A three-dimensional model for tissue deposition on complex surfaces

Abstract

Biological processes are controlled by the biochemical composition and the physical properties of the environment. For example, geometrical features have been shown to influence cellular, multicellular and tissue behaviour. Moreover, the properties of these soft living materials affect their surface tension and thus, their shape. Two-dimensional (2D) models of geometry-driven growth suggest this interplay as responsible for the excellent control of tissue patterning throughout life. In this study, a digital 2D model of curvature-driven growth applicable to images from tissue culture experiments is extended to three dimensions. Artificial geometries were used to test the relevance and the precision of the simulations. The implementation of cell migration was also explored to better simulate the in vitro three-dimensional (3D) system. This model may be applied to computed tomography data, which could help in understanding to what degree surface curvature controls many biological processes such as morphogenesis, growth, bone healing, bone remodelling and implant integration.

Keywords::

• curvature-driven growth
• biological tissue growth
• 3D
• image-based modelling

Acknowledgements

We thank Peter Fratzl for fruitful discussions and advice. We also acknowledge funding from the Leibniz prize of Peter Fratzl running under DGF contract number FR2190/4-1. CB is part of the Berlin Brandenburg School for Regenerative Therapies (GSC 203).