Dose Translation
Calculate Human Equivalent Dose (HED) from Animal NOAEL.
1. Standard Conversion (Appendix B)
When animal weights are within the standard FDA "working range", the conversion uses fixed Km factors:
2. Km Factor Derivation
The Km factor represents the ratio of body weight to body surface area. It is calculated as:
3. Reference Values (Table 3)
| Species | Ref Weight | Range (kg) | BSA (m2) | Km |
|---|
4. Dynamic Conversion (Power Formula)
If an animal's weight falls outside the standard range, the calculator auto-switches to the Power Formula to maintain accuracy:
5. BSA Estimation Logic
The tool estimates Body Surface Area (BSA) using the inverse of the Km definition: BSA = Weight / Km. By calculating the theoretical Km first (using allometry), we derive a BSA that accurately reflects the animal's geometry (BSA ∝ Weight0.67), rather than assuming a fixed ratio.
Compare how Km shifts when you assume Body Surface Area (BSA) is fixed vs. when it scales allometrically.
Why Linear Scaling Fails (The Square-Cube Law)
In biology, scaling an animal's weight linearly does not scale its surface area linearly. This is known as the Square-Cube Law:
- Volume (Weight) increases by the cube of length (L3).
- Surface Area increases by the square of length (L2).
Therefore, Surface Area is proportional to Weight raised to the power of 2/3 (or 0.67).
The Error: The "Linear Km" calculation assumes Surface Area grows 1:1 with Weight. This underestimates the Km factor for larger animals, leading to potentially dangerous overdoses when scaling from small to large species.