Three-dimensional rendering of trabecular bone microarchitecture using a probabilistic approach

  • Matthew Kirby
  • Abu Hena Morshed
  • Joel Gomez
  • Pengwei Xiao
  • Yizhong Hu
  • X. Edward Guo
  • Xiaodu WangEmail author
Original Paper


In the past, researchers have attempted to model trabecular bone using computational techniques. However, only a few of these models are visually similar, but not representative of the microstructural characteristics of real trabecular bones. In this study, we hypothesized that probabilistic modeling approaches could be used to generate representative digital models that capture the microstructural features of real trabecular bones. To test this hypothesis, we proposed a novel mathematical framework to build the digital models and compared the digital models to real bone specimens. First, an initial three-dimensional cellular structure was generated using Voronoi tessellation, with the faces and edges of the Voronoi cells considered as a pool of potential trabecular plates and rods, respectively. Then, inverse Monte Carlo simulations were performed to select, delete, or reassign plates and rods until the underlying size, orientation, and spatial distributions of the plates and rods converged to the target distributions obtained from real trabecular bone microstructures. Next, digital graphics techniques were used to define the thickness of trabecular plates and the diameter of trabecular rods, followed by writing the model into a Standard Tessellation Language file and then smoothing the model surfaces for a more natural appearance. To verify the efficacy of the digital model in capturing the microstructural features of real trabecular bones, forty-six digital models with a large variation in microstructural features were generated based on the target distributions obtained from trabecular bone specimens of twelve human cadaveric femurs. Then, the histomorphological parameters of the digital models were compared with those of the real trabecular bone specimens. The results indicate that the digital models are capable of capturing major microstructural features of the trabecular bone samples, thus proving the hypothesis that the proposed probabilistic modeling approach could render real trabecular bone microstructures.


Trabecular bone Microstructure Digital model Voronoi tessellation Inverse Monte Carlo simulation Probabilistic modeling 



The authors are grateful to Dr. Yufei Huang for his constructive comments and discussion on probabilistic modeling and Mr. Peter Mancuso for his assistance in developing the code to render trabecular thickness (plate thickness and rod diameter) in the digital model. This work received computational support from UTSA’s HPC cluster SHAMU, operated by the Office of Information Technology.

Compliance with ethical standards

Conflict of interest

All authors state that they have no conflict of interest.

Supplementary material


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe University of Texas at San AntonioSan AntonioUSA
  2. 2.Biomedical EngineeringColumbia UniversityNew YorkUSA

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