TABLE OF CONTENTS

8. DERMAL ROUTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

8.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

8.2 SURFACE AREA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2

8.2.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2

8.2.2. Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2

8.2.3. Body Surface Area Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3

8.2.3.1. Costeff, 1966 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3

8.2.3.2. U.S. EPA, 1985 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-4

8.2.3.3. Phillips et al., 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-5

8.2.3.4. Wong et al. (2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-6

8.2.3.5. U.S. EPA Analysis of NHANES III Data . . . . . . . . . . . . . . . . 8-6

8.2.4. Application of Body Surface Area Data . . . . . . . . . . . . . . . . . . . . . . . . 8-7

8.3 ADHERENCE OF SOLIDS TO SKIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8

8.3.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8

8.3.2. Adherence of Solids to Skin Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8

8.3.2.1. Kissel et al., 1996a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8

8.3.2.2. Kissel et al., 1996b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8

8.3.2.3. Holmes et al., 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-9

8.3.2.4. Kissel et al., 1998 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-10

8.4 RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12

8.4.1. Body Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12

8.5 REFERENCES FOR CHAPTER 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-15

APPENDIX 8A - Formulas for Total Body Surface Area . . . . . . . . . . . . . . . . . . . . . 8A-1
LIST OF TABLES

Table 8-1. Total Body Surface Area of Male Children in Square Metersa . . . . . . . . . . . . . . . 8-17

Table 8-2. Total Body Surface Area of Female Children in Square Metersa . . . . . . . . . . . . . 8-18

Table 8-3. Percentage of Total Body Surface Area by Body Part For Children . . . . . . . . . . 8-19

Table 8-4. Descriptive Statistics For Surface Area/body Weight (SA/BW) Ratios (m2/kg) . 8-20

Table 8-6. Mean and Percentile Skin Surface Area (m2

) Derived from EPA Analysis of

NHANES III (All Children) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-21

Table 8-7. Mean and Percentile Skin Surface Area (m2

) Derived from EPA Analysis of

NHANES III (Male Children) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-22

Table 8-8. Mean and Percentile Skin Surface Area (m2

) Derived from EPA Analysis of

NHANES III (Female Children) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-23

Table 8-9. Summary of Field Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-24

Table 8-10. Geometric Mean and Geometric Standard Deviations of Solids Adherence by

Activity and Body Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25

Table 8-11. Summary of Groups Assayed in Round 2 of Field Measurements . . . . . . . . . . . 8-26

Table 8-12. Attire for Individuals within Children’s Groups Studied . . . . . . . . . . . . . . . . . . 8-27

Table 8-13. Geometric Means (Geometric Standard Deviations) of Round 2 Post-activity

Loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-28

Table 8-14. Summary of Controlled Green House Trials - Children Playing . . . . . . . . . . . . 8-29

Table 8-15. Preactivity Loadings Recovered from Greenhouse Trial Children Volunteers . 8-30

Table 8-19. Confidence in Solids Adherence to Skin Recommendations . . . . . . . . . . . . . . . 8-32

Table 8A-1. Estimated Parameter Values for Different Age Intervals . . . . . . . . . . . . . . . . . 8A-4

Table 8A-2. Summary of Surface Area Parameter Values for the Dubois and Dubois Model

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8A-5

LIST OF FIGURES

Figure 8-1. Schematic of Dose and Exposure: Dermal Route . . . . . . . . . . . . . . . . . . . . . . . . . 8-2

Figure 8-2. Skin Coverage as Determined by Fluorescence vs. Body Part for Adults

Transplanting Plants and for Children Playing in Wet Soils . . . . . . . . . . . . . . . . . . . . 8-33

Figure 8-3. Gravimetric Loading vs. Body Part for Adult Transplanting Plants in Wet Soil

and for Children Playing in Wet and Dry Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-33
8-1

1 8. DERMAL ROUTE

2

3 8.1 INTRODUCTION

4 Children may be more highly exposed to environmental toxicants through dermal routes

5 than adults. For instance, children often play and crawl on contaminated surfaces and are more

6 likely to wear less clothing than adults. These factors result in higher dermal contact with

7 contaminated media. In addition, children have a higher surface area relative to body weight. In

8 fact, the surface-area-to-body weight ratio for newborn infants is more than two times greater

9 than that for adults (Cohen-Hubal et al., 1999).

10 Dermal exposure can occur during a variety of activities in different environmental media

11 and microenvironments (U.S. EPA, 1992a; 1992b, 2004). These include:

12

13 C Water (e.g., bathing, washing, swimming);

14 C Soil (e.g., outdoor recreation, gardening, construction);

15 C Sediment (e.g., wading, fishing);

16 C Liquids (e.g., use of commercial products);

17 C Vapors/fumes (e.g., use of commercial products); and

18 C Indoors (e.g., carpets, floors, counter tops).

19

20 The major factors that must be considered when estimating dermal exposure are the

21 chemical concentration in contact with the skin, the extent of skin surface area exposed, the

22 duration of exposure, the absorption of the chemical through the skin, the internal dose, and the

23 amount of chemical that can be delivered to a target organ (i.e., biologically effective dose) (see

24 Figure 8-1). This chapter focuses on measurements of body surface areas and dermal adherence

25 of solids to the skin. For guidance on how to use these factors to assess dermal exposure, readers

26 are referred to Dermal Exposure Assessment: Principles and Applications (U.S. EPA, 1992b)

27 and Risk Assessment Guidelines (RAGs) Part E (U.S. EPA, 2004).
8-2

Applied

Dose

Potential

Dose

Chemical Organ Effect

Exposure

Internal

Dose

Biologically

Effective 

Dose

Metabolism

Skin

Uptake

Figure 8-1. Schematic of Dose and Exposure: Dermal Route

Source: U.S. Environmental Protection Agency (1992a).

1 8.2 SURFACE AREA

2 8.2.1. Background

3 The total surface area of skin exposed to a contaminant should be determined using

4 measurement or estimation techniques before conducting a dermal exposure assessment. This

5 section presents estimates of skin surface area for the whole body and individual body parts. 

6 Additionally information is presented on the application of skin surface area data to specific

7 exposure scenarios. 

8

9 8.2.2. Measurement Techniques

10 Coating, triangulation, and surface integration are direct measurement techniques that

11 have been used to measure total body surface area and the surface area of specific body parts. 

12 Consideration has been given for differences due to age, gender, and race. The results of the

13 various techniques have been summarized in Development of Statistical Distributions or Ranges

14 of Standard Factors Used in Exposure Assessments (U.S. EPA, 1985). 

15 The coating method consists of coating either the whole body or specific body regions

16 with a substance of known density and thickness. Triangulation consists of marking the area of
8-3

1 the body into geometric figures, then calculating the figure areas from their linear dimensions. 

2 Surface integration is performed by using a planimeter and adding the areas.

3 The triangulation measurement technique developed by Boyd (1935) has been found to

4 be highly reliable. It estimates the surface area of the body using geometric approximations that

5 assume that parts of the body resemble geometric solids. More recently, Popendorf and

6 Leffingwell (1976), and Haycock et al. (1978) have developed similar geometric methods that

7 assume body parts correspond to geometric solids, such as the sphere and cylinder. A linear

8 method proposed by DuBois and DuBois (1916) is based on the principle that the surface areas

9 of the parts of the body are proportional, rather than equal to the surface area of the solids they

10 resemble.

11 In addition to direct measurement techniques, several formulas have been proposed to

12 estimate body surface area from measurements of other major body dimensions (i.e., height and

13 weight) (U.S. EPA, 1985). Generally, the formulas are based on the observation that body

14 weight and height are correlated with surface area and are derived using multiple regression

15 techniques. A discussion and comparison of formulas to determine total body surface area are

16 presented in Appendix 8A.

17

18 8.2.3. Body Surface Area Studies

19 8.2.3.1. Costeff, 1966

20 Costeff (1966) developed an empirical formula for calculating the surface area of

21 children based on weight only:

22

23 SA = 4W + 7

W + 90 (1)

24 where:

25

SA = surface area (m2 26 );

27 Constants = 4, 7, and 90; and

28 W = weight (kg).

29

30 This simple formula applies to the weight range between 1.5 and 100 kg. 
8-4

1 8.2.3.2. U.S. EPA, 1985

2 U.S. EPA (1985) analyzed the direct surface area measurement data of Gehan and

3 George (1970) using the Statistical Processing System (SPS) software package of Buhyoff et al.

4 (1982). For their analysis, Gehan and George (1970) selected 401 measurements made by Boyd

5 (1935) that were complete for surface area, height, weight, and age. Boyd (1935) had reported

6 surface area estimates for 1,114 individuals using coating, triangulation, or surface integration

7 methods (U.S. EPA, 1985).

8 U.S. EPA (1985) used SPS to generate equations to calculate surface area as a function of

9 height and weight. These equations were then used to calculate body surface area distributions

10 of the U.S. population using the height and weight data obtained from the National Health and

11 Nutrition Examination Survey (NHANES) II and the computer program QNTLS of Rochon and

12 Kalsbeek (1983).

13 The equation proposed by Gehan and George (1970) was determined by U.S. EPA (1985)

14 to be the best choice for estimating total body surface area. However, the paper by Gehan and

15 George (1970) gave insufficient information to estimate the standard error about the regression. 

16 Therefore, U.S. EPA (1985) used the direct measurements of 401 individuals and re-analyzed the

17 data using the formula of Dubois and Dubois (1916) and SPS to obtain the standard error.

18 Regression equations were developed for specific body parts using the Dubois and

19 Dubois (1916) formula and using the surface area of various body parts provided by Boyd (1935)

20 and Van Graan (1969) in conjunction with SPS. Equations to estimate the body part surface area

21 of children were not developed because of insufficient data.

22 The percentile estimates for total surface area of male and female children presented in

23 Tables 8-1 and 8-2 were calculated using the total surface area regression equation and

24 NHANES II height and weight data, and using QNTLS. Estimates were not included for

25 children younger than 2 years old because NHANES height data were not available for this age

26 group. For children, the error associated with height and weight cannot be assumed to be zero

27 because of their relatively small sample sizes. Therefore, the standard errors of the percentile

28 estimates could not be estimated. This is because it cannot be assumed that the errors associated

29 with the exogenous variables (height and weight) are independent of those associated with the

30 model, i.e. there are insufficient data to determine the relationship between these errors.
8-5

1 Measurements of the surface area of children's body parts are summarized as a

2 percentage of total surface area in Table 8-3. Because of the small sample size, it is unclear how

3 accurately these estimates represent averages for the age groups. Note that the proportion of

4 total body surface area contributed by the head decreases from childhood to adulthood, whereas

5 the proportion contributed by the leg increases.

6

7 8.2.3.3. Phillips et al., 1993

8 Phillips et al. (1993) observed a strong correlation (0.986) between body surface area and

9 body weight and studied the effect of using these factors as independent variables in the lifetime

10 average daily dose (LADD) equation. The authors concluded that, because of the correlation

11 between these two variables, the use of body surface area to body weight (SA/BW) ratios in

12 human exposure assessments is more appropriate than treating these factors as independent

13 variables. Direct measurement (coating, triangulation, and surface integration) data from the

14 scientific literature were used to calculate SA/BW ratios for two age groups of children (infants

15 aged 0 to 2 years and children aged 2.1 to 17.9 years). These ratios were calculated by dividing

16 body surface areas by corresponding body weights for the 401 individuals analyzed by Gehan

17 and George (1970) and summarized by U.S. EPA (1985). Distributions of SA/BW ratios were

18 developed, and summary statistics were calculated for the two age groups and the combined data

19 set. 

20 Summary statistics for the two children’s age groups are presented in Table 8-4. The

21 shapes of these SA/BW distributions were determined using D'Agostino's test. The results

22 indicate that the SA/BW ratios for infants are lognormally distributed. SA/BW ratios for

23 children were neither normally nor lognormally distributed. According to Phillips et al. (1993),

24 SA/BW ratios should be used to calculate LADDs by replacing the body surface area factor in

25 the numerator of the LADD equation with the SA/BW ratio and eliminating the body weight

26 factor in the denominator of the LADD equation.

27 The effect of gender and age on SA/BW distribution was also analyzed by classifying the

28 401 observations by gender and age. Statistical analyses indicated no significant differences

29 between SA/BW ratios for males and females. SA/BW ratios were found to decrease with

30 increasing age.

31
8-6

1 8.2.3.4. Wong et al. (2000)

2 Wong et al. (2000) reports on surveys that gathered information on activity patterns

3 related to dermal contact with soil. Two random dialing national phone surveys were conducted. 

4 The initial Soil Contact Survey (SCS-I) was conducted in 1996 (also reported on by Garlock et

5 al., 1999) and the second Soil Contact Survey (SCS-II) was conducted in 1999. Information

6 about children were gathered from adults over the age of 18. SCS-I had 450 participants with

7 complete responses and SCS-II had 483 participants with complete responses.

8 SCS-I gathered information on 211 children. For older children (those between the ages

9 of 5 and 17 years) information was gathered on their participation in “gardening and yardwork,”

10 “outdoor sports,” and “outdoor play activities.” For children less than 5 years old, information

11 was gathered on “outdoor play activities” including whether the activity occurred on a

12 playground or yard with “bare dirt or mixed grass and dirt” surfaces. An effort was also made to

13 determine the clothing worn while participating in these play activities during warm weather

14 months (April though October). For both groups of children, information was gathered

15 concerning frequency of hand washing and bathing, 

16 Results of SCS-I indicate that most children wore short pants, a dress or skirt, short

17 sleeve shirts, no socks, and leather or canvas shoes during the outdoor play activities of interest. 

18 Using the survey data on clothing and total body surface area data from U.S. EPA (1985),

19 estimates were made of the skin area exposed (expressed as percentages of total body surface

20 area) associated with various age ranges and activities (Table 8-5). 

21

22 8.2.3.5. U.S. EPA Analysis of NHANES III Data

23 The Third National Health and Nutrition Examination Survey (NHANES III), 1988-94

24 was conducted on a nationwide probability sample of approximately 33,994 persons aged 2

25 months and older. The survey was designed to obtain nationally representative information on

26 the health and nutritional status of the population of the United States through interviews and

27 direct physical examinations. A number of anthropometrical measurements were taken for each

28 participant in the study, including body weight. Unit nonresponse to the household interview

29 was 14 percent, and an additional 8 percent did not participate in the physical examinations

30 (including body weight measurements). 
8-7

1 Certain subpopulations were over sampled to ensure a prespecified minimum sample size

2 for each analytic domain. These over sampled subpopulations include children, older persons,

3 Mexican-Americans, African-Americans, and people living in certain geographic areas. Sample

4 data were assigned weights to account both for the disparity in sample sizes for these groups and

5 for other inadequacies in sampling, such as the presence of non-respondents. The weight for

6 each participant was calculated as the reciprocal of the participant's probability of selection, with

7 adjustments for other variabilities in sampling rates such as changes made to the sampling rates

8 at the time of data collection. 

9 Body weight data from NHANES III study were used to calculate estimated body surface

10 areas for children in the standard age categories using the empirical relationship found in

11 Appendix 8A. The methodology was similar to that used in U.S. EPA (1985), as described in

12 Section 8.2.3.2, but more recent NHANES data were used. The resulting skin surface areas are

13 presented in Tables 8-6 (all children), 8-7 (male children), and 8-8 (female children).

14

15 8.2.4. Application of Body Surface Area Data

16 The skin area studies summarized above address total skin surface area. Application of

17 these data to many exposure scenarios involve some reduction in exposed skin area. This section

18 discusses how this issue has been addressed in EPA guidance.

19 For swimming and bathing scenarios, past exposure assessments have assumed that 75 to

20 100 percent of the skin surface is exposed (U.S. EPA, 1992b). More recent guidance

21 recommends assuming 100% exposure for these scenarios with a central default recommendation

of 6,600 cm2 22 for children aged 0-6 years in residential settings (U.S. EPA, 2004).

23 It is generally assumed that adherence of solids to skin occurs only on the areas of the

24 body not covered by clothing. Past guidance has presented clothing scenarios that suggest that

25 roughly 10 to 25 percent of the skin area is uncovered (U.S. EPA, 1992b). Since some studies

26 have suggested that exposure can occur under clothing, the upper end of this range was selected

27 in Dermal Exposure Assessment: Principles and Applications (U.S. EPA, 1992b) for deriving

defaults. More recent guidance suggests a central default value of 2,800 cm2 28 exposed skin area

29 for children aged 0-6 in residential settings (US EPA, 2004). This was derived assuming a

30 clothing scenario that limited exposure to head, hands, forearms, lower legs and feet. 

31
8-8

1 8.3 ADHERENCE OF SOLIDS TO SKIN

2 8.3.1. Background

3 A variety of solid residues can accumulate on skin including soil, household dust,

4 sediments and commercial powders. The amount of material adhering to the surface of the skin

5 is a required parameter for calculating dermal dose when the exposure scenario involves dermal

6 contact with a chemical in a solid matrix. A number of studies have measured this factor and

7 they have been used to support EPA guidelines (U.S. EPA 1992b and 2004). This section

8 summarizes the studies that estimate the adherence of solids to skin for use as exposure factors.

9

10 8.3.2. Adherence of Solids to Skin Studies

11 8.3.2.1. Kissel et al., 1996a

12 Kissel et al. (1996a) conducted soil adherence experiments using five soil types

13 obtained locally in the Seattle, WA, area: sand, loamy sand, loamy sand, sandy loam,

14 and silt loam. All soils were analyzed by hydrometer (settling velocity) to determine

15 composition. Clay content ranged from 0.5 to 7.0%. Organic carbon content,

16 determined by combustion, ranged from 0.7 to 4.6%. Soils were dry-sieved to obtain

17 particle size ranges of <150, 150-250, and >250 μm. For each soil type, the amount of

18 soil adhering to an adult female hand, using both sieved and unsieved soils, was

19 determined by measuring the soil sample weight before and after the hand was pressed

20 into a pan containing the test soil. Loadings were estimated by dividing the recovered

21 soil mass by total hand area, although loading occurred primarily on only one side of the

22 hand. Results showed that generally, soil adherence to hands was directly correlated

23 with moisture content, inversely correlated with particle size, and independent of clay

24 content or organic carbon content.

25

26 8.3.2.2. Kissel et al., 1996b

27 Further experiments were conducted by Kissel et al. to estimate soil adherence

28 associated with various indoor and outdoor activities: greenhouse gardening, tae kwon

29 do karate, soccer, rugby, reed gathering, irrigation installation, truck farming, and

30 playing in mud (Kissel et al., 1996b). Several of the activities studied involved children,

31 as shown in Table 8-9 
8-9

1 A summary of field studies by activity, gender, age, field conditions, and

2 clothing worn is presented in Table 8-9. The subjects’ body surfaces (forearms, hands,

3 lower legs for all sample groups; faces and/or feet pairs in some sample groups) were

4 washed before and after the monitored activities. Paired samples were pooled into

5 single ones. Mass recovered was converted to loading using allometric models of

6 surface area. Geometric means for soil adherence by activity and body region are

7 presented in Table 8-10. The results presented are based on direct measurement of soil

8 loading on the surfaces of skin before and after activities that may be expected to have

9 soil contact (Kissel et al., 1996b). The results indicate that the amount of soil adherence

10 to the hands is higher than for other parts of the body.

11

12 8.3.2.3. Holmes et al., 1999

13 Holmes et al. (1999) collected pre- and post-activity soil loadings on various

14 body parts of individuals within groups engaged in various occupational and

15 recreational activities. These groups included children at a daycare center (Daycare

16 kids) and playing indoors in a residential setting (Indoor kids). This study was

17 conducted as a follow up to previous field sampling of soil adherence on individuals

18 participating in various activities (Kissel et al., 1996b). For this round of sampling, soil

19 loading data were collected utilizing the same methods used and described in Kissel et

20 al. (1996b). Information regarding the groups of children studied and their observed

21 activities is presented in Table 8-11.

22 The daycare children studied were all at one location, and measurements were

23 taken on three different days. The children freely played both indoors in the house and

24 outdoors in the backyard. The backyard was described as having a grass lawn, shed,

25 sand box, and wood chip box. In this setting, the children engaged in typical activities

26 including: playing with toys and each other, wrestling, sleeping, and eating. The

27 number of children within each day’s group and the clothing worn is described in Table

28 8-12.

29 The five children measured on the first day were washed first thing in the

30 morning to establish a preactivity level. They were next washed at noon to determine

31 the postactivity soil loading for the morning (Daycare kids No. 1a). The same children
8-10

1 were washed once again at the close of the day for measurement of soil adherence from

2 the afternoon play activities (Daycare kids No. 1b).

3 For the second observation day (Daycare kids No. 2), postactivity data were

4 collected for five children. All the activities on this day occurred indoors. For the third

5 daycare group (Daycare kids No. 3), four children were studied. 

6 On two separate days, children playing indoors in a home environment were

7 monitored. The first group (Indoor kids No. 1) had four children while the second group

8 (Indoor kids No. 2) had six children. The play area was described by the authors as

9 being primarily carpeted. The clothing worn by the children within each day’s group is

10 described in Table 8-12.

11 The geometric means and standard deviations of the postactivity soil adherence

12 for each group of children and for each body part are summarized in Table 8-13. 

13 According to the authors, variations in the soil loading data from the daycare

14 participants reflect differences in the weather and access to the outdoors.

15 An advantage of this study is that it provides a supplement to soil loading data

16 collected in a previous round of studies (Kissel et al., 1996b). Also, the data support the

17 assumption that hand loading can be used as a conservative estimate of soil loading on

18 other body surfaces for the same activity. The activities studied represent normal child

19 play both indoors and outdoors, as well as for different combinations of clothing. The

20 small number of participants is a disadvantage of this study. Also, the children studied

21 and the activity setting may not be representative of the U.S. population.

22

23 8.3.2.4. Kissel et al., 1998

24 In this study, Kissel et al.(1998) measured dermal exposure to soil from staged

25 activities conducted in a greenhouse. A fluorescent marker was mixed in soil so that

26 soil contact for a particular skin surface area could be identified. The subjects, which

27 included a group of children, were video-imaged under a long-wave ultraviolet (UV)

28 light before and after soil contact. In this manner, soil contact on hands, forearms, lower

29 legs, and faces was assessed by presence of fluorescence. In addition to fluorometric

30 data, gravimetric measurements for preactivity and postactivity were obtained from the

31 different body parts examined.
8-11

1 The studied group of children played for 20 minutes in a soil bed of varying

2 moisture content representing wet and dry soils. For wet soils, both combinations of

3 long sleeves and long pants and short sleeves and short pants were tested. Children only

4 wore short sleeves and short pants during play in the dry soil. Clothing was laundered

5 after each trial. Thus, a total of three trials with children were conducted. The

6 parameters describing each of these trials are summarized in Table 8-14.

7 Before each trial, each child was washed in order to obtain a preactivity or

8 background gravimetric measurement. Preactivity data are shown in Table 8-15. Body

9 part surface areas were calculated using U.S. EPA (1985) for the range of heights and

10 weights of the study participants.

11 For wet soil, postactivity fluorescence results indicated that the hand had a much

12 higher fractional coverage than other body surfaces (see Figure 8-2). No fluorescence

13 was detected on the forearms or lower legs of children dressed in long sleeves and pants.

14 As shown in Figure 8-3, postactivity gravimetric measurements showed higher

15 soil loading on hands and much lower amounts on other body surfaces, as was observed

16 with fluorescence data. According to Kissel et al. (1998), the relatively low loadings

17 observed on non-hand body parts may be a result of the limited area of contact rather

than lower localized loadings. A geometric mean dermal loading of 0.7 mg/cm2 18 was

19 found on the children’s hands following play in wet soil. Mean loadings were lower on

20 hands in the dry soil trial and on lower legs, forearms, and faces in both the wet and dry

21 soil trials. Higher loadings were observed for all body surfaces with the higher moisture

22 content soils.

23 This report is valuable for showing soil loadings from soils of different moisture

24 content and providing evidence that dermal exposure to soil is not uniform for various

25 body surfaces. There is also some evidence from this study demonstrating the protective

26 effect of clothing. Disadvantages of the study include a small number of study

27 participants and a short activity duration. Also, no information is provided on the ages

28 of the children involved in the study.

29

30 8.3.2.5. Shoaf et al., 2005
8-12

1 The purpose of this study was to obtain sediment adherence data for children

2 playing in a tide flat. The study was conducted on one day in late September 2003 at a

3 tide flat in Jamestown, Rhode Island. Nine subjects (three females and six males) ages 7

4 to 12 years old participated in the study. This study reports direct measurements of

5 sediment loadings on five body parts (face, forearms, hands, lower legs and feet) after

6 play in a tide flat. Each of nine subjects participated in two timed sessions and pre- and

7 post-activity sediment loading data were collected. Geometric mean (geometric standard

deviations) dermal loadings (mg/cm2 8 ) on the face, forearm, hands, lower legs and feet

9 for the combined sessions were 0.04 (2.9), 0.17 (3.1), 0.49 (8.2), 0.70 (3.6) and 21 (1.9),

10 respectively. Participants’ parents completed questionnaires regarding their child’s

11 typical activity patterns during tide flat play, exposure frequency and duration, clothing

12 choices, bathing practices and clothes laundering. 

13 The primary advantage of this study is that it provides adherence data specific to

14 children and sediments which had previously been largely unavailable. Results will be

15 useful to risk assessors considering exposure scenarios involving child activities at a

16 coastal shoreline or tide flat. The limited number of participants (9) and sampling over

17 just one day and one location, make extrapolation to other situations uncertain.

18

19 8.4 RECOMMENDATIONS

20 8.4.1. Body Surface Area

21 Body surface area estimates have been derived from direct measurements and

22 from correlations with height and weight. Re-analysis of data collected by Boyd (1935)

23 by several investigators (Gehan and George, 1970; U.S. EPA, 1985; ; Phillips et al.,

24 1993) constitutes much of this literature. The U.S. EPA (1985) study summarizes and

25 compares previous reports in the literature, provides statistical distributions for adults,

26 and provides data for total body surface area and body parts by gender for children. The

27 results are based on selected measurements from the original data collected by Boyd

28 (1935). The EPA analysis of NHANES III data uses correlations with body weight and

29 height for deriving skin surface area (see Section 8.2.3.5 and Appendix 8A). NHANES

30 III used a statistically based survey design which should ensure reasonable

31 representativeness of the general population. 
8-13

1 The recommendations for body surface area for children are summarized in

2 Table 8-17. The recommendations for total body surface area are based on the EPA

3 analysis of NHANES III data and are presented for the standard age groupings in Tables

4 8-6 to 8-8. The recommendations in Table 8-17 refer to Table 8-3 for body part

5 percentages which were based on U.S. EPA (1985). Age specific body part areas can be

6 obtained by applying these percentages to the total body part areas in Tables 8-6 to 8-8.

7 Table 8-18 presents the confidence ratings for various aspects of the recommendations

8 for body surface area and indicates an overall confidence rating of medium.

9 For bathing and swimming exposure scenarios, an assumption of 100% skin area

10 exposure is recommended. For exposure scenarios involving contact with solids, it is

11 reasonable to assume that clothing reduces the contact area. RAGS Part E (US EPA,

12 2004) presents default assumptions for exposed skin areas of children in a residential

13 setting. The child resident was assumed to wear a short-sleeved shirt and shorts (no

14 shoes). Therefore, the exposed skin was limited to face, hands, forearms (45% of total

15 arms), lower legs (40% of total legs), and feet. The percentages of total skin area for

16 these body parts can be obtained from Table 8-3 and applied to the total skin area in

17 Tables 8-6 to 8-8, to derive age specific exposure areas. This clothing scenario is

18 characteristic of warm weather situations and should be adjusted based on judgement to

19 represent other climatic conditions. Although, it is generally assumed that adherence of

20 solids to skin occurs to only the areas of the body not covered by clothing, it is

21 important to understand that soil and dust particles can get under clothing and be

22 deposited on skin to varying degrees depending on the protective properties of the

23 clothing. Assessors should consider this possibility for the scenario of concern and use

24 larger skin areas if judged appropriate. 

25

26 8.4.2. Adherence of Solids to Skin

27 The adherence factor (AF) describes the amount of material that adheres to the

28 skin per unit of surface area. Although most research in this area has focused on soils, a

29 variety of other solid residues can accumulate on skin including household dust,

30 sediments and commercial powders. Studies on soil adherence have shown that 1) soil

31 properties influence adherence, 2) soil adherence varies considerably across different
8-14

1 parts of the body and 3) soil adherence varies with activity (U.S. EPA, 2004). Ideally

2 exposure assessors should use adherence data derived from testing that matches the

3 exposure scenario of concern in terms of solid type, exposed body parts and activities as

4 closely as possible. It is recommended that assessors use Tables 8-9 and 8-10 for this

5 purpose. These tables provide body-part specific adherence values for a variety of

6 solids (garden soils, indoor dust, sediment, etc.) and activities. Table 8-9 lists the age

7 range covered by each study. This should be used as a general guide to the ages covered

8 by these data. The small number of subjects in these studies prevents the development

9 of recommendations for narrower age groups. 

10 EPA guidance under RAGS Part E (US EPA, 2004) provides body part area11 weighted adherence factors that can facilitate dermal exposure calculations. These

12 values were derived by adding the mass of solid adhering to various body parts and

13 dividing by the total exposed skin area. These values as summarized in Table 8-16 can

14 be directly applied to the total exposed skin surface area.

15 The solids adherence recommendations are summarized in Table 8-17. The

16 overall confidence rating for the adherence recommendations is medium as shown in

17 Table 8-19. Insufficient data are available to develop distributions or probability

18 functions. Note also that the skin adherence studies have not considered the influence of

19 skin moisture on adherence. Skin moisture varies for an individual depending on factors

20 such as activity and ambient temperature/humidity. It also varies across individuals. It

21 is uncertain how well this variability has been captured in the adherence studies. 

22 The dermal adherence value represents the amount of material on the skin at the

23 time of measurement. EPA, 1992b recommends interpreting adherence values as

24 representative of contact events. Assuming that the amount measured on the skin

25 represents its accumulation between washings and that people wash at least once per

26 day, these adherence values can be interpreted as daily contact rates (U.S. EPA, 1992b). 

27 The rate of solids accumulation on skin over time has not been well studied, but

28 probably occurs fairly quickly. Therefore pro-rating the adherence values for exposure

29 time periods of less than one day is not recommended. 
8-15

1 8.5 REFERENCES FOR CHAPTER 8

2

3 Boyd, E. (1935) The growth of the surface area of the human body. Minneapolis, Minnesota: University

4 of Minnesota Press.

5

6 Buhyoff, G.J.; Rauscher, H.M.; Hull, R.B.; Killeen, K.; Kirk, R.C. (1982) User's Manual for Statistical

7 Processing System (version 3C.1). Southeast Technical Associates, Inc.

8

9 Cohen-Hubal, E.A.; Sheldon, L.S.; Burke, J.M.; McLundy, T.R.; Berry, M.R.; Rigas, M.L.; Zartarian,

10 V.G.; Freeman, N.C.G. (1999) Children’s exposure assessment: A review of factors influencing

11 children’s exposure, and the data available to characterize and assess that exposure. Research

12 Triangle Park, NC: U.S. Environmental Protection Agency, National Exposure Research

13 Laboratory.

14

15 Costeff (1966) A simple empirical formula for calculating approximate surface area in children. Arch.

16 Dis. Child. 41:651-683.

17

18 Dubois, D.; Dubois, E.F. (1916) A formula to estimate the approximate surface area if height and weight

19 be known. Arch. of Intern. Med. 17:863-871.

20

21 Gehan, E.; George, G.L. (1970) Estimation of human body surface area from height and weight. Cancer

22 Chemother. Rep. 54(4):225-235.

23

24 Garlock T.J., Shirai, J.H. and Kissel, J.C. (1999) Adult responses to a survey of soil contact related

25 behaviors. J. Exposure Anal. Environ. Epid. 1999: 9: 134-142.

26

27 Geigy Scientific Tables (1981) Nomograms for determination of body surface area from height and mass. 

28 Lentner, C. (ed.). CIBA-Geigy Corporation, West Caldwell, NJ. pp. 226-227.

29

30 George, S.L.; Gehan, E.A.; Haycock, G.B.; Schwartz, G.J. (1979) Letters to the editor. J. Ped. 94(2):342.

31

32 Haycock, G.B.; Schwartz, G.J.; Wisotsky, D.H. (1978) Geometric method for measuring body surface

33 area: A height-weight formula validated in infants, children, and adults. J. Ped. 93(1):62-66.

34

35 Holmes, K.K.; Kissel, J.C.; Richter, K.Y. (1996) Investigation of the influence of oil on soil adherence to

36 skin. J. Soil. Contam. 5(4):301-308.

37

38 Holmes, Jr., K.K., J.H. Shirai, K.Y. Richter, and J. C. Kissel (1999) Field Measurement of Dermal

39 Loadings in Occupational and Recreational Activities, Environmental Research, Section A, 80,

40 148-157. 

41

42 Kissel, J.; Richter, K.; Duff, R.; Fenske, R. (1996a) Factors Affecting Soil Adherence to Skin in Hand43 Press Trials. Bull. Environ. Contamin. Toxicol. 56:722-728.

44

45 Kissel, J.; Richter, K.; Fenske, R. (1996b) Field measurements of dermal soil loading attributable to

46 various activities: Implications for exposure assessment. Risk Anal. 16(1):116-125.

47

48 Kissel, J.C., Shirai, J. H., Richter, K.Y., and R.A. Fenske (1998) Investigation of Dermal Contact with

49 Soil in Controlled Trials, Journal of Soil Contamination, 7(6): 737-752.

50

51

52

53 Phillips, L.J.; Fares, R.J.; Schweer, L.G. (1993) Distributions of total skin surface area to body weight

54 ratios for use in dermal exposure assessments. J. Expos. Anal. Environ. Epidemiol. 3(3):331-338.

55
8-16

1 Popendorf, W.J.; Leffingwell, J.T. (1976) Regulating OP pesticide residues for farmworker protection. 

2 In: Residue Review 82. New York, NY: Springer-Verlag New York, Inc., 1982. pp. 125-201.

3

4 Rochon, J.; Kalsbeek, W.D. (1983) Variance estimation from multi-stage sample survey data: the

5 jackknife repeated replicate approach. Presented at 1983 SAS Users Group Conference, New

6 Orleans, Louisiana, January 1983.

7

8 Sendroy, J.; Cecchini, L.P. (1954) Determination of human body surface area from height and weight. J.

9 Appl. Physiol. 7(1):3-12.

10

11 Shoaf, MB; J.H. Shirai, G. Kedan, J. Schaum, J.C. Kissel. 2005. Child Dermal Sediment Loads Following

12 Play in a Tide Flat. J Expo Anal Environ Epidemiol. 15:407-412.

13

14 U.S. EPA. (1985) Development of statistical distributions or ranges of standard factors used in exposure

15 assessments. Washington, DC: Office of Research and Development, Office of Health and

16 Environmental Assessment. EPA 600/8-85-010. Available from: NTIS, Springfield, VA. 

17 PB85-242667.

18

19 U.S. EPA. (1992a) Guidelines for exposure assessment. Federal Register. FR 57:104:22888-22938. 

20 May 29, 1992.

21

22 U.S. EPA. (1992b) Dermal exposure assessment: principles and applications. Washington, DC: Office

23 of Research and Development, Office of Health and Environmental Assessment/OHEA. U.S.

24 EPA/600/8-9-91.

25

26 U. S. Environmental Protection Agency (U.S. EPA) (1996) Analysis of the National Human Activity

27 Pattern Survey (NHAPS) Respondents from a Standpoint of Exposure assessment. Office of

28 Research and Development, Washington, D.C., EPA/600/R-96/074.

29

30 U.S. EPA. (2004) Risk Assessment Guidance for Superfund Volume I: Human Health Evaluation Manual

31 (Part E, Supplemental Guidance for Dermal Risk Assessment). EPA/540/R/99/005. 

32 http://www.epa.gov/superfund/programs/risk/ragse/index.htm

33

34 Van Graan, C.H. (1969) The determination of body surface area. Supplement to the South African J. of

35 Lab. and Clin. Med. 8-2-69.

36

37 Wong, EY; JH Shirai; TJ Garlock and JC Kissel. Adult proxy responses to a survey of children’s dermal

38 soil contact activities. J Expo Anal Environ Epidemiol. 10:509-517.

39

40
8-17

Table 8-1. Total Body Surface Area of Male Children in Square Metersa

Age

(yr)b

Percentile

5 10 15 25 50 75 85 90 95

2 < 3

3 < 4

4 < 5

5 < 6

6 < 7

7 < 8

8 < 9

9 < 10

10 < 11

11 < 12

12 < 13

13 < 14

14 < 15

15 < 16

16 < 17

17 < 18

 3 < 6

 6 < 9

 9 < 12

12 < 15

15 < 18

0.527

0.585

0.633

0.692

0.757

0.794

0.836

0.932

1.01

1.00

1.11

1.20

1.33

1.45

1.55

1.54

0.616

0.787

0.972

1.19

1.50

0.544

0.606

0.658

0.721

0.788

0.832

0.897

0.966

1.04

1.06

1.13

1.24

1.39

1.49

1.59

1.56

0.636

0.814

1.00

1.24

1.55

0.552

0.620

0.673

0.732

0.809

0.848

0.914

0.988

1.06

1.12

1.20

1.27

1.45

1.52

1.61

1.62

0.649

0.834

1.02

1.27

1.59

0.569

0.636

0.689

0.746

0.821

0.877

0.932

1.00

1.10

1.16

1.25

1.30

1.51

1.60

1.66

1.69

0.673

0.866

1.07

1.32

1.65

0.603

0.664

0.731

0.793

0.866

0.936

1.00

1.07

1.18

1.23

1.34

1.47

1.61

1.70

1.76

1.80

0.728

0.931

1.16

1.49

1.75

0.629

0.700

0.771

0.840

0.915

0.993

1.06

1.13

1.28

1.40

1.47

1.62

1.73

1.79

1.87

1.91

0.785

1.01

1.28

1.64

1.86

0.643

0.719

0,796

0.864

0.957

1.01

1.12

1.16

1.35

1.47

1.52

1.67

1.78

1.84

1.98

1.96

0.817

1.05

1.36

1.73

1.94

0.661

0.729

0.809

0.895

1.01

1.06

1.17

1.25

1.40

1.53

1.62

1.75

1.84

1.90

2.03

2.03

0.842

1.09

1.42

1.77

2.01

0.682

0.764

0.845

0.918

1.06

1.11

1.24

1.29

1.48

1.60

1.76

1.81

1.91

2.02

2.16

2.09

0.876

1.14

1.52

1.85

2.11

a

Lack of height measurements for children <2 years in NHANES II precluded calculation of surface areas

for this age group.

b

Estimated values calculated using NHANES II data.

Source: U.S. EPA (1985).
8-18

Table 8-2. Total Body Surface Area of Female Children in Square Metersa

Percentile

Age (yr)b 5 10 15 25 50 75 85 90 95

 2 < 3

 3 < 4

 4 < 5

 5 < 6

 6 < 7

 7 < 8

 8 < 9

 9 < 10

10 < 11

11 < 12

12 < 13

13 < 14

14 < 15

15 < 16

16 < 17

17 < 18

0.516

0.555

0.627

0.675

0.723

0.792

0.863

0.897

0.981

1.06

1.13

1.21

1.31

1.38

1.40

1.42

0.532

0.570

0.639

0.700

0.748

0.808

0.888

0.948

1.01

1.09

1.19

1.28

1.34

1.49

1.46

1.49

0.544

0.589

0.649

0.714

0.770

0.819

0.913

0.969

1.05

1.12

1.24

1.32

1.39

1.43

1.48

1.51

0.557

0.607

0.666

0.735

0.791

0.854

0.932

1.01

1.10

1.16

1.27

1.38

1.45

1.47

1.53

1.56

0.579

0.649

0.706

0.779

0.843

0.917

1.00

1.06

1.17

1.30

1.40

1.48

1.55

1.57

1.60

1.63

0.610

0.688

0.758

0.830

0.914

0.977

1.05

1.14

1.29

1.40

1.51

1.59

1.66

1.67

1.69

1.73

0.623

0.707

0.777

0.870

0.961

1.02

1.08

1.22

1.34

1.50

1.62

1.67

1.74

1.72

1.79

1.80

0.637

0.721

0.794

0.902

0.989

1.06

1.11

1.31

1.37

1.56

1.64

1.75

1.76

1.76

1.84

1.84

0.653

0.737

0.820

0.952

1.03

1.13

1.18

1.41

1.43

1.62

1.70

1.86

1.88

1.83

1.91

1.94

 3 < 6

 6 < 9

 9 < 12

12 < 15

15 < 18

0.585

0.754

0.957

1.21

1.40

0.610

0.790

0.990

1.27

1.44

0.630

0.804

1.03

1.30

1.47

0.654

0.845

1.06

1.37

1.51

0.711

0.919

1.16

1.48

1.60

0.770

1.00

1.31

1.61

1.70

0.808

1.04

1.38

1.68

1.76

0.831

1.07

1.43

1.74

1.82

0.879

1.13

1.56

1.82

1.92

a

Lack of height measurements for children <2 years in NHANES II precluded calculation of surface areas

for this age group.

b

Estimated values calculated using NHANES II data.

Source: U.S. EPA (1985).
8-19

Table 8-3. Percentage of Total Body Surface Area by Body Part For Children

Age (yr) N

M:F

Percent of Total

Head Trunk Arms Hands Legs 

Mean Min-Max Mean Min-Max Mean Min-Max Mean Min-Max Mean Min-Ma

< 1 2:0 18.2 18.2-18.3 35.7 34.8-36.6 13.7 12.4-15.1 5.3 5.21-5.39 20.6 18.2-22

1 < 2 1:1 16.5 16.5-16.5 35.5 34.5-36.6 13.0 12.8-13.1 5.68 5.57-5.78 23.1 22.1-242 < 3 1:0 14.2 38.5 11.8 5.30 23.2 3 < 4 0:5 13.6 13.3-14.0 31.9 29.9-32.8 14.4 14.2-14.7 6.07 5.83-6.32 26.8 26.0-284 < 5 1:3 13.8 12.1-15.3 31.5 30.5-32.4 14.0 13.0-15.5 5.70 5.15-6.62 27.8 26.0-295 < 66 < 7 1:0 13.1 35.1 13.1 4.71 27.1 7 < 88 < 9

9 < 10 0:2 12.0 11.6-12.5 34.2 33.4-34.9 12.3 11.7-12.8 5.30 5.15-5.44 28.7 28.5-28

10 < 1111 < 1212 < 13 1:0 8.74 34.7 13.7 5.39 30.5 

13 <14 1:0 9.97 32.7 12.1 5.11 32.0 

14 < 1515 < 1616 < 17 1:0 7.96 32.7 13.1 5.68 33.6 17 < 18 1:0 7.58 31.7 17.5 5.13 30.8 

N: Number of subjects, (males and females)Source: U.S. EPA (1985).
8-20

Table 8-4. Descriptive Statistics For Surface Area/body Weight (SA/BW) Ratios (m2/kg)

Age (yrs.) Mean

Range

Min-Max SDa SEb

Percentiles

5 10 25 50 75 

0-2 0.0641 0.0421-0.1142 0.0114 7.84e-4 0.0470 0.0507 0.0563 0.0617 0.0712.1 - 17.9 0.0423 0.0268-0.0670 0.0076 1.05e-3 0.0291 0.0328 0.0376 0.0422 0.045

aStandard deviation.bStandard error of the mean.

Source: Phillips et al. (1993).
8-21

Table 8-5. Estimated skin surface exposed during warm weather outdoor activities

Skin area exposed (% of total)

Play Gardening/yardwork Organized Team Sport

Age (years) <5 5-17 5-17

n 41 437 65

Mean 38.0 33.8 29.0

Median 36.5 33.0 30.0

S.D. 6.0 8.3 10.5

Source: Wong et al. (2000).

Table 8-6. Mean and Percentile Skin Surface Area (m2

) Derived from EPA Analysis of NHANES III (All

Children)

Age

Group N mean

percentiles

5th 10th 15th 25th 50th 75th 85th 90th 95th

2 to <3 months 234 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4

3 to <5 months 556 0.4 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4

6 to <11 months 1163 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5

1 to <2 years 1230 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6

2 to <3 years 1224 0.6 0.5 0.5 0.6 0.6 0.6 0.6 0.6 0.7 0.7

3 to <5 years 3214 0.7 0.6 0.6 0.7 0.7 0.7 0.8 0.8 0.9 0.9

6 to <11 years 2694 1.1 0.8 0.8 0.9 0.9 1.0 1.2 1.3 1.3 1.4

11 to <16 years 2181 1.5 1.2 1.2 1.3 1.4 1.5 1.7 1.8 1.9 2.0

16 to <21 years 1891 1.8 1.5 1.5 1.5 1.6 1.8 1.9 2.0 2.1 2.2

Source: EPA Analysis of NHANES III data
8-22

Table 8-7. Mean and Percentile Skin Surface Area (m2) Derived from EPA Analysis of NHANES III

(Male Children)

Age

Group N mean

percentiles

5th 10th 15th 25th 50th 75th 85th 90th 95th

2 to <3 months 103 0.4 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4

3 to <5 months 287 0.4 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5

6 to <11 months 589 0.5 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5

1 to <2 years 613 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6

2 to <3 years 627 0.6 0.5 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7

3 to <5 years 1556 0.7 0.6 0.6 0.7 0.7 0.7 0.8 0.8 0.9 0.9

6 to <11 years 1373 1.1 0.8 0.8 0.9 0.9 1.0 1.2 1.3 1.3 1.4

11 to <16 years 1037 1.6 1.2 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.0

16 to <21 years 890 1.9 1.6 1.6 1.7 1.7 1.8 2.0 2.0 2.1 2.3

Source: EPA Analysis of NHANES III data
8-23

Table 8-8. Mean and Percentile Skin Surface Area (m2) Derived from EPA Analysis of NHANES III

(Female Children)

Age

Group N mean

percentiles

5th 10th 15th 25th 50th 75th 85th 90th 95th

2 to <3 months 131 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4

3 to <5 months 269 0.4 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4

6 to <11 months 574 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5

1 to <2 years 617 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6

2 to <3 years 597 0.6 0.5 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.7

3 to <5 years 1658 0.7 0.6 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9

6 to <11 years 1321 1.1 0.8 0.8 0.9 0.9 1.0 1.2 1.3 1.3 1.4

11 to <16 years 1144 1.5 1.2 1.3 1.3 1.4 1.5 1.6 1.8 1.8 1.9

16 to <21 years 1001 1.7 1.4 1.5 1.5 1.5 1.6 1.8 1.9 2.0 2.1

Source: EPA Analysis of NHANES III data
8-24

Table 8-9. Summary of Field Studies

Activity Month

Eventa

(hrs) Nb M F

Age

(yrs) Conditions Clothing

Indoor

Tae Kwon Do Feb. 1.5 7 6 1 8-42 Carpeted floor All in long sleeve-long pants

martial arts uniform, sleeves

rolled back, barefoot

Indoor Kids No. 1 Jan. 2 4 3 1 6-13 Playing on carpeted floor 3 of 4 short pants, 2 of 4 short

sleeves, socks, no shoes

Indoor Kids No. 2 Feb. 2 6 4 2 3-13 Playing on carpeted floor 5of 6 long pants, 5 of 6 long

sleeves, socks, no shoes

Daycare Kids No. 1a Aug. 3.5 6 5 1 1-6.5 Indoors: linoleum surface;

outdoors: grass, bare

earth, barked area

4 of 6 in long pants, 4 of 6

short sleeves, shoes

Daycare Kids No. 1b Aug. 4 6 5 1 1-6.5 Indoors: linoleum surface;

outdoors: grass, bare

earth, barked area

4 of 6 in long pants, 4 of 6

short sleeves, no shoes

Daycare Kids No.2c Sept. 8 5 4 1 1-4 Indoors, low napped

carpeting, linoleum

surfaces

4 of 5 long pants, 3of 5 long

sleeves, all barefoot for part of

the day

Daycare Kids No. 3 Nov. 8 4 3 1 1-4.5 Indoors: linoleum surface,

outside: grass, bare earth,

barked area

All long pants, 3 of 4 long

sleeves, socks and shoes

Outdoor

Soccer No. 1 Nov. 0.67 8 8 0 13-15 Half grass-half bare earth 6 of 8 long sleeves, 4 of 8

long pants, 3 of 4 short pants

and shin guards

Gardeners No. 1 Aug. 4 8 1 7 16-35 Weeding, pruning,

digging a trench

6 of 8 long pants, 7 of 8 short

sleeves, 1 sleeveless, socks,

shoes, intermittent use of

gloves

Archeologists July 11.5 7 3 4 16-35 Digging with trowel,

screening dirt, sorting

6 of 7 short pants, all short

sleeves, 3 no shoes or socks,

2 sandals

Kids-in-mud No. 1 Sept. 0.17 6 5 1 9-14 Lake shoreline All in short sleeve T-shirts,

shorts, barefoot

Kids-in-mud No. 2 Sept. 0.33 6 5 1 9-14 Lake shoreline All in short sleeve T-shirts,

shorts, barefoot

Shoreline Play Sept 0.33-

1.0

9 6 3 7-12 Tidal flat No shirt or short sleeve Tshirts, shorts, barefoot

a

Event duration

b

Number of subjects

c

Activities were confined to the house

Sources: Kissel et al. (1996b); Holmes et al. (1996), Shoaf et al. (2005).
8-25

Table 8-10. Geometric Mean and Geometric Standard Deviations of Solids Adherence by Activity and

Body Regiona

Activity Nb

Post-activity Dermal Solids Loadings (mg/cm2)

Hands Arms Legs Faces Feet

Indoor

Tae Kwon Do 7 0.0063

1.9

0.0019

4.1

0.0020

2.0

0.0022

2.1

Indoor Kids No. 1 4 0.0073

1.9

0.0042

1.9

0.0041

2.3

0.012

1.4

Indoor Kids No. 2 6 0.014

1.5

0.0041

2.0

0.0031

1.5

0.0091

1.7

Daycare Kids No. 1a 6 0.11

1.9

0.026

1.9

0.030

1.7

0.079

2.4

Daycare Kids No. 1b 6 0.15

2.1

0.031

1.8

0.023

1.2

0.13

1.4

Daycare Kids No. 2 5 0.073

1.6

0.023

1.4

0.011

1.4

0.044

1.3

Daycare Kids No. 3 4 0.036

1.3

0.012

1.2

0.014

3.0

0.0053

5.1

Outdoor

Soccer No. 1 8 0.11

1.8

0.011

2.0

0.031

3.8

0.012

1.5

Gardeners No. 1 8 0.20

1.9

0.050

2.1

0.072

--

0.058

1.6

0.17

--

Archeologists 7 0.14

1.3

0.041

1.9

0.028

4.1

0.050

1.8

0.24

1.4

Kids-in-mud No. 1 6 35

2.3

11

6.1

36

2.0

24

3.6

Kids-in-mud No. 2 6 58

2.3

11

3.8

9.5

2.3

6.7

12.4

Shoreline Play 9 0.49 

8.2

0.17 

3.1

0.70

3.6

0.04 

2.9

21

1.9

a

Means are presented above the standard deviations. The standard deviations generally exceed the means

by large amounts indicating high variability in the data.

b

Number of subjects.

Sources: Kissel et al. (1996b); Holmes et al. (1996); Shoaf et al. (2005).
8-26

Table 8-11. Summary of Groups Assayed in Round 2 of Field Measurements

Activity Month Eventa

 (hrs) nb Males Females Ages

Daycare kids No. 1a Aug. 3.5 6 5 1 1 - 6.5

Daycare kids No. 1b Aug. 4 6 5 1 1 - 6.5

Daycare kids No. 2 Sept. 8 5 4 1 1 - 4

Daycare kids No. 3 Nov. 8 4 3 1 1 - 4.5

Indoor kids No. 1 Jan. 2 4 3 1 6 - 13

Indoor kids No. 2 Feb. 2 6 4 2 3 - 13

a

 Event duration.

b

 Number of subjects.

Source: Holmes et al. (1999).
8-27

Table 8-12. Attire for Individuals within Children’s Groups Studied

Activity na

Pants Sleeves Socks

Shoes

Long Short Long Short High Low

Daycare kids No. 1a 6 4 2 1 5 1 5 low leather or canvas

shoes - 6

Daycare kids No. 1b 6 4 2 1 5 1 5 barefoot - 3

low leather or canvas

shoes - 3

Daycare kids No. 2 5 4 1 2 3 NA NA barefoot - 2

shoes/socks 1⁄2 day and

barefoot 1⁄2 day - 3

Daycare kids No. 3b 4 4 0 3 1 0 4 low shoes - 4

Indoor kids No. 1 4 1 3 2 2 0 4 no shoes (socks only) - 4

Indoor kids No. 2 6 5 1 5 1 0 6 no shoes (socks only) - 6

a

 Number of subjects.

b

 All children wore jackets when engaged in outdoor activities.

NA - “Not Available”: 3 children wore socks for 1⁄2 day in the morning but no specific information is provided on the

type of socks worn.

Source: Holmes et al. (1999).
8-28

Table 8-13. Geometric Means (Geometric Standard Deviations) of Round 2 Post-activity Loadings

Activity na

Postactivity Dermal Soil Loadings (mg/cm2)

Hands Forearms Lower legs Facesb Feet

Daycare kids No. 1a 4 0.11 (1.9) 0.026 (1.9) 0.030 (1.7) 0.079 (2.4)

Daycare kids No. 1b 6 0.15 (2.1) 0.031 (1.8) 0.023 (1.2) 0.13 (1.4)

Daycare kids No. 2 6 0.073 (1.6) 0.023 (1.4) 0.011 (1.4) 0.044 (1.3)

Daycare kids No. 3 6 0.036 (1.3) 0.012 (1.2) 0.014 (3.0) 0.0053 (5.1)

Indoor kids No. 1 5 0.0073 (1.9) 0.0042 (1.9) 0.0041 (2.3) 0.012 (1.4)

Indoor kids No. 2 4 0.014 (1.5) 0.0041 (2.0) 0.0031 (1.5) 0.0091 (1.7)

a

 Number of subjects (number of data points for specific non-hand body parts may deviate slightly). b

 Children’s feet rather than faces were washed in order to reduce the chance of a child’s refusal to participate.

Source: Holmes et al. (1999).
8-29

Table 8-14. Summary of Controlled Green House Trials - Children Playing

Activity Ages Duration

(min)

Soil moisture

(%)

Clothinga n Male Female

Playing 8-12 20 17-18

16-18

3-4

L

S

S

4

9

5

3

5

3

1

4

2

a

 L, long sleeves and long pants; S, short sleeves and short pants.

Source: Kissel et al. (1998).

Table 8-15. Preactivity Loadings Recovered from Greenhouse Trial Children Volunteers

Area n

Body part surface area (cm2

) Geometric mean

(95% C.I.) (:g/cm2

)

Hands 12 420-798 9.4

(5.4 - 15.8)

Forearms 12 584-932 3.4

(2.3 - 5.2)

Lower legs 12 1,206-2,166 1.0

(0.7 - 1.5)

Face 12 388-602 0.8

(0.5 - 1.5)

Source: Kissel et al. (1998).
8-30

Table 8-16. Area Weighted Adherence Factors

Exposure Scenario

Age

(years)

Geometric Mean Area Weighted 

Adherence Factor (mg/cm2)

 Indoor Children 1-13 0.01

Daycare Children (playing indoors and outdoors) 1-6.5 0.04

Children Playing (dry soil) 8-12 0.04

Children Playing (wet soil) 8-12 0.2

Children-in-mud 9-14 21

Source: U.S. EPA, 2004

Table 8-17. Summary of Recommended Values for Skin Surface Area and Solids Adherence

Factor Central

Tendency

Upper Percentile Multiple Percentiles

Whole body

surface area

— see Tables 8-6, 8-7, and

8-8

see Tables 8-6, 8-7, and

8-8

Body part

surface areas

--- see Table 8-3 see Table 8-3

Solids

adherence

see Tables 8-9, 8-

10, 8-16
8-31

Table 8-18. Confidence in Body Surface Area Measurement Recommendations

Considerations Rationale Rating

Study Elements

 • Level of Peer Review Studies were from peer reviewed journal articles.

EPA report was peer reviewed before distribution.

High

 • Accessibility The journals used have wide circulation.

EPA report available from National Technical

Information Service.

High

 • Reproducibility Experimental methods are well-described. High

 • Focus on factor of interest Experiments measured skin area directly. High

 • Data pertinent to U.S. Experiments conducted in the U.S. High

 • Primary data Re-analysis of primary data in more detail by two

different investigators .

Low

 • Currency Neither rapidly changing nor controversial area;

estimates made in 1935 deemed to be accurate and

subsequently used by others.

Low

 • Adequacy of data collection

 period

Not relevant to exposure factor; parameter not

time dependent.

NA

 • Validity of approach Approach used by other investigators; not

challenged in other studies.

High

 • Representativeness of the

 population

Not statistically representative of U.S. population. Medium

 • Characterization of

variability 

Individual variability due to age, race, or gender

not studied.

Low

 • Lack of bias in study design Objective subject selection and measurement

methods used; results reproduced by others with

different methods.

High

 • Measurement error Measurement variations are low; adequately

described by normal statistics.

Low/Medium

Other Elements

 • Number of studies 1 experiment; two independent re-analyses of this

data set.

Medium

 • Agreement among

researchers

Consistent results obtained with different analyses;

but from a single set of measurements.

Medium

Overall Rating This factor can be directly measured. It is not

subject to dispute. Influence of age, race, or

gender have not been detailed adequately in these

studies.

Medium
8-32

Table 8-19. Confidence in Solids Adherence to Skin Recommendations

Considerations Rationale Rating

Study Elements

 • Level of Peer Review Studies were from peer reviewed journal articles. High

 • Accessibility Articles were published in widely circulated

journals.

High

 • Reproducibility Reports clearly describe experimental method. High

 • Focus on factor of interest The goal of the studies was to determine soil

adherence to skin.

High

 • Data pertinent to U.S. Experiments were conducted in the U.S. High

 • Primary data Experiments were used to directly measure soil

adherence to skin; 

High

 • Currency New studies were presented. High

 • Adequacy of data collection

 period

Seasonal factors may be important, but have not

been studied adequately.

Medium

 • Validity of approach Skin rinsing technique is a widely employed

procedure.

High

 • Representativeness of the

 population

Soil/dust studies were limited to the State of

Washington and sediment study limited to Rhode

Island. May not be representative of other locales.

Low

 • Characterization of

variability 

Variability in soil adherence is affected by many

factors including soil properties, activity and

individual behavior patterns.

Low

 • Lack of bias in study design The studies attempted to measure soil adherence in

selected activities and conditions to identify

important activities and groups.

High

 • Measurement error The experimental error is low and well controlled. High

Other Elements

 • Number of studies The experiments were controlled as they were

conducted by a few laboratories; activity patterns

were studied by only one laboratory.

Medium

 • Agreement among

researchers

Results from key study were consistent with

earlier estimates from relevant studies and

assumptions, but are limited to hand data.

Medium

Overall Rating Data are limited, therefore it is difficult to

extrapolate from experiments and field

observations to general conditions. Application of

results to other similar activities may be subject to

variation.

Medium
8-33

Figure 8-2. Skin Coverage as Determined by Fluorescence vs. Body Part for Adults

Transplanting Plants and for Children Playing in Wet Soils

Figure 8-3. Gravimetric Loading vs. Body Part for Adult Transplanting Plants in Wet Soil

and for Children Playing in Wet and Dry Soils
APPENDIX 8A

Formulas FOR TOTAL BODY SURFACE AREA
8A-1

SA KW2/3 = (8A-1)

SA a0 H

a1

W

a 2 = (8A-2)

1 APPENDIX 8A

2 Formulas FOR TOTAL BODY SURFACE AREA

3

4 Most formulas for estimating surface area (SA), relate height to weight to surface

5 area. The following formula was proposed by Gehan and George (1970):

6

7

8

9 where: 

10

11 SA = surface area in square meters;

12 W = weight in kg; and 

13 K = constant. 

14

15 While the above equation has been criticized because human bodies have

16 different specific gravities and because the surface area per unit volume differs for

17 individuals with different body builds, it gives a reasonably good estimate of surface

18 area.

19 A formula published in 1916 that still finds wide acceptance and use is that of

20 DuBois and DuBois. Their model can be written:

21

22 where: 

23

24 SA = surface area in square meters; 

25 H = height in centimeters; and 

26 W = weight in kg.

27

The values of a0 (0.007182), a1 (0.725), and a2 28 (0.425) were estimated from a

29 sample of only nine individuals for whom surface area was directly measured. Boyd

30 (1935) stated that the Dubois formula was considered a reasonably adequate substitute

31 for measuring surface area. Nomograms for determining surface area from height and

32 mass presented in Volume I of the Geigy Scientific Tables (1981) are based on the

33 DuBois and DuBois formula. 

34 Boyd (1935) developed new constants for the DuBois and DuBois model based

35 on 231 direct measurements of body surface area found in the literature. These data

36 were limited to measurements of surface area by coating methods (122 cases), surface

37 integration (93 cases), and triangulation (16 cases). The subjects were Caucasians of

38 normal body build for whom data on weight, height, and age (except for exact age of

39 adults) were complete. Resulting values for the constants in the DuBois and DuBois

model were a0 = 0.01787, a1 = 0.500, and a2 40 = 0.4838. Boyd also developed a formula

41 based exclusively on weight, which was inferior to the DuBois and DuBois formula

42 based on height and weight.

43 Gehan and George (1970) proposed another set of constants for the DuBois and

44 DuBois model. The constants were based on a total of 401 direct measurements of

45 surface area, height, and weight of all postnatal subjects listed in Boyd (1935). The
8A-2

SAi a0Hi

a Wi

a

ei 1 2 = (8A-5)

1 methods used to measure these subjects were coating (163 cases), surface integration

2 (222 cases), and triangulation (16 cases).

3 Gehan and George (1970) used a least-squares method to identify the values of

4 the constants. The values of the constants chosen are those that minimize the sum of

5 the squared percentage errors of the predicted values of surface area. This approach

6 was used because the importance of an error of 0.1 square meter depends on the

7 surface area of the individual. Gehan and George (1970) used the 401 observations

8 summarized in Boyd (1935) in the least-squares method. The following estimates of

the constants were obtained: a0 = 0.02350, a1 = 0.42246, and a2 9 = 0.51456. Hence,

10 their equation for predicting SA is:

11

SA = 0.02350 H0.42246W0.51456 12 (8A-3)

13

14 or in logarithmic form:

15

16 lnSA = -3.75080 + 0.42246 lnH + 0.51456 lnW (8A-4)

17 where: 

18

19 SA = surface area in square meters;

20 H = height in centimeters; and

21 W = weight in kg.

22

23 This prediction explains more than 99 percent of the variations in surface area

24 among the 401 individuals measured (Gehan and George, 1970).

25 The equation proposed by Gehan and George (1970) was determined by the

26 U.S. EPA (1985) as the best choice for estimating total body surface area. However,

27 the paper by Gehan and George gave insufficient information to estimate the standard

28 error about the regression. Therefore, the 401 direct measurements of children and

29 adults (i.e., Boyd, 1935) were reanalyzed in U.S. EPA (1985) using the formula of

30 Dubois and Dubois (1916) and the Statistical Processing System (SPS) software

31 package to obtain the standard error.

32 The Dubois and Dubois (1916) formula uses weight and height as independent

33 variables to predict total body surface area (SA), and can be written as:

34

35

36

37

38

39

40

41

42

43

44 or in logarithmic form:
8A-3

ln(SA)i ln a0 + a1 ln Hi a2 ln Wi ln ei = ++ (8A-6)

SA = 0.0239 H0.417W0.517 (8A-7)

a0 3.73 (0.18), a1 0.417 (0.054), a2 =− = = 0.517 (0.022)

1

2

3

4

5

6

7 where:

8

SAi = surface area of the i-th individual (m2 9 ); 

10 Hi = height of the i-th individual (cm);

11 Wi = weight of the i-th individual (kg);

a0, a1 12 , and a2 = parameters to be estimated; and 

13 ei = a random error term with mean zero and constant variance.

14

15

16

17 Using the least squares procedure for the 401 observations, the following parameter

18 estimates and their standard errors were obtained:

19

20

21

22

23 Th

24 e model is then:

25

26

27

28

29 or in logarithmic form:

30

31 ln SA = 3.73 + 0.417 lnH + 0.517 lnW (8A-8)

32

33 with a standard error about the regression of 0.00374. This model explains more than

34 99 percent of the total variation in surface area among the observations, and is

35 identical to two significant figures with the model developed by Gehan and George

36 (1970).

37 When natural logarithms of the measured surface areas are plotted against

38 natural logarithms of the surface predicted by the equation, the observed surface areas

39 are symmetrically distributed around a line of perfect fit, with only a few large

40 percentage deviations. Only five subjects differed from the measured value by 25

41 percent or more. Because each of the five subjects weighed less than 13 pounds, the

42 amount of difference was small. Eighteen estimates differed from measurements by

43 15 to 24 percent. Of these, 12 weighed less than 15 pounds each, 1 was overweight (5

44 feet 7 inches, 172 pounds), 1 was very thin (4 feet 11 inches, 78 pounds), and 4 were

45 of average build. Since the same observer measured surface area for these 4 subjects,

46 the possibility of some bias in measured values cannot be discounted (Gehan and

47 George 1970).
8A-4

SA 0.024265H0.3964W0.5378 = (8A-9)

1 Gehan and George (1970) also considered separate constants for different age

2 groups: less than 5 years old, 5 years old to less than 20 years old, and greater than 20

3 years old. The different values for the constants are presented below:

4

5 Table 8A-1. Estimated Parameter Values for Different Age Intervals

6

7 Age

8 group

Number

of persons a0 a1 a2

9 All ages 401 0.02350 0.42246 0.51456

10 <5 years old 229 0.02667 0.38217 0.53937

11 $ 5 - <20 years

12 old

42 0.03050 0.35129 0.54375

13 $ 20 years old 30 0.01545 0.54468 0.46336

14

15 The surface areas estimated using the parameter values for all ages were

16 compared to surface areas estimated by the values for each age group for subjects at

17 the 3rd, 50th, and 97th percentiles of weight and height. Nearly all differences in

18 surface area estimates were less than 0.01 square meter, and the largest difference was

0.03 m2 19 for an 18-year-old at the 97th percentile. The authors concluded that there is

no advantage in using separate values of a0, a1, and a2 20 by age interval.

21 Haycock et al. (1978) without knowledge of the work by Gehan and George

(1970), developed values for the parameters a0, a1, and a2 22 for the DuBois and DuBois

23 model. Their interest in making the DuBois and DuBois model more accurate

24 resulted from their work in pediatrics and the fact that DuBois and DuBois (1916)

25 included only one child in their study group, a severely undernourished girl who

26 weighed only 13.8 pounds at age 21 months. Haycock et al. (1978) used their own

27 geometric method for estimating surface area from 34 body measurements for 81

28 subjects. Their study included newborn infants (10 cases), infants (12 cases), children

29 (40 cases), and adult members of the medical and secretarial staffs of 2 hospitals (19

30 cases). The subjects all had grossly normal body structure, but the sample included

31 subjects of widely varying physique ranging from thin to obese. Black, Hispanic, and

32 white children were included in their sample. The values of the model parameters

33 were solved for the relationship between surface area and height and weight by

34 multiple regression analysis. The least squares best fit for this equation yielded the

following values for the three coefficients: a0 = 0.024265, a1 = 0.3964, and a2 35 =

36 0.5378. The result was the following equation for estimating surface area:

37

38

39 expressed logarithmically as:

40

41 ln SA = ln 0.024265 + 0.3964 ln H + 0.5378 ln W (8A-10)

42

43
8A-5

1 The coefficients for this equation agree remarkably with those obtained by Gehan and

2 George (1970) for 401 measurements.

3 George et al. (1979) agree that a model more complex than the model of DuBois

4 and DuBois for estimating surface area is unnecessary. Based on samples of direct

5 measurements by Boyd (1935) and Gehan and George (1970), and samples of

6 geometric estimates by Haycock et al. (1978), these authors have obtained parameters

7 for the DuBois and DuBois model that are different than those originally postulated in

8 1916. The DuBois and DuBois model can be written logarithmically as:

9

10

lnSA = lna0 + a1 lnH + a2 11 lnW (8A-11)

12

13

The values for a0, a1, and a2 14 obtained by the various authors discussed in this

15 section are presented to follow:

16

17

18 Table 8A-2. Summary of Surface Area Parameter Values for the Dubois and Dubois Model

19

20 Author

21 (year)

Number

of

persons

a0 a1 a2

22 DuBois and DuBois

23 (1916)

9 0.007184 0.725 0.425

24 Boyd (1935) 231 0.01787 0.500 0.4838

25 Gehan and George

26 (1970)

401 0.02350 0.42246 0.51456

27 Haycock et al. (1978) 81 0.024265 0.3964 0.5378

28

29

30 The agreement between the model parameters estimated by Gehan and George

31 (1970) and Haycock et al. (1978) is remarkable in view of the fact that Haycock et al.

32 (1978) were unaware of the previous work. Haycock et al. (1978) used an entirely

33 different set of subjects, and used geometric estimates of surface area rather than

34 direct measurements. It has been determined that the Gehan and George model is the

35 formula of choice for estimating total surface area of the body since it is based on the

36 largest number of direct measurements.

37 Sendroy and Cecchini (1954) proposed a method of creating a nomogram, a

38 diagram relating height and weight to surface area. However, they do not give an

39 explicit model for calculating surface area. The nomogram was developed

40 empirically based on 252 cases, 127 of which were from the 401 direct measurements

41 reported by Boyd (1935). In the other 125 cases the surface area was estimated using

42 the linear method of DuBois and DuBois (1916). Because the Sendroy and Cecchini

43 method is graphical, it is inherently less precise and less accurate than the formulas of

44 other authors discussed above.