Article

# Allometric shape vector projection: a new method for the identification of allometric shape characters and trajectories applied to the human astragalus (talus).

Research Department of Genetics, Evolution and Environment, Division of Biosciences, University College London, London, UK.

Journal of Theoretical Biology (Impact Factor: 2.35). 03/2011; 272(1):64-71. DOI: 10.1016/j.jtbi.2010.11.030 Source: PubMed

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**ABSTRACT:**Orientation of the subtalar joint axis dictates inversion and eversion movements of the foot and has been the focus of evolutionary and clinical studies for a number of years. Previous studies have measured the subtalar joint axis against the axis of the whole foot, the talocrural joint axis and, recently, the principal axes of the talus. The present study introduces a new method for estimating average joint axes from 3D reconstructions of bones and applies the method to the talus to calculate the subtalar and talocrural joint axes. The study also assesses the validity of the principal axes as a reference coordinate system against which to measure the subtalar joint axis. In order to define the angle of the subtalar joint axis relative to that of another axis in the talus, we suggest measuring the subtalar joint axis against the talocrural joint axis. We present corresponding 3D vector angles calculated from a modern human skeletal sample. This method is applicable to virtual 3D models acquired through surface-scanning of disarticulated 'dry' osteological samples, as well as to 3D models created from CT or MRI scans.Journal of biomechanics 01/2012; 45(6):1103-7. · 2.66 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Most modelling of whole bones does not incorporate trabecular geometry and treats bone as a solid non-porous structure. Some studies have modelled trabecular networks in isolation. One study has modelled the performance of whole human bones incorporating trabeculae, although this required considerable computer resources and purpose-written code. The difference between mechanical behaviour in models that incorporate trabecular geometry and non-porous models has not been explored. The ability to easily model trabecular networks may shed light on the mechanical consequences of bone loss in osteoporosis and remodelling after implant insertion. Here we present a Finite Element Analysis (FEA) of a human ankle bone that includes trabecular network geometry. We compare results from this model with results from non-porous models and introduce protocols achievable on desktop computers using widely available softwares. Our findings show that models including trabecular geometry are considerably stiffer than non-porous whole bone models wherein the non-cortical component has the same mass as the trabecular network, suggesting inclusion of trabecular geometry is desirable. We further present new methods for the construction and analysis of 3D models permitting: (1) construction of multi-property, non-porous models wherein cortical layer thickness can be manipulated; (2) maintenance of the same triangle network for the outer cortical bone surface in both 3D reconstruction and non-porous models allowing exact replication of load and restraint cases; and (3) creation of an internal landmark point grid allowing direct comparison between 3D FE Models (FEMs).Journal of biomechanics 12/2012; · 2.66 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Hip joint diameter is highly correlated with body size in primates and so can potentially provide important information about the biology of fossil hominins. However, quantifying hip joint size has been difficult or impossible for many important but fragmentary specimens. New three-dimensional technologies can be used to digitally fit spheres to the acetabular lunate surface, potentially allowing hip joint diameter estimates for incomplete joint surfaces. Here we evaluate the reliability of sphere-fitting to incomplete lunate surfaces in silico using three-dimensional polygonal models of extant anthropoid hipbones. Measurement error in lunate sphere-fitting was assessed at the individual observer level, as well as between observers. Prediction error was also established for acetabular sphere size estimates for smaller divisions of the lunate surface. Sphere-fitting techniques were then applied to undistorted regions of lunate surface in Plio-Pleistocene hominin pelves, with a range of diameters constructed from extant error estimates. The results of this study indicate that digital sphere-fitting techniques are precise and that the lunate does not need to be completely preserved to accurately infer hip dimensions, although some aspects of joint size and morphology can influence sphere size estimates. Joint diameter is strongly predicted by spheres fit to the cranial and caudal halves of the lunate in all anthropoids. We present new hip joint size estimates for a number of fossil hominins, and outline additional applications for digital sphere-fitting as a morphometric technique. Am J Phys Anthropol, 2013. © 2013 Wiley Periodicals, Inc.American Journal of Physical Anthropology 02/2013; · 2.48 Impact Factor

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