Sample problem1:

Sample problem 2:

Variables:

1. D = dose
2. C = ambient concentration (in air, water, etc.)
3. I = intake (breathing, drinking,etc.)
4. T = time of exposure
5. P = risk (probability of effect)
6. R = risk factor (the slope of a dose response curve)
7. EC = excess cases
8. N = number of people exposed
9. AC = acceptable concentration
10. E-6 = one out of a million (ten to the power of -6)

Fundamental equations:

1. D = C I T
2. R = P / D
3. P = R D
4. EC = P N
5. AC = E-6 / R I T

Sample problem 1:
 
1.  Assume the following:
 
    C = ambient concentration of 1 mg/m3
 
    I = daily inhalation intake of 
        20 cubic meters per day (20 m3/day) 
 
    T = lifetime exposure of 28,470 days 
        (78 years x 365 days = 28,470 days)
 
 
2. What is the daily dose and lifetime dose?
 
   D = CIT = (1 mg/m3)(20 m3/day)(1 day) = 20 mg/day
 
   D = CIT = (20 mg/day)(28,470 days) = 569,400 mg = .5694 kg/lifetime
 
3. Assume that the adjusted value of P is 0.1 for a test animal
   population given a lifetime dose of 10 kg.  What is the unit risk factor?
 
   R = P/D = (0.1)/10 kg = .01/kg
 
4. What is the lifetime risk to the risk group in this study?
 
   P = RD = (.01/kg)(.5694 kg) = .005694
 
5. What are the excess cases expected for a town of 100,000 people
   exposed to this chemical?
 
   EC = PN = (.005694)(100,000) = 569.4 deaths over a lifetime of exposure
 
6. What is the acceptable concentration for this chemical (assume that
   one in a million risk is an acceptable risk).
 
   AC = E-6/RIT = E-6/(.01/kg)(20 m3/day)(28,470 days)
 
      = E-6/5,694 = 1.7562 x e-10 kg/m3 = .17562 microgram/m3
 
 
 
 
 
Sample problem 2
 
Safety Factor Method:
 
A neurotoxin has a NOEL of .05 gm/day in male rats.  
The EPA Science Advisory Board recommends an 
uncertainty factor of 10.  What is the reference dose 
for humans?
 
 
                    .05 gm/day * 70 kg 
reference dose =    ------------------ = .7 gm/day
                    .5 kg * 10
 
 
Notes: 
 
1. For dose scaling purposes, assume humans weigh 70 kg and the
   male rats weigh .5 kg. 
2. With no other information, we assume no latency and a     
   lifetime of exposure and study (the simplest 
   conditions).
3. Remember that reference dose is a daily dose!
   Doses should always be expressed as a daily dose. 
4. Pay close attention to the units at all times!