Related Experiment Video
Updated: May 6, 2026

Precise, High-throughput Analysis of Bacterial Growth
Published on: September 19, 2017
On the analytical solution for the Pütter-Bertalanffy growth equation
Shuhei Ohnishi1, Takashi Yamakawa2, Tatsuro Akamine3
1School of Marine Science and Technology, Tokai University, Shimizu, Shizuoka 424-8610, Japan.
Abstract:
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.
Related Concept Videos
Growth Models with Integration: Problem Solving
Exponential Equations for Modeling Growth
Modeling with Differential Equations
Population Growth
Derivatives: Problem Solving
Exponential Growth

