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[Mathematical formulation possibilities of growth processes]
Gegenbaurs Morphologisches Jahrbuch
|January 1, 1981
Summary
This study reviews mathematical models of biological growth, tracing their history from ancient Mesopotamia to modern differential equations. It presents three new physicochemical models for cell, cell population, and mammalian embryo-fetal growth.
Area of Science:
- Mathematical Biology
- Physicochemical Processes
- Developmental Biology
Context:
- Historical overview of mathematical growth models, from early compound interest to differential equations.
- Gompertz (1825) and Verhulst (1838) introduced early organismic growth models.
- Von Bertalanffy's (1941) differential equation, while significant, has limited practical application.
Purpose:
- To survey the evolution and possibilities of mathematical growth modeling.
- To introduce novel physicochemical models for biological growth.
- To provide practical mathematical frameworks for understanding growth dynamics.
Summary:
- Presents a historical perspective on mathematical modeling of biological growth.
- Introduces three new differential equation models based on physicochemical processes.
- These models describe the growth of single cells, cell populations, and mammalian embryofetus.
Impact:
- Offers new, practical mathematical tools for biological growth research.
- Enhances understanding of cellular and developmental growth mechanisms.
- Facilitates quantitative analysis in developmental and cell biology.