Deformable Cell Model of Tissue Growth
Abstract
:1. Introduction
2. Deformable Cell Model
2.1. Forces
- If the length of a side becomes twice as large as its initial length , then an additional vertex is introduced in the middle of the side. At the moment of side division, the stretching force is preserved. Hence the number of vertices depends on cell deformation. This allows us to better describe cell shape in the case of large deformations.
- If the length l of a side becomes sufficiently large, that is , with some , , then the initial length increases irreversibly in such a way that it satisfies the equality . In this case, if the stretching force is removed, then the spring will not return to its initial length but to some greater length. This corresponds to the irreversible deformation of the cell wall when it grows. Here, is a material parameter characterizing plastic deformation observed for biological tissues. In the simulations presented below, we set .
2.2. Cell Growth and Division
2.2.1. Cell Growth
2.2.2. Cell Division
3. Numerical Modelling of Tissue Growth
3.1. All Cells Grow and Divide
3.2. Pressure-Dependent Proliferation
3.3. External Supply of Nutrients
3.4. Wound Healing
4. Analytical Approximation of the Growth Rate
4.1. Approximate Model
4.2. Constant Proliferation
4.3. Pressure-Dependent Proliferation
5. Discussion
Author Contributions
Conflicts of Interest
References
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Bessonov, N.; Volpert, V. Deformable Cell Model of Tissue Growth. Computation 2017, 5, 45. https://doi.org/10.3390/computation5040045
Bessonov N, Volpert V. Deformable Cell Model of Tissue Growth. Computation. 2017; 5(4):45. https://doi.org/10.3390/computation5040045
Chicago/Turabian StyleBessonov, Nikolai, and Vitaly Volpert. 2017. "Deformable Cell Model of Tissue Growth" Computation 5, no. 4: 45. https://doi.org/10.3390/computation5040045
APA StyleBessonov, N., & Volpert, V. (2017). Deformable Cell Model of Tissue Growth. Computation, 5(4), 45. https://doi.org/10.3390/computation5040045