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Experimental study of deformation and microcracking in human cortical bone Ebacher, Vincent 2011

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EXPERIMENTAL STUDY OF DEFORMATION AND MICROCRACKING IN HUMAN CORTICAL BONE  by  Vincent Ebacher  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies (Materials Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  May 2011   © Vincent Ebacher, 2011ii ABSTRACT Human bone is a complex biological material with up to seven levels of hierarchical structure. Due to this complexity, it is still not fully understood how the various structures contribute to the macroscopic mechanical response. Such understanding is important to assess the mechanical contributions of the bone material to whole bone fractures. It is well known that microcracking is associated with bone’s inelastic deformation and contributes to its resistance to fracture. Multiple microcracks suggest control over their development. Yet, the structure – microcracking interactions in cortical bone, particularly at the lamellar and Haversian systems levels, are still unclear. Following a qualitative, structure – mechanical function relations approach, the present dissertation provides further insight into how bone resists fracture by distributed microcracking. This was achieved through a detailed study of bone’s deformation and fracture processes using mechanical testing on human cadaver bones and a combination of microscopy techniques, including laser scanning confocal microscopy, to characterize the structure – microcracking relations. Particular interest was given to compression and bending, two loading modes involved in falls resulting in hip fractures. Haversian bone derived part of its fracture resistance through microcracking largely controlled by the concentric lamellae and underlying fibrillar organisation surrounding each Haversian canal. Multiple microcracks developed stably within the osteonal wall due to different fibrillar orientation in each lamella. Such process happened to most osteons resulting in well-distributed damage, hence providing inelastic deformation to the tissue. Haversian bone’s resistance to fracture would thus depend on its intact lamellar structure. Changes in number and iii organisation of the lamellae would likely alter bone’s ability to control microcracks and may lead to bone fragility. Based on a tibia study, long bones’ fracture resistance in bending was found to be linked to Haversian bone’s behavior. As a result of post-yield strain redistribution associated with tensile and compressive microcracking, bone’s compressive behavior was also found to play an important role in the bending response. Directly applying fundamental research to the clinical field, a preliminary analysis of the superior cortex of fractured femoral necks retrieved from patients revealed compressive microcracking. Such evidence emphasizes the importance of bone’s hierarchical structure in hip fracture.  iv PREFACE A version of Chapter 4 has been published. Ebacher V, Tang C, McKay H, Oxland TR, Guy P, and Wang R. (2007) Strain Redistribution and Cracking Behavior of Human Bone during Bending. Bone. 40:1265-75. With the exception of the mechanical bending tests on whole tibiae done by CT, VE conducted all the experiments and wrote the manuscript. Note that part of the Introduction in the original publication has been moved to the literature review (Chapter 2). The study was approved by the Clinical Research Ethics Review Board at the UBC (Ethics Certificate # C04-0030). A version of Chapter 5 has been published. Ebacher V and Wang R. (2009) A Unique Microcracking Process Associated with the Inelastic Deformation of Haversian Bone. Adv Funct Mater. 19:57-66. VE conducted all the experiments and wrote the manuscript. Note that part of the Introduction in the original publication has been moved to the literature review (Chapter 2). The study was approved by the Clinical Research Ethics Review Board at the UBC (Ethics Certificate # C04-0030). A version of Chapter 6 has been submitted for publication. Ebacher V, Guy P, Oxland TR, and Wang R. (09 JA 2011) Sub-Lamellar Microcracking and the Roles of the Canalicular Network in Human Haversian Bone. VE conducted all the experiments and wrote the manuscript. Note that part of the Introduction in the original publication has been moved to the literature review (Chapter 2). The study was approved by the Clinical Research Ethics Review Board at the UBC (Ethics Certificate # H09-02073). The study in Chapter 7 was approved by the Clinical Research Ethics Review Board at the UBC (Ethics Certificate # H03-70629).  v TABLE OF CONTENTS ABSTRACT.................................................................................................................................... ii PREFACE...................................................................................................................................... iv TABLE OF CONTENTS................................................................................................................ v LIST OF TABLES......................................................................................................................... ix LIST OF FIGURES ........................................................................................................................ x LIST OF ABBREVIATIONS...................................................................................................... xix ACKNOWLEDGEMENTS.......................................................................................................... xx CHAPTER 1 INTRODUCTION................................................................................................. 1 CHAPTER 2 LITERATURE REVIEW...................................................................................... 3 2.1 HIP FRACTURES – EPIDEMIOLOGY AND OUTCOMES .......................................................... 3 2.2 HIP FRACTURES – AETIOLOGY: AN OVERVIEW................................................................. 3 2.3 THE MATERIAL BONE ....................................................................................................... 4 2.3.1 Human Haversian Bone: Product of Remodeling..................................................... 7 2.4 MECHANICAL PROPERTIES OF CORTICAL BONE ................................................................ 9 2.5 HIERARCHICAL STRUCTURE – MECHANICAL FUNCTION RELATIONS .............................. 11 2.5.1 Molecular and Fibrillar Levels................................................................................ 11 2.5.2 Lamellar, Osteonal, and Tissue Levels ................................................................... 12 2.5.3 Microcracks and Microcracking in Bone................................................................ 14 2.5.4 Bone Deformation and Whole Bone Fracture ........................................................ 16 2.5.5 Summary of Existing Problems .............................................................................. 17 CHAPTER 3 SCOPE AND OBJECTIVES .............................................................................. 19 CHAPTER 4 STRAIN REDISTRIBUTION AND CRACKING BEHAVIOR OF HUMAN BONE DURING BENDING ........................................................................................................ 21 4.1 MATERIALS AND METHODS ............................................................................................ 21 4.1.1 Mechanical Tests .................................................................................................... 22 4.1.2 Fracture and Microdamage Analyses...................................................................... 24 4.2 RESULTS.......................................................................................................................... 26 4.2.1 Strain Measurements............................................................................................... 26 4.2.2 Fracture and Microdamage Analyses...................................................................... 31 vi 4.3 DISCUSSION..................................................................................................................... 36 4.3.1 Strain Redistribution during Bending ..................................................................... 37 4.3.2 Poisson’s Ratio........................................................................................................ 39 4.3.3 Role of Bone Microstructure .................................................................................. 40 4.4 CONCLUSIONS ................................................................................................................. 42 CHAPTER 5 A UNIQUE MICROCRACKING PROCESS ASSOCIATED WITH THE INELASTIC DEFORMATION OF HAVERSIAN BONE.......................................................... 43 5.1 EXPERIMENTAL ............................................................................................................... 43 5.1.1 Mechanical Tests – Monotonic Loading................................................................. 44 5.1.2 Mechanical Tests – Step-wise Loading .................................................................. 45 5.1.3 Fracture and Microdamage Analyses...................................................................... 47 5.2 RESULTS.......................................................................................................................... 49 5.2.1 Effects of Loading Orientation on Stress-Strain Curves and Basic Mechanical Properties .............................................................................................................................. 49 5.2.2 Effects of Loading Orientation on Macro-Scale Fracture Patterns and Microdamage Morphologies ........................................................................................................................ 51 5.2.3 Damage Development in the Transverse Orientation: Initiation and Propagation . 55 5.2.4 Deformation Process: Strain Distribution around Osteons..................................... 58 5.3 DISCUSSION..................................................................................................................... 61 5.3.1 A Unique Microcracking Process ........................................................................... 61 5.3.2 Role of Osteonal Lamellae...................................................................................... 62 5.3.3 Role of Cement Lines, Pre-Existing Cracks, and Neighboring Osteons ................ 64 5.3.4 Implications to Bone Quality .................................................................................. 65 5.4 CONCLUSIONS ................................................................................................................. 66 5.5 SUPPORTING INFORMATION............................................................................................. 67 5.5.1 Microdamage within the Bulk of the Bone Specimens .......................................... 67 5.5.2 Role of Pre-existing Cracks in the Fracture Process............................................... 68 5.5.3 Variations of the Microcrack Morphologies........................................................... 69 CHAPTER 6 SUB-LAMELLAR MICROCRACKING AND THE ROLES OF THE CANALICULAR NETWORK IN HUMAN HAVERSIAN BONE............................................ 71 6.1 MATERIALS AND METHODS ............................................................................................ 72 vii 6.1.1 Specimens and Mechanical Testing........................................................................ 72 6.1.2 Laser Scanning Confocal Imaging Analysis........................................................... 73 6.1.3 Numerical Simulation ............................................................................................. 75 6.2 RESULTS.......................................................................................................................... 77 6.2.1 Multi-Scale Cracking in Bone: The Advantages of LSCM.................................... 77 6.2.2 Bone's Porosity: the Canaliculi Network ................................................................ 81 6.2.3 Cracking Process in Transverse Compression: Initiation and Development within the Bulk ................................................................................................................................. 82 6.2.4 Mechanical Simulation ........................................................................................... 85 6.2.5 Surface and Bulk Damage ...................................................................................... 86 6.3 DISCUSSION..................................................................................................................... 87 6.3.1 Relevance of Transverse Compression................................................................... 88 6.3.2 Role of Canaliculi in Crack Initiation and Growth................................................. 88 6.3.3 Sub-Lamellar Cracking: Towards the Nature of Cracks in Bone ........................... 90 6.3.4 Hierarchical Cracking in Human Haversian Bone.................................................. 91 6.3.5 Possible Role of Canaliculi as Physiological Sensors ............................................ 92 6.4 CONCLUSIONS ................................................................................................................. 93 6.5 SUPPLEMENTARY INFORMATION ..................................................................................... 93 6.5.1 Variations of Microcrack Morphologies under Transverse Compression.............. 93 6.5.2 Numerical Simulations with Transversely Isotropic Properties ............................. 95 6.5.3 Multi-Scale Deformation Process ........................................................................... 96 CHAPTER 7 TOWARDS UNDERSTANDING THE MECHANISMS OF FEMORAL NECK FRACTURES - A CASE STUDY................................................................................................ 98 7.1 METHODS AND MATERIALS............................................................................................. 98 7.1.1 Specimen Preparation ............................................................................................. 98 7.1.2 Microcracking Observations................................................................................... 99 7.2 RESULTS.......................................................................................................................... 99 7.3 DISCUSSION................................................................................................................... 101 7.3.1 Microcracking in the Femoral Neck ..................................................................... 102 7.3.2 Buckling in the Superior Cortex ........................................................................... 102 7.3.3 Microcracking and Hip Fragility .......................................................................... 103 viii 7.4 CONCLUSIONS ............................................................................................................... 104 CHAPTER 8 CONCLUSIONS AND PERSPECTIVES........................................................ 105 8.1 CONCLUSIONS ............................................................................................................... 105 8.1.1 Design Principles to Resist Fracture in Haversian Bone ...................................... 105 8.1.2 Applications to Whole Bone and Hip Fractures ................................................... 106 8.1.3 Bridging the Gap between Bone’s Micro- and Nano- Scales ............................... 107 8.2 LIMITATIONS ................................................................................................................. 107 8.3 RECOMMENDATIONS ..................................................................................................... 108 REFERENCES ........................................................................................................................... 110 APPENDICES ............................................................................................................................ 135 APPENDIX A        CHAPTER 4 – ADDITIONAL DATA .............................................................. 135 Specimens ........................................................................................................................... 135 Mechanical Tests ................................................................................................................ 135 Load-Strain and Strain Rate Curves ................................................................................... 135 Macro-Scale Fracture Patterns............................................................................................ 135 Microdamage Observations ................................................................................................ 135 APPENDIX B        CHAPTER 5 – ADDITIONAL DATA .............................................................. 144 Specimens ........................................................................................................................... 144 Mechanical Tests ................................................................................................................ 144 Stress-Strain Curves............................................................................................................ 144 Microdamage Observations ................................................................................................ 144 APPENDIX C        DIGITAL IMAGE CORRELATION ACCURACY .............................................. 147 Selection of the Interrogation Window Size and Overlap .................................................. 147 Determination of the Strain Accuracy ................................................................................ 148   ix LIST OF TABLES Table 5.1. Properties calculated from the compressive stress-strain curves (mean ± sd). .......... 50 Table 5.2. Cross-hatched microcrack angles in cortical bone specimens loaded along three different orientations (mean ± sd). ............................................................................. 53 Table 6.1. Selected lamellar elastic properties for bone under transverse compression (based on [41,68,127,128,170,244,252-255]). ........................................................................... 76 Table 6.2. Spacing of canaliculi and intralamellar cracks in transversely compressed cortical bone specimens (mean ± sd). ..................................................................................... 81   x LIST OF FIGURES Figure 2.1. Bone’s hierarchical structure. Reprinted and adapted from [92] with permission from Elsevier......................................................................................................................... 5 Figure 2.2. Cortex of human long bone. Reprinted and adapted from [104] (Fig. 40, p.76) with permission from Elsevier (Urban & Schwarzenberg).................................................. 6 Figure 2.3. Haversian bone’s microstructure: (a) Bright field optical image of a Haversian system (transverse section) and the surrounding interstitial bone (I). Pairs of thin/thick or dark/bright concentric lamellae line the central Haversian canal (H). Osteocyte lacunae are also seen (three are identified by asterisks); (b) Schematic of the rotated plywood structure where each pair of lamellae consists of five sub-layers with a progressive rotation of both the collagen fibrils and the mineral platelets. The fibrils in the first sub-layer are follow the circumferential direction (thin/dark lamella) while those of the fifth one are aligned with the osteons (thick/bright lamella). (b) reprinted and adapted from [114] with permission from Elsevier. ......... 8 Figure 2.4. Schematic of cortical bone’s stress-strain curves for longitudinal tension and compression. Reprinted from [126] with permission from Elsevier.......................... 10 Figure 4.1. Typical load-strain curves: (a) Cortical bone specimen; (b) Whole tibia specimen; Inserts: Configurations of the four-point bending on cortical bone specimens and proximal tibiae specimens, respectively; SG: Strain Gage, PMMA: Poly (methyl methacrylate).............................................................................................................. 26 Figure 4.2. Longitudinal and transverse strain ratios (tensile strain over compressive strain, -εT/εC) for (a) cortical bone specimens, (b) whole bone specimens. Tensile and compressive Poisson’s ratios (ν = -εt/εl) for (c) cortical bone specimens, (d) whole bone specimens. The error bars are standard deviations............................................ 28 Figure 4.3. Tensile and compressive stress-strain curves for five cortical bone specimens. ....... 29 Figure 4.4. Typical load-time curves and variations of strain rates: (a) Cortical bone specimen; (b) Whole tibia specimen. .......................................................................................... 30 Figure 4.5. Side views of typical "butterfly" macro-scale fracture patterns: (a) Cortical bone specimen; (b) Whole tibia specimen; (c) pQCT (peripheral Quantitative Computed xi Tomography) cross-section of tibia at the location of the strain gage (58%). White area shows geometry of bone cortex.......................................................................... 31 Figure 4.6. Microdamage morphologies under bright field (.1) and epi-fluorescence (.2) modes: (a) Compression surface showing cross-hatching microdamage far away from the final fracture site; (b) Compression surface showing scale-type microdamage at the final fracture site; (c) Tensile surface showing diffuse microdamage at the final fracture site. Principal stress along length of images................................................. 33 Figure 4.7. Side view of tensile diffuse microdamage in the fracture process zone visualized under epi-fluorescence mode. .................................................................................... 34 Figure 4.8. (a) Tensile diffuse microdamage in both osteonal (O) and interstitial (I) bone visualized under epi-fluorescence mode; (b) Corresponding bright field mode micrograph; (c) Corresponding BSE image. Tensile stress along top-bottom axis of images. ....................................................................................................................... 35 Figure 4.9. (a) Compressive cross-hatching microdamage localized within an individual Haversian system (H) visualized under epi-fluorescence mode; (b) Corresponding BSE image. Compressive stress along top/right-bottom/left axis of images. Arrows mark two of the shear cracks...................................................................................... 36 Figure 5.1. Typical compressive stress-strain curves for human cortical bone loaded along three different orientations: longitudinal (0°), oblique (45°), and transverse (90°). The transverse orientation shows much higher inelastic strain than the other two........... 49 Figure 5.2. Compressive microdamage morphologies of human cortical bone loaded along different orientations. a) Longitudinal (0°); b) Transverse (90°); c) Oblique (45°). left: epi-fluorescence images; right: bright field images. At this magnification, the microdamage morphologies all look similar and are characterized by their oblique cross-hatched patterns. Compressive load applied vertically. ................................... 52 Figure 5.3. Microcracks on transversely compressed bone specimens. a) Epi-fluorescence image showing four groups of arc-shaped circumferential microcracks (bright green) formed at the four quadrants of an osteon (center); b) Epi-fluorescence image showing the influence of neighboring osteons on the angle of the cross-hatched microdamage. The cracking of the central osteon is obviously attracted to the osteons to the lower left and upper right; c) SEM micrograph showing arc-shaped xii microcracks at various stages of development along the osteonal lamellae. Photo was taken from the lower left quadrant of the osteon in (a). The lamellae have alternating bright (thin lamellae marked by arrowheads) and dark (thick lamellae) contrast; d) Closer observations of (c) (asterisks) showing the short micro-radial cracks in the thick lamellae and their merging into a circumferential microcrack. Compressive load applied horizontally............................................................................................ 54 Figure 5.4. Damage development in cortical bone. a) Bright field micrograph showing two osteons. Photo taken after the compression test; Epi-fluorescence micrographs showing progressive observations of microcracks development: b) Microcrack initiation within the two osteons at initial loading; c) More arc-shaped microcracks within the osteons upon further loading. Cracking in interstitial bone (arrow) links the osteonal cracks; d) Extensive damage at the final state. Note the very little interaction between the two central osteons aligned with the loading axis. Compressive load applied horizontally...................................................................... 56 Figure 5.5. Frequency distribution of the location of arc-shaped microcrack initiation under transverse compression. Sixty-nine osteons at the initiation stage were examined. All osteons considered were divided into five locations: A1-2) at the Haversian canal: radial crack and circumferential crack, respectively; B) first third of the osteonal wall; C) middle third of the osteonal wall; D) at or close to the cement line; E) outside of osteon (interstitial bone). A1 and A2 are considered as cracks at the Haversian canal, while B and C are intra-osteonal wall cracks. The error bars represent the standard error of the estimate of the compiled proportions for a confidence level of 95% (p < 0.05)............................................................................ 57 Figure 5.6. Deformation process in cortical bone. a) Bright field optical image before loading; b) Epi-fluorescence image showing microdamage after loading; c) Maximum shear strain field for the elastic stage (~0.7% far-field compressive strain) showing strain concentration near Haversian canals; d) Maximum shear strain field for the inelastic stage (~1.7% far-field compressive strain) showing shear connections between the osteons. Note the match between the strain field and the microdamage pattern in (b). Compressive load applied horizontally...................................................................... 58 xiii Figure 5.7. Strain distribution surrounding an osteon. a) Epi-fluorescence micrograph showing the final microdamage pattern around the Haversian canal; b) Maximum shear strain oriented obliquely to the loading direction. Note that εmax = [(εx - εy)2/4 + (εxy)2]1/2, where the shear strain εxy corresponds to an average value of the displacement gradients exy and eyx shown in (c) and (d): εxy = (exy + eyx)/2 [226,241]; Shear components along the planes roughly corresponding to those of the maximum shear strain: c) Shear component (exy) on the y-plane along the x-direction; d) Shear component (eyx) on the x-plane along the y-direction. The radial shear is most probably related to the extensive cracking seen in the form of short micro-radial cracks within the thick lamellae; e) Optical micrograph showing a shear band formed at a later stage of deformation. Insert in (a): Approximate stress state in the damaged regions: the principal compressive and tensile strains are oriented parallel and perpendicularly to the loading direction, respectively, and the maximum shear strain planes are oblique to the loading direction. Compressive load applied horizontally. 60 Figure 5.8. Epi-fluorescence images of arc-shaped circumferential microcracks (bright green) within the bulk of transversely compressed bone specimens (central longitudinal section transverse to the bone's long axis). The microdamage seen on the surfaces is also observed in the bulk of the tissue, suggesting that extensive damage existed through the entire volume of the bone material. Compressive load applied vertically..................................................................................................................................... 67 Figure 5.9. Pre-existing cracks in the interstitial bone prior to loading (left, arrowed, Epi-fluorescence) and after compressive failure (center, Epi-fluorescence) together with their corresponding bright field images (right): a) An oblique pre-existing crack that did not propagate; b) An oblique pre-existing crack that did propagate but was not involved in the final fracture of the specimen. Compressive load applied horizontally..................................................................................................................................... 68 Figure 5.10. SEM micrographs of the microcracks in osteonal lamellae. a) Long linear cross-hatched cracks in an osteon presumably of the Type L structure (collagen fibers aligned mainly along the Haversian canal axis); b) Micro-radial cracks within the thick lamellae. Note that no circumferential cracks developed. Note also the cross-xiv hatched linear cracks in the interstitial bone (upper right). Haversian canal to the lower left. Compressive load applied horizontally. ................................................... 69 Figure 6.1. Multi-scale microcracking in human cortical bone under transverse compression. (a) Schematics of the transverse (90°) loading orientation with respect to the osteons; (b) Bright Field (BF) image of the macroscopic oblique fracture pattern; (c) Epi-Fluorescence (EF) image of distributed cross-hatched damage at the osteonal-interstitial level; (d) BF image of arc-shaped microcracks within the osteonal bright layers (arrowheads); (e) Laser Scanning Confocal Microscope (LSCM) image showing multiple intralamellar cracks in the four quadrants of an osteon; (f-g) Low resolution EF and high resolution LSCM images taken from the lower left quadrant (dotted line) of the osteon in (e). LSCM reveals a sub-lamellar cross-hatched pattern composed of fine radially and circumferentially oriented cracks with spacing similar in size to fibrillar bundles. Compressive load applied vertically for a-b-c and horizontally for d-e-f-g............................................................................................... 78 Figure 6.2. Multi-scale microcracking in human cortical bone under longitudinal compression. (a) Schematics of the longitudinal (0°) loading orientation with respect to the osteons; (b) Stereomicroscope image of the macroscopic oblique fracture pattern; (c) Epi-fluorescence image of distributed cross-hatched damage at the osteonal-interstitial level. Note the morphological similarity with transverse compression damage; (d) Backscattered Electron (BSE) micrograph of osteonal oblique microcrack formed at the Haversian canal (HC) and extending to the boundary (approximated by dashed line) between osteonal (O) and interstitial (I) bone. Notice the "stairway-like" changes of orientations (arrowheads) with the layers as well as the uncracked ligaments (insert: empty arrowheads) and lamellae (arrows). Insert location shown by dotted line; (e) Laser Scanning Confocal Microscope (LSCM) images showing smaller cracks within the larger oblique microcrack. The identified osteocyte lacunae (asterisks), ligament bridging (empty arrowheads) and full circle correspond to the same locations in (d). Note the change in crack morphology near the osteonal-interstitial boundary (bottom image); (f) High resolution 3D LSCM image of localized, finely spaced cross-hatched cracking near a Haversian canal (HC). The z-planes ("cut views" at locations shown by white lines) show deep xv oblique cracking; (g) LSCM images of crack interactions with osteocyte lacunae (asterisk) and canaliculi (double arrows). Compressive load applied vertically for a-b-c and horizontally for d-e-f-g.................................................................................. 80 Figure 6.3. Laser Scanning Confocal Microscope (LSCM) imaging of the canalicular network and the intralamellar cracking sequence within the bulk of transversely compressed bone specimens. (a) Image of a 5 µm deep z-stack showing the lacuno-canalicular network within an intact osteon. Insert: magnified image of a few canaliculi and their cross-sections (dotted ellipse); (b) Multiple circumferential crack initiations at the canaliculi. A single canaliculus could initiate more than one crack (double arrow). Notice that, in this loading orientation, no cracks are directly associated with osteocytes lacunae (asterisks); (c) Views (xy, xz, and yz) of a single crack associated with a canaliculus (arrowhead). Dashed lines are approximated lamellar boundaries; (d) Merging process of the circumferential cracks in the circumferential and depth (z-plane) directions; (e) Bright and dark (arrowheads) layers damage associated with the formation of a shear band. The microcracks have a "sheet-like" appearance through the depth (z-plane). Note also the radially oriented microcrack at the Haversian canal. Compressive load applied horizontally for b-d-e and obliquely for c. ...................... 83 Figure 6.4. Physical interpretation and mechanical simulation of cracks-structures’ interactions in bone under transverse compression. (a) Schematic of multiple circumferential crack nucleations and mergings in osteonal layers with fibrils oriented parallel to the osteons; (b) Proposed interfibrillar nature of the sub-lamellar cracks (light grey) with respect to the rotated mineralized collagen fibrils (minerals in black) and the surrounding non-collagenous proteins (small grey lines); (c) Numerical model developed to simulate elastic stress/strain concentration at a radially oriented canaliculi (y-direction) under pure shear (stress state depicted in (a)). The arrows at the top denote the degrees of freedom; (d) Strain concentration at a canaliculus (center) for an isotropic material. The orientation shown is the same as in (c). ........ 86 Figure 6.5. Variations of microcrack morphologies. (a) LSCM image showing flame-like cracking (double arrows) at the ends of the arc-shaped microcracks; (b) SEM micrograph of surface cracks. Both circumferential (arrowheads) and radial (double arrows) cracks can be seen; (c-d) Respective surface and bulk LSCM images of (b). xvi Notice the bright borders of the surface cracks (c) and the cross-hatched patterns beneath (d). Compressive load applied horizontally.................................................. 94 Figure 6.6. Effect of the mineralized collagen fibril orientations on the strain concentration around a canaliculus (center) under pure shear (stress state depicted in Figs. 6.4a-c). Transversely isotropic material simulating the cross-sectional osteonal bright (a) and dark (b) layers. Note the elongated shape through the depth (z-direction) and the higher strains in the bright compared to the dark layer. The orientation shown is the same as in Figure 6.4c................................................................................................ 96 Figure 7.1. Buckling in the superior cortex of a femoral neck segment retrieved from a patient with hip fracture: (a) Simple schematic of the proximal femur during a fall. Dotted circle shows the superior cortex; (b) Optical Microscope (OM) image of a longitudinal section (along the femoral neck axis) of the superior cortex. Note the lamellar structure and the large porosity (P); (c) Corresponding Epi-Fluorescence (EF) image showing microcracking. The tensile microcracks (arrowheads) at the periosteal and the compressive cross-hatched microcracks (empty arrowheads) at the endosteal indicate outward bending. ........................................................................ 100 Figure 7.2. Interlamellar shear and microbuckling in the superior cortex of a femoral neck segment retrieved from a patient with hip fracture: (a-b) Optical Microscope (OM) and Epi-Fluorescence (EF) images of a longitudinal section (along the femoral neck axis) of the superior cortex. Arrowheads in (a) indicate the final fracture surface and point out to the adjacent highly deformed lamellae; (c-d) OM and Laser Scanning Confocal Microscope (LSCM) images of the dotted area in (b). The microcracks are parallel to the lamellae boundaries and consist of multiple small cracks crossing the canaliculi. Two osteocyte lacunae are identified (asterisks).................................... 101  Figure A.1. Load-strain curves for all 10 cortical bone specimens (a) and 15 whole tibia specimens (b). The × indicate debonding of the strain gage. Figures 4.1a-b correspond to black curves....................................................................................... 136 Figure A.2. (a) Variations of strain rates at the tensile (top) and compressive (bottom) surfaces for all 10 cortical bone specimens. The × indicate debonding of the strain gage. Figure 4.4a corresponds to black curves. ................................................................. 137 xvii Figure A.2. (b) Variations of strain rates at the tensile (top) and compressive (bottom) surfaces for all 15 whole tibia specimens. The × indicate debonding of the strain gage. Figure 4.4b corresponds to black curves. ............................................................................ 138 Figure A.3. (a) Cortical bone specimen bending fracture patterns. Note the similarity with A.3b. Top surfaces under compression. Figure 4.5a corresponds to asterisk. ................... 139 Figure A.3. (b) Whole tibia specimen bending wedge "butterfly" fracture patterns (B2, B3). Top surface under compression. One tibia with butterfly fracture was not photographed. Figure 4.5b not shown.............................................................................................. 140 Figure A.3. (c) Whole tibia specimen oblique fracture patterns (A2). Top surface under compression. ............................................................................................................ 141 Figure A.4. (a) Epi-fluorescence images of tensile surface microdamage for 6 cortical bone specimens. Tensile stress horizontal. Figure 4.6c corresponds to asterisk. ............. 142 Figure A.4. (b) Epi-fluorescence images of compressive surface microdamage for 6 cortical bone specimens (same as A.3a). Compressive stress vertical for first 3 images and horizontal for last 3 images. Figure 4.6a corresponds to asterisk. ........................... 143 Figure B.1. Compressive stress-strain curves for all specimens loaded monotonically along three different orientations: 7 longitudinal (0°), 7 transverse (90°), and 3 oblique (45°). 145 Figure B.2. Epi-fluorescence images of compressive cross-hatched microdamage in 4 cortical bone specimens loaded along different orientations: Top 4, Longitudinal (0°); Bottom 4, Transverse (90°). Compressive load applied vertically. Figures 5.2a-5.2b-5.8a and Figures 6.1c-6.2c not shown...................................................................... 146 Figure C.1. Nominal strain accuracy of the DIC technique for the prescribed experimental conditions. The maximum shear strains (εmax) computed for three introduced rigid displacements indicated that the nominal strain accuracy decreased with decreasing final interrogation window size. The dashed line is a guide to the eye. .................. 149 Figure C.2. Strain accuracy validation. The average shear strain (εavr) over the entire field of view corresponded well with the introduced shear strain (0.43% in the example above). The strain accuracy (error bars) could thus be estimated by the largest of the differences between the average and the maximum or minimum shear strains. The error on the strain increased with decreasing final interrogation window size........ 150 xviii Figure C.3. Strain magnitude validation. The curves (from left to right) correspond to the maximum shear strain distributions for progressively higher macroscopic compressive strains. The maximum shear strains (εmax) at the peak of each strain distribution roughly corresponded to half the macroscopic compressive strains. The blue and red curves (arrows) with respective peaks at strain (εmax) of 0.35% and 0.75% correspond to the strain fields shown in Figures 5.6c-d. .............................. 151   xix LIST OF ABBREVIATIONS   BF  Bright Field optical microscopy (reflected light) BSE  Backscattered Electron Microscopy CB  Cortical Bone DIC  Digital Image Correlation EF  Epi-Fluorescence Microscopy L-DIC  Differential Interference Contrast LSCM  Laser Scanning Confocal Microscopy NCPs  Non-Collagenous Proteins OM  Optical Microscopy (reflected light) PBS  Phosphate-Buffered Saline solution PMMA Poly(methyl methacrylate) pQCT  peripheral Quantitative Computed Tomography sd  standard deviation SEM  Scanning Electron Microscopy SG  Strain Gage TEM  Transmission Electron Microscopy WB  Whole Bone   xx ACKNOWLEDGEMENTS I would like to express my gratitude to Dr. Rizhi Wang, my supervisor, for his guidance, enthusiasm, and inspiration through the years and for sharing his passion for biological materials. I wish to thank my committee members Dr. Thomas Oxland and Dr. Tom Troczynski for their constructive feedback and valuable advices over the course of the project. I also wish to thank the UBC Orthopaedic and Injury Biomechanics Group under Dr. Thomas Oxland and the UBC Centre for Hip Health and Mobility under Dr. Heather McKay for their strong support and for the use of their facilities through the project. Special thanks to Dr. Pierre Guy for his most valuable expertise and continuing interest in this work and to Dr. Danmei Liu and Cecelia Tang for their assistance with some experiments. I am also thankful to the UBC Life Science Institute Imaging facility for the use of their LSCM. Thank you to all my colleagues at the lab for great times and most interesting discussions: Dr. Ke Duan, Youxin Hu, Mehdi Kazemzadeh Narbat, Millie Kwan, Chia-Jade Lee, Shanshan Lu, Menghan Ma, Leandro de Macedo Soares Silva, and Allen Tang. This work was supported by the Canadian Institutes of Health Research and the Michael Smith Foundation for Health Research. I am also grateful for the University Graduate Fellowship from UBC, the Pacific Century Graduate Scholarship from the Province of British Columbia, and the Cy and Emerald Keyes Fellowship in Metals and Materials Engineering. Finally, I am most indebted to my family, my wife Lori-Ann and my two sons Xavier and Alexandre, for their unconditional love and infinite support each and every day. I am also deeply thankful to my mother and my late father who always supported my choices in life.  1 CHAPTER 1 INTRODUCTION Human bone is a hierarchical material composed of up to seven levels of structural organisation, from the mineralized collagen fibrils at the nanometer level, to lamellar and Haversian bone at the microstructural level, and cortical and trabecular bone at the whole bone level [1,2]. It is generally hypothesized that the various levels complement each other to achieve the macroscopic mechanical functions [1-3]. However, how whole bones’ mechanical performance is linked to their complex structure is still not fully understood. Yet, in the context of hip fractures where low bone mass and increased fall incidences cannot fully explain the increased in hip fracture risk with age [4-12], such fundamental understanding of the hierarchical structure – mechanical function relations is key to assess the mechanical contributions and the consequences of pathological conditions of the bone material in whole bone fractures. It is well recognised that bone’s capacity to deform through microcracking contributes to its resistance to fracture [2,13-24]. Such deformation mechanism requires well-controlled crack initiation and growth. Although crucial to prevent early fracture, how bone’s hierarchical structure controls the microcracking process is still unclear. The present dissertation examines, through a qualitative approach, the deformation and microcracking processes in human bone and their relations to its Haversian microstructure, i.e. the detailed structure/porosity – deformation/microcracking relations. The proximal femur consists of both cortical and trabecular bone. Although their relative importance is still debated [25-29], it is generally agreed that both would contribute to hip strength [30]. Falls have been associated with 90 % of hip fractures [31-34]. Compression and bending have been suspected to strongly contribute to femoral neck fractures resulting from falls 2 [26,35-40]. Compression is also a major mode of biomechanical loading [2]. Bone’s compressive response is different from its tensile response [2,41] and yet has been far less studied. The emphasis of this dissertation is on cortical bone’s compressive behavior and its role in bone fractures, in particular bending fractures. First, the relations between the bending responses at the architectural level (whole bone) and the material level (bone’s microstructure) are established. The relation between bone’s compressive and bending strengths and the importance of microcracking in the failure process are also investigated. Second, the contributions of bone’s Haversian microstructure and porosity to its inelastic deformation under compression are studied. Third, the involvement of finer structures in the microcracking process and the nature of cracks in bone are examined. Finally, a preliminary case study on how the techniques and knowledge can be applied to the study of hip fractures is presented.  3 CHAPTER 2 LITERATURE REVIEW 2.1 HIP FRACTURES – EPIDEMIOLOGY AND OUTCOMES Hip fractures are a serious issue to both the society and the individuals, particularly the elderly population [42]. In Canada, about 23,000 hip fractures occur each year [43] at a cost of $650 million [44] and, with an aging population, these numbers are projected to almost quadruple by 2041 [43,44]. Similar increasing trends are also expected worldwide [45] passing from 1.7 million in 1990 to an estimated 6.3 million in 2050 [46]. The outcomes of such fractures are severe: 10-20% result in mortality and 50% in reduced mobility [46-48]. There is also an associated increased risk of subsequent fractures of the second hip or other sites [48-52]. Prevention of hip fractures (both primary and secondary) is thus an ideal solution to the problem. This requires a complete understanding of their aetiology, from the loads involved during fracture to the pathological structural and material conditions and related mechanical consequences leading to hip fragility. 2.2 HIP FRACTURES – AETIOLOGY: AN OVERVIEW The risk of hip fracture is known to increase with age [5]. This rise has been mainly attributed to an age-related decrease in bone mass due to osteoporosis (i.e., bone fragility) [44,53-56] and increase in the incidences of falls which have been associated with 90% of fractures [31-34]. However, low bone mass does not completely explain the apparent fragility of the proximal femur [4-12]. It is now generally accepted that hip fragility is a combined result of the structural and material characteristics [4-12,53,57]. The proximal femur has a complex architecture consisting of a trabecular (or cancellous) bone core lined by a cortical bone shell (see Fig. 2.1). Its cross-section is roughly elliptical with 4 the inferior cortex being thicker [58,59]. The relative importance of trabecular and cortical bone in hip fracture is still a matter of debate [25-29]. Many agree that both would contribute to hip strength [30]. The deterioration of trabecular bone’s microarchitecture with age is recognised as a contributor to bone fragility [27,57,60]. As for cortical bone, age-related changes in geometry of the femoral neck, particularly along the inferoanterior-superoposterior axis [12,28,39,61], is suspected to influence fracture incidences [37,62-67]. Based on the expected bending of the proximal femur during a fall [26,35] and the observed thinning of the superior cortex with age, localized buckling (or cortical instability [36,37]) in the superior cortex under compression has been proposed as a potential mechanism resulting in hip fragility [39]. The mechanical properties of cortical bone vary with age, gender, and anatomical sites [2,3,68]. Interestingly, in parallel to the increased incidence of hip fractures, the strength and toughness of the bone material have been found to decline with age [69-74]. This trend has been related to increase in mineral content and porosity [69,75-81] as well as accumulation of microdamage [82-86] and changes in collagen [71-73,86]. Microstructural (including porosity) changes [87-90] and microcracks [91] have also been found in certain regions of the proximal femur and suspected to contribute to its overall fragility and associated fracture. However, the detailed reasons why microstructural changes would lead to bone fragility remain not well understood. Understanding the contribution of the altered bone material to hip fragility starts with a fundamental understanding of how the behavior of the bone material is related to its unique hierarchical structure, i.e., the hierarchical structure – mechanical function relations. 2.3 THE MATERIAL BONE Bone is composed of up to seven levels of hierarchical structure (Fig. 2.1) [1,2]. It is generally thought that bone’s mechanical performance comes from this unique organisation [1-5 3,92]. A clear description of this complex structure is thus essential to understand the structure – mechanics relations. Note however that the detailed organisation of bone at the molecular, fibrillar, and sub-lamellar levels is still being investigated and thus continually refined [1,93-98].   Figure 2.1. Bone’s hierarchical structure. Reprinted and adapted from [92] with permission from Elsevier.  Bone is made of approximately 70 wt% mineral, 20 wt% organic, and 10 wt% water [99]. Its nanostructure consists of mineralized collagen fibrils (about 100 nm in diameter), with non-collagenous proteins (NCPs) and carbonated apatite (Ca5(PO4, CO3)3(OH)) platelets present both inside and on the surface [95]. The type I collagen fibrils are formed from parallel triple-helical collagen molecules, 300 × 1.5 nm in size [1]. The mineral platelets, approximately 50 × 25 × 2-3 nm in size [92,100,101], are well-aligned within the gap zones between the staggered collagen molecules and both the platelets inside and on the fibril’s surfaces are predominantly parallel with the fibril’s long axis [95,100,101]. NCPs comprise less than 10% of the total protein content 6 in bone [1]. They would act as an interfibrillar "glue" between the mineralized collagen fibrils [102,103]. The basic building blocks of bone, the mineralized collagen fibrils, are usually present as bundles (also called fibers or arrays) through parallel alignment with adjacent fibrils [1]. Most of the structural diversity between species occurs due to the variety of patterns formed by the fibrillar bundles [1]. Four common patterns are woven bone, parallel-fibered bone (or arrays of parallel fibrils), radial fibril arrays, and lamellar bone [1,2]. The latter pattern is the most common in humans.   Figure 2.2. Cortex of human long bone. Reprinted and adapted from [104] (Fig. 40, p.76) with permission from Elsevier (Urban & Schwarzenberg).  At the architectural level, human long bones are composed of cortical and trabecular bone (Fig. 2.2). Both are lamellar but differ in the way the lamellar structure is organised at higher hierarchical levels. Trabecular bone is highly porous, typically more than 50 vol% [2,3]. It 7 consists of an arrangement of rods and plates, the trabeculae, (about 100-300 µm in size), each of which is made of primary lamellar bone [2,3]. Cortical bone has a porosity of about 5-15 vol% [2,3]. The cortex of human long bones is generally lined by a layer of circumferential lamellar bone while the core is Haversian bone (Fig. 2.2). 2.3.1 Human Haversian Bone: Product of Remodeling The most well-known hierarchical structure in human cortical bone is the Haversian system or secondary osteon (Fig. 2.2). Haversian bone is the result of remodeling, a process by which bone adapts to the mechanical environment [2,3,89]. During remodeling, osteoclasts are responsible for bone resorption while osteoblasts deposit new bone in the form of Haversian systems [2]. The longitudinally oriented Haversian systems are cylindrical structures (about 200 µm in diameter) consisting of a central Haversian canal (about 50 µm in diameter) surrounded by concentric layers of bone lamellae (usually up to 20 to 30 lamellae [105], each about 3-8 µm thick [92]). They are bounded by hyper-mineralized cement lines [106] and embedded into interstitial lamellar bone (remnants of older Haversian systems [105,107]). Such a structure clearly differs from circumferential lamellar bone where the lamellae are organized in extended planar arrays [108] and plexiform or fibrolamellar bone (a combination of lamellar and parallel-fibered bone) where the majority of the collagen fibrils are parallel to the bone axis [2]. The Rotated Plywood Motif Under the optical microscope, the difference in collagen fibrils’ orientation results in the commonly observed pairs of thin/thick or dark/bright osteonal lamellae (Fig. 2.3a) [97,109-111]. Each pair of lamellae actually consists of a rotated plywood structure with five sub-layers (Fig. 2.3b) [1,93,112,113] where the fibrils progressively rotate from being predominantly 8 circumferentially aligned in the dark layers to roughly longitudinal in the bright layers on transverse sections [97,109-111]. The mineral platelets within an individual sub-layer are aligned to each other [1,112,113]. They are parallel to the lamellar boundaries within the dark layers and at high angle to the lamellar boundaries within the bright layers [112].    Figure 2.3. Haversian bone’s microstructure: (a) Bright field optical image of a Haversian system (transverse section) and the surrounding interstitial bone (I). Pairs of thin/thick or dark/bright concentric lamellae line the central Haversian canal (H). Osteocyte lacunae are also seen (three are identified by asterisks); (b) Schematic of the rotated plywood structure where each pair of lamellae consists of five sub-layers with a progressive rotation of both the collagen fibrils and the mineral platelets. The fibrils in the first sub-layer are follow the circumferential direction (thin/dark lamella) while those of the fifth one are aligned with the osteons (thick/bright lamella). (b) reprinted and adapted from [114] with permission from Elsevier.  The Porosity Network Haversian bone’s complex structure is further permeated by the porous lacuno-canalicular network (Fig. 2.3a; see also Fig. 6.3a). Encasing the osteocyte bone cells (formerly osteoblasts), the osteocyte lacunae are longitudinally oriented oblate ellipsoids (10-30 µm in size) mainly located near the lamellar boundaries. They are linked together and to the Haversian canals by a large number of irregular, tubular-shaped canaliculi (about 200 nm in diameter and at the distribution density of 1x106 canaliculi/mm3) [3,115] containing the cellular processes. The 9 network comprised of the osteocytes and their processes has been proposed to serve as a sensing and signalling system for remodeling [116-121,121-125]. 2.4 MECHANICAL PROPERTIES OF CORTICAL BONE It is generally accepted that human cortical bone macroscopically behaves as a transversely isotropic material [41]. The elastic modulus generally varies by a factor of 1.5-2.0 [2,41,68] between the longitudinal (0°) and transverse (90°) orientations with respect to the bone’s long axis (and therefore most of the osteons). Although the properties also vary with age, gender, and location [2,3,68], the stress-strain curves for longitudinal tension and compression generally correspond to those schematically drawn in Figure 2.4 [126]. They show asymmetry [2,41,68,127,128]. Bone’s elastic modulus is about 17 ± 3 GPa in tension and compression [128,129]. However, bone yields and fractures at lower stresses in tension than in compression. In tension, bone yields at about 110 MPa (0.5-0.7 % strain [81,130-134]) which is followed by a mild strain hardening (~ 1 GPa [41,127]) reaching strength and ultimate strain of the order of 128 ± 9 MPa and 2.7 ± 0.8 %, respectively [128]. In compression, yield happens at higher stress and strain (about 150 MPa and 0.7-1 %, respectively [68,131,135]) followed by a short hardening up to stresses of 190 ± 18 MPa and then softening reaching strains of about 2.1 ± 0.3 % [128]. As for human cortical bone’s bending strength, it is reported to be between 150 and 190 MPa [2,127,130].  The shear response of bone has been less extensively studied [41,136-140]. Early work using torsion experiments reported shear modulus and strength of about 3.3 ± 0.4 GPa and 68 ± 4 MPa, respectively [41]. More recent studies [139,140] found yield strains of 1.3 ± 0.1 %, yield stress of 56 ± 4 MPa, and ultimate strains of 5.2 ± 0.9 %. 10   Figure 2.4. Schematic of cortical bone’s stress-strain curves for longitudinal tension and compression. Reprinted from [126] with permission from Elsevier.  A few papers reported Poisson’s ratio values for wet bones ranging from 0.19 to 0.48 [41,126,127,141-144]. Early measurements [141] and recent investigations [126,142,143] showed that the tensile Poisson’s ratio would decrease with load or fatigue cycle, indicating that, under tensile stress, bone’s inelastic deformation would not be volume conservative. Conversely, it was found that deformation was nearly volume conservative in compression [126]. Although they would provide a better understanding of the mechanical responses under different modes of loading, human cortical bone’s compressive and tensile Poisson’s ratios and especially their changes during deformation remain to be clarified. Bone is also viscoelastic [127], partly due to the hydrated state of the tissue [2,68,127]. This implies that its properties are affected by strain rates [135,145], an important aspect when considering traumatic fractures [146]. Of particular interest is the decrease (but not complete disappearance) of post-yield deformation with increasing strain rates [135,145,147]. Such 11 behavior has been associated with strain and damage localization and significantly affects bone’s resistance to fracture [23]. Bone exhibits rising crack resistance with crack extension (R-curve) [148-155]. The crack initiation toughness in bone can be fairly low (< 2.5 MPa·m½) but toughness increases during crack growth to values of 25 MPa·m½ for 500 µm long cracks [153]. The implication of such behavior is that bone is damage tolerant [16,156-158]. It derives its resistance to fracture due to stable crack growth rather than by resisting crack initiation [153,159]. The design principles used in bone to achieve the macroscopic properties are still not well understood. More specifically, the relative importance of the mechanisms behind bone’s high resistance to fracture is still heavily debated [20,24,153-155,159-163]. One approach looks at the mechanisms that hinder the propagation of relatively long cracks in bone. Those mechanisms are surely involved in the later stages of failure when a potentially fatal crack is developing. However, as for other biological materials, bone’s resistance to fracture also relies on the inelastic (post-yield) deformation occurring prior to the development of a fatal crack [16,17,20,24,140,156,164]. Such inelastic deformation may also be locally present around longer cracks. Another, albeit closely related, approach thus focuses on the mechanisms and structures involved in such deformation, namely the hierarchical structure – mechanical function relations. 2.5 HIERARCHICAL STRUCTURE – MECHANICAL FUNCTION RELATIONS 2.5.1 Molecular and Fibrillar Levels Mechanics at the molecular level mainly revolve around the concepts of "sacrificial bonds" and "hidden lengths" within the interfibrillar matrix [102,103,165,166]. Essentially, the highly coiled non-collagenous proteins (NCPs) network would contain weak bonds (sacrificial 12 bonds) between different parts of the coiled protein backbone which would break under load and lead to the unfolding of the molecular chains (hidden lengths) [102,103]. This adhesive "glue" layer between the mineralized collagen fibrils is thought to be responsible for some of the energy dissipated during loading [102,165]. Interestingly, these bonds would later reform and have been hypothesized to lead to crack healing [102,165]. Recent progress has clearly shown the active involvement of bone’s nanostructure in the tensile deformation process [133,134,157,167-169]. The main theory is that the staggered configurations of both the minerals inside the collagen fibrils and the mineralized fibrils within the interfibrillar matrix would result in better overall mechanical performance (i.e., balance between stiffness, strength, and toughness) through shear stress transfer via the softer phases (collagen and NCPs, respectively) [133,134,167,168]. In the inelastic stage, it is proposed that decoupling of mineral-collagen and fibril-interfibrillar matrix would lead to considerable frictional energy dissipation [133,134,168]. A similar "intrafibrillar" model (i.e., considering only the mineral and collagen inside the fibrils) was put forward by Mercer et al. [126] where the hardening was explained by stretching of the collagen. The proposed molecular and nanometer level mechanisms suggest that the condition of the organic phases (collagen and NCPs) in bone would be crucial to prevent early fractures [134]. However, the involvement of higher hierarchical levels (i.e., different fibrillar bundle orientations, lamellae, osteons) in bone fracture is not considered. 2.5.2 Lamellar, Osteonal, and Tissue Levels In Haversian bone, the different orientations of the mineralized collagen fibrils form the concentric lamellar structure of the osteons. The obvious advantage of Haversian bone over other types of structures such as circumferential lamellar bone and plexiform bone is that it enables 13 cortical bone to adapt to the mechanical environment through remodeling [2,3,89]. The alternating lamellae of different fibril and mineral orientations have also been hypothesized to be a good strategy to impede crack propagation and prevent catastrophic failures [111,170]. However, extensive comparative studies found osteonal bones to be weaker than plexiform bones in tension, compression and shear [2,3,41,127]. A question, then, is: does osteonal bone provide any mechanical advantages over other types of bone? There have been experimental evidences in the literature on the positive involvement of osteons in the fracture process. Piekarski [171] found that osteons could be pulled out of the interstitial bone at a slow cracking rate, similar to the fiber pull-out phenomenon in composites. Similar fracture morphology was also observed by Zioupos et al. [172]. Hiller et al. [173] found that the osteonal pull-out led to an increased fatigue life in equine bone. In their bending study, Liu et al. [108] observed that the two halves of the fractured osteonal bones still remained connected well after the main fracture event, whereas in circumferential lamellar bone they separated. Despite these progresses, many unanswered questions remain. The detailed contributions of osteonal lamellae to bone fracture and the involvement of Haversian canals are still obscure. Dangers Associated with Porosity From a mechanics point of view, the presence of numerous Haversian canals, and for this purpose osteocyte lacunae and canaliculi, introduces detrimental defects to bone. These could become stress concentration sites and lead to early failure, as is the case for some engineering materials [174]. Surprisingly, human Haversian bone exhibits remarkable inelastic deformation after yielding (Fig. 2.4) [2,16,17,23,41,81,126-128,140,175]. It is well-accepted that, at the micro-scale, bone’s inelastic deformation mostly arises from microcracking [16,17] easily visible through the development of whitening zones across the tissue [2,14,22,23] corresponding to high 14 deformation bands forming beyond yielding [176]. Such inelastic deformation, i.e., the capacity of bone to produce and contain microcracks (sometimes referred to as pre-failure damage tolerance or pre-fracture toughness), would be critical to its resistance to fracture [16,17,20,24,140,156,164]. Indeed, it could provide mechanical robustness by redistributing stress to alleviate strain concentration [157,169,177-180]. A reduction of post-yield deformation would also result in a more brittle (or "fragile") behaviour. Inelastic deformation through microcracking (or distributed microcracks) requires well-controlled crack initiation and growth. How bone’s hierarchical structure is designed to control such a cracking process starting at the nano-scale, however, is still not well understood. 2.5.3 Microcracks and Microcracking in Bone Microcrack morphologies in tension and compression are totally different [14,15,18,21]. Compressive microcracks are relatively straight and long [14,18,19,21,181], and oriented at approximately 30°-40° from the bone’s long axis [2,13,14,127,182] forming a typical cross-hatched pattern. In equine osteonal bone, they appear at strains around 0.8-1.0 % [21]. It has been speculated that they would result from shear band formation [14,126]. Although this morphology is the most commonly observed, "scale-type" cracks were also reported in fatigued bovine bone [15]. Tensile microcracks, generally present in both interstitial and osteonal bone, are of diffuse nature and consist of smaller microcracks (~ 2-10 µm) forming flame-like arrays [17,18,21,181,183,184] oriented normally to the tensile stress [16,17,185]. In equine osteonal bone, they first appear at strains around 0.4-0.5 % [21,186]. They increase in density as strain is increased [21] but do not coalesce to form longer microcracks (> 100 µm) until very high strains 15 are reached [18,19,21,181,186]. Another type of tensile damage consists of long microcracks (~ 100 µm) that have been associated with cement lines or interlamellar boundaries [15,82,187]. Torsion loading introduces long shear microcracks at the lamellar boundaries (including the cement lines) within both osteonal and interstitial bone. High inelastic strains have been associated with the control of those microcracks by the lamellae [140]. Diffuse microcracking and linear microcracks are present in-vivo [91,163,184,188-190]. In cortical bone, relatively long and isolated microcracks (referred to as pre-existing cracks) are most commonly, but not exclusively, found in interstitial bone [83,84,183,189,191-197] and usually extend to the osteons [85]. They have been generally associated with fatigue [82,84,191,193,198]. Microcracks have been shown to accumulate under fatigue loading at strains (< 0.15 %) and strain rates (< 0.03 s-1) [82,191,198] similar to those measured in-vivo [199,200]. They would develop rapidly during the first stage of fatigue but their growth would be limited until just before fracture [201-203]. Under cyclic compression, Haversian systems were found to act as barriers to the growth of long interstitial microcracks [202,203]. Although the mechanism is still unclear, it has also been suggested that in-vivo microcracks would be one of the stimuli that trigger bone’s remodeling response and remodeling would in turn remove microcracks [121,122,125,186,191,204-208]. Microcrack initiation has been linked to Haversian canals [2,15,21] and osteocyte lacunae [21,181,186,209] where high local strains (reaching up to 3.8 times tissue strain) have been observed to develop [210,211]. Considering their strong potential as stress concentrators [212], the canaliculi could also act as intrinsically weak sites in bone. Indeed, they have been suspected to initiate fine cracks [213] and influence the damage process [207,214]. Although such 16 mechanical role could be significant in light of their dense distribution [3], their involvement in crack development is still obscure.  At the later stages of cracking, relatively long microcracks (~100 µm in size) have been shown to interact with osteons [202,203] and cement lines [85,153]. Bone lamellae [169,213], uncracked ligaments, and individual fibrils [159,160] bridging also further increase bone’s crack growth resistance (R-curve) [148-155]. However, the nature and interactions of cracks (i.e., structure – microcracking relations) at the lamellar, sub-lamellar, canalicular, and fibrillar levels is still largely unknown [163]. It is thus difficult to understand how widespread microcracking occurs at the tissue level. Novel mechanisms must be present to make bone less sensitive to Haversian canals, osteocyte lacunae, and canaliculi. A detailed study of the deformation and fracture process would reveal such mechanisms and the design secrets of osteonal bone. 2.5.4 Bone Deformation and Whole Bone Fracture Physiologically, long bones (including the proximal femur) rarely fail due to pure tension or compression, but rather fail as a result of added torsion and bending loads [215-217]. Torsion is definitely of importance to whole bone and hip fractures and should be investigated further at both the material and architectural levels. Bending is also responsible for many long bone fractures [216] and it is suspected to be involved in femoral neck fractures associated with falls [26,35]. When a long bone is subjected to bending, one side is under compressive stress, while the other side is under tensile stress. Considering the asymmetrical stress-strain behaviour of bone (Fig. 2.4) [2,41,68,127,128], both stress and strain would undergo continuous redistribution across the bone thickness during the post-yield stage of deformation. Understanding the detailed stress and strain redistribution process before fracture and its dependence on bone microstructure 17 and geometry holds a key to the understanding of bone bending strength. Yet, experimental studies on such a deformation process have been limited. The dynamic strain redistribution in bone subjected to bending was first studied by Burstein et al. [175] who developed an analytical model based on force balance, assuming idealized elastic-perfectly plastic asymmetric stress-strain behaviors. Their analysis showed that the discrepancy between measured bending and tensile strengths were due to inelastic deformations and asymmetric yield strengths of bone resulting in a shift of the neutral axis of the beams towards the compressive surface. Simkin & Robin [218] also demonstrated that bending moment and strain and stress distributions across a bending beam at failure could be predicted based on force and moment balance theory and a graphical method involving post-yield stresses. More recently, Fondrk et al. [219] used a damage model based on the non-linear tensile behavior of cortical bone to simulate cantilever bending and showed that the neutral axis shifted towards the compressive surface following tensile yielding. All these studies emphasized the importance of post-yielding processes. As Currey [130] concluded with his study on a wide variety of bone types, post-yield deformations are one of the main factors that determine the bending strength of compact bone. Hence, an exhaustive study on post-yield (inelastic) deformation and its dynamic redistribution is essential to the understanding of bone fracture process in bending. Such a study on human cortical bone is still lacking. More importantly for the clinical field is the lack of such study on whole bones. 2.5.5 Summary of Existing Problems The detailed structure – mechanics relations across bone’s hierarchy are still not fully understood. In particular, it is still unclear how human cortical bone’s Haversian microstructure is involved in the fracture process and contributes to whole bones’ mechanical response. 18 Both bending and compression are of particular interest when considering whole bone and hip fractures. It is thus important to understand the origin of whole bone’s bending strength through the study of the deformation and fracture process in bending, essentially the post-yield strain redistribution, and its relation to the microstructural level. In such a process, both bone’s tensile and compressive behaviors and the associated microcracking must be considered. Microcracking clearly contributes to bone’s resistance to fracture. Such a deformation process relies on well-controlled microcrack initiation and growth. Microcrack morphologies at the osteonal-interstitial level are generally well documented. However, their relations with Haversian bone’s lamellar, sub-lamellar, and fibrillar structures remain poorly defined. Hence, how multiple microcracks are controlled and distributed across the tissue is still not well understood, particularly in the presence of bone’s extensive porosity network. A detailed study of bone’s deformation and microcracking processes would reveal the roles of its hierarchical structure in resisting fracture. Further linking microcracking to the mineralized collagen fibrils would provide a clear picture of bone’s deformation prior to the formation of a fatal crack.  19 CHAPTER 3 SCOPE AND OBJECTIVES Bone’s mechanical properties are generally hypothesized to arise from its complex hierarchical structure. Despite recent progress on the deformation process at the mineralized collagen fibril level, knowledge on the active involvement of higher hierarchical levels such as the Haversian systems and their concentric lamellae in bone fracture has been relatively limited. Hence, it is not fully understood how whole bones’ mechanical performance relates to the different features of their underlying structure. In the long term, such knowledge is important to assess the mechanical contributions and the consequences of pathological conditions of the bone material in whole bone fractures. Following a hierarchical structure – mechanical function relations approach, the scope of this dissertation is to provide, at a qualitative level, a fundamental understanding of bone’s resistance to fracture through a detailed study of the deformation and microcracking processes and their relations to bone’s hierarchical structure. Fractures of the proximal femur have been associated with falls involving significant bending and compression. Compression is also a major mode of biomechanical loading and bone deforms differently in compression than in tension showing relatively higher strength but lower inelastic strains. At the microstructural level, bone’s capacity to deform inelastically through controlled microcracking contributes to its high resistance to fracture. Without such capacity, bone would behave in a more brittle manner. The focus of the present dissertation is to understand how Haversian bone deforms under compression and bending, i.e., the detailed structure – microcracking relations, and how this response may influence whole bone fractures.    20 The specific objectives of this dissertation are: • To investigate the deformation and fracture process of human bones in bending through a detailed study of post-yield strain redistribution and its relation to compressive and tensile microcracking at the Haversian systems level. • To establish the links between the bending fracture of whole bones and cortical bone specimens in terms of strain redistribution, Poisson’s ratios, microcracking morphologies, and macro-scale fracture patterns. • To study the roles of bone’s hierarchical structure at the osteonal-interstitial, lamellar, and sub-lamellar levels in the deformation and microcracking processes under compression, i.e., structure – microcracking relations. • To bridge the gap between the microcracking phenomenon and bone’s basic building blocks, the mineralized collagen fibrils. • To demonstrate how the techniques and fundamental knowledge can be applied to the understanding of the mechanisms of hip fracture. The research chapters (Chapters 4-5-6-7) are organised as follows. Chapter 4 focuses on the understanding of bone’s (both whole bones and cortical bone specimens) bending response. The relations to bone’s compressive behavior and microcracking at the material level are established. The details of bone’s compressive response are studied in chapters 5 and 6. Chapter 5 concerns the roles of Haversian systems and Haversian canals in the deformation and microcracking process. Chapter 6 investigates microcracking at the lamellar and sub-lamellar levels with emphasis on the involvement of the canaliculi network. Finally, in chapter 7, the approach is taken to the clinical field in a preliminary analysis of the superior cortex of fractured femoral necks retrieved from patients. ------------------------------------- 1 A version of Chapter 4 has been published. Ebacher V, Tang C, McKay H, Oxland TR, Guy P, and Wang R. (2007) Strain Redistribution and Cracking Behavior of Human Bone during Bending. Bone. 40:1265-75. 21 CHAPTER 4 STRAIN REDISTRIBUTION AND CRACKING BEHAVIOR OF HUMAN BONE DURING BENDING 1 Bending is involved in many bone fractures [216] including femoral neck fractures associated with falls [26,35]. The purpose of this study was to investigate the deformation and fracture process of human bones in bending through the study of strain redistribution and its relation to microdamage at the microstructural level. The fracture of whole bones was compared with cortical bone specimens in terms of strain redistribution, Poisson’s ratios, microdamage morphologies, and macro-scale fracture patterns. The role of human bone osteonal microstructure on microdamage development was also examined. 4.1 MATERIALS AND METHODS A total of nineteen un-embalmed human cadaver long bones (15 tibiae, 4 femora) were used in this study. They were obtained from the Department of Anatomy at the University of British of Columbia. The tibiae specimens, 5 males and 5 females (5 pairs plus 5 right), were used for the whole bone study. Age at death ranged from 67-88 years. The femora specimens, 3 males and 1 female selected based on thickness of the cortex, were used for the cortical bone study. Age at death ranged from 69-77 years. All bones were visually examined for macroscopic defects or pre-fracture and were stored at -20°C until testing. The study was approved by the Clinical Research Ethics Review Board at the University of British Columbia. 22 4.1.1 Mechanical Tests For the whole bone study, the distal 25% of each tibia specimen was first removed in order to be used as part of another investigation. The remaining proximal 75% sections of the tibial shafts were fractured in four-point bending under wet conditions using a servohydraulic testing machine (Instron 8874, 25 kN load cell) with a crosshead speed of 6.0 mm/min. The inner loading span, between the 50% and 66% sites from the distal end, was adjusted with respect to specimen length by changing the positions of the load application points. The outer support span was set consistently to be three times the length of the loading span. Therefore, the removal of the distal 25% did not interfere with our measurements and our goal of studying the strain redistribution. To ensure stability and alignment, the distal end was embedded in PMMA and a PMMA support was added at the proximal end. Prior to mechanical testing, rosette strain gages (Omega KFG-2-120-D17-11L1M2S) were mounted at the center of the span (~58% of the bone length from the distal end) on both the lateral and medial surfaces, which would be subjected to compression and tension, respectively (Fig. 4.1b). These surfaces were defined according to the orientation of the proximal condyle. The strain gage application procedure followed standard guidelines (Vishay Intertechnology Inc.; Malvern, USA). Briefly, surface preparation consisted of cleaning with water, degreasing with diluted isopropyl alcohol, lightly abrading with 400-grit silicon carbide paper, and finally conditioning with M-Prep Conditioner A and neutralizing with M-Prep Neutralizer 5A. Then, the strain gages were aligned and bonded to the surface using M-Bond 200 Adhesive combined with M-Bond 200 Catalyst and coated with a thin layer of coating (M-Coat) to protect them from moisture. Data were collected using a data acquisition system managed by LabVIEW software (National Instruments; Austin, USA). From these measurements, principal strains, strain rates, longitudinal strain ratios (longitudinal strain on the 23 tensile surface over that on the compressive surface, -εT/εC), transverse strain ratios, as well as Poisson’s ratios (ν = -εt/εl) were calculated. Since the cross-sections of tibiae specimens were not standard and the surfaces were not flat, the absolute values of the strain ratios and the Poisson’s ratios would vary from bone to bone. Hence, for comparison purposes, the ratios were normalized with respect to their individual value at 10% of the fracture load. For the cortical bone study, ten cortical bone specimens were cut longitudinally from the mid-diaphysis of the four femora using a low-speed diamond saw (Isomet 1000, Buehler) under constant water irrigation. Two to four samples, with the final dimensions of 35 mm × 4 mm × 3 mm, were obtained from each femur. They were first manually ground into rectangular beams and then mechanically polished using diamond suspensions down to 1.0 µm. The upper and lower surfaces (4 mm sides) were sectioned to be roughly parallel to the radial direction of the femoral cortex to minimize structural variations across the beam thickness (3 mm sides) and allow a better comparison between the compressive and tensile behaviors when subjected to bending. The specimens were placed in a phosphate-buffered solution (0.05 PBS, pH 7.2) until rosette strain gages (Omega KFG-1-120-D17-11L1M2S) were applied to the center of the upper and lower surfaces, corresponding to compressive and tensile surfaces. Four-point bending tests were conducted under wet conditions using a servohydraulic testing machine (Instron Dynamight, 1 kN load cell). A crosshead speed of 0.5 mm/min was chosen so that the strain rate on the specimen surface would be close to that measured in the long bone bending tests. The inner loading span (l) was 15 mm and the outer support span (L) was 30 mm. The same calculations were performed as described for the whole bone study. Additionally, assuming pure bending (i.e., strains vary linearly across the beam thickness and plane sections remain plane 24 during deformation) and time-independent stress-strain relations, the stress-strain curves were calculated via the following de-convolution equations [126,179]: ( ) −+−=TCTCTTddMddMbh εεεεεσ 1212 TCTCdd εεσσ =  where σT,C are the stresses on the tensile and compressive surfaces, εT,C are the strains on the tensile and compressive surfaces, h is the thickness of the beam, b is the width of the beam, M is the bending moment, and P is the load (M = P (L-l) / 4). 4.1.2 Fracture and Microdamage Analyses Following mechanical testing, whole tibia macro-scale fracture patterns were classified by an orthopaedic surgeon (Pierre Guy, M.D.) according to the A.O. classification [215]. The specimens were then carefully examined under a stereomicroscope (Nikon SMZ 1000) to characterize the macro-scale damage and to locate potential sites for further microdamage analysis. Eight of the fifteen tibiae specimens with typical macro-scale fracture patterns (in terms of A.O. fracture type) and load-strain curves were selected for microdamage observations. They were transversely cut into segments (comprising the selected sites for microdamage observations) using a hand saw under constant irrigation at positions that were at least 1 cm away from the main fracture surfaces. For the observation of microdamage, both cortical bone and segments of tibiae specimens were stained using a procedure based on the work of Zioupos & Currey [220] and Fazzalari et al. [185]. The specimens were first put into acetone overnight for defatting and then fixed and dehydrated into a graded series of ethanol/water solutions (80%, 90%, and 100%) for periods of 25 24 hours per step. They were then stained under vacuum for 24 hours in a filtered saturated solution of fluorescein (Fisher Scientific) and 70% ethanol. Finally, they were rinsed in 100% ethanol for at least one hour before being air-dried. The selected sites on the lateral (compressive) and medial (tensile) surfaces of the tibiae specimens were then carefully cut using the diamond saw under constant water irrigation, embedded in epoxy resin (Epothin, Buehler), and finally ground and polished using a mechanical polishing machine (Isomet 1000, Buehler) to expose the surface of the cortices. The compressive and tensile surfaces, which were either the original upper and lower surfaces of the cortical bone specimens or the surfaces parallel to the original upper and lower surfaces of the tibiae specimens, of all the prepared specimens were ultimately examined under an optical microscope (Nikon Eclipse E600) using both the white light and the epi-fluorescence light (with excitation at approximately 490 nm and emission at approximately 525 nm). Microdamage introduced during the bending tests would be stained by the fluorescein dye and appear bright green under the fluorescence microscope. The dye also stained some elements of the bone microstructure such as osteocyte lacunae and Haversian systems. The angles between the stained shear cracks and the bone’s long axis were measured on the surfaces, assuming that the crack planes were perpendicular to the analyzed surfaces. As the gray levels obtained from backscattered electron (BSE) images are sensitive to the average atomic number, this technique has often been used to quantify bone mineral content [221-225]. Thus, to relate the occurrences of microdamage with variations in degree of mineralization, selected specimens were carbon coated by vacuum evaporation (JEE-4B Vacuum Evaporator, JEOL – Japan Electron Optics Laboratory Co. Ltd., Tokyo, Japan) and further examined under scanning electron microscope (Hitachi S-3000N, Hitachi Ltd., Tokyo, Japan) using the backscattered electron (BSE) detector. 26 4.2 RESULTS 4.2.1 Strain Measurements The principal strains generally corresponded to the longitudinal and transverse directions of the specimen’s long axis. Figure 4.1 presents typical load-strain curves for both cortical bone and whole tibiae specimens (see Appendix A for all curves). 050100150200250300350-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6Strain (%)Load (N) Longitudinal Compressive Longitudinal Tensile Transverse Compressive Transverse Tensile SG Bone Long Axis (a) 0500100015002000250030003500400045005000-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6Strain (%)Load (N) SG PMMA Lateral Medial 50%   66% Longitudinal Compressive Longitudinal Tensile Transverse Compressive Transverse Tensile (b)  Figure 4.1. Typical load-strain curves: (a) Cortical bone specimen; (b) Whole tibia specimen; Inserts: Configurations of the four-point bending on cortical bone specimens and proximal tibiae specimens, respectively; SG: Strain Gage, PMMA: Poly (methyl methacrylate). 27 The curves are similar in shape between the two groups. The longitudinal strains on both the tensile and the compressive surfaces initially increase linearly with load, which is followed by a non-linear stage where the tensile strain becomes progressively higher than its compressive counterpart. This clearly depicts a strain redistribution taking place during the post-yield deformation process within both cortical bone and whole bone specimens. In order to better understand such a phenomenon, the longitudinal and transverse strain ratios (strain on the tensile surface over that on the compressive surface, -εT/εC) as well as the Poisson’s ratios (ν = -εt/εl) were plotted against the load normalized with respect to the fracture load of individual specimens (Figs. 4.2a-b: strain ratios; Figs. 4.2c-d: Poisson’s ratios). As the load in cortical bone specimens increased, the longitudinal strain ratio initially remained more or less constant to approximately 60% of the fracture load, and then increased until fracture. The redistribution of the longitudinal strains towards the tensile surface implies that the neutral axis in the bending specimens moves towards the compressive surface. The transverse strains followed an opposite trend and redistributed towards the compressive surface. This is better understood by analyzing the tendency of the Poisson’s ratios during loading. The tensile Poisson’s ratio decreased from 0.35 ± 0.03 to 0.21 ± 0.04 as load increased. Assuming that human cortical bone is transversely isotropic [2,41,68,142], this suggests that, in the inelastic regime, the volume of bone would not remain constant: bone expands under tension in the way that the transverse strain does not increase proportionally to the increase of the longitudinal strain. On the compressive side, starting from 0.34 ± 0.01, Poisson’s ratio increased just prior to fracture. Although the value did not reach 0.5, the increasing trend suggests that the deformation mechanism of bone under compression would be nearly volume conservative and thus would involve shear [226]. Note finally that, although more pronounced probably due to architecture, 28 the same trends in both strain ratios and Poisson’s ratios were observed in whole tibiae (Figs. 4.2b,d).    Figure 4.2. Longitudinal and transverse strain ratios (tensile strain over compressive strain, -εT/εC) for (a) cortical bone specimens, (b) whole bone specimens. Tensile and compressive Poisson’s ratios (ν = -εt/εl) for (c) cortical bone specimens, (d) whole bone specimens. The error bars are standard deviations.  The stress-strain curves for five cortical bone specimens (Fig. 4.3) show very similar tensile and compressive moduli (23 ± 3 GPa and 23 ± 2 GPa, respectively). The tensile curves are close to each other in both shape and stress level. The ultimate stress reaches ~110 MPa. 29 Yield generally occurs before 100 MPa, which is followed by a very mild hardening and then a slight softening up to an ultimate strain of approximately 1.0 to 1.5 %. The compressive curves are more scattered and the strength values are higher than the tensile ones, in the range of 150-200 MPa. The compressive yield point is also higher than the tensile yield but its ultimate strain is generally lower for an individual specimen. Note that, due to possible strain gage debonding at later stage of the tests, it was not possible to calculate the curves all the way to the final fracture so that a complete description of the fracture process in bending could not be obtained.   Figure 4.3. Tensile and compressive stress-strain curves for five cortical bone specimens.  Typical curves of the longitudinal strain rates during the bone deformation process are shown in Figure 4.4 (see Appendix A for all curves). The strain rates in tension and compression are first similar but then differ, the tensile strain rate increasing at the expense of its compressive counterpart. Later in the process, the tensile strain rate reaches a maximum before dramatically decreasing prior to the final fracture. Note that the increase of the tensile strain rate corresponds 30 approximately to the tensile yield point. Also, the maximum tensile strain rate is reached prior to maximum load, meaning that the loading capability of the bone is still increasing. This strain rate peak also suggests that the strains would become localized away from the strain gage.     Figure 4.4. Typical load-time curves and variations of strain rates: (a) Cortical bone specimen; (b) Whole tibia specimen.  Note finally that whole tibiae specimens showed similar trends to cortical bone specimens although there were some differences due to architectural effects and influence of the 31 set-up: the tensile strain rate was initially higher than the compressive one and increased significantly more than for the cortical bone specimens, both strain rates increased after their initial steady states and prior to the decrease in compressive strain rate. 4.2.2 Fracture and Microdamage Analyses The macro-scale fracture patterns of the whole tibiae classified according to the A.O. classification [215] were as follows: five specimens showed an oblique fracture (A2), nine a bending wedge or "butterfly" fracture (B2) and one a fragmented wedge fracture (B3). The macro-scale fracture patterns of the standard beam specimens were very similar to the "butterfly" fractures of whole bones (Fig. 4.5; see also Appendix A).   Figure 4.5. Side views of typical "butterfly" macro-scale fracture patterns: (a) Cortical bone specimen; (b) Whole tibia specimen; (c) pQCT (peripheral Quantitative Computed Tomography) cross-section of tibia at the location of the strain gage (58%). White area shows geometry of bone cortex.  The fracture path is straight and runs transversely to the beam on the tensile side, while it is oblique on the compressive side. It suggests a difference in failure modes when bone is subjected to different stress states. Clinically, the "butterfly" fracture pattern usually consists of two macro-scale oblique shear cracks on the compressive side connected to a transverse crack on the tensile side, thus forming a "Y" shape [215]. In this study, half of the standard beam specimens showed only one of these shear cracks (Fig. 4.5a), while most of the whole tibiae 32 showed at least two oblique shear cracks although all were not necessarily paths of final failure (Fig. 4.5b). At the microscopic level, a clear difference in microdamage morphologies was also observed between the compressive and the tensile surfaces in both the standard beam (see Appendix A) and the whole bone specimens. On the compression surface, most of the microdamage had typical "cross-hatched" pattern (Fig. 4.6a) where the discrete microcracks are long and straight but oblique to the specimen’s long axis. Based on ten measurable macro-scale cracks on ten different cortical bone specimens, the average angle between the crack plane and the bone’s long axis (assuming that the crack plane is perpendicular to the surface used for the measurement) was 27.4 ± 7.4°. Based on 59 microcracks from eight different cortical specimens, the average angle was 28.4 ± 4.5°. Scale-type cracks (Fig. 4.6b) were also observed at different locations on the compressive surface. This type of damage was not stained by the fluorescein dye and could only be seen under normal reflected light. Note that these scale-type cracks follow a similar curvature to the macro-scale crack on the compressive surface (Fig. 4.6b). The tensile surface showed extensive diffuse microdamage (Fig. 4.6c) generally oriented transversely to the longitudinal tensile stress and running into and across the surface. Although not necessarily continuous, both cross-hatching and diffuse microdamage seemed uniformly distributed along the entire region subjected to the maximum bending moment (inner loading span) of the standard beam specimens.     33    Figure 4.6. Microdamage morphologies under bright field (.1) and epi-fluorescence (.2) modes: (a) Compression surface showing cross-hatching microdamage far away from the final fracture site; (b) Compression surface showing scale-type microdamage at the final fracture site; (c) Tensile surface showing diffuse microdamage at the final fracture site. Principal stress along length of images.  34 When following the fatal macro-scale cracks from the tensile side to the compressive side, diffuse microcracks were observed (Fig. 4.7) in the fracture process zones until just before the tensile crack merges to the shear crack on the compressive side where the damage in the process zone is not detectable. This clearly indicates different crack propagation mechanisms.   Figure 4.7. Side view of tensile diffuse microdamage in the fracture process zone visualized under epi-fluorescence mode.  Closer observation of the stained specimens under bright field and epi-fluorescence modes revealed the important role of bone ultrastructure in the process of fracture. Both tensile and compressive microdamage showed initiation at stress concentrators such as Haversian canals (Fig 4.6). However, tensile microdamage could initiate in both osteonal and interstitial bone. In Figure 4.8, the diffuse microcracks seen on the specimen’s surface are obviously developed in interstitial bone as they do not extend to the lamellae of neighboring osteons. According to the 35 BSE image, the interstitial area has a higher degree of mineralization, indicating that the initiation of tensile microdamage could also be related to bone mineral density distribution.   Figure 4.8. (a) Tensile diffuse microdamage in both osteonal (O) and interstitial (I) bone visualized under epi-fluorescence mode; (b) Corresponding bright field mode micrograph; (c) Corresponding BSE image. Tensile stress along top-bottom axis of images. 36 Compressive cross-hatched microcracks were more structure dependent as they were frequently localized within individual Haversian systems (Fig. 4.9). They did not appear to initiate within or extend easily to the interstitial bone surrounding the osteon, a region shown to be more highly mineralized in the BSE image. Consequently, the cross-hatching pattern often developed into bands that were confined within individual osteons suggesting that the presence of Haversian canals and the size, geometry, and properties of Haversian systems would significantly affect compressive microcrack initiation and development.   Figure 4.9. (a) Compressive cross-hatching microdamage localized within an individual Haversian system (H) visualized under epi-fluorescence mode; (b) Corresponding BSE image. Compressive stress along top/right-bottom/left axis of images. Arrows mark two of the shear cracks.  4.3 DISCUSSION The strain measurement and the staining procedure enabled a direct comparison of the failure process of whole bone and cortical bone specimens. The combination of bright field and epi-fluorescence optical microscopy as well as BSE electron microscopy further allowed us to relate microdamage development to bone microstructure. Therefore, it was possible to characterize bone fracture process from the material level to the structural level. When subjected to bending, whole tibiae specimens failed similarly to standard cortical bone specimens in terms 37 of strain redistribution, microdamage development, and macro-scale fracture patterns. Our observations both at the micro-scale and the macro-scale clearly highlighted the different damage mechanisms under tensile and compressive stress states. The similarity between the measured shear angles formed by individual microcracks (28.4 ± 4.5°) and macro-scale cracks (27.4 ± 7.4°) evokes a potential relation between compressive microdamage and macro-scale cracks in the form of microcrack growth or coalescence as it is the case in tension [21,227]. Therefore, the "butterfly" bending fractures observed clinically in long bones [215] could be the result of a compressive failure as well as a tensile failure of bone material starting at the microstructural level. 4.3.1 Strain Redistribution during Bending Bone shows a discrepancy between its bending and tensile strengths [2,41,68,127,128], similar to synthetic fiber composites [228]. It was showed that this discrepancy was due to inelastic deformations as well as asymmetric tensile and compressive strengths [130,175,218,219,228-230]. In cortical bone, the inelastic strains appearing after yielding are mainly associated with microdamage [16,17]. Thus, their dynamic redistribution would determine the ultimate properties of bone in bending. In spite of this, very little attention has been given to the understanding of this phenomenon. In both the whole bones and the standard beam specimens, our results clearly show that, as bone is loaded to fracture, the inelastic tensile strains become progressively higher than the compressive ones (Figs. 4.1-4.2). This strongly confirms that strain redistribution takes place in human cortical bone subjected to bending. These results not only strengthen the analyses by previous researchers [175,218,219] but add the fact that the tendencies are also observed in whole human tibiae specimens. This implies that the basic response to bending loads and the 38 deformation process taking place prior to final failure are essentially the same even though whole bone architecture may affect the magnitude of the response. Therefore, bone fracture at the material level plays a fundamental role to the structural failure. Assuming a linear strain distribution across the beam thickness, it was possible to calculate the tensile and compressive stress-strain curves from a bending test [126,179,228,230,231]. The ensuing curves (Fig. 4.3) reveal tendencies that agree relatively well with the literature [2,41,68,127,128] and that evidently support the strain redistribution occurring during bending as tensile yielding happens prior to compressive yielding. The possibility of strain gage debonding at later stage of the tests may be one reason why the compressive strengths are somewhat lower than reported in the literature [2], although Reilly & Burstein [127] reported values of 131 to 159 MPa. The elastic moduli are also relatively high as compared to the values of 17.7 ± 3.6 GPa given in Reilly & Burstein [41]. One possible explanation could be the stiffening effect of the strain gages and their mounting medium due to an increased beam thickness. However, this error was estimated to be approximately 1 GPa. What can be learned from these curves is that the tensile behavior seems relatively constant in shape and levels from one specimen to another as compared to the more scattered compressive behavior. This suggests that, as opposed to compressive microdamage, the development of tensile microdamage would not be very sensitive to variations in bone’s microstructural features (e.g. porosity and Haversian systems) occurring from one specimen to another. Additionally, since it was observed that microdamage was uniformly distributed over the stressed surfaces, it is safe to assume that, at least prior to the maximum tensile strain rate, the strain measurements would be representative of the deformation process and therefore, that the strain rates (Fig. 4.4) would give very good insight on the rate of microdamage accumulation prior to the final failure. Our results suggest 39 that, in contrast to compressive microdamage, tensile microdamage would start to develop early in the fracture process and would accumulate increasingly rapidly as a result of the shift of the neutral axis. This is consistent with the study by Diab & Vashishth [201] who found that diffuse microdamage on the surface of bovine cortical beams subjected to fatigue reached an early saturated state as compared to compressive microdamage. Reilly & Currey [21] also reported that in equine cortical bone, tensile microdamage appeared at very low strains prior to compressive microcracks and increased in density with strain but only coalescing into longer microcracks at very high strains. Nonetheless, our results add the fact that these trends were also observed in whole bone specimens, implying the presence of the same damage accumulation process. 4.3.2 Poisson’s Ratio Poisson’s ratio is an important parameter to the study of bone deformation process. In spite of this, reports on human cortical bone’s compressive and tensile Poisson’s ratios remain very limited. Our results showed very similar values for tensile and compressive Poisson’s ratios of human cortical bone in the elastic regime: 0.35 ± 0.03 and 0.34 ± 0.01, respectively. However, opposite trends were found when considering the inelastic stage: decreasing tensile Poisson’s ratio and increasing compressive Poisson’s ratio. Indeed, early measurements of tensile Poisson’s ratio of cortical bone by Ko [141] showed values decreasing from 0.8 to 0.45 as load increased, although the absolute values were not reliable due to experimental inaccuracies (a value of 0.8 being thermodynamically impossible based on the theory of isotropic elasticity [232]). Fondrk et al. [142] examined the trend of the volumetric strains under rapid tensile loading of human and bovine cortical bone and found an average Poisson’s ratio value of 0.352 ± 0.021, which is comparable to our result. They concluded that bone’s volume was increasing 40 with load and associated the phenomenon with the development of new internal surfaces. Pidaparti & Vogt [143] tested human cortical bone specimens in tensile fatigue and found a Poisson’s ratio of 0.28 which was decreasing with the loading cycles as a result of damage accumulation. Mercer et al. [126] also concluded that bovine bone dilates under tension because the transverse strains were negligible but that the deformations are nearly volume conservative under compression. Under the assumption of transverse isotropy for human cortical bone [2,41,68,142], our results confirm these findings and show that whole bones also deform according to the same deformation mechanisms. More importantly, they emphasize the difference between the inelastic deformation mechanisms of human bone in tension and compression giving rise to different damage patterns. 4.3.3 Role of Bone Microstructure The ability of bone to develop microdamage in order to dissipate energy is the key to prevent its early failure. This ability will depend on the properties of the different elements of its microstructure. Yet, at least for human bone, the understanding of the influence of bone microstructure on the development of microdamage has been very limited. It has been shown that the stress concentration effect around Haversian canals [2,15,21] and osteocyte lacunae [186] provided sites for microdamage initiation. From our observations, tensile microdamage could also initiate in the more highly mineralized interstitial bone (Fig. 4.8). This could be explained based on the fact that yield strain decreases as mineral content increases [81]. In Figure 4.8, both the osteonal bone and the interstitial bone would undergo the same strain because of continuity of strain, and the zone with higher degree of mineralization (i.e. the interstitial bone) would yield sooner through microcracking. Local variations of bone mineral content could therefore contribute to tensile microdamage initiation. We hypothesize that this 41 would make tensile microdamage less sensitive to the presence of Haversian canals than compressive microdamage, resulting in more homogeneous damage as seen from a lower magnification (Fig. 4.6c). Note that the tensile stress-strain curves (Fig. 4.3), showing little variations from one specimen to another, also support this hypothesis. In contrast, our observations of compressive surfaces showed a strong influence of local Haversian systems. The cross-hatched shear cracks were not only initiated at the Haversian canals, they were also often confined within each Haversian system (Fig. 4.9). To our knowledge, this crack localization within individual osteons has not been reported before. The underlying mechanism is probably related to the fact that the degree of mineralization, and hence the elastic modulus [75,77,130], within each Haversian system is lower than that in the surrounding interstitial bone, as can be seen from the BSE micrograph in Figure 4.9b. Such a difference in elastic modulus has been known to increase the cracking resistance when a crack approaches the interface from the side with lower modulus (the Haversian system) [233]. The weak interface at the cement line [15,82,107,187] could also be involved in crack arresting even though crack deflection at the cement line was not observed in the current study. The susceptibility of Haversian systems to microdamage may also be related to their low shear strength. It was reported that osteons with lower degree of mineralization had lower shear strength [234]. Therefore, Haversian systems may have a lower shear strength than the more highly mineralized interstitial bone, and would be prone to early shear cracking especially in the presence of stress concentration. It is not clear whether microdamage localization is associated with any specific collagen fibril organization existing inside the Haversian systems. Ascenzi & Bonucci [182] reported that the compressive strength of osteon samples was lower in those having marked longitudinal spiral course of collagen fiber bundles in successive lamellae. 42 Variations in mineral content and collagen fiber orientation within lamellar sublayers may also impede the development of microcracks as suggested by Gupta et al. [170] and contribute to the local cross-hatched microcracks. 4.4 CONCLUSIONS Our results therefore indicate that compressive cracking is not only more sensitive to the presence of Haversian canals than tensile cracking, but also depends on the mineralization, size, geometry, and microstructure of the Haversian systems. The scattering in shape and levels of compressive stress-strain curves (Fig. 4.3) also supports these observations. It can be concluded that, as a result of the strain redistribution process, bone’s compressive behavior, which is more sensitive to variations in bone’s microstructural features (e.g. porosity and Haversian systems), plays a significant role in bone’s resistance to fracture in bending. Since cortical bone porosity increases with age [235-238], the cracking sensitivity to Haversian canals (i.e. porosity) found here in the senior population may not directly apply to a younger population. Nevertheless, the results are highly relevant to the senior population with the highest bone fracture risk. Bone microstructure at the Haversian system level plays an important role in bone deformation and fracture. Further work is thus needed to understand the origins of the compressive microcracks within the secondary osteons.  ------------------------------------- 2 A version of Chapter 5 has been published. Ebacher V and Wang R. (2009) A Unique Microcracking Process Associated with the Inelastic Deformation of Haversian Bone. Adv Funct Mater. 19:57-66. 43 CHAPTER 5 A UNIQUE MICROCRACKING PROCESS ASSOCIATED WITH THE INELASTIC DEFORMATION OF HAVERSIAN BONE 2 The purpose of this study was to investigate the inelastic deformation mechanisms of osteonal bone under compression. Compression is a major mode of biomechanical loading of bones in the human body and it is well known that bone deforms differently in compression than in tension (Chapter 4) [2,239]. It is also clear that bone’s compressive behavior has an important influence on its bending response (Chapter 4) [239]. In this study, we were particularly interested in how the detrimental effects of Haversian canals were alleviated by bone's hierarchical structure and how a high loading capacity was maintained over the long inelastic stage of transversely compressed cortical bone [41]. The approach consisted of comparing bone’s mechanical response when loaded along different orientations to better understand the structure – mechanical properties relations. 5.1 EXPERIMENTAL A total of three un-embalmed human cadaveric femoral shafts were used in this study. The specimens (2 males, 64 and 69 years old; 1 female, 55 years old) were obtained from the Department of Anatomy at the University of British of Columbia. All bones were visually examined for macroscopic defects or pre-fractures and were stored at -20°C until machining and testing. The study was approved by the Clinical Research Ethics Review Board at the University of British Columbia. 44 5.1.1 Mechanical Tests – Monotonic Loading Compressive monotonic loading was used to study the mechanical response of bone along three different orientations, i.e. longitudinal (0°), transverse (90°), and oblique (45°) to the long axis of the femoral shaft. A total of 7 longitudinal, 7 transverse (5 from one femur and 1 from each of the other two femora for each orientation), and 3 oblique (1 from each of the three femurs used) specimens were cut from the mid-diaphysis of the femoral shafts (between 45-65% sites from the distal end) using a low-speed diamond saw (Isomet 1000, Buehler) under constant water irrigation. The four sides of the rectangular specimens were aligned either tangentially or normally to the endosteal and periosteal surfaces. The specimen surfaces were manually ground into rectangular prisms, mechanically polished using diamond suspensions down to 1.0 µm, and finally vibration polished using 0.05 µm colloidal silica suspension down to their final dimensions of 3 mm × 3 mm × 6 mm. The specimens were then placed in a phosphate-buffered solution (0.05 PBS, pH 7.2, 4°C) until mechanical testing. Compression tests were conducted under wet conditions using a servohydraulic testing machine (Instron 8874, 25 kN load cell) at a crosshead speed of 0.1 mm/min. Load was applied through a 5 mm diameter polished tungsten carbide hemisphere to ensure a uniform stress transfer to the specimens. For each orientation, 2 specimens were loaded to fracture to obtain the full load-displacement curves and the others were unloaded prior to final fracture (i.e. at about 5% drop from the peak load) in order to get a clear depiction of the microdamage state within the specimens prior to the formation of the macroscopic fatal crack. From the measurements of load and displacement, engineering stresses and strains (from the compliance corrected displacements) were calculated and elastic modulus, strength, yield strength and strain, and strain at peak stress were obtained. The yield point was determined using the standard 0.002 strain offset method. Assuming normally distributed data, 45 one-way analysis of variance (ANOVA) and post hoc pairwise multiple comparison Holm-Sidak t-test (Primer of Biostatistics version 6.0; McGraw-Hill Companies, USA) were used to assess the differences among the three groups (longitudinal, transverse, and oblique). The significance level was set at p < 0.05. 5.1.2 Mechanical Tests – Step-wise Loading Compressive step-wise loading was used to further explore the deformation process and the damage development in the transverse orientation. Five rectangular specimens of 2.5 mm × 2.5 mm × 5 mm were made from the same three femoral shafts (3 from one femur and 1 from each of the other two femora) in the same manner as described for the monotonic loading specimens. The central third of the two transverse surfaces (with respect to the osteons’ long axis) of each specimen were first imaged under the white light of an optical microscope (Nikon Eclipse E600) before being placed in a phosphate-buffered solution (0.05 PBS, pH 7.2, 4°C). Two strategies were used to monitor the deformation and damage occurring during loading of the specimens: a) a four-step loading with in-situ staining to monitor the development of damage and b) a step-wise loading combined with digital image correlation to examine the deformation process. In the first strategy, two of the specimens (from the same femur) were first stained for 30 minutes in an aqueous solution of 2% fluorescein (Fisher Scientific) and rinsed in tap water for 10 minutes before mechanical testing. They were then examined under epi-fluorescence light (with excitation at approximately 490 nm and emission at approximately 525 nm) to detect the presence of any pre-existing microcracks. The specimens were subsequently loaded in compression to a load corresponding to the first noticeable deviation from the linear stage in the load-displacement curve, using an electromechanic testing machine (Minimat Materials Tester 2000, 1kN load cell) at a crosshead speed of 0.1 mm/min. Load was applied through a polished 46 tungsten carbide hemisphere onto the specimens which were immersed into an aqueous solution of 2% fluorescein for in-situ staining. Following unloading, the specimens were kept in the staining solution for 30 more minutes and then rinsed in tap water for 10 minutes before epi-fluorescence microscopy examination to detect microcrack initiation, a procedure based on the study of Reilly & Currey [21]. The micro-cracked sites were photographed for later comparison of microdamage evolution. This loading-unloading-imaging procedure was repeated two more times, each time at a larger strain into the non-linear stage, before failing the specimens at the fourth loading cycle. We also employed digital image correlation (DIC) technique to obtain the in-plane displacement and strain fields [210,240]. This information provides insight into the deformation of this heterogeneous material at the micro-scale. An advantage of strain mapping cortical bone over conventional materials is that the high contrast surface patterns required to obtain good DIC results are provided by the intrinsic microstructural features of the bone tissue. Thus, in the second strategy of the step-wise loading tests, the remaining three specimens (from the three different femora) were loaded under wet conditions at a crosshead speed of 0.1 mm/min while an area (approximately 722 × 538 µm) at the center of the transverse surfaces was imaged with an optical microscope (Nikon Eclipse E600) under reflected light at different deformation stages. A sequence of 1392 × 1040 pixels 8-bits images were captured for each specimen using a digital camera (QImaging QICAM Fast 1394) by temporarily stopping the crosshead at progressively higher loads (approximately every 50 N and around the peak load). Loads and displacements were recorded and engineering stresses and strains (from the compliance corrected displacements) were calculated. The images were then processed with the DaVis imaging software (La Vision Inc.; Ypsilanti, USA) using a multi-pass correlation strategy with a final 47 interrogation window size (area used to search corresponding patterns between images) of 64 × 64 pixels and 75% overlap to compute the in-plane displacement fields and finally the in-plane strain fields (strain accuracy of about 0.3%; see Appendix C for more information). Following processing, the strain patterns and their angles with respect to the loading axis were compared with the microdamage patterns (see next section) in order to understand the nature of the deformation involved in the failure process. 5.1.3 Fracture and Microdamage Analyses Following mechanical testing, all specimens were dehydrated and stained according to a procedure described in Ebacher et al. (see 4.1.2) [239]. Briefly, the procedure involved defatting and fixation using acetone followed by dehydration using a graded series of ethanol/water solutions (80%, 90%, and 100%) and the final staining under vacuum in a filtered saturated solution of fluorescein and 70% ethanol for periods of 24 hours per step. All four surfaces parallel to the loading direction were examined under the optical microscope (Nikon Eclipse E600) using both the white and epi-fluorescence lights. Microdamage introduced during the compressive tests would be stained by the fluorescein dye and appear bright green under the fluorescence microscope. The dye also stained some elements of the bone microstructure such as osteocyte lacunae and Haversian canals. The angles of the stained microcracks on the surfaces were measured with respect to the specimens' long axis and statistically compared for differences relatively to their orientations using ANOVA and Holm-Sidak t-test with a confidence level of 95% (p < 0.05). For the transverse specimens, additional high magnification reflected white light observations were done at selected sites using an optical microscope (Nikon Eclipse LV100) equipped with a differential interference contrast (L-DIC) device which, under polarized light 48 mode, offers certain topographic capabilities. Sites with typical microdamage morphologies were selected to provide further details on microdamage morphology, microdamage development, and their relations to microstructural features (osteons, interstitial bone, osteonal lamellae etc.). Scanning electron microscopes (SEM) were also used to examine the microcracks at higher resolutions. Specimens were sputter-coated with a thin layer of gold and examined with two scanning electron microscopes (Hitachi S-3000N and Hitachi S-4700, Hitachi Ltd., Tokyo, Japan). The location of microdamage initiation was also determined by examining osteons at an early stage of cracking (from the step-wise loading experiment), i.e. showing less than 10 microcracks at a specific site. Each osteonal site considered was divided into five locations: A1-2) at the Haversian canal: radial crack and circumferential crack, respectively; B) first third of the osteonal wall; C) middle third of the osteonal wall; D) at or close to the cement line; E) outside of osteon (interstitial bone). For every site, all potential locations of initiation were recorded to obtain the total number of occurrences of each location. Proportions were then calculated along with the standard error of the estimate of the proportions for a confidence level of 95% (p < 0.05). Additionally, as pre-existing cracks in interstitial bone can be considered as potential points of weakness [84,191,193,195], pre-loading and post-failure images of pre-existing cracks (from the step-wise loading experiment) were compared to verify if the cracks had propagated, and thus could have potentially caused the failure. Since microdamage covered most of the specimens' surfaces, the proportions of damaged osteons from the middle third of five transverse specimens unloaded prior to final fracture were also counted in order to assess the extent of the damage. Finally, two of the five specimens were used to verify if the state of microdamage seen on the surfaces was representative of the bulk of the specimens. One of their surfaces normal to 49 the osteons (transverse to the bone's long axis) was ground and polished as described earlier to a depth of 1.5 mm, thus exposing the central longitudinal section for epi-fluorescence observations. 5.2 RESULTS 5.2.1 Effects of Loading Orientation on Stress-Strain Curves and Basic Mechanical Properties Comparing bone response when loaded along different orientations provides insight into the structure-mechanical properties relations. In this study, compressive stress-strain curves (Fig. 5.1; see Appendix B for all curves) and their ensuing properties (Table 5.1) were obtained for human cortical bone loaded along three orientations, i.e. longitudinal (0°), transverse (90°), and oblique (45°) to the bone’s long axis (and therefore most of the osteons).   Figure 5.1. Typical compressive stress-strain curves for human cortical bone loaded along three different orientations: longitudinal (0°), oblique (45°), and transverse (90°). The transverse orientation shows much higher inelastic strain than the other two.  50 Bone clearly shows distinct responses along different loading orientations, consistent with the literature [41]. The longitudinal specimens had the highest elastic modulus (16 ± 2 GPa) and compressive strength (143 ± 6 MPa). They yielded at 141 ± 5 MPa, strain hardened rapidly to a peak corresponding to strains of about 1.3 ± 0.2 %, dropped in load and failed at strains generally below 4%. The transverse specimens had the lowest elastic modulus (8 ± 1 GPa) and strength (91 ± 9 MPa). They yielded at a lower stress of 79 ± 7 MPa, but showed a mild strain hardening reaching strains of 3.3 ± 0.8 % at peak stress before failing at strains as high as 7%. As for the oblique specimens, they showed behaviors and properties in-between the other two orientations. It is obvious that the transverse orientation exhibited extensive inelastic deformation as compared to the other two despite the bone being loaded perpendicularly to the Haversian canals, a configuration offering multiple stress concentration sites. Therefore, for a porous material composed of 70 wt% carbonated apatite, a ceramic, the relatively long strain-hardening behavior is remarkable and suggests the involvement of a novel deformation mechanism governed by the particular organization of bone's microstructure.  Table 5.1. Properties calculated from the compressive stress-strain curves (mean ± sd). Orientations Elastic Modulus (GPa) Strength  (MPa) Strain at Peak Stress (%) Yield Strain  (%) Yield Strength (MPa) Longitudinal (0°) 16 ± 2 143 ± 6 *1.3 ± 0.2 *1.07 ± 0.14 141 ± 5 Transverse (90°) 8 ± 1 91 ± 9 3.3 ± 0.8 *1.15 ± 0.07 79 ± 7 Oblique (45°) 13.3 ± 0.3 113 ± 11 *1.7 ± 0.4 *0.98 ± 0.08 104 ± 10 [*] Respective properties were found to be significantly different between the three groups with the exception of yield strain values for all three groups and strain at peak stress values between the longitudinal and the oblique groups for which no statistical difference was found.  51 5.2.2 Effects of Loading Orientation on Macro-Scale Fracture Patterns and Microdamage Morphologies Inelastic deformation in cortical bone is generally associated with microcracking [16]. Hence, for each orientation, two specimens were loaded to fracture to obtain the full load-displacement curves and observe the macro-scale fracture patterns while the others were unloaded prior to final fracture (i.e. at about 5% drop from the peak load) in order to assess the microdamage state within the specimens prior to the formation of the fatal crack. Following mechanical testing, all specimens were stained according to a procedure described in Ebacher et al. (see 4.1.2) [239] in order to observe microdamage morphologies under epi-fluorescence microscopy. The macro-scale fractures happened oblique to the loading axis. There did not seem to be any differences among the three orientations. The micro-scale fracture patterns, however, showed obvious orientation dependence. Figure 5.2 (see also Appendix B) shows typical microdamage morphologies of the cortical bone specimens compressed along the three orientations. At such low magnifications, the microdamage in the three orientations is homogeneously distributed over the entire surface of the specimens. The obvious oblique damage pattern looks very similar to the frequently reported cross-hatched microdamage in cortical bone when it is compressed longitudinally (Figs. 4.6a-4.9a) [13,14,182,239]. However, we found that the cross-hatching angle in the transverse specimens (38 ± 7° between the crack plane and the loading axis) was significantly higher than the ones in the longitudinal and oblique specimens (Table 5.2). This difference suggests that the failure process would be sensitive to microstructural features such as osteons' orientations.  52            Figure 5.2. Compressive microdamage morphologies of human cortical bone loaded along different orientations. a) Longitudinal (0°); b) Transverse (90°); c) Oblique (45°). left: epi-fluorescence images; right: bright field images. At this magnification, the microdamage morphologies all look similar and are characterized by their oblique cross-hatched patterns. Compressive load applied vertically.  53 Table 5.2. Cross-hatched microcrack angles in cortical bone specimens loaded along three different orientations (mean ± sd). Orientations Number of Specimens Number of Microcracks Cross-hatched Microcrack Angle Longitudinal (0°) 7 63 *27 ± 4° Transverse (90°) 7 87 *38 ± 7° Oblique (45°) 3 31 *31 ± 7° [*] The angles between the stained cross-hatched microcracks and the specimens’ long axis were found to be significantly different between the three groups.  Surprisingly, at higher magnifications, each set of cross-hatched microdamage in the transverse specimens actually consisted of up to four groups of arc-shaped circumferential microcracks radiating out from each Haversian canal into the four quadrants of the osteon (Figs. 5.3a,b). These microcracks appeared as continuous lines under an optical microscope. They were mostly present within the thick layers of the osteonal lamellae and followed the general contour of the lamellar boundaries. The same cracking morphologies were also observed within the bulk of the specimens (Supporting Information Fig. 5.8), suggesting homogeneous damage throughout the entire thickness of the bone specimens. Scanning electron microscopy revealed further interesting details: the circumferential cracks were often preceded by short radial cracks (Figs. 5.3c,d). These radial cracks were 2-5 µm apart and confined within the thick lamella. A circumferential crack would propagate through coalescence with those micro-radial cracks. Such a damage pattern was totally different from that on specimens compressed along the Haversian canals. In the later case, the cross-hatched microdamage consisted of linear microcracks oblique to the bone lamellae, observations concurrent with those we reported in an earlier study (Chapter 4) [239]. As for microdamage in the obliquely compressed specimens, it showed a mixture of 54 both linear cross-hatched cracks and arc-shaped cracks. The higher scatter in the shear crack angle for the transverse and oblique specimens (Table 5.2) suggests that the arc-shaped cracking was influenced by surrounding microstructural elements, mainly neighboring osteons. Indeed, Figure 5.3b shows an example where the cracking of the central osteon is attracted to the osteons to the lower left and upper right. This indicates that the spatial distribution of osteons would be an important factor to the fracture resistance of cortical bone.       Figure 5.3. Microcracks on transversely compressed bone specimens. a) Epi-fluorescence image showing four groups of arc-shaped circumferential microcracks (bright green) formed at the four quadrants of an osteon (center); b) Epi-fluorescence image showing the influence of neighboring osteons on the angle of the cross-hatched microdamage. The cracking of the central osteon is obviously attracted to the osteons to the lower left and upper right; c) SEM micrograph showing arc-shaped microcracks at various stages of development along the osteonal lamellae. Photo was taken from the lower left quadrant of the osteon in (a). The lamellae have alternating bright (thin lamellae marked by arrowheads) and dark (thick lamellae) contrast; d) Closer observations of (c) (asterisks) showing the short micro-radial cracks in the thick lamellae and their merging into a circumferential microcrack. Compressive load applied horizontally.  55 Since bone inelastic deformation happens predominantly through microcracking [16], the unique arc-shaped cracking within the osteonal wall is the main cause for the high inelastic strain observed in the transversely compressed cortical bone. The apparent active involvement of the osteonal microstructure in the cracking process led us to investigate further this remarkable cracking mechanism. 5.2.3 Damage Development in the Transverse Orientation: Initiation and Propagation The development of arc-shaped microcracks was further investigated by executing step-wise compressive loading experiments together with in-situ fluorescein staining, to see where the microcracks initiated and how they interacted with bone's microstructure. Figure 5.4 shows images taken at different stages. Shortly after macroscopic yielding, multiple nucleations of the arc-shaped microcracks occurred predominantly within the osteons (Fig. 5.4b). Further loading increased the number of cracks within each osteon and caused the two groups of arc-shaped cracks from neighboring osteons to link through cracking along the interstitial bone lamellae (Figs. 5.4c,d). This process eventually led to extensive cracking in most osteons (80 ± 5%) across the specimen width (Fig. 5.2b), followed by final macroscopic fracture.   56       Figure 5.4. Damage development in cortical bone. a) Bright field micrograph showing two osteons. Photo taken after the compression test; Epi-fluorescence micrographs showing progressive observations of microcracks development: b) Microcrack initiation within the two osteons at initial loading; c) More arc-shaped microcracks within the osteons upon further loading. Cracking in interstitial bone (arrow) links the osteonal cracks; d) Extensive damage at the final state. Note the very little interaction between the two central osteons aligned with the loading axis. Compressive load applied horizontally.  To determine more precisely where the damage started within the osteons, we followed sixty-nine osteons at an early stage of cracking. Figure 5.5 shows the frequency distribution of five potential initiation locations. It can be seen that there was a higher incidence of initial intra-osteonal wall cracking (49% for locations B and C) as compared with the lamella at the Haversian canal (31% for locations A1 and A2). As for the cement line area (location D), a region frequently considered to be a point of weakness in cortical bone [3,191], it did not seem to be a 57 major damage initiation site for this particular loading orientation as compared with the osteonal lamellae.   Figure 5.5. Frequency distribution of the location of arc-shaped microcrack initiation under transverse compression. Sixty-nine osteons at the initiation stage were examined. All osteons considered were divided into five locations: A1-2) at the Haversian canal: radial crack and circumferential crack, respectively; B) first third of the osteonal wall; C) middle third of the osteonal wall; D) at or close to the cement line; E) outside of osteon (interstitial bone). A1 and A2 are considered as cracks at the Haversian canal, while B and C are intra-osteonal wall cracks. The error bars represent the standard error of the estimate of the compiled proportions for a confidence level of 95% (p < 0.05).  Regarding damage initiation within bone tissue (as opposed to within osteons), pre-existing linear cracks in interstitial bone were also considered as potential points of weakness [84,191,193,195]. These cracks are generally considered to be of a fatigue origin in human cortical bone [84,191,193]. They were often present in the interstitial bone areas of our specimens prior to loading. We followed the progress of nineteen such cracks during loading. They did not propagate significantly in most cases (only 5 cracks propagated out of the 19 observed, see Supporting Information Fig. 5.9), even though many of them were parallel or oblique to the compressive loading axis and thus would normally tend to propagate due to the 58 tensile stress at the crack tips. Additionally, although some of the pre-existing cracks were near the final fracture path, none of them were located right in the path, suggesting that they did not directly contribute to the failure along this orientation. 5.2.4 Deformation Process: Strain Distribution around Osteons As the failure of a material is generally related to high local stresses and strains in the vicinity of defects, it is important to know the magnitude and distribution of these stresses and strains around the defects. Hence, the local strain development during deformation was examined using digital image correlation (Fig. 5.6) [210,240].       Figure 5.6. Deformation process in cortical bone. a) Bright field optical image before loading; b) Epi-fluorescence image showing microdamage after loading; c) Maximum shear strain field for the elastic stage (~0.7% far-field compressive strain) showing strain concentration near Haversian canals; d) Maximum shear strain field for the inelastic stage (~1.7% far-field compressive strain) showing shear connections between the osteons. Note the match between the strain field and the microdamage pattern in (b). Compressive load applied horizontally.  59 Within the elastic range (Fig. 5.6c), the shear strain developed unevenly across the bone specimen and concentrated near the Haversian canals at angles oblique to the loading axis. In the inelastic stage (Fig. 5.6d), the shear strain further developed and linked the osteons together. The shear angle varied slightly along the oblique path due to the influence of neighboring osteons. It can be seen that the shear strain pattern corresponds very well with the damage patterns observed after unloading (Fig 5.6b), confirming the assumption of shear induced cracking. In addition to comparing the strain patterns to the microdamage patterns, we considered the relative amplitude of the individual shear components (i.e., the displacement gradients exy and eyx) as well as the orientations of the principal strains. Figure 5.7 shows the strain distribution surrounding an osteon at a stage approximately corresponding to the macroscopic yield of the specimen. As can be seen in Figures 5.7c-d, the shear component acting along the radial direction, and thus roughly parallel to the short micro-radial cracks in Figure 5.3d, is the dominant shear while the circumferential shear component is relatively negligible. This suggests that radial shear would be responsible for the short micro-radial cracking seen within the thick layers of osteons. Notice also that both the principal compressive and tensile strains followed the same distribution as the maximum shear strain, although they were oriented oblique to the microcracks, i.e. parallel and perpendicularly to the loading direction, respectively (Fig. 5.7a Insert). Interestingly, a shear band formed at at the final stage of failure (Fig. 5.7e).      60          Figure 5.7. Strain distribution surrounding an osteon. a) Epi-fluorescence micrograph showing the final microdamage pattern around the Haversian canal; b) Maximum shear strain oriented obliquely to the loading direction. Note that εmax = [(εx - εy)2/4 + (εxy)2]1/2, where the shear strain εxy corresponds to an average value of the displacement gradients exy and eyx shown in (c) and (d): εxy = (exy + eyx)/2 [226,241]; Shear components along the planes roughly corresponding to those of the maximum shear strain: c) Shear component (exy) on the y-plane along the x-direction; d) Shear component (eyx) on the x-plane along the y-direction. The radial shear is most probably related to the extensive cracking seen in the form of short micro-radial cracks within the thick lamellae; e) Optical micrograph showing a shear band formed at a later stage of deformation. Insert in (a): Approximate stress state in the damaged regions: the principal compressive and tensile strains are oriented parallel and perpendicularly to the loading direction, respectively, and the maximum shear strain planes are oblique to the loading direction. Compressive load applied horizontally.  61 5.3 DISCUSSION The combination of digital image correlation during mechanical testing, microcrack staining, as well as optical and electron microscopy provided us with a clear picture of the unique inelastic deformation and cracking mechanisms in cortical bone compressed transversely. It was shown that the multiple crack nucleation and propagation processes were obviously governed by the unique structure of the osteonal lamellae and the distribution of the osteons within the cortical bone. Such remarkable hierarchical structure makes osteonal bones highly resistant to catastrophic failure. 5.3.1 A Unique Microcracking Process Ascenzi et al. reported the arc-shaped microcracking in 1973 [242]. However, it attracted little attention in the past three decades. One possible reason is that the cracking was done manually on thin (45 µm) single osteon discs, which made it difficult to evaluate its relevance to bone performance at the tissue level. There has also been concerns about testing on a single osteon because the cement line was absent [2,3]. Our study showed that the arc-shaped microcracking happened at the cortical bone level. We also discovered that most arc-shaped cracks formed through multiple nucleations of short micro-radial cracks and their subsequent coalescence within the thick lamellae. This well-controlled microcracking process represents a unique mechanism in osteonal bone to relax the stress concentration caused by Haversian canals. It enabled a homogeneous deformation throughout the whole bone specimen, and thus directly contributed to the high inelastic strain observed at the macroscopic level. When a brittle and isotropic material containing circular holes is under uniaxial compression, it cracks at the holes’ edges under tensile stress and fails by "slabbing" parallel to the loading axis [174]. Bone does not follow this classical failure mode. Crack initiation at the 62 cortical bone level can be qualitatively related to the maximum theoretical shear stress [242]. In an infinite, uniaxially loaded plate containing a circular hole, the maximum shear stress develops at 45° to the loading axis and at a small distance away from the hole's edge [243]. This generally concurred with our observations that the arc-shaped cracks formed more often in lamellae away from the canal’s edge (Fig. 5.5) and that the cross-hatched microcrack bands formed at 38 ± 7° to the loading axis (Table 5.2). Additionally, we tested the assumption of shear induced cracking via in-plane strain mapping using digital image correlation [176,210,240], and found that, indeed, the maximum shear strain followed the damage patterns (Fig. 5.6): the shear strain initially concentrated near the Haversian canals at angles oblique to the loading axis and later, further developed and linked the osteons together. Interestingly, the highest shear component (i.e. radial shear) in each quadrant of the osteons was generally aligned with the multiple micro-radial cracks observed under SEM (Fig. 5.3d), while the circumferential shear component was relatively negligible in the damaged zone (Figs. 5.7c,d). This suggests that radial shear would be responsible for the extensive cracking seen in the form of short micro-radial cracks within the thick layers of osteons. 5.3.2 Role of Osteonal Lamellae The unique deformation and microdamage patterns in osteonal bone led us to consider the roles of the osteonal lamellae surrounding each Haversian canal. Under optical microscope, human osteonal lamellae consist of alternating dark/thin and bright/thick layers (Figs. 5.4a-5.6a). The mineralized collagen fibrils are predominantly aligned in the circumferential direction in the thin layer, and along the Haversian canal in the thick layer [110]. At higher resolution, each pair of the thin/thick lamellae consists of five successive layers of parallel fibrils oriented progressively every 30°, forming a rotated plywood structure. The plate-shaped carbonated 63 apatite crystals within an individual sub-layer are aligned to each other [1,112,113]. The crystal layers are parallel to the lamellar boundaries within the thin lamellae and at a high angle to the lamellar boundaries within the thick lamellae [112]. Osteocyte lacunae, 10-30 µm in size, are also present near the lamellar boundaries. They are connected by radially oriented canaliculi, which are small (100-200 nm in size) but highly populated (1x106 canaliculi/mm3) [3]. As mineralized collagen fibrils are highly anisotropic in resisting deformation and fracture [108,133,244], the plywood-like fiber organization in bone lamellae enables each osteon to resist the tensile stresses generated at the Haversian canal's edges through the circumferentially aligned fibrils, while facilitating the inter-fibrous shear cracking in the thick layers [242]. The current study shows that this lamellar structure and the microcracking behavior of an individual osteon resulted in a unique damage development in cortical bone. When osteonal bone was compressed transversely, shear strain concentration developed at the four quadrants of each osteon. In the thick lamellae where the mineralized collagen fibrils are largely parallel to the shear plane, shear cracks could initiate at some intrinsically weak sites such as the radially oriented canaliculi and the weak interfibrillar area [244]. Another crack nucleation site in the thick lamellae could be the weak planes created by the well-aligned apatite plates oblique to the lamellar boundaries [112]. The radial propagation of the shear cracks would be stopped by the circumferentially organized collagen fibrils in the thin lamellae (Figs. 5.3c,d). Meanwhile, neighboring micro-radial cracks would begin to merge into the arc-shaped circumferential cracks, possibly under a mixed stress state of shear and tension. The propagation of an arc-shaped crack in the circumferential direction would stop as it passed beyond the stress concentration zone. Further loading would then cause more radial and arc-shaped microcracks to nucleate and develop in neighboring lamellae, other quadrants of the same osteon, or other osteons. Such a cracking process would be 64 stopped by the interstitial bone surrounding each osteon. Interstitial bone is also lamellar. However, its lamellae are usually oriented in a different direction from the neighboring osteonal lamellae and would thus require further loading to develop microcracks. Before extensive cracking happens in interstitial bone, most osteons (80 ± 5%) in the cortical bone would have experienced crack initiation and multiplication, which translates into high macroscopic inelastic strain without a drop in loading capacity. Interestingly, the final stage of the compression failure involved shear band formation, a phenomenon speculated by Currey [14] and Mercer et al. [126] for longitudinal compression, but that has never been demonstrated experimentally. In Figure 5.7e, at the peak load, the circular microcracks in the thick layers of the osteonal bone destabilized the thin lamellae and caused them to buckle. As a result, shear bands formed in a way similar to kink bands in fiber composites [245] and eventually led to shear failure. Although the microcracking discussed above was the dominating mechanism, we did observe some deviations in microcrack morphologies that were either related to the Type L osteons reported in the literature [3,110], the presence of osteocyte lacunae, or the geometry of the osteons (Supporting Information Fig. 5.10). 5.3.3 Role of Cement Lines, Pre-Existing Cracks, and Neighboring Osteons Osteonal bones have cement lines outlining every osteons and often have pre-existing linear cracks within the interstitial bone. These two features are frequently reported to be points of weakness [3,84,191,193,195]. In the present study, pre-existing linear cracks did not seem to be largely involved in the cracking process as most of them did not propagate significantly (Supporting Information Fig. 5.9), consistent with the results of O'Brien et al. [202,203] Surprisingly, cement lines did not seem to have strong influences on the crack initiation process (Fig. 5.5). Nevertheless, cement lines seemed to have the role of deviating in-coming cracks at a 65 later stage of the deformation, in agreement with recent reports [153,202,203]. More importantly, the distribution of osteons could noticeably affect the angle of the cross-hatched cracks. The arc-shaped microcracks tended to be attracted to the direction of a neighboring osteon (Fig. 5.3b). Therefore, the alignment of osteons in the oblique direction would promote crack interactions, and even the formation of shear bands (Fig. 5.7e). Osteonal bone on the transversal section can be roughly represented by a plate with randomly distributed holes. Obviously, the spatial distribution of osteons affects both the amplitude and the location of the maximum shear stress that governs the fracture process [246]. 5.3.4 Implications to Bone Quality In clinical and laboratory assessments of human bone quality, osteon population density, Haversian canal size, osteon size, and porosity have been found to vary with sex, age, physical activity, etc. [3,89] These structural features are also closely related to bone strength and toughness [69,247,248]. However, detailed mechanisms behind these correlations at the material level are obscure. Based on this study, bone resistance to fracture ultimately depends on how many cracks develop and how uniformly they are distributed. At a given porosity, higher osteon population density and more bone lamellae surrounding each canal (i.e. thicker osteonal wall) should lead to larger number of arc-shaped cracks and therefore higher fracture resistance. Increase in porosity as a result of an increase in Haversian canal size would directly cause higher local stress concentration (consider a larger hole in a plate with finite width [246]) and lower strength. Although the above discussions are based on transversely loaded osteonal bones, the general concept also fits longitudinally compressed bone. In the later case, multiple cross-hatched linear cracking also happened to most osteons (Fig. 5.2a), and each osteon showed a 66 certain capability of confining microcracking (Fig. 4.9) [239]. These two processes introduce inelastic deformation to cortical bone, although to a lesser degree. 5.4 CONCLUSIONS Osteonal bones demonstrate high inelastic strains at the macroscopic level. The secrets lie in the unique concentric lamellar structure of the osteons and their even distribution within the bone cortex. This structure facilitates well-controlled multi-nucleations, and stable, progressive development of microcracks, therefore relaxing the stress concentration at the Haversian canals. Although the multiple circumferential cracks happened in specimens compressed transversely, their circular morphology is similar to the shear cracks in human bone submitted to torsion [140]. The microcracking mechanism reported here may thus represent a novel strategy of bone in meeting a complicated biomechanical environment. To fully understand the nature of the microcracking process, it is essential to study the structure and mechanics of osteonal lamellae down to nanometer level. Recently, there has been extensive research on nano-scale bone structure and mechanics [134,157,160,169]. A close linkage with these progresses in the context of osteonal lamellae will provide a better picture of bone mechanics across the whole structural hierarchy. The osteon and the lamellar structure may also inspire novel structural designs of fiber composites. Current engineering fiber composites have robust performance under tensile stress, but suffer from delamination and buckling under compression. With the increased applications of fiber composites in challenging structures such as airplanes, some of the structural designs in osteonal bone could be adopted to resist complicated stress conditions. 67 5.5 SUPPORTING INFORMATION 5.5.1 Microdamage within the Bulk of the Bone Specimens Most of the microdamage observations were done on the external surfaces of the rectangular specimens. To verify whether the state of microdamage (morphology, distribution, and extent) as seen on these surfaces was representative of the situation in the bulk of the material, two transverse specimens were ground and polished to expose their central longitudinal sections (plane normal to the osteons and thus transverse to the bone's long axis). Epi-fluorescence observations revealed a similar pattern happening within the bulk of the specimens (Fig. 5.8). Oblique damage was homogeneously distributed over the newly exposed surfaces and consisted of arc-shaped circumferential microcracks present within the thick layers of the osteonal lamellae, following the general contours of the lamellar boundaries, and radiating out from each Haversian canal. The microdamage was thus homogeneous throughout the entire volume of the transverse bone specimens.    Figure 5.8. Epi-fluorescence images of arc-shaped circumferential microcracks (bright green) within the bulk of transversely compressed bone specimens (central longitudinal section transverse to the bone's long axis). The microdamage seen on the surfaces is also observed in the bulk of the tissue, suggesting that extensive damage existed through the entire volume of the bone material. Compressive load applied vertically.  68 5.5.2 Role of Pre-existing Cracks in the Fracture Process Pre-existing linear cracks in interstitial bone were also considered as potential points of weakness [84,191,193,195]. These linear cracks are generally considered to be caused by fatigue in human cortical bone [84,191,193]. They were often present in the interstitial bone areas of our specimens prior to loading. We followed the progress of nineteen pre-existing cracks during loading. They did not propagate significantly in most cases (only 5 cracks propagated out of the 19 observed), even though many of them were either parallel or oblique to the compressive loading axis and should tend to propagate due to the tensile stresses at the crack tips. Figure 5.9 shows two typical cases: one crack propagated upon loading but was stopped at the osteon, while the other did not propagate at all. Additionally, although some of the pre-existing cracks were near the final fracture path, none of them were directly located in the path, suggesting that they did not apparently contribute to the failure in this orientation.         Figure 5.9. Pre-existing cracks in the interstitial bone prior to loading (left, arrowed, Epi-fluorescence) and after compressive failure (center, Epi-fluorescence) together with their corresponding bright field images (right): a) An oblique pre-existing crack that did not propagate; b) An oblique pre-existing crack that did propagate but was not involved in the final fracture of the specimen. Compressive load applied horizontally.  69 5.5.3 Variations of the Microcrack Morphologies The majority of the osteons in our bone specimens had the thin/thick layer appearance under both optical microscope and scanning electron microscope. These osteons showed arc-shaped cracks. However, there was a small number of osteons (estimated to be 10-15% of the osteon population in our specimens) in which the lamellar structure was not obvious under both OM and SEM. It is suspected that these were the Type L osteons reported in the literature [3,110], which have their collagen fibers aligned mainly along the Haversian canal axis. In those osteons, arc-shaped cracking was not seen. Instead, long linear cross-hatched cracks and relatively long, radial cracks were present (Fig. 5.10a). Since the population of those osteons was relatively low in the specimens we analyzed, they did not seem to have a significant impact on the overall deformation. It would be interesting to know under what circumstances higher populations of those osteons would exist.    Figure 5.10. SEM micrographs of the microcracks in osteonal lamellae. a) Long linear cross-hatched cracks in an osteon presumably of the Type L structure (collagen fibers aligned mainly along the Haversian canal axis); b) Micro-radial cracks within the thick lamellae. Note that no circumferential cracks developed. Note also the cross-hatched linear cracks in the interstitial bone (upper right). Haversian canal to the lower left. Compressive load applied horizontally.  Finally, note that although the arc-shaped cracks appeared as continuous lines under epi-fluorescence microscopy, they showed a variety of morphologies under SEM. In addition to the 70 typical crack morphologies shown in Figure 5.3, there were osteons (usually elongated) in which only short micro-radial cracks developed within the thick lamellae (Fig. 5.10b). They would not merge into continuous circumferential cracks even at later stages of deformation. In some cases, very fine linear circumferential cracks developed, with minimum involvement of the intra-lamellar radial cracks. Osteocyte lacunae were also often found to initiate circumferential cracks. These cracks were usually large and many of them were present in the thin osteonal lamellae.  ------------------------------------- 3 A version of Chapter 6 has been submitted for publication. Ebacher V, Guy P, Oxland TR, and Wang R. (09 JA 2011) Sub-Lamellar Microcracking and the Roles of the Canalicular Network in Human Haversian Bone. 71 CHAPTER 6 SUB-LAMELLAR MICROCRACKING AND THE ROLES OF THE CANALICULAR NETWORK IN HUMAN HAVERSIAN BONE 3 The study in Chapter 5 has shown the crucial role of the concentric lamellae in redistributing stress around each Haversian canal through the stable development of multiple intralamellar microcracks [249]. In that study, transverse compressive loading proved to be an excellent strategy to investigate the structure – microcracking relations at the osteonal and lamellar levels. Yet, the nature of cracks at the sub-lamellar and fibrillar levels as well as the precise location of crack initiation and the details of the intralamellar cracking process remained unclear [249,250]. Additionally, microcracks in longitudinally compressed bone specimens and their interactions with bone hierarchical structure have not been studied at high resolution. The purpose of the present study was to investigate the detailed structure – microcracking relations at the lamellar and sub-lamellar levels of human Haversian bone. In light of their high distribution density [3], the roles of the bone canaliculi in the development of intralamellar cracks were also investigated in depth. This was carried out through high resolution imaging with a laser scanning confocal microscope following both longitudinal and transverse compressive loading schemes. The observations provide insight into the structural design in Haversian bone to achieve high resistance to catastrophic fracture in spite of its extensive porosity network. They further allow for the consideration of the relation between cracks and the mineralized collagen fibrils and thus represent a first step to bridge the gap between microcracking and the deformation mechanisms active at the nano-scale. 72 6.1 MATERIALS AND METHODS The present investigation consisted of high resolution laser scanning confocal microscope (LSCM) imaging of the microcracking process under compression in human cortical bone. Eleven rectangular bone specimens and one whole human tibia specimen were used. Mechanical characteristics and initial fluorescence microscopy analyses of those specimens have been reported previously (Chapters 4-5) [239,249,250]. All studies were approved by the Clinical Research Ethics Review Board at the University of British Columbia. 6.1.1 Specimens and Mechanical Testing As formerly described (Chapter 5) [249,250], the eleven cortical bone specimens were extracted from three unembalmed human cadaveric femoral shafts (2 males, 64 and 69 years old; 1 female, 55 years old). They were mechanically ground into rectangular prisms, polished on all surfaces using diamond suspensions down to 1.0 µm, and vibration polished using 0.05 µm colloidal silica suspension down to their final dimensions of either 3 mm × 3 mm × 6 mm (six specimens) or 2.5 mm × 2.5 mm × 5 mm (five specimens). The specimens were then loaded under monotonic (eight specimens) or step-wise (three specimens) compression (Instron 8874, 25 kN load cell or Minimat Materials Tester 2000, 1 kN load cell) at a crosshead speed of 0.1 mm/min under wet conditions. For the whole tibia specimen (69 years old male; Chapter 4) [239], the proximal 75% section of the shaft was fractured in four-point bending (outer support span set to be three times the length of the inner loading span) under wet conditions using a servohydraulic testing machine (Instron 8874, 25 kN load cell) with a crosshead speed of 6.0 mm/min. The lateral and medial surfaces (defined according to the orientation of the proximal condyle) were subjected to compression and tension, respectively. 73 6.1.2 Laser Scanning Confocal Imaging Analysis Following mechanical testing, the specimens were stained with fluorescein (Fisher Scientific) in order to label the microcracks. The dye also stained the specimens’ original surfaces and porosity network. Ten (eight transverse and two longitudinal) compression specimens and the bending specimen were dehydrated and stained according to a procedure described elsewhere (see 4.1.2) [239]. Briefly, the specimens were sequentially immersed into acetone and a series of ethanol/water solutions (80%, 90%, and 100%) for periods of 24 hours per step, followed by overnight staining under vacuum in a filtered saturated solution of fluorescein and 70% ethanol. They were then taken through various preparation and imaging steps to characterize the microcracking. As for the remaining compression specimen, it was stained for 30 minutes in an aqueous solution of 2% fluorescein, rinsed 10 minutes in tap water to remove the excess stain, and directly taken to LSCM for examination under water immersion (both specimen and objective lens) in order to verify if secondary staining occurred during subsequent preparation steps. Subsequent to staining, selected sites from the bending specimen were carefully cut using a diamond blade saw (Isomet 1000, Buehler) under constant water irrigation, embedded in epoxy resin (Epothin, Buehler), and finally ground and polished (Isomet 1000, Buehler) to expose the near-surfaces of the cortices. Four transversely compressed specimens were ground and polished to their central sections (two specimens were ground normally to the osteons (Chapter 5) [249,250] and two others parallel to the osteons) in order to characterize the cracking in the bulk. All specimens were first examined under the optical microscope using reflected white light (BF; Nikon Eclipse LV100) as well as epi-fluorescence light (EF; Nikon Eclipse E600) with excitation at approximately 490 nm and emission at approximately 525 nm. Specific sites were 74 then imaged at higher magnification under the LSCM (Olympus FluoView FV1000, Olympus Canada Inc., Markham, Canada). Three specimens were sputter-coated with a thin layer of gold for scanning electron microscope (SEM; Hitachi S-3000N and/or Hitachi S-4700, Hitachi Ltd., Tokyo, Japan) examination. These steps allowed for the description of the microcracks’ morphology and development in relations to bone’s hierarchical structures (osteons, osteonal lamellae, osteocyte lacunae, canaliculi etc.). Since microcracks covered most of the compressed specimens’ surfaces, the extent of damage was assessed by counting the proportions of damaged osteons from the middle third of five additional specimens unloaded prior to final fracture (Chapter 5) [249]. LSCM imaging was carried out under oil immersion (objective lens) while the specimens were immersed in an in-house built chamber filled with pure ethanol (Commercial Alcohols Inc.) with the exception of one specimen which was immersed in water (see above). The 488 nm line of a multi-line Argon laser was used for excitation and the specimens emitted at 519 nm. The z-step (z-axis defined as the depth of the image) was set at 200 nm (resolution in z of approximately 587 nm) and the specimens were typically imaged to a depth of 20 µm starting at the surface. A 20 µm z-stack thus consisted of a series of 100 images, each 200 nm apart (but capturing light from 587 nm thick planes), to a depth of 20 µm. Using the acquired z-stacks, it was possible to obtain three-dimensional (3D) information of the cracking and the surrounding porosity network. All z-stack images were reviewed qualitatively for microcracks' shape and approximate dimensions. For transversely compressed bone, crack spacing was measured in fifteen damaged regions from seven different specimens. As the canaliculi were suspected to influence the microcracking, fourteen osteonal regions (ten transverse regions from five specimens and four 75 longitudinal regions from two specimens) were analyzed using ImageJ 1.43s (National Institutes of Health; USA) to obtain quantitative information on the canaliculi density, spacing, and dimensions. Density calculations were accomplished by counting the intensity peaks of profiles plotted along three lines on 15 µm z-stack images (accumulation of virtual slices displayed as one slice; Fig. 6.3a) and dividing the count by the volume subtended by each line. Canaliculi spacing was obtained by digitally measuring the distance between the intensity peaks along the same lines. Two different measures were obtained: spacing for a single thin plane of approximately 587 nm and for projections over 15 µm. Canaliculi volume fraction (vol%) was also estimated based on their averaged measured density and reported diameter [115]. The cracks and canaliculi spacings were compared using one-way analysis of variance (ANOVA) and post hoc pairwise multiple comparison Holm-Sidak t-test (Primer of Biostatistics version 6.0; McGraw-Hill Companies, USA) with a confidence level of 95% (p < 0.05). Canaliculi cross-sectional dimensions were obtained by measuring (using Adrian's FWHM routine (plug-in) in ImageJ) the full width at half maximum (FWHM) of a single intensity peak on 44 optically zoomed areas (Fig. 6.3a insert) from eight specimens. The measurements were calibrated based on 200 nm diameter fluorescent microspheres images (TetraSpeck microspheres 0.2 µm, Molecular Probes Inc.). Ratios of the long-to-short axis were calculated for all measurements to get an approximation of the cross-sectional shape of the canaliculi. 6.1.3 Numerical Simulation Transverse compression loading induced microcracks in high shear zones surrounding the Haversian canals (Chapter 5) [249]. Within these zones, shear would act along and across the length (corresponding to the osteonal radial and circumferential directions, respectively) of the radially oriented canaliculi (Fig. 6.4a). As such stress state represents a fairly uncommon 76 scenario [251], a mechanical simulation (ABAQUS/CAE Version 6.7-5; Dassault Systèmes) of the 3D elastic stress and strain fields surrounding a single canaliculus under pure shear acting along and across its length was performed in order to support the observations of crack initiation at the canaliculi. The approach consisted of using a model with realistic dimensional proportion of a canaliculus within a single osteonal layer, i.e., a solid block of 5 × 5 × 5 µm with a centrally located, 3 µm long and 200 nm diameter, cylindrical hole (Fig. 6.4c). The boundary conditions ensured that translations and rotations occurred only in the plane normal to the shear planes (i.e., plane normal to the osteons). The effect of the mineralized collagen fibril orientations was assessed by first inputting isotropic material properties and then comparing with the results obtained for transversely isotropic properties simulating the bright and dark layers of the osteonal wall (Table 6.1).  Table 6.1. Selected lamellar elastic properties for bone under transverse compression (based on [41,68,127,128,170,244,252-255]). Elastic Modulus (GPa)  Poisson’s Ratio  Shear Modulus (MPa) Simulations Ex Ey Ez  νxy νxz νyz  Gxy Gxz Gyz Isotropic 18  0.35  6667 Transversely Isotropic B 6 6 18  0.12 0.35 0.35  2687 6667 6667 Transversely Isotropic D 18 6 6  0.35 0.35 0.12  6667 6667 2687 a B and D stand for cross-sectional osteonal bright and dark layers, respectively.  77 6.2 RESULTS 6.2.1 Multi-Scale Cracking in Bone: The Advantages of LSCM As reported previously (Fig. 5.1) [249], when compared to the longitudinal orientation, transversely compressed human osteonal bone (transverse to the bone's long axis and therefore most of the osteons) showed lower elastic modulus and strength but higher strain at failure following a mild strain hardening behavior. Transverse Compression Cracking Transverse compression loading resulted in an oblique fracture plane parallel to the osteons (Figs. 6.1a-b). At the osteonal-interstitial level, extensive cross-hatched damage was homogeneously distributed within the bulk (Fig. 6.1c). At the level of a single osteon (Figs. 6.1d-e), each set of cross-hatched cracks consisted of groups of intralamellar (within the bright/thick layers) arc-shaped microcracks radiating out into the quadrants along oblique directions from the Haversian canal, confirming earlier observations (Fig. 5.3) [249,250]. Under the fluorescence microscope (EF) where background light lessens resolution, arc-shaped microcracking appeared as single, blurry cracks inside each lamella (Fig. 6.1f). Very interestingly, the damage inside each arc-shaped microcrack was resolved into finer cracks under the Laser Scanning Confocal Microscope (LSCM) (Fig. 6.1g). These intralamellar microcracks also formed a cross-hatched pattern (Fig. 6.1g, Table 6.2) composed of relatively long circumferentially oriented cracks, 0.9 ± 0.2 µm (ranging from 0.7 to 1.7 µm) apart, and radially oriented cracks, 0.8 ± 0.1 µm (ranging from 0.5 to 1.2 µm) apart, with lengths ranging from below 1 µm up to about 10 µm.   78             Figure 6.1. Multi-scale microcracking in human cortical bone under transverse compression. (a) Schematics of the transverse (90°) loading orientation with respect to the osteons; (b) Bright Field (BF) image of the macroscopic oblique fracture pattern; (c) Epi-Fluorescence (EF) image of distributed cross-hatched damage at the osteonal-interstitial level; (d) BF image of arc-shaped microcracks within the osteonal bright layers (arrowheads); (e) Laser Scanning Confocal Microscope (LSCM) image showing multiple intralamellar cracks in the four quadrants of an osteon; (f-g) Low resolution EF and high resolution LSCM images taken from the lower left quadrant (dotted line) of the osteon in (e). LSCM reveals a sub-lamellar cross-hatched pattern composed of fine radially and circumferentially oriented cracks with spacing similar in size to fibrillar bundles. Compressive load applied vertically for a-b-c and horizontally for d-e-f-g.  79 The detailed morphology was generally very similar from one osteon to another. The intralamellar microcracking could vary in the extent of circumferential and radial cracking (Figs. 6.3b-e) and the orientation of the radial cracks. Thin layer damage (Fig. 6.3e) and flame-like cracking at the ends of the circumferential microcracks (Supplementary Fig. 6.5a) were also often observed. All crack patterns were confirmed to be non-artifactual as water-immersion LSCM imaging of the fresh (non-dehydrated and stained in an aqueous fluorescein solution) specimen showed the same features. Longitudinal Compression Cracking The fracture following longitudinal compression was oblique to the osteons (Figs. 6.2a-b). At the level of osteonal and interstitial bone, the well-known cross-hatched microcracks developed in 69 ± 5 % of osteons resulting in well-distributed damage (Fig. 6.2c). Higher magnification observations revealed the interactions of cracks with the lamellar and sub-lamellar structures. Within the osteons, the cross-hatched microdamage consisted of relatively long microcracks developing oblique to the bone lamellae (Fig. 6.2d). Although roughly linear, those cracks could locally change orientation between layers in a "stairway-like" manner (Fig. 6.2d), being slightly more parallel to the lamellar boundaries (and loading direction) within the dark layers where the fibrils are oriented along the osteons [97,110,256]. Uncracked ligaments (and lamellae) were also mostly observed within these layers (Fig. 6.2d insert). High resolution LSCM images (Figs. 6.2e-g) further showed that the microcracks consisted of a number of smaller cracks, particularly near the stairway steps and the osteonal-interstitial boundary where the cracking morphology changed to arrays of small wavy and generally less oblique cracks spreading into a wider area ahead of the main crack tip. 80           Figure 6.2. Multi-scale microcracking in human cortical bone under longitudinal compression. (a) Schematics of the longitudinal (0°) loading orientation with respect to the osteons; (b) Stereomicroscope image of the macroscopic oblique fracture pattern; (c) Epi-fluorescence image of distributed cross-hatched damage at the osteonal-interstitial level. Note the morphological similarity with transverse compression damage; (d) Backscattered Electron (BSE) micrograph of osteonal oblique microcrack formed at the Haversian canal (HC) and extending to the boundary (approximated by dashed line) between osteonal (O) and interstitial (I) bone. Notice the "stairway-like" changes of orientations (arrowheads) with the layers as well as the uncracked ligaments (insert: empty arrowheads) and lamellae (arrows). Insert location shown by dotted line; (e) Laser Scanning Confocal Microscope (LSCM) images showing smaller cracks within the larger oblique microcrack. The identified osteocyte lacunae (asterisks), ligament bridging (empty arrowheads) and full circle correspond to the same locations in (d). Note the change in crack morphology near the osteonal-interstitial boundary (bottom image); (f) High resolution 3D LSCM image of localized, finely spaced cross-hatched cracking near a Haversian canal (HC). The z-planes ("cut views" at locations shown by white lines) show deep oblique cracking; (g) LSCM images of crack interactions with osteocyte lacunae (asterisk) and canaliculi (double arrows). Compressive load applied vertically for a-b-c and horizontally for d-e-f-g. 81 Further down in scale, longer microcracks near the Haversian canals would sometimes locally develop finer cracks (Fig. 6.2f), similar in size and spacing to those of transversely compressed bone. The microcracks also interacted with osteocyte lacunae (Fig. 6.2g), consistent with the literature [21,181,186], and there were some evidence of crack interactions with canaliculi which, in some cases, may have initiated small cracks (Fig. 6.2g). At the resolution of LSCM, the interactions of the finer cracks with bone’s hierarchical structures were not as clear as those in transversely compressed specimens. Therefore, the latter were the focus of the following sections. 6.2.2 Bone's Porosity: the Canaliculi Network The fluorescent dye also stained the densely distributed canalicular network. As seen on a z-stack LSCM image of an intact osteon, the canaliculi distribution is fairly uniform (Fig. 6.3a). In agreement with the literature [3], the average osteonal canaliculi density was 1.6 ± 0.8 × 106 canaliculi/mm3. This would correspond to a volume fraction of about 5.0 %. The average canaliculi spacing was 4.3 ± 1.4 µm on a 587 nm thin plane, but decreased to 1.5 ± 0.5 µm over a depth of 15 µm (Table 6.2).  Table 6.2. Spacing of canaliculi and intralamellar cracks in transversely compressed cortical bone specimens (mean ± sd).   Intralamellar Cracks Spacing  Canaliculi Spacing   Circumferential Radial  587 nm plane over 15 µm Number of Specimens (regions)  7 (15) 7 (15)  7 (14) 7 (14) Measurements  0.9 ± 0.2 µm 0.8 ± 0.1 µma  4.3 ± 1.4 µma 1.5 ± 0.5 µma a The radial cracks and canaliculi spacings were all found to be significantly different.  82 Although the measurements might have been affected by the angles the canaliculi made relative to the imaging plane, the canaliculi shape (Fig. 6.3a insert) was found to be slightly elliptical (long-to-short axis ratio of 1.3 ± 0.3), with no apparent preferred orientation. 6.2.3 Cracking Process in Transverse Compression: Initiation and Development within the Bulk Although most of the osteons in the transversely compressed specimens were damaged (Chapter 5) [249], they were at various stages of damage development. Even the different quadrants within a single osteon showed different stages (Fig. 6.1e). This allowed for the study of crack initiation and development. Figures 6.3b to 6.3e present observations of the cracking sequence within the bulk from early initiation to a late stage corresponding to the formation of a shear band. First, this multi-scale damage process initiated as small circumferential cracks at the canaliculi (Figs. 6.3b-c) within the bright layers of each quadrants of the osteons. Interestingly, multiple crack nucleations not only occurred at numerous canaliculi but also along the length of a single canaliculus (Fig. 6.3b). Although also acting as crack initiation sites (Chapter 5) [249], osteocyte lacunae are far fewer than canaliculi and did not seem to play a critical role in the process.       83         Figure 6.3. Laser Scanning Confocal Microscope (LSCM) imaging of the canalicular network and the intralamellar cracking sequence within the bulk of transversely compressed bone specimens. (a) Image of a 5 µm deep z-stack showing the lacuno-canalicular network within an intact osteon. Insert: magnified image of a few canaliculi and their cross-sections (dotted ellipse); (b) Multiple circumferential crack initiations at the canaliculi. A single canaliculus could initiate more than one crack (double arrow). Notice that, in this loading orientation, no cracks are directly associated with osteocytes lacunae (asterisks); (c) Views (xy, xz, and yz) of a single crack associated with a canaliculus (arrowhead). Dashed lines are approximated lamellar boundaries; (d) Merging process of the circumferential cracks in the circumferential and depth (z-plane) directions; (e) Bright and dark (arrowheads) layers damage associated with the formation of a shear band. The microcracks have a "sheet-like" appearance through the depth (z-plane). Note also the radially oriented microcrack at the Haversian canal. Compressive load applied horizontally for b-d-e and obliquely for c.  84 Following initiation, the cracks started to merge together and formed longer circumferential cracks. As the main crack propagated, other cracks initiated at canaliculi ahead of the main crack tip and eventually merged with the main crack (Fig. 6.3d). A similar merging mechanism also took place in the depth-direction (Fig. 6.3d z-plane) where the canaliculi-initiated cracks would interact and eventually connect together. Hence, the micro-scale arc-shaped cracks, formed from a collection of numerous finer cracks (Fig. 6.3e z-plane), penetrated deep into the lamellar structure taking a "sheet-like" (long but relatively flat) appearance that apparently followed the curvature of the lamellar boundaries through the depth. The longitudinal sections imaging also supports these observations and thus indicates that crack growth also happened parallel to the osteons. As a single canaliculus could initiate more than one crack, the circumferential cracking usually occurred on more than one plane thus resulting in many parallel, but not necessarily independent (linked through the depth and/or via radial cracking), circumferential cracks. During the development of the circumferential cracks, radial cracking also occurred and linked the circumferential cracks together (Figs. 6.1e-g-6.3e). At this stage, further crack-canaliculi interactions seemed also possible. However, the relatively larger canaliculi spacing (Table 6.2) could not explain the high density of the radial cracks, thus suggesting a possible interaction with the mineralized collagen fibrillar bundles. The next stage of damage development is less clear but could involve the lengthening and widening of the sub-lamellar cross-hatched (Figs. 6.1e-6.3e). At certain points, the damaged bright layer would not provide adequate support to the dark layer fibrils. This would eventually culminate into shear band formation at the level of the osteon (Fig. 5.7e) [249] through kink failure resulting in damage within the dark layers and a radially oriented microcrack at the Haversian canal (Fig. 6.3e). 85 6.2.4 Mechanical Simulation From the numerical simulation, the local shear stresses and strains increased by a factor of about 1.4 along the z-axis (depth direction parallel to the osteons) of the canaliculi and spanning their entire length (Fig. 6.4d). Hence, weak points at these locations would likely initiate cracking. This corresponds fairly well with the crack initiation observations (Fig. 6.3c) and also supports the merging process observed along the depth direction (Fig. 6.3d). Inputting transversely isotropic properties to simulate the elastic behaviors of the bright and dark layers slightly changed the shapes of the concentration zones, being more elongated through the depth (z) within the bright layer (Supplementary Fig. 6.6a) and more confined, rather stretching along the circumferential direction (x), within the dark layer (Supplementary Fig. 6.6b). As the simulation assumed the stress to be the same within both layers, the shear strains in the bright layer were also much higher. Taken along with the observations that crack initiation occurred within the bright layers, these results support a strain-controlled failure of bone, concurrent with the literature [81,160].    86       Figure 6.4. Physical interpretation and mechanical simulation of cracks-structures’ interactions in bone under transverse compression. (a) Schematic of multiple circumferential crack nucleations and mergings in osteonal layers with fibrils oriented parallel to the osteons; (b) Proposed interfibrillar nature of the sub-lamellar cracks (light grey) with respect to the rotated mineralized collagen fibrils (minerals in black) and the surrounding non-collagenous proteins (small grey lines); (c) Numerical model developed to simulate elastic stress/strain concentration at a radially oriented canaliculi (y-direction) under pure shear (stress state depicted in (a)). The arrows at the top denote the degrees of freedom; (d) Strain concentration at a canaliculus (center) for an isotropic material. The orientation shown is the same as in (c).  6.2.5 Surface and Bulk Damage LSCM observations revealed that the microcracks morphology on the original loaded surfaces slightly differed from that of the bulk. On the surface, relatively larger intralamellar cracks were present and the observed crack density was lower (Supplementary Fig. 6.5b). The 87 cracks were dark in appearance but their borders and immediate surroundings were highly stained (Supplementary Fig. 6.5c), thus verifying that they were not of an artifactual nature but rather the result of loading. They usually penetrated through the depth of the lamellae no more than about 5 µm and the deeper regions beneath those surface cracks showed cross-hatched patterns (Supplementary Fig. 6.5d). Surface cracking could be oriented in either the radial or circumferential directions, but the radial direction seemed to be favored in the early stages of damage development (Figs. 5.3c-d-5.10b) [249]. The cracks most probably developed due to a slightly different stress state present at the surface. 6.3 DISCUSSION A recent study (Chapter 5) [249] showed that the osteons’ concentric lamellar structures relaxed the stress concentration at the Haversian canals through controlled multiple initiations and progressive development of intralamellar circular cracks in high shear regions (Fig. 6.1d). The stable process led to well-distributed damage (Fig. 6.1c) giving rise to high macroscopic inelastic deformation. In the present study, LSCM following transverse compression loading enabled high resolution 3D imaging of the intralamellar cracks within the bulk. The initial stages were shown to involve multiple nucleations and crack coalescence through the canaliculi (Figs. 6.3b-c-d). The process resulted in extensive sub-lamellar cross-hatched cracks regularly spaced 0.5 to 1.7 µm apart (Fig. 6.1g), a size comparable to the mineralized collagen fibril bundles. Hence, the high crack density not only conferred enhanced inelastic strain capacity to the lamellae but also strongly suggested cracking controlled at the fibrillar level. The findings further led us to consider the nature of cracks in bone and the roles of the canaliculi in Haversian bone’s remodeling response. A cracking process where crack initiation and growth are controlled at multiple scales would render a material damage tolerant [16,156-158] and could represent a key 88 structural design behind both Haversian bone’s resistance to fracture and mechanical adaptation responses. 6.3.1 Relevance of Transverse Compression In this study, particular emphasis was placed on microcracking following transverse compression. Transverse compression is not a normal mode of biomechanical loading in the human body. However, in the fundamental context of the hierarchical structure – mechanical function relations, it is useful to understand the roles of Haversian systems and their concentric lamellae in the deformation. The relation between microcracks and the lamellae could be clearly seen (Fig. 6.1). Transverse compression also allows us to understand the behavior of bone lamellae under shear. A similar stress state is likely to be present within the osteonal wall during torsion loading. Circular shear microcracks were observed in human bone submitted to torsion [140]. The osteonal lamellae have also been hypothesized to impede the propagation of incoming microcracks [111,170]. Interestingly, long interstitial microcracks, such as those pre-existing cracks commonly found in-vivo [83-85,183,189,191-197], are bound to encounter osteons during their growth. Although crack deflection at cement lines is present (Chapter 5) [153,202,203], the lamellae – microcrack interactions observed in this study are also likely to hinder the propagation of interstitial microcracks. 6.3.2 Role of Canaliculi in Crack Initiation and Growth Material failures are generally associated with high local stresses and strains around defects. In bone, high strains and microcrack initiation have been linked to Haversian canals [2,15,21,249] and osteocyte lacunae [21,181,186,209-211] while the roles of the highly populated canaliculi (Fig. 6.3a) have not been demonstrated. As illustrated schematically in 89 Figure 6.4a, the present study showed that in the bulk of transversely compressed bone, multiple short circumferential cracks (Figs. 6.3b-c) initiated in the high strain zones surrounding the canaliculi (Fig. 6.4d) within the osteons’ concentric lamellar wall. These cracks eventually merged together (Fig. 6.3d), by a process similar to shear micro-voids coalescence in metals [257], and developed into long, roughly parallel cracks along both the circumferential and longitudinal (depth) osteonal directions (Fig. 6.4a; x and z directions, respectively). Note that this process is different from near-surface events (Supplementary Figs. 6.5b-c-d; Chapter 5) [249]. Considering their orientation [212], the canaliculi may have similar roles in other loading modes. They have been suspected to expand into intralamellar cracks under tension [213] and to interact with diffuse damage in human [214] and rat [207] bone. Torsion loading, for which inelastic strains have been associated with circular cracking [140], may introduce a similar shear state within the osteonal wall (Fig. 6.4a) and hence is likely to involve the canaliculi. Pre-existing microcracks, generally attributed to in vivo fatigue [84,191,193], also develop in human bone and are thought to contribute to fragility and stress fractures [84,193,198]. Those were examined in a previous study (Chapter 5) [249]. Upon re-visiting the BF and EF images, more than half were found to be parallel to the interstitial lamellae boundaries suggesting that canaliculi may be similarly involved in their initiation and growth. Longitudinal compression in this study seemed less sensitive to canaliculi (rather being more sensitive to the larger osteocyte lacunae (Fig. 6.2g) [21,181,186] and Haversian canals porosity (Chapter 4) [239]) as only a few possible cases of canaliculi crack initiation were found (Fig. 6.2g). Nonetheless, the observations of transversely compressed specimens suggest that the canaliculi size, geometry, and distribution could influence bone’s inelastic response. If they are to facilitate crack development, the 90 stabilization provided by the surrounding structures and higher hierarchies would be crucial to prevent early fractures. 6.3.3 Sub-Lamellar Cracking: Towards the Nature of Cracks in Bone All cracks start at the lower hierarchical levels of the bone material. Recent studies have shown the involvement of non-collagenous molecules [102,165,166], nano-scale heterogeneity [258], and mineralized collagen fibrils [133,134,157,167-169] in bone’s deformation process. It has been a challenge to relate microcracks to such fine structures. LSCM has proven a powerful technique to investigate sub-microscopic bone cracks and porosity [17,98,125,163,184,214]. Its resolution actually approaches the size of bone’s basic building block, the mineralized collagen fibrils. The present LSCM study revealed a clear sub-lamellar cross-hatched pattern involving a high density of very fine cracks (Figs. 6.1g-6.2f) only a few microns in length and less than 1 µm apart. Such high crack density would provide enhanced inelastic strain capacity to the lamellae, further stabilizing the cracking process at higher hierarchical levels. Under transverse compression, this extensive cracking developed intralamellarly within the osteonal bright layers (Figs. 6.1d-e-g). Considering the local fibrillar orientation parallel to the osteons, the regular crack spacing, which was smaller than the canaliculi spacing (Table 6.2), strongly suggests that a repeating structure of about 800 nm in size, such as the mineralized collagen fibril bundles, would govern the cracking. Indeed, the radial cracks are reminiscent of shear-induced tension matrix cracks in 2D fiber-reinforced composites under interlaminar shear [177]. This similarity explains their intralamellar confinement. The radial cracks would evolve without significant fibrils interactions in the bright layer while being forced to interact with the fibrils impeding their growth near the dark layer. 91 The nature of the cracking was not directly investigated in this study. Nevertheless, the size and regularity of the sub-lamellar cross-hatched pattern under transverse compression suggest an interfibrillar (as opposed to intrafibrillar) nature akin to interfacial and matrix shear cracking in transversely compressed fiber-reinforced polymers [259]. This interpretation is well supported by TEM observations following loading of single osteons [213,242]. Such a scenario, illustrated in Figure 6.4b, would likely involve the non-collagenous proteins’ "sacrificial bonds" [102,165,166,260], a concept supported by observations of a thin "substance" covering the fibrils in fractured bone [242,261,262], as well as the extrafibrillar minerals/proteins interfaces [24]. However, what may be interfibrillar cracks in this study differs from tensile diffuse damage [16-18,21,181,183-185,214] where direct stretching of the longitudinally aligned fibrils is likely to result in intrafibrillar as well as interfibrillar [213] cracking. 6.3.4 Hierarchical Cracking in Human Haversian Bone Bone is known for its unique hierarchical structure which is thought to give rise to its exceptional mechanical performance [1-3,92]. However, how bone’s hierarchical design involved in the deformation and cracking processes is still not well understood [163]. Along with observations from the initial study (Chapter 5) [249], the present study showed that, despite the presence of canaliculi, osteocyte lacunae, and Haversian canals, both longitudinal and transverse compression developed well-distributed damage at the tissue level (Figs. 6.1c-6.2c) due to structure-microcrack interactions at multiple levels (Figs. 6.1-6.2). Indeed, both loading orientations showed fine cross-hatched cracking (Figs. 6.1g-6.2f) likely related to the fibrillar bundles. At the lamellar level, uncracked ligaments (lamellae and/or fibrillar bundles; Figs. 6.1d-6.2d) and changes of crack orientation (Figs. 6.2d-e-6.3e) were associated with local fibril orientations. Changes in crack morphology near the osteonal-interstitial boundary (Fig. 6.2e; 92 Chapter 5) [249] also indicated a change in crack growth mechanism probably due to the more highly mineralized interstitial bone and/or cement lines [85,153]. The latter change may have lead to microcrack confinement at the osteonal-interstitial level (Fig. 4.9) [239]. These interactions stabilized the cracking process, hence provided inelastic strain capacity to the tissue. Comparing the mechanical responses (Fig. 5.1) [249] in the two loading orientations considered here, the extent of damage resulting from those interactions would likely determine the degree of bone’s inelastic deformation. 6.3.5 Possible Role of Canaliculi as Physiological Sensors One of the characteristics that distinguishes Haversian bone from other hard tissues such as the dentin of teeth is its ability to adapt to the mechanical environment through remodeling [2,3,89]. Interestingly, both strains [210,211,263] and microcracks [121,122,125,186,191,204-208] have been proposed as potential stimuli for mechanosensation through disturbances of the lacuna-canalicular network fluid flow [116-121,123] and/or the osteocyte syncitium integrity [121,122,124,125]. Relatively long microcracks have been shown to rupture the osteocyte processes [125]. Since canaliculi are the main nano-scale structures involved in fluid transport, high strains and/or cracking of the canaliculi would surely lead to disturbances in the fluid flow. As cracks must first initiate at that scale, the canaliculi, with their uniform distribution and high density (Fig. 6.3a) [3,264], would indeed be good sensors for damage detection. According to the canaliculi spacing results (Table 6.2), any crack longer than about 6 µm (consider the size of a single crack in tensile "diffuse" damage) would encounter a canaliculus. This may thus represent an early damage detection strategy used by osteocytes to activate the remodeling response. 93 6.4 CONCLUSIONS In light of the current progress, bone’s resistance to fracture is achieved through multiple microcracks’ interactions with bone’s fibrillar, lamellar, and osteonal structures. Controlled cracking allows stress redistribution around bone’s many concentration sites, thus providing robustness at multiple length scales. Such damage tolerance strategy, for which a material controls cracks rather than avoiding them, is common in biological materials [16,17,156,157,164,178,179,265,266]. It stands well in the intact structure of healthy bones and may even be used positively through mechanical adaptation. However, absent these interactions due to altered structures or loading conditions, bone may become more susceptible to catastrophic fractures owing to its multiple porosity. The present observations enabled us to consider the relations between microcracking and the mineralized collagen fibrils. In order to fully understand bone’s deformation and fracture, it is important to incorporate the whole structural hierarchy. Further work is thus needed to directly link sub-lamellar cracks to the deformation mechanisms at the level of the mineralized collagen fibrils and to address whether or not the findings apply to other loading modes. 6.5 SUPPLEMENTARY INFORMATION 6.5.1 Variations of Microcrack Morphologies under Transverse Compression The morphology of the intralamellar cracks slightly changed depending on the stage of damage development. However, other variations also occurred due to changes in the local stress field (Fig. 6.5). Flame-like cracking was often observed at the ends of the circumferential microcracks (Fig. 6.5a). Those presumably formed similarly to wing cracks in compressed brittle solids [267] or due to a slight bending associated with shear band formation [241,268]. 94       Figure 6.5. Variations of microcrack morphologies. (a) LSCM image showing flame-like cracking (double arrows) at the ends of the arc-shaped microcracks; (b) SEM micrograph of surface cracks. Both circumferential (arrowheads) and radial (double arrows) cracks can be seen; (c-d) Respective surface and bulk LSCM images of (b). Notice the bright borders of the surface cracks (c) and the cross-hatched patterns beneath (d). Compressive load applied horizontally.  Compared to the bulk, lower crack density (Chapter 5) [249] and larger intralamellar microcracks were observed at the surface (Fig. 6.5b). Laser Scanning Confocal Microscopy (LSCM) revealed that their borders were highly stained (Fig. 6.5c) and that deeper regions (about 6 µm beneath) showed sub-lamellar cross-hatched cracking (Fig. 6.5d). Some of the radial cracks were also found to be opened canaliculi suggesting that the latter acted as near-surface defects. 95 The average canaliculi spacing of 4.3 ± 1.4 µm on a 587 nm thin plane (obtained with LSCM) seems indeed similar to the spacing of the surface radial cracks (Figs. 6.5b-c; Chapter 5) [249]. It was previously observed that, different from the cracking process within the bulk (Figs. 6.3b-c-d-e), radial cracks developed into circumferential arc-shaped microcracks near the surface (Chapter 5) [249]. This is most probably due to a slightly different stress state at the surface where transverse tension may have had a more marked effect, opening radial cracks and canaliculi. The difference found here between surface and bulk microcracking emphasizes the importance of investigating the bulk. It also highlights the advantages of LSCM over conventional material sciences techniques such as Scanning Electron Microscopy (SEM) to study cracks in bone. 6.5.2 Numerical Simulations with Transversely Isotropic Properties The effect of the cross-sectional osteonal bright and dark layers’ mineralized collagen fibril orientations was assessed by comparing the results obtained for isotropic and transversely isotropic material properties (Table 6.1). The local shear strains surrounding a canaliculus under pure shear acting along and across its length (y and x directions, respectively) increased by a factor of about 1.3 and 1.5, respectively. The shape of the concentration zones also changed, stretching along the fibrils, i.e., along the osteons (z) in the bright layers (Fig. 6.6a) and circumferentially in the dark layers (Fig. 6.6b). Finally, at the same imposed stress, the bright layers, where the cracks initiated, showed higher strains.  96    Figure 6.6. Effect of the mineralized collagen fibril orientations on the strain concentration around a canaliculus (center) under pure shear (stress state depicted in Figs. 6.4a-c). Transversely isotropic material simulating the cross-sectional osteonal bright (a) and dark (b) layers. Note the elongated shape through the depth (z-direction) and the higher strains in the bright compared to the dark layer. The orientation shown is the same as in Figure 6.4c.  6.5.3 Multi-Scale Deformation Process The initial circumferentially-oriented cracks observed in transversely compressed specimens suggest higher resistance along the radial direction. However, in light of previous digital image correlation measurements (Fig. 5.7) [249], the radial shear component would be larger than the circumferential component. A possible explanation to these observations may lie in the two different scales involved. As the osteonal cracking process culminated into the formation of a shear band, a hypothetical scenario could be that, at the level of the osteonal wall, a simple radial shear stress state induced progressive rotation within the kink zone [268,269] thus resulting in high radial shear as measured with the spatial resolution (estimated to be about 10 µm) of the digital image correlation study. However, akin to the slip in soft layers permitting the rotation within the kink zones of layered geological materials [270], such rotation would only be possible if accommodated by circumferential deformation of the bright layer. Thus, at the level 97 of a single bright layer (generally less than 10 µm), this would translate into high strains in the elastic stage followed by circumferential cracking later on in the process.   98 CHAPTER 7 TOWARDS UNDERSTANDING THE MECHANISMS OF FEMORAL NECK FRACTURES - A CASE STUDY Bone microcracking patterns are closely related to the local stress state to which bone is submitted during failure (Chapter 4). Retrieved bone fragments from patients with femoral neck fractures therefore carry valuable information (in the form of microcracks) to track down the possible fracture process. The purpose of this case study was to demonstrate the feasibility and potential of a full scale study with the goal of understanding the mechanisms involved in hip fracture. As compression in the superolateral cortex of the femoral neck has been suspected to be a strong determinant of femoral neck fractures resulting from a sideways fall (Fig. 7.1a) [36-40], the focus is on this particular region. The pilot study was approved by the Clinical Research Ethics Review Board at the University of British Columbia. 7.1 METHODS AND MATERIALS Bone segments (1-3 cm thick "rings" including the fracture site) from two fractured femoral necks were collected by an orthopaedic surgeon (Pierre Guy, M.D.) during routine hemiarthroplasty surgery. They were stored at -20°C until preparation for microcracking analysis. 7.1.1 Specimen Preparation The segments were first rinsed and cleaned with a low pressure water jet. They were then stained according to the procedure described previously (see 4.1.2) in order to reveal the microcracking. To summarize, they were defatted in acetone and dehydrated in a graded series of ethanol/water solutions before being stained in a filtered saturated solution of fluorescein (Fisher Scientific) and 70% ethanol, rinsed in ethanol, and finally air-dried. The specimens were then 99 embedded in epoxy resin (Epothin, Buehler). Their superior cortex was then carefully cut using a diamond saw (Isomet 1000, Buehler) and ground and polished using a mechanical polishing machine (Isomet 1000, Buehler) to obtain up to five longitudinal-radial (with respect to the femoral neck long axis) sections. 7.1.2 Microcracking Observations All sections were examined with an optical microscope under both white light mode (BF; Nikon Eclipse LV100) and epi-fluorescence mode (EF; Nikon Eclipse E600; excitation and emission at approximately 490 nm and 525 nm, respectively) to discern the patterns of microcracking. Microcracks within both cortical and trabecular bone would be stained by fluorescein. One site was also taken to the laser scanning confocal microscope (LSCM; Olympus FluoView FV1000, Olympus Canada Inc., Markham, Canada) for high magnification imaging. 7.2 RESULTS Microscopic observations revealed microcracking in the superior cortex and adjacent trabecular region of both fractured femoral necks. Damage was observed at more than 1 cm away from the fracture in one specimen. Various morphologies were observed (Figs. 7.1-7.2) and mainly related to local compression or shear. A particular pattern showed compressive cross-hatched microcracking near the endosteal surface (inner surface of the cortical shell) and a few tensile microcracks near the periosteal surface (outer surface of the cortical shell), indicating bending towards the periosteal surface (Fig. 7.1c). In the case shown in Figures 7.1b-c the pattern was located in the vicinity of a large porosity. 100      Figure 7.1. Buckling in the superior cortex of a femoral neck segment retrieved from a patient with hip fracture: (a) Simple schematic of the proximal femur during a fall. Dotted circle shows the superior cortex; (b) Optical Microscope (OM) image of a longitudinal section (along the femoral neck axis) of the superior cortex. Note the lamellar structure and the large porosity (P); (c) Corresponding Epi-Fluorescence (EF) image showing microcracking. The tensile microcracks (arrowheads) at the periosteal and the compressive cross-hatched microcracks (empty arrowheads) at the endosteal indicate outward bending.  Another pattern consisted of long microcracks running parallel to the lamellae along the femoral neck’s long axis (Figs. 7.2a-b). Higher magnification images (Figs. 7.2c-d) further showed that the microcracks were composed of multiple, similarly oriented small cracks preferentially located within one layer of the cortex’s lamellar organisation. Those cracks clearly crossed the canaliculi. At the final fracture surface, the lamellae were also highly deformed (Figs. 7.2a-b). 101       Figure 7.2. Interlamellar shear and microbuckling in the superior cortex of a femoral neck segment retrieved from a patient with hip fracture: (a-b) Optical Microscope (OM) and Epi-Fluorescence (EF) images of a longitudinal section (along the femoral neck axis) of the superior cortex. Arrowheads in (a) indicate the final fracture surface and point out to the adjacent highly deformed lamellae; (c-d) OM and Laser Scanning Confocal Microscope (LSCM) images of the dotted area in (b). The microcracks are parallel to the lamellae boundaries and consist of multiple small cracks crossing the canaliculi. Two osteocyte lacunae are identified (asterisks).  7.3 DISCUSSION Microcrack staining combined with fluorescence (EF) and laser scanning confocal (LSCM) microscopy of bone segments retrieved from patients with fractured femoral necks allowed to understand the local stress states presumably present at the time of fracture in the 102 superior cortex. Under this assumption, the observations support the hypothesis of buckling in the superior region [36,37,39], but suggest that it may take different forms. Through the use of bone’s well-known stress related differences in microcracking morphologies [14,15,18,21], this novel approach has the potential to provide a full understanding of femoral neck fracture from the architectural level to the fine details at the sub-lamellar level. 7.3.1 Microcracking in the Femoral Neck Staining and fluorescence microscopy (both EF and LSCM) are well developed and commonly used techniques to investigate microcracking in bone [14,16,17,23,83,163,185,195]. However, their application to bone segments retrieved from patients with femoral neck fractures in order to understand the stress state that lead to fracture has not yet been reported. Assuming that they developed during fracture, the presence of recognisable microcracking patterns demonstrates the feasibility of a study on the mechanisms of hip fracture using this approach. It also further confirms that bone derives part of its resistance to fracture from its capacity to deform through microcracking. 7.3.2 Buckling in the Superior Cortex It has been previously hypothesized that the thin superior cortex of the femoral neck would be unstable under compression leading to localized buckling and subsequent hip fracture [36,37,39]. Imaging studies have also suggested compressive yielding in the same region [38]. Under the assumption that the microcracking patterns were the result of the fracture process, the presence of cross-hatched microcracks first confirms that the superior cortex was under compressive stress at fracture [26,35]. The thin cortex showing compressive microcracks on the endosteal surface and tensile microcracks on the periosteal surface clearly indicates outward 103 bending (Fig. 4.7) which, when induced by compression, would correspond to buckling (Figs. 7.1b-c). Interestingly, this region included a large porosity (different from Haversian canals) suggesting that it may have had a role in the local failure. The other pattern observed here (Fig. 7.2) also supports the hypothesis of buckling, albeit resulting from a slightly different process possibly involving shear. Indeed, the morphology, i.e., layer dependent microcracks generally following the lamellar boundaries, is reminiscent of the intralamellar arc-shaped microcracks associated with shear within the osteonal lamellar wall (Figs. 5.6-5.7). LSCM further showed that the microcracks consisted of multiple fine cracks roughly normal to the canaliculi, another interesting similarity with the circumferential cracks developing through the canaliculi network (Fig. 6.3). These similarities suggest an interlamellar shear microcracking process occurring in the superior cortex. Although dependent on the structure (e.g., cortex’s thickness, trabeculae and marrow support [271-274]), such post-yield deformation is ultimately controlled by bone’s hierarchical structure (Chapters 5-6) and, very interestingly, culminates into shear band formation (Fig. 6.7e). It is suspected that the deformed lamellae at the fracture site (Figs. 7.2a-b) resulted from shear band formation which can be considered as a form of buckling (or more properly termed microbuckling) at the lamellar/fibrillar level. This case thus clearly highlights the importance of bone at the material level. 7.3.3 Microcracking and Hip Fragility These preliminary observations suggest that buckling in the superior cortex is likely to be involved in femoral neck fractures, but may take different forms depending on the combined material and structural characteristics. Considering bone’s response to bending (Chapter 4), such local failure would compromise the overall resistance of the femoral neck. Under the assumption 104 that they developed during fracture, these evidences thus support that the superior cortex would be a region of weakness in the hip [39,62] and may initiate its fracture [40]. However, whether or not buckling is the main cause of fracture remains unsolved. Bone’s behavior under such loading configuration is practically unknown. Further study is therefore warranted not only to confirm and support the present observations but also to identify other mechanisms involved in femoral neck fracture and their relative contribution to hip fragility. In particular, the proposed role of the altered Haversian systems and their associated porosity in the anterior quadrant [87-90] needs to be clarified. These questions could likely be answered through a complete analysis and large scale study of retrieved bone segments. Based on the current understanding, it can be speculated that, in such an evaluation of bone fragility, a lesser degree (extent and distribution) of microcracking would indicate a more fragile hip. 7.4 CONCLUSIONS Microcracking analysis of bone segments retrieved from patients with femoral neck fractures offers a good opportunity to understand the basic mechanisms involved in hip fractures. Such novel approach may provide an answer as to what makes bone in the hip so fragile. 105 CHAPTER 8 CONCLUSIONS AND PERSPECTIVES 8.1 CONCLUSIONS This dissertation mainly examined the design principles used in human Haversian bone to resist fracture through a detailed study of its compressive deformation and microcracking processes, namely how these processes were influenced by its porosity network, controlled by its hierarchical structure, and involved in whole bone fractures. The following conclusions were made regarding the defined specific objectives (Chapter 3). 8.1.1 Design Principles to Resist Fracture in Haversian Bone The major contribution of this work to the bone research field is the role of Haversian systems in the failure process. The main conclusion is that Haversian bone’s lamellae and their underlying sub-lamellar organisation allow for the development of extensive distributed microcracking providing bone with enhanced inelastic strain capacity, reduced sensitivity to porosity, and hence higher resistance to fracture (Chapters 5-6). Alterations to this unique structure are therefore likely to result in early fractures, i.e. bone fragility. Microcrack initiation is sensitive to Haversian bone’s porosity network, namely the Haversian canals, the osteocyte lacunae, and, under certain conditions, the canaliculi (Chapters 5-6). Consistent with a damage tolerance strategy, its resistance to fracture therefore resides in its ability to control and distribute microcracks, i.e., the stability and the number of microcracks (Chapters 5-6), rather than avoiding crack initiation. Such ability relies on controlled crack growth at multiple hierarchical levels with the lamellar organisation of the osteonal wall as a central, most crucial feature (Chapter 5). Within each lamella (there can be up to 30 in the osteonal wall), the cracks are influenced by the local fibrillar orientations (Chapters 5-6). At the 106 osteonal-interstitial boundary, the local microstructural change (e.g., different lamellar orientation and degree of mineralization of osteonal/interstitial bone and/or presence of cement lines) further affects crack development (Chapters 4-5-6). Those interactions stabilize the microcracking process and allow for the development of inelastic strain, thus delaying the formation of a fatal macro-scale crack. Although crack deflection at cement lines is present, such interactions are also likely to hinder the propagation of interstitial microcracks, such as those pre-existing cracks found in-vivo, which are bound to encounter osteons during their growth. Organising the mineralized collagen fibrils into lamellae could therefore represent a general design principle in bone to meet a complicated biomechanical environment. Such structure would enable to redistribute stress through microcracking around concentration sites and, although affected by their distribution, achieve a certain "insensitivity" to its porosity (Chapter 5). Absent this inelastic strain capacity, bone would be more susceptible to early fractures. 8.1.2 Applications to Whole Bone and Hip Fractures Whole tibiae’ resistance to fracture in bending is linked to the behavior of Haversian bone (Chapter 4). Bone’s compressive response also plays an important role in its resistance to fracture in bending. Such relation results from strain redistribution happening during the post-yield stage of deformation which relies on the development of both uniform tensile and compressive microcracking (Chapter 4). The resistance to fracture of whole bones (architectural level) in bending therefore largely depends on Haversian bone’s ability to control and distribute microcracks through intact lamellar and fibrillar organisations (Chapters 5-6; see 8.1.1). In the context of hip fragility, changes in Haversian bone’s microstructure, namely in the size of the Haversian canals and the number and organisation of the surrounding concentric lamellae, are thus likely to render the femoral neck more susceptible to fracture during a fall. Interestingly, 107 microcracking patterns corresponding to local compression were found in the superior cortex of femoral necks retrieved from patients with hip fractures (Chapter 7). These findings emphasize the importance of microcracking as an active deformation mechanism in whole bones and the contribution of bone’s properties and hierarchical structure in hip fracture. 8.1.3 Bridging the Gap between Bone’s Micro- and Nano- Scales "Micro"-cracking in Haversian bone clearly involves multiple scales, i.e. the osteonal-interstitial, the lamellar, and the fibrillar levels (Chapters 5-6), confirming that damage tolerance is achieved by controlling microcrack development at multiple hierarchical levels [157,169]. A combination of imaging techniques (e.g., BF, EF, LSCM, SEM, and BSE) is thus essential to understand the structure – microcracking relations across the whole hierarchy. In particular, the use of LSCM provided high quality images of fine sub-lamellar cracking strongly influenced by the osteonal lamellae seen under BF, SEM, and BSE (Chapters 5-6). This approach thus enabled us to study the relation between microcracking and bone’s basic building block, the mineralized collagen fibrils (Chapter 6). The findings further allow us to speculate that "intralamellar" cracking or lamellae-controlled cracking, i.e. cracks first developing in certain layers, may also apply to the early stages of microcracking in tension and shear. Further investigation is thus warranted to link microcracking to the deformation mechanisms acting at the fibrillar level and obtain a better understanding of bone fractures across the whole structural hierarchy. 8.2 LIMITATIONS A first limitation is that the work is of an experimental nature. The contributions of the described mechanisms can thus only be appreciated at a qualitative level. 108 A second limitation of this work is the focus on the compressive behavior. Although compression is clearly important, the tensile behavior should also be considered in bone fractures. The bending study (Chapter 4) shows that, without the development of tensile post-yield deformation, strain redistribution is not possible thus further limiting bone’s bending strength. A third limitation is that the loading rates used are far less that those involved in traumatic fractures [146]. High strain rates have been shown to decrease bone’s post-yield deformation [135,145,147] and lead to localized damage [23]. Yet, the case study (Chapter 7) did show microcracking in fractured femoral necks. A last limitation concerns the relatively low number of specimens in light of the variability associated with different individuals’ gender, age, anatomical location, etc [2,3,68,89,275]. In this respect, specimens were always taken from similar locations in at least three different individuals including both genders. The conclusions may thus more specifically apply to the femoral and tibial shafts in the senior population which is also the population with the highest risk of fractures. 8.3 RECOMMENDATIONS The following may be recommended for future studies. • Similar studies for tension and shear deformation and microcracking along with an investigation on the very nature of cracks in bone in order to obtain a better understanding of bone’s failure process across the whole structural hierarchy (see 8.1.3). Additional characterization techniques could involve heavy metal staining and electron microscopy [250] as well as super resolution microscopy. 109 • Modeling of the observations to obtain a better understanding of the mechanics involved and the potential effects of microstructural changes (see 8.1.1-8.1.2) such as decreased osteon population density and increased size, altered shape, and decreased lamellar lining of Haversian canals (Chapters 5-6) [87-90]. 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Göttingen, Germany: LaVision GmbH; 2007.  135 APPENDICES The first two appendices (Appendices A-B) are included to give more information about the variability observed in each study. Note that digital images were not taken for all specimens. Therefore, the figures involving epi-fluorescence microscopy observations show images from four specimens in addition to those shown in the core of the dissertation. APPENDIX A       CHAPTER 4 – ADDITIONAL DATA Specimens  Whole bone specimens: 15 tibiae – 5 pairs and 5 right – 5 males and 5 females – 67-88 years  Cortical bone specimens: 10 specimens from 4 femora – 3 males and 1 female – 69-77 years Mechanical Tests All specimens were subjected to four-point bending. Load-Strain and Strain Rate Curves Figure A.1 shows the load-strain curves for all specimens (see Figure 4.1). Figure A.2 shows the strain rate curves for all specimens (see Figure 4.4). Macro-Scale Fracture Patterns All macro-scale fracture patterns are shown in Figure A.3 (see Figure 4.5). Microdamage Observations Microdamage morphologies on the tensile and compressive surfaces of six cortical bone specimens are shown in Figure A.4 (see Figure 4.6). 136      Figure A.1. Load-strain curves for all 10 cortical bone specimens (a) and 15 whole tibia specimens (b). The × indicate debonding of the strain gage. Figures 4.1a-b correspond to black curves.  01000200030004000500060007000-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4Longitudinal Strain (%)Load (N)(b) Tension    Compression 050100150200250300350-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6Longitudinal Strain (%)Load (N)(a) Tension     Compression 137   0.000.020.040.060.080.100.120.140.0 0.2 0.4 0.6 0.8 1.0Normalized LoadStrain Rate × 10-3 (s-1)Tension 0.000.020.040.060.080.100.120.140.0 0.2 0.4 0.6 0.8 1.0Normalized LoadStrain Rate × 10-3 (s-1)Compression  Figure A.2. (a) Variations of strain rates at the tensile (top) and compressive (bottom) surfaces for all 10 cortical bone specimens. The × indicate debonding of the strain gage. Figure 4.4a corresponds to black curves.  138   0.000.050.100.150.200.250.300.350.400.0 0.2 0.4 0.6 0.8 1.0Normalized LoadStrain Rate × 10-3 (s-1)Tension 0.000.040.080.120.160.200.0 0.2 0.4 0.6 0.8 1.0Normalized LoadStrain Rate × 10-3 (s-1)Compression   Figure A.2. (b) Variations of strain rates at the tensile (top) and compressive (bottom) surfaces for all 15 whole tibia specimens. The × indicate debonding of the strain gage. Figure 4.4b corresponds to black curves.  139                Figure A.3. (a) Cortical bone specimen bending fracture patterns. Note the similarity with A.3b. Top surfaces under compression. Figure 4.5a corresponds to asterisk. * 140              Figure A.3. (b) Whole tibia specimen bending wedge "butterfly" fracture patterns (B2, B3). Top surfaces under compression. One tibia with butterfly fracture was not photographed. Figure 4.5b not shown. 141            Figure A.3. (c) Whole tibia specimen oblique fracture patterns (A2). Top surfaces under compression.  142             Figure A.4. (a) Epi-fluorescence images of tensile surface microdamage for 6 cortical bone specimens. Tensile stress horizontal. Figure 4.6c corresponds to asterisk.  * 143             Figure A.4. (b) Epi-fluorescence images of compressive surface microdamage for 6 cortical bone specimens (same as A.3a). Compressive stress vertical for first 3 images and horizontal for last 3 images. Figure 4.6a corresponds to asterisk.  * 144 APPENDIX B        CHAPTER 5 – ADDITIONAL DATA Specimens  Cortical bone specimens: 22 specimens from 3 femora – 2 males and 1 female – 55-69 years Mechanical Tests  Monotonic compression loading along different orientations: 7 longitudinal (0°), 7 transverse (90°), and 3 oblique (45°); 5 from one femur and 1 from each of the other two femora for each orientation except oblique (1 from each femora)  Step-wise transverse compression loading: 2 specimens (both from the same femur) for damage development experiment, 3 specimens for DIC experiment (1 from each femora) Stress-Strain Curves Figure B.1 shows the compressive stress-strain curves for all specimens loaded monotonically (see Figure 5.1). Microdamage Observations Microdamage morphologies four additional cortical bone specimens are shown in Figure B.2 (see also Figures 5.2a-5.2b-5.8a and Figures 6.1c-6.2c).   145       Figure B.1. Compressive stress-strain curves for all specimens loaded monotonically along three different orientations: 7 longitudinal (0°), 7 transverse (90°), and 3 oblique (45°).   0204060801001201401600.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0Strain (%)Stress (MPa)θ = 0º θ = 45º θ = 90º 146             Figure B.2. Epi-fluorescence images of compressive cross-hatched microdamage in 4 cortical bone specimens loaded along different orientations: Top 4, Longitudinal (0°); Bottom 4, Transverse (90°). Compressive load applied vertically. Figures 5.2a-5.2b-5.8a and Figures 6.1c-6.2c not shown.  147 APPENDIX C       DIGITAL IMAGE CORRELATION ACCURACY The present appendix gives more details about the accuracy of digital image correlation (DIC) technique used to obtain the in-plane displacement and strain fields of transversely compressed bone specimens (Chapter 5). Digital image correlation for strain mapping relies on the detection of recognisable patterns in a series of images taken at different levels of deformation. As images can be obtained at any length scale, the technique is of particular relevance to hierarchical materials [176,276,277]. The strain accuracy mainly depends on the resolution (both optical and digital) of the imaging system, the recognisable patterns in the images, and the size of the interrogation window used for the correlation [277]. Selection of the Interrogation Window Size and Overlap The interrogation window is the search area used to find recognizable patterns in the series of images. The overlap is the distance, smaller than the interrogation window size, by which the interrogation window is translated during the search process. For fixed imaging conditions (e.g., optical and digital resolutions, uniformity of illumination, image contrast and intensity, etc) and testing conditions (e.g., size and distribution of the features forming recognisable patterns, displacements between successive images, etc), the choice of the interrogation window size and overlap determines the spatial resolution and accuracy of the computed displacement and strain fields [240,278]. Generally, decreasing interrogation window sizes result in increasing variations on the computed displacements and thus larger errors on the strains [176,210,278]. Hence, the choice of the interrogation window size and overlap is a compromise between spatial resolution and strain accuracy [176,210,278]. An iteration process 148 with multiple iterations (termed "multi-pass") at progressively decreasing interrogation window sizes allows to improve the spatial resolution (by having smaller final interrogation window size) while maintaining good strain accuracy [278]. Such strategy was used in the present work. In the study presented in Chapter 5, DIC was performed using the intrinsic microstructural features of the bone tissue. Those mainly consisted of the regular patterns formed by the lamellae (~ 2-8 µm in size) along with the more randomly distributed osteocyte lacunae (< 15 µm in size). An initial multi-pass correlation with all images (1392 × 1040 pixels) using a relatively large final interrogation window size (128 × 128 pixels) resulted in displacements of 2-5 µm between the images. Considering the digital resolution of the images (0.52 µm/pixel), an interrogation window size of 64 × 64 pixels (with 75% overlap) was selected, which corresponds to the "rule of thumb" of about four times the displacements between the images and the size of the repeating patterns. According to the DaVis software product manual [278], the error on the computed strains for those parameters would range between 0.3 to 0.6 %. Determination of the Strain Accuracy Due to its dependence on the imaging and testing conditions, there is no universal optimum as to the size of the interrogation window for good strain accuracy and spatial resolution [176,277]. A validation study, based on the current literature of bone deformation measured with DIC [176,210,240,277], was thus performed to verify the strain accuracy for the selected interrogation window size. The first step consisted of introducing rigid displacements (corresponding to those obtained from the initial correlation with all images; see above) to the reference image and computing the shear strain fields. As rigid displacements should result in zero strain, the limit of the technique in accurately measuring strains for the prescribed experimental conditions could be 149 estimated (Fig. C.1). The nominal strain accuracy was found to be about 0.3% at the selected final interrogation window size of 64 × 64 pixels. The error increased dramatically for a final interrogation window size of 32 × 32 pixels (Fig. C.1). As commonly reported [176,210,278], the decrease in strain accuracy was due to the increasing variations on the computed displacement fields as the interrogation window size decreased (strains being directly calculated from the displacement gradients). 0.00.20.40.60.81.01.21.41.60 16 32 48 64 80 96 112 128 144Interrogation Window Size (pixels)Maximum Shear Strain  ε max (%)  Figure C.1. Nominal strain accuracy of the DIC technique for the prescribed experimental conditions. The maximum shear strains (εmax) computed for three introduced rigid displacements indicated that the nominal strain accuracy decreased with decreasing final interrogation window size. The dashed line is a guide to the eye.  The second step consisted of introducing known shear strains to the reference image and compiling the average and range of the computed shear strains over the entire field of view. As the strain should be homogeneous, any variation indicated an error related to the strain accuracy of the system (Fig. C.2). The compiled average shear strain corresponded to the introduced shear strain within 0.02%. The strain accuracy, estimated by the largest of the differences between the 150 average and the maximum or minimum shear strains, was found to be about 0.26% for the selected final interrogation window size of 64 × 64 pixels (Fig. C.2). From the preceding two steps, it was concluded that the strain accuracy for the present study was 0.3%. 0.00.10.20.30.40.50.60.70.80 16 32 48 64 80 96 112 128 144Interrogation Window Size (pixels)Average Shear Strain  ε avr (%)  Figure C.2. Strain accuracy validation. The average shear strain (εavr) over the entire field of view corresponded well with the introduced shear strain (0.43% in the example above). The strain accuracy (error bars) could thus be estimated by the largest of the differences between the average and the maximum or minimum shear strains. The error on the strain increased with decreasing final interrogation window size.  The last step consisted of comparing the strains obtained with DIC using the "real" series of images (i.e., those that included both rigid displacements and deformations) with the macroscopic (or far-field) strains calculated from the compliance corrected displacements of the mechanical testing machine’s crosshead. The strain distribution (i.e., the number of pixels at a certain strain) over the entire field of view used for DIC was obtained for progressively higher macroscopic strains (Fig. C.3). The maximum shear strain at the peak, i.e., the strain associated with the most pixels, roughly corresponded to half the macroscopic compressive strain (as expected from theory [226]). This was particularly true within the elastic stage where the 151 deformation is more homogeneous (see Figure 5.6c) [176,210]. Such comparison thus validated the magnitudes of the strains measured with DIC. Compiling the strain distribution over the entire field of view also quantitatively showed that the strains got progressively more heterogeneous (wider distribution) as the deformation progressed. 0500001000001500002000000.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Maximum Shear Strain ε max  (%)Pixels Count  Figure C.3. Strain magnitude validation. The curves (from left to right) correspond to the maximum shear strain distributions for progressively higher macroscopic compressive strains. The maximum shear strains (εmax) at the peak of each strain distribution roughly corresponded to half the macroscopic compressive strains. The blue and red curves (arrows) with respective peaks at strain (εmax) of 0.35% and 0.75% correspond to the strain fields shown in Figures 5.6c-d. 

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