On the analytical solution for the Pütter–Bertalanffy growth equation

This study develops the basic idea of Pütter and Bertalanffy addressing the allometric scaling of anabolism and catabolism on somatic growth dynamics. We proposed a standardized form of the Pütter–Bertalanffy equation (PBE), which is given as the extended model of Richards function, and subsequently...

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Bibliographic Details
Published in:Journal of theoretical biology 2014-02, Vol.343, p.174-177
Main Authors: Ohnishi, Shuhei, Yamakawa, Takashi, Akamine, Tatsuro
Format: Article
Language:English
Subjects:
Allometry
Bertalanffy model
Growth and Development
Humans
Models, Biological
Ontogenetic growth
Pütter model
Richards model
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Summary:This study develops the basic idea of Pütter and Bertalanffy addressing the allometric scaling of anabolism and catabolism on somatic growth dynamics. We proposed a standardized form of the Pütter–Bertalanffy equation (PBE), which is given as the extended model of Richards function, and subsequently solved it. The analytical solution of the PBE was defined by an incomplete beta function and can take a wide range of shapes in its growth curve. The mathematical behavior of PBE due to the change in parameter values was briefly discussed. Most forms of solution consistently hold the implicit functional type with respect to the variable of body size. •We developed the basic idea of allometric scaling in somatic growth dynamics.•We proposed a standardized form of the Pütter–Bertalanffy equation.•The analytical solution was successfully obtained.•We discussed the mathematical behavior of the equation.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2013.10.017