title: Comparison of the trabecular architecture and the isostatic stress flow in the human calcaneus.
abstract: 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 degrees, 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.
authors.affiliation: Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel. gefen@eng.tau.ac.il
authors.forename: A
authors.initials: A
authors.lastname: Gefen
authors.forename: R
authors.initials: R
authors.lastname: Seliktar
mesh_terms: D000328:Adult; D002102:Cadaver; D002111:Calcaneus / Q000033:anatomy & histology*; D003198:Computer Simulation; D004548:Elasticity; D005260:Female; D020342:Finite Element Analysis; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D013314:Stress, Mechanical; D016474:Weight-Bearing / Q000502:physiology*