Annals of Biomedical Engineering

, Volume 45, Issue 6, pp 1543–1554 | Cite as

Anisotropic Permeability of Trabecular Bone and its Relationship to Fabric and Architecture: A Computational Study

  • T. C. Kreipke
  • G. L. Niebur


Trabecular bone is a porous, mineralized tissue found in vertebral bodies, the metaphyses and epiphyses of long bones, and in the irregular and flat shaped bones. The pore space is filled with bone marrow, a highly cellular fluid. Together, the bone and marrow behave as a poroelastic solid. In poroelasticity theory, the permeability is the primary material property that governs the momentum transfer between the solid and fluid constituents. In the linearized theory, the permeability of a material depends on the shape and connectivity of the pores. Developing a model of the relationship between trabecular microarchitecture and permeability could lead to improved simulations of trabecular bone mechanical response, which can be used to investigate bone adaptation, mechanobiological signaling, and progression of diseases such as osteoporosis. This study used finite element models of the trabecular pore space to calculate the complete anisotropic permeability tensor of 12 human and 18 porcine femoral trabecular bone samples. The sensitivity of the simulations to model assumptions and post-processing was analyzed to improve confidence in the result. The orthotropic permeability tensor depended on the fabric tensor, trabecular spacing, and structure model index through a power law relationship. Porosity and fabric alone also provided a reasonable prediction, which may be useful in cases where the image resolution is insufficient to obtain detailed measures of architecture.


Permeability Poroelasticity Trabecular bone Trabecular architecture Computational modeling Bone marrow Size effects Convergence 



This research was supported by the U.S. National Science Foundation Award CMMI 1435467. We wish to thank an anonymous reviewer for encouraging us to explore the Kozeny–Carman relationship further.

Conflicts of Interest

The authors have no conflicts of interest with the material presented in this paper.


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© Biomedical Engineering Society 2017

Authors and Affiliations

  1. 1.Tissue Mechanics Laboratory, Bioengineering Graduate Program, and Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.147 Multidisciplinary Research BuildingNotre DameUSA

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