Years‐identification mathematical model of paeonia lactiflora pall. based on the allometric‐scaling

The fixed number years‐identification of Chinese material medicinal was a difficulty in the process of the traditional Chinese pharmacology, the phenomenon was found in our study of telomerase that the speed of the vascular cambium outside expanding growth fluctuated in a definite value. Based on it, we put forward a hypothesis that the radial length of the vascular cambium to expand (Δ b )and the radius of cross section (Δ r ) are constant in every activity cycle if the external environment factors unchanged every year. Therefore, We defined that the proportion ( k ) of Δ r and Δ b is constant (Δ r /Δ b = k ). Then, each of Δ b and Δ r fluctuating in a fixed value in every year, because of the different rainfall, temperature, and sunniness every year. The hypothesis was proved correct within the domain of definition range, through the extrapolation of mathematical method. Hence, the telomerase experimental results just become effective evidence on mechanism. The conclusion we obtained include the following three: the telomerase experimental show that the activity gradually decreased in the Paeonia overall taproot, while, the it does not seem significantly change in the parts of the cambium cells with increasing age; Microscopy studies and mathematical models exploration gave us an identification method which can determine the growth years of Chinese medicinal materials (Refers to a kind of herbs exclusive which contains taproot), and, for example, we can use the mathematical model y = 0.02 x −0.5 $ \left(P = {0.08 \over {k^2}{n}\Delta {b}}-{0.0016 \over \Delta {b }^2{ n}^2{ k}^2}\right) $ to identify the years of the Paeonia lactiflora Pall; the power function of allometric‐scaling explored at microscopic cellular‐level firstly. Ginseng, for example, more definitive proved a mathematical relationship of the allometric scaling in the taproot of plants. Microsc. Res. Tech., 2013. © 2012 Wiley Periodicals, Inc.