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A test of a new method and software for the rapid estimation of cross-sectional geometric properties of long bone diaphyses from 3D laser surface scans

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Abstract

This paper introduces a new methodological approach to the quantification of cross-sectional geometric properties based on 3D laser scan data. A variety of methods have been used to calculate estimates of rigidity in the diaphyses of long bones. CT scan, biplanar radiograph, and periosteal mould techniques have all been applied to collect image data of bone sections to assess biomechanical properties (cross-sectional area and second moments of area). Whilst direct quantification of both endosteal and periosteal contours allows the greatest accuracy, such data correlate highly with a periosteal-only approach that is of greater practical application in many contexts. The advent of non-invasive 3D laser scan technologies presents a method to capture bone surface morphology that can be applied to the study of variation in the cross-sectional properties of human bones. This study tests the correspondence between cross-sectional geometric properties derived from laser scans to those obtained through traditional approaches (periosteal moulding and biplanar radiography). A custom-built program, AsciiSection, is introduced for the automated analysis of biomechanical properties direct from 3D coordinate data. The results indicate that the AsciiSection method is of comparable if not greater accuracy than traditional moulding techniques. The study suggests that there is a strong correlation between mid-diaphyseal cortical bone distribution and cross-sectional geometry calculated using laser scans. The approach provides a viable alternative to traditional techniques for the estimation of biomechanical properties and also allows the collection of rich data and descriptions of morphological variation along the diaphysis.

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Notes

  1. For TA, expected relative \( {\text{PE = }}\left. {{{{\left( {\left( {1 - \left( {{{{\% {\text{MA}}}} \left/ {{100}} \right.}} \right)} \right)} \right)}} \left/ {{\left. {\left( {{1} - \left( {{{{\% {\text{MA}}}} \left/ {{100}} \right.}} \right)} \right)} \right) * 100}} \right.}} \right) \). And for J, following the formula for circular sections (Sparacello and Pearson 2010), expected relative \( {\text{PE}} = \left. {\left( {{{{\left( {{1} - \left( {{1} - \left( {{{\left( {{{{\% {\text{MA}}}} \left/ {{{1}00}} \right.}} \right)}^{{2}}}} \right)} \right)} \right)}} \left/ {{\left( {{1} - \left( {{{\left( {{{{\% {\text{MA}}}} \left/ {{{1}00}} \right.}} \right)}^{{2}}}} \right)} \right)}} \right.}} \right) * {1}00} \right) \).

Abbreviations

CSG:

Cross-sectional geometry

TA :

Total area of section

CA :

Cortical area

I x :

Second moment of area, x-axis

I y :

Second moment of area, y-axis

I max :

Principle moment of area, max

I min :

Principle moment of area, min

J :

Polar second moment of area

I max/I min :

Cross-sectional shape max–min axes

I x /I y :

Cross-sectional shape, x- to y-axes

med :

Added to above abbreviations when referring to property calculated on a section including the medullary cavity

%CA :

Per cent cortical area

PM:

Periosteal moulding method

BR:

Biplanar radiograph method (biplanar radiography + periosteal moulding)

LS:

Laser scan method

CT:

Computed tomography scanning method

2D:

Two dimensional

3D:

Three dimensional

PE:

Per cent error

BIAS%:

Mean relative PE

PPE:

Per cent prediction error

%SEE:

Per cent standard error of the estimate

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Acknowledgements

Funding for this research was provided by the Natural Environment Research Council, UK. We would also like to thank the following institutions and individuals for access to skeletal collections under their care, or for their assistance: Maggie Bellatti and Mercedes Okumura, Duckworth Collection, University of Cambridge; Margaret Clegg, Heather Bonney, and Robert Kruszynski, Natural History Museum, London; Giorgio Manzi, Museo di Antropologia “G. Sergi”, Universita di Roma, Sapienza; Monica Zavattaro, Museo di Storia Naturale, Firenze; Jerry Cybulski, Janet Young, Stacey Girling, and Megan Gardiner, Canadian Museum of Civilization, Gatineau. Thanks also to the two anonymous reviewers for comments which improved this paper.

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  1. Division of Biological Anthropology, Department of Archaeology and Anthropology, University of Cambridge, Pembroke Street, Cambridge, CB2 3DZ, UK

    Thomas G. Davies, Colin N. Shaw & Jay T. Stock

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  1. Thomas G. Davies
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Correspondence to Thomas G. Davies.

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Davies, T.G., Shaw, C.N. & Stock, J.T. A test of a new method and software for the rapid estimation of cross-sectional geometric properties of long bone diaphyses from 3D laser surface scans. Archaeol Anthropol Sci 4, 277–290 (2012). https://doi.org/10.1007/s12520-012-0101-8

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