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:**The hominoid foot is of particular interest to biological anthropologists, as changes in its anatomy through time reflect the adoption of terrestrial locomotion, particularly in species of Australopithecus and Homo. Understanding the osteological morphology associated with changes in whole foot function and the development of the plantar medial longitudinal foot arch are key to understanding the transition through habitual bipedalism in australopithecines to obligate bipedalism and long-distance running in Homo. The talus is ideal for studying relationships between morphology and function in this context, as it is a major contributor to the adduction–abduction, plantar–dorsal flexion and inversion–eversion of the foot, and transmits all forces encountered from the foot to the leg. The talar surface is predominantly covered by articular facets, which have different quantifiable morphological characters, including surface area, surface curvature and orientation. The talus also presents challenges to the investigator, as its globular shape is very difficult to quantify accurately and reproducibly. Here we apply a three-dimensional approach using type 3 landmarks (slid semilandmarks) that are geometrically homologous to determine overall talar shape variations in a range of living and fossil hominoid taxa. Additionally, we use novel approaches to quantify the relative orientations and curvatures of talar articular facets by determining the principal vectors of facet orientation and fitting spheres to articular facets. The resulting metrics are analysed using phylogenetic regressions and principal components analyses. Our results suggest that articular surface curvatures reflect locomotor specialisations with, in particular, orang-utans having more highly curved facets in all but the calcaneal facet. Similarly, our approach to quantifying articular facet orientation appears to be effective in discriminating between extant hominoid species, and may therefore provide a sound basis for the study of fossil taxa and evolution of bipedalism in Australopithecus and Homo.Journal of Anatomy 05/2014; · 2.23 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139-45.Bone & joint research. 01/2014; 3(5):139-45. - [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; · 2.51 Impact Factor

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