Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 2, pp 327–345 | Cite as

Anisotropic stiffness and tensional homeostasis induce a natural anisotropy of volumetric growth and remodeling in soft biological tissues

  • F. A. Braeu
  • R. C. Aydin
  • Christian J. CyronEmail author
Original Paper


Growth in soft biological tissues in general results in anisotropic changes of the tissue geometry. It remains a key challenge in biomechanics to understand, quantify, and predict this anisotropy. In this paper, we demonstrate that anisotropic tissue stiffness and the well-known mechanism of tensional homeostasis induce a natural anisotropy of the geometric changes resulting from volumetric growth in soft biological tissues. As a rule of thumb, this natural anisotropy makes differential tissue volume elements dilate mainly in the direction(s) of lowest stiffness. This simple principle is shown to explain the experimentally observed growth behavior in a host of different soft biological tissues without relying on any additional heuristic assumptions or quantities (such as ad hoc defined growth tensors).


Growth and remodeling Volumetric Mechanobiology Aneurysm Computational modeling Anisotropic growth 



This work was supported by the Emmy Noether program of the German Research Foundation DFG (CY 75/2-1) and the International Graduate School for Science and Engineering (IGSSE) of Technical University of Munich. The authors thank D. Bigoni from University of Trento, Italy, for fruitful discussions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Computational MechanicsTechnical University of MunichMunichGermany
  2. 2.Institute of Continuum Mechanics and Materials MechanicsHamburg University of TechnologyHamburgGermany
  3. 3.Institute of Materials Research, Materials MechanicsHelmholtz-Zentrum GeesthachtGeesthachtGermany

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