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Area of Science:

  • Mechanics of Materials
  • Mathematical Biology
  • Biophysics

Background:

  • Two primary frameworks, the constrained-mixture growth model and the kinematic growth model, are widely used to model biological growth.
  • Understanding the mathematical relationship between these models is crucial for their effective application.

Purpose of the Study:

  • To investigate the mathematical reconciliation of the constrained-mixture growth model and the kinematic growth model.
  • To provide practical guidelines for users of these biological growth modeling frameworks.

Main Methods:

  • Mathematical analysis to compare the theoretical underpinnings of the constrained-mixture and kinematic growth models.
  • Thermodynamic considerations for mass deposition under stressed conditions in both models.

Main Results:

  • The kinematic growth model is mathematically consistent with a specific form of the constrained-mixture growth model.
  • This consistency holds when only one generation of solid exists at a time, with the entire mass being reconfigured instantaneously.
  • Both models necessitate a cellular energy supply for solid mass deposition under stress, with minimal energy requirements.

Conclusions:

  • The study successfully reconciled the two prevalent theories of biological growth.
  • The conditions under which the constrained-mixture growth model simplifies to the kinematic growth model were elucidated.