Title Computational and experimental analysis of the mechanical performance of SLS generated ...

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Computational and experimental analysis of the mechanical
Title performance of SLS generated polymer-ceramic bone scaffold
materials
Author(s) Doyle, Heather
Publication
2014-09-30
Date
Item record http://hdl.handle.net/10379/4829
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Computational and Experimental Analysis
of the Mechanical Performance of SLS
Generated Polymer-Ceramic Bone Scaffold
Materials

Heather Doyle B.E. (2010)
Supervisor: Prof. Peter McHugh

A thesis submitted to the National University of Ireland as fulfilment of
the requirements for the Degree of Doctor of Philosophy.
Biomedical Engineering,
National University of Ireland, Galway.

September 2014
Contents

Contents 

Abstract ....................................................................................................................... v 
Acknowledgements ................................................................................................... vii 
List of Publications .................................................................................................... ix 

1  Introduction ...................................................................................................... 1 
1.1  Chapter Summary .......................................................................................... 1 
1.2  Selective Laser Sintering ............................................................................... 1 
1.3  Orthopaedic Scaffolds ................................................................................... 4 
1.4  Functional Requirements of Orthopaedic Scaffolds ...................................... 7 
1.4.1  Influence of Local Elastic Properties on New Bone Formation ............ 7 
1.4.2  Elastic Properties of Native Bone ........................................................ 10 
1.5  Elastic Properties of Scaffold Materials ...................................................... 16 
1.5.1  Degradation of Scaffold Materials ....................................................... 18 
1.6  Computational Modelling in Orthopaedic Applications ............................. 21 
1.6.1  Generation of High Resolution Finite Element Meshes ...................... 21 
1.6.2  Micromechanical Modelling of Multiphase Materials ......................... 23 
1.6.3  Computational Modelling of Critical-Sized Defects............................ 26 
1.7  Removal of Fracture Fixation Devices ........................................................ 33 
1.8  Thesis Objectives......................................................................................... 37 
1.9  Thesis Outline .............................................................................................. 40 
1.10  References ................................................................................................... 43 

2  Theory .............................................................................................................. 55 
2.1  Chapter Summary ........................................................................................ 55 
2.2  Continuum Mechanics ................................................................................. 55 
2.2.1  Notation ................................................................................................ 55 
2.2.2  Deformation and Stress ........................................................................ 56 
i
Contents

2.2.3  Material Constitutive Behaviour .......................................................... 61 
2.2.4  Estimating the Elastic Modulus of Multi-Phase Materials .................. 65 
2.3  Numerical Implementation for the Deformation of Solids.......................... 68 
2.3.1  Equilibrium Equations and Principle of Virtual Work ........................ 68 
2.3.2  The Finite Element Method ................................................................. 69 
2.4  References ................................................................................................... 73 

3  Predicting the Elastic Properties of Selective Laser Sintered PCL/β-TCP
Materials. ......................................................................................................... 74 
3.1  Chapter Summary ........................................................................................ 74 
3.2  Introduction ................................................................................................. 75 
3.3  Methods ....................................................................................................... 78 
3.3.1  Materials and Fabrication ..................................................................... 78 
3.3.2  Structural and Morphological Characterisation ................................... 79 
3.3.3  Mechanical Characterisation ................................................................ 82 
3.3.4  Finite Element Analysis of Full Struts ................................................. 84 
3.3.5  Micromechanical Finite Element Analysis .......................................... 90 
3.4  Results ....................................................................................................... 109 
3.4.1  Structural and Morphological Characterisation ................................. 109 
3.4.2  Mechanical Characterisation .............................................................. 111 
3.4.3  Micromechanical Finite Element Analysis ........................................ 113 
3.4.4  Macro-Scale Analysis of Struts .......................................................... 117 
3.5  Discussion ................................................................................................. 120 
3.6  Conclusions ............................................................................................... 128 
3.7  References ................................................................................................. 130 

4  Evaluation of a Microstructure-Based Modelling Methodology for PCL/β-
TCP SLS Scaffold Materials. ....................................................................... 135 
4.1  Chapter Summary ...................................................................................... 135 
4.2  Introduction ............................................................................................... 136 
4.3  Materials and Methods .............................................................................. 138 
4.3.1  Materials, Fabrication and Tensile Testing ........................................ 138 
ii
Contents

4.3.2  Structural and Morphological Characterization ................................. 139 
4.3.3  Micromechanical Modelling Analysis ............................................... 139 
4.3.4  Computational Modelling of Full Strut Geometries .......................... 142 
4.4  Degree of Anisotropy ................................................................................ 144 
4.5  Results ....................................................................................................... 145 
4.5.1  Materials, Fabrication and Tensile Testing ........................................ 145 
4.5.2  Structural and Morphological Characterization ................................. 146 
4.5.3  Micromechanical Modelling Results ................................................. 147 
4.5.4  Full Strut Modelling ........................................................................... 147 
4.5.5  Degree of Anisotropy ......................................................................... 151 
4.6  Discussion ................................................................................................. 154 
4.7  Conclusions ............................................................................................... 160 
4.8  References ................................................................................................. 162 

5  Evaluating the Influence of Ceramic Content on the Degradation of
PCL/β-TCP SLS Materials. ......................................................................... 166 
5.1  Chapter Summary ...................................................................................... 166 
5.2  Introduction ............................................................................................... 167 
5.3  Materials and Methods .............................................................................. 171 
5.3.1  Materials and Fabrication ................................................................... 171 
5.3.2  Accelerated Degradation .................................................................... 173 
5.3.3  Mechanical Testing ............................................................................ 174 
5.3.4  Structural and Morphological Characterisation ................................. 175 
5.4  Results ....................................................................................................... 176 
5.4.1  Mechanical Testing ............................................................................ 176 
5.4.2  Structural and Morphological Characterisation ................................. 183 
5.5  Discussion ................................................................................................. 186 
5.6  Conclusions ............................................................................................... 194 
5.8  References ................................................................................................. 195 

iii
Contents

6  Computational Modelling of Ovine Critical-Sized Tibial Defects. .......... 199 
6.1  Chapter Summary ...................................................................................... 199 
6.2  Introduction ............................................................................................... 200 
6.3  Methods ..................................................................................................... 206 
6.3.1  Summary of Model Development ...................................................... 206 
6.3.2  In Vivo Study Data ............................................................................. 208 
6.3.3  Generation of Model Geometries: Intact Tibiae ................................ 209 
6.3.4  Generation of Model Geometries: Tibiae with Scaffold and Callus .. 211 
6.3.5  Four-Point Bending Test Model Development .................................. 218 
6.3.6  Elastic Property Assignment .............................................................. 221 
6.3.7  Compression Test Model Development ............................................. 229 
6.3.8  Stress Distribution Analysis ............................................................... 231 
6.3.9  Callus Assessment Measurements ..................................................... 233 
6.4  Results ....................................................................................................... 235 
6.4.1  Four-Point Bending Simulations: Intact Tibia ................................... 235 
6.4.2  Four-Point Bending Simulations: Tibia with Callus and Scaffold .... 236 
6.4.3  Compression Simulations: Tibia with Callus and Scaffold ............... 243 
6.4.4  Callus Assessment Methods ............................................................... 251 
6.5  Discussion ................................................................................................. 254 
6.6  Conclusions ............................................................................................... 261 
6.7  References ................................................................................................. 264 

7  Conclusions and Recommendations ............................................................ 270 
7.1  Chapter Summary ...................................................................................... 270 
7.2  Thesis Summary ........................................................................................ 270 
7.3  Limitations ................................................................................................. 274 
7.4  Future Research ......................................................................................... 277 
7.5  Conclusion ................................................................................................. 281 
7.6  References ................................................................................................. 282 

iv
Abstract

Abstract 

The load-bearing ability of orthopaedic scaffolds in critical-sized defects is of critical
importance. 3D printing methods such as selective laser sintering (SLS) have great
potential for the fabrication of patient-specific scaffolds. The incorporation of
ceramic particles is desirable to promote osteogenesis; however the influence of
these particles on the microstructure and mechanical behaviour of SLS materials is
unclear.
A multiscale modelling methodology is developed to predict the macroscale elastic
properties of polymer-ceramic SLS materials with complex microstructures. The
relationship between micromechanics-evaluated elastic properties and average grey-
value is found to be material-specific. The macroscale elastic modulus of SLS
materials with different volumes of β-TCP particles is accurately predicted when
element-specific assignment of elastic properties based on grey-value is used.
Increasing the ceramic content of these SLS materials is shown to result in a slight
increase in stiffness but significant reductions in strength. Changes in mechanical
properties under simulated physiological degradation conditions are evaluated, and
are shown to be dependent on the incorporation of ceramic particles.
Computational models of critical-sized ovine tibial defects with implanted scaffolds
are generated. The ability of each defect to withstand bending and compressive
v
Abstract

loading is analysed, demonstrating the influence of callus volume and of both
scaffold volume and stiffness on defect load-bearing. Clinically-used metrics for the
prediction of the safety of removing external fixation are evaluated for each defect
and deficiencies in these measurements are demonstrated by comparison with
simulation results.
In conclusion, the use of both mechanical testing methods and computational
modelling in this thesis has led to an improved understanding of the influence of
ceramic content on mechanical properties as well as the development of a multiscale
modelling methodology to prediction macroscale mechanical properties.
Computational modelling of real defect geometries has resulted in a non-invasive
method to assess defect stability and load-bearing capacity.

vi
Acknowledgements

Acknowledgements 

Firstly, I would like to express my sincere gratitude to my supervisor Prof. Peter
McHugh for your patience, knowledge, support and guidance over the years. I
wouldn’t be here without your support and understanding.
I also wish to acknowledge the Irish Research Council for Science and Engineering
Technology (IRCSET), who funded this PhD research and the Irish Centre for High
End Computing (ICHEC), for the use of their computational facilities. Thank you to
Stefan Lohfeld for assistance with sample fabrication and to Pat McDonnell and
Noel Harrison for their valuable technical input. Thanks also to Prof. Tony Keaveny
and the University of California Education Abroad Program (UCEAP) for the
opportunity to study at UC, Berkeley. I would also like to thank Pat Kelly and
William Kelly from the Mechanical and Biomedical Engineering Laboratory NUIG
for technical assistance and to Jane Bowman and Sharon Gilmartin for all the help
throughout the years.
Thank you to my friends and fellow postgraduate students who have been a greatly
appreciated source of advice, help and encouragement. I would especially like to
thank Caoimhe, Claire, Evelyn, Donnacha, James, Nicola and Ted for all the
technical help, insightful suggestions and advice on this work. Thank you to those on
vii
Acknowledgements

the second floor, past and present, for the lunch time entertainment. Thank you also
to my friends from Galway for all of your moral support throughout these years.
To my parents, Ann and Paul, thank you for your never-ending love, support and
encouragement. A special thanks to Eimear and Evan. Shane, thank you for all of your
support through everything and for keeping me sane!
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