Biomechanics of felid skulls: A comparative study using finite element approach Uphar Chamoli Supervisor: Dr. Stephen Wroe Submitted in partial fulfilment of the requirements for the degree of Master of Philosophy School of Biological, Earth and Environmental Sciences, Faculty of Science, The University of New South Wales August 2011 CERTIFICATE OF ORIGINALITY I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, nor material which to a substantial extent has been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged. Signature ...................... Date.............................. ii Dedicated to my parents and my deep rooted faith in Karma iii A major component of this thesis is published in Journal of Theoretical Biology x Chamoli, U. & Wroe, S., 2011. Allometry in the distribution of material properties and geometry of the felid skull: Why larger species may need to change and how they may achieve it. Journal of Theoretical Biology 283(1):217- 226. Some of the other methodologies used in this project, OR developed during the course of this project are also published in following journals x Attard, M., Chamoli, U., Ferrara, T., Rogers, T., and Wroe, S., 2011. Skull mechanics and implications for feeding behaviour in a large marsupial carnivore guild: the thylacine, Tasmanian devil and spotted-tailed quoll. Journal of Zoology. doi:10.1111/j.1469-7998.2011.00844.x x Wroe, S., Ferrara, T. L., McHenry, C. R., Curnoe, D., Chamoli, U., 2010. The craniomandibular mechanics of being human. Proceedings of the Royal Society B: Biological Sciences, 277: 3579-3586. iv ABSTRACT Shape and scale-related effects on biomechanical construct of organisms depend strongly on the properties and distribution of materials of which they are built, with an inherent requirement for avoiding failure over the entire lifetime. The cat family (Felidae) has been considered morphologically and behaviourally conservative, and hence an appropriate focus for investigations into the role of allometry. Here I apply three-dimensional (3D) finite element analysis (FEA) to models representing the skulls of seven extant felid species in order to (1) more fully assess their biomechanical performance; and (2) to predict allometric trends regarding overall geometry and relative distributions of cortical and cancellous bone. Results derived from incorporating material properties distribution for cortical and cancellous bone in the finite element models (FEMs) largely support the contention that mechanical behaviour in the felid skull is conservative across species. A negative allometric trend between cortical bone volume and total skull bone volume, and positive allometry between total skull bone volume and skull surface area were also observed. Further mathematical modelling using beam mechanics suggests that these allometric trends reflect a need for larger species to respond to physical challenges associated with increased size, and, that changes in skull shape, bone composition, or a combination of both, may be required to accommodate these challenges. I conclude that as felids become larger, overall skull bone volume relative to surface area increases by adding less dense and more compliant cancellous bone. This brings an overall saving in mass and a reduced burden on metabolism to produce biologically expensive cortical bone, without compromising much on the overall stiffness. In a further study, I constructed v 3D FEMs of two extinct sabretooth predators (Smilodon fatalis and Thylacosmilus atrox) to investigate functional convergence. Relative to the conical-toothed Panthera pardus, predicted jaw muscle driven bite forces in both were low, but their skulls appeared well-adapted to resist forces generated by cervical muscles. Although findings for S. fatalis are consistent with an extension of 'normal' biting behaviour, estimated jaw adductor driven bite forces for T. atrox considered with evidence for a major translational component, suggest that it was more specialised. vi ACKNOWLEDGEMENTS I feel very honoured to have the opportunity to work on this project in the Computational Biomechanics Research Group’s lab in the School of Biological, Earth and Environmental Sciences at UNSW. I am deeply indebted to my advisor Dr. Stephen Wroe for instilling in me the love and passion for Science, and for his unwavering support and encouragement all through my MPhil. Thank you Steve for the academic, moral and financial support – without any of these, I wouldn’t have ever conceived of completing this project. I am very grateful to all my brilliant, generous colleagues in the group for sharing their intellectual diversity, and for stimulating discussions and free exchange of ideas throughout the duration of this project, particularly William Parr, Toni Ferrara, Marie Attard, Peter Aquilina, Natalie Rogers and Naomi Tsafnat. Thanks to Assoc. Prof. Phil Clausen of University of Newcastle, Callaghan for help with engineering basics, Prof. Timothy Rowe of University of Texas, Austin and Prof. Lawrence Witmer of Ohio University, Athens for access to CT scan data. Thanks to Assoc. Prof. David Cohen, Head of School-BEES, for providing additional funding to help me write this thesis. My gratitude for the entire Nodiyal family for assimilating me into their family will always be deep and long. A special thanks to kids – how relaxing it is to come home after a tiring day at work and talk to kids – loved you for your innocence. Thank you to Neeta and Tanu for putting up with my constant complaining nature, and for having those mind-boggling maths and physics discussions. Lastly, big thanks to my brother and sister for having faith in me and my potential! vii TABLE OF CONTENTS Certificate of Originality..............................................................................................(ii) Abstract.......................................................................................................................(v) Acknowledgement......................................................................................................(vii) List of Abbreviations...................................................................................................(xii) List of Softwares used................................................................................................(xiii) List of Figures.............................................................................................................(xiv) List of Tables..............................................................................................................(xvii) List of Appendices.....................................................................................................(xviii) Chapter 1 Introduction 1.1. Finite Element Analysis and Biology............................................................ 2 1.2. Comparing Biomechanical Performance in Extant Felid Skulls.................... 4 1.3. Allometry in Material Properties distribution and Geometry of Extant Felid Skulls.........................................................................................6 1.4. Bone: A Composite Structure........................................................................9 1.5. A study of convergence in the biomechanical performance of two extinct mammalian sabretooths Smilodon fatalis and Thylacosmilus atrox........... 12 1.6. Main Aims................................................................................................... 18 Chapter 2 Methods and Materials 2.1 Digital Reconstruction of Felid Skulls using Computer Tomography (CT) Scan data..................................................................................................... 19 2.2 Finite Element Modelling Protocols in Strand7............................................ 22 2.2.1 Model Pre-processing......................................................................... 22 2.2.1.1 Modelling Major Muscle Sub-groups...................................... 23 viii 2.2.1.2 Jaw Hinge Mechanism................................................................ 25 2.2.1.3 Gape Angle and Hinge Rotation Co-ordinate System................. 26 2.2.1.4 Estimation of Temporalis and Masseteric Muscle Force: Dry Skull Method................................................................................26 2.2.1.5 Muscle Fibres Attachment, Pre-tension and Distribution...........30 2.2.1.6 Assigning Material Properties to Beam and Brick Elements.......33 2.2.1.7 Boundary conditions for simulating bilateral canine and unilateral carnassial bite case......................................................................35 2.2.1.8 Occipital Link Constraints............................................................37 2.2.1.9 Quantitative Estimation of Cortical and Cancellous Bone Volume using CT Intensity Data...............................................................38 2.2.1.10 Controlling Size differences ......................................................40