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Are Homeostatic States Stable? Dynamical Stability in Morphoelasticity.
Alexander Erlich1, Derek E Moulton2, Alain Goriely3
1School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
Bulletin of Mathematical Biology
|September 23, 2018
Summary
Biological tissues maintain mechanical homeostasis through growth laws. This study reveals that the stability of this process in tubular structures depends on anisotropic growth, offering a basis for experimental validation.
Area of Science:
- Biomechanics
- Morphoelasticity
- Tissue Engineering
Background:
- Biological growth is influenced by mechanical cues like pressure and tension.
- Living tissues actively regulate internal mechanical stress, a state known as mechanical homeostasis.
- Morphoelasticity describes the interplay between mechanics and geometry in growing biological materials.
Purpose of the Study:
- To investigate the stability of mechanical homeostasis in tubular biological structures.
- To analyze the influence of spatially heterogeneous residual stress on growth dynamics.
- To determine the role of anisotropic growth responses in maintaining tissue stability.
Main Methods:
- A novel discretization approach was employed to study a continuous tubular system.
- The stability of equilibrium states in a homeostasis-driven growing dynamical system was precisely analyzed.
- The impact of spatially heterogeneous residual stress on system dynamics was modeled.
Main Results:
- The stability of the homeostatic state was found to depend non-trivially on the anisotropy of the growth response.
- Explicit results were obtained regarding the stability of equilibrium states in the dynamical system.
- The study highlights the critical role of anisotropy in homeostasis-driven growth.
Conclusions:
- The stability of mechanical homeostasis in tubular structures is intricately linked to anisotropic growth.
- The findings provide a theoretical foundation for experimentally testing homeostasis-driven growth laws.
- Understanding anisotropy is key to predicting and controlling biological tissue growth and stability.
Keywords:
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