### Abstract

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

Lizard skulls vary greatly in shape and construction, and radical changes in skull form during evolution have made this an intriguing subject of research. The mechanics of feeding have surely been affected by this change in skull form, but whether this is the driving force behind the change is the underlying question that we are aiming to address in a programme of research. Here we have implemented a combined finite element analysis (FEA) and multibody dynamics analysis (MDA) to assess skull biomechanics during biting. A skull of *Uromastyx hardwickii* was assessed in the present study, where loading data (such as muscle force, bite force and joint reaction) for a biting cycle were obtained from an MDA and applied to load a finite element model. Fifty load steps corresponding to bilateral biting towards the front, middle and back of the dentition were implemented. Our results show the importance of performing MDA as a preliminary step to FEA, and provide an insight into the variation of stress during biting. Our findings show that higher stress occurs in regions where cranial sutures are located in functioning skulls, and as such support the hypothesis that sutures may play a pivotal role in relieving stress and producing a more uniform pattern of stress distribution across the skull. Additionally, we demonstrate how varying bite point affects stress distributions and relate stress distributions to the evolution of metakinesis in the amniote skull.

### Introduction

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

This study addresses the mechanical function of the skull of the lizard *Uromastyx hardwickii* (Squamata, Agamidae) using a combined finite element analysis (FEA) and multibody dynamics analysis (MDA) approach. *Uromastyx* is generally considered to be one of the two basal agamid genera (the other being *Leiolepis*) and is interesting as (1) being primarily herbivorous, (2) having a specialized arrangement of the pterygoideus muscle whereby an additional external slip attaches to the outside of the skull, and (3) in having a skull that is said to be essentially akinetic (lacking obvious intracranial movements) but hyperstreptostylic (Throckmorton, 1976). *Uromastyx* is a common ground-living lizard in India, Africa and the Middle East and has therefore been quite well described in the literature (e.g. Saksena, 1942; El-Toubi, 1945; George, 1955; Islam, 1955; Throckmorton, 1976). With regard to mechanical function we are concerned to investigate the relationship between sutures and stress distribution, the extent to which there is potential for metakinesis, and the effects of varying bite point on stresses.

The application of FEA and MDA has increased rapidly in the area of functional morphology, as these technologies have the potential to advance our understanding of the driving forces that shape bone, as well as more complex and specific structures such as the skull (e.g. McHenry et al. 2007; Curtis et al. 2008). The advantages of using these mechanical engineering tools is that forces acting upon the skull can be estimated and then applied to a model of it to estimate patterns of strain and stress across the skull. In conjunction with knowledge of evolutionary paths, this information can be used to develop hypotheses regarding the genetic and epigenetic factors that shape the skeleton. Both MDA and FEA warrant a brief overview.

MDA involves two or more rigid bodies whose motions can be independent of each other, or whose motions are constrained by joints or specified contact surfaces and springs. As the term rigid body implies, no deformation of the geometries occurs, and as such, deformation does not affect gross body motion. This area of dynamics can be divided into two disciplines: (1) a kinetic analysis, which is the study of motion produced under the action of forces, and (2) a kinematic analysis, which is the study of motion regardless of the masses or forces. For example, a kinetic simulation is applied when assessing jaw motion that is driven by the masticatory muscles, and a kinematic simulation is applicable when a rotation is defined to a joint and motion is produced without concern for mass and muscle forces (e.g. Geradin & Cardona, 2001; Hannam, 2003). FEA works by dividing the geometry of the problem under investigation (e.g. a skull) into a finite number of sub-regions, called elements, which are connected together at their corners (and sometimes along their mid-sides). These points of connection are called nodes. For stress analysis, a variation in displacement (e.g. linear or quadratic) is then assumed through each element, and equations describing the behaviour of each element are derived in terms of the (initially unknown) nodal displacements. These element equations are then combined to give a set of system equations which describes the behaviour of the whole problem. After modifying the equations to account for the loading and constraints applied to the problem, these system equations are solved. The output is a list of all the nodal displacements. The element strains can then be calculated from the displacements, and the stresses from the strains. More detailed descriptions of FEA principles and its applications to craniofacial mechanics are available (e.g. Fagan, 1992; Richmond et al. 2005; Rayfield, 2007).

MDA, predominately an engineering tool, was brought to the area of biomechanics to study human movement, and more recently it is being used by those interested in functional morphology (e.g. Langenbach et al. 2002; Sellers & Crompton, 2004; de Zee et al. 2007; Curtis et al. 2008; Moazen et al. 2008). MDA can be used to estimate the loading conditions that act, for example, on the skull during biting and which, if modelled accurately, will provide more precise data for FEA. Whereas MDA is a relatively under-utilized tool in this area, FEA is widely applied, with some authors adopting inductive methods (Preuschoft & Witzel, 2002, 2005) and some deductive methods (e.g. Rayfield et al. 2001; Dumont et al. 2005; Ross et al. 2005). Recent FEA studies have become increasingly complex, with approximations in material properties of bone (e.g. Strait et al. 2005; Wang & Dechaw, 2006) and the representation of muscle loading (e.g. Grosse et al. 2007; Wroe et al. 2007) being addressed more thoroughly. However, so far there are few combined MDA and FEA studies in the literature (e.g. Koolstra & van Eijden, 2005, 2006; Curtis et al. 2008).

The aim of this present phase of our work is to evaluate the potential of an MDA approach to the loading of skulls using a finite element model of *Uromastyx*. In this paper, the resulting MDA load data are used to explore the variation of stress across the skull to consider the possible role of sutures, the potential for metakinesis and the effects of varying bite point. During each simulation, gape angle, muscle force, bite force and joint force all vary with time, with the MDA solution outputting the load data at discrete time steps. These load steps are then transferred to the FE analysis, where the variation of stress and strain over time can be examined. In this study we also compared the results of FEA models that used MDA load data with models using loading methods more widely described in the literature.

### Conclusions

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

Despite these limitations, this work demonstrates the benefits of using MDA to estimate the biomechanical loads for application to FE models of skulls. We feel this is the best way to properly test hypotheses in functional morphology in a more objective way, where muscle data, joint data and bite data can all be obtained and then applied to calculate stress and strains throughout the skull. More work is required to improve the complexity and realism of both the MDA and FEA models, but the results shown here demonstrate the effects of different bite positions on patterns of strain in the lizard skull, suggest a selective advantage for the elaboration of joints involved in relative movements of the braincase against the dermal skull, and provide evidence of a functional role for cranial sutures. Additional loading scenarios need to be considered in the MDA, such as unilateral biting, and in the FEA the inclusion of sutures and anisotropic material properties would allow more accurate stress and strain results.