Helwin H, Peil J
Gegenbaurs Morphol Jahrb. 1977;123(5):641-55.
The body height growth (of masculine beings) was modelled in a phenomenologic-mathematical manner by partitioning the time course of measured growth curve in parts every of which corresponds to a separated growth period. This partitioning was reached in a natural way so that a superposition of the single spurts yields the whole measured course. Every growth batch will be described in its time course by one term of inverse tangent function. The biological meaning and an explanation of the succession of the growth spurt as an effect of control circuits need further exploratory work. For detailed statements on acceleration phenomena concerning the body height growth this analysis gives possibilities for comparing the single growth spurts of the mean growth process of two populations in question. For measured values given by BROCK (1954) and SALZLER (1967) there are five growth periods in the time intervall reaching from time of conception until the end of the first year. Comparing the mathematical functions of the corresponding growth spurts for these two groups one can conclude that the second spurt (fetal spurt) is responsible for an increase of birth body height and the fourth for an increase of body height in the suckling age of the latter group against the former one.
男性身体高度的增长以现象学 - 数学方式进行建模，通过将测量的生长曲线的时间进程划分为若干部分，每个部分对应一个独立的生长阶段。这种划分是以自然的方式实现的，使得各个生长突增的叠加产生整个测量过程。每个生长阶段在其时间进程中将由反正切函数的一项来描述。生长突增的相继发生作为控制回路的一种效应，其生物学意义及解释需要进一步的探索性研究。对于有关身体高度增长的加速现象的详细阐述，该分析为比较两个相关群体平均生长过程中的单个生长突增提供了可能。对于布罗克（1954年）和萨尔茨勒（1967年）给出的测量值，从受孕时刻到第一年末的时间间隔内有五个生长阶段。比较这两组相应生长突增的数学函数，可以得出结论，第二个突增（胎儿期突增）导致出生时身体高度的增加；而对于后一组相对于前一组而言，第四个突增导致哺乳期身体高度的增加。
