Log-normal distribution of the trace element data results from a mixture of stocahstic input and deterministic internal dynamics.
In previous article, we showed a log-normal distribution of boron and lithium in human urine. This type of distribution is common in both biological and nonbiological applications. It can be observed when the effects of many independent variables are combined, each of which having any underlying distribution. Although elemental excretion depends on many variables, the one-compartment open model following a first-order process can be used to explain the elimination of elements. The rate of excretion is proportional to the amount present of any given element; that is, the same percentage of an existing element is eliminated per unit time, and the element concentration is represented by a deterministic negative power function of time in the elimination time-course. Sampling is of a stochastic nature, so the dataset of time variables in the elimination phase when the sample was obtained is expected to show Normal distribution. The time variable appears as an exponent of the power function, so a concentration histogram is that of an exponential transformation of Normally distributed time. This is the reason why the element concentration shows a log-normal distribution. The distribution is determined not by the element concentration itself, but by the time variable that defines the pharmacokinetic equation.
Usuda
Kan
K
Department of Hygiene and Public Health, Osaka Medical College, Takatsuki City, Japan.
Kono
Koichi
K
Dote
Tomotaro
T
Shimizu
Hiroyasu
H
Tominaga
Mika
M
Koizumi
Chisato
C
Nakase
Emiko
E
Toshina
Yumi
Y
Iwai
Junko
J
Kawasaki
Takashi
T
Akashi
Mitsuya
M
D000328:Adult; D001895:Boron / Q000652:urine*; D006801:Humans; D008094:Lithium / Q000652:urine*; D008297:Male; D008875:Middle Aged; D016011:Normal Distribution; D013269:Stochastic Processes
D008094:Lithium; D001895:Boron