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.

Question

BlackTom AI · Accepted Answer

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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