Surface curvatures of trabecular bone microarchitecture

H. Jinnai, H. Watashiba, T. Kajihara, Y. Nishikawa, M. Takahashi, M. Ito

Research output: Contribution to journalArticlepeer-review

78 Citations (Scopus)


Microstructure of trabecular bone has been examined with a particular emphasis on surface curvatures in two-phase (trabecular and intertrabecular space- i.e., marrow space) structures. Three trabecular bone samples, quantified as 'plate-like,' 'rod-like,' and a mixture of these two structural elements according to the structure model index (SMI), were subjected to analysis based on (differential) geometry. A correspondence between the SMI and the mean curvature was found. A method to measure surface curvatures is proposed. The gaussian curvatures averaged over the surfaces for the three analyzed bone structures were all found to be negative, demonstrating their surfaces to be, on average, hyperbolic. In addition, the Euler-Poincaré characteristics and the genus, both characterizing topological features of bone connectivity, were estimated from integral gaussian curvature (Gauss-Bonnet theorem). The three bone microstructures were found to be topologically analogous to spheres with one to three handles.

Original languageEnglish
Pages (from-to)191-194
Number of pages4
Issue number1
Publication statusPublished - 2002
Externally publishedYes


  • Differential geometry
  • Hyperbolic surface
  • Parallel surface method
  • Surface curvatures
  • Three-dimensional (3D) image analysis
  • Trabecular bone microstructure

ASJC Scopus subject areas

  • Endocrinology, Diabetes and Metabolism
  • Physiology
  • Histology


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