An improved trabecular bone model based on Voronoi tessellation

Yijun Zhou; Per Isaksson; Cecilia Persson

doi:10.1016/j.jmbbm.2023.106172

An improved trabecular bone model based on Voronoi tessellation

J Mech Behav Biomed Mater. 2023 Dec:148:106172. doi: 10.1016/j.jmbbm.2023.106172. Epub 2023 Oct 10.

Authors

Yijun Zhou¹, Per Isaksson², Cecilia Persson³

Affiliations

¹ Division of Biomedical Engineering, Department of Materials Science and Engineering, Uppsala University, Box 35, Uppsala, 75121, Sweden. Electronic address: yijun.zhou@angstrom.uu.se.
² Division of Applied Mechanics, Department of Materials Science and Engineering, Uppsala University, Box 35, Uppsala, 75121, Sweden. Electronic address: per.isaksson@angstrom.uu.se.
³ Division of Biomedical Engineering, Department of Materials Science and Engineering, Uppsala University, Box 35, Uppsala, 75121, Sweden. Electronic address: cecilia.persson@angstrom.uu.se.

PMID: 37852087
DOI: 10.1016/j.jmbbm.2023.106172

Abstract

Background and objective: Accurate numerical and physical models of trabecular bone, correctly representing its complexity and variability, could be highly advantageous in the development of e.g. new bone-anchored implants due to the limited availability of real bone. Several Voronoi tessellation-based porous models have been reported in the literature, attempting to mimic the trabecular bone. However, these models have been limited to lattice rod-like structures, which are only structurally representative of very high-porosity trabecular bone. The objective of this study was to provide an improved model, more representative of trabecular bone of different porosity.

Methods: Boolean operations were utilized to merge scaled Voronoi cells, thereby introducing different structural patterns, controlling porosity and to some extent anisotropy. The mechanical properties of the structures were evaluated using analytical estimations, numerical simulations, and experimental compression tests of 3D-printed versions of the structures. The capacity of the developed models to represent trabecular bone was assessed by comparing some key geometric features with trabecular bone characterized in previous studies.

Results: The models gave the possibility to provide pore interconnectivity at relatively low porosities as well as both plate- and rod-like structures. The mechanical properties of the generated models were predictable with numerical simulations as well as an analytical approach. The permeability was found to be better than Sawbones at the same porosity. The models also showed the capability of matching e.g. some vertebral structures for key geometric features.

Conclusions: An improved numerical model for mimicking trabecular bone structures was successfully developed using Voronoi tessellation and Boolean operations. This is expected to benefit both computational and experimental studies by providing a more diverse and representative structure of trabecular bone.

Keywords: Numerical modelling; Porous structure; Trabecular bone; Voronoi tessellation.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Bone and Bones*
Cancellous Bone*
Permeability
Porosity
Spine