The Sprague-Dawley rats in the BaP trial weigh 325 grams on average. Assume the NOAEL from the trial was 25 mg/kg/d. Calculate the human equivalent dose (HED) assuming dose scales to the 0.7 power of body weight and a standard 60 kg human body weight.

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We start by clarifying the values involved in the calculation. The rat average body weight is 325 grams, i.e., 0.325 kg. The NOAEL in the rat is 25 mg/kg/day. The human body weight to be used for the equivalence is 60 kg, and the allometric scaling is given as dose scales with body weight to the 0.7 power.

Option 1: 0.65 mg/kg/day. To compute the human equivalent dose per kg, apply the scaling factor (BW_rat / BW_human)^{0.7} to the rat NOAEL. The ratio is 0.325 / 60 = 0.0054167. Raising this to the 0.7 power gives (0.0054167)^{0.7} ≈ 0.026. Multiplying by the rat NOAEL: 25 mg/kg/day × 0.026 ≈ 0.65 mg/kg/day. This matches the value around 0.65 mg/kg/day, indicating the HED per kilogram of human body weight.

Option 2: 0 mg/kg/day. This would imply no dose is transferred across species, which is inconsistent with the allometric scaling approach and the nonzero NOAEL in the animal. Since the scaling factor is a positive number less than 1, the HED should be reduced but not zero; thus 0 mg/kg/day is incorrect.

To recap the core steps: (1) compute BW_rat/BW_human = 0.325/60; (2) raise to the 0.7 power to obtain the allometric scaling factor; (3) multiply the rat NOAEL (25 mg/kg/day) by this factor to yield the human equivalent dose per kg body weight. The numerical result of these steps is approximately 0.65 mg/kg/day, not zero, aligning with the general expectation that HED is a fraction of the animal NOAEL when scaling to humans of different size.

If one were to express the daily dose for a 60 kg human, you would multiply the HED by 60 kg to obtain approximately 39 mg/day, but since the question asks for HED and provides 60 kg as part of the scaling, the primary outcome is the per-kilogram value around 0.65 mg/kg/day.

EH 206 Homework 1

The Sprague-Dawley rats in the BaP trial weigh 325 grams on average. Assume the NOAEL from the trial was 25 mg/kg/d. Calculate the human equivalent dose (HED) assuming dose scales to the 0.7 power of body weight and a standard 60 kg human body weight.

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