An anisotropic stress-driven growth model for soft tissue based on Eulerian deformation tensor and growth potential

• Published in: Acta mechanica 2021-03, Vol.232 (3), p.933-948
• Main Author: Lee, Eun-Ho
• Format: Article
• Language: English
• Subjects: Analysis; Anisotropy; Aorta; Biomedical engineering; Classical and Continuum Physics; Control; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Finite element method; Growth models; Heat and Mass Transfer; Mathematical analysis; Mathematical models; Original Paper; Simulation; Soft tissues; Solid Mechanics; Tensors; Theoretical and Applied Mechanics; Three dimensional models; Tissue engineering; Tubes; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-020-02885-3

An anisotropic stress-driven growth model of living tissue is presented for tissue engineering based on Eulerian deformation tensor and growth potential. The evolution of growth is simply defined by the homeostatic pressure and Cauchy stress caused by the left Cauchy–Green deformation tensor that is an Eulerian deformation measure. For more generality, anisotropy is considered by proposing the concept of growth flow and growth potential that are inspired by the flow rule of plasticity theory. This method is then able to make three-dimensional anisotropic growth modeling. The Eulerian tensor-based characteristic enables easy implementation into finite element method (FEM). The presented model was implemented into an FEM code and validated by a theoretical solution of thick-walled hollow tubes of soft tissue in homeostatic state, and aortic stenting simulation was also performed for biomedical engineering application. The simulation results show good agreement with the references. The effect of the anisotropic function is also discussed with one element tension simulation. Finally, it is shown that the proposed model can capture experimental data of a growing tumor tissue, and a future work is discussed.