pipes, wall coverings, wire coatings, and vehicle parts. Due to its chemical properties and apparent low toxicity, VC was also used during the 1960s and early 1970s as a propellant in aerosol insecticides, spray paints, and other consumer products. Nonpro- pellant uses including as a refrigerant and inhalable anesthetic have also been documented until its use in consumer products was banned in 1974.(1−3) VC alone has no current consumer applications; it is a confirmed human carcinogen and a highly regulated chemical.

1699 0272-4332/09/0100-1699$22.00/1 C© 2009 Society for Risk Analysis

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1.1. VC Toxicity

In the early 1960s, the American Conference of Governmental Industrial Hygienists’ (ACGIH) Threshold Limit Value (TLV) for VC was 500 ppm; Patty’s Industrial Hygiene and Toxicology reported that VC was of relatively low toxicity.(4−6) The tox- icity of VC was established in the early 1970s from case studies of the PVC manufacturing sector, which experienced the highest documented exposures to this compound. Routine maintenance work during PVC production resulted in airborne VC concentra- tions up to 1,000 ppm during the tasks of tank clean- ing and the manual removal of partially polymer- ized PVC from vessel walls with spatulas. These high levels of exposure are believed to have produced a specific pathological syndrome called “vinyl chloride disease.”(7) Symptoms included CNS depression re- sembling alcohol intoxication, headache, dizziness, and acroosteolysis (bone loss and ulceration in the extremities), as well as damage to the liver, spleen, cardiovascular, respiratory, and circulatory sys- tems.(8) In 1971, the first long-term animal study appeared, which reported a possible link between VC exposure and carcinogenic activity, including the possibility of increased incidence of skin, respira- tory, and bone tumors. However, concerns about the methods used in the study resulted in addi- tional toxicological and epidemiological studies on VC.(9) VC was initially linked to a rare form of liver cancer known as hepatic angiosarcoma (HAS) in PVC manufacturing workers through published stud- ies in 1974.(10,11) Subsequent studies have confirmed the link between VC exposures and HAS.(12,13)

HAS has been linked to four different risk fac- tors, including exposures to VC, inorganic arsenic, androgenic anabolic steroids, and thorium dioxide (Thorotrast). For nearly 75% of angiosarcoma cases, however, the cause is unknown.(12) A physiologi- cally based pharmacokinetic (PBPK) model devel- oped to predict cancer risk from VC exposure found that cancer incidence predicted using animal models overestimated the incidence in humans.(14)

1.2. VC Epidemiology and Occupational Exposure Limits

HAS is a rare form of liver cancer even among high-risk populations.(15) During the late 1970s and early 1980s, estimates of HAS incidence within the general population ranged from 0.4 to 2.5 per 10,000,000 in the United States and Europe.(12,16−18)

The range of cumulative VC exposures necessary to increase the risk of disease has also been determined from epidemiology studies. The largest published study to date of PVC workers with documented oc- cupational exposures to VC found no increase in rel- ative risk for HAS below 500 ppm-years of cumula- tive exposure to VC, and also found that the lowest cumulative lifetime exposure to VC for which a doc- umented HAS case occurred was 288 ppm-years.(18)

The latency period associated with VC-related HAS is estimated to be approximately 21 years, with no case identified before 15 years following the first exposure.(18,19)

Following the early epidemiological studies men- tioned above as well as investigations by the Na- tional Institute for Occupational Safety and Health (NIOSH) and the U.S. Congress, the U.S. Occupa- tional Safety and Health Administration (OSHA) reduced the VC permissible exposure limit (PEL) from 100 ppm (parts per million) to 1 ppm in 1974. At the same time, the U.S. Consumer Prod- uct Safety Commission (CPSC) banned the use of VC in consumer products in the United States. Cur- rent occupational exposure limits (OELs) for VC set by both OSHA and ACGIH remain at 1 ppm. Fig. 1 illustrates historical occupational exposure limits established by ACGIH and OSHA for VC

Fig. 1. Occupational exposure limits for VC over time: ACGIH TLV and OSHA PEL. Solid and dotted lines indicate contempo- raneous exposure guidelines as established by the American Con- ference of Governmental Industrial Hygienists (dotted line) and the Occupational Safety and Health Administration (solid line). Guidelines are expressed in parts per million (ppm).

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1701

beginning in 1946. The VC ban in consumer prod- ucts has remained in place, and the rates of HAS in the general population remain exceedingly low. Among VC workers and other high-risk subgroups, Zocchetti estimated that an increased incidence of HAS of 1,000 times that found in the general popula- tion would only produce one to two cases per year in 10,000 individuals.(15)

In the late 1960s and early 1970s, when VC was used as a propellant in a variety of consumer prod- ucts, many individuals could have been exposed to varying concentrations of VC from either occupa- tional or consumer uses. In particular, the use of VC in occupational settings by hairdressers or hair stylists presents a scenario for which frequent ex- posures might have occurred over time. However, an excess incidence of HAS or other liver cancers has not been found in epidemiological studies of hairdressers.(20−24)

1.3. Hairspray Product Use in the United States During the Time Period of Interest

According to a 1972 U.S. consumer industry analysis, approximately one-half of all American women used hairspray in the early 1970s. Sales of hairsprays grew at about 5.1% per year from 1967 to 1972, a much lower annual increase compared with the first half of the 1960s, and was associated with the rising increase in popularity of more relaxed and nat- ural hairstyles in the late 1960s.(25,26)

Hairsprays in the early 1970s typically consisted of a resin that was capable of forming a thin film on the hair surface (1.5–2% by weight of the for- mulation), ethyl alcohol (42–58% by weight of the formulation), and propellants (30–50% by weight of the formulation). Certain hairsprays also contained additives such as plasticizers, conditioners, and pro- teins. U.S. consumer data in 1972 indicated that there were approximately 150 different brands of hairspray in the market. Sales were highest for the Aqua Net, Breck, and Alberto VO5 brands. Sales of hairsprays to beauty parlors were estimated at about $35 million at the manufacturing level in 1972. Leading brands included La Maur, Alberto-Culver, and Fabergé.(26)

The purpose of our study was two-fold: first, we wanted to present a multizone modeling approach that could provide robust estimates of both expo- sure and risk that could be used in a wide variety of consumer product risk assessments. Second, we wanted to address a concern among the population of hairdressers who believe they could be at increased

risk for HAS as a result of using VC-containing hairsprays prior to 1974. We were unable to find any published studies that measured VC-containing hairspray use among hairdressers. As a result, we used several modeling approaches with multiple con- centration zones (based on contaminant generation source, generation rate, and ventilation characteris- tics, among other factors) to characterize airborne concentrations of VC in salons. The study focuses on VC in aerosol hairspray products for hairdressers in the United States prior to the CPSC ban on the sale of VC-containing consumer products in 1974. In order to characterize possible differences in ex- posure potential and risk related to salon size, sev- eral possible salon sizes were evaluated. Specifically, four scenarios were considered, including a home sa- lon with a single stylist, a small professional salon with an average of two stylists, a medium-sized pro- fessional salon with an average of four stylists, and a large professional salon with an average of nine stylists. A Monte Carlo uncertainty and sensitivity analysis was also conducted. The estimated airborne concentrations and associated cumulative dose esti- mates were then compared against hairspray propel- lant measurement studies and epidemiology studies in the published literature.

2. METHODOLOGY

In order to more accurately estimate the air- borne concentrations in a salon in which a hair- dresser might work, as well as the background con- centrations of VC due to the use of hairspray by other hairdressers, a multizone approach was used to incorporate both types of exposures. First, a two- zone transient model was used for the assessment of hairdresser exposures in a commercial salon en- vironment. Second, both the transient two-zone and a steady-state three-zone model were used to assess hairdresser exposures in a residential environment. Finally, a steady-state mixing factor model was used to confirm and compare against the results of the primary transient two-zone model, mainly to ensure that the results were not dependent upon the model selected.

Estimates of airborne concentration were gener- ated for two types of VC-containing hairspray usage conditions: first, exposure estimates were calculated based on the estimated percentage of hairsprays con- taining VC. This was based on the market availability of these hairsprays. Second, exposure estimates were also calculated for a hypothetical situation in which

1702 Sahmel et al.

all of the hairsprays used in a salon contained VC. Three types of exposure estimates were computed: (a) 15-minute peak concentrations for the period im- mediately after applying hairspray, (b) 8-hour time- weighted averages (TWAs) over a typical salon work day, and (c) working-life VC exposures over the pe- riod in which VC was reported in U.S. hairspray (for the purposes of comparison to occupational exposure limits or risk criteria).

Once point estimates were calculated based on the most likely parameter for each of the four sa- lon scenarios using either the two-zone (commercial and residential salons) or three-zone (residential sa- lon only) model, a Monte Carlo uncertainty and sen- sitivity analysis was conducted. These were intended to characterize the range of possible results based on the parameter uncertainty, and to understand the magnitude of the effect of each of the different pa- rameters on the final model results (i.e., parameter sensitivity). This type of analysis is extremely use- ful for evaluating the uncertainty, for example, lack of precision, in the point estimates for total cumula- tive VC exposure. It also enables one to understand the impact of the unknown precision of certain indi- vidual model parameters. A 95th percentile value for the airborne concentration for each scenario was also calculated using this method to characterize the pos- sible exposure of a worker at the upper end of the distribution.

Following the estimation of exposure concentra- tions using the multizone approach, cumulative ex- posure estimates were calculated for each of the four salon scenarios. Cumulative exposure estimates were calculated assuming a potential exposure time of 8 hours per day, 5 days per week, and 50 weeks per year, and were reported in units of ppm-years. This dose metric allowed for comparison to the epi- demiological literature on VC. Finally, the calculated concentrations were compared to measured data col- lected by Hoffman, which assessed concentrations of hairspray propellants in a working salon prior to 1974.(27)

2.1. The Transient Two-Zone Model

Nicas presented a two-zone model for the pre- diction of both time-variable near-field (NF) breath- ing zone and far-field (FF) room airborne particulate or chemical concentrations in occupational exposure situations.(28) This model was modified to incorpo- rate hairspray usage patterns and generation rates. Model symbols and abbreviations are provided in

Appendix A and a complete list of equations is pro- vided in Appendix B. Briefly, the near field and far field were defined by a pair of coupled mass balance equations:

VN × dCN = [change in mass in NF zone] = (GE/C F1) × dt

+ β × CF dt − β × CN × dt = [mass generated inside NF zone]

+ [mass entering NF from FF zone] − [mass leaving NF zone] (1)

VF × dCF = [change in mass in FF zone] = β × CN × dt − [β + Q] × CF × dt = [mass entering from NF zone]

− {[mass leaving FF and entering NF zone] + [mass leaving FF zone and exhausted outside]}

(2 )

where VN and VF represented the volumes of the NF and FF zones (m3), CN and CF were the NF and FF airborne concentrations (ppm), GE was the constant mass emission rate (mg/min), β was the airflow rate between the NF and FF zones (m3/min), Q the effec- tive room supply air rate (m3/min), CF 1 was a conver- sion factor (mg/m3 per ppm at standard temperature and pressure), and dt was an infinitesimal time inter- val (min) (Appendix A). Each zone in the model was assumed to be well mixed with airflow between the zones (β) dictated by the magnitude of random air- flow (i.e., dispersion) or induced air movements (i.e., fans or blowers) in the space of interest. To construct a daily exposure history, the concentration profiles for multiple hairspray events were superimposed and two sets of solutions to Equations (1) and (2) were used to account for both times during spraying (GE > 0) and after spraying (GE = 0) (Appendix B). The worker’s airborne breathing zone concentration con- sisted of the summation of a worker’s own hairspray usage plus the background contribution of hairspray from co-worker usage.

Ventilation in the FF was defined by the effec- tive room supply air rate (Q) and was comparable to studies of minimum ventilation requirements and the American Society for Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) room ven- tilation recommendations typically presented in units of cubic feet per minute (cfm). Considering the align- ment of a hairdresser and the aerosol hairspray can,

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1703

Fig. 2. Conceptual schematic of the two-zone model as applied to a hairspraying scenario. Air exchange in the near field is repre- sented by β while far-field air exchange is represented by Q. The near field is approximated by a hemisphere with the vertical axis in line with the hairdresser’s body while standing behind a customer.

the NF was defined as a hemisphere sliced on the ver- tical axis with the base in line with the hairdresser’s body. A hemisphere radius (RN ) of approximately arm’s length or 0.78 m (2.5 ft) was selected for the hairspray scenarios, consistent with the conventional industrial hygiene definition of the breathing zone (Fig. 2)(29) as well as other published studies that have used the transient two-zone model. The two- zone model has been used to predict chemical or par- ticulate exposure for a diverse range of published ex- posure scenarios (Table I).

Equations (1) and (2) do not account for the frac- tion of products that contained VC. Historical doc- umentation indicated that the majority of products between 1967 and 1974 did not contain VC (see de- tailed discussion below); therefore, cumulative expo- sure (ppm-year) model outputs were subsequently adjusted to account for the estimated fraction of products containing VC (FC).

The sensitivity analysis conducted for the results of the transient two-zone model relied upon Monte Carlo statistical techniques to estimate the plausi- ble range of exposures to VC that a stylist might have experienced. The 95th percentile exposure es- timate for each scenario was used to characterize the likely high-end exposure of a worker at the upper end of the exposure distribution. A high-end exposure estimate is defined as conceptually greater than the 90th percentile of the population distribution but not beyond the true maximum exposure.(30) A software

package from Decisioneering Inc. (Boulder, CO) was used to perform this analysis.

2.2. The Three-Zone Steady-State Model

For the home salon scenario, in addition to the transient two-zone model, a three-zone steady-state model consisting of the breathing zone (zone 1), room of use (i.e., home salon, zone 2), and rest of home (zone 3) was used to investigate whether the predicted breathing zone concentration was ap- preciably underestimated by combining together the volume of the room of use and rest of home in the two-zone model.(31) A system of equations represent- ing the mass balance for the three zones was used to calculate the steady-state concentration in each zone (Appendix B). In this model, natural airflow between zones was assumed with balanced flow (i.e., flow from the rest of the home to the salon exactly balanced by flow from the rest of home to the salon). Whole house air exchange was allocated to the salon and rest of home based on the fractional volume of each zone.

2.3. The Steady-State Mixing Factor Model

Although the multizone models were selected as the primary models for this analysis, the steady- state mixing factor model was used for comparison to examine the reproducibility of the model estimates. The multizone models were used because the tran- sient “personal exposure cloud,” which is thought to occur while using hairspray, cannot be easily rep- resented by a conventional steady-state model that pairs the assumptions of a well-mixed room with a safety factor to account for imperfect mixing. However, the steady-state mixing factor model is a frequently used approach described in a number of industrial hygiene texts including the OSHA Techni- cal Manual, ACGIH Manual of Recommended Prac- tice for Design, and AIHA Mathematical Models for Estimating Occupational Exposures to Chemi- cals.(28,32,33) Although the mixing factor approach has been criticized for defying the law of conservation of mass, reasonable agreement between the two-zone model and the steady-state model is achievable with the careful and appropriate selection of mixing fac- tors.(28,34) The steady-state model was included in this assessment to evaluate whether the study con- clusions were affected by model selection.

Gaffney et al. (2008) presented a methodology for relating the steady-state mixing factor model

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Table I. Comparison of Application of Two-Zone Model for Commercial Beauty Salons to Other Applications Reported in Peer-Reviewed Literature (29,34,79−90,92,93)

Study Author (Country) Year Scenario Chemical(s)

Near-Field Geometry (Volume)

Flow Rate Between Near Field and

Far-Field Far-Field Air

Change Rate

Sahmel (model shown in Figure 2)

2008 Occupational use of hairspray

Vinyl chloride Hemisphere around breathing zone of radius arm’s length, or 0.78 m [2.5 feet] (1 m3)

5.7 m3/min to 23 m3/min based on random air speed of 0.05–0.20 m/sec

Small salon: 1.3–3.2 Medium salon: 1.3–4.5 Large salon: 3.0–6.9

Gaffney (United States)

2008 Cleaning semiconductor wafers

Methanol Hemisphere above table of radius 1 m (2.1 m3)

11.3 m3/min 5.1–9.5 per hour

Armstrong (United States)

2007 Quantitative microbial risk assessment (QMRA) model for Legionnaires’ disease at whirlpool spa

Legionella Cylinder around spa (>38 m3)

>90 m3/min based on geometric mean random air speed of 0.06 m/s and minimum cylinder radius of 2 m

0.5–1.2 per hour based on mixing height of 3 m

Eickmann (Germany)

2007 Generic two-zone model description

Not applicable Hemisphere, sphere, or cube

Not applicable Not applicable

Spencer (United States)

2007 Solvent exposure during metal part disassembly

Solvent (e.g., cyclohexane)

Hemisphere around work zone of radius 1 m with no flow across flat face (2.1 m3)

10.34 m3/min [enclosed area with no ventilation] to 190 m3/min [well-ventilated] based on random air speed of 0.06 to 1 m/sec

4.3 per hour

Keil (United States) 2006 Chemical exposure at a university teaching laboratory

Methylene chloride Hemisphere around work zone of radius 1 m (2.1 m3)

Average of 11.2 m3/min based on random air speed of 0.06 m/sec

17–20 per hour

Nicas (United States)

2006 Solvent parts washer usage

Benzene Cube around parts washer (0.26 m3)

7.05–11.6 m3/min based on random air speed of 0.15 m/sec

2–3 per hour

Vernez (Switzerland)

2006 Application of waterproofing sprays

Respirable aerosol particles containing solvent

Hemisphere around work zone

8.4–15.65 m3/min 1–3 per hour

Von Grote (Switzerland)

2006 Occupational dry cleaning exposure

Perchloroethylene (PCE)

Cube around dry cleaning stations (100 m3)

13 m3/min to 20 m3/min

6–10 per hour

Vernez (Switzerland)

2004 Application of waterproofing sprays

Respirable aerosol particles containing solvent

Hemisphere around work zone (2 m3)

0.3–1.7 m3/min 1–5 per hour

Keil (United States) 2003 Organic solvent spill

n-pentane Hemisphere around spill with radius 0.5 m (0.26 m3)

2.7 m3/min based on random air speed of 0.57 m/sec

4.9 per hour

Nicas (United States)

2003a Fumigation of commodities– manual processing (e.g., foods)

Methyl bromide Cube at work station (1 m3)

7.7 m3/min [low random air speed condition of 0.05 m/sec]

3 per hour

(Continued)

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1705

Table I. Continued

Study Author (Country) Year Scenario Chemical(s)

Near-Field Geometry (Volume)

Flow Rate Between Near Field and

Far-Field Far-Field Air

Change Rate

Nicas (United States)

2003b Splash loading of gasoline

Benzene Hemisphere around loading zone with radius 0.76 m (0.92 m3)

13.9 m3/min based on random air speed of 0.13 m/sec

Not specified

Von Grote (Switzerland)

2003 Occupational metal degreasing

Trichloroethylene (TCE) Perchloroethyene (PCE)

Box including degreasing machine and workspace (100 m3)

10–12.5 m3/min 5.5–6.5 per hour

Keil (United States) 2000 Worker located 1 meter from evaporating pollutant in a generic work room

Generic solvent Hemisphere around work zone

5.8–22.1 m3/min based on random air speed of 0.06 m/sec and geometric standard deviation of 0.032

2.4 per hour

Nicas (in Keil 2000, United States)

2000 Application of adhesive

Toluene Hemisphere above table of radius 0.78 m (1 m3)

5 m3/min based on random air speed of 0.04 m/sec

6 per hour

Keil (United States) 1998 Parts washing operation

Toluene Wash station work area

6.7 m3/min Unspecified (room airflow was 766 m3/min)

daily average concentration to the two-zone model represented by the following equations modified to adopt the symbols and units used in this assessment (Appendix B):

CTW A,N =

( GW,day

k + GCW,day

) Q · TW · C F1

(3)

CTW A,F = (GW,day + GCW,day)

Q · TW · C F1 (4)

where CTWA,N was the breathing zone concentration (ppm), GW was the constant mass emission rate for the worker of interest (mg/day), GCW was the con- stant mass emission rate for co-worker(s) (mg/day), k was the imperfect mixing factor, Q was the room sup- ply air rate (m3/min), TW was the length of workshift (min/day), and CF 1 was a conversion factor (mg/m3

per ppm at standard temperature and pressure).(34)

The imperfect mixing factor was selected based on an analysis of NF to FF concentrations as a function of Q, Vf , and β described by Cherrie et al.(35) For scenarios where the ventilation rate is very low, the steady-state model tends to overestimate true expo- sure if the concentration profile has not returned to

background levels at the end of the exposure period. Therefore, the steady-state approach provides a con- servative or higher estimate of exposure.

2.4. Selection of Model Parameters

A detailed literature search was conducted for each model parameter where possible or applicable to ensure that each was fully characterized for the particular scenarios of interest. A description of each key parameter is provided below and summarized in Table II. The ranges and probability distributions used in the Monte Carlo sensitivity analysis are sum- marized in Table III.

2.4.1. U.S. Fraction of Aerosol Hairspray Products Containing VC (FC)

According to the CPSC’s Bureau of Economic Analysis report entitled Background Analysis of Vinyl Chloride Usage, approximately 2 billion cans of VC-containing aerosol consumer products were filled between 1969 and 1974, which accounted for 15% of the U.S. aerosol production during these years.(36)

Therefore, the total number of cans produced dur- ing this time period was approximately equal to 13.3 billion. The report further estimated that aerosol

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Table II. Input Values for the Near-Field/Far-Field Hairspray Propellant Exposure Model

Simulation #1 Simulation #2 Simulation #3 Simulation #4 Residential Setting Small Salon Medium Salon Large Salon

Input Parameters Number of stylists, 1+NCW 1 2 4 9 Maximum number of occupants, NO 3 6 12 27

Daily averaging time, TW (minutes) 1440 480 480 480

Years worked during VC usage, DH 7.25 7.25 7.25 7.25

Occupational equivalent years worked during VC usage, OEa

21.75 7.25 7.25 7.25

Radius of near-field hemisphere, RN (m)

0.78 0.78 0.78 0.78

Far-field volume (commercial salon or total residential volume), VF (m3)b

356 142 198 275

Random air speed, S (m/min) 6.0 6.0 6.0 6.0

Unit ventilation rate, Q’ (m3/min/person)c,d

– 0.708 0.708 0.708

Residential air exchange rate, AR (hr−1)c

0.87 – – –

Spray frequency—worker, EW (events/day)e

9.5 9.5 9.5 9.5

Spray frequency—co-worker(s), ECW (events/day)e

0 9.5 28.5 76

Mass of hairspray applied per customer, ME (g/customer)

12 12 12 12

Hairspray generation rate, GH (g/min)

34.2 34.2 34.2 34.2

Average VC content, WH (%/w/w)f 10% 10% 10% 10%

Percentage of aerosol hairspray cans containing VC, FC (%)

3.50% 3.50% 3.50% 3.50%

Imperfect mixing factor—steady-state model, k (hr−1)

0.6 0.7 0.5 0.4

Conversion factor, CF 1 (mg/m 3 per

ppm at standard conditions) 2.56 2.56 2.56 2.56

Calculated Parametersg

Near-field volume, VN (m3) 0.994 0.994 0.994 0.994

Interzonal airflow, β(m3/min) 11.47 11.47 11.47 11.47

Salon or residence air flow, Q (m3/min)c

5.162 4.248 8.496 19.116

VC generation rate GE (mg/min) 3420 3420 3420 3420

Commercial air exchange rate, AC (hr−1)

– 1.8 2.6 4.2

Spray duration, TE (min) 0.35 0.35 0.35 0.35

aStandard occupational year defined as 5 days/week, 50 weeks/year, and 8 hours/day equal to 2,000 hours/year. Residential setting includes a total of 24 hours consisting of 8 hours working and 16 hours in the home after working for a total of 6,000 hours per year. bA home size of 356 m3 was selected based on 1980 data from the U.S. Department of Energy on single-family home floor area distribution with an assumption of 2.4 m ceilings. cResidential ventilation rate based on air exchange rate data; commercial ventilation rate based on contemporaneous rules and practices. dFlow rate of 0.708 m3/min/person equates to 25 cfm/person. eExpected value based on Pr[E] and Pr[Ej = k | n] as described in Appendix B. fBased on the weighted average midpoint content by year for products sold on the market of 12.5% for 1967 to 1968, 8.9% (range = 5.2–12.5%). gSee Appendix B for equations used to determine calculated parameters.

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1707

Table III. Probability Distributions Assigned for the Near-Field/Far-Field Model and Predicted Cumulative Exposure Based on 10,000 Monte Carlo Iterations

Probability Distributions Assigneda

Simulation #1 Simulation #2 Simulation #3 Simulation #4 Residential Setting Small Salon Medium Salon Large Salon

Model Input Random air speed, S (m/min) Triangular Triangular Triangular Triangular

[3, 12] [3, 12] [3, 12] [3, 12] Mode = 6 Mode = 6 Mode = 6 Mode = 6

Unit commercial ventilation rate, Q’ Triangular Triangular Triangular (m3/min/person)b Not applicable [0.425, 0.991] [0.425, 0.991] [0.425, 0.991]

Mode = 0.708 Mode = 0.708 Mode = 0.708 Residential air exchange rate, AR (hr−1) Lognormal

Geo. mean = 0.68 Not applicable Not applicable Not applicable Geo. std. dev. = 2.01

Probability of a customer per 15-minute period (per stylist), Pr[E]c

29.6% 29.6% 29.6% 29.6%

Shop or home volume, VF (m3) Empirical 113 to 226 (21.2%) Triangular Triangular Triangular 226 to 340 (33.3%) [59, 192] [69, 411] [137, 357] 340 to 453 (22.7%) Mode = 142 Mode = 198 Mode = 275 453 to 679 (16.7%)

679 (6.1%)

Mass of hairspray applied per customer, ME Triangular Triangular Triangular Triangular (g/customer) [6.3, 16.3] [6.3, 16.3] [6.3, 16.3] [6.3, 16.3]

Mode = 12 Mode = 12 Mode = 12 Mode = 12 Hairspray Generation Rate, GH (g/min)d Triangular Triangular Triangular Triangular

[18, 46] [18, 46] [18, 46] [18, 46] Mode = 34 Mode = 34 Mode = 34 Mode = 34

VC content, WH (%/w/w) 1967–1968:12.5% 1969 uniform [6%, 12.5%]

1970–1972: uniform [5.2%, 12.5%] 1973–1974: uniform [6%, 12.5%]

Percentage of aerosol hairspray cans containing Uniform Uniform Uniform Uniform VC, FC (%) [0.4, 6.56] [0.4, 6.56] [0.4, 6.56] [0.4, 6.56]

Model Output Distribution—Cumulative Exposure, CE (ppm-year)

Mean 1.0 1.2 1.2 1.2

CV 0.95 0.38 0.35 0.33

5th percentile 0.23 0.57 0.61 0.66

95th percentile 2.78 2.01 1.95 1.96

aInputs include type of distribution, range, and parameters. bCorresponds to a range of 15–35 cfm/person. cCorresponds to an expected number of customers of 9.5 per day per stylist. dDistribution based on U.S. Department of Energy data for 1980.

cans of paints, finishes, and similar coatings ac- counted for 75–90% of all VC-containing consumer products. Based on these data, the total number of VC-containing aerosol cans that were not paints or coatings was estimated to be between 0.2 and 0.5 billion cans, or 1.5–3.75% of all aerosol consumer products.

During U.S. Senate hearings conducted in Au- gust 1974 by Senator John V. Tunney before the Environment Subcommittee of the Commerce Com- mittee, Dr. Robert Schaffner of the Food and Drug Administration indicated that VC was not widely used in aerosol consumer products, and was used by only a small percentage of hairspray

1708 Sahmel et al.

manufacturers.(37) A Cosmetic, Toiletry, and Fra- grance Association (CTFA) survey reported that no hairspray product company had manufactured any VC-containing products after June 1973. In the first half of 1973, the CTFA reported that only two com- panies produced any VC-containing products. The total volume produced was reported to be approx- imately 1,625,000 cans, whereas the total hairspray production volume for 1973 was reported to be ap- proximately 450,000,000 cans, for an estimated per- centage of VC-containing cans of less than 0.4%.(38)

A study conducted at the University of Pennsyl- vania reported that VC was present in 1 of 62 aerosol hair products evaluated (1.6%), and in 1 of 168 general aerosol products evaluated (0.6%).(39) Addi- tional data based on EPA studies reported by Brid- bord et al. indicated that vinyl chloride was found in 4 out of 61 aerosol products that were evaluated (6.56%). Bridbord et al. also reported that VC was not a common ingredient of hairspray products, par- ticularly when compared to Freon 11 and 12.(40)

An evaluation of the 1960s and 1970s literature on aerosol science appears to indicate that fluorocar- bon propellants (i.e., propellants 11 and 12, Freon 11 and 12, and P-11 and 12) were far more commonly used than VC in aerosol hairspray products. The Aerosol Handbook found that VC blends were not as popular as other propellant blends in the 1970s, and that the ”standard blend” used in hairsprays dur- ing this time consisted of a mixture of P-12 (53%), P- 11 (36%), and isobutane (11%).(41) A review of The Chemical Formulary book series from the 1950s to the 1970s, which contain data on commercial prod- uct formulas and recipes, demonstrated that aerosol hairspray formulations commonly used during this period appear to have primarily contained propel- lants 11 and 12 only.(42,43) According to a number of articles published in Manufacturing Chemist and Aerosol News, and Aerosol Age, VC was rarely listed as an ingredient of aerosol or hairspray mixtures, and other propellants were mentioned much more fre- quently in the context of current or future products or research.(44−56)

Based on the above detailed literature analy- sis, the fraction of cans of hairspray that potentially contained VC (Fc) was assigned a uniform distribu- tion with a range of 0.4% to 6.56%, with the point estimate set equal to the midrange value of 3.5%. This fraction was used to calculate VC concentra- tions for all salon sizes, although the VC concentra- tion assuming 100% VC-containing hairspray prod- uct use was also calculated for all salon scenarios for comparison.

2.4.2. Duration of Use of VC as a Propellant in Hairsprays (DH )

Some companies selling aerosol hairspray prod- ucts during the 1960s and 1970s produced documen- tation showing that VC was evaluated for potential inclusion in their hairsprays. No documentation or information could be found showing that VC was used as a component of aerosol hairspray products in the United States before 1967. Certain Clairol hairspray products appeared to have used VC as a component of the aerosol propellant from 1967 to 1973.(57) Other hairspray manufacturers did not ap- pear to have begun using VC as a propellant un- til 1968 or 1969, based on information from aerosol hairspray contract filler companies.(58) According to the available information, the date range for the availability of VC-containing hairspray products in the United States (DH ) was determined to be 7.25 years, using a starting date of 1967 and an ending date of the spring of 1974, approximately one year after the CTFA reported that all major hairspray companies had removed VC from their hairspray products.(38)

2.4.3. Determination of VC Content in the Hairspray Products (WH )

Hairspray formulation records (provided by Clairol and additional confidential formulation records from other companies) were used to develop a concentration estimate for the likely VC content of hairspray products on the market during the pe- riod of interest. In all available formulation records, VC was incorporated into the products as one com- ponent of a propellant blend that also typically con- tained Propellants 11 and/or 12. The uniform dis- tribution range and midpoint estimate of the VC concentration in these products by weight (WH ) was 12.5% for 1967 to 1968, 9.25% for 1969 (range = 6– 12.5%), 8.9% for 1970 to 1972 (range = 5.2–12.5%), and 9.25% for 1973 to April 1974 (range = 12.5– 6%).(41,57) The weighted average of the point esti- mates for the entire 7.25-year period VC was used was 10%, which was consistent with the reported range in The Aerosol Handbook.(41)

2.4.4. Estimated Salon Volume (VF )

There is no systematic research on the size of salons during the 1960–1980 time period. However, between 1996 and 1997, Labreche et al. tabulated floor areas by salon size for 25 salons in Montreal,

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1709

Canada.(59) For salons with 1–2 stylists, the aver- age floor surface area was 51.8 m2 (range = 21.6– 70.0 m2); for salons with 3–4 stylists, the average floor surface area was 72.1 m2 (range = 25–150 m2); and for salons with 5–9 stylists, the average floor surface area was 100.4 m2 (range = 50.0–130 m2). The salon volumes (VF ) were assigned triangular distributions based on these floor area data and a typical commer- cial ceiling height of 2.743 m (9 ft). The above data used in the assessment reflect slightly different vol- umes than those reported in a study of 28 salons by van Muiswinkel et al. where the average salon vol- ume for a salon with 3.5 stylists was 195 m3.(60)

2.4.5. Salon Ventilation Characteristics and Contemporaneous ASHRAE Guidelines (Q’)

Recommended or required air ventilation for an indoor space has been consistently characterized in the literature and in ASHRAE publications in terms of the necessary volume of air introduced over time into a space, most commonly in units of cubic feet per minute (cfm). ASHRAE guidance in the 1960s and 1970s also supports the use of volume of ventilation air per person in an indoor space as a more appropri- ate way to characterize ventilation rather than other measures such as air changes per hour, the value of which is highly dependent upon the size of the space to be ventilated.(61,62)

Typically, the volume of air that is recommended or required for a given space will also be specified per person or per occupant within the space. A ven- tilation text published in 1845 described the need to provide sufficient quantities of fresh air to minimize the possibility of buildup of potentially toxic, foul, or unpleasant concentrations of gases within an indoor space.(63) In this publication, it was determined that at least 10.25 cfm of ventilation air was needed to re- move both bodily scents and exhaled carbon dioxide per person in an indoor space. Additional research done by Yaglou et al. found that a healthy, clean per- son who has recently bathed required 15–18 cfm per person to dilute body odors.(64)

Researchers also recognized from the early part of the 20th century that the volume of space avail- able per occupant is a key variable (along with the temperature of objects in the space) in determining the amount of dilution ventilation needed per per- son. According to Yaglou et al., “with simple venti- lation and with 200 cu ft of air space per person, the air quality was poor to bad when the air supply was under 3 cfm per person, improving rapidly as the air

supply increased to 15 cfm.”(64) The importance of air space per person is also illustrated by the fact that in 1970, ASHRAE recommended a mere 7 cfm of ven- tilation air per person when the air space was 500 cu ft per person, but advised an increase to 25 cfm when the air space was 100 cu ft per person.(65)

The 1964 ASHRAE Guide and Data Book rec- ommended 10–15 cfm per person of ventilation air in commercial areas such as drug stores, grocery stores, or stores with lunch counters. A store with a lunch counter was selected as the best possible comparison with a hair salon because a lunch counter would also need to control both heat generation (i.e., a cook- ing stove versus hair dryers) as well as air contam- inant generation (i.e., cooking odors and smoke vs. hairspray and hair dyes). The 1964 ASHRAE stan- dard also specifically recommended 0.35–0.45 cfm per square foot of space in public buildings. Given the average floor space for the 1–2, 3–4, and 5–9 hairdresser salons presented in Labreche et al. with a maximum of 6, 12, and 27 occupants, respectively (using a total occupant number of three times the number of hairdressers working in a salon, assum- ing one active and one waiting customer per hair- dresser), the standard recommended between 14 and 42 cfm/person.(59)

In 1973, ASHRAE published the first ventila- tion standards for natural and mechanical ventilation in the form of Standard Number 62–73. This stan- dard provided recommended ventilation rates for many different types of public buildings and com- mercial establishments. Specified ventilation flow rates for hair salons included 25 cfm as a mini- mum ventilation rate, with a recommended rate of 30–35 cfm.(62) Table IV includes a summary of key ventilation guidelines, rules, and practices in the 1960s and 1970s.

Additional research has documented a need for published minimum ventilation rates in spaces with retail customers or commercial business visitors. These studies have shown that customers are more sensitive to poor ventilation rates than employees, who tend to become more accustomed to their envi- ronment. As a result, businesses require a minimum level of ventilation in order to ensure the comfort, happiness, and repeat business of their customers. Cain et al. found that for visitors to a particular space, a ventilation rate of “7.5 L/sec per occupant seems necessary to assure 80% acceptance.”(66) This cor- responds to a ventilation rate of 15.9 cfm per occu- pant. Similarly, Berg-Munch et al. found that: “In a space occupied by sedentary persons, a steady-state

1710 Sahmel et al.

Table IV. U.S. Ventilation Guidelines, Rules, and Practices in the 1960s and 1970s (61,62,65)

Year Published Information Given Notes Publication

1964 10–15 cfm per person Includes guidelines for retail stores (not specific to salons)

ASHRAE Guide and Data Book, Chaps. 18–19, pp. 235–252, American Society of Heating, Refrigerating, and Air Conditioning Engineers; Atlanta, GA, 1964.

1964 0.35–0.45 cfm per square foot Section about public buildings (assuming 15 ft. by 20 ft. and 8 people, range becomes 13.125–16.875 cfm per person)

ASHRAE Guide and Data Book, Chaps. 18–19, pp. 235–252, American Society of Heating, Refrigerating, and Air Conditioning Engineers; Atlanta, GA, 1964.

1970 15–18 cfm for healthy, clean person to simply dilute body odor

Does not include additional ventilation required to address nonhuman sources of compounds released to indoor air

Klauss, AK; Tull, RH; Roots, LM; Pfafflin, JR. History of the Changing Concepts in Ventilation Requirements. ASHRAE Journal, June 1970; pp. 51–55.

1973 Minimum rate of 25 cfm per person and recommended rate of 30–35 cfm (hair salons)

First standard to include a guideline specific to salons

ASHRAE Standards for Natural and Mechanical Ventilation, 62–73, American Society of Heating, Refrigerating, and Air Conditioning Engineers; Atlanta, GA, 1973.

ventilation rate of 8 L/sec per person is required in order to satisfy 80% of people entering the space (visitors). People remaining in the space (occupants) are less dissatisfied than the visitors are.”(67) This equates to a ventilation rate of 16.9 cfm per occupant.

In this study, the total flow rate for each salon (Q) was calculated by multiplying the maximum es- timated occupancy (three times the number of hair- dressers) by the recommended ASHRAE unit flow rate (Q’) of 25 cfm per person for hair salons, which is likely to have been necessary to dilute the air con- centrations of hair products used and the heat from the dryers, as well as for general customer and stylist comfort.(61,62,65) A minimum airflow rate of 15 cfm per person was selected for a business establishment such as a salon based on the literature reviewed. A triangular distribution with the full range of 15– 35 cfm per person was adopted in the sensitivity analysis.

2.4.6. Mass of Hairspray Applied per Customer (ME)

A study in the trade publication of CTFA, the Cosmetic Journal, evaluated beauty salon air qual- ity by measuring average hairspray use by mass per

customer during a typical day in a salon during the early 1970s. The mass of hairspray used per customer (ME) was determined by measuring the weight differ- ence for all cans of hairspray used in a given day, and resulted in a calculated range of 6.3–16.3 grams of hairspray use per customer. A triangular distribution with this measured range was used for the sensitivity analysis, and a point estimate of 12 was used based on the average of the measured data. The usage mass is unlikely to be appreciably affected by the type of pro- pellants used, and data based on non-VC propellants such as isobutane/fluorocarbon mixtures were con- sidered representative of hairsprays containing VC.

2.4.7. Hairspray Generation Rate (GH )

The average of mass generation rates represent- ing variation between full and empty containers was determined from reported data.(68) Long-term aver- age exposure was not expected to be sensitive to this parameter because as the can empties, longer spraying times are required to apply the same mass, which affects the peak concentration, but not cu- mulative long-term average exposure. A triangular distribution with a mode of 34 grams per minute (g/min) and range of 18–46 g/min was assigned.

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1711

2.4.8. Probability of a Hairspray Event per Increment of Time (Pr[E])

To realistically assess transient hairspray usage in a salon, the probability of a salon worker spray- ing hairspray for 15-minute intervals throughout the work day (Pr[E]) was conceptualized as a series of Bernoulli trials. The 95% upper confidence probabil- ity of a hairspray event occurring during a 15-minute interval was calculated using 12 days of contempo- raneous customer data presented in Hoffman repre- senting both winter and summer months.(27) The re- sultant probability of 0.296 per 15-minute period, or a 29.6% chance that a salon worker will be spray- ing hairspray during a 15-minute time interval during the work day, corresponds to an expected value of customers per stylist (EW ) of 9.5 customers per day and expected value of customers summed across all co-workers of 9.5–76 depending on salon size. This probability also corresponded to the range used in our probabilistic assessment (e.g., 5–14 customers per day).

2.4.9. Random Air Speed (S)

Random air speed (S) was estimated using data from Baldwin and Maynard, which indicated that a value of 0.1 m/sec was typical for offices and stores.(69) This range is consistent with Nicas where a range of 0.05 m/sec (3.1 m/min) to 0.25 m/sec (15 m/min), and a most likely value of 0.15 m/sec (9.1 m/min), was used for an indoor space and as- sessment of exposure from use of a parts washer.(29)

Similarly, Leino et al. reported mean air speeds of 0.09 m/sec (5.4 m/min) and 0.13 m/sec (7.8 m/min) for small (n = 10) and large (n = 10) Finnish hairdress- ing salons, respectively.(70) A triangular distribution with a range of 3 to 12 with a mode of 6 m/min was therefore used for this parameter.

2.4.10. Residential Air Exchange Rate (AR) and Room-to-Room Air Exchange Rate (ARTR)

In 1988, Nazaroff aggregated the two largest U.S. studies containing air exchange rate data up to that time. One study consisted of 1,048 tracer gas mea- surements in 266 low-income dwellings across 14 cities and the second study consisted of November to March measurements of 312 homes with a me- dian age of less than 10 years. The distribution was aggregated (geometric mean = 0.68, geometric stan- dard deviation = 2.01) in an attempt to best represent

the U.S. mixture of “leaky” homes and more energy- efficient modern structures. The arithmetic mean of 0.87/hr, based on a log normal distribution assump- tion, was used as the point estimate and the full dis- tribution was used in the sensitivity analysis.(71)

The room-to-room salon air change rate (ARTR) required in the three-zone model (i.e., air exchange between salon zone 2 and rest of home zone 3) was estimated based on ASHRAE 62-1973 guidelines for airflow in residential kitchens and three assumed oc- cupants. The range of calculated room-to-room air change rates was 1.5–6.4. Room-to-room air change rates between 3 and 6 per hour for U.S. EPA test home data cited in the indoor air quality RISK model documentation are considered typical.(72)

3. RESULTS

3.1. Transient Two-Zone Model Results

The point estimate of the transient two-zone model daily TWA exposure using a market share estimate of VC-containing hairsprays (range of 0.4– 6.6% of products used) for the small, medium, and large salons was 0.18 ppm, and for a residential salon was 0.03 ppm. For the scenario in which all hairspray products used were assumed to contain VC, the point estimates of the TWA exposure for the commercial salons were 5.0–5.1 ppm, and for the residential sa- lon was 0.9 ppm (Table V). Cumulative exposure es- timates were then calculated assuming a potential ex- posure time of 8 hours per day, 5 days per week, and 50 weeks per year over a time duration of 7.25 years as discussed above under market availability of VC-containing hairsprays. The point estimate for cu- mulative exposure assuming a market share estimate of VC-containing hairsprays was 1.28–1.30 ppm-year for small, medium, and large salons, and 0.66 ppm- years for the home salon scenario. For the scenario in which only VC-containing hairspray products were used, the cumulative dose was 37 ppm-year for the commercial salons and 19 ppm-year for the residen- tial salon (assuming 7.25 years of possible exposure). Fig. 3 illustrates exposure patterns over time, both for the near field and far field, and for the full day compared with a typical 30-minute period. It should be noted that breathing rates were not taken into account when calculating cumulative exposure esti- mates because OSHA and other regulatory agencies make the assumption for the purposes of conserva- tive estimates that the same concentration found in the breathing zone is actually inhaled, and that 100%

1712 Sahmel et al.

Table V. Summary of Key Model Results: TWA Concentration, TWA Point Estimates, and Cumulative Exposure Estimates

Location

Calendar Years of Exposure

Occupational Equivalent Years

of Exposure

TWA Averaging

Time (Hours)

Point Estimate

TWA – (ppm) Mean

Upper Bound

Cumulative Point Estimate

Exposure (ppm-year)

Mean Upper Bound

Market Fraction of Products Used (0.4–6.56%) Contain VC Residential salon 7.25 21.75 24 0.03 0.05 0.13 0.66 1.0 2.8 Small commercial

salon 7.25 7.25 8 0.18 0.16 0.28 1.28 1.2 2.0

Medium commercial salon

7.25 7.25 8 0.18 0.17 0.27 1.29 1.2 2.0

Large commercial salon

7.25 7.25 8 0.18 0.17 0.27 1.30 1.2 2.0

All Products Used (100%) Contain VC Residential salon 7.25 21.75 24 0.9 1.4 3.6 19 30 79 Small commercial

salon 7.25 7.25 8 5.0 4.7 7.4 37 34 54

Medium commercial salon

7.25 7.25 8 5.1 4.7 7.1 37 34 52

Large commercial salon

7.25 7.25 8 5.1 4.9 7.2 37 35 52

Fig. 3. Predicted daily airborne VC time-concentration profile in a large salon for a typical iteration of the probabilistic model assuming all hairspray products were formulated with VC. The near field (NF) represents a hairdresser’s personal breathing zone exposure and the far field (FF) represents ambient levels of VC in the salon including co-worker VC releases. Large peaks (>50 ppm) correspond to worker hairspray events affecting NF breathing zone, whereas small peaks (<25 ppm) represent co-worker hairspray events contributing to FF ambient VC levels in the salon. Hairspray events are randomly distributed in the model in 15-minute increments such that individual small peaks can include the contribution of multiple co-workers.

of this inhaled dose is ultimately absorbed. How- ever, the average quantity of VC retained in human lung tissue has been observed to be approximately 42%.(73,74)

In the sensitivity analysis, input distributions were considered for salon airflow rate, residential air exchange rate, random air speed, salon or home volume, VC weight content, probability of having a customer per 15-minute period, mass of hairspray applied per customer, and percentage of hairspray

products that contained VC (Table III). The 95th percentile (upper bound) TWA concentration for the small, medium, and large salons from the Monte Carlo analysis was 0.3 ppm, and for the home salon scenario was 0.1 ppm. The 95th percentile of cumu- lative exposure for the small, medium, and large sa- lon scenarios was 2.0 ppm-years, and for the home salon was 2.8 ppm-year. For the scenario in which all hairspray products used were assumed to con- tain VC, the 95th percentile of cumulative exposure

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1713

Table VI. Summary of Results: Sensitive Parameters

Small Medium Large Residential Commercial Commercial Commercial

Parameters Considered in Sensitivity Analysis Salon Salon Salon Salon

Probability of a customer per 15-minute period –Worker 9.6% 12.1% 5.7% 3.3% Probability of a customer per 15-minute period –Co-worker Not applicable 6.7% 6.8% 5.0% Fraction of products containing VC 8.8% 31.0% 35.1% 34.1% Weight content of VC VC 0.9% 2.8% 4.3% 3.8% Salon airflow rate (cfm/person) Not applicable −15.2% −16.1% −19.6% Random air speed (m/sec) −1.5% −1.8% −1.5% −1.6% Salon/home volume (m3) −23.8% 0.0% −0.5% 0.0% Residential air change rate (ACH) −48.7% Not applicable Hairspray generation rate (g/s) −0.1% 0.0% 0.0% 0.0% Amount of hairspray used (g/customer) 6.6% 30.2% 30.1% 32.6%

100% 100% 100% 100%

for the commercial salon scenarios was 52–54 ppm- year, and for the residential salon was 79 ppm-year (Table V). Parameters contributing at least 1% to the variance in cumulative exposure included: probabil- ity of a customer per 15-minute period, the fraction of products containing VC, the weight content of VC in a hairspray product, salon airflow rate, and mass of hairspray used per customer (Table VI). For each of these parameters, published literature was available to develop reliable point estimates. The 95th per- centile cumulative exposure calculations were within a factor of 3 of the mean, or central tendency, ex- posure, which illustrates that knowledge of the pre- cise values for each of the various parameters is not necessary in order to accurately estimate, with confi- dence, the likely true concentration (that is, sensitiv- ity is not a great concern).

Table VII presents some of the other interesting outcomes from the transient two-zone model. The highest instantaneous peak estimated for all three

professional salon scenarios was 134–135 ppm with a 95th percentile of 207 ppm. The highest 15-minute TWA estimate was 12–14 ppm with a 95th percentile of 17–20 ppm. Finally, the ratio of breathing zone to room airborne VC concentrations of 1.2–1.3 for com- mercial salons was similar to the ratio of personal to area concentration of 1.4 calculated from ethanol data reported in van Muiswinkel et al. for Dutch salons.(60)

3.2. Residential Multizone Model Comparison

The two-zone model was used for the residen- tial setting because of typical residence ventilation characteristics and the fact that room-to-room air exchange is far higher than the air exchange rate for the entire residence. For room air change rates between 3 and 6 per hour (typical of U.S. EPA test home data cited in the indoor air quality RISK model documentation), predicted breathing zone

Table VII. Summary of Additional Model Results: Ratio of Near-Field to Far-Field Concentrations, Air Change Rate Estimates, Peak Exposures

Ratio of Worker Breathing Zone (Personal) to Room

(Area) Concentration (Unitless)

Estimated Air Change Rate (Calculated from

cfm/Person Parameter for Commercial Locations)

Highest 15-Minute TWA

(ppm)

Highest Instantaneous Peak (ppm)

Number of Upper Lower Upper Upper Upper Location Stylists Mean Bound Bound Mean Bound Mean Bound Mean Bound

Residential salon 1 1.4 2.2 0.2 0.9 2.1 9 18 126 200 Small commercial salon 2 1.2 1.3 1.3 2.0 3.2 14 20 135 207 Medium commercial salon 4 1.2 1.3 1.3 2.5 4.5 12 18 134 207 Large commercial salon 9 1.2 1.3 3.0 4.6 6.9 12 17 135 207

1714 Sahmel et al.

concentrations were less than a factor of 1.05–1.2 larger than those predicted by the two-zone model that confirmed that the interzonal airflow rate (β) is the key limiting parameter (Table VIII).(72)

3.3. Steady-State Imperfect Mixing Model Comparison

Estimates of the daily average airborne con- centration of VC based on the steady-state imper- fect mixing model were consistent with the tran- sient two-zone model (Table IX, Fig. 4). Cumulative exposure estimates were 0.73 ppm-years for the res- idential salon, 1.3 ppm-years for the small salon, 1.4 ppm-years for the medium-sized salon, and 1.3 ppm-years for the large salon scenario. Short-term peaks or 15-minute average airborne concentrations cannot be estimated using the steady-state model.

3.4. Model Evaluation

Contemporaneous airborne concentration data for hairspray propellant components were col- lected in 1972 at the Central Beauty Salon by Hoffman and are suitable for model comparison. The characteristics of this salon included 10 stylist stations, 28 chairs, and 21 dryers.(27) The air ex- change rate was 6 to 8 per hour with an average duct airflow rate (including recycled air) of 2,060 cfm (equal to duct cross-sectional area multiplied by face velocity). The hairspray usage rate was 6– 16 g/customer and two propellant blends were used including P-12/P-11/Isobutane (w/w: 43%/48%/9%) and P-12/P-11/Methylene Chloride/Isobutane (w/w: 42%/31%/19%/8%). The weight content of the pro- pellant in the hairsprays was 50%. Probabilistic model estimates were prepared for propellants P- 11 and P-12 using the following parameters from the Hoffman study: daily customers (11 stylists av- eraging 104 customers/day), air exchange rate (6 to 8 hr−1 paired with an estimated effective vol- ume of 225–275 m3), hairspray usage rate (6–16 g/customer), and propellant component weight con- tent (16–24%). The estimated average P-11 and P- 12 concentrations using the model described in this study were within a factor of 1.8 of the measured data reported in Hoffman (Fig. 5).(27) Nicas et al. showed that for a similar two-zone model appli- cation, the modeled benzene concentrations were also within a multiplicative range of one-half to two-fold the measured concentrations determined through a simulation study.(29) The underprediction

of the model in the summer months is likely at- tributable to the greater rate of air recirculation that reduces the effectiveness of dilution ventila- tion and was difficult to estimate from the informa- tion provided by the author. Additionally, although the sampling plan used by Hoffman included mea- surement of both hourly background samples and peak samples collected immediately after hairspray events, the samples were all collected using a can- ister grab sampling method. At the time the study was conducted in the early 1970s, the authors con- sidered this method more robust than sampling us- ing a continuous monitoring instrument, since instru- mentation during that era did not provide a specific quantitative result for the air contaminants of inter- est. However, this sampling method may still have af- fected the consistency of the results and the resulting certainty in the study outcomes.

Other studies reporting indoor propellant concentrations are consistent with Hoffman (Table X).(27) Peak concentrations greater than 100 mg/m3 occur, but full-shift TWA average concentrations of propellants are typically 0.1–60 mg/m3 (typical propellants in aerosol hairsprays include ethanol, propane, isobutane, Propellant 11, Propellant 12, butane, and dimethylether). Ethanol is frequently reported in studies of hair salons because it is a common solvent used in many salon products, including hairsprays, and is considered to be an indicator for solvent exposure in salons in general.(59,60,75) In hair styling products such as gels, lotions, emulsions, and sprays, the concentration of liquid ethanol in the solution may be 50–90% (w/w).(70) VC was formulated at lower weight con- tents in hairspray (i.e., ≤15% w/w) than ethanol and was not used in gels, lotions, or emulsions. As a result, it would be present at lower airborne concen- trations than the ethanol concentrations reported in Table X.

3.5. Comparison to Acceptable Cumulative Exposure Levels Identified by OSHA and ACGIH

These cumulative exposure estimates were com- pared against the current OSHA PEL for VC as well as the ACGIH TLV for VC (Fig. 1). The PEL and TLV for VC are both currently set at 1 ppm as an 8- hour TWA exposure. Assuming exposure to 1 ppm is an acceptable airborne concentration for workers for a 40-hour work week, this corresponds to an ac- ceptable lifetime dose of 40–45 ppm-years, which is

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1715

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1716 Sahmel et al.

Table IX. Comparison of Point Estimates to Uncertainty Analysis for Market Fraction of VC-Containing Products Used (0.4– 6.56%)

Point Estimate: Steady-State Mixing Model

Sensitivity Analysis : Two-Zone Model Cumulative Exposure

Point Estimate: Transient Two-

Zone Model Mixing Factor Concentration Mean Upper Bound Location (ppm-Year) (Unitless) (ppm-Year) (ppm-Year) (ppm-Year)

Residential salon 0.66 0.625a 0.73 1.03 2.78 Small commercial salon 1.28 0.714b 1.33 1.18 2.01 Medium commercial salon 1.29 0.476c 1.40 1.20 1.95 Large commercial salon 1.30 0.385d 1.31 1.23 1.96

aMixing factor of 0.625 based on Cherrie (1999) modeled worker NF to FF conc. ratio of 1.6 for V = 300 m3, ACH = 1, and β = 10 m3/min. bMixing factor of 0.714 based on Cherrie (1999) modeled worker NF to FF conc. ratio of 1.4 for V = 100 m3, ACH = 1–3, and β = 10 m3/min. cMixing factor of 0.476 based on Cherrie (1999) modeled worker NF to FF conc. ratio of 2.1 for V = 100 m3, ACH = 1–3, and β = 10 m3/min. cMixing factor of 0.385 based on Cherrie (1999) modeled worker NF to FF conc. ratio of 2.5 for V = 300 m3, ACH = 3, and β = 10 m3/min.

Fig. 4. Comparison of point estimate of VC exposure to the probabilistic mean of the cumulative exposure estimates from the uncertainty analysis for the scenario in which a market fraction (0.4–6.56%) of products used contain VC.

20–35 times higher than the calculated estimate of the cumulative lifetime dose of 1.3 ppm-years (with a 95th percentile of 2.0 ppm-years). When comparing the OSHA acceptable lifetime dose to the scenario in which only VC-containing hairsprays were used, the cumulative dose associated with VC exposure was 37 ppm-years, which although far higher, was still below the 40–45 ppm-year estimate (assuming 7.25 years of exposure). However, at the 95th percentile, this scenario produced estimates above the OSHA acceptable lifetime dose (52–54 ppm-year for the

commercial salons and 79 ppm-year for the home salon).

4. DISCUSSION The results of this study illustrate the capacity of

appropriately selected models to characterize com- plex exposure generation rate and decay rate sce- narios if the model input parameters are sufficiently robust. The correlation between modeled concen- trations and measured concentrations of airborne hairspray propellants used in hair salons during the

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1717

Fig. 5. Comparison of model estimates to contemporaneous measured airborne propellant concentrations at a large salon with 10 operator stations.

Table X. Survey of Measured Airborne Concentrations of Propellant Components in Hairspray ( 27,59,60,70,75,91 )

Components

Flourocarbon 12 Flourocarbon 11 Methylene Reference Notes (Freon 12) (Freon 11) Chloride Et OH

Labreche et al., 2003

26 salons; personal sampling; avg. 8 hr TWA

– – – 40 mg/m3 (range: 0.17–447 mg/ m3)

Hollund and Moen, 1998

Area sampling – – – 33.3 mg/m3 w/o ventilation; 9.5 mg/m3

w/ventilation

1–2 minute “peak” concentrations during release of pollutant

20–1580 mg/m3 5.6–1010 mg/m3 <3.5–451 mg/m3 8–491 mg/m3

Hoffman, 1973 Daily concentration: Table VII: Summer

20–64 mg/m3 11–56 mg/m3 – 17–55 mg/m3

Daily concentration: Table VIII: Winter

5–25 mg/m3 6–28 mg/m3 <3–7 mg/m3 8–21 mg/m3

Kersemaekers, 1998

Presence or absence of ventilation device predictive of exposure grouping; avg. 8 hr TWA

– – – w/ventilation: 7.4 mg/m3

– – – w/o ventilation: 17.4 mg/ m3

Ventilation determined based on – – – Leino, 1999 whether subjects experienced

discomfort; peak total VOC (not specific to ethanol)

– – – 45 mg/m3

van Muiswinkel et al., 1997

33 salons; seasonal range; 8hr TWA

– – – 0.1–57 mg/m3

time period of interest underscores the utility of the transient two-zone model to predict TWA concentra- tions for various occupational and consumer use sce- narios. Additionally, the results of the steady-state model demonstrate the successful application of a

simple screening model to replicate the results of a more precise but parameter-intensive higher tier model, increasing confidence that the results of the analysis are not highly dependent on the type of model selected.

1718 Sahmel et al.

Our analysis indicates that potential exposures to VC through the occupational use of hairsprays in home salons or professional hair salons during the 1960s–1970s was not likely to have been suf- ficient to cause or increase the risk of developing HAS. When employing the assumption that only VC- containing hairsprays were used in a salon, 95th per- centile TWA concentration estimates were found to be in the range of 7–8 ppm for all three professional salon scenarios. Such concentrations correspond to a theoretical lifetime cumulative dose of 37 ppm- years, with a 95th percentile upper bound of 52–54 ppm-years, assuming 7.25 years of possible exposure. Considering the lowest reported cumulative expo- sure in the published literature associated with a case of HAS (288 ppm-years) and the finding of no in- crease in relative risk for HAS below 500 ppm-years of cumulative exposure, the findings suggest that the potential for exposure to VC from hairspray use in the United States would not be sufficient to lead to HAS.(18) These results are also consistent with the epidemiology literature for hair stylists, which does not show an increased incidence of HAS or any other liver tumors among hair stylists or employees of hair salons during the time period of interest.(20−24) Our assessment of the health risk is also consistent with the PBPK analysis of Reitz et al., who compared the delivered VC dose at various concentrations with the incidence of HAS.(14)

It was also found that the volume of the space evaluated had only a minimal effect on the estimated airborne concentrations of VC. This was true even with the use of a wide range of possible ventila- tion rates in the sensitivity analysis. As mentioned in some texts, for commercial spaces, ventilation, as characterized by volumetric airflow, was far more im- portant in predicting concentrations over an 8-hour work day than the size of the room. This is consistent with historical and current ventilation guidelines that emphasize occupancy-dependent airflow rates rather than target air exchange rates. In contrast, in residen- tial spaces where air flow tends to be induced by ther- mal gradients and wind flow rather than mechanical ventilation, home volume was found to be a sensitive parameter.

The Monte Carlo analysis indicated that the 95th percentile estimate of airborne concentration (and dose) was only a factor of 2 higher than the point estimate. In this assessment, home volumes as low as 113 m3 (3991 ft3) and air change rates as low as 0.08 ACH were considered. These values are poten- tial outliers because they are extremely low, and this

positively skewed the mean probabilistic result rela- tive to the point estimate when a 24-hour averaging time was considered.

In addition to the salon studies considered in this analysis, two early 1970s studies assessed VC in hair- spray. Gay et al. evaluated potential VC concentra- tions following a single 30-second or 60-second hair- spray event in three rooms of different volumes: a simulated home bathroom, an office room, and a public restroom.(76) In the study, the authors col- lected short-term (2 minute) area samples at differ- ent time periods of slightly more than 2 hours. The ventilation and hairspray usage rates were not mea- sured. None of the scenarios evaluated described the use of hairspray in a salon by professional hair- dressers, and the study was conducted under re- stricted ventilation conditions (e.g., closed vents, windows, passageways, and doors) that limited the applicability of the reported measurements to con- ditions in a typical hair salon. In spite of these differ- ences, the Gay et al. measurement results are consis- tent with the concentration profile predicted by the two-zone model for a discrete release of hairspray when the generation rate, weight content, and ven- tilation conditions are considered.

A second study by Bridbord et al. evaluated exposure to halogenated hydrocarbons; however, with respect to hairspray, the authors reported the data from the Gay study.(40) In addition to these studies, the Netherlands National Institute for Pub- lic Health and the Environment (RIVM) default hairspray scenario for the ConsExpo 4.1 Consumer Exposure and Uptake Models was evaluated for potential use in this study.(77) Although the RIVM default parameters were considered in this as- sessment, the ConsExpo 4.1 experimentally cal- ibrated spray model is intended to character- ize very low volatility or nonvolatile compounds and is not appropriate for volatile compounds or gases.

The strength of this modeling effort would have been improved had there been reliable VC measure- ments against which the modeling results could have been compared. However, given the number of pub- lished studies that have measured similar airborne contaminant concentrations in hair salons, the results appear to be precise and reliable.(59,60,75) The P-11 and P-12 data from Hoffman were useful for model evaluation, since the vapor pressures for the hair- spray propellants P-11, P-12, and VC of 0.9, 5.7, and 3.3 atm, respectively, reflect the similar volatility of these compounds.(27)

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1719

The duration of use of VC as a propellant in hair- spray was based on available company documenta- tion, published literature, and a personal interview with an individual who was integrally involved in the manufacture of hairsprays during the period of inter- est. Although it is believed that a realistic parameter of 7.25 years was used (including an additional year to account for previously purchased VC-containing hairspray product inventory at salons), it is possible that VC may have been used in some hairspray prod- ucts before 1967. In this case, the concentration es- timates presented would not be affected, but cumu- lative exposure values might change. Additionally, the fraction of products containing VC evaluated in this study was specific to the U.S. market. Companies in Germany, for example, appear to have used VC- containing propellants in aerosol products, including hairsprays, earlier (1950s) and in greater quantities than in the United States.(78) Because the fraction of hairspray products containing VC was the most sen- sitive factor for all commercial salons, and because the data used to evaluate this parameter were spe- cific to the United States, an analysis of a scenario in which all the hairspray products used in a salon con- tained VC was an important consideration and key part of this study. At the 95th percentile of cumula- tive exposure estimates assuming the use of only VC- containing hairsprays (for all salon scenarios), the estimated cumulative exposures were approximately one-fourth of the lowest cumulative lifetime dose as- sociated with HAS and less than one-fifth of the cu- mulative dose identified in prior studies showing an increased risk of HAS.(14,18) Although this scenario is probably relatively unlikely given the small frac- tion of VC-containing hairsprays that appeared to be available in the United States, it demonstrates that even exclusive use of VC-containing hairspray prod- ucts during the time period of interest might not be expected to have resulted in sufficient exposure to in- crease the risk of HAS, under a wide range of oper- ating conditions for hair salons, and for similar dura- tions of use.

The model equations used in this study are likely to be applicable to a wide range of scenarios in which the generation and decay rates and associated concentrations of volatile substances in an enclosed space are of interest. The use of multiple zones may be helpful to better understand the differences (or lack of differences) in concentrations at progressively greater distances from the generation source when information about ventilation rates and other impor- tant parameters is known or can be characterized

with confidence. The uncertainty analysis was also a critical part of this study and demonstrated the pos- sible range of model estimates given variability in the model parameters. Finally, a source of evaluation data (in this case, propellant measurements from a working hair salon) was critical to understanding the capabilities of the models used.

ACKNOWLEDGMENTS

The authors are grateful to Clairol for providing formulation details and other available information regarding hairspray products during the time period of interest. The authors are also grateful to Mont- fort Johnsen for the information he provided via per- sonal interview. The original research upon which this study is based was funded by multiple compa- nies involved historically in the production of VC and VC-containing products. None of the companies that funded the original research reviewed the article prior to submission. One of the authors has served as an expert witness in litigation related to work- place exposures to VC. Cited references are avail- able upon request from the corresponding author. The authors would like to thank Matthew Ground for his assistance in preparing this article, as well as Pamela Williams for her research contributions while employed by ChemRisk.

APPENDIX A: MODEL SYMBOLS

The symbols and abbreviations below are used in the exposure model provided in Appendix B and dis- cussed in the text. The units are indicated in paren- thesis.

Abbreviations

CW Co-worker(s) E Event F Far field N Near field O Occupants W Worker H Hairspray R Residential

Indices

a zone a—three-zone model b zone b—three-zone model i parameter i—two-zone dynamic model j 15-minute period j

k stylist k

1720 Sahmel et al.

Symbols

AR residential air change rate (hr−1) ARTR residential room-to-room air

change rate (hr−1) AC commercial air change rate (hr−1)

β interzonal airflow rate (m3/min) C1 concentration in zone 1—three-

zone model (mg/m3) C2 concentration in zone 2—three-

zone model (mg/m3) C3 concentration in zone 3—three-

zone model (mg/m3) CE cumulative exposure (ppm-year)

CN(Tp, j ) near-field concentration for event initiated period j after TP minutes (ppm)

CF (Tp, j ) far-field concentration for event initiated period j after TP minutes (ppm)

CTOTAL,N(TS ) total near-field concentration summed across all events at time TS (ppm)

CTOTAL,F (TS ) total far-field concentration summed across all events at time TS (ppm)

CTWA,N[t1,t2 ] time-weighted average near-field concentration between time t1 and t2 (ppm)

CTWA,F [t1,t2 ] time-weighted average far-field concentration between time t1 and t2 (ppm)

DH number of calendar years of hair- spray usage (years)

ECW number of co-worker hairspray events per day; this is a proba- bilistic value dependent on Pr[Ej = k | n]

EW number of worker hairspray events per day; this is a probabilistic value dependent on Pr[E]

Ej,w, number of worker hairspray events in period j

Ej,cw, number of co-worker hairspray events in period j

fi secondary intermediate parameter i of dynamic two-zone model

FC fraction of cans containing vinyl chloride

GE worker vinyl chloride mass gen- eration rate during spray event (mg/min)

GH hairspray generation rate during spray event (g/min)

Gcw,day daily co-worker(s) vinyl chlo- ride mass generation rate during (mg/day)

Gw,day daily worker vinyl chloride mass generation rate during (mg/day)

k imperfect mixing factor (unitless) λi primary intermediate parameter i

of dynamic two-zone model ME hairspray usage rate during a single

hairspray event (g/customer) NCW number of co-workers

NO number of occupants in salon NP number of 15-minute periods per

day OE occupational equivalent years

(years) Pr[E] probability of a hairspray event in a

15-minute period for one stylist Pr[Ej = k | n] probability of k hairspray events in

a 15-minute period given n stylists Qab airflow from zone a to zone b—

three-zone model (m3/day) Q’ unit ventilation rate (m3/min/

occupant) Q salon ventilation rate (m3/min)

RN radius of near-field hemisphere (m) S random air speed (m/min) t time (min)

T P,j time elapsed since initiation of hair- spray event in period j (min)

TE duration of single hairspray event (min)

TS time elapsed since beginning of shift (min)

TW length of work day or exposure pe- riod (min)

VN near-field volume (m3) VF far-field volume (m3) VS salon volume—residential three-

zone model (m3) VR rest of home volume—residential

three-zone model (m3) WH vinyl chloride content in hairspray

(g/g)

Conversion factors

CF1 2.56 mg/m3 per ppm for vinyl chloride at standard temperature and pressure

CF2 1,000 mg/g

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1721

CF3 60 min/hour CF4 24 hour/day

APPENDIX B: MODEL FORMULATION

Transient Two-Zone Model

In the model below, separate equations are used to describe the transient concentration profile during and after each spray event. The total exposure pro- file is calculated by superimposing the concentration profile for each individual event and consideration of the fraction of products containing VC.

VC generation rate:

GE = GH WHC F2 Duration of single hairspray event:

TE = ME GH

Interzone airflow rate (β) and near-field volume:

β = 1 2

( 4π ( RN)

2 )( 1

2 S )

VN = 1 2

( 4 3 π ( RN)

3 )

Ventilation rate:

Q = Q′ No

Q = ARVF C F3

AC = Q · C F3 VF

Probability of k hairspray events in 15-minute period j given n stylists:

Pr[Ej,cw = k | n] = ⎛ ⎝ n

k

⎞ ⎠ Pr[E]k(1 − Pr[E])(n−k)

Pr[Ej,w = 1 | n = 1] = Pr[E] Number of hairspray events per day at salon:

NP = TW/(15 min)

ECW = NP∑ j =1

Ej,cw

EW = NP∑ j =1

Ej,w

Expected value [EW+ECW] =NpPr[E] + Np∑NCW k=1 ·k( nk )Pr[E]k(1 − Pr[E])(n−k).

Near-field and far-field concentration during spray event for generation rate GE (mg/min) for time 0 ≤ Tp,j ≤ TE:(28)

CN(Tp, j ) = [ f1 + f2 exp(λ1 Tp, j ) + f3 exp(λ2 Tp, j )]

C F1

CF(Tp, j ) = [ f6 + f7 exp(λ1 Tp, j ) + f8 exp(λ2 Tp, j )]

C F1 where:

λ1 = 0.5 [

− (

β × VF + VN(β + Q) VN × VF

)

+ √(

β × VF + VN(β + Q) VN × VF

)2 − 4

( β × Q

VN × VF

) ]

λ2 = 0.5 [

− (

β × VF + VN(β + Q) VN × VF

)

− √(

β × VF + VN(β + Q) VN × VF

)2 − 4

( β × Q

VN × VF

) ]

f1 = GE/Q + GE/β

f6 = GE/Q

f2 = GE (

β × Q + λ2 × VN(β + Q) β × Q × VN(λ1 − λ2)

)

f3 = −GE (

β × Q + λ1 × VN(β + Q) β × Q × VN(λ1 − λ2)

)

f7 = GE ( λ1 × VN + β

β

)( β × Q + λ2 × VN(β + Q)

β × Q × VN(λ1 − λ2) )

f8 = −GE ( λ2 × VN + β

β

)( β × Q + λ1 × VN(β + Q)

β × Q × VN(λ1 − λ2) )

Near-field and far-field concentration after spray event for generation rate G (mg/min) for time Tp,j > TE:(28)

CN(Tp, j ) = [ f4 exp(λ1[Tp, j − TE]) + f5 exp(λ2[Tp, j − TE])]

CF (Tp, j ) = [ f9 exp(λ1[Tp, j − TE]) + f10 exp(λ2[Tp, j − TE])]

1722 Sahmel et al.

where:

CN,t ′ = CN(TE)

CF,t ′ = CF (TE)

f4 = (

β(CF,t ′ − CN,t ′ ) − λ2 × VN × CN,t ′ VN(λ1 − λ2)

)

f5 = (

β(CN,t ′ − CF,t ′ ) + λ1 × VN × CN,t ′ VN(λ1 − λ2)

)

f9 = (

λ1 × VN + β β

)

× (

β(CF,t ′ − CN,t ′ ) − λ2 × VN × CN,t ′ VN(λ1 − λ2)

)

f10 = (

λ2 × VN + β β

)

× (

β(CN,t ′ − CF,t ′ ) + λ1 × VN × CN,t ′ VN(λ1 − λ2)

)

Concentration as a function of time TS (superpo- sition of contribution all current and past 15-minute events):

CTOTAL,N(TS ) =

⌈ TS 15

⌉ ∑ j =1

FC (Ej,wCN(TS −15[ j −1])

+ Ej,cw CF(TS −15[ J −1]) )

CT OT AL,F (TS ) =

⌈ TS 15

⌉ ∑ j =1

FC (Ej,wCF(TS−15[ j −1])

+ Ej,cw CF(TS −15[ J −1]) )

Time-weighted average concentration:

CTW A,N[t1,t2 ] = 1

t2 − t1

∫ TS=t2 Ts =t1

CT OT AL,NF (TS )dTS

CTW A,F [t1,t2 ] = 1

t2 − t1

∫ TS=t2 Ts =t1

CT OT AL,NF (TS )dTS

Occupational equivalent cumulative exposure assuming standard 8-hour workday:

OE = DH TW 480

C E = CTW A,N[0,TW ] OE

Steady-State Mixing Factor Model

Equations specific to the steady-state mixing fac- tor model are provided below.

VC generation rate:

Gw,day = MEWH EWC F2

Gcw,day = Gw,day NCW

Time-weighted average concentration:

CTW A,N[0,TW ] = FC Gw, day

k + Gcw,day

Q · Tw · C F1

CTW A,F [0,TW ] = FC Gw,day + Gcw,day

Q · Tw · C F1

Steady-State Three-Zone Model

Equations specific to the steady-state three-zone model are provided below.

Compartments: Zone 0: Outside Zone 1: Near field Zone 2: Salon area Zone 3: Rest of home Flow rates (assumes balanced flow between

rooms and negligible outdoor concentration):

VR = VF −VS

Q20 = ARVSC F4

Q30 = ARVRC F4

Q12 = Q21 = β · C F3C F4

Q23 = Q32 = ART RVSC F4

Mass balance at a steady state:

−C1 Q12 + C2 Q21 + Gw,day = 0

C1 Q12 + C3 Q32 − C2(Q21 + Q23 + Q20) = 0

C2 Q23 − C3(Q32 + Q30) = 0

Multizone Exposure Modeling: Historical Use of Vinyl Chloride in Hairspray 1723

Solve system of equations (e.g., Cramer’s Rule):⎛ ⎜⎜⎜⎝

−Q12 Q12

0

Q21

−(Q21 + Q23 + Q20) Q23

0

Q32

−(Q32 + Q30)

⎞ ⎟⎟⎟⎠

⎛ ⎜⎜⎜⎝

C1

C2

C3

⎞ ⎟⎟⎟⎠

=

⎛ ⎜⎜⎝

−Gw,day 0

0

⎞ ⎟⎟⎠

Time-weighted average concentration: Near field: CTW A,N[0,TW ] = FC C1/C F1 Salon: CTW A,F [0,TW ] = FC C2/C F1 Rest of home: CTW A,F [0,TW ] = FC C3/C F1

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