Integrations of increase functions according to the L. V. Bertalanffy conception of organic growth
Sager, G.
Anatomischer Anzeiger 144(2): 147-157
1978
ISSN/ISBN: 0003-2786 PMID: 742706 Document Number: 137516
The Bertalanffy (1941, 1949) conception of the change of organic mass M with time t as given by the difference dM/dt = aMm-bMn is transferred to the shap dW/dt = kWm(En-Wn) with W being an element of growth, i.e. length, weight or population and E its final value after reaching adultness. The integration of this expression, resulting in the growth function W, can be performed globally only for m=1. In other cases the integrals become individual with quite different solutions, some of them being presented here for means of comparison. The results show that many growth functions exclude W = 0, and all reach the final value W = E after infinite time although with quite different degrees of approximation. Moreover the graphs allow a survey as to which results this type of growth function can yield. Finally the mathematical deficiencies give rise to investigate modified types of increase functions.