Vertebral Endplate Morphology and Permeability


The vertebra-disc interface in the human spine is a preferential path for both metabolites and fluid exchanges. With aging, degeneration and/or tissue calcification such interface experiences alterations of its components: the cartilaginous and the bony endplate (BEP). BEP permeability could thus be relevant for the fluid and nutrient exchanges between vertebra and intervertebral discs (IVDs). No protocol exists to date to quantify tissue permeability values in vivo, and in vitro studies should face the extremely reduced BEP thickness. As an alternative, μCT and computational fluid dynamics (CFD) were combined to evaluate the 3D microstructure and the resistance to fluid flow of the BEP, in order to calculate the tissue permeability and explore how results could be derived from clinical images.


  • Endplates from eight human vertebrae acquired using CT
  • Images segmented and measured in Simpleware ScanIP
  • Volume meshes generated in Simpleware +FE for permeability simulation in ANSYS Fluent
  • Results agree with several experimental measurements


Malandrino, A., Lacroix, D., Hellmich, C., Ito, K., Ferguson, S. J., Noailly, J., 2014. The role of endplate poromechanical properties on the nutrient availability in the intervertebral disc. Osteoarthritis and Cartilage, 22(7), 1053–1060.

Thanks to the following authors: 

A. Malandrino and J. Noailly (Institute for Bioengineering of Catalonia) •
D. Lacroix (University of Sheffield) • S.J. Ferguson (ETH, Zurich) •
K. Ito (Eindhoven University of Technology) • C. Hellmich (Vienna University of Technology)

Image Processing

CT scans of endplates from eight human lumbar vertebrae were used, coming from two different collaborative studies with different voxel resolutions (12 or 16 μm). A total of 50 3D parallelepiped samples (2.5 x 2.5 x 3 mm3) were created in image segmentation software ScanIP.

The models considered a squared cross section of the bony endplate. The third dimension was aligned with the superior-inferior direction. In the densest regions of each sample, the porosity was evaluated with the ScanIP measurements tool.

Meshing and CFD

Meshes were created with ScanIP +FE for CFD analyses with ANSYS Fluent. Parameters of meshing were kept constant to an optimum that ensured a good compromise between computational cost and convergence of the results. BEP permeation was simulated through application of a mass flux at the inlet. The pressure at the outlet cross section was null. A "no-slip" condition was imposed on the other surfaces.

The macroscopic intrinsic permeability k was evaluated by using the Darcy relation, k=μQinL/ρA(Pin-Pout), where Qin is the mass flux at the inlet through the cross-section A, μ and ρ are the dynamic viscosity and density of water, respectively, and L is the distance between the two sections characterized by the pressures Pin and Pout.


Positive correlation was found between the permeability and porosity values pooled for all endplates (R2=0.86). Such outcome suggests that permeability values could be defined from CT attenuation coefficients. The range of intrinsic permeability values found in this study was very large, covering part of the range previously measured for both trabecular and cortical bones. However, it agrees with several experimental measurements.