# Empirical factor developed by Layton

I need to understand the empirical factor developed by Layton … In APIC guidance indicates a factor of 2000.

This is for a toxicological criterion.

Best Regards.

MAC

Dear MAC…

Generally, to calculate the MACO formula, we need the “dose” of the previous product and next product. But, if the previous product is an intermediate, we don’t know the “dose” In such case, we use NOEL formula.

Before knowing the empirical factor, understand the relation between NOEL and LD50.

NOEL (toxicology): The highest dose or concentration of a substance (drug / chemical), at no adverse effect is found in exposed test organisms where higher doses or concentrations resulted in an adverse effect. Simply, the highest amount of a substance which cannot be harm to an organism.

Lethal dose 50: The dose required to kill half the members of a tested population after a specified test duration

NOEL can be determined by multiplying oral LD50’s by a factor. This factor is called empirical factor which is derived from animal models developed by Layton at al. For many compounds, the relationship of the NOEL to the LD50 was typically less than 1/1,000 to 1/2,000 (means, NOEL = LD50/2000)

So, finally, NOEL = LD50 x human body average weight x empirical factor.

Dear Ramyaraj725

Thank you very much for the time spent to answer my question.

I would like to understand the mathematical model developed by Layton for factors 1/1000 to 1/2000. Because I found another empirical factor (weight of adult human / animal weight) ^ 2/3 , which I would like to compare with the model of Layton.

Thank you again!

From Layton’s animal model: Layton reviewed published data regarding LD50 values and NOELs from longer term studies for small mammals. Using these ratios for a large number of chemicals, including some pesticides, he came up with a recommendation to use a factor in the range of 5 x 10-6 to 1 x 10-5 to convert a LD50 to an acceptable daily intake (ADI)

i.e., ADI (mg/kg/day) = LD50 x 5 x 10-6 (say equation – 1)

Relation between ADI and NOEL: ADI is derived by dividing NOEL with a safety factor, conventionally 100, to account for the differences between test animals and humans (factor of 10) and possible differences in sensitivity between humans (another factor of 10).

i.e., ADI (mg/kg/day) = NOEL / 100 (say equation – 2)

From the above two equations…

NOEL / 100 = LD50 x 5 x 10-6

NOEL = LD50 x 5 x 10-6 x 100

NOEL (mg/kg/day) = LD50 / 2000 (since 5 x 10-6 x 100 = 1/2000)

NOEL (mg/day) = LD50 x 70 kg (average adult weight) / 2000

Further, I didn’t find “(weight of adult human / animal weight) ^ 2/3” in any guideline. If you have such guideline, please forward me along with Layton’s article (full copy) if available…

Hello Dear,

I found “(weight of adult human / animal weight) ^ 2/3” in this article, but is in spanish…