A comparison of Reduced Life Expectancy (RLE) model with Haber's Rule to describe effects of exposure time on toxicity

• Published in: Environmental pollution (1987) Vol. 204; pp. 26 - 31
• Main Authors: Verma, Vibha, Yu, Qiming J., Connell, Des W.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 01.09.2015
• Subjects: Constants; Constraining; Data points; Environmental Exposure - adverse effects; Estimation of long term toxicity; Exposure; Haber's Rule; Humans; Lethal Dose 50; Life Expectancy; Long term effects; Long term effects of exposure time; Mathematical models; Models, Biological; Normal Life Expectancy; Reduced Life Expectancy model; Time Factors; Toxicity; Long term effects of exposure time; Reduced Life Expectancy model; Normal Life Expectancy; Haber's Rule; Estimation of long term toxicity
• ISSN: 0269-7491; 1873-6424
• DOI: 10.1016/j.envpol.2015.04.008

The Reduced Life Expectancy (RLE) Model (LC50 = [ln(NLE) – ln(LT50)]/d) has been proposed as an alternative to Haber's Rule. The model is based on a linear relationship between LC50 (Lethal Exposure Concentration) and lnLT50 (Lethal Exposure Time) and uses NLE (Normal Life Expectancy) as a limiting point as well as a long term data point (where d is a constant). The purposes of this paper were to compare the RLE Model with Haber's Rule with available toxicity data and to evaluate the strengths and weaknesses of each approach. When LT50 is relatively short and LC50 is high, Haber's Rule is consistent with the RLE model. But the difference between the two was evident in the situation when LT50 is relatively long and LC50 is low where the RLE model is a marked departure from Haber's Rule. The RLE Model can be used to appropriately evaluate long term effects of exposure. •The strength and weakness of Haber's Rule in relation to the RLE model is needed.•Haber's Rule now used universally is quite inappropriate for environmental toxicity.•Normal life expectancy, a new parameter l is used to evaluate effects of exposure time on toxicity.•According to RLE model when LC50 approaches zero, then LT50 = Normal Life Expectancy.•The RLE model can be used to evaluate long term effects of exposure-accurately and easily. The RLE approach is a more appropriate alternative particularly to evaluate long term effects of exposure. It can be easily used to estimate long term effects of exposure.