title: [Mathematical formulation possibilities of growth processes].
abstract: A survey is given of the possibilities to construct mathematical models of growth. Growth as a phenomenon of life is well known since the earliest times of mankind as one can see from the languages. In Old Mesopotamia, Sumerians and Accadians were able to calculate compound interest but they had no idea to apply the formulae to living beings, neither to their children nor to cattle or fruits of the earth. About 4000 years past the finding of the compound interest calculus, Gompertz (1825) and Verhulst (1838) gave formulae (differential equations) which describe the organismic growth for the first time. A landmark of biological growth's research was the publication of the v. Bertalanffy's (1941) growth differential equation which describes the growth velocity as the difference between anabolism and catabolism. But the v. Bertalanffy's equation is more of theoretical value than of practical one. The present writer shows three models in the form of differential equations to describe the growth of a single cell, of a homogeneous cell population in mitotic activity, and of the human (or higher mammalian) embryofetus on the basis of physicocochemical processes.
mesh_terms: D000818:Animals; D002455:Cell Division; D005333:Fetus / Q000502:physiology; D006128:Growth; D006801:Humans; D008037:Linguistics; D008938:Mitosis; D008954:Models, Biological
vernacular_title: Möglichkeiten der mathematischen Formulierung von Wachstumsprozessen.