Automated generation of tissue-specific three-dimensional finite element meshes containing ellipsoidal cellular inclusions

Abstract

Finite element analysis provides a means of describing cellular mechanics in tissue, which can be useful in understanding and predicting physiological and pathological changes. Many prior studies have been limited to simulations of models containing single cells, which may not accurately describe the influence of mechanical interactions between cells. It is desirable to generate models that more accurately reflect the cellular organisation in tissue in order to evaluate the mechanical function of cells. However, as the model geometry becomes more complicated, manual model generation can become laborious. This can be prohibitive if a large number of distinct cell-scale models are required, for example, in multiscale modelling or probabilistic analysis. Therefore, a method was developed to automatically generate tissue-specific cellular models of arbitrary complexity, with minimal user intervention. This was achieved through a set of scripts, which are capable of generating both sample-specific models, with explicitly defined geometry, and tissue-specific models, with geometry derived implicitly from normal statistical distributions. Models are meshed with tetrahedral (TET) elements of variable size to sufficiently discretise model geometries at different spatial scales while reducing model complexity. The ability of TET meshes to appropriately simulate the biphasic mechanical response of a single-cell model is established against that of a corresponding hexahedral mesh for an illustrative use case. To further demonstrate the flexibility of this tool, an explicit model was developed from three-dimensional confocal laser scanning image data, and a set of models were generated from a statistical cellular distribution of the articular femoral cartilage. The tools presented herein are free and openly accessible to the community at large.

Keywords::

• tissue
• cartilage
• cell
• finite element
• tetrahedral
• mesh

Acknowledgements

The authors would like to thank Mark van Turnhout and the Department of Biomedical Engineering at the Eindhoven University of Technology for providing the CLSM data used in this study.

Additional information

Funding

This study was supported by the National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health [grant number R01EB009643, Principal Investigator: Ahmet Erdemir].