Warning against the indiscriminate use of a biological half-time model in deriving the critical concentration of metals

For heavy metals, many studies obtained short biological half-times (BHTs) by administrations of heavy metals. Tsuchiya and Sugita, however, first reported the possibility of a long BHT for cadmium (Cd) calculated from Cd accumulations in postmortem human organs and tissues by age using a non-linear regression method employing a differential equation. According to their reports, the Cd BHTs (point estimators) were 12.1-22.7 years by sex, renal cortex and medulla. The minimums and the maximums of the Cd BHTs on the 95% confidence regions of estimators were 6.9-70.2 years by sex and kidney part. It is presumed that the range of the 95% confidence region for the individual BHTs of renal Cd exists in a range from a few years to at least 100 years because of large individual variations in exposure, absorption rate and excretion rate. Point estimators of BHTs, however, include the assumption that all subjects have been exposed to the same level of Cd at the same year of age over a period of decades and have equal absorption and excretion rates of Cd. Therefore, it is not adequate to calculate a safety level for Cd in the industrial environment or foodstuffs using a value of Cd BHT (point estimator) based on Cd accumulation applying a mathematical model. BHTs of metals require careful evaluation and must not be used indiscriminately to derive a critical concentration, for example, using a mathematical model.