Biomechanics of the Human Optic Chiasmal Compression Xiaofei Wang

Biomechanics of the Human Optic Chiasmal Compression

Xiaofei Wang

A thesis submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Engineering and Information Technology

The University of New South Wales

August 2014

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THE .UNIVERSITY OF NEW SOUTH WAl.,,~S Thesis/Dissertation Sheet

Surname or Family name: Wang

First name: Xiaofei Other name/s:

Abbreviation for degree as given in the University calendar: PhD

School: Engineering and Information Technology Faculty: UNSW Canberra at ADFA

Title: Biomechanics of the human optic chiasmal compression

Abstract 350 words maximum: (PLEASE TYPE)

Bitemporal hemianopia is a type of partial visual field defect in which vision is impaired in the temporal halves of the visual fields of both eyes. Bitemporal hemianopia has many known causes but the most common cause is the chiasmal compression caused by a pitu itary tumour. However, the precise mechanism of bitemporal hemianopia is still not clear. This thesis aims to explore the possible causes of bitemporal hemianopia by investigating the biomechanics of chiasmal compression. · ·

Simple optic chiasmal compression models and nerve fibre models were developed first, using finite element modelling, for analysis of the mechanical behaviours of the chiasm. An ilndividual-specific optic ch iasmal compression model was then built to account for more accurate geometry and material properties of the chiasm. Multi-scale analyses were then performed to examine the micro-scale interactions of the nerve fibres using representative .volume elements. To further improve the fidelity of the model, the detailed nerve fibre arrangements in the optic chiasm were investigated using photomicrographic image analysis of the human chiasmal slices. Finally, an ex viva experiment of optic chiasmal compression was conducted for further validation of the numerical method.

Strain distributions in the optic chiasm and optic nerve fibres were obtained from the numerical models. The results of the chiasmal model broadly agreed with the limited experimental results in the literature, ind icating that the fin ite element modelling can be a useful tool for analysing chiasmal compression. Simulation results showed that, under the same loading conditions, the strain distribution in crossed nerve fibres was much more nonuniform and locally higher than in uncrossed nerve fibres. This strain difference may account for the phenomenon of bitemporal hemianopia. The nerve fibre arrangement study added more details to the present understanding of fibre trajectories in the optic chiasm. The FEM model simulated the ex viva experiment reasonably well which further underlines the usefulness of FEM in investigating the ch iasmal compression .

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:~:~:~io~todigttal~ .···· ··························· J-7/11 /01~ Date ···· ··· ······· ·· ·· ·· ·· ··· ···· ...... Acknowledgements

I would like to thank my supervisor Associate Professor Andrew Neely for giving me the opportunity to do my PhD thesis. This thesis would have not been possible without his continuous support, patience, encouragement and immense knowledge. He is not only a supervisor but also a friend.

I would also like to thank my co-supervisor Professor Christian Lueck in the Canberra

Hospital and the Australian National University, for his tremendous support and guidance. He always provides detailed and valuable feedback quickly. I am very grateful for having a chance to work with him.

I would like to thank my colleagues Neeranjali Jain and Swaranjali Jain, for their extremely useful inputs to this project.

I would also like to thank the following people for their involvement in this project and helpful discussions: Gawn McIlwaine, Dr Murat Tahtali, Thomas Lillicrap and

Professor Sanjiv Jain. It’s an honour to work with so many smart people.

I would like to thank all my friends and colleagues in Canberra for making my time here enjoyable and memorable.

Most of all, I would like to thank Jinge Luo, Yafei Wang, Yali Wang and my parents for their constant support and encouragement.

Publications Arising from this Thesis

Journal Articles

1. Wang X, Neely A, McIlwaine G and Lueck C. Multi-scale analysis of optic chiasmal compression by finite element modelling. Journal of Biomechanics. 47 (10), pp. 2292-2299.

2. Wang X, Neely A, McIlwaine G, Tahtali M, Lillicrap T and Lueck C. Finite element modelling of optic chiasmal compression. Journal of Neuro- Ophthalmology. (In press) published online, DOI: 10.1097/WNO.0000000000000145

3. Jain N, Jain S, Wang X, Neely A, Tahtali M, Jain S and Lueck C. Visualisation of nerve fibre orientations in the human optic chiasm using photomicrographic image analysis. (Prepare to submit to Journal of Anatomy)

4. Wang X, Neely A, Jain N, Jain S, Tahtali M, Jain S and Lueck C. Biomechanics of the human optic chiasmal compression. (Prepare to submit to Investigative Ophthalmology & Visual Science)

Refereed Conference Papers

1. Wang X, Neely A, Lueck C, Tahtali M, McIlwaine G and Lillicrap T. Parametric studies of optic chiasmal compression biomechanics using finite element modelling, 7th Australasian Congress on Applied Mechanics, ACAM 7 9-12 December 2012, Adelaide, Australia.

2. Wang X, Neely A, McIlwaine G and Lueck C. Biomechanics of chiasmal compression: sensitivity of the mechanical behaviours of nerve fibres to variations in material property and geometry. 11th World Congress on Computational Mechanics, 20-25 July 2014, Barcelona, Spain.

Conference Abstracts and Poster Presentations

1. McIlwaine G, Wang X, Neely A, Tahtali M, Lueck C. Why does chiasmal compression cause bitemporal hemianopia? The Oxford Ophthalmological Conference, Oxford, UK, 1-4 July, 2012

2. Lueck C, Wang X, Neely A, Tahtali M, McIlwaine G, Lillicrap T. Finite element modelling of chiasmal compression: nearer to an understanding of

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bitemporal hemianopia? The 39th Meeting of the North American Neuro- Ophthalmology Society, Snowbird, UT, USA, 9-14 February, 2013.

3. Lueck C, Wang X, Neely A, Tahtali M, Lillicrap T, McIlwaine G (2013). Finite Element Modelling of Chiasmal Compression: Sensitivity to Tissue Properties and Geometry of the Model. The Annual Scientific meeting of the European Neuro-Ophthalmological Society, Oxford, UK, 10-13 April, 2013. Neuro- Ophthalmology. Vol. 37 (Supp1), p.76

4. Wang X, Neely A, McIlwaine G, Tahtali1 M, Lillicrap T, Lueck C. Finite Element Modelling of Optic Chiasmal Compression. The Canberra Health Annual Research Meeting, Canberra, Australia, 20-23 August, 2013.

5. Wang X, Neely A, Tahtali1 M, Lillicrap T, McIlwaine G, Lueck C. Finite Element Modeling of Chiasmal Compression: Varying the Model’s Parameters. The Canberra Health Annual Research Meeting, Canberra, Australia, 20-23 August, 2013.

6. Lueck C, Wang X, Neely A, Tahtali M, McIlwaine G, Lillicrap T. Finite element modelling of chiasmal compression: nearer to an understanding of bitemporal hemianopia? The 29th Annual Clinical and Scientific Meeting of the Neuro-Ophthalmology Society of Australia, Noosa, Australia, 5-8 September, 2013

7. Jain N, Jain S, Wang X, Neely A, Tahtali M, Jain, S, Lueck C. Visualisation of nerve fibre orientation in the human optic chiasm using photomicroscopic image analysis. The Annual Scientific Meeting of The Australian and New Zealand Association of Neurologists, Adelaide, Australia,19-22 May, 2014

8. Neely A, Wang X, Lillicrap T, Tahtali T, Jain N, Jain S, Jain S, McIlwaine G and Lueck C. Biomechanical investigations of human neurological conditions. Australian Biomedical Engineering Conference 2014, Canberra, Australia, 20-22 August, 2014

Abstract

Bitemporal hemianopia is a type of partial visual field defect in which vision is impaired in the temporal halves of the visual fields of both eyes. Bitemporal hemianopia has many known causes but the most common cause is the chiasmal compression caused by a pituitary tumour. However, the precise mechanism of bitemporal hemianopia is still not clear. This thesis aims to explore the possible causes of bitemporal hemianopia by investigating the biomechanics of chiasmal compression.

Simple optic chiasmal compression models and nerve fibre models were developed first, using finite element modelling, for analysis of the mechanical behaviour of the chiasm.

An optic chiasmal compression model using individual-specific geometry was then built to account for more accurate geometry and material properties of the chiasm. Multi- scale analyses were then performed to examine the micro-scale interactions of the nerve fibres using representative volume elements. To further improve the fidelity of the model, the detailed nerve fibre arrangements in the optic chiasm were investigated using photomicrographic image analysis of the human chiasmal slices. Finally, a preliminary ex vivo experiment of optic chiasmal compression was developed and conducted for further experimental investigation of the chiasmal compression and validation of the numerical method.

v peripheral chiasm cannot explain the vertical cutoff of visual field in bitemporal hemianopia. The strain distribution in the chiasm was significantly affected by the chiasmal geometry and contact patterns between the chiasm and the tumour, indicating that future clinical investigation of bitemporal hemianopia should not only focus on the tumour size.

Simulation results showed that, under the same loading conditions, the strain distribution in crossed nerve fibres was much more nonuniform and locally higher than in uncrossed nerve fibres. Parametric study using Design of Experiment showed that the crossing angle was the leading factor that influences the responses of the nerve fibre model. Considering that there are likely to be certain strain thresholds of nerve fibre dysfunction, based on previous research, the locally higher strain may shut down the conduction of crossed fibres while the uncrossed fibres are unimpaired. Therefore, this strain difference between crossed and uncrossed fibres may account for the phenomenon of bitemporal hemianopia.

The nerve fibre arrangement study added more details to the present understanding of fibre trajectories in the optic chiasm. A large portion of the nerve fibres in the peripheral part of the chiasm were crossed nerve fibres, which contradicts the traditional understanding.

The preliminary experiment was successfully conducted and the finite element model simulated the chiasmal distortion measured in the ex vivo experiment to within 16% differences. Given the assumptions made within the model, this further underlines the usefulness of finite element modelling in investigating the chiasmal compression.

Table of Contents

Statement of Originality ...... i

Acknowledgements ...... ii

Publications Arising from this Thesis ...... iii

Abstract ...... v

Table of Contents ...... vii

List of Figures ...... xii

List of Tables ...... xxi

Nomenclature...... xxii

Glossary and Abbreviations ...... xxiii

Chapter 1 ...... 1

Introduction ...... 1 1.1 Human optic system ...... 1 1.2 Anatomy of optic chiasm and its adjacent structures ...... 4 1.3 Bitemporal hemianopia ...... 6 1.4 Other visual field defects ...... 8 1.5 Finite element modelling in biomechanics ...... 9 1.6 Aims and objectives ...... 11 1.7 Contributions ...... 13 1.8 Thesis outline ...... 13

Chapter 2 ...... 17

Bitemporal hemianopia and nerve injury caused by mechanical loading ...... 17 2.1 Bitemporal hemianopia ...... 17 2.1.1 Visual field loss pattern of bitemporal hemianopia ...... 17 2.1.2 The elevation of the chiasm and the visual field defect ...... 19

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2.2 Existing theories to explain bitemporal hemianopia ...... 23 2.3 Axonal injury caused by mechanical deformation ...... 27 2.3.1 Axonal injury mechanisms ...... 27 2.3.2 Mechanical measurements used to evaluate nerve damage ...... 29

Chapter 3 ...... 31

Generic optic chiasmal models and nerve fibre models ...... 31 3.1 Introduction ...... 31 3.2 Optic chiasmal model ...... 32 3.2.1 Geometry ...... 32 3.2.2 Material properties ...... 33 3.2.3 Simulations ...... 34 3.2.4 Data analysis ...... 36 3.3 Nerve fibre model ...... 38 3.4 Assumptions ...... 40 3.5 Results ...... 41 3.5.1 Mechanical deformation of the chiasm with increasing tumour volume ...... 41 3.5.2 Von Mises strain distribution...... 42 3.5.3 Pressure distribution ...... 45 3.5.4 Nerve fibre model ...... 46 3.6 Sensitivity study of the generic models ...... 48 3.6.1 Variations of the chiasmal compression model ...... 49 3.6.2 Variation of the nerve fibre model...... 53 3.6.3 Results of the chiasmal model ...... 53 3.6.4 Results of the nerve fibre model ...... 61 3.7 Discussion ...... 62

Chapter 4 ...... 67

Optic chiasmal model based on Visible Human Project ...... 67 4.1 Geometry ...... 68 4.2 Material properties ...... 69 4.3 Boundary condition, loading and meshing ...... 75

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4.4 Output measurements ...... 76 4.5 Sensitivity study of the individual-specific model ...... 76 4.5.1 Variation of the tumour growing direction ...... 76 4.5.2 Variation of the tumour diameter ...... 77 4.5.3 Variations of the loading site ...... 77 4.5.4 Variation of the stiffness of pia mater ...... 78 4.5.5 Variation of the stiffness of nerve tissue ...... 78 4.5.6 Variation of the tumour stiffness ...... 78 4.5.7 Effects of the elevation of the chiasm ...... 79 4.6 Results ...... 79 4.6.1 The baseline model ...... 79 4.6.2 Results of the parametric studies ...... 82 4.7 Discussion ...... 88

Chapter 5 ...... 91

Microscopic nerve fibre model using multi-scale analysis ...... 91 5.1 Multi-scale approach using finite element modelling ...... 91 5.2 Nerve fibre model ...... 92 5.2.1 Geometry ...... 92 5.2.2 Material properties ...... 95 5.2.3 Boundary conditions applied to RVEs ...... 96 5.2.4 Simulations ...... 98 5.2.5 Output measurements ...... 99 5.2.6 Results ...... 99 5.3 Sensitivity study of the RVE model using design of experiments ...... 101 5.3.1 Design of experiments ...... 102 5.3.2 Analysing DOE results ...... 105 5.4 A new nerve fibre-packing pattern of uncrossed fibres...... 108 5.5 Discussion ...... 110

Chapter 6 ...... 115

Axonal trajectory in the optic chiasm and its influences on the strain distribution in nerve fibres ...... 115 6.1 The patterns of nerve fibre organization in the chiasm ...... 116 6.2 Visualisation of nerve fibre distribution in the optic chiasm using photomicrographic image analysis ...... 121 6.2.1 Materials and data acquisition ...... 122 6.2.2 Image processing and analysis...... 123 6.2.3 Recognition of predominant fibre orientations in each ROI ...... 125 6.3 Fibre trajectory results and discussion ...... 130 6.3.1 Fibre trajectory results ...... 130 6.3.2 Discussion ...... 134 6.4 Strain distribution in the nerve fibres ...... 137 6.4.1 Crossing locations ...... 138 6.4.2 RVE models ...... 139 6.4.3 Results of RVE models and discussions ...... 141 6.5 Conclusions ...... 144

Chapter 7 ...... 147

Ex vivo experimental study of the optic chiasmal compression ...... 147 7.1 Sample preparation ...... 147 7.2 Experimental setup ...... 147 7.3 Deformation measurement ...... 151 7.4 Experimental procedure ...... 151 7.5 Simulation of the experiment ...... 152 7.5.1 Geometry reconstruction ...... 152 7.5.2 Mesh and boundary conditions ...... 157 7.5.3 Material properties ...... 157 7.5.4 Assumptions made in this simulation ...... 160 7.6 Comparison of the experimental and simulation results ...... 161 7.7 Discussion ...... 165

Chapter 8 ...... 169

Conclusions and recommendations for future research ...... 169 8.1 Summary ...... 169 8.2 Conclusions ...... 171 8.3 Recommendations for future study ...... 173 8.3.1 Material properties of nerve tissue ...... 173 8.3.2 Anatomy of the chiasm ...... 175 8.3.3 Pituitary tumour ...... 175 8.3.4 Multi-scale analysis ...... 176 8.3.5 Microstructure of the optic chiasm ...... 176 8.3.6 Nerve fibre arrangements in the optic chiasm ...... 177 8.3.7 Ex vivo experiment of the chiasmal compression ...... 178 8.3.8 Other recommendations ...... 179

References ...... 181

Appendix A. Anatomical coordinate system ...... 201

Appendix B. Foley catheter ...... 202

Appendix C. Mesh density study ...... 203 C.1 The chiasmal model in Chapter 3 ...... 203 C.2 The chiasmal model in Chapter 4 ...... 204 C.3 RVE model in Chapter 5 ...... 205

Appendix D. Myelinated nerve fibre structure ...... 207

Appendix E. APDL script used to apply constraint equations on two opposite faces ...... 208

Appendix F. RVE model verification ...... 210

Appendix G. MATLAB codes for orientation data processing ...... 212

Appendix H. Drawings of the mounting apparatus ...... 219

Reference for Appendix ...... 221

List of Figures

Figure 1.1 The human optic system (http://thebrain.mcgill.ca)...... 2

Figure 1.2 Schematic diagram of the optic nerve passing through the optic canal. A: arachnoid; D: dura; EB: Eyeball; OC: Optic canal; ON: optic nerve (Hayreh, 2011)...... 2

Figure 1.3 The schematic diagram of human visual pathway...... 4

Figure 1.4 A human optic chiasm (arrow) attached to the cadaveric brain (Courtesy of Professor Sanjiv Jain)...... 5

Figure 1.5 (a) Sagittal section (the plane which divides human body into right and left halves; see Appendix A) of a normal chiasm above diaphragma sella. (b) Pre- fixed chiasm. (c) Post-fixed chiasm (Walsh, 2010)...... 6

Figure 1.6 Progression of visual field loss in chiasmal compression (Hedges, 1969)...... 7

Figure 1.7 Coronal MRI images of a rapidaly growing pituitary tumour during a 22- month-long observation period (Honegger et al., 2003)...... 8

Figure 1.8 The procedures of finite element analysis ...... 10

Figure 2.1 Visual fields of a patient experiencing severe chiasmal compression (Collin, 1993). (a) Visual field of the left eye: an almost complete temporal hemianopia. (b) Visual field of the right eye: complete temporal hemianopia with loss of nasal field. Dark colour represents the lost field...... 18

Figure 2.2 Improved VFs after three years after surgery (Collin, 1993)...... 19

Figure 2.3 The distance of the optic chiasm from the baseline measured on coronal and sagittal images (Ikeda and Yoshimoto, 1995)...... 21

Figure 2.4 Relationship between the BP-Height and the percentages of cases have abnormal visual fields. BP-height is the distance between a certain reference line (BP) and the inferior aspect of the chiasm...... 22

Figure 2.5 A sagittal MRI scan of a pituitary tumour that has expanded upward to compress the optic chiasm. (http://www.mayfieldclinic.com) ...... 23

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Figure 2.6 The optic tracts were pinned to the adjacent bony structure. The optic chiasm were then elevated by a balloon (Hedges, 1969)...... 24

Figure 2.7 Figure shows two pressure transducers were inserted in the central and left temporal aspect of the chiasm to measure the pressure during chiasmal compression. A Foley catheter was placed under the chiasm to elevate it (Kosmorsky et al., 2008)...... 27

Figure 3.1 (a) A normal human optic chiasm (Won et al., 2010). (b) The finite element model. (c) Key dimensions of the model (Unit: mm). The faces indicated by white arrows in (b) were named as “distal face” for descriptions of the model. ICA: internal carotid artery; OC : optic chiasm; OmN: oculomotor nerve; ON: optic nerve; OT: optic tract...... 33

Figure 3.2 (a) Demonstration of the planes of symmetry. (b) Demonstration of Paths A and B, and points 1, 2 and 3 as referred to in the text. By placing symmetric constraints on the planes of symmetry, computational time was reduced by the use of a quarter model...... 35

Figure 3.3 The nerve fibre model. (a) Uncrossed nerve fibres. (b) Crossed nerve fibre. The bottom faces and cross sections (indicated by white arrows) were constrained by frictionless supports...... 39

Figure 3.4 Deformation of the chiasm as a result of various inflation pressures in the tumour (balloon)...... 42

Figure 3.5 a-e. Von Mises strain distribution in the deformed ¼ chiasm (see Figure 3.2b) as a result of increasing tumour size in five steps (see text for details). The location of the undeformed chiasm is shown as a frame of black lines and the scale is given in (f)...... 43

Figure 3.6 Strain values along Path A when the chiasm was elevated to various levels...... 44

Figure 3.7 Strain values along Path B when the chiasm was elevated to various levels. 45

Figure 3.8 Pressure distribution along Path A compared to data from the experiment by Kosmorsky et al. (2008)...... 46

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Figure 3.9 Calculated average cross-sectional strain for uncrossed and crossed nerve fibres along Path A...... 47

Figure 3.10 Microscopic model output plotted against results of study on guinea pig

optic nerve. TC: level below which no axon would be injured; TB: level which

provided the best discrimination between injured and uninjured axons; TL: level above which all axons would be injured. The bold line demonstrates the step which is generated by the switch from crossed to uncrossed fibres...... 48

Figure 3.11 (a) Loading Case A: The tumour offset anteriorly (or posteriorly) to the chiasm. (b) Loading Case B: The tumour offset laterally to the right (or left). The offset distances between the centre of the chiasm and the centre of the sphere were indicated in the figure...... 50

Figure 3.12 Demonstration of (a) Path C and (b) Path D; as the red bold lines in the figure...... 50

Figure 3.13 (a) Schematic diagram of the optic nerve passing through the optic canal. (Hayreh, 2011). (b) Schematic diagram of section 1-1 in (a). A: arachnoid; D: dura; EB: Eyeball; OC: Optic canal; ON: optic nerve...... 51

Figure 3.14 Model with new constraints...... 52

Figure 3.15 Von Mises strain distribution along Path A in models with various elastic moduli of pia mater...... 54

Figure 3.16 Von Mises strain distribution along Path A in models with various elastic moduli of nerve tissue...... 55

Figure 3.17 Changes of strain at Point 3 (Figure 3.2b) due to variations of the material properties of nerve tissue...... 56

Figure 3.18 Effect of varying sheath thickness on the stain distribution within the chiasm...... 57

Figure 3.19 The strain distribution along Path C for a tumour sitting anteriorly (or posteriorly) of the chiasm (Loading Case A)...... 58

Figure 3.20 The strain distribution along Path D for a tumour sitting anteriorly (or posteriorly) of the chiasm (Loading Case A)...... 58 xiv

Figure 3.21 The strain distribution along Path C for a tumour offset laterally to the right (Loading case B)...... 59

Figure 3.22 The strain distribution along Path D for a tumour offset laterally to the right (Loading case B)...... 59

Figure 3.23 The von Mises strain distribution along Path A in models with various constraint types...... 60

Figure 3.24 Effects of variations in crossing angles on average cross-sectional von Mises strain in nerve fibres...... 61

Figure 3.25 Change in average von Mises strain in nerve fibres located at Point 1 as a function of crossing angle between nerve fibres...... 62

Figure 4.1 The optic nerve and chiasm (highlighted part) were segmented from one of the slices of the Visible Human Project of the United States (Mikula et al., 2007)...... 68

Figure 4.2 The tumour growing at the direction of positive Z axis...... 75

Figure 4.3 The tumour growing direction was roughly perpendicular to the chiasm; as indicated by the arrow...... 77

Figure 4.4 Comparison of the deformation predicted by the FEM model with a coronal MRI scan of a patient with optic chiasmal compression (Evanson, 2009)...... 80

Figure 4.5 The von Mises strain distribution of a coronal section of the deformed optic chiasm. (a) Lines used to calculate the strain values in (b). (b) The average cross-sectional von Mises strain along the left-right orientation. (c) The contour plot of the von Mises strain...... 81

Figure 4.6 The average cross-sectional von Mises strain along the left-right orientation. The elevation of the chiasm was 5.27mm...... 83

Figure 4.7 The von Mises strain along the left-right orientation...... 84

Figure 4.8 Von Mises strain distribution along the left-right orientation. The elevation of the chiasm is 5.32 mm...... 84

Figure 4.9 The von Mises strain along the left-right orientation in models with different pia mater stiffness. “1.5” and “0.5” denote that pia mater stiffness is 1.5 and 0.5 times stiffer than the baseline model...... 85

Figure 4.10 The von Mises strain along the left-right orientation in models with different pia mater stiffness. “0.5” and “2” denote that the nerve tissue stiffness is 0.5 and 2 times stiffer than the baseline model...... 86

Figure 4.11 Von Mises strain distribution in the chiasm. The elevation of the chiasm is 5.10 mm. The dotted line shows the results of the baseline model...... 86

Figure 4.12 Contour plot of the vertical elevation of a cross-section of the model (unit: mm)...... 87

Figure 4.13 von Mises strain on different loading steps...... 88

Figure 5.1 (a) Illustration of the axons wrapped by myelin sheaths (Standring, 2008). (b) Coloured scanning electron micrograph (SEM) of optic nerve fibres. (Steve Gschmeissner/Science Photo Library: http://www.sciencephoto.com/media/442847/view#) ...... 93

Figure 5.2 The macroscopic model of the optic chiasm and tumour and the microscopic RVE models. OC: optic chiasm; ON: optic nerve; OT: optic tract...... 94

Figure 5.3 Location of the strain point and orientations of the crossed and uncrossed nerve fibres...... 96

Figure 5.4 (a) The von Mises strain distribution in RVEs. (b) The injury and non-injury regions in the nerve fibres based on strain in the axonal direction...... 100

Figure 5.5 The average cross-sectional (a,b) von Mises strain and (c,d) axonal strain distribution of the axons and myelin sheaths as a function of the location along the nerve fibre. ‘crossed_sheath_1’ in the legend means the ‘myelin sheath’ in

the ‘crossed mode at the ‘x1 direction’ according to Figure 5.2...... 100

Figure 5.6 Comparison of the relative sensitivities of maximum cross-sectional average strains of the model to the input parameters and their combinations. A: cross- sectional shape; B: g-ratio; C: sheath stiffness; D: MECS stiffness; E: crossing angle. Only the statistically significant effects are shown...... 107

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Figure 5.7 Comparison of the relative sensitivities of maximum strains of the model to the input parameters and their combinations. A: cross-sectional shape; B: g-ratio; C: sheath stiffness; D: MECS stiffness; E: crossing angle. Only the statistically significant effects are shown...... 108

Figure 5.8 (a) The hexagonal packing compared with (b) the square packing in baseline model...... 109

Figure 6.1 Schematic diagram of (a) uncrossed and (b) crossed extramacular fibres through the optic nerve, chiasm and tract (Hoyt and Luis, 1962)...... 117

Figure 6.2 Schematic diagram of crossed and uncrossed macular fibres through the primate chiasm (Hoyt and Luis, 1963). ON: optic nerve; OT: optic tract...... 117

Figure 6.3 A horizontal section of the human optic chiasm. The schematic illustrates the relative location of each microscopic image (A - G). H and I are the magnifying images from A and D (Neveu et al., 2006)...... 118

Figure 6.4 Fibre tracking results for three optic chiasms (A, B and C in three rows respectively) using DTI (Roebroeck et al., 2008). Left column shows the traced crossing fibres; middle column shows the traced uncrossed fibres; right column shows the results of tracing fibres between two optic nerves and two optic tracts...... 120

Figure 6.5 Schematic diagram illustrates the concept of Wilbrand’s knee in which the nasal fibres form a loop into the contralateral optic nerve...... 121

Figure 6.6 Flowchart of the fibre distribution analysis procedures...... 122

Figure 6.7 Image taken from the microscopy scanner. The physical dimension of this image is 13.21 mm × 8.78 mm (width by height)...... 123

Figure 6.8 (a) The photomicrographic image of one ROI. (b) Angle values used in (c). (c) Histogram of orientation distribution...... 124

Figure 6.9 Two ROIs that show the crossed and uncrossed optic nerve fibres along with their orientation histograms...... 125

Figure 6.10 Data were extended to the range between -180 to 179 for further processing. (a) Original data. (b) Extended data...... 126 xvii

Figure 6.11 The original data with peaks indicated by triangular markers...... 126

Figure 6.12 Artefacts at 0 and 90 degrees...... 127

Figure 6.13 (a) False peaks (blue line) were removed. (b) Magnifying figure shows details of the data in the red box in (a)...... 128

Figure 6.14 The orientation histogram data before and after filtered with a Butterworth low-pass filter; triangular markers indicate the identified peaks after filtering.129

Figure 6.15 Illustration of the threshold used to remove “low” peaks...... 130

Figure 6.16 Fibre orientations in various slices. The right column shows the schematic diagram of a coronal section of the optic chiasm and the horizontal line represents the relative location of the corresponding slice in superior-inferior direction...... 131

Figure 6.17 (a) Fibre orientations in slice 141. (b) Microscopic image of one of the ROI indicated in (a) shows the detailed distribution of axons...... 136

Figure 6.18 Illustrations of the paths have the same relative location in (a) Chiasm A and (b) Chiasm B. The fibre orientations on the path of Chiasm B were enlarged and shown below; the corresponding crossing angles are listed below the orientation plot in degrees...... 139

Figure 6.19 The representative volume element (RVE) for fibres cross at a given angle. (a) Illustration of two layers of fibres crossing. (b) RVE. (c) RVE model without MECS in order to show the internal structure more clearly...... 140

Figure 6.20 Von Mises strain distribution on the path indicated in Figure 6.18a...... 141

Figure 6.21 Maximum average von Mises strains in axons and sheaths of the nerve fibres along the path in Figure 6.18. Crossed ROIs are indicated by circular markers; Arrows indicate strain “steps”...... 142

Figure 6.22 Maximum von Mises strains in axons and sheaths of the nerve fibres along the path in Figure 6.18. Crossed ROIs are indicated by circular markers; Arrows indicate strain “steps”...... 142

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Figure 7.1 The designed mounting apparatus used to fix the optic chiasm. (a) The mounting apparatus was placed on the sample bed of the micro-CT; (b) The inner structure of the experimental setup...... 149

Figure 7.2 3D printed mounting apparatus...... 149

Figure 7.3 Experimental setup for performing ex vivo chiasmal compression studies. (a) The chiasm glued to the mounting apparatus along with the Foley catheter and the syringe. (b) The sample bed and bore of the micro-CT. (c) The chiasm was elevated by the expanding balloon of the Foley catheter...... 150

Figure 7.4 The chiasm was glued to the mounting apparatus and preserved in formalin...... 152

Figure 7.5 3D Slicer interface with the Editor module on the left side and the DICOM images on the right...... 153

Figure 7.6 Summary of steps to create a 3D model in Slicer...... 154

Figure 7.7 The mesh and the overlaid reconstructed surface model of the undeformed chiasm were displayed using different colours as indicated...... 155

Figure 7.8 Workflow of the solid model generation in CATIA...... 155

Figure 7.9 Photo of the experiment and the FEM model in ANSYS ...... 156

Figure 7.10 Boundary conditions of the FEM model. Short wide arrows indicate fixed faces; long narrows arrows indicate fixed edges...... 157

Figure 7.11 (a) A coronal section of the undeformed chiasm. (b) Contour plot of the vertical displacement of the coronal section of the deformed optic chiasm. .... 161

Figure 7.12 The experimental deformation from the CT scan and the FEM predicted deformation (wire frame) of a coronal section of the chiasm. (a) The undeformed chiasm. (b) The deformed chiasm...... 163

Figure 7.13 The experimental deformation from the CT scan and the FEM predicted deformation (wire frame) of a sagittal section of the chiasm. (a) The undeformed chiasm. (b) The deformed chiasm. The contrast of the CT scan was adjusted to show the boundary between the balloon and the chiasm more clearly...... 163

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Figure 7.14 The posterior part of the chiasm that was damaged during dissection, as indicated by an ellipse...... 165

List of Tables

Table 3.1 Assumed mechanical properties of tissues used in the FEM simulations...... 34

Table 3.2 Parametric study cases of the chiasmal model ...... 53

Table 4.1 List of material studies of brain tissue ...... 71

Table 4.2 Material properties used for the chiasmal model in ANSYS ...... 74

Table 4.3 Comparison of the hydrostatic pressures predicted by the simulation and the averaged experimental measurements from Kosmorsky et al. (2008) (Unit: kPa) ...... 82

Table 5.1 Ogden hyperelastic constants used in the RVE models ...... 96

Table 5.2 Factors and their levels of the DOE study ...... 103

Table 5.3 Design of the DOE simulations ...... 104

Table 5.4 Simulation responses and their abbreviations ...... 105

Table 5.5 Comparison of the strains in various models...... 110

Table 7.1 Material properties used for fixed tissues...... 159

Table 7.2 Mechanical properties of the Foley catheter...... 160

Table 7.3 Comparison of the results predicted by the simulation and the experimental measurements...... 162

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Nomenclature

E elastic modulus

ν Poisson's ratio h height of the chiasm

displacement of node i

푢푖 the Cartesian coordinate of a point

푥푘 the average strain

휀푖̅ � the periodic part of the displacement on a point of the boundary faces ∗ 푢푖 C material constants for polynomial hyperelastic material models

μ material constant for Ogden hyperelastic material models

α material constant for Ogden hyperelastic material models

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Glossary and Abbreviations

Arachnoid the meninges that between the pia and the dura

Astrocytes star-shaped glial cells in the central nervous system

Axon a long process of a neuron that conducts impulse away from the cell body

Bitemporal hemianopia a type of partial visual field defect in which vision is impaired in the temporal halves of the visual fields of both eyes

Contralateral on the opposite side of the body

Demyelination the loss of myelin sheath around axons

Diaphragma sella a sheet of dura mater that almost roofs the pituitary fossa

Dura mater the outermost layer of the meninges that surround the brain and spinal cord

Glial cell a type of supportive cells in the central nervous system g-ratio ratio of the axonal diameter to nerve fibre diameter

Ipsilateral on the same side of the body

Ischaemia an inadequate blood supply to an organ or part of the body

Macula the area of the retina responsible for central high resolution vision

Myelin sheath a layer of material formed by myelin that surrounds the axon

Nerve fibre thread-like extension of a nerve cell that consists of axon and its myelin sheath (if present)

Pia mater the innermost layer of the meninges that covers the brain and spinal cord

Remyelination the process of forming new myelin sheaths on demyelinated axons

Sella turcica a saddle-shaped bony indentation within the skull base

Stress the force acting within the material per unit area

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Strain a normalized measure of deformation of an object compared to its original shape

White matter brain tissue that transmit signals from one region of the brain to another

Wilbrand’s knee nasal optic nerve fibres form a loop into the contralateral optic nerve

3D three dimensional

CNS central nervous system

DICOM digital imaging and communications in medicine

DOE design of experiment

DTI Diffusion tensor imaging

FEM finite element modelling

MECS material of the extra-cellular space

MRI magnetic resonance imaging

OC optic chiasm

ON optic nerve

OT optic tract

ROI region of interest

RVE representative volume elements

SEM scanning electron micrograph

VF visual field

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Chapter 1

Introduction

Bitemporal hemianopia is a type of partial visual field (VF) defect in which vision is impaired in the temporal halves of the VFs of both eyes. Bitemporal hemianopia has many known causes but the most common cause is the chiasmal compression caused by a pituitary tumour (Blumenfeld, 2010; Kosmorsky et al., 2008). However, the precise mechanism of bitemporal hemianopia is still not clear. This work aims to investigate the biomechanics of chiasmal compression using finite element modelling (FEM) and understand its role in the cause of bitemporal hemianopia.

This chapter provides a brief introduction to the human optic pathway, bitemporal hemianopia, pituitary adenoma and finite element modelling. The structure of this thesis will also be introduced at the end of this chapter.

1.1 Human optic system

The human optic system, which is part of the central nervous system (CNS), includes the eye (including retina), optic nerve, optic chiasm, optic tracts, lateral geniculate body, optic radiation and visual cortex (Figure 1.1). In this research, the interested parts are the optic nerve, optic chiasm and the optic tract.

Figure has been removed due to Copyright restrictions.

http://thebrain.mcgill.ca/flash/d/d_02/d_02_cr/d_02_cr_v

is/d_02_cr_vis_2a.jpg

Figure 1.1 The human optic system (http://thebrain.mcgill.ca).

The optic nerves start from the ganglion cells of the retina in the eyeball and then travel backwards to the brain through the optic canal. In the optic canal region the bony canal and the optic nerve are fixed to each other by fibrous adhesions (Figure 1.2) (Hayreh,

1964, 2011). The intracranial part of the optic nerve lies behind the optic canal, which is the region of interest in this research. In this portion, the nerve is covered by pia mater and there is no dura mater sheath compared with that in the orbit and the optic canal

(Hayreh, 2011).

Figure has been removed due to Copyright restrictions.

See Figure 2.32 in reference (Hayreh, 2011)

Figure 1.2 Schematic diagram of the optic nerve passing through the optic canal. A: arachnoid; D: dura; EB: Eyeball; OC: Optic canal; ON: optic nerve (Hayreh, 2011).

There are about one million optic nerve fibres for each optic nerve. Each nerve fibre is constituted by the axon and its myelin sheath. These nerve fibres vary in diameter, which is between 0.1 and 8.3 µm with a mean cross-sectional area of 1.42 µm2 (Jonas et al., 1990). It is believed that the smaller fibres come from the central retina and the larger fibres from the peripheral retina (Hayreh, 2011). The nerve fibres in the optic nerve are arranged in bundles separated by neuroglia, but these bundles are absent in the optic chiasm (Neveu et al., 2006).

In the human visual system, information from the right visual field of both eyes is processed by the left side of the brain and vice versa. This is achieved by means of partial crossing of optic nerve fibres in the optic chiasm: nerve fibres from the nasal hemiretinas (which receive their input from the temporal VFs) cross over in the optic chiasm and enter the contralateral optic tracts whereas the nerve fibres arising from the temporal hemiretinas (which receive input from the nasal VFs) pass directly backwards to the ipsilateral optic tracts (Figure 1.3). The uncrossed nerve fibres are confined laterally (Neveu and Jeffery, 2007). Lesions in the nasal retina only cause the degeneration of the central chiasmal region (Hoyt and Luis, 1963), which denotes that the nasal nerve fibres occupy the central chiasm. In the optic chiasm, these nerve fibres kiss, cross, converge and curve to form the complex microstructure of chiasm

(Roebroeck et al., 2008).

Nasal visual field

Temporal Temporal visual field visual field

Nasal hemiretina Temporal Temporal hemiretina hemiretina Eye

Optic nerve

Optic chiasm Optic tract

Figure 1.3 The schematic diagram of human visual pathway.

While the concept of hemidecussation described above is now universally accepted, there are still many unanswered questions about the detailed nerve fibre trajectory in the optic chiasm such as the existence of Wilbrand’s knee in which nasal optic nerve fibres form a loop into the contralateral optic nerve (will be discussed in detail in Chapter 6)

(Horton, 1997; Lee et al., 2006). Previous research (Hoyt and Luis, 1962, 1963;

Roebroeck et al., 2008; Sarlls and Pierpaoli, 2009; Wedeen et al., 2008) has demonstrated that the nasal nerve fibres cross over in the chiasm, but no detailed distribution of fibres were provided. Therefore, one objective of this thesis is to study the detailed nerve fibre arrangements in the optic chiasm, which is necessary to investigate the biomechanics of the optic nerve fibres in chiasmal compression.

1.2 Anatomy of optic chiasm and its adjacent structures

The optic chiasm is about 14 mm wide, 3.5 mm thick and 8 mm for anterior-posterior extent. Figure 1.4 shows a human optic chiasm attached to the brain.

Figure 1.4 A human optic chiasm (arrow) attached to the cadaveric brain (Courtesy of Professor Sanjiv Jain).

The anatomy of the adjacent region of the optic chiasm is complex. The pituitary gland sits in a bony indentation within the skull base called the sella turcica and is covered by the diaphragma sella which is a sheet of dura mater (Swearingen and Biller, 2008). The pituitary gland is about two to eight millimetres in diameter (Herse, 2014). It has two major parts with different structure and function as illustrated in Figure 1.5.

The optic chiasm lies about 10 mm above the diaphragma sella (Figure 1.5) at an incline between 15° and 45° from the horizontal (Anderson et al., 1999). In 79% of people, the optic chiasm is located just above the diaphragma sella (Figure 1.5). But because of the normal variation in the length of the optic nerves, the chiasm may be in a preﬁxed position (lies above the diaphragma sella anteriorly; accounting for 12% of people) or postﬁxed (lies above the diaphragma sella posteriorly; accounting for 4% of people)

(O'Connell, 1973; Walsh, 2010). Compression of pre-fixed and post-fixed chiasm may

5 result in other kind of visual defects rather than a bitemporal hemianopia (Poon et al.,

1995). Because most of people have normal chiasm position and the correlation of chiasmal position and the visual field defects was unclear, this thesis only investigated the normal chiasmal position, i.e., the tumour is located just below the chiasm.

Figure has been removed due to Copyright restrictions.

See Figure 8-1, 8-2 and 8-3 in reference (Walsh, 2010)

Figure 1.5 (a) Sagittal section (the plane which divides human body into right and left halves; see Appendix A) of a normal chiasm above diaphragma sella. (b) Pre-fixed chiasm. (c) Post- fixed chiasm (Walsh, 2010).

1.3 Bitemporal hemianopia

In bitemporal hemianopia, vision is missing in the temporal half of both the right and left visual field and there is a vertical cutoff of the vision loss, i.e., the temporal visual field is impaired while the neighbouring nasal visual field is unaffected. Compression of the chiasm by, for example, a pituitary tumour typically results in a bitemporal hemianopia because the nerve fibres arising from both nasal hemiretinas are selectively damaged (McIlwaine et al., 2005).

The defects of bitemporal hemianopia most commonly start in the upper temporal field and then affect the lower temporal field (Anderson et al., 1999; Hedges, 1969; Walsh,

2010). As the compression continues, the lower nasal field may become involved and the last quadrant of the field to be lost is the upper nasal quadrant (Figure 1.6). The actual field loss is more complicated than illustrated in Figure 1.6, especially when the 6 nasal fields are involved. The field loss process in two eyes are usually asynchronous and asymmetric (Cushing and Walker, 1914).

Figure has been removed due to Copyright restrictions.

See Figure 1 in reference (Hedges, 1969)

Figure 1.6 Progression of visual field loss in chiasmal compression (Hedges, 1969).

Bitemporal hemianopia is highly localizing to the chiasm and it has many known causes, particularly compression of the chiasm. Rarer causes of chiasmal compression include craniopharyngiomas, germinomas, metastatic tumours, and giant carotid aneurysms

(Blumenfeld, 2010; Oliver, 1964) but the most common cause is a pituitary tumour which compresses the chiasm from below as it grows up out of the pituitary fossa

(Blumenfeld, 2010; Kosmorsky et al., 2008). Hence, this thesis will examine this most common cause by analysing the biomechanics of optic chiasm compressed by a pituitary tumour.

A pituitary tumour is the tumour arising from the pituitary gland. A pituitary tumour is the most common lesion in the sellar region. It account for 10-20% of all primary intracranial tumours (Fadzli et al., 2013). Most pituitary tumours are pituitary adenomas, which are benign, slow-growing tumours. Normally, the tumour takes years to grow before it touches the optic chiasm (Honegger et al., 2003). Figure 1.7 shows the magnetic resonance imaging (MRI) results of a patient with a rapidly growing pituitary tumour. Depending on the size, pituitary adenomas are generally classified into

7 microadenomas which are less than 10 mm, and macroadenomas which are more than

10 mm. Macroadenoma can compress the optic pathway and cause visual disturbance.

Figure has been removed due to Copyright restrictions.

See Figure 3 in reference (Honegger et al., 2003)

Figure 1.7 Coronal MRI images of a rapidaly growing pituitary tumour during a 22-month-long observation period (Honegger et al., 2003).

Vision may recover rapidly after surgical removal of the pituitary tumour (Anik et al.,

2011; Kayan and Earl, 1975) but this is not always the case. Although the fact that chiasmal compression by a pituitary tumour results in bitemporal hemianopia is well recognized, the reason why compressive lesions of the chiasm selectively damage the crossed nasal nerve fibres is still not clear. Several explanations have been offered over the last 50 years to explain the mechanism, but these all remain theoretical. More details of bitemporal hemianopia and its possible mechanisms will be introduced in Chapter 2.

1.4 Other visual field defects

Even though bitemporal visual field changes are the commonest visual field defects when a pituitary adenoma compresses the optic pathway (Poon et al., 1995), there are large variations of the visual loss patterns. Different sites of compression account for different patterns of VF loss. For example, homonymous hemianopia will present when the optic tracts are involved (Bynke and Cronqvist, 1964). These field defects may help 8 understand the mechanisms of bitemporal hemianopia. Investigations of bitemporal hemianopia caused by chiasmal compression will, in turn, give insights into other visual field loss caused by optic pathway compression. Therefore, the methods developed in this thesis for the investigation of bitemporal hemianopia are also useful for other visual field defects.

1.5 Finite element modelling in biomechanics

Finite element modelling (FEM) is widely used in engineering to simulate complex structural interactions numerically. It also provides an effective tool for detailed analysis of biological structures and so this method has been increasingly used as an alternative to complicated, practically unfeasible, or unethical experiments in the medical area

(Bellezza et al., 2000; Cirovic et al., 2006; Sigal et al., 2004).

Recently, studies using computational modelling to investigate the biomechanics of brain tissue have become increasingly acceptable, especially in the field of traumatic brain injury. FEM has also been used in various areas of ophthalmology such as modelling the biomechanics of the optic nerve head in glaucoma (Bellezza et al., 2000;

Girard et al., 2009a; Girard et al., 2009b; Norman et al., 2011; Sigal et al., 2004; Sigal et al., 2007) and modelling injury to the optic nerve from blunt trauma (Cirovic et al.,

2006). The use of finite element modelling in soft tissue analysis has been verified on numerous occasions (Luo et al., 2008; Ueno et al., 1995; Willinger et al., 1999; Yang and King, 2003).

The finite element analysis requires the idealization of an actual physical problem into a mathematical model first (which corresponds to mechanical idealization) to describe the geometry, material, boundary and loading conditions of the physical problem (Bathe,

1996). Finite element methods can only numerically solve the mathematical model and all assumptions made in the mathematical model will be reflected in the predicted response. Therefore, the choice of appropriate mathematical models is crucial in engineering simulations. Figure 1.8 summarizes the procedures of finite element analysis.

Figure 1.8 The procedures of finite element analysis (simplification of Fig 4.8 in Bathe, 1996).

Once a mathematical model has been solved by the finite element analysis and the results have been interpreted, a refined mathematical model could be considered to improve the fidelity of the model. In this thesis the chiasm was considered to be a 3D structure. Chiasmal tissues were considered to be single-phase continuums undergoing large deformations. Because the tumour growth is extremely slow, static analysis was used in this simulation. In Chapter 3, a simple mathematical model was used first; improvements of this simple mathematical model were then made in subsequent chapters.

Although standard finite element methods have been used in this thesis to simulate the chiasmal compression, it is worth mentioning that meshless methods are a new and promising approach, which are starting to gain in popularity in biomechanics research

(Li and Liu, 2004; Miller et al., 2010; Miller et al., 2012). This is because they can easily handle simulations of very large deformations and very complex geometry (Li and Liu, 2004; Doblare et al., 2005), which is common in biomechanics. Since it is not necessary to generate a mesh, the meshless model could be easily used for quick analysis such as intra-operative simulation (Miller et al., 2010). However, the research reported here used the far more well-established finite element method.

1.6 Aims and objectives

The aim of this work was to improve our understanding of the possible mechanisms of bitemporal hemianopia by studying the biomechanics of optic chiasmal compression, more specifically, to investigate if there is a mechanical explanation for bitemporal hemianopia. Finite element models of the human optic chiasmal compression were developed in different length scales to quantify strain distribution in the macroscopic optic chiasm and microscopic nerve fibres under different loading conditions. The specific objectives were:

1. To develop a generic optic chiasmal model with simple geometry and linear

elastic material models. This model will be used to simulate the experiment by

Kosmosky et al. (2008) by inflating a spherical balloon under the chiasm. All

materials in this initial model are modelled as linear elastic, homogeneous

materials for simplicity. To account for variations in physical and geometrical

micro-structural properties within the optic chiasm, nerve fibre models are built

to characterize the local heterogeneous microstructure. Sensitivity studies are

performed to analyse the effects of variation in various parameters in the

simulation.

2. To then build an individual-specific optic chiasmal compression model to

account for more accurate geometry and material properties. The geometry of

the chiasm is built from human head slices of the visible human project of the

United States (Mikula et al., 2007). The material properties used in this model

are more realistic hyperelastic material models based on existing experimental

studies.

3. To build a microscopic nerve fibre model using techniques of multiscale

analysis to allow a more accurate load transfer from macro-scale to micro-scale.

The detailed strain distributions in the nasal and temporal nerve fibres can thus

be obtained from this model.

4. To visualise the nerve fibre distribution in the optic chiasm using

photomicrographic image analysis of the human optic chiasmal slices. This

information is essential to understand the mechanism of the selective damage to

nasal nerve fibres in bitemporal hemianopia.

5. To develop and perform an ex vivo optic chiasmal compression experiment for

further validation of the FEM models of the chiasmal compression.

1.7 Contributions

In this work, finite element modelling was used to investigate the biomechanics of optic chiasmal compression. The possible mechanisms of bitemporal hemianopia in the context of chiasmal compression were discussed. The contributions of this work are:

• Improved our understanding of bitemporal hemianopia by using finite element

modelling to quantify the mechanical behaviours of chiasm under compression.

• Built models of chiasmal compression both on macroscopic chiasmal scale and

microscopic nerve fibre scale and studied the biomechanics of the optic chiasmal

compression in detail. This thesis is the first to look into the biomechanics of

chiasmal compression in different length scales. The strain differences in

crossed and uncrossed nerve fibres may account for bitemporal hemianopia.

• Investigated detailed nerve fibre distributions in the optic chiasm using

photomicrographic image analysis and its influences on the biomechanics of

nerve fibres in the chiasm. This study is the first to use microscopic images to

visualize the fibre distributions of the whole chiasm. The results show that the

nerve fibre arrangements in the optic chiasm are more complicated than the

traditional understanding.

• An ex vivo experiment of optic chiasmal compression was designed and

performed which provides preliminary validations of the FEM model. The

experimental setup and procedures could be used for further examinations of the

biomechanics of the optic chiasm.

1.8 Thesis outline

This thesis is structured as follows.

Chapter 2 presents a general review of the existing explanations of bitemporal hemianopia and the axonal injury caused by mechanical deformation.

In Chapter 3, a generic optic chiasmal compression model and nerve fibre models are developed using commercial FEM package. The detailed description of the development of the model is presented. The results are used to explain the mechanism of bitemporal hemianopia. Parametric studies are performed to investigate the effects of variations of several parameters used in the generic models.

In Chapter 4, a specific optic chiasmal model is presented. The geometry is reconstructed from the visible human project of the USA. Nonlinear material models are used for nerve tissues.

In Chapter 5, nerve fibre models using representative volume elements (RVE) are developed to investigate the effects of different nerve fibre packing patterns. Parametric studies using design of experiment (DOE) are performed to study the significances of several parameters in the nerve fibre model.

In Chapter 6, the nerve fibre trajectory in the optic chiasm is investigated using photomicrographic image analysis. The fibre orientations and crossing angles are then incorporated into the RVE model to investigate their influences on the strain distributions in nerve fibres.

In Chapter 7, an ex vivo experiment of the human chiasmal compression is presented.

The deformation of the chiasm is obtained by micro-CT scanning. The experiment is simulated using finite element modelling and the simulation results are compared with the experimental results.

In Chapter 8, conclusions and future recommendations concerning the investigation of the biomechanics of chiasmal compression and bitemporal hemianopia are discussed.

Chapter 2

Bitemporal hemianopia and nerve injury caused by mechanical loading

This chapter is a brief summary of the symptoms and mechanisms of bitemporal hemianopia. The mechanism of nerve injury caused by mechanical deformation was also introduced, which is essential for understanding the outputs of the biomechanics of the optic chiasm compression.

2.1 Bitemporal hemianopia

2.1.1 Visual field loss pattern of bitemporal hemianopia

As described in Chapter 1, in bitemporal hemianopia caused by pituitary adenoma, the field loss commonly starts in the upper temporal field and then affects the lower temporal field. Further compression of the chiasm will cause the loss of nasal fields

(Figure 2.1). The recovery of the visual field after removal of the pituitary adenoma is in a reverse order.

The field loss pattern is dependent on the position of the chiasm, the size, shape and expanding direction of the tumour and the nerve fibre distribution in the chiasm. For example, the field defects when the chiasm is compressed from superior (see the anatomical coordinate in Appendix A) by craniopharyngioma begin in the inferior temporal quadrants and progresses in a clockwise direction in the left field and anticlockwise in the right (Powell et al., 2003).

Decompression of the optic chiasm after removal of the tumour can result in a recovery of visual fields although the recovery level varies considerably in different cases, for example, younger patients (Anik et al., 2011; Cohen et al., 1985) and patients with short duration of symptoms (Gnanalingham et al., 2005) are more likely to recover their visual fields after surgery.

The improvement of visual field after surgery may contain two phases (Anik et al., 2011;

Smith et al., 1981). In the first phase, VF improvement is due to the decompression of the visual pathways, which leads to a restoration of signal conduction. The first phase usually happens in the first hours and days after surgery (Kerrison et al., 2000). The second phase takes several years and is due to restoration of axonal transport and remyelination (Kayan and Earl, 1975). These two phases reflect different pathophysiological mechanisms and they may co-exist for a certain time period. The mechanisms for these two phases are still not well understood. It is reported that more than 50% of eventual recovery takes place within the first 3 months after surgery (Anik et al., 2011). Figure 2.2 shows the slightly improved VFs of the patient in Figure 2.1 three years after surgery.

Figure 2.2 Improved VFs after three years after surgery (Collin, 1993).

2.1.2 The elevation of the chiasm and the visual field defect

The presence and completeness of bitemporal hemianopia varies and depends on the size of the tumour and relative position of the chiasm. In a normal positioned chiasm, tumour size is a significant factor for the severity of field loss.

The relationship between visual field defects and tumour size has been investigated by a number of researchers.

Bynke and Cronqvist (1964) measured the vertical extents of the suprasellar portion of pituitary adenomas in 48 patients within which 37 of them were with bitemporal hemianopia. They found that the minimum height of the suprasellar extension to cause visual field defect is 8 mm. To cause more than half of visual field loss, a 19 mm suprasellar extension is needed. However, the actual elevation of the chiasm was unknown because it depends on the original distance between the sella and the chiasm.

The rate of VF loss accelerates as the tumour size grows.

In 1995, Ikeda and Yoshimoto (1995), by studying 50 cases of pituitary adenoma (only

26 of them had visual disturbance) and 17 control cases, reported that visual disturbance appears when the chiasm was elevated to more than 8 mm above a baseline on the sagittal image and more than 13 mm above a baseline on the coronal image. The position of the chiasm in control cases was 4.3 mm above the baseline on the sagittal image and 6.6 mm on the coronal image (Figure 2.3).

Figure 2.3 The distance of the optic chiasm from the baseline measured on coronal and sagittal images (Ikeda and Yoshimoto, 1995).

In 2002, Eda et al. (2002) investigated 28 patients with pituitary adenoma and bitemporal visual defect. In cases that the optic chiasm roughly located above the centre of the tumour, the average height of the tumours was 28.8 mm. Again, data on the elevation of optic chiasms were unobtainable because the tumour size does not represent the elevation of the chiasm. In the same year, Fujimoto et al. (2002) found that a tumour touching the chiasm slightly can hardly cause field loss. Considerable elevation is needed to cause field defect.

Unlike Eda et al. (2002) and Fujimoto et al. (2002) who used Japanese subjects, Frisen and Jensen (2008) investigated the relation between deformation of the chiasm with visual field loss in Caucasian subjects. The authors concluded that, on average, it takes a

6.3 mm elevation of the chiasm to induce visual field disturbance in 50% of the cases. It

21 needs an additional 5 mm elevation to cover 90% of the cases with field disturbance

(Figure 2.4).

Rivoal et al. (2000) reviewed their patients with acromegaly from 1951 through 1996.

62 cases (20.2%) of them had visual field defects, which were caused by pituitary adenoma. In these 62 cases, 47% of them were bitemporal field defects, the remaining were unilateral defects or other types of defect. The average size of the pituitary adenoma for these 62 cases was 22.7 mm, in which the size was measured as the length of the longest axis of the adenoma. Lee et al. (2011) reported that patients with visual field defect caused by pituitary macroadenoma have an average tumour volume of 10.57 cm3. However, the geometry of the tumour is complex (Figure 2.5), thus the volume of the chiasm or the longest axis of the tumour cannot determine the actual elevation of the chiasm. In the numerical models of this thesis, the tumour was represented by a hemisphere rather than a whole tumour for simplicity.

Figure has been removed due to Copyright restrictions.

Source: http://www.mayfieldclinic.com/Images/PE-

Pituitary3.jpg

Figure 2.5 A sagittal MRI scan of a pituitary tumour that has expanded upward to compress the optic chiasm. (http://www.mayfieldclinic.com)

It is obvious that there is a strong correlation between elevation of the chiasm and VF defect. However, considerable individual variations were recorded in these studies above. The actual value for a specific subject depends on the specific anatomy and other properties such as nerve injury threshold. However, even though the elevations of chiasm or tumour sizes are unobtainable in the literature and they do not necessarily reflect the actual deformation of the optic chiasm, these papers above still provide some basic details of the chiasmal deformation in bitemporal VF defect.

2.2 Existing theories to explain bitemporal hemianopia

To produce bitemporal field loss, the nasal nerve fibres must be damaged, but why nasal fibres are selectively damaged is still not clear. Several explanations have been offered over the last 50 years to explain the mechanism of bitemporal hemianopia.

In 1969, Hedges (1969) dissected autopsy specimens and inserted a Foley catheter (see

Appendix B for the structure of the Foley catheter) under the chiasm, inflating the

23 balloon to simulate a growing pituitary tumour (Figure 2.6). Hedges used this experiment to investigate why the last quadrant of the field to be lost is the upper nasal quadrant under severe chiasmal compression. He observed that upper temporal fibres were increasingly stretched as the Foley catheter balloon was inflated whereas the lower fibres were less stretched. Indeed, the distance from optic foramen to mid-chiasm on the lower surface appeared to decrease. Hedges considered the findings of his experiment were analogous to bending one’s finger, during which the upper skin is stretched while the lower skin is relaxed. However, this analogy seems inappropriate because in his experiment the optic nerves were intact and the optic tracts were pinned to adjacent structures while when one bends one’s finger the distal end of the finger is unconstrained and free to move. Hedges’ method of measuring length also needs to be questioned: he simply measured the distance between two points which is, of course, not the actual length of a curved optic nerve. Even if all of his test results are assumed to be correct, he does not explain why chiasmal compression selectively affects the crossed nasal fibres first.

Figure has been removed due to Copyright restrictions.

See Figure 4 in reference (Hedges, 1969)

Figure 2.6 The optic tracts were pinned to the adjacent bony structure. The optic chiasm was then elevated by a balloon (Hedges, 1969).

Direct compression of the chiasm may not be the sole mechanism involved in visual field defect (Rivoal et al., 2000). In the same year, Bergland and Ray (1969) reported on the arterial blood supply of the optic chiasm found at autopsy examination of 480 human specimens. They found that the chiasm was supplied by both a superior and an inferior group of arteries. However, the crossed fibres in the centre of the chiasm appeared to receive their arterial supply solely from the inferior group of vessels. They noted that these inferior vessels were commonly distorted when a pituitary tumour compressed the chiasm and concluded that compression-induced bitemporal hemianopia resulted from ischaemia (lack of blood supply) of the central chiasm rather than from direct neural compression. However, there are problems with this theory. First, it seems unlikely that the blood vessels are organised so as to distinguish between nasal and temporal nerve fibres. Second, if the temporal fibres receive blood from both superior and inferior vessels, damage to their inferior supply should result in a defect of the nasal

VF which should accompany bitemporal hemianopia; in clinical practice this phenomenon does not occur until late in the course of pituitary compression

(Kosmorsky et al., 2008). Third, craniopharyngiomas often compress the chiasm from above but they also give rise to bitemporal defects (Powell et al., 2003) though, in theory, the inferior vessels supplying the nasal fibres should be unaffected. These arguments make the vascular theory less likely.

In 2005, McIlwaine et al. (2005) proposed a mechanical theory to account for bitemporal hemianopia. This theory suggests that because uncrossed fibres are arranged parallel to each other, they have a larger contact area than crossed fibres which are arranged roughly perpendicular to each other. Therefore, at any given compressive pressure, the smaller contact area of the crossed fibres will lead to a significantly higher

25 local stress distribution than that in the uncrossed fibres, resulting in greater damage to nerve function in crossed fibres. This simple mechanical explanation assumed that pressure across the chiasm was uniform and did not take account of the fact that nerve fibres are 3D-deformable bodies which can deform in a non-uniform and non-linear manner when under pressure. It is therefore possible that the difference in stress distribution in crossed and uncrossed fibres is not simply due to the actual area of contact. This theory will be examined in the following chapters using finite element modelling which will include complex nerve fibre structure and interactions between fibres.

To investigate how the pressure in the central chiasm differs from that in the peripheral chiasm during chiasmal compression from below by an expanding tumour, Kosmorsky et al. (2008) performed a similar experiment to that of Hedges (1969) by inflating a

Foley catheter under the optic chiasm of cadaveric dissection specimens. In this case,

Kosmorsky et al. introduced two pressure transducers to measure the actual pressures at central and peripheral points of the chiasm (Figure 2.7). Their experimental results clearly demonstrated higher pressures at the centre of the chiasm than at the periphery and they suggested that it was this pressure difference that explained why nasal fibres were disrupted when temporal fibres could still function. In Chapter 3, finite element models will be built based on this experiment to help clarify what happens during chiasmal compression.

Figure has been removed due to Copyright restrictions.

See the video in reference (Kosmorsky et al., 2008)

http://www.sciencedirect.com/science/article/pii/S016164200

7007725#mmc1

2.3 Axonal injury caused by mechanical deformation

2.3.1 Axonal injury mechanisms

The mechanism by which VF defects are caused by compression of the optic pathway is uncertain. Understanding of the injury mechanisms of nerve tissue is essential for interpreting the results obtained by biomechanical analysis. Although research on the mechanism of axonal injury caused by mechanical deformation has been performed extensively using animal models and numerical simulations, the relationship between mechanical loads and pathological effects is still not well understood.

Mechanical loads applied to the nerve tissue induce many complex responses both at the tissue and at the cellular level. Under severe injury, the nerve fibres may be directly disconnected by external force. However, in chiasmal compression, injury will be much more moderate.

Moderate axonal injury may cause disruption of ion channels, disruption of axonal transport, microtubules damage, neurofilaments damage, demyelination and glial matrix damage (Balaratnasingam et al., 2008; Cliffordjones et al., 1985; Gaetz, 2004;

Gennarelli et al., 1989; LaPlaca et al., 2007; Maxwell and Graham, 1997).

Cliffordjones et al. (1980, 1985) implanted a rubber balloon into the cat orbit to compress the optic nerve. After a certain period of compression, the cat was killed and the compressed optic nerve was sliced and observed under a microscope. The pathological changes of the optic nerve could be observed by comparing with the control cats. After 11 days of compression, the predominant pathological process in the nerve fibres was demyelination with either complete or partial loss of the myelin sheath of the axons. After compression for 21 to 176 days, remyelinated nerve fibres were observed in most of the cats. The remyelination could explain the slower vision recovery after surgical removal of the pituitary tumour in bitemporal hemianopia.

However, the rapid vision recovery that happens minutes or hours after surgery should not be the results of remyelination.

If an axon is stretched at a low level (strain is 5% or less), the ion channels could be disrupted and thus cause failure of generation and propagation of action potentials

(Gennarelli, 1996). The nerve function could be fully restored after minutes of this minor injury (Gennarelli, 1996; Shi and Pryor, 2002). If the stretch level increases to 5-

10%, additional ionic disturbance was presented which causes local swellings of the injured axon and potential impairment of the axonal transport. However, these axonal changes could be restored. This could explain the rapid vision recovery stage after removal of the pituitary tumour in bitemporal hemianopia, however the precise mechanism is still unclear.

Besides the ion channels disturbance and swelling of axons, neurofilaments disturbance was also observed by Pettus et al. (1994) using cat models. Neurofilament disarray and misalignment and significant decrease in the interfilaments distance were recorded in the experiment. Loss of axonal microtubules could also be presented during the nerve injury (Maxwell et al., 1997; Pettus and Povlishock, 1996). Stretch injury to guinea pig optic nerves (Maxwell and Graham, 1997) showed that there was loss of microtubules at the node of Ranvier (see Appendix D) first and then with time increasing microtubules between nodes were subsequently affected. Astrocytes (star-shaped glial cells) play a crucial role in maintaining the well-being of axons. Research of the pig optic nerve head (Balaratnasingam et al., 2008) showed that elevated intraocular pressure could cause morphological changes in the astrocytes three hours after the intraocular pressure elevation.

These impairments do not happen successively, some of them are interactive. For example, there is evidence that disturbance of the myelin sheath influences the neurofilament spacing (de Waegh et al., 1992) and the ion channels (Shi and Pryor,

2002) in the axon.

2.3.2 Mechanical measurements used to evaluate nerve damage

The failure criteria of commonly used engineering materials such as metals, plastics and concrete are well established. However, the understanding of the nerve failure under mechanical deformation is still limited. Bain (1998) found that there could have certain strain thresholds to cause nerve failure, which make it possible to predict the conditions of axons experiencing mechanical deformation. In the experiment of Bain (1998), the optic nerves of anesthetized guinea pig were stretched and both the stretch and the

29 potential conductive ability were measured. Statistical methods were used to obtain three thresholds which will be discussed in details in Chapter 3.

There is ongoing discussion concerning the best mechanical measure of nerve damage

(Sigal et al., 2007). It is still not clear which kind of strain/stress has pathological relevance in nerve tissue failure. In published brain injury research, pressure is usually used to validate the simulation results against experimental results of pressure measurements. Numerical predictions of pressure and von Mises stress/strain are also frequently employed to investigate brain injury. However, the pressure value and the von Mises stress are different quantities although they are both derived from principle stresses. Consequently, a region that has larger von Mises stress may experience smaller pressure. Therefore, the result will be different when predicting nerve injury by using pressure and by von Mises stress/strain, which may reduce or even negate the reliability of predicting nerve injury by using these parameters. First principle strain is also commonly used in brain injury research (Lee and Winkelstein, 2012; Russell et al.,

2012). Sigal et al. (2007) suggested that maximum principal strain, minimum principal strain, and maximum shearing strain, which all have clear physical interpretation, should have most meaningful relevance in optic nerve head biomechanics. Galle et al.

(2010) showed that the cellular level injury in spinal cord is the consequences of many combinations of tissue level stresses or strains rather than any single component.

By performing experiments on and FEM analysis of guinea pig spinal cord, Ouyang et al. (2008) found that the axon damage revealed by histology coincided with higher levels of von Mises stress. Because von Mises stress is related to von Mises strain, this work will mainly use von Mises strain as the measurement of nerve injury. Other measurements will also be used and will be discussed in each chapter.

Chapter 3

Generic optic chiasmal models and nerve fibre models

3.1 Introduction

The chiasmal compression experiment by Kosmorsky et al. (2008), described in Chapter

2, is very useful but it did not provide a detailed picture of the pressure distribution across the chiasm as a whole. Because it is essentially impractical to carry out further experiments on chiasmal compression in vivo, in this chapter, an initial and simple finite element model has been used to extend the work of Kosmorsky et al. (2008) and

McIlwaine et al. (2005) by modelling the complex biomechanics of chiasmal compression which has, in turn, allowed the author to begin to test their theories.

The optic chiasm was modelled as a biomechanical structure to help clarify what happens during chiasmal compression. There were two main aims. First, the recent experiment of Kosmorsky et al. (2008) was simulated so as to model the detailed strain distribution across the entire chiasm and compare these values with the measurements.

Second, nerve fibre models were built to investigate variations in the physical and geometrical micro-structural behaviour within the chiasm to determine whether the distinction between crossed and uncrossed nerve fibres was likely to contribute to the development of bitemporal hemianopia, as suggested by the proposed theory of

McIlwaine et al. (2005). The models in this chapter were developed for preliminary study. Therefore, linear elastic material models, although overly simplistic, were employed at this initial stage of the modelling. This procedure was also used by many other biomechanics studies (eg, Kaczmarek et al, 1997). The limitations resulting from

31 the assumptions and simplifications used here will be improved in subsequent chapters based on the findings of this chapter.

3.2 Optic chiasmal model

3.2.1 Geometry

The optic chiasm was modelled as a simplified representation of its actual geometry

(Figure 3.1). The shape and dimensions of the model were based on data from the literature (Li et al., 2002; Parravano et al., 1993; Schmitz et al., 2003; Wagner et al.,

1997). For the sake of simplicity, the plane of the chiasm was assumed to be horizontal and perpendicular to the direction of tumour growth; in reality, the chiasm is higher in its posterior part and pituitary tumours can compress it from a large variety of angles.

The optic nerves and tracts were modelled as elliptical in cross-section, the ellipses having major radii of 3 mm and minor radii of 1.75 mm (Figure 3.1c). The width of the whole chiasm was taken to be 14.0 mm, its height 3.5 mm and its antero-posterior extent 8 mm. The optic chiasm, optic nerves and optic tracts were considered to be composed of nerve tissue incased in a pia mater sheath of 0.06 mm (Sigal et al., 2004) thickness. The angles between the two optic nerves and between the two optic tracts were both assumed to be 75°.

The Foley catheter balloon (the structure of a Foley catheter could be found in

Appendix B), representing a growing tumour in the experiment of Kosmorsky et al.

(2008), was modelled as a hemisphere with an external diameter of 20 mm and an outer layer 0.5 mm thick – these figures were chosen to conform to the details of the Foley catheter balloon used in the experiment by Kosmorsky et al. (2008). Kosmorsky et al. dissected autopsy specimens and inserted a Foley catheter directly under the chiasm

32 thereby enabling them to use balloon inflation to simulate a growing pituitary tumour.

The study by Kosmorsky et al. was used for the purposes of validating the model in this chapter.

(b)

14 6 8 3.5

1-1 75˚ (c)

Figure 3.1 (a) A normal human optic chiasm (Won et al., 2010). (b) The finite element model. (c) Key dimensions of the model (Unit: mm). The faces indicated by white arrows in (b) were named as “distal face” for descriptions of the model. ICA: internal carotid artery; OC: optic chiasm; OmN: oculomotor nerve; ON: optic nerve; OT: optic tract.

3.2.2 Material properties

Assigning suitable material properties is important to ensure accurate finite element analysis. Accurate data on the mechanical properties of biological tissues are relatively scarce because of the practical difficulties in measuring these properties. Properties of brain material reported in the literature vary from study to study by up to an order of 33 magnitude due to variability in testing method, strain rate, specimen preparation, regional differences, and whether measurements were made in situ or in vitro (Chafi et al., 2009; Gefen and Margulies, 2004; Miller 2011). Because the use of FEM in ophthalmology is still in its infancy, most analyses have assumed simple linear elastic material properties for all tissues and a similar approach is taken here for the initial study although more sophisticated and realistic models will be introduced in later chapters.

For the purposes of this study, material properties at both macroscopic and microscopic levels were derived from the literature (Table 3.1). For simplification, all materials in this model were assumed to be composed of linear elastic, isotropic material and were characterised by elastic modulus (E) and Poisson’s ratio (ν) as given in Table 3.1. A density of 1000 kg/m3 was used for all tissues (Beckmann et al., 1999).

Table 3.1 Assumed mechanical properties of tissues used in the FEM simulations

Tissue on Elastic Poisson’s Tissue which model Modulus Reference Ratio (ν) based (E) (MPa)

Human pia Zhivoderov et al. (1983) and Sheath 3.0 0.49 mater Sigal et al. (2004)

Optic Porcine brain 0.03 0.49 Sigal et al. (2004) nerve

Tumour Human sclera 5.5 0.47 Kobayashi et al. (1971)

3.2.3 Simulations

Normally, the tumour takes years to grow as discussed in Chapter 1. Therefore, this simulation was considered to be a static structural analysis. As the deformation of the

34 chiasm is large (more than 1h, where h is the height of the chiasm), large deformation analysis (geometrically nonlinear) was used.

Because the model of the chiasm was symmetrical in two planes, computational time could be significantly reduced by restricting the model to only 1/4 of the entire chiasm and placing symmetric constraints on the planes of symmetry (Figure 3.2). The model was created, meshed and post-processed using commercial FEM software (ANSYS 13.0,

Ansys, Inc., Canonsburg, PA). The model was discretised into a hexahedron-dominant mesh with 47,112 elements. Specifically, SOLID186 and SOLID187 elements in

ANSYS were used for the hexahedral and tetrahedral elements, respectively. SOLID186 is a 20-node higher order hexahedral element and SOLID187 is a 10-node higher order tetrahedral element. Preliminary studies demonstrated that this mesh density was sufficient to provide mesh-independent results (see details in Appendix C). The solution of the model required approximately 4 hours on a desktop workstation (Windows 7,

Intel Core i7 860 CPU and 16 GB of memory; no GPU acceleration).

Plane of symmetry

Nasal nerve Temporal fibre region nerve fibre region Point 2

Point 3 Path A Path B

Plane of symmetry Point 1

(b) (a)

The boundary conditions of the simulation were as follows: the distal face (indicated in

Figure 3.1b) of the optic nerve was fixed to represent the connection of the optic nerve to the optic canal by fibrous adhesions (Hayreh, 1964). The tumour (balloon) was fixed at its inferior surface. The contact between the tumour and chiasm was considered to be frictionless. The core tissues of the optic nerve, chiasm and tract were bonded to their pial sheath. Pressure was applied to the interior surface of the tumour to inflate it. The maximum pressure applied was 0.145 MPa but this was interpreted in terms of the degree of displacement of the centre of the inferior surface of the chiasm. Applied pressure was increased in five discrete steps which resulted in elevation of the chiasm by 0.11h, 0.26h, 0.40h, 0.63h, and 0.94h where h was the height of the chiasm (3.5 mm).

This allowed an approximate simulation of the gradual process of compression that occurs in vivo.

Within the model, certain lines and points were defined to enable ease of data extraction for further analysis (Figure 3.2b). Two lines (Paths) were constructed perpendicularly across the chiasm. Path A was drawn horizontally from the centre point of the chiasm to a point on its peripheral (temporal) aspect. It was assumed that the central half of Path A represented the region composed of nasal (crossed) fibres while the outer half represented the region of temporal (uncrossed) fibres. Path B was drawn vertically from the inferior centre to the superior centre of the chiasm. Points 1 and 2 represented the geometric centres of the inferior and superior surfaces of the chiasm, respectively. Point

3 is the geometric centre of the chiasm.

3.2.4 Data analysis

Strain is a tensor and is determined by both absolute value and orientation. However, reporting all the strain components is unhelpful in interpreting the results because the 36

“failure criteria” of nerves relating to each of the strain components remains unclear.

The use of the individual components in this initial study would be less intuitive and make graphical presentation of results much more difficult. Scalars are much more practical for use as parameters in mathematical analysis because they only have one value (Sigal et al., 2004). Accordingly, the output of the model was given as either pressure or von Mises strain.

Although there is ongoing discussion concerning the best mechanical measure of nerve damage as described in Chapter 2, for this work the commonly used value of von Mises strain was reported. Von Mises strain is a scalar strain value that can be computed from the strain tensor. It is commonly used in structural studies to predict the failure trend of materials using von Mises yield criterion and many biomechanical studies have used it in axonal injury analyses because of its potential relevance to nerve failure (Anderson,

2000; Raul et al., 2006; Ueno et al., 1995). Pressure was also determined to permit validation based on the experimental pressure measurements reported by Kosmorsky et al. (2008). Pressure was derived from principal stresses using appropriate equations

(Ueno et al., 1995).

As above, the chiasm was subcategorized into two regions (Figure 3.2b): the nasal nerve fibre region and the temporal nerve fibre region. Von Mises strain and pressure results were expressed as a function of relative position on Paths A and B as defined above.

The results of the calculated values of pressure were compared with the measured values from the study by Kosmorsky et al. (2008). This required a certain degree of assumption as physical displacement of the chiasm was not measured in that study and the precise degree of elevation was not clear due to the complex deformations and

37 displacements of structures surrounding the balloon and the possible movement of the catheter itself both during and between experiments. In the video, which accompanies the experiment, the chiasm appears to be elevated to a level that is a little higher than its height (i.e. > 1h). Unfortunately, there was considerable scatter in the experimental data and the correlation between tumour volume and pressure was inconsistent which results in uncertainties of the experiment. Details of their experimental measurements were presented in the results section of this chapter.

3.3 Nerve fibre model

The chiasm model described above treats nerve tissue as a homogenous substance. This simplification was made in order to examine the strain distribution across the chiasm as a whole. On a nerve fibre scale, however, nerve fibres must be considered as individual structures which can make contact with each other in different ways. This particularly applies to the difference between crossed and uncrossed fibres as discussed above. To take account of this difference, two additional micro-structural FEM models were established, one for nasal (crossed) fibres, the other for temporal (uncrossed) fibres.

For this purpose, a simple geometric model analogous to that described by McIlwaine et al. (2005) was used. The model adopted two half-cylinders to represent two nerve fibres

(Figure 3.3). The diameter of the nerve fibres was set at 1 μm on the basis of measurements from the literature (Jonas et al., 1990). For the purposes of simplification of the model, the length of the nerve segment was taken to be the same as the diameter of the nerve fibre. Additionally, it was assumed that the nasal fibres crossed each other perpendicularly (the worst case scenario), whereas the temporal fibres were aligned in parallel. Material properties of individual nerve fibres are not available in the literature

38 so, even though optic nerve fibres are myelinated and therefore surrounded by a sheath, the fibre was considered to be homogeneous for the purposes of the microscopic model.

Accordingly, the same properties were used as in the macroscopic model of the chiasm.

Pressure Pressure

(a) (b)

Figure 3.3 The nerve fibre model. (a) Uncrossed nerve fibres. (b) Crossed nerve fibre. The bottom faces and cross sections (indicated by white arrows) were constrained by frictionless supports.

Local pressure values were derived from the results of the macro-scale simulation of the chiasm along Path A (Figure 3.2b) when the chiasm was elevated to 0.94h. These local pressure values were then applied to the two micro-scale nerve fibre models to investigate the strain in the nerve fibres as a function of whether the nerves were crossed or uncrossed.

The average von Mises strain of the mid-section of either nerve fibre (half cylinder;

Figure 3.3) in each model was calculated as the main output for the nerve fibre model, which was referred to as “average cross-sectional strain” hereafter in this chapter.

Output of the nerve fibre model was calculated along Path A for both crossed and uncrossed fibres for the condition of maximum elevation (i.e. 0.94h). The detailed nerve fibre distribution in the optic chiasm is still unclear. It is generally believed that the

39 nasal nerve fibres cross in the central part chiasm while the temporal fibres are routed in a roughly parallel manner in the peripheral part of the chiasm (Neveu and Jeffery, 2007).

Accordingly, the output of the crossed model was applied to the central half of Path A

(assumed to contain the nasal, crossed fibres) while the output of the parallel model was applied to the lateral half (assumed to contain the temporal, uncrossed fibres). The outputs of the nerve fibre model were compared to the axonal injury thresholds (Bain,

1998).

3.4 Assumptions

It should be pointed out that the models in this chapter were developed for preliminary study of the biomechanics of optic chiasmal compression using finite element modelling.

A number of simplifying assumptions have been made which is the common practice in the field of biomechanics, especially at the initial stage. These assumptions were summarized here:

1. The geometry of the optic chiasm was built from some key dimensions (such as

width and height) found in the literature. However, the chiasm has a complex

geometry which cannot be fully described by these simple dimensions.

2. The material properties used in the model were all linear elastic and isotropic for

this initial study.

3. There was no direct loading transfer between the chiasmal model and the nerve

fibre model.

4. In the nerve fibre models, the nerve fibre was considered to be homogeneous.

5. There was no extracellular matrix existing between nerve fibres.

6. The nerve fibre size was uniform.

7. Nerve fibres were straight (no undulation).

8. Nerve fibres travel individually.

9. The crossing nerve fibres were restricted to the central part of the chiasm.

10. The material properties for individual nerve fibres were borrowed from the brain

white matter.

Subsequent chapters describe how the fidelity of the models was increased based on the findings of this chapter.

3.5 Results

3.5.1 Mechanical deformation of the chiasm with increasing tumour volume

Figure 3.4 shows the displacement and deformation of Face 1 (Figure 3.2b) of the chiasm at various inflation pressures of the balloon used to represent the growing tumour. The distance between Point 1 and Point 2 (Figure 3.2b) became smaller with increasing elevation of the chiasm. This indicated that chiasmal height decreased as a result of compression by the tumour.

6.0

4.0

2.0

Deformation (mm) 0 0 0.03 0.06 Inflation pressure in the balloon (MPa)

6.0

4.0

2.0

Deformation (mm) 0 0.085 0.115 0.145 Inflation pressure in the balloon (MPa) Figure 3.4 Deformation of the chiasm as a result of various inflation pressures in the tumour (balloon).

3.5.2 Von Mises strain distribution

Figure 3.5 shows the modelled deformation of nerve tissue in the chiasm along with contours of von Mises strain distribution as a result of increasing the inflation pressure in the tumour. The undeformed chiasm and balloon are shown on each image as wire frames, for reference. Elevation of the chiasm increased with increasing inflation pressure. The degree of displacement of Point 1 is given with reference to the baseline height of the chiasm, h (3.5 mm). As can be seen, the five steps of increased pressure, and thus simulated-tumour growth resulted in elevation of Point 1 by factors of 0.11h,

0.26h, 0.40h, 0.63h and 0.94h, respectively (see Figure 3.4). Strain was always highest in the central half of the chiasm. Of particular note, as tumour size was increased, the point of maximum strain was initially located in the lower-central portion of the chiasm.

This point gradually moved upwards towards the centre of the chiasm as tumour size

(balloon pressure) and chiasmal deformation were increased. More detailed analysis of these effects is given in Figure 3.6 and Figure 3.7.

(a) 0.11h (b) 0.26h

Figure 3.6 shows the von Mises strain distribution along Path A (Figure 3.2b) as the chiasm was elevated to various levels by the growing tumour. As can be seen, von

Mises strain was always greatest at the centre of the chiasm and gradually decreased with increasing horizontal distance away from the centre. Previous research showed that the complex fibre configuration (potential crossing, shape curving) were mainly located in the central part of the chiasm while the peripheral part of the chiasm is occupied by

43 uncrossed temporal fibres (Neveu et al., 2006; Roebroeck et al., 2008). Therefore, the central half of Path A was assumed to represent the nasal (crossed) fibres while the outer half was assumed to represent the temporal (uncrossed) fibres. Thus, at any level of chiasmal elevation, the strain observed in the region of the crossed fibres was greater than that in the region of uncrossed fibres.

0.94h 0.14 0.63h 0.12

0.40h 0.10 0.26h 0.08 0.11h 0.06

von Mises strain Mises von 0.04

0.02

0.00 0 1 2 3 4 5 6 Distance from the centre of the chiasm (mm)

Figure 3.6 Strain values along Path A when the chiasm was elevated to various levels.

Figure 3.7 shows the von Mises strain distribution along Path B (Figure 3.2b). When the chiasm was only just elevated, the von Mises strain in the lower nasal fibre region was significantly higher than that in the upper nasal fibre region. As the deformation of the chiasm was increased, the strain in the upper nasal fibre region increased and the point of maximum strain moved upwards towards the vertical centre of the chiasm. This type of strain progression would explain why upper visual fields are typically affected first as noted by Cushing and Walker (1914).

0.14

0.12 0.94h

0.10 0.63h 0.40h 0.08 0.26h 0.06 0.11h

von Mises strain Mises von 0.04

0.02

0.00 0 1 2 3 Distance from the inferior centre of the chiasm (mm)

Figure 3.7 Strain values along Path B when the chiasm was elevated to various levels.

3.5.3 Pressure distribution

To enable validation of the model with experimental data, local hydrostatic pressures were calculated through stress values. Figure 3.8 shows the calculated values of pressure along Path A derived from the model along with the individual pressure measurements made by Kosmorsky et al. (2008). Kosmorsky et al. only used two transducers to measure pressure, one located at the centre of the chiasm and the other at the periphery of the chiasm. The exact location of the measured points would have been dependent on the depth of penetration of the transducer needle and was therefore unclear as they were not accurately specified. On the basis of measurements taken from the authors’ video, the location of their central transducer was assumed to be at the centre of the chiasm while the peripheral transducer was assumed to be at 4.6mm from the centre of the chiasm, as indicated in Figure 3.8. Eight pressure measurements at the centre and eight at the periphery have been plotted accordingly.

Figure 3.8 Pressure distribution along Path A compared to data from the experiment by Kosmorsky et al. (2008).

3.5.4 Nerve fibre model

Figure 3.9 shows the results of the nerve fibre model under the pressures provided in

Figure 3.8 at maximum elevation (0.94h). The calculated average von Mises strain is plotted for both crossed and uncrossed nerve fibres as a function of position in the chiasm along Path A. Crossed nerve fibres clearly experience higher average strain levels than uncrossed nerve fibres at any position.

0.14 0.12

strain crossed 0.1 0.08 Mises 0.06 uncrossed 0.04 0.02 Average von Average 0 0 1 2 3 4 5 6 Distance from the centre of the chiasm (mm)

Figure 3.9 Calculated average cross-sectional strain for uncrossed and crossed nerve fibres along Path A.

Figure 3.10 shows the outputs of the nerve fibre model along with three threshold values obtained from an in vivo study of guinea pig chiasms Bain (1998). Bain (1998) analysed the microstructure of the optic nerve of guinea pigs and was able to define three strain thresholds (TL = 0.12, TC = 0.04 and TB = 0.06) of axonal injury. TL and TC represent the limits of injury, i.e. the strains above and below which all axons will or will not be injured, respectively. TB, defined by using a statistical procedure, represents the strain threshold that had the best ability to discriminate injured and uninjured nerve fibres. The thresholds were derived from uniaxial tensile tests of the guinea pig optic nerve, which is different from the complex strain state in the simulation. Therefore, the uniaxial tensile strain thresholds were converted to von Mises strain thresholds. It should be noted that, the threshold used here is only indicative of the potential consequences of the strain differences in crossed and uncrossed nerve fibres and hence no quantitative conclusion can be drawn. To account for the demarcation between the response of the nasal and temporal fibres, the bold line in Figure 3.10 illustrates the effect of passing from crossed (i.e., nasal) fibres to uncrossed (i.e., temporal) fibres

47 while moving from the centre of the chiasm towards the periphery. It can be seen that the strain difference between the crossed nasal nerve fibres and the uncrossed temporal nerve fibres was large, which may begin to explain the sharp vertical cutoff of the vision loss observed in bitemporal hemianopia.

Nasal nerve fibres Temporal nerve fibres 0.14

0.12 TL

strain 0.10

Mises 0.08

0.06 TB

0.04 TC Average von Average 0.02

0.00 0 1 2 3 4 5 6 Distance from the centre of the chiasm (mm)

Figure 3.10 Microscopic model output plotted against results of study on guinea pig optic nerve.

TC: level below which no axon would be injured; TB: level which provided the best

discrimination between injured and uninjured axons; TL: level above which all axons would be injured. The bold line demonstrates the step which is generated by the switch from crossed to uncrossed fibres.

3.6 Sensitivity study of the generic models

Material properties are crucial to accurate finite element modelling. However, data on the material properties of tissues involved in this model are relatively scarce because of the practical difficulties in measuring these properties. Furthermore, properties of brain material reported in the literature vary from study to study. It is therefore important to examine the sensitivity of the predicted strain distributions in the model to changes in

48 these values. Accordingly, the sensitivity of modelled chiasmal compression biomechanics to variations in the geometry and mechanical properties of the optic chiasm and nerve fibres were examined. The model in the section above was taken as the baseline model. All variations were based on the baseline model.

3.6.1 Variations of the chiasmal compression model

3.6.1.1 Material properties of pia mater and nerve tissue

On the basis of the various values quoted in the literature (Sigal et al., 2004; Sigal et al.,

2009), the elastic modulus of pia mater used in parametric study was varied in five steps, two on either side of the value of 3 MPa quoted in the literature, i.e. 1 MPa, 2 MPa, 3

MPa (baseline), 4 MPa, and 5 MPa. The elastic modulus of nerve tissue was also varied in five steps, specifically 0.01 MPa, 0.03 MPa (baseline), 0.06 MPa, 0.09 MPa, and 0.12

MPa.

3.6.1.2 Thickness of the pial sheath

There is some disagreement in the literature regarding the precise thickness of the pia mater sheath surrounding the chiasm in cadaveric specimens and very little information regarding its thickness in vivo (Hayreh, 2011). Reports of the thickness of the pia mater of the intraorbital portion of the optic nerve vary between 0.06 – 0.144 mm

(Balaratnasingam et al., 2009; Pache and Meyer, 2006). For this parametric study, the thickness of the pial sheath was therefore modelled at 0.03 mm, 0.05 mm, 0.06 mm

(baseline), 0.1 mm and 0.2 mm.

3.6.1.3 Changes of relative locations of the pituitary tumour

In reality, the chiasm may not be loaded centrally because of the variations of the tumour shape and the growing direction of the tumour (eg, Figure 1.7). To investigate

49 this effect, the spherical tumour was simply offset laterally and antero-posteriorly. The relative locations of the tumour and the chiasm are illustrated in Figure 3.11. 4 mm 4

6 mm

(a) (b)

Again, two paths were defined to illustrate the results. Path C was defined as the line travel through the central point of the chiasm from left to right and Path D travel through the central point from anterior to posterior (Figure 3. 12 ).

left right posterior

(a) (b)

Figure 3.12 Demonstration of (a) Path C and (b) Path D; as the red bold lines in the figure.

The geometry and the material properties used in this simulation were same as those of the baseline model. The elevations of the chiasm in these two cases were different and were indicated in the results section. 50

3.6.1.4 Constraint type of the distal face

In the baseline model, the distal face (see Figure 3.1) of the optic nerve was simply fixed. However, in reality, the anatomy of that region is very complex. The pial sheath is attached to the dura mater, which is attached to the bone (Figure 3.13). The arachnoid is connected to the pia mater by arachnoid trabeculae to form the pia-arachnoid complex

(Xin et al., 2006). At the optic canal, the arachnoid is very thin and the arachnoid space is extremely narrow (Hayreh, 1964). Therefore, in this study, the arachnoid and the pia mater were considered to be a single structure and the thickness and mechanical properties of pia mater were used for this structure.

Figure has been removed due to Bone

See Figure 2.32 in reference (Hayreh, Pia 2011) Nerve tissue (b) 1-1

In this model, the detailed structures around the optic canal were constructed (Figure

3.14). The thickness of the dura mater was taken as 0.3 mm (Snell and Lemp, 1998).

The thickness of the bone was taken as 1mm and fixed at its peripheral face. The elastic modulus and Poisson's ratio for dura mater were 31.5 MPa and 0.45 respectively (Voo

51 et al., 1996). The elastic modulus and Poisson's ratio for bone were 6,000 MPa and 0.21, respectively (Willinger et al., 1999).

The optic nerve was extended 30 mm to the eyeball and fixed there (Figure 3.14). The optic tract is embedded into the brain but the connection between brain tissue and the optic tract is unclear. For simplicity, the optic chiasmal model was still considered to be symmetric in two directions, i.e., the same constraint was applied to the optic tract as well.

Three contact patterns were applied between the pia mater and dura mater: bonded, no separation and frictionless covering the range of possibilities. The optic nerve tissue and dura were connected to each other by thick fibrous bands (Figure 3.13) (Hayreh, 1964), it is therefore assumed that bonded connection is more realistic than the other two extreme types of connection. The “no separation” contact in ANSYS does not allow separation of contacted faces but small amounts of frictionless sliding is allowed between contact faces.

Bone Dura Pia

Fixed

Figure 3.14 Model with new constraints.

3.6.2 Variation of the nerve fibre model

The angle at which nasal (crossed) nerve fibres cross each other could vary from 0° to

90° rather than always being the perfect perpendicular intersection assumed in the baseline model. Therefore, it was considered important to analyse the effect of different crossing angles between optic nerve fibres. Seven crossing angles were used in the parametric study as follows: 0°, 15°, 30°, 45°, 60°, 75° and 90°.

3.6.3 Results of the chiasmal model

Table 3.2 shows a summary of the parametric study cases of the chiasmal model. The results of the parametric study were presented in detail separately in this section.

Table 3.2 Parametric study cases of the chiasmal model

Case Factor Variation range 1 Modulus of pia mater 1 – 5 MPa 2 Modulus of nerve tissue 0.01 – 0.12 MPa 3 Thickness of pial sheath 0.03 – 0.2 mm Relative locations of the Tumour offset laterally (6 mm); Tumour offset 4 pituitary tumour anteriorly (4 mm) Constraint types of the distal More realistic structure was built and three types of 5 surface connection were considered

3.6.3.1 Material properties of pia mater and nerve tissue

Figure 3.15 shows the modelled von Mises strains along Path A (Figure 3.2b) using various elastic moduli of the pia mater. The figure shows that a higher elastic modulus

(and therefore stiffer sheath) resulted in higher strains in the chiasm, but the pattern of strain distribution across the optic chiasm was similar in each case. It is observed that the height of the chiasm after deformation was smaller with a stiffer sheath compared with the softer sheath model, i.e., the chiasm was squeezed more if the sheath is stiffer.

This may be because that the softer sheath was more liable to deform, as compared to stiffer sheath, when the interior nerve tissues were squeezed.

0.18 Elastic modulus of pia mater 0.16 5 MPa 0.14 4 MPa

3 MPa 0.12 2 MPa 0.10 1 MPa

0.08

von Mises strain Mises von 0.06

0.04

0.02

0.00 0 2 4 6 Distance from the centre of the chiasm (mm)

Figure 3.15 Von Mises strain distribution along Path A in models with various elastic moduli of pia mater.

Figure 3.16 illustrates the von Mises strains along Path A in the chiasmal model using the five elastic moduli of nerve tissue. It shows that a smaller elastic modulus resulted in higher strains in the chiasm. Variation in the elastic modulus of the nerve tissue did not affect the pattern of strain distribution, i.e., the nasal fibre region always experienced a higher level of strain than the temporal fibre region. As expected, the changes from the central to the peripheral chiasm were always gradual.

0.20 0.18 Elastic modulus of nerve tissue 0.01 MPa 0.16 0.03 MPa 0.06 MPa 0.14 0.09 MPa 0.12 0.12 MPa

0.10 0.08

von Mises strain Mises von 0.06 0.04 0.02 0.00 0 2 4 6 Distance from the centre of the chiasm (mm)

Figure 3.16 Von Mises strain distribution along Path A in models with various elastic moduli of nerve tissue.

Figure 3.17 demonstrates the changes in von Mises strain at Point 3 in the geometric centre of the chiasm (Figure 3.2b) as the elastic modulus of the nerve tissue was varied.

Note that the strain and elastic moduli in Figure 3.17 were expressed as ratios of the values used in the baseline model. The slope of the curve was large when the relative modulus was small. The slope decreased with increasing modulus ratio, which indicates that the von Mises strain ratio becomes less sensitive to the nerve tissue stiffness when the nerve tissue stiffness is high.

1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 Ratio von Mises strain of 0.00 0.00 1.00 2.00 3.00 4.00 Ratio of elastic modulus of the nerve tissue

Figure 3.17 Changes of strain at Point 3 (Figure 3.2b) due to variations of the material properties of nerve tissue.

3.6.3.2 Thickness of the pial sheath

Figure 3.18 displays the von Mises strain along Path A as the sheath thickness was varied when the pressure in the balloon reached 0.145 MPa. Von Mises strain increased with increasing thickness of the sheath, which is consistent with the results of varying the elastic modulus of pia mater. In all cases, strains in the central chiasm were greater than those in the temporal chiasm.

Varying the thickness of the pial sheath had a significant effect on the strain distribution, especially when the thickness was very large (0.2 mm) which changed the trend of the curve in the peripheral part of the chiasm. It is easy to obtain measurements of the thickness of the pial sheath of the intraorbital portion of the optic nerve from the literature, but there is little information on pial sheath thickness in the optic chiasm. The range of the sheath thicknesses selected for the parametric study was based on the values for the thickness of the intraorbital portion of the optic nerve. It would be important to obtain a more accurate measurement of pial sheath thickness in vivo for use in future studies.

0.20 Thickness of pial sheath 0.18 0.2 0.16 0.1 0.14 0.06 0.12 0.05 0.03 0.10 0.08

von Mises strain Mises von 0.06 0.04 0.02 0.00 0 2 4 6 Distance from the centre of the chiasm (mm)

Figure 3.18 Effect of varying sheath thickness on the stain distribution within the chiasm.

3.6.3.3 Changes of the relative location of the tumour

The von Mises strain values on Path C and Path D in loading case A and B (as illustrated in Figure 3.11) were illustrated in Figure 3.19 to Figure 3.22. The elevation of the central point of the chiasm in Loading Case A and Loading Case B were 2.99 mm and 2.67 mm, respectively.

0.14

0.12

0.1

0.08

0.06

Von Mises strain Mises Von 0.04

0.02

0 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 (Left) Path C (mm) (Right)

Figure 3.19 The strain distribution along Path C for a tumour sitting anteriorly (or posteriorly) of the chiasm (Loading Case A).

0.14

0.12

0.1

0.08

0.06

Von Mises strain Mises Von 0.04

0.02

0 -4 -3 -2 -1 0 1 2 3 4 (Anterior) Path D (mm) (Posterior)

Figure 3.20 The strain distribution along Path D for a tumour sitting anteriorly (or posteriorly) of the chiasm (Loading Case A).

0.16 0.14

0.12 0.1 0.08 0.06

Von Mises strain Mises Von 0.04 0.02 0 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 (Left) Path C (mm) (Right)

Figure 3.21 The strain distribution along Path C for a tumour offset laterally to the right (Loading case B).

0.14

0.12

0.1

0.08

0.06

Von Mises strain 0.04

0.02

0 -4 -3 -2 -1 0 1 2 3 4 (Anterior) Path D (mm) (Posterior)

Figure 3.22 The strain distribution along Path D for a tumour offset laterally to the right (Loading case B).

It can be seen from Figure 3.19 to Figure 3.22 that the peak strain locations in the chiasm were correlated with the compression site of the chiasm. In clinical cases, it is

59 common that the chiasm is not compressed centrally, which indicates that the strain distribution differences in the central and peripheral chiasm could not explain the vertical cutoff of VF in bitemporal hemianopia.

3.6.3.4 Constraint type of the distal face of the optic nerve

0.16 Constraint type 0.14 baseline 0.12 bonded

0.10 no separation frictionless 0.08

0.06 von Mises strain Mises von 0.04

0.02

0.00 0 2 4 6 Distance from the centre of the chiasm (mm)

Figure 3.23 The von Mises strain distribution along Path A in models with various constraint types.

Figure 3.23 shows the von Mises strain distribution along Path A in models with various constraint methods. It can be seen that the results of bonded constraint model were very close to the results of the baseline model. For the “no separation” and frictionless constraints, the strain values were smaller but the distribution trend were still the same.

Although this parametric study included three types of connection between pia and dura mater, the bonded connection was considered to be the most realistic one because, in vivo, the pia mater was bonded to the dura by fibrous materials as discussed above

(Figure 3.13). The results of the baseline model were very close to the results of the

60 bonded model, which indicates that the constraint type in the baseline model is reasonable. Furthermore, the other two connection cases, which may not reflect the real connection in vivo, only changed the strain values in the chiasm. The strain distribution patterns were still the same as bonded model, indicating that variations of the constraint types of the distal faces would not change the strain distribution trend in the regions of interest.

3.6.4 Results of the nerve fibre model

Figure 3.24 shows the calculated average von Mises strain on the middle cross-section

(cross-sections with their normal along the length of the axon) in all nerve fibres along

Path A (Figure 3.2b) as a function of changing the crossing angle of the nerve fibres.

Increasing the angle of crossing had a significant effect on the von Mises strain values.

0.16 Crossing angle 0.14 90°

0.12 75° 60° 0.1 45° 30° 0.08 15° 0.06 0°

0.04 Average von Mises strainAverage

0.02

0 0 2 4 6

Location of nerve fibres in the chiasm (mm)

Figure 3.24 Effects of variations in crossing angles on average cross-sectional von Mises strain in nerve fibres.

Figure 3.25 illustrates the change in the average von Mises strain of nerve fibres at

Point 1 (Figure 3.2b) as a result of varying their crossing angles. At a given load, average strain increased with increasing crossing angle. It can be seen from Figure 3.24 and Figure 3.25 that when the crossing angles were near the two extremes (i.e. from 0° to 15° and from 75° to 90°), the change in strain for a given change in angle was smaller than when the crossing angles ranged between 15° and 75°.

0.14

0.13

0.12

0.11 Average strain Average 0.10

0.09 0 15 30 45 60 75 90 Crossing angle (degree)

Figure 3.25 Change in average von Mises strain in nerve fibres located at Point 1 as a function of crossing angle between nerve fibres.

3.7 Discussion

In this chapter, finite element modelling was used to simulate chiasmal compression numerically in order to quantify the strain distribution across the chiasm and so gain a clearer understanding of the strains experienced by individual nerve fibres. Models of chiasm compressed by a pituitary tumour growing centrally beneath it show that:

• strain is higher in the centre of the chiasm where the nasal (crossed) fibres are

situated.

• strain is higher if nerve fibres cross each other than if they run parallel to each

other.

• the calculated pressures obtained from the simulation are broadly in agreement

with the pressures measured experimentally by Kosmorsky et al. (2008), even

though uncertainties exist in both the experiment and the simulation.

The calculated strain and pressure distributions across the chiasm suggest that if this was the only factor involved in disrupting chiasmal transmission, there should be a graded involvement of both nasal (crossed) and temporal (uncrossed) fibres rather than the sharp vertical cutoff noted clinically. Parametric studies show that the area experiencing larger strain was not located at the centre of the chiasm if the chiasm was not loaded centrally. However, the differences in strains experienced by nasal and temporal fibres in the FEM model may explain the vertical cutoff as they suggest that for any given degree of compression, crossed fibres are more vulnerable than uncrossed fibres.

It was assumed for the baseline model that temporal nerve fibres run parallel to each other (Neveu et al., 2006). However, there may, in fact, be small crossing angles between these temporal nerve fibres. Given that the difference in average strain values resulting from varying the crossing angles between nerve fibres from 0° to 15° was small (Figure 3.25), it is reasonable to assume an uncrossed nerve fibre model (with a crossing angle of 0°, Figure 3.3a) to represent the temporal nerve fibres. The exact arrangement of nasal (crossed) nerve fibres in the chiasm is still unclear from the literature. However, it is certain that they must cross somewhere, even if the precise crossing angle varies somewhat from one location to another. This study suggests that there was relatively little effect of changing the crossing angle from 75° to 90°, 63 implying that modelling the nasal fibres as crossing each other at 90° (Figure 3.3b) is not unreasonable. This study also shows that further study to determine the precise arrangement and directions of crossings of nerve fibres in the chiasm is needed to understand the strain differences in individual nerve fibres better. The detailed crossing angles and locations of the nerve fibres in the chiasm will be investigated using photomicrographic image analysis in Chapter 6.

The results of the parametric studies of the chiasmal model suggest that the absolute values of strain distributions in the chiasm were sensitive to all the parameters chosen in this research. However, in all conditions, the patterns of strain distribution were similar to each other if the chiasm was centrally loaded. Specifically, the nasal fibre region always experienced higher strains than the temporal fibre region.

The mechanical properties of nerve tissue are known to be affected by both ageing

(Prange and Margulies, 2002) and disease (Sparrey et al., 2009). The parametric studies suggest that, while the absolute value of strain may be affected by individual variations

(eg., age and health condition), the relative difference between strain in the central and peripheral parts of the chiasm is likely to be preserved.

In the parametric studies, only one parameter was varied at a time while the other parameters were maintained at the values used in the baseline model. The effects of varying each parameter can be clearly evaluated by this procedure but, in reality, variations of multiple parameters may occur simultaneously which was not considered in this initial study. In Chapter 5, design of experiment (DOE) will be used to consider the effects of potential interactions between factors for the nerve fibre model.

It should be noted in passing that this initial, simple model does not address the precise mechanism of interruption of nerve impulse conduction at an axonal level for which there are several possible mechanisms including disruption of ion channels, demyelination and/or frank axonal transection as described in Chapter 2 (Cliffordjones et al., 1980; Cliffordjones et al., 1985; Maxwell et al., 1997).

It should also be pointed out that this finite element analysis only studied the mechanical response of the chiasm to compression; other factors such as ischemia were not investigated. Therefore, it is still possible that ischemia of the central aspect of the chiasm (Bergland and Ray, 1969) plays a role in generating the visual field defect.

However, ischemia would not account for the cutoff at the vertical meridian whereas the model in this chapter does.

Although the results of the computer simulation agreed well with the results of the post- mortem study by Kosmorsky et al. (2008), the degree to which both cases represent the reality of a slowly-growing pituitary tumour is not clear. Precise details of the growth pattern of these tumours and how this can best be represented by finite element modelling require further consideration.

It is worth pointing out that this model derived values for the various geometric parameters from the literature but that these geometric parameters did not all come from the same report. For example, the cross-sectional dimensions of the optic nerve were obtained from one study (Parravano et al., 1993), but the angle between the two optic nerves was derived from another study (Schmitz et al., 2003). It is therefore possible that the geometry of this model does not reflect an overall ‘average’ geometry. More accurate data on the thickness of the pial sheath in the chiasm are also needed to

65 improve the accuracy of the model. An individual-specific model will be built in

Chapter 4 for deeper understanding of the effects of chiasmal geometry.

In this initial simulation, linear elastic material properties were assumed for all tissues.

However, in practice, biological tissues have mechanical properties that are non-linear and anisotropic and studies have shown that brain tissue behaves in a more complex, hyperelastic manner (Eilaghi et al., 2010; Meaney, 2003; Prange and Margulies, 2002), especially under large deformations (Abolfathi, 2009). There are also viscoelastic models (Fung, 1993; Girard et al., 2007; Miller, 1999) which take time-dependent creep and stress relaxation, as well as rate-dependent behaviours of tissue, into account. All of these factors will eventually need to be incorporated into the model. Hyperelastic isotropic material models will be used in later chapters and the reasons for assuming isotropic material will be discussed in Chapter 4. In the meantime, it is believed that the simple linear elastic material properties assumed in this chapter have provided a reasonable first approximation which allows an improved understanding of optic chiasm biomechanics.

In conclusion, although earlier studies identified the potential benefits of applying FEM to this problem (Kosmorsky et al., 2008; McIlwaine et al., 2005), to the authors’ knowledge this is the first attempt to develop a three-dimensional model of chiasmal compression and to use it to investigate the stains progression and distribution in detail.

Despite the limitations of this chapter acknowledged above, even this simple biomechanical model provides an improved understanding of the mechanism of bitemporal hemianopia. Improving the fidelity of the model will reduce levels of uncertainty and may well give the model clinical relevance as it could permit clinicians to modify their clinical management of patients with these temporal VF defects.

Chapter 4

Optic chiasmal model based on Visible Human Project

In Chapter 3, the biomechanics of chiasmal compression were studied using simple finite element models and the preliminary results provided an improved understanding of the mechanism of bitemporal hemianopia. The influences of several factors such as material stiffness on the biomechanics of the optic chiasmal compression were also studied. These models demonstrated the feasibility of using finite element modelling to study the chiasmal compression. However, the geometric data in that model were taken from several sources in the literature and as it was perfectly symmetric that it may not represent the complex 3D geometry of the optic chiasm. Similarly, linear elastic material models were used for simplification. In this chapter, a realistic 3D model of the chiasm and nonlinear (finite deformation, nonlinear material model and contact) finite element procedures were employed to increase the fidelity of the simple simulation performed in Chapter 3. The model used an individual-specific geometry which maintained the original chiasmal geometry by using 3D reconstruction from human head slices. Nonlinear materials were employed in this large deflection problem.

Note that it was not the primary aim of this chapter to establish a patient-specific modelling approach, but rather to investigate the use of a more realistic chiasm geometry and tissue material models. The optic chiasm is tiny (about 14 mm wide, 3.5 mm thick and 8 mm for anterior-posterior extent) compared to the brain. In practice, at this moment, it is impossible to get a chiasmal model of a patient because in vivo scanning like MRI has very poor resolution. The author has scanned his own brain in the hospital and found it is unrealistic to rebuild the accurate geometry of the chiasm

67 through MRI scans. Although ex vivo scanning using state-of-the-art technique could obtain high-resolution images, it is unfortunately unrealistic, at present, to do this in a living patient.

4.1 Geometry

The geometry of the chiasmal model was obtained from the 3D construction of human head slices of the Visible Human Project of the United States (Mikula et al., 2007). In the Visible Human Project, the frozen cadaver was sliced axially and cross-sectional images were taken.

To build a 3D model, these images were firstly converted to grayscale using MATLAB and segmented manually using 3D Slicer (Pieper et al., 2006), a free open source software for biomedical research, to obtain the boundaries of the optic nerves, chiasm and tracts (Figure 4.1). Segmented images were used to build the 3D model.

Figure 4.1 The optic nerve and chiasm (highlighted part) were segmented from one of the slices of the Visible Human Project of the United States (Mikula et al., 2007).

A 3D model containing only the surface information was then generated in Slicer and saved as an STL file. The STL file was processed using CATIA V5 (Dassault Systemes,

France) to form a solid model which was then imported into the FE package ANSYS

(Ansys Inc., Canonsburg, PA, USA) for analysis. Because of the low resolution of these images, it was hard to discern the pial sheath. Therefore, the reconstructed slices were assumed to be comprised entirely of nerve tissue. A surrounding pial sheath of 0.06 mm thickness (Sigal et al., 2004) was then added to the model in ANSYS. A detailed description of the 3D reconstruction procedures in 3D Slicer and CATIA will be presented later in Chapter 7.

In this improved chiasmal model, a spherical balloon was again used to represent a tumour. Although research into pituitary tumour size has been reported (Lee et al., 2011) variations in tumour geometry and the contact patterns between tumour and chiasm are still not well understood. However, inspection of the MRI scans of patients experiencing chiasmal compression (Egger et al., 2010; Fahlbusch and Gerganov, 2012;

Honegger et al., 2008) indicates that it is reasonable to use an initially spherical balloon to represent the tumour. The diameter of the tumour used in the study described here was 12 mm.

4.2 Material properties

For simplicity, linear elastic material models have been widely used in the finite element analysis of biological structure (Bellezza et al., 2000; Cirovic et al., 2006;

Norman et al., 2011; Sigal et al., 2004; Sigal et al., 2007) as discussed in Chapter 3.

However, in reality, the stress-strain behaviour of biological tissue is nonlinear. The material properties of brain matter have been investigated extensively in the literature.

Brain tissue is complex and it is relatively incompressible and nonlinear (Abolfathi,

2009; Miller, 1999; Miller and Chinzei, 2002). Material properties of the brain tissue are age, type and location dependent. Table 4.1 summarizes some of the material property tests that have been reported for brain tissue. Hyperelastic material models are usually used for brain tissues that undergo large deformations (Abolfathi, 2009; Bilston

2011).

Loading rate can influence the mechanical response of materials dramatically (Bilston,

2011). Viscoelastic material models have usually been used for rate-dependent loading cases. For example, small strain behaviour of the brain tissue under impact may be well represented by a linear viscoelastic model (Abolfathi, 2009). Miller (1999) reported that the time-dependent terms in the material model can be ignored and it does not introduce an appreciable error on the analytical solution for slow loading experiments. The chiasm is compressed at an extreme slow rate. Normally, the tumour takes years to grow before it touches the optic chiasm as discussed in Chapter 1. A tumour with a volume increase rate greater than 0.0007 per day is usually classified as rapidly growing tumours whereas this rate for slow growing tumours is less than 0.0002 per day (Honegger et al.,

2003). Given the extremely slow strain rate in this case, viscous behaviours of the materials were not incorporated in this work.

Moreover, the chiasmal tissue is anisotropic given that the nerve fibres passing through the optic nerve and chiasm at certain orientations. The anisotropy depends on the alignment of these nerve fibres. However, at this moment, the nerve fibre orientations in the optic chiasm are still not well understood. Therefore, the anisotropic behaviour of the chiasmal tissue was not incorporated in this work because it cannot improve the fidelity of the model without accurate knowledge of the fibre routing.

Table 4.1 List of material studies of brain tissue

Reference Test method Test specimen Constitutive model

Unconfined Linear viscoelastic, Miller (1999) Swine brain tissue compression Hyperelastic

Miller and Chinzei Uniaxial tension Swine brain tissue Hyper-viscoelastic (2002)

Hyperelastic, 5- Eilaghi et al. Sclera from Biaxial extension parameter Mooney- (2010) human eye Rivlin model

Arbogast and guinea pig optic Shear test Viscoelastic Margulies (1999) nerve

Nicolle et al. Oscillatory Porcine white Hyperelastic, 3 order (2004) experiment matter Ogden formulation

Franceschini Uniaxial tension Human brain Hyperelastic, Ogden (2006) and compression white matter formulation

Hrapko et al. Porcine brain Shear experiments Viscoelastic (2006) tissue

Prange and Shear and Procine brain Hyperelastic, Ogden Margulies (2002) compression test tissue model

Kaster et al. Porcine brain Hyperelastic, Yeoh Indentation test (2011) tissue model

Aimedieu and Traction test at low Bovine brain pia Load-deformation Grebe (2004) strain rate matter curves were provided

Bovine white Mehdizadeh et al. Stress-strain curves were Tension test matter and grey (2008) given matter

In this model, the optic chiasm, optic nerves and optic tracts were considered to be composed of isotropic nerve tissue surrounded by a pial sheath. For the large deformation problem in this study, the material properties of the pial sheath and the nerve tissue were modelled as nonlinear materials in keeping with the limited previously reported work available in the literature.

The nonlinear material properties of pial sheath were described by a second-order polynomial hyperelastic model (Ho and Kleiven, 2009). The strain energy potential of a polynomial hyperelastic model is:

1 = 푁 ( 3) ( 3) + 푁 ( 1) 푖 � 2푘 푖푖 1 2 푊 � 퐶 퐼 − 퐼 − � 푘 퐽 − 푖+�=1 푘=1 푑 Where:

= the strain energy per unit volume

푊 = first deviatoric strain invariant

퐼1 = second deviatoric strain invariant

퐼2 = determinant of the elastic deformation gradient

퐽 , and are material constants

푁 퐶푖푖 푑푘 The deviatoric strain invariant are defined as (for P = 1, 2, 3):

= 2 − 3 퐼푃 퐽 퐼푃 Where:

2 2 2 1 = 1 + 2 + 3

퐼 휆 휆 휆 2 2 2 2 2 2 2 = 1 2 + 2 3 + 3 1

퐼 휆 휆 휆 휆 휆 휆 2 2 2 3 = 1 2 3

퐼 휆 휆 휆 are principal stretches.

휆푃 White matter is one of the two components of the central nervous system and consists mostly of glial cells and myelinated axons that transmit signals from one region of the cerebrum to another and between the cerebrum and lower brain centres. The structure of optic nerve tissue and white matter is the same. Optic nerve tissue was frequently used to investigate the brain white matter injury mechanisms under mechanical loading (Bain and Meaney, 2000; Garthwaite et al., 1999; Gennarelli et al., 1989). Therefore, the material properties of brain white matter in reference (Franceschini, 2006) were used for the optic nerve tissue. It was implemented using a second order Ogden hyperelastic model in ANSYS (ANSYS, 2010).

The strain energy potential of an Ogden hyperelastic model is:

1 = 푁 ( + + 3) + 푁 ( 1) 훼푖 훼푖 훼푖 푖 2푘 휇 1 2 3 푊 � 푖 휆 휆 휆 − � 푘 퐽 − 푖=1 훼 푘=1 푑 Where:

= the strain energy potential

푊 = (P = 1, 2, 3) = deviatoric principal stretches, defined as 1 −3 휆푃 휆푃 퐽 휆푃 = principal stretches

휆푃 73

= determinant of the elastic deformation gradient

퐽 , , and are material constants

푁 휇푖 훼푖 푑푘 The material properties of pituitary tumour were not available in the literature. The spherical balloon used to represent the tumour was therefore simply modelled using linear elastic material properties of sclera. The effect of material properties of the tumour will be investigated in the parametric studies later in this chapter as it could change the way that it deforms the chiasm.

The parameters of these material models were all taken from the limited soft tissue data available in the literature (Franceschini, 2006; Ho and Kleiven, 2009) (Table 4.2). The densities used for the sheath, optic nerve and tumour were 1130 kg/m3, 1130 kg/m3 and

1000 kg/m3, respectively (Beckmann et al., 1999; Ho et al., 2009).

Table 4.2 Material properties used for the chiasmal model in ANSYS

Tissue on Material model and Tissue which model Material constants reference based

C10=1.5269×105 Pa ; C01=- Hyperelastic-2nd 7.1920×104 Pa; C20=1.2554×107 Pa ; Sheath Pia mater Polynomial (Ho and C11=-1.7873×107 Pa ; C02=7.27×106 Kleiven, 2009) Pa

Hyperelastic-2nd Optic Brain white =1044 Pa; =4.309; =1183Pa; Ogden nerve mater 1 1=7.736 2 (Franceschini, 2006) 휇 훼 휇 훼2 Linear elastic Tumour Elastic Modulus= 5.5MPa; Poisson’s Sclera (Bellezza et al., (balloon) ratio=0.47 2000)

4.3 Boundary condition, loading and meshing

Anteriorly, the optic nerves are connected to the optic canal by fibrous adhesions

(Hayreh, 1964) and posteriorly the optic tracts are embedded in the brain as discussed in detail in Chapter 3. Therefore, the distal faces of the optic nerves and optic tracts were fixed in the model. More complex arrangements, better representing the actual anatomy of these attachments, were tested in Chapter 3 but were found to have negligible influence on the strain distributions in the regions of interest in the chiasm. Pressure was applied to the interior surface of the tumour to inflate it and then a displacement in the superior direction (Figure 4.2) was applied at its inferior surface to further elevate the chiasm. This was in keeping with the experiment of Kosmorsky et al. (2008) in which a

Foley catheter balloon was inflated beneath a cadaveric chiasm to represent a growing tumour. The contact between the balloon and chiasm was considered to be frictionless.

The core tissues of the optic nerve, chiasm and tract were bonded to their respective pial sheaths.

Figure 4.2 The tumour growing at the direction of positive Z axis

Quadratic elements were used in the simulation. The pial sheath was meshed using tetrahedral elements. The tumour and the nerve tissue were meshed using hexahedral

75 elements and a small amount of tetrahedral elements (as in Chapter 3, SOLID186 and

SOLID187 were used for the hexahedral and tetrahedral elements). There were 212,115 nodes and 78,263 elements in this model. Modelling using a coarser mesh was found to have little effect on predicted strain output (Appendix C.2), which indicates that the mesh density used in the model was fine enough.

4.4 Output measurements

The optic chiasm compressed by a tumour produces complex deformations of the chiasm. In this model, the commonly used value of von Mises strain has been reported.

Pressure (Ueno et al., 1995) was also determined to permit validation based on experimental pressure measurements reported by (Kosmorsky et al., 2008).

4.5 Sensitivity study of the individual-specific model

Using the chiasmal compression model described above as the baseline model, parametric studies were performed to allow a broad study into the effect of various parameters on the strain distributions in the chiasmal model. Variations of nerve tissue stiffness, tumour stiffness, tumour growing directions and elevation of the chiasm were investigated.

Parametric studies considered the following scenarios:

4.5.1 Variation of the tumour growing direction

The chiasm is higher in its posterior part. In the baseline model, the tumour growing direction was assumed to be inferior-superiorly (z direction in Figure 4.2). In reality, the tumour could compress the chiasm in a large variety of angles. In order to study the influence of the tumour growing direction, a new model with the balloon growing 76 roughly perpendicular to the optic chiasm was built (Figure 4.3). A pressure of 0.27

MPa was firstly applied on the interior of the balloon and then a displacement was applied to the balloon. All other parameters were the same as those in the baseline model.

Figure 4.3 The tumour growing direction was roughly perpendicular to the chiasm; as indicated by the arrow.

4.5.2 Variation of the tumour diameter

The radius of the balloon in the baseline model was chosen to be 6 mm through observation of MRI scans of a patient experiencing chiasmal compression. But the tumour size varies substantially between individuals (Rivoal et al., 2000; Lee et al.,

2011). To test the influences of the tumour size on the strain distributions in the chiasm, a larger tumour with a radius of 10 mm was chosen in this model.

4.5.3 Variations of the loading site

In the baseline model, the optic chiasm was loaded roughly centrally. However, the compression site could vary because of the differences of tumour shape and growing directions. It is therefore interesting to see the effect of changing the locations of the

77 tumour on the output of this model. The tumour was moved 3.25 mm laterally towards right.

4.5.4 Variation of the stiffness of pia mater

The hyperelastic material models used for the pia mater were considered to be the same as in the baseline model. Corresponding parameters were modified to vary the stiffness of the pia mater to 0.5 or 1.5 times stiffer than in the baseline model. It should be noted that data on the material properties of pia mater is scant. The stiffness chosen here were only used to investigate the possible influences of the pia mater stiffness on the biomechanics of the optic chiasm. The stiffness of pia mater reported in the literature may vary by an order of magnitude or more from one study to another.

4.5.5 Variation of the stiffness of nerve tissue

The stiffness of nerve tissue was varied from 0.5 to two times stiffer than that in the baseline model using the same method as varying the stiffness of pia mater.

4.5.6 Variation of the tumour stiffness

Information on the material properties of the pituitary tumour is scarce. A balloon using material properties of sclera was employed in the baseline model to simulate a Foley catheter balloon used in the experiment of Kosmorsky et al. (2008). However, in real life, the tumour stiffness varies, thus in this case the tumour was modelled as a soft solid hemisphere. The soft hemisphere was then displaced upward roughly perpendicular to the chiasm to elevate the chiasm.

The material properties of tumours rely on their matrix tissue which is inter-individually variable. Research using magnetic resonance elastography (MRE) found that the stiffness of the same type of brain tumours may vary significantly among individual 78 patients (Pierallini et al., 2006; Xu et al., 2007). The elastic modulus of pituitary tumour was not available from the literature. The elastic modulus of the tumour was therefore taken as 0.0384 MPa which is from the mouse breast tumour (Barnes et al., 2009). The

Poisson’s ratio was 0.49. The material properties used here was close to the stiffness of brain tissue. The material properties of nerve tissue and pial sheath were the same as in the baseline model.

4.5.7 Effects of the elevation of the chiasm

In the baseline model, the chiasm was elevated to 5.56 mm which is able to cause bitemporal hemianopia (Ikeda and Yoshimoto, 1995). However, in real cases, the elevation of the chiasm can vary significantly (Bynke and Cronqvist, 1964 Ikeda and

Yoshimoto, 1995 Eda et al., 2002 Fujimoto et al., 2002 Frisen and Jensen, 2008).

Therefore the effects of elevation level on the strain distributions in the optic chiasm were investigated.

The chiasm in the baseline model was further elevated to 9.27 mm. The results when the chiasm was elevated to 3.07 mm, 5.56 mm (baseline) and 9.27 mm are presented below.

The height of the chiasm (h) in this model was approximately between 2.6 to 3.4 mm.

These three elevation values were chosen to represent the chiasm was elevated to around 1h, 2h and 3h, respectively.

4.6 Results

4.6.1 The baseline model

The chiasm was elevated inferior-superiorly to 5.56 mm, a level expected to result in bitemporal hemianopia (Ikeda and Yoshimoto, 1995). Figure 4.4 shows a coronal

79 section of the deformed chiasm in the simulation, along with a clinical MRI scan taken from a patient experiencing chiasmal compression. The deformation pattern in the simulation was quite similar to the in vivo MRI scan.

Figure 4.4 Comparison of the deformation predicted by the FEM model with a coronal MRI scan of a patient with optic chiasmal compression (Evanson, 2009).

Figure 4.5 shows the von Mises strain distribution in a coronal section of the chiasm at an elevation of 5.56 mm. This coronal section roughly cuts the chiasm into halves. As illustrated in Figure 4.5a, 41 lines were defined in the section. The average von Mises strain of each line was derived and plotted as a function of the line’s location in the left- right direction. It can be seen that the strain at the central part of the chiasm was generally higher than that at the peripheral aspect.

(a)

0.15

0.1

0.05 von Mises strain

(b) 0 -6 -4 -2 0 2 4 6 Location (mm)

0.1795 0.1389 0.0982 0.0575 0.0168

0.1976 0.1592 0.1185 0.0778 0.0371

(c)

The pressure values predicted by the simulations when the chiasm was elevated to 5.56 mm were compared to the experimental pressure measurements made by Kosmorsky et al. (2008) in Table 4.3. It should be noted that the generic model in Chapter 3 was compared to the same experiment by Kosmorsky et al. The comparison was performed here again using the individual-specific model for two reasons: 1) it aimed to see whether the use of new geometry and material models in the individual-specific model can still produce results that close to the experiment; 2) the experiment by Kosmorsky

81 et al. was the only experiment of chiasmal compression with quantitative measurements in the literature.

Kosmorsky et al. used only two pressure transducers, one located at the centre of the chiasm and the other at the periphery. Table 4.3 shows that the model’s results were close to the experimental data for cadaver No. 2. Kosmorsky et al. did not report the precise locations of their measurements, which leads to uncertainty in the appropriate peripheral values to use for the comparison.

Table 4.3 Comparison of the hydrostatic pressures predicted by the simulation and the averaged experimental measurements from Kosmorsky et al. (2008) (Unit: kPa)

Cadaver Cadaver Location Simulation No. 1 No. 2

Central 2.63 1.23 1.32

Peripheral 0.80 0 0.33

4.6.2 Results of the parametric studies

The outputs were chosen to be the linearised von Mises strain distribution on a cross- section of the chiasm, which is the same as in the baseline model as described in Figure

4.5 and corresponding text. Because there were variations in geometry, material properties or loading conditions in the parametric studies, the results were presented when the centre of the chiasm was elevated to around 5.56 mm which is the elevation in the baseline model. The exact elevation of the chiasm in each model may not be the same as in the baseline model due to the configuration changes in different scenarios. In cases where the elevation of the chiasm was not equal to 5.56 mm, the exact value was

82 indicated in the corresponding figure caption. The results of the baseline model were also plotted as a dotted line for reference.

4.6.2.1 Variation of the tumour growing direction

Figure 4.6 shows the von Mises strain distribution along the left-right orientation of the chiasm when tumour growth direction was roughly perpendicular to the chiasm. It can be seen that the trend of the strain distribution was still the same as in the baseline model, which indicates that the loading direction has limited influence on the strain distribution in this case.

0.15

0.1

0.05 von Mises strain

perpendicular baseline 0 -6 -4 -2 0 2 4 6 Location (mm) Figure 4.6 The average cross-sectional von Mises strain along the left-right orientation. The elevation of the chiasm was 5.27mm.

4.6.2.2 Variation of the tumour diameter

Figure 4.7 shows the von Mises strain distribution in the chiasmal cross-section with a larger tumour size. In Figure 4.7, the peak strain locations slightly moved peripherally with the increasing of tumour diameter. Although the peak strain values were close to the baseline model, the strains in the central part of the chiasm were lower than that of the baseline model.

0.15

0.1

0.05 von Mises strain

larger tumour baseline 0 -6 -4 -2 0 2 4 6 Location (mm)

Figure 4.7 The von Mises strain along the left-right orientation.

4.6.2.3 Variations of the loading site.

Figure 4.8 illustrates the von Mises strain distribution in the chiasmal cross-section when it was compressed laterally. It can be seen that the strain distribution changed significantly when the chiasm was not loaded centrally. As expected, the peak moved towards right compared to the baseline model.

0.2

0.15

0.1 von Mises strain 0.05 offset laterally baseline 0 -6 -4 -2 0 2 4 6 Location (mm)

Figure 4.8 Von Mises strain distribution along the left-right orientation. The elevation of the chiasm is 5.32 mm.

4.6.2.4 Varying the stiffness of pia mater

Figure 4.9 shows that a stiffer pial sheath resulted in higher strains in the chiasm, which is consistent with the results of the general model in Chapter 3. But the strain distribution pattern remains the same.

0.15

0.1

von Mises strain 0.05 1.5 baseline 0.5 0 -6 -4 -2 0 2 4 6 Location (mm)

4.6.2.5 Varying the stiffness of nerve tissue

Figure 4.10 shows the strain distribution in the chiasmal cross-section in models with different stiffness of the nerve tissue. As can be seen, a softer nerve tissue resulted in higher strains in the chiasm. As would be expected, changes of the stiffness of the nerve tissue only influenced the strain level but not the strain distribution trend.

0.15

0.1 von Mises strain 0.05 0.5 baseline 2 0 -6 -4 -2 0 2 4 6 Location (mm)

4.6.2.6 Varying the stiffness of the tumour

Figure 4.11 shows that the strain distribution pattern changed in the model with a new tumour.

0.15

0.1

0.05 von Mises strain

soft tumour baseline 0 -6 -4 -2 0 2 4 6 Location (mm)

Figure 4.11 Von Mises strain distribution in the chiasm. The elevation of the chiasm is 5.10 mm. The dotted line shows the results of the baseline model.

The tumour stiffness could change the interaction behaviours between the tumour and the chiasm and thus influence the strain distributions in the optic chiasm. Because the pial sheath is much stiffer than the softer tumour, the tumour tends to deform to accommodate the outline geometry of the optic chiasm (Figure 4.12). The deformed tumour tends to elevate the chiasm more evenly across left-right orientation and thus cause a more even strain distribution compared with the baseline model (the deformed baseline model was illustrated in Figure 4.4).

It can be seen from the MRI scan in Figure 4.4 that the chiasm was forced to deform to comply with the curved surface of the tumour, which is different from what was observed in the softer tumour model shown in Figure 4.12. This indicates that the softer tumour model might not represent the real in vivo interaction of the chiasm and the tumour properly. For this reason, the subsequent chapters will still use a balloon to represent the tumour.

6.34 5.57 4.78 3.99 0 6.76 5.97 5.18 4.39 3.60

Figure 4.12 Contour plot of the vertical elevation of a cross-section of the model (unit: mm).

4.6.2.7 Effects of the elevation of chiasm

Figure 4.13 shows the von Mises strain distribution at various elevation levels. The strain differences between the central part and the peripheral part of the chiasm become

87 larger as the elevation increasing. However, strain distributions show a similar pattern at various elevation levels.

0.45 9.27 mm 5.56 mm 0.4 3.07 mm 0.35

0.3

0.25

0.2

von Mises strain 0.15

0.1

0.05

0 -6 -4 -2 0 2 4 6 Location (mm)

Figure 4.13 von Mises strain on different loading steps.

4.7 Discussion

Table 4.3 shows that the model’s simulation results were close to the experimental data of Kosmorsky et al.’s cadaver No. 2 (Kosmorsky et al., 2008). In the simulation, the chiasm was elevated to 5.56 mm as this degree of elevation has been shown to cause bitemporal hemianopia (Ikeda and Yoshimoto, 1995). Unfortunately, the degree of elevation of the chiasm was not measured in the experiment performed by Kosmorsky et. al. (2008) (personal communication with the authors). From the volume data reported, cadaver No.1 appears to have a much larger elevation compared to cadaver

No.2. This may explain why the results of the simulation agree closely with the

88 measurements from one cadaver but less closely with those of the other one (see Table

4.3). Nevertheless, the pattern of pressure distribution was nominally the same, i.e. the central aspect of the chiasm bore significantly higher pressure than the peripheral aspect of the chiasm. As material properties and the geometry of human chiasms vary between individuals and, considering the difficulties of performing experiment in vivo, it is believed that the simulation is a good approximation to what happens in vivo.

Sensitivity studies were however performed to quantify the dependence of the results on the uncertain input parameters in this complex system.

Generally, the strain at the central part of the chiasm was higher than that at the peripheral aspect. These results were similar to that in the generic model of Chapter 3.

However, the maximum strain was not located in centre of the chiasm (Figure 4.5) which is different from the results of Chapter 3. In the chiasm of this chapter, the paracentral part of the chiasm is thicker than the central part. The thicker part will be squeezed more and thus results in higher strain at that part, which could explain the strain distribution in Figure 4.5.

Variations of several parameters in the model resulted in different strain distributions in the chiasm. Material properties were found to have minimal influence on the strain trend in the chiasm. As expected, loading location has a significant influence on the strain distribution which is consistent with the model in Chapter 3.

Parametric study showed that the tumour stiffness affects the strain distributions significantly because it affected the interactions between tumour and the chiasm and thus resulted in a different deformation pattern of the chiasm. It should be noted that the

89 softer tumour in the parametric study might not well represent the in vivo situation as discussed above.

The strain distribution is mainly relying on the final deformation state of the chiasm which is determined by many factors such as the tumour growth patterns, tumour location and stiffness of the tissue involved etc. These parameters have yet to be investigated in more details in future studies.

The results of the individual-specific model in this chapter will be used as input loading in Chapter 5 and Chapter 6 for the analyse of nerve fibre biomechanics.

Chapter 5

Microscopic nerve fibre model using multi-scale analysis

In the chiasmal model, it is reasonable to assume that the chiasm tissues are macroscopically homogeneous (Post et al., 2012; Sigal et al., 2009). However, at the cellular level, the fibre arrangements vary in different locations. Therefore, it is essential to take the fibre-packing pattern into account when investigating the behaviour of individual nerve fibres. In Chapter 3, the nerve fibre models were built to investigate the crossed and uncrossed nerve fibres. However, there was no direct transition of deformation from the macroscopic chiasm model to the nerve fibre models.

In this chapter, a multi-scale procedure was adopted to link the macroscopic chiasmal model and the microscopic nerve fibre models. Representative volume elements (RVE) were used to represent both the crossed and uncrossed configurations of the nerve fibres in the chiasm. The outputs of the macroscopic chiasmal model in Chapter 4 were used as inputs for the RVEs.

5.1 Multi-scale approach using finite element modelling

In composite materials research, the multi-scale analysis has often been used to determine the overall material properties of the composite materials from the known mechanical properties of its constituents (Kabele, 2007; Naik et al., 2008; Xia et al.,

2003). This method can also provide the local strain/stress distribution within each constituent. Recently, multi-scale analysis was used to investigate the brain white matter

91 properties (Abolfathi et al., 2009; Karami et al., 2009) and traumatic brain injury on axonal level (Cloots et al., 2011; Wright and Ramesh, 2012).

In this method, the tissues involved were assumed to be macroscopically sufficiently homogeneous, but microscopically heterogeneous. It is assumed that, in a small region of material in the macroscopic model, the material can be formed by spatially repeated

RVEs. In this chapter, the mechanical loads representing the macroscopic level deformation have been applied on the RVEs as boundary conditions.

5.2 Nerve fibre model

5.2.1 Geometry

The optic pathway belongs to the central nervous system (CNS). Therefore, the nerve fibres in the optic chiasm should have a similar structure as other fibres in the CNS. In the CNS, the axons are wrapped by myelin sheaths, which are produced by oligodendrocytes (Figure 5.1). Figure 5.1 also shows a scanning electron micrograph

(SEM) of optic nerve fibres. A single oligodendrocyte may myelinate up to 50 axons in separate myelin sheaths (Standring, 2008). Myelinated segments are separated by the node of Ranvier. The presence of the insulating myelin sheath forces the electrical impulse to “jump” between nodes and thus speeds the rate of transmission along the axon (Appendix D).

The thickness of the myelin sheath is usually indicated by the g-ratio which is the ratio of the axonal diameter divided by the diameter of the nerve fibre (axon plus its myelin sheath). This ratio is usually between 0.6 and 0.8 with interspecies variation (Guy et al.,

1989; Sherman and Brophy, 2005). It has been reported that the value of g-ratio is constant in any given animal: bigger axons thus have thicker myelin sheaths (Sherman 92 and Brophy, 2005). However, differences of g-ratio between fibres in the same animal body were reported as well (Berthold et al., 1983; Fields, 2008).

An axon, as part of the nerve cell, has a complex structure (Ouyang et al., 2010) but the detailed structure of an axon was not included in the model and it was beyond the scope of this thesis. In this work the axon was considered to be homogenous based on previous study (Abolfathi et al., 2009).

Figure has been removed due to Copyright restrictions.

(a) Figure 3.42 in reference (Standring, 2008)

(b) http://www.sciencephoto.com/media/442847/view#

An RVE should be able to capture the major features of the underlying microstructure of the macroscopic model and can repeat itself to form the larger-scale structure

(Ghanbari and Naghdabadi, 2009). The RVEs for the crossed and uncrossed nerve fibres in this work are shown in Figure 5.2.

At a nerve fibre scale, it was assumed that the temporal uncrossed nerve fibres were aligned in parallel, whereas the nasal nerve fibres crossed each other perpendicularly

(Figure 5.2). The micro-scale RVE models were developed based on these two types of nerve fibre packing. An individual nerve fibre was considered to be circular in cross- section and to consist of an axon surrounded by a myelin sheath. In the optic nerve, the nerve fibres contact each other directly (Sandell and Peters, 2002) (Figure 5.1b). The space between the nerve fibres is the extracellular space. Hereafter the abbreviation

MECS (Material of the Extra-Cellular Space) will be used to refer to the material occupying this space.

For simplicity, the diameter of nerve fibres was taken to be 1.35 μm based on measurements of nerve fibre area reported in the literature (Jonas et al., 1990). The g- ratio (axon diameter/total fibre diameter) was assumed to be 0.8 (Guy et al., 1989;

Sherman and Brophy, 2005). The effect of g-ratio value on the output of the model will be reported later in this chapter.

ON x Crossed nerve fibres x1 2

Uncrossed nerve fibres 1 μm 1 μm Macroscale(whole optic chiasm) Microscale(nerve fibres) RVEs

Figure 5.2 The macroscopic model of the optic chiasm and tumour and the microscopic RVE models. OC: optic chiasm; ON: optic nerve; OT: optic tract.

5.2.2 Material properties

There is little information of the material properties of each constituent in the RVEs.

Myelin sheaths are formed by oligodendrocytes, one of the several types of glial cell in the CNS. Astrocytes are another type of glial cell. Previous studies have shown that glial cells are softer than axons by a factor of 2 to 3 (Arbogast and Margulies, 1999; Lu et al., 2006; Shreiber et al., 2009).

For simplicity, the material properties of axons were considered to be the same as those used for the nerve tissue in the macroscopic chiasmal model, and a three times softer material stiffness model was used for the myelin sheath (Table 5.1).

The glial matrix, comprising the cell bodies of astrocytes and oligodendrocytes, is the main substance in the optic nerve tissue other than axons and myelin sheaths. However, the cell bodies of astrocytes and oligodendrocytes are large compared to axons so they tend to occupy the space outside a bundle of nerve fibres, i.e., they would be unlikely to be present in the extracellular space between nerve fibres in the RVE models. Therefore, it was assumed that the extracellular space is mostly filled by fluid-like material, specifically modelling it as a soft material, which was nearly incompressible with a very low shear modulus. For simplicity, the material constants of MECS were directly modified from those of the axons to generate a material approximately as soft as the cerebrospinal fluid (Chafi et al., 2009). All the material constants are reported in Table

5.1.

Table 5.1 Ogden hyperelastic constants used in the RVE models

Tissue (Pa) (Pa)

1 Axon 휇1044.01 휇1183.02 4.309훼1 7.736훼2 Myelin sheath2 348.0 394.3 4.309 7.736 MECS3 52.2 59.2 4.309 7.736 1Franceschini (2006) 2modified to be 1/3 the stiffness of the axon material model 3modified to be 1/20 the stiffness of the axon material model

5.2.3 Boundary conditions applied to RVEs

The strain vector of a point in the central part of the chiasm, when elevated inferiorly- superiorly to 5.56 mm in Chapter 5, was applied to the RVEs (Figure 5.2). The assumed orientation of the crossed and uncrossed nerve fibres were illustrated in Figure 5.3.

Crossed Uncrossed

Figure 5.3 Location of the strain point and orientations of the crossed and uncrossed nerve fibres.

RVEs can be stacked together in rows and columns to form the actual structure at the macro level as shown in Figure 5.2. Therefore, periodic boundary conditions must be applied to the RVE models to insure that there is no overlap or separation between neighbouring RVEs after deformation.

Xia et al. (2003) developed a periodic boundary condition for RVEs which can easily be used in FEM analysis. The displacements of the boundary surfaces of a RVE are given by:

= + (1) ∗ 푢푖 휀푖̅ �푥푘 푢푖 where is the Cartesian coordinate of a point, is the average strain and is the ∗ 푘 푖� 푖 periodic푥 part of the displacement on the boundary휀 faces̅ which is unknown. Considering푢 two opposite faces with their normal along the axis (Figure 5.2), the displacements

� on these two faces can be written as: 푥

= + (2) �+ �+ ∗�+ 푢푖 휀푖̅ �푥푘 푢푖 = + (3) �− �− ∗�− 푢푖 휀푖̅ �푥푘 푢푖 where refers to the positive direction and refers to the negative direction. + − 푗 푥� 푗 푥� As opposite faces in the deformed RVE should have the same shape so that they can repeat to form a continuous body, the local fluctuations and must be identical ∗�+ ∗�− 푖 푖 on these two faces. Therefore, the relative displacement 푢between these푢 two faces is:

= = (4) �+ �− �+ �− � 푢푖 − 푢푖 휀푖̅ ��푥푘 − 푥푘 � 휀푖̅ �∆푥푘 where is the average strain which is obtained from the macroscopic model and � 푖� 푘 are known휀̅ from the geometry of the RVE. ∆푥

Equation (4) can be applied to the RVE using constraint equations in ANSYS. In order to apply these constraint equations, the mesh on the opposite faces of the RVE has to be identical. This was achieved by meshing one face first and then copying this mesh to the

97 corresponding opposite face. Because there were many nodes, the ANSYS Parametric

Design Language (APDL) was used to find each node pair and impose corresponding constraint equations on them. The corresponding APDL script can be found in

Appendix E. The node at one corner of the model was fixed to avoid rigid body motion.

As large deflection analysis was used, to help convergence, dummy nodes in ANSYS were used to allow the deformation applied to the RVE to increase gradually.

Using the procedures described above, strain loads from the macro-scale model were imposed on the RVE, which allowed transition of the actual strains from the macroscopic deformation field to the micro level. It is acknowledged that the loading transition was one-way in this initial study, i.e., only the outputs of the macroscopic model were applied to the microscopic model. Two-way multi-scale analysis could be performed in future studies which will be discussed in Chapter 8.

5.2.4 Simulations

The interface behaviour of the three materials in the RVE models is an important parameter that influences the mechanical response. Based on previous studies (Arbogast and Margulies, 1999; Cloots et al., 2012), it was assumed that there was no slip or separation at the interfaces of different materials, i.e., all the materials were assumed to be fully compatible at their interfaces.

Tetrahedral higher order elements (SOLID187 in ANSYS) were used to mesh the model.

The mesh density was verified to be fine enough to provide reasonable results

(Appendix C.3).

5.2.5 Output measurements

In the RVE model simulations, both the von Mises strain and the strain value along the axonal direction (axonal strain) were reported as the later has been argued to be a better measure of axonal injury in brain white matter (Cloots et al., 2011; Wright and Ramesh,

2012) although whether this is the case in the chiasm is unclear. As the myelin sheath plays an important role in the failure of conduction of nerve fibres (LaPlaca et al., 2007;

Shi and Pryor, 2002), the strain status in axons and myelin sheaths were reported separately.

5.2.6 Results

Figure 5.4a shows the von Mises strain field of the axons and sheaths in both crossed and uncrossed RVE models. It can be seen that the strain distribution patterns were very different. The maximum von Mises strain in the crossed model was higher than the uniform level in the uncrossed model.

By performing an in vivo study of the guinea pig optic nerve, Bain was able to define an axonal strain threshold of 0.06 to cause functional nerve injury at an axonal level (Bain,

1998). The axonal strains in the simulations were compared with this threshold and the injury and non-injury regions in the nerve fibres are plotted in different colours in

Figure 5.4b. In general, as expected, some part of the crossed nerve fibres were functionally injured while the uncrossed nerve fibres were relatively unaffected.

0.1828 0.1676 0.1523 0.1371 0.1218 0.1066 0.0913 0.0761 0.0608 (a) 0.0456

injuried (b) uninjured

Figure 5.4 (a) The von Mises strain distribution in RVEs. (b) The injury and non-injury regions in the nerve fibres based on strain in the axonal direction.

) 0.1 0.09 0.14 0.08 0.12 0.07

(mm/mm 0.1 0.06 0.05 0.08 strain (mm/mm) strain strain strain 0.04 0.06 0.03 Crossed_Axon_1 0.04 Crossed_Sheath_1

Crossed_Axon_2 Mises Mises 0.02 Crossed_Sheath_2 Uncrossed_Axon_1 0.01 on 0.02 Uncrossed_Sheath_1 V Von Von 0 0 0 0.5 1 0 0.5 1 (a) The location along the nerve fibre segment (μm) (b) The location along the nerve fibre segment (μm)

0.07

) 0.07 ) 0.06 0.06 0.05 0.05

(mm/mm 0.04 0.04 0.03 0.03 strain strain strain (mm/mm strain Crossed_Sheath_1 0.02 Crossed_Axon_1 0.02 Crossed_Axon_2 Crossed_Sheath_2 0.01 0.01 Uncrossed_Sheath_1

Axonal Uncrossed_Axon_1 Axonal 0 0 (c) 0 0.5 1 0 0.5 1 The location along the nerve fibre segment (μm) (d) The location along the nerve fibre segment (μm)

Figure 5.5 The average cross-sectional (a,b) von Mises strain and (c,d) axonal strain distribution of the axons and myelin sheaths as a function of the location along the nerve fibre.

‘crossed_sheath_1’ in the legend means the ‘myelin sheath’ in the ‘crossed mode at the ‘x1 direction’ according to Figure 5.2.

100

In Figure 5.5, the average von Mises strains and axonal strains of the cross-sections (i.e. sections with their normal along the nerve fibre length) of the axons and the myelin sheaths were plotted along the nerve fibre length. It can be seen that, under the same loading conditions, the strain distribution in crossed nerve fibres was more non-uniform and some parts of the crossed nerve fibres experienced higher strains than the uncrossed fibres. It should be noted that some parts of the crossed nerve fibres experienced lower strains than the uncrossed fibre as can be seen in Figure 5.5. However, the crossed fibre will still be damaged first because the damage to only a small section of a nerve fibre will totally shut down its signal transmission.

5.3 Sensitivity study of the RVE model using design of experiments

It can be seen from the results above that the differences of strain distributions along the fibres in crossed and uncrossed models were quite significant. The crossed nerve fibres experienced a higher local strain than the uncrossed fibres. This indicates that the crossing angle of nerve fibres is a significant factor that influences the strain distribution in the nerve fibres. However, the results were based on the assumed g-ratio, cross- sectional shape, material stiffness etc. Unfortunately, the data necessary to populate the various parameters used in the microscopic nerve fibre model are scarce in the literature and, even when these parameters are reported, the values can vary considerably from study to study. It is unclear whether the crossing angle will remain as a significant factor with the variation of other factors. Accordingly, this section investigated the sensitivity of the RVE models to variations of their material properties and geometry.

A Design of Experiments (DOE) approach was used to investigate the impact of uncertainties of these factors on the outputs, or responses, of the RVE model. DOE is an

101 established tool which permits better understanding and control of variability in engineering. There has been a recent increase in interest in using DOE for sensitivity analysis in biomechanics (Malandrino et al., 2009; Shen et al., 2008; Yao et al., 2008).

In particular, DOE provides information about the effects of possible interactions between factors, something that is not obtainable when testing one factor at a time

(OFAT).

5.3.1 Design of experiments

A five-factor two-value, or two-level, full factorial analysis was designed to investigate the effect of five parameters in the RVE model systematically. Full factorial analysis was used to allow examination of the effects of individual factors and all possible interactions of those factors. The five factors and their levels are listed in Table 5.2. The definition of these factors will be introduced later. The high and low levels of a given factor were based on a reasonable range derived from data reported in the literature.

Table 5.3 shows the design matrix that reflects all possible combinations of high and low levels for each factor. The high and low levels of each factor were coded as +1 and

-1, respectively. A total of 32 (25) simulations were performed based on the configurations in Table 5.3 using ANSYS, and the simulation responses were then processed using Minitab, which is a widely used statistics package (Version 15, State

College, PA).

Two cross-sectional shapes were chosen as either a circle or a round-cornered square.

These geometries were based on the microscopic appearance of nerve fibres within the optic nerve. Both shapes had the same cross-sectional area which was based on the nerve fibre area quoted in the literature (Jonas et al., 1990). Note that the change of

102 cross-sectional shape necessarily resulted in a change in the volume fraction of nerve fibres (i.e. volume of fibres / total volume of the RVE). Fibre fractions for the circular and round-cornered square cross-sections were 78.5% and 90%, respectively. Of note,

90% is believed to be the average fibre fraction in the optic nerve (Arbogast and

Margulies, 1999).

For mammals, the g-ratio usually varies between 0.6 and 0.8 (Guy et al., 1989; Sherman and Brophy, 2005). In this paper, the g-ratio for nerve fibre with a round-cornered square cross-section was calculated as the horizontal width (see figure in Table 5.2) of the axon divided by the width of the nerve fibre.

According to the literature, the stiffness of the myelin sheath is two to three times softer than the axon (Arbogast and Margulies, 1999; Lu et al., 2006; Shreiber et al., 2009). All material properties were modified from those of the axon. The material properties of the axon were list in Table 5.1.

Table 5.2 Factors and their levels of the DOE study

Factor Factor name Low level (-1) High level (1)

A Cross-sectional shape

Round-cornered square Circle B g-ratio 0.6 0.8 1/3 1/2 C Sheath stiffness (of the axon) (of the axon) 1/20 1/10 D MECS stiffness (of the axon) (of the axon) E Crossing angle 0 ˚ (parallel) 90 ˚ (perpendicular)

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Table 5.3 Design of the DOE simulations

Cross- Sheath Matrix Simulation Crossing sectional g-ratio (B) stiffness stiffness No. angle (E) shape (A) (C) (D) 1 -1 -1 -1 -1 -1 2 1 -1 -1 -1 -1 3 -1 1 -1 -1 -1 4 1 1 -1 -1 -1 5 -1 -1 1 -1 -1 6 1 -1 1 -1 -1 7 -1 1 1 -1 -1 8 1 1 1 -1 -1 9 -1 -1 -1 1 -1 10 1 -1 -1 1 -1 11 -1 1 -1 1 -1 12 1 1 -1 1 -1 13 -1 -1 1 1 -1 14 1 -1 1 1 -1 15 -1 1 1 1 -1 16 1 1 1 1 -1 17 -1 -1 -1 -1 1 18 1 -1 -1 -1 1 19 -1 1 -1 -1 1 20 1 1 -1 -1 1 21 -1 -1 1 -1 1 22 1 -1 1 -1 1 23 -1 1 1 -1 1 24 1 1 1 -1 1 25 -1 -1 -1 1 1 26 1 -1 -1 1 1 27 -1 1 -1 1 1 28 1 1 -1 1 1 29 -1 -1 1 1 1 30 1 -1 1 1 1 31 -1 1 1 1 1 32 1 1 1 1 1

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5.3.2 Analysing DOE results

Responses of the model include the von Mises strain and the axonal strain in both the axon and its myelin sheath as described above. In the baseline model, only the cross- sectional average strains were reported. However, the mechanism of nerve failure due to mechanical strain is still unclear. Therefore, in this parametric study, the maximum strains were reported as well. It is assumed that these two types of strain may both have potential correlations with nerve failure. Accordingly, the responses were divided into two categories: the maximum strain and the maximum cross-sectional average strain.

The outputs and their abbreviation were listed in the Table 5.4.

Table 5.4 Simulation responses and their abbreviations

Strain Parts Output description Abbreviation type Maximum cross- von sectional average von M_CS_VON-A Maximum Mises Strain of the axon Cross- Maximum cross- sectional sectional average Average Axonal M_CS_AXONAL-A Axon axonal strain of the axon von Maximum von Strain M_VON-A Maximum Mises of the axon point Maximum axonal Axonal M_AXONAL-A strain of the axon Maximum cross- von sectional average von M_CS_VON-S Maximum Mises Strain of the sheath Cross- Maximum cross- sectional sectional average Average Axonal M_CS_AXONAL-S Sheath axonal strain of the sheath von Maximum von Strain M_VON-S Maximum Mises of the sheath point Maximum axonal Axonal M_AXONAL-S strain of the sheath

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The effects for individual and coupled variables were analysed using Pareto charts in

Minitab. The effect of an individual variable is called a main effect and the effect of coupled variables is the interaction effect. Figure 5.6 and Figure 5.7 show the statistically significant factors (95% confidence level) for various strain responses, which were determined by the method of Lenth (1989) in Minitab. The horizontal bars represent the effects of individual factors or interaction of these factors. Because one numerical simulation yields only one set of results, there are no replicates which are necessary to evaluate error in physical experiments. Lenth’s method is specially designed for the study of numerical simulations to overcome this issue.

It can be seen from Figure 5.6 that crossing angle was ranked as either the first or the second most significant factor for these four cross-sectional average outputs. Crossing angle was 0.21% and 4.52% less significant than the g-ratio for two outputs

(M_CS_VON-A and M_CS_VON-S). However, for an individual person, the g-ratio will vary only slightly, or even remain constant (Sherman and Brophy, 2005). It can be therefore concluded that, for any given g-ratio, the crossing angle is the most significant factor that affects a wide range of outputs of the model.

Figure 5.7 shows that among the four responses, two (M_AXONAL-A, M_AXONAL-S) were predominantly affected by the crossing angle. For these responses, the effect of crossing angle was 472% and 240% greater than that of the second most important factor, respectively. For the remaining two responses (M_VON-A, M_VON-S), crossing angle was ranked as the second most significant factor, which was 8.2% and

51.2% less significant than the most significant factors, respectively. For M_VON-S, g- ratio was the most significant factor while MECS stiffness was the most significant response for M_VON-A.

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response: M_CS_VON-A response: M_CS_AXONAL-A B E E A D AE DE A D BD C

DE CE AC ADE AE AD

Term AB BE B C BDE CD BD CE ABE ADE AB ABE BCE BE BC 0 0.002 0.004 0.006 0 0.002 0.004 0.006 0.008 0.01 Effect Effect response: M_CS_VON-S response: M_CS_AXONAL-S B E AE E A D B A BE AE C CE C ADE BD AD

Term BE DE D ADE ABDE AC ABD CE AC ACE AB ACD DE ACDE 0 0.004 0.008 0.012 0.016 0 0.005 0.01 0.015 Effect Effect

Figure 5.6 Comparison of the relative sensitivities of maximum cross-sectional average strains of the model to the input parameters and their combinations. A: cross-sectional shape; B: g-ratio; C: sheath stiffness; D: MECS stiffness; E: crossing angle. Only the statistically significant effects are shown.

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response: M_VON-A response: M_AXONAL-A D E E A B AE A AD AD B AE C DE CE Term BE DE BD ABD AB ADE ADE ABDE ABD D 0 0.005 0.01 0 0.005 0.01 0.015 Effect Effect

response: M_VON-S response: M_AXONAL-S

B E E C

A CE

Term D DE BC D AB A

0 0.01 0.02 0.03 0 0.01 0.02 0.03 Effect Effect

5.4 A new nerve fibre-packing pattern of uncrossed fibres

In the DOE study, five parameters were varied based on the baseline model. The nerve fibre volume fraction was the same for crossed and uncrossed models. However, the uncrossed RVE in the baseline model reflects only one possible packing pattern of the uncrossed nerve fibres. In this section, a new model was built to further investigate the effects of possible nerve fibre patterns on the biomechanics of uncrossed nerve fibres in

108 the optic chiasm. Note that the actual packing patterns of nerve fibres are complicated due to variations of nerve fibre size and shape.

The new uncrossed RVE model used a hexagonal fibre-packing as illustrated in Figure

5.8. Note that the hexagonal packing method has different volume fraction of nerve fibres. Fibre fractions for the baseline model and the new model were 78.5% and 90.7% respectively. The same deformations as in the baseline model were applied on this model.

New uncrossed RVE Baseline uncrossed RVE

Figure 5.8 (a) The hexagonal packing compared with (b) the square packing in baseline model.

The maximum cross-sectional average von Mises strains of the new model are listed in

Table 5.5. The corresponding results of the baseline crossed and uncrossed models are also included in Table 5.5 for comparison.

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Table 5.5 Comparison of the strains in various models.

Uncrossed Uncrossed Crossed Component (Hexagonal (baseline – square (baseline) packing) packing)

Axon 0.085 0.087 0.096

Sheath 0.134 0.119 0.143

It can be seen from Table 5.5 that the fibre packing patterns has substantial influence on the strain values in the myelin sheath but not in the axon. The strain in the sheath of the hexagonal packing uncrossed model was close to the crossed model but the crossed model always has a much more non-uniform strain distribution because of the strain concentration in crossed nerve fibres. In composite materials, the volume fraction of the fibres is an extremely important factor that influences the mechanical behaviours of the composite. The differences of the volume fractions of these models may make it inappropriate to compare their results directly without considering the influence of the fibre volume fraction. Nonetheless, both the hexagonal and square packing patterns possibly exist in the optic chiasm.

5.5 Discussion

The numerical results showed that the distributions of both the von Mises strain and the axonal strain in the crossed nerve fibres were much more non-uniform than those in the uncrossed nerve fibres. Furthermore, the crossed nerve fibres experienced a higher local strain than the uncrossed fibres, which may explain the failure of crossed nerve fibres while uncrossed nerve fibres are still functioning as a single point failure can shut down

110 the whole nerve fibre. The different strain distributions in crossed and uncrossed nerve fibres might explain the vertical cutoff of the visual field defect in bitemporal hemianopia.

It should be pointed out that the strain applied on the crossed and uncrossed RVE models was the same, using a value which was extracted from the central part of the chiasm. Given that the central part of the chiasm generally experiences higher strains than the peripheral part, even greater differences of strain distribution should exist in some of the nasal and temporal nerve fibres as the crossing nasal fibres tend to pass through the central region of the chiasm while the uncrossed temporal fibres pass further to the periphery. The detailed nerve fibre distribution patterns in the chiasm and its effect on the strain distributions in the nerve fibres will be investigated later in

Chapter 6.

Ideally, the RVE models should be validated by experiments. However, the paucity of experimental data of nerve compression on axonal scale has made the validation of the

RVE model infeasible. It requires very specialist resources to perform a nerve fibre interaction experiment and these resources were not available for this work. Instead, the techniques used in the RVE models were tested via application to another analogous problem, albeit not in soft tissue. Specifically, the software and procedure in this research were applied to model a composite woven structure reported in the literature

(Wang et al., 2007) and found to successfully reproduce the results reported in the reference (Appendix F).

The complex nature of the human nervous system poses a significant challenge to the understanding of the mechanism of nerve failure. Although the exact mechanism of

111 conduction failure of axons is still not well understood as discussed in Chapter 2, the von Mises strain and axonal strain reported in this chapter have been shown to be highly relevant to functional nerve injury (Chatelin et al., 2011; Cloots et al., 2011; Ouyang et al., 2008). The absolute values of axonal strain obtained in the simulations were similar to the strain threshold of axonal dysfunction found by Bain (1998). However, given the complexity of this biological system, the actual threshold for axonal functional injury may vary widely among individuals. Therefore, it should be noted that the threshold used here is only indicative of the potential consequences of the strain differences in crossed and uncrossed nerve fibres. Higher fidelity modelling will be rquired to draw more accurate quantitative conclusions on this injury mechanism.

The effect of varying five parameters of the nerve fibre model was systematically analysed using DOE. The results indicated that crossing angle was the leading factor influencing all the responses of the model. It should be noted that the range of variation of the g-ratio and the stiffness of materials in this sensitivity study were based on the ranges reported in the literature derived from different animals. However, for an individual person, the g-ratio will vary only slightly, or even remain constant (Sherman and Brophy, 2005). In other words, a large variation of g-ratio from 0.6 to 0.8 would be unlikely to occur in a single optic chiasm. Similarly, the MECS stiffness would be likely to remain fairly constant in a single individual.

It can be concluded that, for any given g-ratio and MECS stiffness, the crossing angle is the most significant factor that affects a wide range of responses of the model.

Furthermore, the crossed models have nonuniform strain distribution along the nerve fibre length as illustrated in Figure 5.5, which may have potential effect on the nerve

112 function (Povlishock, 1993). Thus, the strain difference between crossed and uncrossed nerve fibres may well account for the phenomenon of bitemporal hemianopia.

Interestingly, compared to the crossing angle and g-ratio, cross-sectional shape was not a very significant factor though it should be noted that only two cross-sections were considered in the DOE study. In reality, the actual cross-sectional geometry of nerve fibres is significantly more complicated than the two regular shapes used in this study.

Patterns of fibre organization at microscopic scale are still not clear in the human chiasm. In the nerve fibre models, it was assumed that the nerve fibres were running separately. However, nerve fibres in the central chiasm may cross in bundles (Neveu et al., 2006; Neveu and Jeffery, 2007). It is speculated that the crossing bundles would bear larger local strains than the parallel bundles. However, it would be interesting to model the crossing bundles when the related anatomical data is available in the future.

It should be pointed out that, in this study, fibre orientation and the location of macroscopic strain were fixed, as in Figure 5.3. The effect of altering orientation in the

RVE models was not considered. A greater understanding of the microstructure of the optic chiasm is needed in order to determine the actual orientation of the nerve fibres within the chiasm, which will be performed in Chapter 6.

All the assumptions of the material properties in the RVE model have made the overall material properties of the nerve tissue in the RVE softer than the nerve tissue used at the macroscopic level. Given that the RVE models were mainly used to study the different behaviours of the crossed and uncrossed nerve fibres and the difficulties of getting material properties of each substance in the literature, it is reasonable to use these simple methods to obtain the material properties for this preliminary study. In addition,

113 this work highlights the need for more accurate information about the material properties of the constituents used in the model.

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Chapter 6

Axonal trajectory in the optic chiasm and its influences on the strain distribution in nerve fibres

It is widely acknowledged that nasal nerve fibres cross over in the optic chiasm to enter the contralateral optic tract as discussed in Chapter 1. However, the fibre crossing angles and the locations of crossed and uncrossed nerve fibres are still unclear.

In chapter 5, due to lack of nerve fibre distribution information, only the strain vector of one point in the macroscopic chiasmal model was applied to the RVE models to investigate the influences of fibre packing patterns on the strain distribution in the nerve fibres. In reality, nerve fibres pass through the chiasm in different locations with varying patterns of organization. Therefore, the distribution of the optic nerve fibres in the optic chiasm needs to be investigated to aid further understanding the optic nerve fibre behaviours. Furthermore, the knowledge of the fibre routing in the chiasm will also lay the groundwork for including the anisotropic behaviours of the chiasmal tissue in future studies. This work also adds more details to our knowledge of the anatomy of the human optic chiasm.

This chapter firstly reviews the nerve fibre organization in the literature. Then a human optic chiasm obtained from post-mortem was sliced and the nerve fibre orientation in the chiasm was studied using photomicrographic image analysis. The crossing angles and locations were then applied to the microscopic RVE models to investigate the strain distributions in nerve fibres.

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6.1 The patterns of nerve fibre organization in the chiasm

As described in Chapter 1, the nasal nerve fibres cross over in the optic chiasm and enter the contralateral brain whereas the temporal fibres pass directly backwards to the ipsilateral brain. This is now universally accepted, however, there is little information on the detailed nerve fibre distributions in the optic chiasm and the results in the literature remain controversial.

It is believed that, in general, temporal nerve fibres travel in a parallel pattern and stay laterally as they pass through the chiasm. In order to understand the nerve fibre route in human, Hoyt and Luis (1962, 1963) performed experiments using Java macaque monkeys whose eye, optic nerve, chiasm, and tract are very similar to those of the human. In their experiment, specific retinal lesions were produced and the subsequent nerve fibre degeneration in sections of the optic nerves, chiasm, and optic tracts were observed under a microscope. Macular and extramacular nerve fibres were investigated separately. The routes of extramacular nerve fibres in the optic nerve, chiasm and tract were illustrated in Figure 6.1. Macular fibres were mixed with extramacular fibres in the chiasm (Figure 6.2). It can be seen that temporal (uncrossed) nerve fibres were located laterally in the chiasm. For the nasal (crossed) fibres, the superior nasal quadrant fibres remain superior and cross through the posterior portion of the chiasm and the inferior nasal quadrant fibres pass through the anterior inferior portion of the chiasm.

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Figure has been removed due to Copyright restrictions.

See Figure 4 and 8 in reference (Hoyt and Luis, 1962)

Figure 6.1 Schematic diagram of (a) uncrossed and (b) crossed extramacular fibres through the optic nerve, chiasm and tract (Hoyt and Luis, 1962).

Figure has been removed due to Copyright restrictions.

See Figure 18 in reference (Hoyt and Luis, 1963)

Figure 6.2 Schematic diagram of crossed and uncrossed macular fibres through the primate chiasm (Hoyt and Luis, 1963). ON: optic nerve; OT: optic tract.

Neveu et al. investigated the human optic nerve fibre route using microscopic images of chiasmal slices and demonstrated that about 35-45% of the hemi-chiasm was occupied

117 by temporally placed axons, which were the temporal fibres (Neveu et al., 2006). Figure

6.3 shows the image of a horizontal silver-stained section of the human optic chiasm from Neveu et al. (2006). The microstructure at various location of the chiasm is shown in Figure 6.3. However, the microscopic images only covered a small region of the chiasmal slice so it can only reflect the nerve fibre distribution in a limited area and thus cannot depict the whole picture of the nerve fibre routes in the optic chiasm.

118

Neveu et al. also found that the nerve fibres in the prechiasmatic region were grouped as fascicles but the fascicles were absent in the chiasm (Neveu et al., 2006). Even though the axon distribution patterns in the central and peripheral chiasm were very different, there was no ‘barrier’ or other structure that clearly separates the crossed fibre region and the uncrossed fibre region (Neveu et al., 2006).

Roebroeck et al. (2008) demonstrated that the complex fibre configurations (potential crossing, sharp curves etc.) were mainly located in the central aspect of the chiasm using ultra high field diffusion tensor imaging (DTI). However, their fibre tracking method only recognized a small amount of the crossed fibres (Figure 6.4). Generally, fibres connecting between optic nerve and ipsilateral optic tract (uncrossed fibres) were overrepresented but the fibres from optic nerve to contralateral optic tracts (crossed fibres) were underrepresented. In Figure 6.4, the right column shows the results of tracing fibres between two optic nerves and two optic tracts. The fibres connecting both optic nerves that should not exist in reality were tracked in considerable numbers. There might be a small amount of nerve fibres connecting two optic tracts (Roebroeck et al.,

2008) but these fibres were overrepresented in Figure 6.4.

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Several other researchers (Sarlls and Pierpaoli, 2009; Yamada et al., 2008) also examined the fibre direction in the optic chiasm using DTI. However, similar to the results of Roebroeck et al. (2008), these results were dependent on the algorithms used to track the fibres and were thus error-prone because DTI cannot image multiple fibre orientations directly.

In 1904, Wilbrand reported that nasal optic nerve fibres form a loop into the contralateral optic nerve which was subsequently referred to as Wilbrand's knee (Lee et 120 al., 2006) (Figure 6.5). The Wilbrand’s knee was also confirmed by Hoyt and Luis

(1962) (Figure 6.1). Horton (1997), by performing experimental studies using primates, has argued that Wilbrand’s knee is an artefact. The artefact idea was confirmed by Lee et al. (2006) by observations of the visual field changes of patients whose optic nerves were divided at the junction of the optic nerve and chiasm during operations. The idea that the Wilbrand’s knee does not exist has been increasingly accepted. However, in

2014, Shin et al. (2014) reported that there was a Wilbrand’s knee in the normal human chiasm they studied.

Wilbrand’s knee

Optic chiasm

Figure 6.5 Schematic diagram illustrates the concept of Wilbrand’s knee in which the nasal fibres form a loop into the contralateral optic nerve.

6.2 Visualisation of nerve fibre distribution in the optic chiasm using photomicrographic image analysis

Because the existing information on the nerve fibre distribution in the optic chiasm is scarce, in this section, photomicrographic images were used to investigate the detailed nerve fibre distribution and the locations of the uncrossed and crossed nerve fibres in

121 the human optic chiasm. The flowchart of the fibre distribution analysis procedures is shown in Figure 6.6. The details of each step are further described below.

Figure 6.6 Flowchart of the fibre distribution analysis procedures1.

6.2.1 Materials and data acquisition

The sample preparation, sectioning, imaging and the data acquisition were performed by medical colleagues Neeranjali Jain and Swaranjali Jain.

A human optic chiasm obtained from cadaver at autopsy was silver-stained en bloc to reveal axon patterns. The chiasm was sectioned in the axial plane at 5 µm intervals, which resulted in 272 slices. Each slice was placed on a glass slide. Two holes were made through the height of the chiasm, which served as fiducial markers for the alignment of slices.

Slices were scanned with a microscopy scanner (Axio Scan.Z1, Carl Zeiss) using brightfield contrast. Each image had a size of approximately 68,000 × 68,000 pixels, but varied by slice size and its orientation under the microscope.

1 Co-developed with Neeranjali Jain and Swaranjali Jain in Faculty of Medicine, University of New South Wales and the Canberra Hospital. 122

6.2.2 Image processing and analysis

The digital files were opened in the ZEN software from Carl Zeiss and rotated to the right orientation manually. Figure 6.7 shows the image of a slice. Each slice was then subdivided into approximately 1,200 smaller regions of interest (ROIs) as JPG files to enable processing on normal desktop computers. The resolution of the images was

0.22μm/pixel which is high enough to show the axons given that the diameter of the axon is about 1 μm.

Figure 6.7 Image taken from the microscopy scanner. The physical dimension of this image is 13.21 mm × 8.78 mm (width by height).

Specialist software ImageJ (Schneider et al., 2012) was used to conduct image analysis of the chiasmal slices. The orientation distribution of the nerve fibres in each ROI were obtained using OrientationJ (Rezakhaniha et al., 2012) which is an ImageJ plugin. The plugin can determine the orientation of objects based on the evaluation of the pixels in a local area. Quantitative fibre orientations with angles ranging from -90 to 89 degrees

123 were plotted as histograms. Figure 6.8 shows an example of the ROI and its

OrientationJ results.

90˚

-45˚ 45˚

(a) 0˚ 0˚ (b)

(c)

Figure 6.8 (a) The photomicrographic image of one ROI. (b) Angle values used in (c). (c) Histogram of orientation distribution.

It can be seen from Figure 6.8 that, the peak of the angle histogram can well reflect the predominant axonal orientations even though the histogram may possibly include the data of other tissues besides axons.

There are two main patterns of axonal distribution in the optic chiasm: crossed and uncrossed, as suggested by Figure 6.3. Typical crossed and uncrossed nerve fibres and their corresponding OrientationJ results were shown in Figure 6.9. It can be seen that the peaks in the histogram reflected the predominant nerve fibre orientation(s) in the corresponding ROI. In the crossed ROI, there were two main peaks which represent the two dominant fibre directions.

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Figure 6.9 Two ROIs that show the crossed and uncrossed optic nerve fibres along with their orientation histograms.

6.2.3 Recognition of predominant fibre orientations in each ROI

The orientation data was processed using custom-written MATLAB code (Appendix G) to recognize the crossing locations and angles. Automatic processes were used to evaluate the nerve fibre distribution in each slice. Because the fibre distributions in some of the ROIs were very complex, the automatic procedure could not recognize the predominant fibre directions in these ROIs correctly, codes were therefore written to allow manually visual confirmation of the peaks obtained by automatic methods.

The original orientation data were between -89 and 90 degrees as this range covers all the possible directions. The peak finding algorithm used later simply compared one value with its neighbouring values (left and right). If the value was greater than both its neighbouring values, this value was recognized as a local peak. Therefore, to be able to

125 recognize potential peaks at 90 degrees, data of each slice were duplicated to cover the range of -180 to 179 as indicated in Figure 6.10.

4 4 x 10 x 10 4 4

3.5 3.5

3 3

2.5 2.5

2 2

1.5 1.5

1 1

0.5 0.5

0 0 -50 0 50 -150 -100 -50 0 50 100 150 (a) Orientation (degrees) (b) Orientation (degrees)

Figure 6.10 Data were extended to the range between -180 to 179 for further processing. (a) Original data. (b) Extended data.

The local fluctuations of the raw data of the orientation histograms make the automatic recognition of the main peaks problematic. Figure 6.11 shows the original histogram with all peaks indicated by triangular markers. To avoid this phenomenon, it is necessary to smooth the data first in order to eliminate the noise.

12000

10000

8000

6000

4000

2000 -150 -100 -50 0 50 100 150 Orientation (degrees)

Figure 6.11 The original data with peaks indicated by triangular markers.

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By observing the distribution data and the actual ROIs, it was found that there were false peaks at 0 and 90 degrees in many ROIs, especially those with fewer nerve fibres.

Similar artefacts were also found in another study by (Payne et al., 2014). Those peaks were very sharp and narrow. These artefacts may be caused by the edges of ROIs and some blank area without nerve fibres. Figure 6.12 shows a ROI with false peaks at 0 and 90 degrees.

4 x 10 4

3.5

2.5

1.5

0.5

0 -200 -100 0 100 200 Orientation (degrees)

Figure 6.12 Artefacts at 0 and 90 degrees.

In order to address these issues discussed above, several algorithms were used to process the orientation histogram data as follows.

6.2.3.1 Removal of false peaks

These false peaks around 0 and 90 degrees (±1˚) were recognized and removed in

MATLAB. Specifically, code was written to identify peaks occurring around 0 and 90 degrees in all ROIs. If a peak was recognized and the peak was narrow enough, it is highly possible that this is a false peak. The distance from the nearest identified local minimum to the peak (d in Figure 6.13) was calculated for each potential false peak. A 127 peak was identified as a false peak if this distance was smaller than 10 degrees, which is based on the observation of all the histograms in one slice. False peaks were removed by joining the nearest identified local minimum (point A in Figure 6.13b) to a point at the same distance away on the other side of the peak (point B in Figure 6.13b). Figure

6.13a shows the curve before and after removal of false peaks.

4 Peak x 10 4 4500

3.5 4000

3 3500

2.5 3000 d A (nearest local minimum ) 2 2500

2000 1.5

1500 1

1000 0.5 500 B d 0 -150 -100 -50 0 50 100 150 -10 0 10 20 (a) Orientation (degrees) (b) Orientation (degrees)

Figure 6.13 (a) False peaks (blue line) were removed. (b) Magnifying figure shows details of the data in the red box in (a).

6.2.3.2 Butterworth smoothing

After the removal of false peaks around 0 or 90 degrees, a fifth-order low-pass

Butterworth digital filter, with a normalized cutoff frequency of 0.07, was applied to remove undesirable high-frequency local fluctuations while leaving the low-frequency components undistorted. The filter successfully removed the high-frequency local peaks to allow the recognition of the predominant orientation(s) (Figure 6.14).

128

11000 unfiltered 10000 filtered 9000

8000

7000

6000

5000

4000

3000

2000 -150 -100 -50 0 50 100 150 Orientation (degrees)

Figure 6.14 The orientation histogram data before and after filtered with a Butterworth low-pass filter; triangular markers indicate the identified peaks after filtering.

6.2.3.3 Thresholding

After the Butterworth smoothing, in some ROIs, there were still some “low” peaks that cannot conceivably represent the predominant orientations. These peaks were filtered out by removing all peaks that were lower than a certain level. A relative threshold of

15% of the maximum peak was applied to the data so that only significant peaks were identified. This threshold was chosen by visual inspection of all the histograms of slice

151. Figure 6.15 shows the threshold level and the peaks recognized by the code before thresholding. In Figure 6.15, the peak smaller than the relative threshold was removed.

129

4 x 10 3

unfiltered 2.5 filtered peaks before thresholding

1.5

0.5 Threshold

0 -150 -100 -50 0 50 100 150 Orientation (degrees)

Figure 6.15 Illustration of the threshold used to remove “low” peaks.

6.3 Fibre trajectory results and discussion

6.3.1 Fibre trajectory results

After all the procedures above, the predominant angles of each ROI could be obtained.

These data were stored in a text file and then transformed to orientations in the physical space. The fibre orientations in each ROI were plotted as bold bars and superimposed on the slice (Figure 6.16). In uncrossed ROIs, there was only one bar to represent the main orientation. In the crossed ROIs, two or more bars were plotted to represent the predominant orientations. The slice numbers, ranging from 1 to 272 from top to bottom of the chiasm, were indicated in each slice in Figure 6.16. A coronal section of the optic chiasm was plotted at the right side of each slice and a horizontal line was used to indicate the relative location of the corresponding slice in superior-inferior direction.

Note that the coronal section was only a schematic diagram.

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131

101

111

121

Figure 6.16 (continued)

132

131

141

151

Figure 6.16 (continued)

133

161

Figure 6.16 (continued)

6.3.2 Discussion

Although many previous studies have explored the nerve fibre trajectory in the optic chiasm, the detailed fibre trajectories in the optic chiasm are still not fully understood, particularly at nerve fibre scale. This study is the first to use microscopic images to visualize the fibre distributions of the whole chiasm. Unlike other technologies that can only track large nerve fibre bundles or “guess” the nerve fibre orientations based on low resolution MRI data, in this thesis, the crossings of nerve fibres can be clearly observed directly from the microscopic images.

In the DTI study of Roebroeck et al. (2008), the nerve fibres curve sharply to adopt a medio-lateral direction through the central chiasm and then curve sharply once again to align with ipsilateral temporal fibres before entering the optic tracts. The fibre distributions in the central part of the chiasm in this chapter are in general agreement with the fibre routing indicated in the DTI images of Roebroeck et al. (2008).

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It can be seen from these slices that the crossing ROIs were mainly located at the paracentral and peripheral part of the chiasm. In traditional understanding, the nerve fibres cross at the central or paracentral part of the chiasm while most of the peripheral fibres are temporal parallel fibres. It is not clear whether these crossing fibres are all nasal fibres or a mixture of nasal and temporal fibres. It can be seen from Figure 6.3 that the sketched chiasm in the figure is like an “X” shape rather than the wider “H” shape of the sample used in this thesis and the sample in Roebroeck et al. (2008). This could be the reason of the peripheral shift of the crossing regions.

As can be seen from slice 131, 141, 151 and 161 in Figure 6.16, some fibres crossed at the junction of the optic nerve and the optic chiasm. This was like the Wilbrand’s knee in which nasal optic nerve fibres form a loop into the contralateral optic nerve. From the microscopic images in this chapter, it can be seen clearly that there were nerve fibres crossing at the junction of the optic nerve and chiasm (Figure 6.17). However,

Wilbrand’s knee cannot be confirmed in this sample because these nerve fibres only presented in the left optic nerve and it is not certain that these nerve fibres were from the contralateral optic nerve.

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(a)

(b)

Figure 6.17 (a) Fibre orientations in slice 141. (b) Microscopic image of one of the ROI indicated in (a) shows the detailed distribution of axons.

The fibre distribution in the optic chiasm is usually considered to be well established and frequently used to validate the algorithms of diffusion tensor imaging (DTI) or diffusion spectrum imaging (DSI) (Roebroeck et al., 2008; Sarlls and Pierpaoli, 2009;

Wedeen et al., 2008; Yamada et al., 2008) which were used for nerve fibre tracking in

136 the brain. Wedeen et al (2008) validated their algorithm by assuming that the crossing of fibres occurs in the central part of the chiasm. However, the fibre orientation results in this chapter and the disagreement on Wilbrand’s knee indicate that the detailed architecture of the optic chiasm has yet to be resolved. Care should therefore be taken when using a chiasm to validate the DTI algorithms.

Because only one sample was used in this histological experiment, it may not reflect the generic fibre distribution in the human optic chiasm. More samples should be studied to better understand the patterns of the nerve fibre distribution.

It can be seen From Figure 6.16 that the fibres cross in the antero-inferior and supero- posterior portions of the chiasm which is consistent with previous research (Figure 6.1)

(Hoyt and Luis, 1963; Standring, 2008).

In this study, the orientations of nerve fibres were obtained in separated 2D slices.

However, the nerve fibres pass through the optic chiasm in 3D. Further study will be needed to investigate the fibre distribution in 3D.

6.4 Strain distribution in the nerve fibres

The crossing angle in each ROI was obtained from the image processing procedures above. These data provided predominant crossing angles of the nerve fibres in a small area (ROI). In Chapter 5, because of the lack of crossing angle and crossing location data, only the strain of a point in the central chiasm was applied to two extreme nerve fibre models (perpendicularly crossed and uncrossed). As the crossing information have now become available, it is useful to build nerve fibre model to represent each ROI to

137 study the influences of micro-structure on the strain magnitude of nerve fibres in the chiasm.

The deformations of the macroscopic optic chiasmal compression model in Chapter 5 were applied to microscopic RVE models to study the strain distribution in the nerve fibres. As there were too many ROIs in each slice and the RVE model is time consuming, only the ROIs on a horizontal line in the middle slice were modelled.

6.4.1 Crossing locations

The chiasm sliced in this chapter was only used for the fibre orientation study in the original plan. Hence this chiasm was not 3D scanned before slicing. Although the images of the slices could be used to build a 3D model of the chiasm, the optic nerves and tracts cannot be reconstructed because the chiasm was cut near the chiasm during autopsy, i.e., only a small part of the optic nerves and tracts were attached with the chiasm. Therefore, the chiasmal compression model in Chapter 4 (Chiasm A) was used to obtain the macroscopic deformation. The crossing angles of nerve fibres in the chiasm of this chapter (Chiasm B) were mapped to “Chiasm A”. Specifically, the ROIs located on a line in slice 141 of “Chiasm B” were scaled and applied on the relatively same location in “Chiasm A”, as illustrated in Figure 6.18.

Because the geometry and nerve fibre distribution in the optic chiasm vary largely between individuals, the nerve fibre orientations, crossing sites and crossing angles in

“Chiasm A” may not well represented by that of “Chasm B”. Future study needs to address this issue.

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6.4.2 RVE models

ANSYS APDL was used to generate parametric RVEs that can simulate nerve fibres crossing at an arbitrary angle. The RVE was illustrated in Figure 6.19. In the RVE, the dimensions vary with changes of crossing angle.

The RVE does not consider the two extreme cases of parallel and perpendicular fibres as these two cases were generated using the same method reported in Chapter 5.

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(b)

(a) (c)

Strains at the centre of each ROI were extracted from the macroscopic chiasmal model and applied on the RVEs as boundary conditions. The detailed procedures can be found in Chapter 5. The von Mises strain distribution along the path in Figure 6.18a is shown in Figure 6.20. Note that the actual strains used to calculate the boundary conditions were individual strain component rather than the von Mises strain which was used for better graphic presentation of the strains. Specific coordinate systems were used for each ROI to make sure that the orientations of nerve fibres in the macroscopic chiasmal model were correlated to the fibre orientations in the RVEs.

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0.15

0.1

von Mises strain 0.05

0 -6 -4 -2 0 2 4 6 Location (mm)

Figure 6.20 Von Mises strain distribution on the path indicated in Figure 6.18a.

6.4.3 Results of RVE models and discussions

The maximum cross-sectional von Mises strain and the maximum von Mises strain (see details in Chapter 5) in the axon and sheath of each RVE model were obtained from the simulations and plotted as a function of their locations in the left-right orientation of the chiasm (Figure 6.21 and Figure 6.22). The circular makers in these figures denote the data of crossing ROIs.

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sheath 0.3 axon

0.25

0.2

0.15

von Mises strain 0.1

0.05

0 -6 -4 -2 0 2 4 6 Location (mm)

0.5 sheath axon 0.4

0.3

0.2 von Mises strain

0.1

0 -6 -4 -2 0 2 4 6 Location (mm)

Figure 6.22 Maximum von Mises strains in axons and sheaths of the nerve fibres along the path in Figure 6.18. Crossed ROIs are indicated by circular markers; Arrows indicate strain “steps”.

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There were “steps” of strains (as indicated by arrows in Figure 6.21 and Figure 6.22) found at the locations where the nerve fibres change from uncrossed to crossed, even though these steps were not very significant. Interestingly, the “step” was quite small when moving from uncrossed to crossed ROIs at the location of roughly 3.5 mm. This is because that the strain magnitude applied to the uncrossed model was greater (Figure

6.20) than the crossed model and the crossed model has a small crossing angle (Figure

6.18b).

In these two figures, only the maximum strains were plotted. However, the strain distributions in the crossed models were more non-uniform which was not reflected in

Figure 6.21 and Figure 6.22. Unfortunately, the effects of the non-uniformity of strain on nerve function are still unknown. It is speculated that non-uniformities could result in disturbance of ion channels and axonal transportation and evoke subsequent damages of nerve fibres.

The nerve fibre distribution in this chapter contradicts the assumption used in previous chapters. In previous chapters, the crossed fibres were assumed to be located at the central part of the chiasm while uncrossed fibres were located at the peripheral part.

However, in this chapter, most fibres in the peripheral part of the chiasm were crossed fibres. Crossed fibres are traditionally considered to be nasal fibres. If these crossed fibres were all nasal fibres, they clearly experienced larger strains than temporal fibres and thus are more vulnerable. In this study, the nerve fibre distribution and the macroscopic chiasmal loading were from two different optic chiasms. Because there were considerable individual variations in the geometry, material properties and nerve fibre arrangements of the optic chiasm, significant inaccuracies could exist in this model.

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It should be pointed out that, for nerve fibres, a single point failure can shut down the whole nerve fibre. However, in this simulation, only the strains on a single path were investigated. Therefore, for a single nerve fibre, the results only reflect the strain at a small segment of the whole nerve fibre; the same nerve fibre passes through the chiasm following a certain route, but unfortunately these routes are still unknown. The strains of the same nerve fibre at other locations of the optic chiasm are hence unavailable.

Further study could cover all the nerve fibres in the chiasm rather than along a single line as used in this study. This also highlights the need for improved understanding of the nerve fibre trajectory in the optic chiasm.

6.5 Conclusions

In this chapter, the fibre distributions in the optic chiasm were reviewed. A human chiasm was sectioned and imaged by a microscopy scanner. An image processing technique was developed for assessing the fibre crossing angles and locations. The nerve fibre crossing data were then applied on the chiasmal compression and RVE models to look into the strains in different nerve fibres.

In this study, a large portion of the crossing fibres were found to be located at the peripheral part of the chiasm, which contradicts the traditional understanding that the crossed fibres are located in the central chiasm. More samples should be examined to understand the nerve fibre distribution in the chiasm in the general population.

The RVE models tried to include nerve fibre crossing status and orientations in different sites of the chiasm. However, only the nerve fibres on a single, central line of the chiasm were investigated, which cannot reflect the behaviours of the whole optic chiasm. The RVE models show that the differences of strain magnitude for

144 neighbouring crossed and uncrossed nerve fibres were not significant. However, the results could be inaccurate because the macroscopic chiasm model and the fibre distributions data were from two different optic chiasms.

Although the results have significant limitations due to lack of accurate data as discussed above, the methodology was demonstrated to be feasible and useful. Further study should be carried out to address these limitations when appropriate data and more samples become available.

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Chapter 7

Ex vivo experimental study of the optic chiasmal compression

The focus of this Chapter is to develop and perform an experiment to test the optic chiamal compression ex vivo. The experiment was performed under a micro-CT machine to allow imaging of the deformed and undeformed chiasmal geometry. The same chiasm under compression was also simulated using FEM. The simulation results were compared with the experimental result to allow validation of the FEM model and better understand the mechanical behaviour of the optic chiasm under compression.

It should be pointed out that the human chiasm and the micro-CT machine only became available at the very late stage of this project. Therefore, this experiment aimed primarily to establish the test technique. Methods of improving the experiment will also be discussed.

7.1 Sample preparation

A human optic chiasm was harvested at autopsy by medical colleagues in the Canberra

Hospital. Because the rare chance of acquiring human optic chiasm and this was the first time to perform this experiment which involved several institutions, the optic chiasm was preserved in formalin before the test.

7.2 Experimental setup

One of the difficulties of conducting this experiment was mounting the chiasm in a simple and reliable way so that it could be compressed from below. A surgical 147 aneurysm clip (Sugita clip; Mizuho Ikakogyo, Tokyo, Japan) had been used to clamp a strip of sheep brain tissue in an initial trial setup, however the brain tissue was transected directly because of its low strength. Moreover, the optic nerves and the tracts were too short to allow a reasonable clamping length. Therefore, the clamp method was not adopted.

Previous study has successfully used surgical superglue to secure fresh brain tissue to glass (Miller and Chinzei, 2002). Therefore, the superglue was tested to glue plastic and fixed sheep brain tissue. The fixed tissues were found to be well glued to plastic, which was an easy and practical way as plastic is widely used in 3D printing which can create customized objects quickly. Compared with the clamping method, the superglue method simply bonded the cross-sections of the optic nerves and tracts, which provides a more defined boundary condition for subsequent finite element modelling.

A mounting apparatus, consisting of four holders and a base, was designed to allow simultaneous compressing of the chiasm and scanning under micro-CT (Figure 7.1).

The size of the holders and base were designed to fit within the size of the micro-CT’s bore. A hemi-spherical depression was created on the base to accommodate the Foley catheter balloon to be used to simulate the tumour. These objects were designed in

CATIA V5 (Dassault Systèmes, France). The engineering drawings of the base and the holders can be found in Appendix H.

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Optic chiasm

Bore of the micro-CT

Balloon

Shaft of the Foley catheter Sample bed

(a) (b)

Figure 7.1 The designed mounting apparatus used to fix the optic chiasm. (a) The mounting apparatus was placed on the sample bed of the micro-CT; (b) The inner structure of the experimental setup.

The mounting apparatus (base and holders) was 3D printed using PLA plastic (Figure

7.2). The holders were printed hollowly with reinforcing ribs inside to reduce the weight and save materials. The printer used in this work was a low cost Ultimaker printer

(www.ultimaker.com, Ultimaker, Geldermalsen, The Netherlands). Because no support material was used to support overhanging structures, the top of the base was printed first to avoid any sudden change of geometry between layers.

Figure 7.2 3D printed mounting apparatus.

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Superglue (Uhu GmbH & Co. KG, Bühl, Germany) was applied to the cross-sections of the optic nerves and tracts first and the small holders were then glued to the nerve tissue.

The holders were then glued to the base. These four holders were always placed on a horizontal surface before they were glued to the base to avoid any torsion of the optic nerves or tracts.

A 10 French paediatric Foley catheter with a balloon capacity of 5 ml (Bard, West

Sussex, UK) was used in this experiment (Figure 7.3) to elevate the chiasm simulating the compression from a tumour growing from beneath. The balloon of the Foley catheter was inserted into the depression of the base. A syringe was used to inject water into the balloon to inflate it. The optic chiasm, mounting apparatus and the Foley catheter were positioned on the sample bed of a micro-CT machine (Figure 7.3; also see

Figure 7.1).

(a) (b) (c)

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7.3 Deformation measurement

In this preliminary study, the focus was on testing the possibility of performing an experiment of this kind and assessing its ability to provide at least some useful calibration data. Thus, only the deformed and undeformed geometry of the optic chiasm were imaged under a micro-CT machine. Imaging was performed using a Quantum FX micro CT system (PerkinElmer Corporation, Massachusetts, USA). The field of view for image acquisition was set to be 30 mm, which was large enough to accommodate the chiasm and gave a relatively high resolution of 59 μm per pixel. After images had been captured, the data were exported as DICOM (Digital Imaging and

Communications in Medicine) images. Scanning time was three minutes per scan and

512 separate planes were captured.

The position of the sample bed of the micro-CT was adjusted so that the area of image acquisition was centred on the optic chiasm in all three dimensions.

7.4 Experimental procedure

Because the micro-CT lab was busy and expensive, to make best use of the available scanning time, the optic chiasm was glued to the mounting apparatus 12 hours before test. The chiasm along with the mounting apparatus were preserved in formalin and transported to the micro-CT lab (Figure 7.4).

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Figure 7.4 The chiasm was glued to the mounting apparatus and preserved in formalin.

The Foley catheter balloon was inflated first to allow it to just touch the optic chiasm and then the setup was scanned under the Micro-CT. The shaft of the Foley catheter was wrapped by tape so that the catheter balloon can be fixed to the base by friction between the tape and the hole of the base (Figure 7.3c). Next approximately 0.7 ml of water was injected into the balloon to elevate the chiasm. However, the actual volume of water was measured from the scanning data.

Several scans were taken with different field of view and scanning speed. The chiasm was dipped in and out of formalin after each scan to keep it from drying out.

7.5 Simulation of the experiment

7.5.1 Geometry reconstruction

The undeformed geometry of the chiasm and the geometry of the Foley catheter were constructed from the initial scan in which the balloon just touched the chiasm.

These DICOM images obtained from the experiment were imported into an open source software package, 3D Slicer (Pieper et al., 2006), as described in Chapter 4. Figure 7.5

152 shows an example of the DICOM image of the experimental setup and the chiasm. As the images were upside down, they were flipped superior-inferiorly to reflect their accurate orientations in the physical space. The regions of interests in each slice were identified using intensity thresholding though some manual image manipulation was still required to identify the chiasm and the experimental setup from the background. A

3D model was then built and saved as an STL file. The steps used to create the 3D model in Slicer are illustrated in Figure 7.6.

Figure 7.5 3D Slicer interface with the Editor module on the left side and the DICOM images on the right.

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Figure 7.6 Summary of steps to create a 3D model in Slicer.

The STL file only contains the mesh of the surfaces of the model, which was imported into CATIA V5 using the module of STL Rapid Prototyping. As the mesh had inconsistencies such as, non-manifold vertices, acute angled triangles, isolated triangles or triangles with inconsistent orientation, etc. the mesh was cleaned up first using the

Digitized Shape Editor and the STL Rapid Prototyping modules in CATIA. More processing of the mesh including automatic hole filling and smoothing was performed.

Some holes on the posterior part of the chiasm were filled manually. Figure 7.7 shows the reconstructed chiasmal surface along with its mesh exported from the 3D Slicer. As can be seen, the surface represented the mesh of the chiasm reasonably although it was not exactly the same as the mesh because of the process of smoothing. The smoothing process allowed easy meshing in the subsequent finite element modelling using ANSYS.

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Figure 7.7 The mesh and the overlaid reconstructed surface model of the undeformed chiasm were displayed using different colours as indicated.

The reconstructed surfaces were then converted to solid bodies using CATIA. The workflow of the 3D solid model reconstruction is illustrated in Figure 7.8.

Figure 7.8 Workflow of the solid model generation in CATIA.

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The Foley catheter balloon was placed in a depression of the base. For simplicity, only the balloon and a short segment of the shaft of the Foley catheter were constructed. Part of the base was constructed to constraint the balloon expansion. Figure 7.9 shows the model in ANSYS.

Figure 7.9 Photo of the experiment and the FEM model in ANSYS

All the solid bodies or surface bodies constructed in the CATIA were saved as .igs files separately. These .igs files can be directly imported into ANSYS with their original coordinate information. A pial sheath of 0.086mm was added onto the optic chiasm in

ANSYS. The thickness of 0.086 mm was measured from the microscopic image of the different chiasm sectioned in Chapter 6 although it is acknowledged that pia mater thickness varies between individuals. The thickness for the shaft and the balloon were

0.4 and 0.12mm respectively. The thickness of the balloon was estimated from the original geometry and deformed geometry of the balloon of the Foley catheter. The thickness was not accurate because the actual deformation of the balloon was very complicated. This may introduce uncertainties into the model.

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7.5.2 Mesh and boundary conditions

The pial sheath, balloon and part of the base were modelled as surface bodies and meshed using shell elements (SHELL181). The optic chiasm nerve tissue was meshed using solid elements (SOLID186 and SOLID187).

The boundary conditions of the simulation were as follow (Figure 7.10): the distal faces of the optic nerve and tracts were fixed to represent the connection of the tissue to the holders by superglue. The balloon was connected with the shaft which was fixed at its end (narrow arrow in Figure 7.10). The base was fixed. The contact between the balloon and chiasm was considered to be frictionless. The core tissues of the optic nerve, chiasm and tract were bonded to their pial sheath. Pressure was applied via the interior surface of the balloon in multiple steps to inflate it gradually.

Figure 7.10 Boundary conditions of the FEM model. Short wide arrows indicate fixed faces; long narrows arrows indicate fixed edges.

7.5.3 Material properties

Since the chiasm used in this chapter was fixed in formalin, the material properties of fresh or dead tissues could not be used in this problem directly. Formalin can change the mechanical properties of soft tissue by cross-linking the proteoglycan monomers, and

157 while this is not ideal it is often unavoidable. The material properties of unfixed brain tissue have been studied widely using various methods although the reported data in the literature still show large discrepancies. However, knowledge of the mechanical properties of the brain tissue after fixation is still scant. Garo et al. (2007) showed that post-mortem time has a significant influence on the mechanical properties of brain tissue. By performing experiments on live, dead and fixed brain tissue (including white and grey matter) of Rhesus monkeys, Metz et al. (1970) showed that fixation of brain tissue increases its stiffness significantly. As their experimental data was not from direct measurements of the force versus deformation and the nonlinear behaviours of the brain tissue, accurate data on the changes of mechanical properties of brain tissue after fixation was unavailable. Generally, their experimental data demonstrated that fixed brain tissue was between 2.1 to 8.4 times stiffer than live and dead tissue. As there is no definitive quantitative data on the mechanical properties of fixed brain tissue in the literature, and noting that it will also depend on the degree/duration of fixation, the material properties of brain tissue used here were directly modified from dead tissues.

Information of the material properties of pia mater after fixation cannot be found in the literature. Therefore, the same modification was performed as the brain tissue.

Specifically, seven times stiffer materials modified from the nerve tissue and pia mater data described in Chapter 4 were used for the fixed tissue. It is unknown whether or not such material models are still adequate for fixed tissues. The modified material properties of nerve tissue and pial sheath are listed in Table 7.1.

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Table 7.1 Material properties used for fixed tissues.

Tissue Material model Material constants

Pial sheath Hyperelastic-2nd C10=1.07×106 Pa ; C01=-5.03×105 Pa; Polynomial C20=8.79×107 Pa ; C11=-1.25×108 Pa ; C02=5.09×107 Pa

Optic nerve Hyperelastic-2nd =7308 Pa; =4.309; =8281 Pa;

Ogden 휇1 =7.736 훼1 휇2 훼2 Besides the mechanical properties, it is reported that the volume of biological tissue could be changed during fixation in formalin (Bahr et al., 1957). However, in this analysis, the geometry of the chiasm was directly obtained from the fixed tissue.

Therefore, the effect of volume change was ignored.

The catheter used to elevate the chiasm was manufactured of 100% silicone. The mechanical properties of the catheter were unclear. It is known that different catheter components have different material properties. Usually, the balloon is manufactured by silicone that has elongations of about 1,000% and a soft durometer of 20 to 30 Shore A

(Shore A is a unit of hardness) (Christmas and Luftig, 2006). In the simulation, only the part near the balloon of the catheter was included. The material properties for the balloon of the Foley catheter were derived from the experimental data of (Nagarajan,

2008) in which the silicone rubber had a hardness of 30 Shore A. The experimental data were fitted to a 3-parameter Mooney-Rivlin model and the material constants used are listed in Table 7.2.

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Table 7.2 Mechanical properties of the Foley catheter.

Hardness C10 (MPa) C01 (MPa) C10 (MPa) (Shore A) Balloon 30 0.030 0.182 0.003

7.5.4 Assumptions made in this simulation

Several assumptions have been made in this simulation as discussed above. These assumptions were summarised here:

1. The thickness of the pia mater sheath was assumed to be 0.086 mm which was

measured from an axial slice of another chiasm. Note that there is considerable

variation of pia thickness between individuals.

2. The material properties for fixed pia mater sheath and nerve tissue were all

assumed. The hyperelastic material models used for pia mater and nerve tissue

were both obtained from dead tissues in the literature. Then the material

constants for each model were modified accordingly to form a seven times

stiffer material to reflect the stiffness change of tissues after fixation.

3. The thickness of the Foley catheter balloon was estimated form the original

geometry and deformed geometry of the balloon. However, because the complex

deformation behaviours of the balloon itself, this estimation may not be accurate

enough.

4. The silicone rubber of the Foley catheter balloon was assumed to have a

hardness of 30 Shore A. The material properties of a type of silicone rubber has

the same hardness in the literature were employed to represent the balloon.

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5. The contact between the balloon and the optic chiasm was assumed to be

frictionless. In the experiment, friction may exist between the rubber balloon and

the optic chiasm.

7.6 Comparison of the experimental and simulation results

The experiment only scanned the undeformed and deformed sample, thus only deformations could be compared between experiment and simulation. Firstly, the relationship of the elevation of the chiasm and the balloon size changes were compared.

Secondly, cross-sections of the undeformed and deformed chiasm in both simulation and experiment were compared.

The balloon volume increase was measured in CATIA for the experiment. In the simulation, volume increase was obtained from the deformed geometry. Figure 7.11 shows a coronal section of the undeformed and deformed optic chiasm in the simulation.

(a)

Point A (b)

Figure 7.11 (a) A coronal section of the undeformed chiasm. (b) Contour plot of the vertical displacement of the coronal section of the deformed optic chiasm.

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The volume increase and the chiasmal elevation in both experiment and simulation are listed in Table 7.3. The displacement of the chiasm was measured at a point located at the lower surface of the chiasm (Point A in Figure 7.11). It can be seen from Table 7.3 that, for nearly the same elevation, the balloon size in the simulation was roughly close to the experimental data (with 15.6% difference).

Table 7.3 Comparison of the results predicted by the simulation and the experimental measurements.

Volume increase Elevation of the chiasm

Experiment 0.872 1.75 mm Simulation 1.008 1.76 mm

To examine the geometric changes of the optic chiasm, the undeformed and the deformed geometry of a coronal and a sagittal cross-section of the chiasm in both experiment and simulation were compared in Figure 7.12 and Figure 7.13. Specifically, the boundary coordinates of the cross-sectional images of the simulation were extracted and transformed to the coordinate system of the CT scans. The boundaries were then superimposed on the experimental CT scans as wire frames, for comparison.

Figure 7.12 shows the comparison of the coronal cross-section which roughly cut the chiasm into halves. As can be seen, in the deformed chiasm, the cross-section of the simulation was reasonably close to that of the experiment. The non-overlapping areas of the cross-sectional images of the chiasm in experiment and simulation were obtained.

The ratio of the total non-overlapping area to the area of the experiment was calculated.

These ratios for the undeformed and deformed cases were 5.7% and 7% respectively.

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(a) (b)

Figure 7.12 The experimental deformation from the CT scan and the FEM predicted deformation (wire frame) of a coronal section of the chiasm. (a) The undeformed chiasm. (b) The deformed chiasm.

Figure 7.13 shows the comparison of the middle sagittal cross-section, which also roughly cuts the chiasm into halves, with the FEM simulation. In the sagittal plane, the cross-section of the simulation was less in agreement with that of the experiment both in the deformed and undeformed chiasms. The non-overlapping area ratios for the undeformed and deformed cases were 6.5% and 16% respectively.

(a) (b)

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For the middle sagittal section (Figure 7.13), the simulation result was in less good agreement with the experiment, especially at the posterior part of the chiasm (arrows indicated). Although all the assumptions made in this simulation could contribute to the deformation differences, the author speculated that the main reason was the geometric differences between the simulation and the experiment. After the original dissection, there were some other tissues connected to the posterior part of the chiasm and these were subsequently removed before the experiment, which resulted in a very complicated, coarse and irregular surface of the posterior part of the chiasm (Figure 7.14). Therefore, extensive smoothing was performed to build the FEM model, which directly caused a decrease in the geometric fidelity in this region. In addition, the pial mater of that part of the chiasm was seriously damaged during the initial dissection so that the nerve tissue in that part was less constrained by the stiffer pial sheath in the experiment. This was not reproduced in the FEM model due to the complexity. Parametric studies in Chapter 3 and Chapter 4 show that the pial sheath thickness is an important factor that influences the height change of the chiasm. However, the thickness in this simulation was measured from the separate chiasm used in the histological study reported in Chapter 6, which may introduce additional uncertainty.

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Figure 7.14 The posterior part of the chiasm that was damaged during dissection, as indicated by an ellipse.

7.7 Discussion

The experiment was successfully performed using the experimental setup and procedure described above, although improvements should be made to the method to measure more data in the chiasm in the future.

It should be noted that this chapter only explored an initial attempt at possible ex vivo chiasmal compression experiments. Further studies need to be performed to allow the measurements of the deformation of the chiasm in macro and micro-scale. Although in this experiment, the axons were invisible under the micro-CT, future study should stain the optic chiasm properly to allow visualization of the nerve fibre (or nerve fibre bundles) under the micro-CT.

Because this was the first time to perform the experiment of this kind, the optic chiasm was preserved in formalin before the test. Future experiments should use unfixed tissue

165 if possible to better represent the in vivo situation. It is acknowledged that post-mortem time and fixation affect the mechanical properties of the material significantly. Future experiments should be performed to test the material property changes caused by these factors.

Although an in vivo experiment can provide a more anatomically accurate representation of the structure and environment of the optic chiasmal compression, ex vivo experiments allow for more thorough investigation because the parameters can be more precisely controlled and manipulated. Ex vivo experiments may allow measurement of pressure, force and strain etc. using existing mature technologies. In future studies, certain markers using materials such as metal, that have a significant density differences compared with nerve tissue, could be painted on the chiasm to allow calculation of local strains.

This initial ex vivo experiment did not permit any traditional quantitative validation of the simulation such as pressure, stress or strain comparisons. However, a validation of the simulations was possible via comparison of the deformed chiasm which has complex geometries and contact patterns. In the simulation, part of the simulated deformed chiasm was in good spatial agreement to that of the experiment while some other parts were less close. The reasons were discussed in the results section above.

Given all the assumptions of the geometry, material properties and contact patterns in this complex system, it is hard to get a simulation that exactly matches the experiment.

However, the middle coronal section was still in good agreement with the experiment

(with 7% difference), which shows the feasibility of using FEM to model the chiasmal compression.

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In the simulation, the balloon was assumed to be homogenous and the material properties of the balloon were taken from other experiments. For the real Foley catheter, due to its inhomogeneous structure, the balloon will expand to one side first but will finally expand in all directions. This behaviour is hard to simulate without knowing the detailed inhomogeneous material distribution of the balloon. This might be the reason that the volume change of the balloon was not quite close to the experimental data (15.6% difference).

The properties of balloon could affect the interaction behaviours between the balloon and the chiasm and thus influence the strain distributions in the optic chiasm. However, in this quasi-static structure, the strain/deformation distribution within the chiasm is relying on the final state of the chiasm rather than the loading path. Therefore, to eliminate the effects of the uncertainties of the balloon itself, in future experiments or simulations, the chiasm could be elevated by a rigid body which has a similar geometry of a real pituitary tumour. The geometry of the rigid body to represent the tumour could be obtained through clinical MRI scan of patient experiencing chiasmal compression.

In the simulation, a uniform pressure was applied to the balloon. However, in the experiment, water was injected into the balloon to inflate it thus making the problem two-phase. For simplicity, the water was not considered in the simulation. Future FEM study should use more appropriate element (for example, HSFLD241 in ANSYS) to include the effect of trapped fluid.

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Chapter 8

Conclusions and recommendations for future research

The precise mechanism of bitemporal hemianopia caused by chiasmal compression is still not clear. Therefore, the general aim of this work was to investigate the biomechanics of the optic chiasmal compression and understand its role in the cause of bitemporal hemianopia. Finite element modelling was used to investigate the strain distribution in the optic chiasm in different length scales when it was compressed by a pituitary tumour from below. The detailed strain distribution results obtained from these

FEM models have significantly improved the understanding of the biomechanics of chiasmal compression and bitemporal hemianopia. This chapter summarises the work of this thesis and the major conclusions are presented. Recommendations for future research are also suggested.

8.1 Summary

A generic optic chiasmal compression model and nerve fibre model were built in

Chapter 3 for initial analysis of the mechanical behaviours of the chiasm. Models of a chiasm, compressed by a pituitary tumour growing centrally beneath it show that strain was higher in the central part of the chiasm where nasal fibres are situated. The nerve fibre models show that strain was higher in crossed (nasal) nerve fibres than in uncrossed (temporal) nerve fibres. However, several limitations of the model required to improve the fidelity were identified and these were addressed in the subsequent chapters.

To improve the accuracy of the model, an individual-specific model was built in

Chapter 4. The geometry was obtained from the 3D construction of human head slices

169 of the Visible Human Project of the United States. Nonlinear material models were employed in this model. Generally, the strain was larger in the central part of the chiasm which is consistent with the results of Chapter 3. However, the detailed strain distribution patterns were different from that of Chapter 3 due to changes of geometry of the chiasm.

In Chapter 5, a multi-scale approach was used to study the strain distributions in nasal and temporal optic nerve fibres. The deformations obtained from the chiasmal model in

Chapter 4 were applied to the microscopic nerve fibre model as boundary conditions.

The results showed that the strain distributions in the crossed nerve fibres were much more non-uniform than those in the uncrossed nerve fibres. Furthermore, the crossed nerve fibres experienced a higher local strain than the uncrossed fibres. Parametric studies showed that crossing angle was the leading factor that influences the strain differences in crossed and uncrossed nerve fibres.

In Chapter 6, the nerve fibre arrangements in the optic chiasm were investigated using photomicrographic image analysis. The nerve fibre trajectory results in this thesis contradicted the traditional understanding of the optic chiasm anatomy. The crossing fibres were mainly located at the paracentral and peripheral part of the chiasm. In the central part of the chiasm, most nerve fibres were parallel to each other or crossing at low angles. Some fibres crossed at the junction of the optic nerve and the optic chiasm which is similar to the phenomenon of Wilbrand’s knee. The RVE modes in this chapter included the effects of local deformation of the chiasm, the crossing angle and orientations of the nerve fibres.

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In Chapter 7, an ex vivo experiment of optic chiasmal compression was conducted to allow validation of the FEM results. The results of the ex vivo experiment were compared with the simulation of the experiments. The experimental technique was established. The differences of the deformations of the chiasmal cross-sections between experiment and simulation were within 16% based on the overlapping area between the measured and simulated deformed chiasm.

8.2 Conclusions

The main conclusions drawn from this thesis are:

• Simulation results in this thesis were broadly in agreement with the limited

experimental results in the literature, which indicate that finite element

modelling is a useful tool for analysing optic chiasmal compression. Although a

few assumptions have been made in this preliminary research due to lack of

information, the methodology used in this thesis was proved to be useful. The

fidelity of the models can be increased by incorporating more accurate data of

the parameters included.

• Generally, strain was higher in the central part of the chiasm which was

consistent with the theory of Kosmorsky et al. (2008). However, the gradual

change of strains from central to peripheral chiasm cannot explain the sharp

vertical cutoff of visual field loss in bitemporal hemianopia.

• Under the same loading conditions, the crossed nerve fibres experienced a

higher local strain than the uncrossed fibres and the strain distribution in the

crossed nerve fibres were much more non-uniform than those in the uncrossed

nerve fibres. Although the nerve failure mechanism is still not well understood,

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the differential effects of mechanical loading on crossed and uncrossed fibres

could possibly explain the phenomenon of bitemporal hemianopia. This result

supports the theory of McIlwaine et al. (2005).

• Parametric study using DOE showed that the crossing angle was the leading

factor influencing all the responses of the nerve fibre model. Depending on the

measure of nerve fibre impairment (response) used, crossing angle was either the

most significant or the second most significant factor. For some of the responses,

it was slightly less significant than g-ratio and the stiffness of MECS, noting

that in reality the g-ratio and the stiffness of MECS vary only slightly in an

individual person. This research also highlights the needs for better

understanding of the relationship between mechanical measurements (such as

maximum von Mises strain) and nerve dysfunction.

• Parametric studies in this thesis show that the strain distribution in the chiasm

was significantly affected by the chiasmal geometry and the way it contacts the

tumour. Previous research has focused on the effects of tumour volume and

height on the visual field defects in bitemporal hemianopia. Future clinical

investigation of bitemporal hemianopia should not only focus on the tumour size

as information on the contact locations and patterns between tumour and the

chiasm are even more important than tumour size.

• In the chiasmal sample studied in this thesis, the crossing nerve fibres were

mainly located at the paracentral and peripheral part of the chiasm and a large

portion of the peripheral fibres were crossed fibres, which contradicts previous

research. In traditional understanding, most of the peripheral fibres should be

temporal parallel fibres. The photomicrographic image analysis in this thesis

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was demonstrated to be an effective method to evaluate the nerve fibre

orientations in the optic chiasm.

• The ex vivo experiment was successfully performed and provided possible

methods for validation of the FEM method. The FEM model simulated the

chiasmal distortion in this preliminary experiment to within 16% difference. It

demonstrated that the method used in the experiment is viable and can be used

in future studies.

More conclusions are reflected in the recommendations below.

8.3 Recommendations for future study

In this study, there was significant uncertainty in many of the parameters used and thus numerous assumptions were made. Future studies should examine these assumptions.

More work also needs to be carried out in the future to improve the accuracy of the model and the experiment. Recommendations for future study have been presented as follows.

8.3.1 Material properties of nerve tissue

The material properties used in this research were either linear elastic or hyperelastic. In large (finite) deformation analysis procedure, the material properties are used to evaluate the stresses and the tangent stress-strain matrices (Bathe 2006). The stress- strain relation is usually nonlinear for large (finite) deformation analysis of biological tissues. In Chapter 3, a linear elastic material model was used for the large deformation problem. Although this issue was addressed in Chapter 4, it is recommended that in future study, more appropriate nonlinear material models should be used to be compatible with finite deformation solution procedure. 173

In this thesis, the material constants were all taken from reports in the literature for other tissues rather than the optic chiasmal tissue. It is acknowledged that the nerve fibre volume fraction in the optic nerve and in the brain is different, which may result in significant differences in material properties. In this study, the optic nerve tissue was assumed to be isotropic which is not the case in vivo given that the nerve fibres passing through the optic nerve and chiasm at certain orientations. Future studies should be carried out to characterize the material properties of tissues involved in the optic chiasm.

This will allow more realistic predictions of the mechanical responses in the optic chiasm.

At an optic nerve fibre scale, the material properties of an axon and its myelin sheath are scarce or non-existent. Some preliminary work has been done to investigate the material properties of axon using atomic force microscope (AFM) (Heredia et al., 2007;

Lu et al., 2006; Ouyang et al., 2010). These techniques could be improved and used to assess the mechanical properties of axon, myelin sheath and extracellular matrix.

Recently, patient-specific biomechanics is gaining in popularity since it could provide personalized information. Patient-specific modelling requires patient-specific material properties. However, the material properties of brain tissue vary substantially between individuals (Rivoal et al., 2000; Lee et al., 2011). At present, despite the improvements in magnetic resonance elastography (Bilston, 2011), reliable methods of measuring in vivo patient-specific material properties of the brain tissue are not yet available (Miller et al., 2010). Research has shown that in some special cases, such as pure displacement and “displacement-zero traction” problems (see Wittek et al., 2009; Miller and Lu, 2013;

Miller et al., 2010), the results are weakly sensitive to unknown properties of tissues.

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Future simulations might make use of these procedures to obtain patient-specific results without the need for patient-specific tissue properties (Miller and Lu, 2013).

8.3.2 Anatomy of the chiasm

In this study, only the optic chiasm and the tumour were included in the FEM model.

However, in reality, the optic chiasm is adjacent and possibly connected to the pituitary stalk and the brain by some tissues. The details of the connection between the chiasm and other tissues are still not clear. Further study should assess the relation between these tissues, especially how the posterior chiasm is connected to the brain. The influences of these connections need to be studied.

8.3.3 Pituitary tumour

In all the simulations, a balloon was used to represent the tumour. The parametric studies showed that the geometry, location and stiffness of the tumour have significant influences on the strain distributions in the optic chiasm. Unfortunately, knowledge of these properties of pituitary tumours is scant.

The material properties of pituitary tumour have been investigated using magnetic resonance elastography (MRE) (Xu et al., 2007) but no quantitative results were given.

Future studies should characterize the material properties of pituitary tumour using direct traditional material test procedures or the indirect MRE method.

A deeper understanding of the material properties of pituitary tumour could also benefit operative treatment of the tumour. In the operation, stiffer pituitary tumours could increase the risk of the surgical procedure because they are harder to remove (Pierallini et al., 2006; Xu et al., 2007). Knowledge of the stiffness of the tumour may help the

175 clinician to plan the surgical protocol, which would therefore be valuable for patients and clinicians.

Statistical data of the pituitary tumour geometry, size, contact patterns between tumour and chiasm and their corresponding visual field defects patterns, would improve the accuracy of the finite element model and therefore allow more profound understanding of the cause of bitemporal hemianopia.

8.3.4 Multi-scale analysis

In the multi-scale analysis of Chapter 5, the deformations of the macroscopic model were applied to the microscopic model as boundary conditions. However, the loading transition was one-way in this initial study, i.e., only the outputs of the macroscopic model were applied to the microscopic model. In this one-way procedure, the material properties on the macroscopic model were predefined. Therefore, the heterogeneous

RVE behaviours could not interact with the macroscopic model.

Two-way multi-scale analysis should be developed for this problem in the future.

Specifically, for every material point in the macroscopic model, the deformation of the macroscopic model is applied on a specific microscopic RVE model as boundary conditions; then the RVE model is solved and the overall material response is calculated and returned back to the macroscopic model.

8.3.5 Microstructure of the optic chiasm

In this research, nerve fibres were considered to have similar sizes and be straight. In reality, the size of nerve fibres varies considerably. Moreover, nerve fibres are undulated. A larger RVE, which contains nerve fibres with various sizes and undulations, could be a possible way to investigate these factors preliminarily. Nerve

176 fibres in the central or paracentral chiasm may cross in bundles. It would be interesting to simulate the crossing fibre bundles in the crossed region when the related anatomy data is available in the future.

A more accurate way to represent the real microstructure is to reconstruct a RVE of the chiasm in 3D from microscopic images. Previous research has successfully obtained a model including the ultra-structural details of a small part of the mouse optic nerve using microscopic images (Ohno et al., 2011). These models would contain the axon, myelin sheath and the glial matrix and thus can reflect the real microscopic structure accurately. These microscopic 3D models could also provide valuable information on the nerve fibre trajectories in the optic chiasm.

8.3.6 Nerve fibre arrangements in the optic chiasm

In Chapter 6, only one sample was investigated in the histological experiment, therefore it may not reflect the generic fibre distribution in the human optic chiasm. More samples should be studied to better understand the patterns of the nerve fibre distribution in the future.

This thesis only investigated the nerve fibre orientations in the chiasm in 2D slices. It provided no information of the 3D distribution of the nerve fibres, which was crucial for understanding the fibre trajectory. The high resolution 3D mapping of the nerve fibres may enable correlation of the strain field of the chiasm with defects in the visual field and give clinicians better predictions of the compression status through simple visual field examination.

There are existing techniques, such as diffusion tensor imaging (DTI), that could map the nerve fibres bundles in 3D in a non-invasive manner (Roebroeck et al., 2008; Sarlls

177 and Pierpaoli, 2009; Wedeen et al., 2012; Wedeen et al., 2008; Yamada et al., 2008).

DTI was usually used to construct the human ‘connectome’ which is a map of the neural connection in the brain (Sporns et al., 2005). However, the crossing patterns of individual nerve fibres cannot be visualized owing to the limited spatial resolution of

DTI. The fibre distribution in the optic chiasm is frequently used to validate the algorithms of DTI. Investigation of the nerve fibre route in the chiasm would also benefit DTI techniques.

In future studies, new techniques should be developed to enable tracing of individual nerve fibres in the chiasm. These techniques could also be used in the ‘connectome’ research to improve the accuracy of these brain neural networks when proper computational resources are available.

In Chapter 4, the strain distributions showed that the paracentral part of the chiasm experiences larger strain than the central part because the paracentral part is thicker. It is speculated that the thicker part of the chiasm might be the part where nerve fibres cross.

This idea needs to be checked in future studies.

8.3.7 Ex vivo experiment of the chiasmal compression

Ex vivo experiments of the optic chiasmal compression allow measurements of pressure, force and strain etc. using existing mature technologies. However, in this study, only geometric changes of the chiasm were measured using CT scanning. Certain markers using materials such as metal that have a significant density differences compared with nerve tissue could be painted on the chiasm to allow calculation of local strains in future studies.

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At present, the microstructure of the optic chiasm cannot be visualized under the micro-

CT. In future studies, it might be possible to look into the microstructure changes of nerve fibre bundles or even a single nerve fibre in the chiasm with proper staining and imaging techniques (Mizutani et al., 2008a; Mizutani et al., 2008b).

These merits of testing the chiasmal compression ex vivo are significant as discussed above. However, the environment of ex vivo experiment differs considerably from that in vivo. Consequently, alterations of mechanical properties of nerve tissues would affect the mechanical responses of the chiasm. To calibrate the differences caused by tissue status (for example, live, dead or fixed tissue), the effect of post-mortem time, fixation, and other testing condition on the material properties of nerve tissue should be investigated.

8.3.8 Other recommendations

This work does not include the electronic behaviours of the optic nerves. However, in the future study, multi-physical simulation which includes mechanical and electrical behaviours of the nerve could be investigated. Ischemia is also a possible factor that causes bitemporal hemianopia even it would not account for the cutoff of visual field.

Future study could investigate the blood flow in the chiasm under compression.

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Appendix A. Anatomical coordinate system

The anatomical coordinate system is also called patient coordinate system. This system consists of three planes to describe the anatomical position of a human.

The planes and axes of this system are indicated in the figure below.

Figure has been removed due to Copyright restrictions.

Source:

http://www.slicer.org/slicerWiki/index.php/File:Coordinate_sytems.png

Figure A1. Illustration of the anatomical coordinate system (Slicer.org). S: Superior, I: Inferior, A: Anterior, P: Posterior, L:Left, R:Right.

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Appendix B. Foley catheter

A Foley catheter is a small tube that inserted into the bladder to drain urine. The structure of a Foley catheter was shown in Figure B.1. The balloon could be inflated by injecting water into it through the inflation funnel. The size of the Foley catheter is described using French unit (Fr) which is a measure of the external diameter of the catheter (3 Fr = 1 mm).

Drainage funnel

Inflation funnel

Shaft

Tip Balloon

Figure B.1. A silicone Foley catheter with the balloon slightly inflated.

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Appendix C. Mesh density study

Mesh convergence study has been undertaken to ensure the accuracy of the models.

These mesh density studies are presented as follows.

C.1 The chiasmal model in Chapter 3

Two mesh densities were studied: baseline mesh that represents the mesh density used in the baseline model in Chapter 3 and a finer mesh model with the same element type as the baseline model. The number of nodes and elements in these two cases are listed in Table C.1.

Table C.1 Number of nodes and elements Number of nodes Number of elements

Baseline 118,657 27,412 Fine 162,774 39,016

The von Mises strain values on Path A (see Figure 3.2 and corresponding text in

Chapter 3 for details) for both cases were plotted in Figure C.1. It can be seen that the strain distribution in both cases were in very good agreement with each other which indicates that the mesh density in baseline model was reasonable.

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0.15 baseline fine

0.1

0.05 von Mises strain

0 0 1 2 3 4 5 6 Distance from the centre of the chiasm (mm)

Figure C.1. Von mises strain distribution on Path A in both cases.

C.2 The chiasmal model in Chapter 4

A baseline mesh model and a coarser mesh model with the same element type were examined. The number of nodes and elements in these two models are listed Table C.2.

Table C.2 Number of nodes and elements Number of nodes Number of elements

Baseline 212,115 78,263 Coarse 123,570 47,021

Figure C.2 shows the von Mises strain distribution in the chiasmal cross-section (see

Figure 4.5 for details) for these two models. The von Mises strain distribution for both meshes were in good agreement with only minor differences. The baseline mesh was therefore used in the simulation in Chapter 4.

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0.15

0.1

von Mises strain 0.05 coarse baseline 0 -6 -4 -2 0 2 4 6 Location (mm)

Figure C.2. The cross-sectional von Mises strain along the left-right orientation.

C.3 RVE model in Chapter 5

A baseline mesh model and a coarser mesh model with the same element type were examined. The number of nodes and elements in these two models are listed Table C.3.

Table C.3 Number of nodes and elements Number of nodes Number of elements

Baseline 264682 216341 Coarse 125316 105447

Figure C.3 illustrates the cross-sectional von Mises strain distribution along the nerve fibre segment. As can be seen, these two mesh densities resulted in nearly identical strain distributions which indicates that the mesh density used in the baseline model was reasonable for this study.

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0.1

0.09

0.08

von Mises strain 0.07 baseline coarse 0.06 0 0.2 0.4 0.6 0.8 1 1.2 µ The location along the nerve fibre segment ( m)

Figure C.3. Cross-sectional von Mises strain distribution along the nerve fibre segment.

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Appendix D. Myelinated nerve fibre structure

The structure of a myelinated nerve fibre is shown in Figure D.1. In myelinated nerve fibres, axons are electrically insulated by their myelin sheaths along most of their lengths, except at nodes of Ranvier. The region between adjacent nodes is called an internode. The internodal length is related to axon diameter and varies between 0.2 and

2.0 mm (Standring, 2008) in human. The node of Ranvier is usually 1–2 μm in length

(Caldwell, 2009).

The insulation between nodes of Ranvier allows the action potential to jump from one node to next, which greatly increases the conduction velocity (Standring, 2008). This conduction is termed as salutatory conduction.

Figure has been removed due to Copyright restrictions.

Source: http://medicalterms.info/anatomy/Myelination/

Figure D.1. Diagram of the structure of a myelinated nerve fibre (http://medicalterms.info/anatomy/Myelination/).

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Appendix E. APDL script used to apply constraint equations on two opposite faces

Two faces with their normal along x axis were presented here as an example. In the script, x+ refers to the face with its normal along the positive x direction and x- refers to the face with its normal along negative x direction; a is the dimensions of the RVE at x direction. Note that the coordinate system used in the RVE model was different from that used in the macroscopic chiasmal model.

! **** apply constraint equations on node pairs on x+ and x- ****

ASEL,S,LOC,X,0,0 ! select x- face by its location CM,xn,AREA ! name the x- face as xn

ASEL,S,LOC,X,a,a ! select x+ face CM,xp,area ! name the x+ faces as xp

CMSEL,S,xn,AREA ! select x- face by predefined component 'xn' NSLA,S,1 ! select the nodes attached to x- face CM,node_xn,NODE ! store the nodes on x- in the component 'node_xn'

CMSEL,S,xp,AREA ! select x+ face by predefined component 'xn' NSLA,S,1 ! select the nodes attached to x+ face CM,node_xp,NODE ! store the nodes on x+ in the component 'node_xp'

CMSEL,S,node_xn ! select nodes on x- *GET,n_xn,node,,COUNT ! count the number of nodes on x- and store the number as “n_xn”

*DIM,node_x, ARRAY,n_xn,2, ! define a (n_xn,2) array to store nodes on x- and x+

*SET,xi,0 !define a variable with the initial value of 0

*CMSEL,S,node_xn ! select nodes on x-

*DO,n_row,1,n_xn ! for all the nodes on x-; 'n_row': row number xi=NDNEXT(xi) ! find the next node which number is greater than ‘xi’ and assign the new number to ‘xi’ node_x(n_row,1)=xi ! assign the node number to 'n_row' in column 1 nlocy=ny(xi) ! find y coordinate value of node 'xi' nlocz=nz(xi) ! find z coordinate value of node 'xi' CMSEL,S,node_xp ! select nodes on x+ node_x(n_row,2)=node(a,nlocy,nlocz) ! find the node near the location (n, nlocy, nlocz)

CMSEL,S,node_xn ! select nodes on x-

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CMSEL,A,node_xp ! also select nodes on x+ CE,NEXT,0,node_x(n_row,1),UX,-1,node_x(n_row,2),UX,1,1,UX,-1 !CE ux CE,NEXT,0,node_x(n_row,1),UY,-1,node_x(n_row,2),UY,1,1,UY,-1 !CE uy CE,NEXT,0,node_x(n_row,1),UZ,-1,node_x(n_row,2),UZ,1,1,UZ,-1 !CE uz CMSEL,S,node_xn ! Only select nodes on x- faces for next step of the loop *ENDDO

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Appendix F. RVE model verification

In Chapter 5, nerve fibre models were built using representative volume element (RVE).

However, the simulation results cannot be validated because there is no experimental data in the literature. It requires very specialist resources to perform a nerve fibre interaction experiment and these resources were not available for this work.

Verification of the whole procedure used in this simulation was performed by applying them to another analogous problem before the RVE model can be validated against experimental data.

A composite woven structure reported in the literature (Wang et al., 2007) was simulated using the software and procedures in this thesis. Figure F.1 shows the results compared with the simulation by Wang et al (2007).

(MPa)

(a) (b)

Figure F.1. Von Mises stress distribution in an RVE of a composite structure. (a) The results obtained using ANSYS and the procedures in this thesis; (b) The results by Wang et al. using MSC NASTRAN. Deformations were exaggerated 100 times.

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The software and procedure in this thesis can reproduce the simulation by Wang et al.

(2007), which indicates that the software and procedure in this simulation were reasonable. However, it should be noted that the nerve fibre models in Chapter 5 were still unvalidated and its accuracy is depending on the assumptions of geometry and the material properties in the model.

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Appendix G. MATLAB codes for orientation data processing

The MATLAB codes written for post processing the nerve fibre orientation data derived from OrientationJ were presented as follows.

Peak recognition: fid1 = fopen('result_1.txt','wt'); fid2 = fopen('result_2.txt','wt'); fid3 = fopen('result_3.txt','wt'); fid4 = fopen('result_4.txt','wt'); fid5 = fopen('result_5.txt','wt'); % Open text files to write data

row_n = 33; % number of rows column_n = 38; % number of columns for i = 1:row_n % number of rows for j = 1:column_n % number of columns file_n = (i-1)*column_n+j; % file name fname1 = sprintf('141_m%04d',file_n); % Slice 141 fname3 = strcat(fname1,'.txt'); fname4 = strcat('avg_',fname1,'.txt'); if exist(fname3,'file') a1=load(fname3); asz=size(a1); b1 = [a1(1:asz(1)/2,1) a1(1:asz(1)/2,2)]; % half data b2 = [a1(asz(1)/2+1:asz(1),1) a1(asz(1)/2+1:asz(1),2)]; b1m = [(b1(:,1)+180),b1(:,2)]; % move data b2m = [(b2(:,1)-180),b2(:,2)];

a2=[b2m;a1;b1m]; % duplicated data

%^^^^^^^^^^^^^^ check the existence of peaks at 0 and 90 ^^^^^^^ [pks2,locs2] = findpeaks(a2(:,2));

flag_0 = 0; for i2=1:length(locs2); % check whether 0 exist if 181==locs2(i2)||180==locs2(i2)||182==locs2(i2) flag_0=1; end end

flag_90 = 0; for i3=1:length(locs2); if 91==locs2(i3)||271==locs2(i3)||90==locs2(i3)||270==locs2(i3)||92==locs 2(i3)||272==locs2(i3) % -89 -90 -91 89 90 91

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flag_90=1; end end

%^^^^^^^^^^^^^ remove data ^^^^^^^^^^^^^^^^^^^ data7=a2; data8=data7; [a2_max,ia2_max,a2_min,ia2_min] = extrema(a2(:,2));

if flag_0==1 locs_0r = locs2(find(locs2>=180& locs2<=182)); locs_0 = locs_0r(1); dis_0 = min(abs(locs_0-ia2_min));

if dis_0 <= 10; dis_0 = dis_0; else dis_0 = 3; end % if dis_0 <=10

unit_v = (a2(locs_0 + dis_0,2) - a2(locs_0 - dis_0,2))/(2*dis_0);

for i_dis = locs_0 - dis_0 +1 : locs_0 + dis_0 - 1 % 0 degree data8(i_dis,2) = data7(locs_0 - dis_0,2) + unit_v * (i_dis - locs_0 + dis_0); end

end % if flag_0 ==0

data9=data8; if flag_90==1

locs_90r= locs2(find(locs2>=270& locs2<=272)); locs_90 = locs_90r(1); dis_90 = min(abs(locs_90-ia2_min));

if dis_90 <= 10; dis_90 = dis_90; else dis_90 = 3; end % if dis_90 <=10

unit_v = (a2(locs_90 + dis_90,2) - a2(locs_90 - dis_90,2))/(2*dis_90);

for i_dis = locs_90 - dis_90 +1 : locs_90 + dis_90 -1 % 0 degree data9(i_dis,2) = data8(locs_90 - dis_90,2) + unit_v * (i_dis - locs_90 + dis_90); data9(i_dis-180,2) = data8(locs_90 - dis_90,2) + unit_v * (i_dis - locs_90 + dis_90);

end

end % if flag_0 ==0 213

data10 = [[data9(181:270,1)-180 data9(181:270,2)]; [data9(91:270,1) data9(91:270,2)]; [data9(91:180,1)+180 data9(91:180,2)]];

%^^^^^^^^butterworth filter^^^^^^^^^^^^^^^^^^^^^ [B,A]=butter(5,0.07,'low'); data10b=filtfilt(B,A,data10);

%^^^^^^^^^plot data^^^

hp=figure('visible','off');

subplot (2,2,[1 2]); plot(a2(:,1),a2(:,2)) %plot title('original vs. modified'); [pks1,locs1] = findpeaks(a1(:,2)); hold on; plot(a1((locs1),1),pks1+50,'k^','markerfacecolor',[1 0 0]); % mark peaks d3 = a1((locs1),1); % without avg hold on; plot(data10(:,1),data10(:,2),'r') %plot

subplot (2,2,[3 4]); title('filtered vs. modified'); plot(data10(:,1),data10(:,2),'r') %plot hold on; plot(data10b(:,1),data10b(:,2)) %plot hold on;

[pks3,locs3] = findpeaks(data10b(:,2)); e = [pks3,locs3]; pkmax=max(pks3); e1 = locs3(find(pks3 >=0.15*pkmax)); % THRESHOLD e2 = e1(find(e1 >=90 & e1 < 270));

e3 = e2;

f1 = data10b((e3),1) ; f2 = data10b((e3),2) ; f3=[f1 f2]; % the peak data

%^^^^^^ width^^^^ num_p = size(f3); num_peaks = num_p(1); % number of peaks width = zeros(num_peaks,1);

for ip = 1:num_peaks % loop for all peaks p_value = f3(ip,2); % peak value p_angle = f3(ip,1); % angle at peak value half_h = p_value/2;

index1 = find(data10b(:,1)==p_angle); index2 = find(data10b(:,1)==p_angle); for k = find(data10b(:,1)==p_angle)-1:-1:1 if data10b(k,2) < half_h break; end 214

index1 = k; end

for k = find(data10b(:,1)==p_angle)+1:354 if data10b(k,2) < half_h break; end index2 = k; end

index = index2-index1; width(ip) = index;

hold on; line([data10b(index1,1),data10b(index1,1)],[0,data10b(index1,2)],'Colo r',[0,1,0]); hold on; line([data10b(index2,1),data10b(index2,1)],[0,data10b(index2,2)],'Colo r',[0,1,0]); hold on; text(p_angle+2,p_value+300,num2str(index));

end % for ip f4 = [f3 width]; f5 = f4';

n_p=size(f1); n_p2=n_p(1);

if n_p2==1

fprintf(fid1,'%15s%5d%5d\t',fname3,i,j); fprintf(fid1,'%12.5e\t%12.5e\t%4d\t',f5); fprintf(fid1,'\n'); end

if n_p2==2

fprintf(fid2,'%15s%5d%5d\t',fname3,i,j); fprintf(fid2,'%12.5e\t%12.5e\t%4d\t',f5); fprintf(fid2,'\n'); end

if n_p2==3

fprintf(fid3,'%15s%5d%5d\t',fname3,i,j); fprintf(fid3,'%12.5e\t%12.5e\t%4d\t',f5); fprintf(fid3,'\n'); end

if n_p2==4

fprintf(fid4,'%15s%5d%5d\t',fname3,i,j); fprintf(fid4,'%12.5e\t%12.5e\t%4d\t',f5); fprintf(fid4,'\n'); end 215

if n_p2>=5

fprintf(fid5,'%15s%5d%5d\t',fname3,i,j); fprintf(fid5,'%12.5e\t%12.5e\t%4d\t',f5); fprintf(fid5,'\n'); end

hold on; plot(data10(e3),f2+300,'k^','markerfacecolor',[1 0 0]); % mark peaks

saveas(hp,fname1,'jpg') close all end % if file exist end % j end % i

fclose('all');

Plot fibre orientations: d1 = 158; d2 = 121; % ROI dimension (resized) = d1*d2 (horizontal pixels * vertical pixels) bar = 50 ; % half of the bar length data1=load('result_1.txt'); data2=load('result_2.txt'); data3=load('result_3.txt'); data4=load('result_4.txt'); sz1 = size(data1); sz2 = size(data2); sz3 = size(data3); sz4 = size(data4);

%^^^^^^^^^^^^^^^^ 1 peak ^^^^^^^^^^^^^^^^^^^^^^^^^ if sz1(1) ~= 0 data_c1 =[(data1(:,3)-1)*d1+d1/2,(data1(:,2)-1)*d2+d2/2]; % central points coordinate data_start = [data_c1(:,1)- bar*cosd(data1(:,4)),data_c1(:,2)+bar*sind(data1(:,4))]; % start points data_end = [data_c1(:,1)+bar*cosd(data1(:,4)),data_c1(:,2)- bar*sind(data1(:,4))]; % end points arrow('Start',data_start,'Stop',data_end,'Length',0,'Width',3); % plot % need to use “arrow.m” which can be found in Matlabcentral hold on; end

%^^^^^^^^^^^^^^^^ 2 peaks ^^^^^^^^^^^^^^^^^^^^^^^^^ if sz2(1) ~= 0

216 data_c1 =[(data2(:,3)-1)*d1+d1/2,(data2(:,2)-1)*d2+d2/2]; % central points coordinate data_start1 = [data_c1(:,1)- bar*cosd(data2(:,4)),data_c1(:,2)+bar*sind(data2(:,4))]; % start points data_end1 = [data_c1(:,1)+bar*cosd(data2(:,4)),data_c1(:,2)- bar*sind(data2(:,4))]; % end points data_start2 = [data_c1(:,1)- bar*cosd(data2(:,7)),data_c1(:,2)+bar*sind(data2(:,7))]; % start points data_end2 = [data_c1(:,1)+bar*cosd(data2(:,7)),data_c1(:,2)- bar*sind(data2(:,7))]; % end points arrow('Start',data_start1,'Stop',data_end1,'Length',0,'Width',3); % plot the first group of arrow hold on; arrow('Start',data_start2,'Stop',data_end2,'Length',0,'Width',3); % plot the first group of arrow hold on; end

%^^^^^^^^^^^^^^^^ 3 peaks ^^^^^^^^^^^^^^^^^^^^^^^^^ if sz3(1) ~= 0 data_c1 =[(data3(:,3)-1)*d1+d1/2,(data3(:,2)-1)*d2+d2/2]; % central points coordinate data_start1 = [data_c1(:,1)- bar*cosd(data3(:,4)),data_c1(:,2)+bar*sind(data3(:,4))]; % start points data_end1 = [data_c1(:,1)+bar*cosd(data3(:,4)),data_c1(:,2)- bar*sind(data3(:,4))]; % end points data_start2 = [data_c1(:,1)- bar*cosd(data3(:,7)),data_c1(:,2)+bar*sind(data3(:,7))]; % start points data_end2 = [data_c1(:,1)+bar*cosd(data3(:,7)),data_c1(:,2)- bar*sind(data3(:,7))]; % end points data_start3 = [data_c1(:,1)- bar*cosd(data3(:,10)),data_c1(:,2)+bar*sind(data3(:,10))]; % start points data_end3 = [data_c1(:,1)+bar*cosd(data3(:,10)),data_c1(:,2)- bar*sind(data3(:,10))]; % end points arrow('Start',data_start1,'Stop',data_end1,'Length',0,'Width',3); % plot the first group of arrow hold on; arrow('Start',data_start2,'Stop',data_end2,'Length',0,'Width',3); % plot the first group of arrow hold on; arrow('Start',data_start3,'Stop',data_end3,'Length',0,'Width',3); % plot the first group of arrow

217 hold on; end

%^^^^^^^^^^^^^^^^ 4 peaks ^^^^^^^^^^^^^^^^^^^^^^^^^ if sz4(1) ~= 0 data_c1 =[(data4(:,3)-1)*d1+d1/2,(data4(:,2)-1)*d2+d2/2]; % central points coordinate data_start1 = [data_c1(:,1)- bar*cosd(data4(:,4)),data_c1(:,2)+bar*sind(data4(:,4))]; % start points data_end1 = [data_c1(:,1)+bar*cosd(data4(:,4)),data_c1(:,2)- bar*sind(data4(:,4))]; % end points data_start2 = [data_c1(:,1)- bar*cosd(data4(:,7)),data_c1(:,2)+bar*sind(data4(:,7))]; % start points data_end2 = [data_c1(:,1)+bar*cosd(data4(:,7)),data_c1(:,2)- bar*sind(data4(:,7))]; % end points data_start3 = [data_c1(:,1)- bar*cosd(data4(:,10)),data_c1(:,2)+bar*sind(data4(:,10))]; % start points data_end3 = [data_c1(:,1)+bar*cosd(data4(:,10)),data_c1(:,2)- bar*sind(data4(:,10))]; % end points data_start4 = [data_c1(:,1)- bar*cosd(data4(:,13)),data_c1(:,2)+bar*sind(data4(:,13))]; % start points data_end4 = [data_c1(:,1)+bar*cosd(data4(:,13)),data_c1(:,2)- bar*sind(data4(:,13))]; % end points arrow('Start',data_start1,'Stop',data_end1,'Length',0,'Width',3); % plot the first group of arrow hold on; arrow('Start',data_start2,'Stop',data_end2,'Length',0,'Width',3); % plot the first group of arrow hold on; arrow('Start',data_start3,'Stop',data_end3,'Length',0,'Width',3); % plot the first group of arrow hold on; arrow('Start',data_start4,'Stop',data_end4,'Length',0,'Width',3); % plot the first group of arrow hold on; end

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Appendix H. Drawings of the mounting apparatus

CAD Drawings of the 3D printed base (Figure H.1) and fixer (Figure H.2) used in

Chapter 7 for ex vivo experiment of the chiasmal compression.

Figure H.1. Drawings of the base (Unit: mm)

219

Figure H.2. Drawings of the fixer. (Unit: mm)

220

Reference for Appendix

Caldwell, J.H., 2009. Action Potential Initiation and Conduction in Axons, in: Squire, L.R. (Ed.), Encyclopedia of Neuroscience. Elsevier.

Standring, S., 2008. Gray's Anatomy: The Anatomical Basis of Clinical Practice. Elsevier Health Sciences UK.

Wang, X.F., Wang, X.W., Zhou, G.M., Zhou, C.W., 2007. Multi-scale analyses of 3D woven composite based on periodicity boundary conditions. Journal of Composite Materials 41, 1773-1788.

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