Assessments of bilateral asymmetry with application in human skull analysis.

M Hou,M Hou,M J Fagan

doi:10.1371/journal.pone.0258146

Abstract

As a common feature, bilateral symmetry of biological forms is ubiquitous, but in fact rarely exact. In a setting of analytic geometry, bilateral symmetry is defined with respect to a point, line or plane, and the well-known notions of fluctuating asymmetry, directional asymmetry and antisymmetry are recast. A meticulous scheme for asymmetry assessments is proposed and explicit solutions to them are derived. An investigation into observational errors of points representing the geometric structure of an object offers a baseline reference for asymmetry assessment of the object. The proposed assessments are applicable to individual, part or all point pairs at both individual and collective levels. The exact relationship between the developed treatments and the widely used Procrustes method in asymmetry assessment is examined. An application of the proposed assessments to a large collection of human skull data in the form of 3D landmark coordinates finds: (a) asymmetry of most skulls is not fluctuating, but directional if measured about a plane fitted to shared landmarks or side landmarks for balancing; (b) asymmetry becomes completely fluctuating if one side of a skull could be slightly rotated and translated with respect to the other side; (c) female skulls are more asymmetric than male skulls. The methodology developed in this study is rigorous and transparent, and lays an analytical base for investigation of structural symmetries and asymmetries in a wide range of biological and medical applications.

Highlights

Often the geometric structure of a biological object is represented by a collection of anatomical landmarks divided into three subsets: two of them contain the paired landmarks on two sides of an object respectively, while the third includes the landmarks shared by both sides
Bilateral symmetry has been an important topic in morphometrics, e.g. [1], while other forms of symmetry have been found [2] traceable on the basis of bilateral symmetry
The current study examines bilateral asymmetry directly in an analytic geometry setting and derives explicit solutions for several types of asymmetry assessments

Summary

Introduction

Often the geometric structure of a biological object is represented by a collection of anatomical landmarks divided into three subsets: two of them contain the paired landmarks on two sides of an object respectively, while the third includes the landmarks shared by both sides. The two sides of the object are typically assumed to be geometrically symmetric about a plane in the closest proximity to the shared landmarks. Symmetry can take different forms and abnormal biological development may be reflected in noticeable structural asymmetries. Bilateral symmetry has been an important topic in morphometrics, e.g. [1], while other forms of symmetry have been found [2] traceable on the basis of bilateral symmetry. Investigation of bilateral asymmetry is important in biological studies for assessing.

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Conclusion