Comparison of the trabecular architecture and the isostatic stress flow in the human calcaneus

A. Gefen*, R. Seliktar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


It is a common theory that the architecture of trabecular bone follows the principal stress trajectories, as suggested by Wolff's pioneering studies of the proximal femur. Since first published in the late 19th-century, this observation (popularized as "Wolff's law") has been supported by numerous studies, but nearly all of them have been focused on the femoral head and neck. In this study, the manifestation of Wolff's law in the human calcaneus has been analyzed. For this purpose, finite element (FE) analysis of the entire complex of the foot during standing was undertaken. Orientation of the principal stress flow through the calcaneus was compared with the trabecular alignment in a single cadaveric calcaneal specimen, by fitting second-order polynomials to real trabecular paths and FE-predicted isostatics and calculating their angle of inclination with the calcaneal cortex at their insertion points. Four dominant trabecular patterns were identified in the cadaveric sagittal section of the specimen of the calcaneus: one directed primarily in the dorsal-plantar direction, one aligned anteriorly-posteriorly, and two that are strongly oblique. Subsequent numerical simulations showed that the dorsal-plantar oriented and posterior oblique trabecular paths are aimed to support compressive stresses, while the antero-posteriorly directed and anterior oblique groups act to bear tension. Insertion angles of real trabecular paths into the calcaneal cortex were similar to those of the isostatics that were computed under musculoskeletal loading conditions of standing (maximum absolute local difference 13°, maximum local error 60%). This suggests that the trabecular patterns of the calcaneus are mainly shaped by isostatics (static principal stress flow) that are characteristic of the standing posture. The present modeling approach can be utilized to explore effects of abnormal alterations in the isostatic flow on the microarchitecture of the calcaneal trabeculae, as well as for better understanding of the mechanisms of calcaneal fractures.

Original languageEnglish
Pages (from-to)119-129
Number of pages11
JournalMedical Engineering and Physics
Issue number2
StatePublished - Mar 2004


FundersFunder number
Ela Kodesz Institute for Medical Engineering and Physical Sciences
Dan David Prize
Tel Aviv University


    • Cancellous bone
    • Finite element analysis
    • Foot biomechanics
    • Wolff's law


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