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EPA-Expo-Box (A Toolbox for Exposure Assessors)

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Flux, or the amount of contaminant that penetrates per unit of time, has been mathematically described by Fick’s Law of Diffusion for membranes which states that the flux of a contaminant across a homogeneous membrane is proportional to the concentration difference between the membrane outer surface and the membrane inner surface and inversely proportional to the thickness of the membrane. The key assumptions inherent in a Fick's Law based approach are:

  • The skin is a homogeneous membrane.
  • The flux of the contaminant across the skin is solely due to passive diffusion.
  • The permeability coefficient and the flux are specific to the vehicle contacting the skin and the animal species in which they are measured.

As shown in U.S. EPA (2004), internal (absorbed) dose for inorganics in water can be calculated as follows:

DAevent = Kp x C x t
DAevent = Absorbed dose (mg/cm2-event)
Kp = Permeability coefficient (cm/hr)
C = Concentration of chemical in vehicle contacting skin (mg/cm3)
t = Time of contact (hours/event)

All parameters must be expressed in consistent units; in some cases, unit conversion factors may be necessary. This absorbed dose is generally expressed as mass of contaminant per unit surface area of skin per event (e.g., mg/cm2 event).

The equation above may be used to estimate the absorbed dose per event (DAevent) when the inorganic contaminant contacting the skin is in the form of a liquid or aqueous mixture and the amount of contaminant on the surface is expressed as a concentration. U.S. EPA (2004) provides alternate forms of this equation for estimating dermal exposure to organics in water. Permeability coefficients have been measured for many contaminants and can also be estimated based on correlations that use molecular weight and octanol-water partition coefficient (Kow) (U.S. EPA, 2004, 1992a).

For dermal contact with solids (e.g., soil, sediment), the concentration of contaminant contacting the skin is a function of the concentration of contaminant in the solid material (e.g., soil) and the amount of solid that adheres to the skin per unit surface area. For surface residues, the amount of chemical contacting the skin is a function of the amount of chemical on the contaminated surface and the fraction of chemical transferred to the skin. For example, the concentration of contaminant in soil (mg/g) may be multiplied by the adherence rate (Adh) of soil to skin (g/cm2-event) to estimate the concentration of contaminant on the skin (g/cm2-event). Likewise, the concentration of contaminant on a contaminated surface (mg/cm2) may be multiplied by the transfer efficiency fraction (TF) (%/100%-event) to estimate the amount of contaminant on the surface of the skin (g/cm2-event). Absorption factors are then applied to estimate the dermally-absorbed dose per event.

Once the absorbed dose per event has been estimated, the average daily dose (ADD) can be calculated. The ADD is calculated as follows and is generally expressed as mass of contaminant per unit body weight over time (e.g., mg/kg-day).

ADDabs = DAevent x SA x EF x ED / BW x AT
ADDabs = Average daily dose (mg/kg-day)
DAevent = Absorbed dose (mg/cm2-event)
SA = Skin surface area available for contact (cm2)
EF = Exposure frequency (events/year)
ED = Exposure duration (years)
BW = Body weight (kg)
AT = Averaging time (days)
  • Surface area (SA) represents the surface of the skin that is exposed
  • Body weight (BW) of an individual, typically expressed in kilograms (kg), is included so that the dose is normalized to that value.
  • Temporal parameters in the dose equation include:
    • Exposure frequency (EF) refers to the frequency with which the exposure occurs and might be provided in events per year or events per day.
    • Exposure duration (ED) is the amount of time that an individual or population is exposed to the contaminant being evaluated and is typically provided in years.
    • Averaging time (AT) is the amount of time over which exposure is averaged and is equal to ED for assessing non-cancer risks. For chronic assessments (e.g., cancer), potential lifetime average daily dose (LADD) is calculated in which lifetime (LT, in days) is substituted for AT.
    • Exposure parameter inputs (e.g., dermal contact factors, body weights, and relevant patterns of behavior such as timeframe of exposure) can be obtained from the Exposure Factors Handbook: 2011 Edition (see Factors tab in this module).

Additional information on exposure scenarios involving the dermal route can be found in the Indirect Estimation Module of the Approaches Tool Set in EPA-Expo-Box. The Exposure Calculation Spreadsheet (XLSX) (241 K) estimates dermal contact dose when user-defined values are entered for the various exposure parameters that are highlighted in BOLD.

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