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Design for fracture control and the mechanical properties of the equine hoof wall Kasapi, Mario Agamemnon 1997

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DESIGN FOR FRACTURE CONTROL AND THE MECHANICAL PROPERTIES OF THE EQUiNE HOOF WALL  by MARIO AGAMEMNON KASAPI B.Sc, The University of British Columbia, 1991 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA November 1997 r>  Mario Agamemnon Kasapi, 1997  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or by his  or  her  representatives.  It is  understood  that  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  y^TSO A. QrC  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  ABSTRACT Morphological and mechanical studies were conducted on the equine hoof wall to help elucidate the relationship between form and function of this complex, hierarchically organized structure. Numerous levels of the morphological hierarchy were investigated to ascertain the functional significance (if any) of each level, and to determine if the presence of any levels reflect manufacturing limitations. Mechanical tests included tensile, fracture and dynamic tests; morphological studies utilized scanning electron, bright field, and polarized light (using both circularly and plane polarized light) microscopy. A universal stage was utilized to permit the accurate determination of fiber orientation in three dimensions. Mechanical tests indicate that the fracture toughness of hoof wall is independent of loading rate, and the wall is highly resistant to the propagation of cracks initiated in all directions tested here. Cracks initiated along potentially dangerous paths appear to be redirected by morphological crack diversion mechanisms formed by specific alignments of a-keratin intermediate filaments. Hoof wall structure at all levels may be explained in terms of fracture control, suggesting that the evolution of hoof wall design has been driven primarily by fracture issues. To avoid compromising the effective transfer of loads to the bony skeletal elements which may otherwise resultfromcrack diversion mechanisms, the properties of a-keratin have been adjusted through the wall thickness. Although inner wall tubules appear to offer some degree of reinforcement, the similarities in mechanical properties of a-keratin from cells of tubules and intertubular material (which form the hoof wall) from the same area of the wall, suggest that these elements are not analogous to fibers and matrix (respectively) of typical composites, but are instead necessary for the proper alignment of intermediate filaments in the hoof wall. Empirical and derived data suggest that the production of hollow (rather than solid) structures is likely the reflection of a manufacturing limitation. ii  T A B L E OF CONTENTS  ABSTRACT  ii  LIST OF TABLES  v  LIST OF FIGURES  vii  LIST OF ABBREVIATIONS  x  PREFACE  xii  ACKNOWLEDGMENTS  xiii  DEDICATION  xiv  CHAPTER 1: GENERAL INTRODUCTION  1  CHAPTER 2: MACRO AND STRAIN-RATE-DEPENDENT MECHANICAL PROPERTIES . . . Introduction Materials and methods Results Discussion  37 38 39 61 90  CHAPTER 3: DESIGN COMPLEXITY AND FRACTURE CONTROL Introduction Materials and methods Results Discussion  100 101 103 112 146  CHAPTER 4: THE FUNCTIONS OF TUBULES  159  Introduction Materials and methods Results Discussion  160 161 169 174  CHAPTER 5: OPTIMIZATION OF CRACK CONTROL AND MATERIAL STIFFNESS THROUGH THE MODULATION OF THE PROPERTIES OF KERATIN  ni  181  CHAPTER 5 (cont.) Introduction Materials and methods Results Discussion  182 185 203 219  CHAPTER 6: GENERAL CONCLUSIONS  232  BIBLIOGRAPHY  238  APPENDIX  247  iv  LIST O F T A B L E S  Chapter 2  Table 2.1: Average initial modulus, total energy, maximum stress and maximum strain for tensile tests at all four strain rates  62  Table 2.2: Average J-integral, stress intensity factor and initial modulus for compact tension tests at all four cross-head rates 63 Table 2.3: Mechanical data from tensile and compact tension tests on samples from inner, middle and outer regions of the equine hoof wall  78  Table 2.4: Fracture toughness data from compact tension tests of the equine hoof wall notched in the radial-longitudinal plane  89  Chapter 3  Table 3.1: Average tubule cortical lamellae thicknesses from the six regions of the equine hoof wall defined in this study 118 Table 3.2: Average number of tubule cortical lamellae from samples from the six regions of the equine hoof wall defined in this study 119 Table 3.3: Average tubule dimensions from the six regions of the equine hoof wall thickness as defined in this study. 121 Table 3.4: Intermediate filament helical angles in lamellae of the tubule cortex from different regions of the hoof wall  125  Table 3.5: Fracture toughness data from CT tests of the equine hoof wall  145  Chapter 4  Table 4.1: Hoof wall hydration and dehydration rates in various directions  170  Chapter 5  Table 5.1: Mean longitudinal mechanical properties for hoof wall macro-scale components of tubule dimension and horse hairs obtained just proximal to the hoof wall. Table 5.2: Hysteresis data for tensile loading of hoof wall macro-scale components. Table 5.3: Change in initial extension resistance after 30 minutes  v  209 211 213  Chapter 5 (cont.)  Table 5.4: Initial nano-scale tensile modulus values of cells from different wall macro-scale components and regions 214 Table 5.5: Birefringence data and corresponding intermediatefilamentvolume fractions of cellsfromtubules and intertubular material 218  vi  LIST OF FIGURES Chapter 1  Figure 1.1: The hierarchical organization of bone  6  Figure 1.2: The molecular organization of intermediate filament substructure . . . . . .  11  >  Figure 1.3: Composite illustration of the hoof wall showing the formation of tubules, and the collagen fiber system through which the hoof wall suspends the bony skeleton. Figure 1.4: Organization of the substructures of the equine hoof wall showing tubule and intertubular components  14 17  Figure 1.5: Diagram of a wedge-shaped sample taken from the equine hoof showing regions of the three tubule types  21  Figure 1.6: Spiral organization of cells as proposed by Nickel (1938a)  24  Figure 1.7: Generalized potential energy curve  28  Figure 1.8: Stress trajectories in an unnotched and notched specimen  30  Chapter 2  Figure 2.1: Composite illustration showing tubules and intertubular material, and compact tension, tensile and dynamic test specimen dimensions Figure 2.2: Exploded diagram of the clevis loading system with a CT specimen Figure 2.3: Typical tracefroma CT test  40 45 47  Figure 2.4: Exploded diagram of the impact pendulum transducer system  49  Figure 2.5: Plots of scaled energy versus notch length, and coefficient h versus displacement. Figure 2.6: Illustrations of compact tension and tensile test specimens Figure 2.7: Typical tensile stress-strain curves for each of the four strain rates used in this study and a representative test at 75% relative humidity from Bertram (1984). . . Figure 2.8: Tensile test scatter plots of initial modulus, total energy, maximum stress and maximum strain versus strain rate Figure 2.9: Scatter plots of initial modulus versus cross-head rate for tensile and compact tension tests, and storage modulus versus frequency  vii  52 57 64 66 68  Chapter 2 (cont.)  Figure 2.10: Compact tension scatter plots of ./-integral and stress intensity factor plotted against cross-head rate for compact tension tests  72  Figure 2.11: Scanning electron micrographs of fracture surfaces of specimens tested at slowest and highest test rates  75  Figure 2.12: Representative tensile stress-strain curves for inner, middle and outer regions of fully hydrated equine hoof wall 79 Figure 2.13: Double-logarithmic scatterplot of initial longitudinal modulus versus water content 81 Figure 2.14: Scanning electron micrographs of compact tension test specimen fracture surfaces  84  Figure 2.15: Illustration of the equine hoof wall and sample compact tension specimens of the toe region photographed in Fig. 2.14  86  Chapter 3  Figure 3.1: Illustration showing compact tension specimen dimensions and orientations.  104  Figure 3.2: Axes and angles as denned in this study  107  Figure 3.3: Circularly polarized light photograph of a tubule and associated intertubular materialfromregion Ilia  113  Figure 3.4: Hoof wall tubule composite diagram  115  Figure 3.5: Hoof wall morphology plotted as a function of position through wall thickness for two animals  122  Figure 3.6: Hoof wall intertubular material composite diagram  128  Figure 3.7: A model of the equine hoof wall with a slice removed to show the positions which define the lateral and medial circularly polarized light micrographs below. 133 Figure 3.8: A model of the equine hoof wall with slices removed to show the positions which define the lateral and medial circularly polarized light micrographs below. 135 Figure 3.9: Scanning electron micrographs of compact tension test specimen fracture surfaces 138 Figure 3.10: Composite diagram of the equine hoof wall showing the orientations of compact tension specimens, the initial notch orientations and the paths of crack propagation. 140 vm  Chapter 3 (cont.)  Figure 3.11: Summary diagram of crack redirection in the hoof wall  152  Chapter 4  Figure 4.1: Illustration showing the faces of a hoof wall block as defined in this study.  162  Figure 4.2: Illustration of the hydration/dehydration chamber  164  Figure 4.3: An image of a cross-section of an equine hoof wall specimen  167  Figure 4.4: Percent of area occupied by tubule medullary cavity, and mean medullary cavity cross-sectional area plotted against region through hoof wall thickness  172  Figure 4.5: Illustration of tubule cellular and intermediate filament organization  178  Chapter 5  Figure 5.1: The chamber used in the tensile testing of specimens of tubule dimensions.  186  Figure 5.2: A video captured cross-sectional image of a tubule test specimen from the inner hoof wall  189  Figure 5.3: A sample of raw strain data plotted as a function of time  191  Figure 5.4: Illustrations of cell strand specimen preparation  195  Figure 5.5: Micro mechanical test system  197  Figure 5.6: Three plots of storage magnitude plotted against test frequency to show the effects of dehydration, freezing and mounting artifacts 204 Figure 5.7: Stress-strain curves for inner tubules, mid-wall tubules, horse body hair, and inner wall and mid-wall intertubular material 206 Figure 5.8: Plots offeree and strain versus time for a mid-wall on-fiber cell strand specimen, stress-strain curves for the same specimen and an across-fiber specimen, and initial modulus regression lines for all tests of specimens from the mid-wall  215  Figure 5.9: Diagram of the hypothesized micro-scale composite that illustrates the possible contribution of the cell interface complex to the mechanical properties of hoof wall tissue 228 Appendix  Figure A. 1: Test of the data correction program ix  250  LIST OF ABBREVIATIONS  a A ASTM B c C C CB CT AL E E' e e / F 4> G Y r / / IF J K KE L £ L LEFM N v ODT P r R p RH o o o o SA SE SEM  Notch length Area American society for testing and materials Birefringence Vi crack length Circumferential Compliance Coronary border Compact tension Change in length, displacement Modulus of elasticity Storage modulus Strain Ultimate or maximum strain Fiber Force Angle measured from the longitudinal axis Strain energy release rate Surface energy Specimen retardation Moment of inertia Second moment of area Intermediate filament J-integral Stress intensity factor Kinetic energy Longitudinal Length of beam from pivot to mass Reference bar length Linear elastic fracture mechanics Newton Poisson's ratio Optical displacement transducer Critical load Interatomic separation distance Radial Radius of curvature at the crack tip Relative humidity Stress Ultimate or maximum stress Stress concentration Yield stress Spectrum analyzer Stratum externum Scanning electron micrograph  u  mass  [e{  u  c  y  x  SI SM t tanc5 0 0 w U V VDA W W to y  Stratum internum Stratum medium Specimen thickness Viscous loss function Extinction angle Angle from the radial-longitudinal plane Potential energy Energy Volume fraction Video dimension analyzer Width Water content Angular velocity Yield  c  xi  PREFACE  Much of the text and figures of this thesis have been previously published by the author in the following manuscripts: Kasapi, M. A. and Gosline, J. M. (1996). Strain-rate-dependent mechanical properties of the equine hoof wall. J. exp. Biol. 199, 1133-1146. Kasapi, M. A. and Gosline, J. M. (1997). Design complexity and fracture control in the equine hoof wall. J. exp. Biol. 200, 1639-1659. Inclusion of the manuscripts in this thesis has been approved by the co-author of the papers, J. M. Gosline.  xn  ACKNOWLEDGMENTS  This thesis was produced with the aid of many people who gave their time, advice and expertise selflessly. If I have omitted anyone from this list, please accept my humble apology and know that I have probably realized the omission just days after publication of this thesis and will have suffered greatly for it. For reviewing the manuscripts that have been produced from this thesis, I wish to sincerely thank (in alphabetical order) Dr. Emily Bell, Volker Deeke, Jennifer Hayward Farmer, Paul Guerette, TaraLaw, Dr. Margo Lillie, Eric Luiker, William Megill, Cynthia Nichols, Christine Ortlepp, Lei Lani Stelle, and the anonymous manuscript referees. A special thanks also goes out to Dr. Margo Lillie for serving as my devil's advocate, and unwitting mentor. Thanks also to William Megill for developing the frequency response correction program used in chapter 2, Robert Scharein for producing the tubule renderings in chapter 3, and the Natural Sciences and Engineering Research Council of Canada for financial support during the first four years of this research. Thanks are extended to the members of my thesis supervisory committee: Drs. Robert Blake, Bill Milsom, Anoush Poursartip and Wayne Vogl for their valued input. Also thanks to my examination committee Drs. R. M. Alexander, J. D. Currey, S. Cockroft, W. Tetzlaff, for their contributions, and Bridie Byrne, Kathy Gorkoff and Diane Mellor for their assistance in administrative matters. I wish to acknowledge the financial and emotional support of my parents preceding and during the years of this research. Without their assistance, this research would not have been conducted. Very importantly, I also wish to thank my wonderful wife Vicki, whose encouragement and understanding of the demands of academia over the last nine years of our relationship have been crucial to the success of this work, but never justly rewarded. Finally, 1 would like to express my deepest thanks to my supervisor, Dr. John M. Gosline, who is one of the finest people I know. Through the years that 1 have endeavored to form this thesis, he has always been very supportive and enthusiastic. Although endowed with an envious gift of intelligence, he is incapable of condescension. He has served as a role model by succeeding in the near impossible task of balancing family, social and academic responsibilities, and has been largely responsible for the success of this thesis and my academic confidence. 1 am honored to have been under his guidance for the last six years.  xm  This thesis is dedicated to my wife and children  xiv  CHAPTER 1: GENERAL INTRODUCTION  1  1. Evolution of the hoof wall.  In the incessant evolutionary arms race between many mammalian predator and prey species, locomotor speed enhancement has been a primary objective. Predators such as large cats can achieve high speeds to overcoming prey, but can only maintain these speeds for short periods and require long rests between exertions. The evolution of obligative herbivores, such as ungulates which are relatively defenseless, has resulted in the development of a number of morphological characteristics that enhance speed and endurance, necessary traits for predator evasion in ungulates. Perhaps the most striking example of such adaptations is seen in the limb. In cursorial or high-speed terrestrial animals, limbs are swung in a pendulum-like fashion. Therefore, any characteristic that makes limb movement easier will be favored. Although a short limb is easier to move, overall speed is compromised as a result of a shorter stride length since speed is proportional to stride length and stride frequency. Longer limbs are therefore more favorable for highspeed locomotion and are characteristic of ungulate morphology. However, a consequence of the high mechanical advantage offered by long limbs is the requirement of a large muscle mass to power movement; as with a pendulum, this mass will tend to lower the swing frequency and raise the swing period. The kinetic energy (KE; energy associated with movement) required to move the limb 'beam' also rises with the mass of the limb. Since:  2 where I is the moment of inertia and co is the angular velocity of the limb, reduction in the kinetic energy requirement is only possible by reducing /, if angular velocity is to be maximized. The goal is therefore to construct a long beam that acts like a short pendulum. In ungulates, this is achieved primarily by retaining the large locomotor muscle masses close to the body. This reduces the overall 2  kinetic energy of the system by lowering the moment of inertia since, in a system where a mass is located along a beam length (and the weight of the beam is negligible), / = mL J, nn  mass and Z  mass  where m is the  is the length of the beam from the pivot to the mass. This strategy is analogous to  moving the weight of a metronome arm closer to the base in order to increase the rate of oscillation. Since the bones of the upper limb are necessarily intimately associated with skeletal muscle, lengthening of the beam (limb) has been achieved by extending the length of the distal bones, the nonmuscularized metapodials and metacarpals. This morphology provides a relatively long stride length with the kinetic energy of a shorter limb. Additional adaptations have evolved in ungulates that reduce the overall weight of the limb terminus to further reduce the energetic cost of locomotion. Ungulates are characterized by a reduced number of digits and by the presence of a hoof. These features are weight-savings strategies that have evolved concomitantly with the distal limb length. With fewer digits, the overall weight of the limb terminus is reduced since less bone mass is required to provide the same stiffness and strength in bending. The horse (genus Equus) is an extreme case of this adaptation, with the adoption of a perissodactyl (mesaxonic) foot in which the load axis runs through the third toe; all other digits are lost except for the second and fourth toes which are reduced to splints. Along with a reduced number of digits has been the evolution of a hoof wall. This wall borders the foot and is the primary load-bearing element. Since the wall terminates the digit, it too has been under selective pressure to minimize weight. Consequently, the hoof wall has become a stable, light-weight concussive structure that provides a stronger, tougher interface than the ancestral pad. These mechanical properties have been achieved through design of the hoof wall as a hierarchically organized structure which is formed from keratin, a protein-based fiber-reinforced composite. It is believed that the use of a polymeric composite as the primary wall material is not simply a consequence of its evolution from the claw which is also made of keratin, but is an integral 3  part of the design for hoof wall toughness.  2. Fiber-reinforced composites.  A composite is anything that is made up of two or more elements, i.e. a mixture. Materials consisting of a fibrous phase embedded in a glue-like matrix phase are called fibrous composites. Most composites exhibit mechanical properties superior to those exhibited by each of the phases if considered separately (e.g. Agarwal and Broutman, 1990). Therefore, composite structures tend to be relatively light-weight. Consequently, composites are now widely used in engineering structures where high toughness (resistance to crack propagation) and weight minimization are required. The fibers of composites have a characteristically high stiffness (or modulus) and serve to provide the majority of the material strength; the matrix binds fibers and transfers stresses to them (usually by shear), aids in withstanding compressive forces, and inhibits cracks from propagating through fibers which would otherwise be in direct contact (Harris, 1980). Composites with weak (but not too weak)fiber-matrixinterfaces also offer a crack-blunting effect by increasing the radius of curvature of the crack tip, and by diverting crack growth to run along the interface (Cook and Gordon, 1964). Crack diversion releases strain energy that would otherwise fuel the crack lengthening process, thereby increasing the fracture toughness. The modulus of a fiber-reinforced composite in any particular direction depends on the moduli and volume fractions of the fibrous and matrix phases. If all fibers are similarly aligned and a tensile force is applied along thefiberaxis, the modulus in that direction is given by the Voigt estimate:  E. =E,V,+E 1 / /  V m  ni  Fn 1 2 t->q.  where E is the modulus of elasticity (or Young's modulus), subscripts /and m denotefiberand matrix, 4  respectively, and V\s the volume fraction. If stressed perpendicular to thefiberaxis, then the modulus in that direction is:  E= 2  Eq. 1.3.  '" EV +E V LjL  J  in  in  f  r  The preceding equations are useful for predicting the modulus of a material given the moduli of the phases, but assume that both the fibrous and matrix phases are linearly elastic and that the fibers are uniform in properties and shape, continuous and aligned similarly. In Eq. 1.3, the fibrous phase must be isotropic (have equal properties in all directions).These criteria are violated to some degree in most biological systems, because the fibers are usually polymeric; therefore these equations must be used with caution. They may, however, be used to provide estimates of the modulus of each phase if the overall modulus and volume fractions of each phase are known. Composites are common in biological systems and numerous biological composites have been studied, including insect cuticle, wood and bone. Insect cuticle consists of chitinfibersin a protein matrix; wood is a composite of cellulose fibers in a lignin matrix. In all cases, structural organization extends beyond the molecular level and can be described as hierarchical. For example, bone is a twophase composite of hydroxyapatite crystal fibers (~5 x 20 x 40 nm) embedded in a collagen fiber matrix (Vincent, 1990). In compact bone, this composite forms lamellae 3-7 pm thick (Katz, 1980) that are organized concentrically to form osteons about 200 pm in diameter; layers of lamellae and groups of osteons are all held together with an organic 'cement' to form the bone structure (Fig. 1.1). The ubiquity of hierarchy in biological support structures suggests a mechanical advantage in these systems.  5  Figure 1.1: The hierarchical organization of bone. Bone is a two-phase composite of hydroxy apatite crystals in a collagen matrix. This composite is organized into concentric lamellae to form osteons which are then assembled into cortical bone (from Vincent, 1990).  6  Tropocollagen  7  3. Hierarchical systems.  Although composites have been made for thousands of years for use in load-bearing structures, the mechanical benefits of hierarchically organized systems have only recently been appreciated. Only through our quest to comprehend how biological systems meet extreme mechanical demands has the efficacy of hierarchical systems been realized. Still, our understanding of how each level of organization contributes to the whole structure is incomplete. The load-bearing capacity of wood has been utilized for years, however, the complexity that seems to offer its high mechanical integrity also makes it difficult to analyze. Fortunately, much has been learned from studies of hierarchical biological systems and, as a result, thefieldof biomimicry has recently emerged. Biomimicry is an attempt to develop materials or structures with advanced mechanical properties through emulation of natural design. Hierarchical systems may offer many advantages to structural materials, including suppression of buckling, an increase in toughness and compressive strength relative to solids of similar density, and may also confer superplasticity (extensive irreversible deformation before failure) to a structure (see Lakes, 1993). In the case of bone, the presence of two levels offiber-reinforcedcomposite design (hydroxyapatite crystalfibersat the molecular level, and osteon fibers at a larger scale), appears to provide large- and small-scale crack deviation mechanisms as propagating cracks experience a composite at multiple scales. It is assumed that large and small-scale crack redirection that results absorbs more energy than that if the structure was a simple composite. Biological hierarchical systems seem to follow three rules (Baer el al, 1992): 1) The structure is organized in discrete levels or scales, 2) The levels are held together by specific interactions between components and 3) The overall orientation of components is such that the design meets a complex spectrum of functional requirements. Cortical bone follows these rules of complex assemblies precisely (see Lakes, 1993), and studies on hoof wall morphology (Nickel, 1938a,/>;  8  Wilkens, 1964; Leach, 1980) have shown that it also follows these rules. Unlike bone, which experiences loads that are usually predictable, spread out over its cross-sectional area and have been dampened to some degree, the hoof wall directly interfaces with the ground and must therefore be capable of enduring high impact loads that, if impacted on an uneven substrate, may be concentrated on a small area of the wall. Its ability to resist failure under extreme loading conditions is attributable to its design as a fracture tough mechanical system. Comprehension of this mechanical system begins with an understanding of the material of which it is formed.  4. The hierarchical organization of the equine hoof wall.  4.1. The nature of alpha-keratin. Keratin is a protein-based fiber-reinforced molecular composite that is prevalent in the integument of terrestrial vertebrates. Hoof, horn, nail, claw and feather are but a few structures formed from this class of proteins. Keratins have filamentous and matrix phases and are characterized by a network of intra- and inter-molecular disulphide bonds that are formed by the oxidation of cysteine residues at the final stages of synthesis (Fraser and MacRae, 1980). Keratins found in the four terrestrial classes of vertebrates are actually a family of closely related structural proteins and are generally classified as either hard or soft. Soft keratins are found in the skin epidermis. Whereas soft keratins are cc-type (i.e. the filamentous phase is primarily composed of a-helices), hard keratins are either a- or P-type (the fibrous phase is dominated by the presence of P-sheets). Hard a-keratins are found in wool, horn, nail and hoof; p-keratins are found in bird beaks, feathers and reptile claws. The key component of the a-keratin composite is a member of a family of closely-related proteins, collectively called intermediate filaments (IFs). There are at least five classes or types of EFs based on domain structure, tissue specificity and nature of intermolecular association (see Stewart, 1993; Quinlan et al. 1996): type I (acidic keratin), II (basic keratin), 111 (vimentin, desmin, glial 9  fibrillary acidic protein, peripherin), IV (neurofilament proteins, nestin) and V (lamins). At least one type of IF is found in most eukaryotic cells. It is now generally accepted that all IFs are composed of two-stranded, parallel-chain, rope-like structures (Fig. 1.2), in which each strand is represented by an a-helix (Crewther et al. 1983; Parry et al. 1987). In keratins, these molecules are heterodimers of a type I and a type II chain (Steinert, 1990); in the epidermis, the association of a Kl (type II) and K10 (type I) chain is most common (Steinert, 1991/-), although there are over 30 known chain isotypes in keratin. Coiled-coil molecules, or protofibrils, are approximately 46 nm long (Fraser and Parry, 1993), 1 run in diameter (Crewther et al. 1983) and are flanked at both the N- and C-terminus by a head and tail segment, respectively (see Herrmann et al. 1996). The structures of these domains are presently unknown; however, it has been deduced that the coiled-coil or rod domain is interrupted periodically with short (0.8-2.5 nm long) non coiled-coil link segments (Fraser et al. 1962; Steinert et al. 1984) referred to as L, , L and L . These links divide the rod domain into 4 segments la, lb, 2a and 2b, 12  2  respectively. A short sequence in region 2b, known as the stutter segment, is believed to cause a slight inconsistency in the alpha-helix (see North et al. 1994; Steinert el al. 1994). Link segments comprise about 11% of the total rod domain length (Fraser and Parry, 1993) and are also rich in cysteine and proline residues in hoof and horn (Vincent, 1990). Steinert et al. (1994) have proposed structures for the link segments and suggest that a cross-over occurs between chains in L . 2  Two neighboring coiled-coil molecules associate in an antiparallel arrangement (Steinert, \99\a,h\  Steinert and Parry, 1993) of which three or more alignments are likely to exist; coiled-coil  alignment is dependent on IF association (Steinert et al. 1993a,/>). The association is stabilized intermolecularly by ionic bonding between basic and acidic residues (Steinert, 1991a,/-), and there seems to be a highly-conserved eight residue overlap between the head and tail regions of parallelaligned molecules in IFs formed from the associations of types III, IV and V chains, and of types I 10  Figure 1.2: (A) Two polypeptide chains form a coiled-coil 'rope' (approximately 45 nm long) with helical and non-helical (shaded portion) segments. 1A, IB, 2A and 2B are coiled coil rod domains; Ll, L12 and L2 are link segments. The shaded area in region 2B is the stutter segment. (B) Ropes are associated in pairs to form anti-parallel unit structures that vary in length; two possible alignments are shown (from Parry et al. 1987).  11  A  12  and II chains in soft (but not hard) a-keratins (Parry, 1995). Sixteen coiled-coil molecules (32 chains) appear to be organized concentrically into 40-80 kDa structures (Grosenbaugh and Hood, 1992) about 7 nm in diameter (Steven, 1990). Although the nature of this organization is still under debate, it appears that IFs assembly requires the formation of an initial 3-4 molecule nucleation site or template before rapid IF assembly of additional molecules is possible (Steinert, 1991 b). Lateral interactions of segment la are also important in IF assembly and stabilization (Poole and Johnson, 1995), as are the eight residue head-to-tail overlap (Parry, 1995) and the acidic components (Sayers etal. 1990). Using X-ray diffraction, Wilk etal. (1995) suggested that coiled-coil molecules are likely  associated to form tetrameric unit structures and that four of these tetramers associate concentrically and supercoil to form unidirectionally oriented IF molecules. IFs associate with a globular, viscoelastic protein matrix (Fueghelman, 1994) that constitutes between 12.6 and 63% of keratin depending on tissue type (Bendit, 1968, 1980). IF-associated proteins are classified into either high sulfur (10-30 kDa) or high glycine-tyrosine (10-20 kDa) fractions (Grosenbaugh and Hood, 1992) based on the predominance of the respective residues. Matrix proteins are stabilized intramolecularly with a large number of disulphide covalent bonds. Keratin intermediate filaments contain a high proportion of cysteine residues in addition to significant quantities of proline and serine (Vincent, 1990). A high-degree of IF orientation in keratinous derivatives suggests that IFs serve to reinforce the tissues along thefilamentaxis.  4.2. Generation and binding of hoof wall cells. Cells of the bulk of the hoof wall are generated at the coronary border (CB) situated at the proximal-most portion of the hoof and are also formed from dermal papillae extending part-way down the hoof (Fig. 1.3). A zone of keratinization exists where cells undergo morphological transformations from generally cuboidal cells to hardened, flattened structures (see Matoltsy, 1976).  Figure 1.3: (A) The plane of section through the equine hoof that reveals B. The bordered area in B is expanded in C. (C) The primary region of the hoof growth (coronary border) and a portion of the hoof wall; collagen fibers of the dermis are also illustrated to show the skeletal suspension system. (D) A close-up of the dermal papillae and coronary border that models the formation of the tubule cortex and intertubular material, respectively (from Leach and Oliphant, 1983).  14  Coronary Border Dermal Papilla Tubule Cortex Intertubular Material Tubule Medulla  Collagen Fibers  15  In endothelial cells, shape changes are induced by stress and controlled by a mechano-sensitive mechanism formed by enzymatic activity, Ca and a microtubule network (IVlalek and Isumo, 1996). 2+  During the transformation of keratinocytes, cellular organelles become degenerate. Many organelles are incorporated into the intracellular keratin matrix while some are exported to the extracelluar space and are believed to become part of an intercellular 'glue' (Matoltsy, 1975). Lining the inside of the plasma membrane of mammalian epidermal cells is a 1 5 nm thick layer of proteins called the cornified cell envelope. The proteins of this envelope are cross-linked by disulphide and isodipeptide bonds (Steven and Steinert, 1994), forming an insoluble network that acts as a barrier and stabilizes cell shape. K10 chains of IFs are cross-linked to the envelope (Ming et al. 1994) and likely aid in the transfer of mechanical stresses to the extracellular matrix and to adjacent cells. Adhesion of mature hoof wall cells appears to be achieved with desmosomes and septate-like junctions (Leach, 1993); it may also be facilitated by a glycoprotein 'glue', as in mammalian epidermis (Matoltsy, 1975), which is likely secreted by keratinocytes via membrane coating vessicles (Leach, 1993), and by a high degree of plasma membrane interdigitation (see Leach, 1980). Although cellular morphology and organization of nail and nail derivatives have been well documented (Hashimoto, 197la,b\ Leach, 1980), intercellular connections of mature hoof cells are not well described. Observations of hard keratins under load have revealed that mature cells conform to strains, suggesting that the intercellular material is both elastic and adhesive (Fraser and MacRae, 1980) and that cell boundaries are probably not a limiting factor in fracture resistance (Woods, 1938).  4.3. Arrangement of cells. The bulk of hoof wall cells are organized into one of two patterns: concentrically into tubules that run the length of the hoof wall, or intertubular material (Fig. 1.4). Intertubular cells are formed 16  Figure 1.4: Organization of the substructures of the equine hoof wall as illustrated in Bertram and Gosline (1988) showing tubule and intertubular components. Scale bar, 100 pm.  17  18  at the coronary border, whereas tubule cells are formed from dermal papillae (see Fig. 1 3C; Banks, 1993). Cells of both components are flattened and generally elliptical (Rosskopf and Geyer, 1987). Nickel (1938a) suggested that IFs in cells of the tubule cortex together formed concentric lamellae of alternating helices. On the basis of a microscopic study of bovine hoof wall, however, Wilkens (1964) suggested that the arrangement of tubule cortex cells more closely resembles the pattern of microsporophyll arrangement of pine cones (although 'pine-cone' was apparently inadvertently translated into 'pin-cushion' in the publication; J. E. Bertram, personal communication) whereby the tubule cell plane lies at an angle to the tubule axis. Polarized light microscopy has revealed that IFs of hoof cells are highly ordered (Nickel, 1938a,/.; Leach, 1980), and it has been assumed that the fibers are arranged in-plane and parallel to the longitudinal axis of the elliptical cells. Planes of intertubular cells in equine hoof wall lie at large angles relative to the longitudinal axis of tubules (Bertram and Gosline, 1986). Baillie and Fiford (1996) modeled the cellular organization of bovine hoof wall and proposed that wall micro structure differed from equine wall. Differences included the sizes and shapes of tubules, the organization of the intertubular material and its association with tubule cortical cells; however, their tubule models are also presented as lamellar structures. Interestingly, cross-sections of mature rhinoceros horn (Makinson, 1954; Ryder, 1962) show marked similarities with sections of equine and bovine hoof wall, although horn tubules are generally larger in diameter (300-500 um; Ryder, 1962) than those in hoof (200-300 pm). Two functions have been offered for tubules. Bertram and Gosline (1986) suggested that they act to reinforce the wall along the tubule axis and are analogous to fibers of fiber-reinforced composites (therefore, intertubular material function as the matrix of the composite). The use of hollow rather than solidfibersin hoof may increase resistance to compressive failure; hollow fibers have been incorporated into synthetic polymer-matrix composites to prevent co-operative buckling of fibers (see Baer et al. 1992). Others have proposed that they act as water vapor conduits to 19  facilitate hydration of distal portions of the hoof wall (Evans el al. 1990). The vital role of moisture in determining soundness of the hoof (Lungwitz and Adams, 1966) and providing high fracture toughness (Bertram and Gosline, 1987) suggests that tubules, at least in part, serve this function. Evaporative moisture from dermal papillae may be carried through the medullae of tubules to more distal regions of the wall; however, Vermunt and Greenough (1995) suggested that the intertubular material is more hydrophillic than tubules. The high degree of IF organization within tubule cells does, however, imply a mechanical function. In examination of thefracturesurface of hydrated bovine horn, Kitchener (1987) noted a high degree of tubule 'pull-out', suggesting that tubules in horn have analogous functions with fibers of composites. He also found extensive delamination of the layers of keratinocytes after fracture, implying that weak lamellar interfaces serve as energy dissipating and crack blunting mechanisms. Human nail, which serves to resist abrasion, does not contain tubules (Hashimoto, \91\a,b).  4.4 Regions and shape of the hoof wall. The hoof wall consists of three regions through its thickness (Fig. 1.5). The stratum externum (SE) forms the outermost covering of the hoof capsule and is the driest portion of the wall. Lipids are abundant in the SE, suggesting that this layer functions primarily to inhibit wall dehydration. This layer is relatively thin and becomes progressively thinner distally (Banks, 1993), therefore, it does not likely contribute directly to the mechanics of the hoof. The stratum medium (SM) constitutes the largest portion of the equine hoof wall, and contains three main types of tubules according to Nickel (1938a). Type I tubules are the innermost and smallest in diameter. Type II tubules are largest in diameter and are found between type I and type III tubules, the latter being the outermost tubule. Tubule density decreases from >27 to <8 tubules per mm progressing inwards (Reilly el al. 1996). 2  Tubules also differ in the quantity of cellular lamellae with similar fibrillar orientation (Nickel, 1938a; 20  Figure 1.5: Diagram of a wedge-shaped sample taken from the equine hoof showing regions of the three tubule types. Sl, stratum internum; SM, stratum medium; SE, stratum externum; dermis; PHI, third phalanx (from Leach, 1980).  21  22  see Fig. 1.6). Bolliger and Geyer (1992) also identify three tubule types based on differential tubule cortical cell morphology and provide detailed illustrations of the micro and macroscopic morphology of equine hoof wall tubules. The stratum internum (SI) is the innermost epidermal portion of the hoof and appears to be primarily responsible for transferring loads to the bony skeleton. Primary and secondary lamellae of the SI form an extensive network of interdigitation with the dermis of the foot and cells of the secondary lamellae are anchored to the underlying basal lamina via hemidesmosomes. The basal lamina is anchored to the dermis which is, in turn, associated with the third phalanx (PHI, coffin bone) via collagen fibers (see Fig. 1.3C). In this manner, the hoof wall suspends the bony skeleton so that ground reaction forces are transferred up the hoof, through the dermis and to the third phalanx. The equine hoof wall resembles an obliquely truncated cone surrounding all but the posteriormost portion of the third phalanx, and forms the outer load-bearing surface of the foot. Mature tissue is worn away distally but is continually regenerated at the coronary border at a rate of approximately 8 mm per month (Geyer and Schulze, 1994; Josseck el al. 1995; Vermunt and Greenough, 1995), although this rate is dependent on diet (Butler and Hintz, 1977; Kempson, 1990; Buffa et al. 1992) and age (Butler and Hintz, 1977). It also varies between fore and hind hooves (Butler and Hintz, 1977) and through the wall thickness (inner and outer wall growth rates are approximately 11 mm and 8 mm per month, respectively; Pollitt, 1990). In addition to growth at the coronary border, hoof tissue is also generated from the stratum basale adjacent to the SI; therefore the thickness of the hoof increases distally.  5. Loading of the hoof wall.  The loading pattern of the hoof wall is complex. Lambert (1971) characterized shock diffusing elements in the horse hoof and suggested that the hoof wall acts like a spring by expanding at the 23  Figure 1.6: Spiral organization of cells as proposed by Nickel (1938a). Lines denote the orientation of the major axis of the elliptical-shaped cells. (A) Type 1 tubules. (B) Type II tubules (C)Type III tubules (from Leach, 1980).  24  25  heel, storing impact energy which has been expressed as a large inward force on the hoof. Thomason etal. (1992) quantified surface strains on the hoof in vivo finding, not surprisingly, that the hoof wall  is loaded primarily in compression, and confirming that expansion of the posterior borders of the hoof occurs; the hoof must effectively cope with the differential strains within the wall as a result of heel expansion and compressive loading from impact. Although it is mainly loaded in compression, hoof tissue in situ probably ultimately fails in tension due to high, localized tensile stresses that result when an uneven substratum is encountered. Tensile properties are therefore of primary interest when evaluating hoof performance. Hoof wall must withstand repeated loads of considerable magnitude without failure. Using a force plate, Pratt and O'Connor (1976) recorded vertical forces up to 5600 N during a canter. Schryver et al, (1978) confirmed that as speed increases, the loads acting on the hoof increase. Considering that horses can weigh up to 9000 N, the average stress acting on the hoof can routinely reach 5 MPa (Bertram and Gosline, 1988). During high-speed locomotion, these stresses will increase considerably. Strain measurements of the outer surface suggest that the wall does not routinely approach strains which may result in failure (Thomason et al, 1992); however, the animal's relatively large size, coupled with its particular high-speed gait patterns and the likelihood of contact with uneven substrata, lead to the potential for the development of high, localized stresses. Unlike bone, which constantly undergoes remodeling, epidermal tissue cannot be repaired or remodeled once it is formed. Hoof wall must therefore be even more tolerant of extreme mechanical insults since any damage (such as cracks) will remain as a threat in the tissue until it is worn off distally. Failure may lead to lameness, infection and subsequent death of the animal. Ungulates such as the horse have necessarily exploited the toughness of keratins and through evolution have developed a complex, hierarchical structure capable of transferring large forces and resisting crack growth. Failure by crack propagation is unusual in this tissue, and the mechanisms that convey high fracture toughness in this 26  material are enigmatic. Therefore, the science of fracture mechanics will play an integral role in the evaluation of the functional design of this complex structure in this thesis.  6. Mechanical properties of materials.  The tensile strength of a material should be governed by the change in interatomic forces as separation distance varies. Interatomic forces are categorized into a short-range repulsion force (as completely filled electron shells overlap) and long-range attraction forces such as Van der Waals forces, ionic bonding, covalent bonding and metallic bonding. Fracture is the process of breaking these bonds. Grouped atoms will normally take on a conformation of the lowest free energy, with interatomic spacing equilibrating at a separation distance, /'„. As r changes with an applied load, the magnitude of the stress o will be determined by the slope of the potential energy curve (i.e. o=du/dr where u is potential energy; see Fig. 1.7). In a homogenous material such as glass, the theoretical maximum or ultimate stress o is approximately EI2n (see Broek, 1986). This value is, however, u  orders of magnitude larger than the observed maximum stress of most real materials. Working with glass fibers, Griffith (1921) showed that most materials contain pre-existing defects as surface and/or internal flaws. When an object is subjected to a tensile stress, the area about the flaw will be unable to cany any stress, resulting in a stress concentration o in front of the crack c  (Fig. 1.8). For internal, ellipsoidal cracks normally studied in material science, o = o ,(l + 2[c/p]') /;  c  n  where o is the mean stress away from the crack, p is the radius of curvature at the crack tip and 2c m  is the length of the crack. This phenomenon of stress concentration explains why the observed breaking stress never reaches its theoretical maximum. Griffith (1921) concluded that the fracture stress of a material: 2yE (l-v )7Tcv 2  27  Eq.lA.  Figure 1.7: Generalized potential energy curve. The stress on a material is determined by the slope of the curve; r is the equilibrium separation distance. 0  28  short-range repulsion longer-range attraction resultant  r (atomic separation distance)  29  Figure 1.8: Stress trajectories in an unnotched (A) and notched (B) specimen. No stress is carried by the material immediately above and below the notch, however, a stress concentration results directly in front of the crack (redrawn from Gordon, 1978).  30  B  A A A AA  A  t t t * *  T T T T T  31  A  A A A  where y is the surface energy and includes work for plastic deformation, and v is Poisson's ratio (the ratio of transverse strain to longitudinal strain). Fracture mechanics is important in characterizing material properties because, although the total energy input to a material may appear sufficient to characterize the toughness of a material, it provides no information about the behavior of a material with a crack or flaw. Linear elastic fracture mechanics (LEFM) attempts to quantify the fracture toughness of a material (taking into account the presence offlaws)using a few mechanical parameters generated from simple tests. One measure of toughness that is obtainable from LEFM is the strain energy release rate G. This parameter represents the strain energy released per unit length of crack growth and was developed for linear elastic materials where all energy released during crack propagation equals the surface energy of the newly formed surface (i.e. G = 2y). In many materials, however, energy is absorbed by crack tip plasticity (permanent deformation of the material at the crack tip) as well as by the formation of new surfaces during crack propagation. For materials in which plasticity effects are significant, the ./-integral technique provides a more accurate measure of toughness (see Broek, 1986). J is a measure of the change in energy per unit change in crack length (Rice, 1968). In purely elastic materials, J and G are equal; in plastic materials, J exceeds G. ./-integral values may be determined by:  (Rice, 1968)  Eq. 1.5.  Jc  The stress intensity factor K is another measure of fracture toughness and was developed to represent the highest stress intensity that a material can withstand in the presence of a crack. Although K is another parameter of LEFM, it may provide useful information in elastic-plastic materials and has been used to represent the fracture toughness of bone (e.g. Behiri and Bonfield, 1984, 1989; Bonfield, 1987) and the equine hoof wall (Bertram, 1984). A common shape for test 32  specimens used in detennining fracture toughness parameters is the compact tension (CT) geometry. As its name implies, these specimens are relatively small and are useful in characterizing properties of biological tissues which are not available in large sizes.  7. Mechanical properties of hoof wall tissue.  Using CT specimens, Bertram and Gosline (1986, 1987) conducted fracture tests on equine hoof wall. They found that toughness of the SM is a function of hydration and that specimens displayed highest fracture toughness at intermediate hydration levels (22.2 KJ m" at 75% RH; 2  Bertram and Gosline, 1987). For comparison, fracture toughness of bone ranges from 0.26 to 2.6KJm" (tested in air; Wright and Hayes, 1977). Interestingly, whole hoof wall is not evenly 2  hydrated. A hydration gradient exists from the inner to the outer portions, the innermost part of the wall consisting of about 33% water by weight and the outermost part about 20% (Leach, 1980). This implies that fracture toughness will vary throughout thickness of the wall. Bertram and Gosline (1987) also noted that specimens showed greatest resistance to crack propagation from notches applied parallel to the tubules (13.5 KJ m" at 100% RH; Bertram and Gosline, 1986). In fact, samples 2  with notches cut perpendicular to the planar orientation of intertubular material usually failed by means of crack diversion along the plane of the intertubular material (approximately 55 degrees to the tubule axis), suggesting that the intertubular material is the mechanically dominant feature of the wall. The compressive and tensile moduli (E and E,, respectively) of hoof wall are inversely e  proportional to water content (Leach, 1980; Bertram and Gosline, 1987, respectively). Although excessive dehydration compromises the ultimate properties of the wall (Bertram and Gosline, 1987), dehydration stiffens and hardens the hoof, providing resistance to abrasion. This may be an example of a mechanical compromise in the hoof wall. Leach and Zoerb (1983) found that E varies c  33  throughout the thickness of the wall and that for SM tissue under compression, £, > E> E-,. where e  the subscripts /, v, 1-e indicate lateral (circumferential), vertical and interior-exterior loading, respectively. They also found that the force-deformation curves of inner SM specimens began to deviate from linearity at much lower deformations than those of outer SM specimens. Since this portion of the curve is thought to indicate the point at which the a-helical arrangement of keratin microfibrils breaks down (Fraser et al. 1972), it appears that the inner wall is less stable than the outer wall. Douglas et al. (1996) documented both the tensile and compressive elastic modulus of the toe and quarters of the equine hoof wall. Their results agreed with those from Leach and Zoerb (1983), finding differences in.E and E ( ranging from approximately 1 GPa to 0.54 GPa from the outer wall t  c  to inner wall, respectively), and they also showed that these properties are conserved around the wall. Tensile strength in hoof wall is determined both genetically and environmentally (e.g. bedding and diet). Hardness, a measure of yield strength, is dependent on time of year (Buffa et al. 1992) and is probably the effect of a variation in moisture content. Two early mechanical studies conducted on the possible effects of diet on hoof wall longitudinal tensile and compressive strength (Goodspeed et al. 1970 and Butler and Hintz, 1977, respectively) yielded conflicting results; however, morphological and some mechanical properties of the wall are both affected by diet. Indeed, poor diet has been shown to result in the loss of tubule structure (Geyer and Schulze, 1994) and poor intercellular attachment; both traits are associated with a reduction in mechanical properties that are manifested as brittle hoof wall (Kempson, 1987, 1990).  8. The purpose of this thesis.  Through the course of evolution, more than one material has been utilized to provide fracture toughness for load-bearing skeletal elements. Indeed, antlers have similar functions to that of 34  keratinized horns, but are made of bone. Presumably, during the evolution of the hoof wall, bone was also available as an alternative material, yet the hoof wall evolved instead from the keratinized claw. Production of the wall from keratin seems at first unintuitive, considering that fully-hydrated bone is roughly 7 times stronger in tension than fully-hydrated hoof wall (see Currey, 1990 and Kasapi and Gosline, 1997, respectively); however, hoof wall material is approximately 6 times tougher than bone (see Bertram and Gosline, 1986 and Currey, 1984, respectively). It appears that strength is of secondary importance at the digit terminus where the probability of crack initiation is high. It is likely that the complex, hierarchical design of the wall is responsible for making it one of the toughest biomaterials known. Unlike many other biological composites whose mechanical and biological functions are intertwined (such as bone), the hoof wall offers a unique opportunity to examine an extensive hierarchical system whose mechanical role is uncoupled from any morphological demands of living systems (e.g. the housing of blood vessels and cells for reparation in bone). Since the hoof wall is a non-living part of the foot, it may be assumed that each component exists either to satisfy a mechanical demand or is the manifestation of manufacturing constraints. Although the fundamental mechanical principles underlying the success of biological hierarchical organization are understood, the hoof may serve as a model biological hierarchical system to further our understanding of the role of complex design in mechanical structures, aid in understanding the contribution of each level of multi-scale systems, and facilitate the development of advanced biomimetic structures. Just as initial studies of biomaterials have aided in directing the future course of material design, it is through continued investigation of these hierarchical structures that we may gain a greater understanding of how each level of organization contributes to the overall system. It is a major goal of the research in this thesis to decipher the role of morphological hierarchy in the mechanics of the hoof wall and add to the understanding of how hierarchical systems, in general, are capable of exhibiting desirable mechanical properties.  The following chapters are presented in the order in which the topics were investigated. Although intuitively one may feel that investigation of a hierarchical system should proceed from the smallest scale of morphology upwards, this is not the case here. Without knowledge of the mechanical behavior of the entire wall thickness, further investigation into the contribution of its components is hardly justifiable. As results from the thesis are presented, the logic of the sequence of experiments becomes apparent. Therefore, the second chapter begins with an investigation into the large-scale mechanical properties of the hoof wall (including specimens of the entire wall thickness and those of the inner, middle and outer thirds of the wall). Concomitant with these mechanical tests, the effects of viscoelasticity on the mechanical properties are also investigated. Hoof wall viscoelasticity (Landeau etal. 1983) is of mechanical interest, because this property has serious implications for a material that is loaded at different strain rates in situ. (Thomason et al. 1992). The morphological study of the third chapter was conducted to better understand the fracture results of chapter 2; tests of hypotheses generated as a result of the morphological findings were conducted with fracture tests also in this chapter. The fourth chapter attempts to resolve the longstanding question as to the function(s) of equine hoof tubules by examining possible roles of these enigmatic wall components. To better understand hoof wall design as a hierarchical system, the last experimental chapter documents the micro mechanics of the wall, including tensile tests of tubules, intertubular material and single cells. The last chapter discusses the relevance of all experimental chapters in terms of design for fracture control and the mechanical properties of the equine hoof wall.  36  CHAPTER 2: MACRO AND STRAIN-RATE-DEPENDENT MECHANICAL PROPERTIES  37  INTRODUCTION Most biological materials are neither purely elastic nor purely viscous in mechanical behaviour; instead, they show a combination of both and are hence termed viscoelastic. A consequence of viscoelasticity is mechanical strain rate sensitivity and a possible transition from a ductile or pseudo-ductile to brittle behaviour, suggesting a drop in fracture toughness with increasing strain rate. Hydration dependence on fracture toughness of hoof wall (Bertram and Gosline, 1987) is one manifestation of viscoelasticity and suggests the possibility for brittle failure of equine hoof wall at high strain rates. Reduced toughness could have serious implications to the horse since, as with most structural biomaterials, loading conditions are rarely static. Increased hoof wall loading rate is concomitant with an increase in animal speed; strain rates on the surface of equine hoof wall have been shown to vary between 0.02 and 1.7 strain s"' for a horse travelling from 1-6 m s" (Thomason 1  et al. 1992). Localized stress concentrations, which may result from impact onto an uneven substratum such as a rocky surface, are coupled with localized strain rates which will greatly exceed those observed on the surface of the wall. Failure may lead to infection and subsequent death of the animal. Although the mechanical effects of hoof wall viscoelasticity with loading rate may have significant consequences for the animal, they have not been previously investigated. In addition, although mechanical studies on the middle SM region have been conducted (Bertram and Gosline, 1986, 1987), the mechanical behaviour of the inner and outer regions, and the entire thickness of the SM have not yet been evaluated. This study quantifies fracture and tensile parameters of hoof tissue encompassing the entire SM and inner, middle and outer SM samples at full hydration to determine the effects of viscoelasticity and the consequence of differential tubule morphology on hoof wall mechanics.  38  MATERIALS AND METHODS 1. Strain-rale mechanical tests.  1.1 Tissue acquisition and preparation. Hooves from nine horses (Equiis caballus L.) were used in this study. Whole feet from horses of variable age and unknown physical condition were obtained from a local (Aldegrove, B.C.) slaughterhouse within a few days of death of the animal (animals were destroyed for reasons other than this study) and were disinfected in 0.02% benzalkonium chloride in distilled water for about lh before use. SM tissue from the toe region of the hoof wall was isolated using a band saw, and only this region was used in the study. Hoof wall tissue was then separated from the third phalanx (coffin bone) using a scalpel. Wall material in direct contact with the ground is mechanically inferior to the rest ofthe hoof (Bertram, 1984), therefore the distal-most 1 cm was discarded. The proximal-most 1 cm was also discarded as this area contains tubule-forming dermal papillae. Three types of test specimen were produced from wall material: compact tension (CT), tensile, and dynamic specimens (Fig. 2.1).  1.2. CT specimens. Hoof wall material from six horses were shaped into 35 CT specimens using a thin sectioning machine (Gillings-Hamco) which had been modified to act as a grinder by adhering waterproof sandpaper (Diamond Grit 180) onto a cutting wheel. A constant flow of tap water kept specimens cool and hydrated during the shaping process. Inner and outer portions of the wall were also ground smooth, removing the SI and SE; the gradual curvature of the wall at this region of the foot allowed flattening of these surfaces with minimal loss of SM tissue. Although a slight variability in specimen dimensions was unavoidable, all sides were parallel. Holes for clevis pins were made using a Maximat7 drill press. Specimen shape (Fig. 2. IF) followed ASTM guidelines for fracture toughness 39  Figure 2.1: (A) Front view of the equine hoof wall showing example positions from where samples were obtained; (B) sketch of a hoof wall sample showing cells forming tubules and intertubular matrix (after Bertram and Gosline, 1986); (C) a keratin intermediate filament, showing the concentric association of tetrameric a-helices; (D) tensile specimen (showing the VDA tracking segment or reference bar); (E) dynamic specimen; (F) CT specimen. All dimensions are approximate and in mm unless otherwise indicated, a, notch length; W, specimen width; L , reference bar; Z,,, parallel segment. K{  40  41  testing (ASTM, 1994c) as closely as possible; however, the morphology of the foot made some modifications unavoidable. Although specimen thickness was occasionally less than that recommended, the full thickness of the SM was used (9.8 ± 1.7 mm; pooled mean ± 1S.D). To simulate an in situ fracture condition to which the hoof may be regularly exposed, CT pieces were notched along the radial-longitudinal plane (parallel to the longitudinal axis of the tubules and across the wall thickness) using a band saw (0.6 mm thick blade), and the notch front was sharpened using a single edge razorblade with the aid of an attachment to the drill press. The graphical method used to determine the fracture toughness parameter./ was adapted from Landes and Begley (1971) and required that a number of specimens be produced with varying initial notch lengths. After preliminary testing, it was decided that only specimens with notch length (a) to specimen width (W) ratios below 0.65 could be used to determine./, because the stressfieldat the notch front of specimens with a/W ratios greater than this was thought to be influenced by the end of the sample. Completed specimens were hydrated in distilled water (with 0.02% sodium azide to prevent bacterial growth) at 4° C for at least 7 days. Testing was performed at full hydration after allowing specimens to equilibrate for 24 h at room temperature (approximately 20° C). Specimens obtained from each horse were equally divided between experimental groups.  1.3. Tensile specimens. Eight hooves from two horses provided material for 16 tensile specimens. Each experimental group received two specimens from each horse (one from a forelimb and one from a hind limb). Tensile specimen morphology (Fig. 2. ID) was based on dimensions recommended by ASTM standard E8M-94a (ASTM, 1994a); however, since the length of hoof columns was limited by the size of the hoof, the overall length was often less than that suggested. Specimen thickness was greater than that recommended in order to include the entire thickness of the SM. To produce specimens of uniform 42  shape, an aluminum template was clamped to a hoof column and the sample milled to shape. Holes for the loading pins were then drilled in appropriate positions. Inner and outer surfaces of the test specimens were carefully ground with the modified Gillings-Hamco apparatus, removing the SI, SE and any minor surface irregularities and flaws. A reference bar was drawn on the inner hoof face of each sample with a black wax pencil to act as a strain reference during the experiment. Completed specimens were hydrated in distilled water with 0.02% sodium azide at 4° C for at least 5 days. Testing was performed at full hydration after allowing specimens to equilibrate for 24 h at room temperature.  1.4. Dynamic 3-point bending specimens. Two 3-point bending dynamic test samples were obtained from different animals. Hoof strips were cut using the thin sectioning machine and then cut to appropriate width and length using a single-edge razorblade. Beams measured approximately 3 1020 mm and included material from the X  x  entire thickness of the SM.  1.5. Test protocol and data analysis. Slower strain rate experiments employed an Instron testing machine (model 1122) with a 500kg load cell. The cross-head speed was limited to 1.7x 10" m s"'; therefore, a large (3.15 m total 2  height) pendulum was constructed to determine mechanical properties at higher strain rates (impact). Four cross-head rates were used in each test type: 1.7><10", 1 . 7 x 1 0 ° , 1.7><10' and 2.5 ± 0.3 m s" 5  (mean ± 1S.D.) for CT tests, 8 . 3 x 1 0 °  2  1.7x10°, 1.7x10° and 3.9  tensile tests [corresponding to tensile strain rates, e, of 1 . 6 x 1 0 °  1  ± 0.4 m s" (mean ± 1S.D.) for 1  ± 0.2><10° 3.2x10"  2  ± 0.5x 10°,  0.33  ± 0.04, and 70 ± 5 s" (mean ± 1 S.D.), respectively]. Although the strain rates recorded by Thomason 1  etal. (1992)  encompassed a more limited range, this test range was believed to encompass the range 43  of strain rates to which an animal may subject the hoof, including local rates experienced at the ground contact surface and at a crack front during high speed locomotion.  1.5.1. CT tests. Instron fracture tests were conducted in mode I crack mouth opening (see Broek, 1988) in distilled water using the clevis system shown in Fig. 2.2. To ensure that the Instron reached the desired speed before loading the specimen, the upper clevis mount was slotted to permit 1.5 cm of cross-head travel before the system was engaged. Data from the Instron were collected by a computer using PC software (Labtech Notebook 6.1.2); load (kg) and time (s) data were converted to force (N) and displacement (m), respectively (Fig. 2.3A) using spreadsheet software. The initial low stiffness (toe) region of the curve was the result of inherent system compliance and was excluded from data analysis by running a linear regression through the linear portion of the curve, extrapolating to the zero load level and using the regression line over the initial nonlinear range (Fig. 2.3B). The experimental design for fracture tests at impact loading was similar in principle to that for slower test rates, with the weighted, swinging end of a pendulum providing the energy to move the 'cross-head' (impact T-bar, Fig. 2.4) at high velocities. A specimen was mounted horizontally in clevis grips; the front and back clevises were attached to a custom-built force transducer and the impact bar, respectively; the latter was supported by a collapsible arm. Specimens were regularly sprayed with distilled water. Displacement was measured with two devices simultaneously: (1) an optical displacement transducer (ODT; Optek Technology Inc. model OPB700; Carrollton, Texas) mounted directly to the front clevis and (2) a goniometer positioned at the pendulum pivot to provide an indirect measurement of displacement. Displacements recorded from the ODT were used in the first (approximately 25%) part of the experiment, and goniometer recordings were used for the remaining part when optical measurements became unreliable. The arm of the pendulum was pulled 44  Figure 2.2: Exploded diagram of the clevis loading system with a CT specimen. Specimens were anchored to the load cell at the top of the Instron; cross-head movement is downward. Buffer slots in the upper clevis allowed the cross-head to reach speed before load was applied to the specimen. The use of pins allowed realignment of components during an experiment.  45  46  Figure 2.3: (A) Typical trace from a CT test (1.7x 10" m s"\ a = 11.65 mm where a is notch length). The rise in load at the end of the trace was the result of specimen reorientation during the experiment. The arrow indicates the critical point as defined in the text. (B) A linear regression was run through the initial linear portion of the curve. The inverse slope of this line gave the specimen compliance (m N"'); the regression line replaced the initial 'toe' of the curve during integration to produce an energy curve which was scaled for a 10 mm thick specimen (C). Zero displacement in C is the intercept of the linear regression and the x-axis in (B). The arrow indicates the scaled energy value which is plotted as a closed symbol in Fig. 2.5A. 5  47  0.000  0.005  0.010  0.015  0.020  Displacement (m)  48  0.025  0.030  0.035  Figure 2.4: Exploded diagram of the impact pendulum transducer system. A force transducer was constructed with a foil strain gauge affixed to the front and back of the beam. An optical displacement transducer was mounted to the clevis on the upper left and a white reflective surface attached to a bracket on the upper right clevis. A U-shaped pendulum striker made contact with an aluminum impact bar at the end of the system. Rubber padding was added to dampen resonances.  49  Direction of pendulum travel  50  back such that the weighted end was raised approximately 0.6 m. Force and displacement data were collected with a digital oscilloscope (Data Precision, model Data 6000A) and were transferred to a computer for analysis. Determination of the ./-integral required quantification of a critical displacement. This was defined in this study as the point at which any further notch opening resulted in crack propagation. In CT specimens whose notch tip undergoes a large degree of plastic deformation (crack tip rounding) prior to crack propagation, this point is nearly impossible to determine from forcedisplacement records. Therefore, CT samples fractured at a cross-head rate of 1.7x 10* m s" were 5  1  video-taped during testing to determine an average failure load. The outer face was filmed since crack extension appeared to initiate in the outer portion of the SM. The load at failure was determined by referring to the corresponding load-displacement traces at the point of visible extension of the notch and calculating the failure load percentage of maximum load. The maximum load was defined as the first peak in load prior to any reduction in the load, regardless of any subsequent increase. This criterion for determining the critical displacement was used for all strain rates. Each force-displacement record was integrated to an arbitrary point beyond failure to obtain an energy curve (Fig. 2.3C; specimen thickness varied slightly between samples, therefore energy values were scaled for a 10 mm thick sample). Since samples tested at a particular cross-head rate had different notch lengths, a series of energy curves was produced (one curve for each initial notch length). Byfindingthe scaled energy value at a particular displacement for each sample, a scaled energy versus notch length curve was produced (Fig. 2.5 A). A series of these curves was generated at incremental cross-head displacements encompassing all critical displacement values, and a linear equation wasfitto each curve. The J-integral was determined by finding the negative value of the slope of the regression line for the critical displacement and dividing by 10 mm. Rather than generating one of these curves for each critical displacement, a function wasfitto the coefficients of 51  Figure 2.5: (A) Energy (scaled for 10 mm thick specimen) as a function of notch length for the 1.7xl0" ms"' CT tests at 3.5 m m displacement (y = -98.12x + 1.39, P<0.0001, r = 0.99); the filled symbol is the value indicated by the arrow in Fig. 2.3C. The ./-integral at this particular displacement would be the negative value of the slope (/.) of the regression line, after normalization for a 10 mm thick specimen. A series of these lines was generated at a number of cross-head displacements, encompassing all critical displacement values. (B) Coefficients (or slopes) of these curves were plotted against displacement to provide an expression which yielded the ./-integral, after normalization for a 10 mm thick specimen (y = 40.8 - 39708x, P<0.0001, r = 1.00). Thefilledsymbol represents the coefficient from Fig. 2.5A. Estimates of the ./-integral may be obtained directly from Fig 2.5B by finding the critical displacement on the x-axis, determining the corresponding value of coefficient b and dividing by 10 mm. 2  s  2  52  53  these curves (Fig. 2.5B) to provide an expression which yielded the ./-integral (after normalization for a 10 mm thick specimen). The stress intensity factor AT was found using the equation provided by ASTM standard E39990 (ASTM, 19946): €1  Eq.2.1.  K=(-^-)Ka/W)  tw A  whereP is the critical load (N), / is specimen thickness (m), W is the specimen width (m), and where: „  (2+a/^(0.886+4.64a/W-13.32a/^ + 14.72a /« -5.6a /^ ) /  / W A  AalW)—  2  2  3  /3  4  4  Eq. 2.2.  (\-alWf  12  Initial circumferential modulus, E for CT tests was found by rearranging the equation provided by ic  ASTM (19946) for CT specimens under plane strain conditions to obtain:  E =^-^-q{a/W)  Eq.  jC  2.3.  where C is the specimen compliance (nr N"') and vis Poisson's ratio, the ratio of lateral strain to longitudinal strain, and where: q(a/W) =  [19.75/(1  -a/W) )] 2  [0.5 + 0.\92(a/W)+  \3S5(a/W) 2  2.9\9(a/W)  3  + \.S42(a/W) ] 4  Eq. 2.4.  The above expression does not contain the thickness term /, since compliance values were already normalized to specimen thickness. Poisson's ratio was estimated at 0.4 from preliminary tests that produced values ranging from 0.38 to 0.46. 54  1.5.2. Tensile tests. Tensile specimens were mounted in the Instron using similar devices as in the CT tests (refer to Fig. 2.2). Tests were conducted in air so specimens were constantly sprayed with distilled water during longer experiments. Displacement (AL) values were obtained directly from the specimen by filming the marked reference bar (L ) (see Fig. 2.1) with a video camera (Panasonic model WVn[  BL200) which interfaced with a video dimension analyser (VDA; 1PM model 303). Outputs of the Instron and VDA were transferred to a computer where load (kg) and displacement (m) values were converted to stress, o (N m'; o = F/A where F is force and A is the original cross-sectional area 2  0  0  over which the force was applied) and strain, e, (AL/L where L is the length of the marked reference 0  0  bar in the unloaded condition; mean 25 mm), respectively. Ultimate data were not used from specimens that failed at any area other than the parallel region, L of the test specimen. ]  Owing to the short duration of impact tests, it was not possible to determine strain by filming a reference bar drawn on the specimen. Instead, strain was determined indirectly by measuring the movement of the T-bar (i.e. cross-head) of the impact apparatus with the ODT and goniometer. A full description of this procedure is outlined in the Appendix. Resonances were avoided by carefully designing each component of the pendulum system; however, a few resonances remained: the 14 kHz primary resonance of the force transducer, one at approximately 4.1 kHz in CT tests and one at about 2.5 kHz in tensile tests. The lower two resonances were probably generated from resonance of the test specimen at impact. These resonances were present in all respective impact tests, but since test durations were approximately 10 ms and 6ms for CT and tensile tests, respectively, they could befilteredout quite easily with minimal signal distortion using a fourth-order, zero phase shift Butterworth's digitalfilter(Winter, 1990) with a 1.0kHz and 2.0 kHz cut-off frequency implemented in the software. A low-passfilterwithin the Instron limited the frequency response of the system and 55  consequently affected load data from higher test rates (i.e. tests conducted at cross-head rates of 1.7xl0" and 1.7><10" m s") for both CT and tensile tests. Data were corrected using a custom3  2  1  designed computer program which reversed the filter effect. Displacement data from highest strain rate (70 s") tensile tests also required similar correction as a result of the limited frequency response 1  of the VDA system (see Appendix for description of procedures).  1.5.3. Dynamic mechanical tests. Dynamic tests employed a three-point bending test apparatus similar to that previously described in Katz and Gosline (1992). Tests were conducted under distilled water and a downwards pre-load of about 30 g was applied to the beams. Small amplitude vibrations at frequencies ranging from 0.04 to 200 Hz were applied to the beams; storage modulus, E', and the viscous loss function, tan<5, were determined as described previously (Katz and Gosline, 1992).  2. Mechanical  tests on inner, middle and outer regions.  2.1. Tissue acquisition and preparation. Equine hooves for this part of the study were obtained from two freshly killed horses of unknown age and mass (destroyed for reasons other than this study) and disinfected as described above. Wall tissue was roughly sectioned using a bandsaw and refrigerated at 4°C in distilled water with 0.02% sodium azide to prevent bacterial growth. Samples were used within nine days of the death of the animal. Procedures for mechanical tests followed those described above, with the following modifications. Blocks of hoof tissue running the full length of the hoof wall and spanning the entire SM (see Fig. 2.6) were cut circumferentially into three strips of approximately equal thickness using a water-cooled thin sectioning machine (Gillings-Hamco). Material loss was minimized by using very 56  Figure 2.6: (A) Front view of the equine hoof wall showing example positions from where columns of tissue were obtained. (B, C) Columns of hoof wall with portions removed to display relative sizes and orientations of compact tension (CT) and tensile specimens, respectively. (D) CT specimen. (E) Tensile specimen. All dimensions are in mm. a, notch length; W, specimen width; diam., diameter; rad. radius.  57  58  thin (0.35 mm) circular saw blades.  2.2. CT tests. Strips of hoof wall were cut to appropriate dimensions for CT tests (Fig. 2.6D) using the thin sectioning machine and were notched using a razor blade affixed to an attachment on a drill press. A total of 65 specimens were produced (22 inner, 31 middle and 12 outer wall) from the four hooves of one animal and were notched upwards along the radial-longitudinal plane (Fig. 2.6B). a/W ratios ranged from 0.23 to 0.51, from 0.10 to 0.53, and from 0.13 to 0.55 for inner, middle and outer wall specimens, respectively. These samples were produced to test for differences in mechanical properties through the wall thickness. All tests were performed at room temperature with samples immersed in distilled water using the test apparatus described by Bertram and Gosline (1987). Samples were tested  at a cross-head speed of 8.3 10" m s' using the Instron with a 50 kg load cell. Data were collected X  5  1  at 10 Hz using Labtech Notebook and were processed with spreadsheet software. CT specimen preparation followed the procedures outlined above. The procedures used to calculate K, the ./-integral and E- were as described above. Poisson's yC  ratio was estimated as 0.40, 0.45 and 0.47 for inner, middle and outer hoof wall, respectively (data not shown). By filming the notch front and corresponding force records for some of the CT tests, it was determined that the critical displacement (the point at which crack extension is initiated) was the point on the load-displacement curve where the first decrease in load was observed. Used CT test specimens were prepared for the scanning electron microscope byfirstdehydrating the tissue with a standard ethanol series. After twofinalwashes in 100% ethanol for 1 h each, specimens were critical-point dried and sputter-coated with gold. Samples were mounted onto aluminum stubs with SPI silver paint and viewed on a Cambridge Stereoscan 250T scanning electron microscope.  59  2.3. Tensile tests. Samples for tensile tests were milled to shape (Fig. 2.6C,E) using a brass template that served as a guide for the milling machine. Tests were conducted with the Instron using a 50 kg load cell, and specimens were held with pneumatic grips. Strain was measured directly with a strain gauge displacement transducer mounted to the front of each specimen. Very fine hypodermic needles (23G1)  were attached to the ends of the transducer to prevent slippage between the transducer arms  and the specimen. Slight needle penetration acted to concentrate stress; therefore maximum data were not usedfromspecimens that failed at the needle marks or near the grips. Tests were conducted on 22 fully hydrated specimens (eight inner, seven middle and seven outer; obtained from all four hooves of an animal) at room temperature with the Instron cross-head rate of 8.3 x 10" m s" (corresponding 5  to a tensile strain rate of 2 . 0 x 1 0 °  ± 0.3x10°  1  s"; mean ± 1 S.D.). Yield strengths were determined 1  using the offset method suggested by ASTM standard E8M-94a (ASTM, 1994a); in these tests, an offset strain of 0.5% was arbitrarily chosen. After mechanical testing, water contents were determined. Although specimens were tested at 100% relative humidity (RH), bulk water may accumulate in the medullary cavity of tubules and distort water content measurements. Therefore, specimens were dehydrated slightly in a 97% RH environmental chamber before weighing to ensure that no bulk water would be present (i.e. water content measurements are for tissue at 97% RH). Samples were then dehydrated at 100°C for 5 days, and water content was calculated as (wet mass minus dry mass)/dry mass.  60  RESULTS 1. Strain-rate mechanical tests  1.1. Tensile and bending parameters. Sample tensile tests for each strain rate are shown in Fig. 2.7, and mechanical test results are summarized in Table 2.1. Total energy, and maximum stress (o ) showed a significant increase with u  increasing strain rate. Although initial longitudinal modulus, E rose with strain rate, after a 'yield' ix  region where the slopes of the stress-strain curves showed a rapid drop, the curves had similar slopes. From lowest to highest strain rates, E increased about threefold (see Fig. 2.8A), and total energy lL  (Fig. 2.8B) and o (Fig. 2.8C) rose about twofold. As expected for a viscoelastic material, hoof wall u  became stiffer with increasing loading rate, however, there was no indication of a transition to brittle behavior. Instead, the material became stiffer, stronger and capable of absorbing more energy before failure as loading rate increased. There were no statistically significant differences in the mean maximum strain e (Fig. 2.8D) with increasing strain rate. u  The determination of E from CT tests was intended to serve as a validation of CT test iC  methodology. If fracture tests are valid and conducted on strain-rate-independent, isotropic materials (e.g. metals), thenis; from CT and tensile tests should be equal. Although a direct comparison is not made between values from the two tests, Fig. 2.9A shows that the trends at lower strain rates were similar. Differences in size between tensile and CT samples, test direction and the specific design of CT specimens made it difficult to assign a particular strain rate to CT tests; however, from lowest to highest cross-head rates, E increased twofold. Uncertainty in CT E values as the result of ic  ic  estimating Poisson's ratio is low, as using the highest measured value of 0.46 would lower E by lC  2.3% and the lowest measurement of 0.38 would raise E- by 6%. The apparent discrepancy between uC  tensile and CT E values at slower strain rates (compare Tables 2.1 and 2.2, see Fig. 2.9A) is probably {  due to differential test directions and/or because smaller CT samples will experience considerably 61  Table 2.1: Average initial modulus, total energy, maximum stress and maximum strain for tensile tests at all four strain rates. Values of are given in parentheses adjacent to mean values; numbers below mean values in brackets are ±1 S.D.  Strain rate  Initial longitudinal modulus, E (GPa)  Total energy (MJ IT)")  Maximum stress (MPa)  Maximum strain  0.28 (4)  5.4 (3)  17(3)  0.45 (3)  [0.07]  [1.1]  [3]  [0.05]  0.32 (4)  5.6(3)  19(3)  0.43 (3)  [0.05]  [2.3]  [5]  [0.13]  0.47 (4)  8.5 (3)  25 (3)  0.50(3)  [0.09]  [1.0]  [2]  [0.04]  70  0.85 (4)  9.7 (2)  30.9 (2)  0.51 (2)  [5]  [0.16]  [0.5]  [0.4]  [0.08]  iL  1.6xl0-  3  [0.2xl0' ] 3  3.2xltT  2  [0.5x10" ] 2  0.33  [0.04]  3  62  Table 2.2: Average J-integral, stress intensity factor and initial modulus for compact tension tests at all four cross-head rates. Numbers in parentheses are ±1 S.D.  Cross-head rate (m s") 1  1.7xl0"  J-integral, J (kJ rrf) 2  Stress intensity factor, K (MN m") 32 /  Initial circumferential modulus, /T (GPa) ic  11  0.71  0.38  (2)  (0.22)  (0.03)  13  1.0  0.49  (4)  (0.3)  (0.09)  12  1.4  0.82  (3)  (0.5)  (0.13)  2.5  12  1.4  0.76  (0.3)  (3)  (0.3)  (0.11)  5  1.7x10°  1.7xl0'  2  63  8  9  9  9  Figure 2.7: Typical tensile stress-strain curves for each of the four strain rates used in this study and a representative test at 75% relative humidity (RH) from Bertram (1984). Although the initial modulus rose with increasing strain rate, the shapes of the curves in the post-yield region are similar.  64  65  Figure 2.8: Tensile test scatter plots of (A) initial longitudinal modulus, E (y = 5.15x 10 x , PO.0001,7^=0.825), (B) total energy 0=7.70* 10 x , P<0.05, ^=0.388), (C) maximum stress (y=2.47xl0 x , P<0.01, r = 0 . 6 3 4 ) and (D) maximum strain plotted against strain rate. Although Instron cross-head speed was constant between samples at a specific test rate, strain rate variation in the marked VDA tracking segment caused data points at a particular test rate to deviate slightly on the x-axis. Maximum strain was not affected by strain rate latest; P>0.05, r =0.10). Each point represents one sample; dotted lines are 9 5 % confidence intervals for the regression line. s  ix  6  7  0H589  2  66  00 6 5 5  0109  IO"  3  IO"  2  10"'  10°  10'  10  2  Strain rate (s")  IO-  1  K)"  2  IO"  1  10°  10'  Strain rate (s")  1  1  67  IO  2  Figure 2.9: (A) Scatter plot of initial circumferential modulus, E- versus cross-head rate for CT tests (squares). The solid regression line (y=\. 10 10 x , P<0.0001, r =0.690) excludes impact data. The regression linefromtensile tests (dashed line), is superimposed for comparison. (B) Scatter plots of storage modulus, E\ versesfrequencyfor two three-point bend dynamic tests (regression line for upper data set: >-=2.05xlOY' , P<0.0001,/- =0.988; regression line for lower data set: .y=1.62xl0 x , P<0.0001, r =0.920). Two frequency ranges were tested successively on each beam: 0.04-2 Hz and 1-200 Hz; about 200 points were collected from each range. lC  x  9  0104  H2  8  0095  2  68  2  2  Strain rate (strain s" ) IO" IO" IO' 10° 10' IO IO 3  10 8xl0  9  crj  fe  8  -  1  2  A  1  I  1  2  I  •  I  3  I  B  -  *3 -o  o  8  6xl0  ^  4xl0  3 4xl0 o  8  <•  • 2xl0  io  8  8  8  in  8  S .2  y  B  8  3  10 8xl0 6xl0  £  -  • 1  I  1  I  Ei —  CT tests Tensile data  4  3  I  2xl0  8  o  -*-»  GO  I  10  8  10" IO" IO" IO" IO"' 10° 10 5  c  2  1  IO" IO' 10° 10 10 10 10 2  1  1  2  Frequency (Hz)  Cross-head rate (m s") 1  69  3  4  higher strain rates than larger tensile specimens tested at similar cross-head rates. In addition, tensile and CT tests were conducted on specimens obtained from different horses and hence inter-animal variability may be a factor. Typical datafromthe middle SM of hoof tested at 75% RH (Bertram, 1984) are included in Fig. 2.7 to illustrate the possibility of a continuing trend towards increasing stiffness and maximum stress with increasing strain rate. This comparison is possible because the mechanical effects resulting from the removal of a low molecular weight solventfroma polymer-solvent system (e.g. dehydration of proteins) and the effects of increasing strain rate are interchangeable (Ferry, 1980). Therefore, the apparent trend of CT E at higher strain rates (Fig. 2.9A) probably does not represent a true plateau; ic  instead, these CT E- impact test data could be underestimated as the result of over smoothing. This uC  is further suggested by the continuing rise in E with strain rate, seen in both tensile and dynamic tests. t  Regression exponents for E from tensile and CT tests are 0.109 and 0.064, respectively. If impact uL  data in CT tests are excluded from thefit,the new exponent (0.104) is much closer to that from tensile tests. Using the new regression, E^ for impact CT tests should average approx. 1.21 GPa. c  Datafromtwo dynamic tests are shown in Fig. 2.9B. Storage moduli E\ regression exponents (0.102 and 0.095) are indicative of strain-rate-dependence, and fall well within the 95% confidence intervals of Fig. 2.8A for tensile tests (exponent 0.109). The agreement of modulus trends from three independent strain rate tests and one hydration study (Bertram, 1984), further suggests that a plateau does not exist over the strain rates used in this study, and that E from CT impact tests are uC  unreliable. The similar trend of CT E data from slower tests with that from tensile and dynamic tests {  indicates that CT methodology is correct. Direct comparisons between dynamic test data and tensile test data must be carried out with caution. Here, an attempt is not made to shift the x-axes of the two types of experiments to compare moduli directly since the two x-axes differ. If a rough comparison is made, E' values from dynamic 70  tests appear to be lower than E values from tensile tests, however, E' is very sensitive to iL  measurement inaccuracies. Inter-animal and inter-sample variability may also contribute to observed differences. The viscous loss function tan <5 averaged 0.145 and was independent of vibration frequency (pooled data /-test; P>0.05, ^=0.003). This result indicates a constant level of energy loss due to viscous processes over the range of frequencies tested in this study.  1.2. Fracture parameters. Stable fracture was observed in all CT tests. A region characterized by a smooth decline in stiffness followed the initial linear region (see Fig. 2.3). Considerable crack tip rounding and plastic (or pseudo-ductile) deformation were visible in video recordings of the notch front of specimens tested at the slowest cross-head speed. The maximum load usually followed a critical point that signified the start of crack growth. The critical load for CT tests at 1.7><10" m s" was 98.9±0.8% 5  1  (mean ± 1 S.D.) of the maximum load. Beyond this point, the force-displacement traces became irregular as the initial notch slowly lengthened into a crack and new surfaces were formed. Fig. 2.10 shows data from fracture tests. The fracture toughness parameter J was unaffected by strain rate (/-test; P>0.05), suggesting that hoof wall does not pass through a brittle failure transition over the range of strains anticipated in situ. Average J was 12±3 kJ m' (pooled mean 2  ±1S.D.).  The stress intensity factor K followed a trend similar to that of E- with mean values doubling v  from the slowest cross-head rate to impact tests (Fig. 2.10B). This estimate of fracture toughness implies that hoof wall becomes tougher with increasing test rate. If impact data are excluded from the regressionfit,the effect of strain rate is even greater. Neither fracture toughness parameter suggests a compromise in toughness (or a transition to brittle failure) with increasing test rate, contrasting with 71  Figure 2.10: CT scatter plots of (A) J-integral and (B) stress intensity factor, K (y= 1.40x1 o x , P<0.0001, r^O.401) plotted against cross-head rate for CT tests. J-integral was not affected by strain rate (Mest, P>0.05, ^=0.0005; one-way analysis of variance, P>0.05). Each point represents one sample. Dotted lines are 95% confidence intervals for the regression line. The dashed regression line in (B) is a fit which exclude impact test data (y=T.82xl0 x , 6  6  P<0.001,r =0.445). 2  72  00903  00578  73  results from fractography.  1.3. Fractography. Scanning electron micrographs (SEMs) of fracture surfaces from two CT specimens conducted at 1.7x 10" and 2.5 m s are shown on Fig. 2.11A and Fig. 2.11B, respectively. The 5  _1  notched surface appears smooth and is visible in the upper right corner of both figures. Curvature of the crack front in Fig. 2.1 IB is an artefact of specimen preparation required for viewing in the scanning electron microscope. Surfaces of specimens fractured at impact were generally smoother than those broken at lower strain rates, implying a more brittle mode of failure at impact, but this difference has not been quantified. Crack propagation was generally parallel with tubules and in the plane of the notch in the outer and inner regions of the SM. In these regions, the crack appeared to favour a path along tubule-intertubular 'boundaries', often completely separating tubules and intertubular matrix during fracture. The path of crack growth in the middle region of the SM was dramatically different than that in the inner or outer regions. Cracks characteristically travelled across the tubule axis, apparently following cellular planes of the intertubular material. Tubule pull-out was evident at all cross-head rates; however, the degree of pull-out was highest in specimens from slowest tests (compare Fig. 2.11C,D). It was not possible to determine from higher-magnification SEMs whether cracks followed intercellular boundaries or an indiscriminate path through cells and cell interfaces, although fracture surfaces of various textures have been observed, suggesting that cracks travel both through cells and (periodically) along cell-tocell interfaces. Note, however, that toughness values were obtained just at the (critical) point of crack initiation and that, although surface pattern and texture is consistent in thefirstfew millimeters of crack growth, most of the surface was formed well after the critical point of the experiment.  74  Figure 2.11: Scanning electron micrographs of fracture surfaces of specimens tested at slowest and fastest test rates. (A) and (C) are low (10x) and high (lOO) magnification scanning electron micrographs, respectively, of fracture surfaces from two samples tested at 1.7x 10" m s"; (B and D ) fracture surfaces of two impact (2.5 m s") test specimens at the same respective magnifications. Scale bars equal 1mm in low-magnification and 100 pm in high-magnification photographs. The notched surface appears smooth and is visible in the upper right corner of A and B. Crack growth follows similar patterns at both extreme test rates; the crack followed the tubule axis in outer and inner regions, whereas crack propagation favoured a path at an angle to tubules in the middle region of the stratum medium. Surfaces of impact specimens were much smoother than those tested at slower rate (compare C and D). Curvatures of notch fronts are artefacts created during the dehydration process required for viewing in the scanning electron microscope. 5  1  75  1  76  2. Mechanical tests on inner, middle and outer wall specimens.  2.1. Tensile parameters. Typical stress-strain curves for inner, middle and outer specimens of the hoof wall SM are shown in Fig. 2.12. The initial longitudinal tensile modulus or stiffness, E-^ increased from 0.30 to 0.56 GPa L  progressing from the inner to outer regions of the wall (see Table 2.3). A multiple-comparison analysis showed a statistically significant difference in E^ between inner and outer regions (P<0.05; L  Student-Newman-Keuls test). DatafromCT tests provided the initial modulus in the circumferential direction,^; in all regions, E^ was lower than E (P<0.01 for all; .-test). Note, however, that the c  iL  contribution of inter-animal variability to these differences has not been determined. E^ of the inner c  region was significantly lower than that of the middle and outer regions; there was no significant difference between the middle and outer regions (P<0.05 for all; Student-Newman-Keuls test). Beyond the initial linear portion, tensile test stress-strain curves of specimens from all regions were characterized by a yield. The average stress at which yield occurred in the outer wall was 1.5 times that in the inner wall (Table 2.3). After the yield region, the shapes of the curves were similar. Although care was taken to ensure that data from tests in which premature failure occurred were rejected, ultimate (maximum) data were less reliable than E , since failure could have been initiated xL  by flaws resulting from specimen preparation; ultimate data from eight specimens were rejected as a result of failure at the grips or at the site of strain-gauge attachment. There were no significant differences in total energy, maximum stress or maximum strain between specimens from different regions of the wall (P>0.05; ANOVA). To determine whether the differences in E could be accounted for by simple hydration iL  effects, initial modulus data were plotted as a function of water content (Fig. 2.13,filledcircles) and compared with Bertram and Gosline's (1987) data for middle region SM tissue (Fig. 2.13, open circles). Although it was unspecified in the publication, the middle region was tested in the study (J.E. 77  Table 2.3: Mechanical datafromtensile and compact tension tests on samples from inner, middle and outer regions of the equine hoof wall. Data are presented as mean ±1 S.E.M. Values with similar symbols are statistically different from one another (P<0.05, Student-Newman-Keuls test). Long. = longitudinal, circ. = circumferential.  Initial long, modulus, E Region (GPa)  { L  Initial circ. modulus, E (GPa)  Total energy (MJ m")  Yield stress (MPa)  8.0±1.6 (N=4)  xc  Inner  0.30±0.03* (N=8)  0.18±0.01 (N=22)  Middle  0.43±0.06 (N=7)  0.31±0.01  0.56±0.05* (N=7)  0.31±0.02 (N=12)  Outer  JV  J  (N-31) v  Maximum stress (MPa)  Maximum strain  6.5±0.4 (N=8)  §  24±4 (N=4)  0.53±0.05 (N=4)  5.9±1.0 (N=5)  7.5±0.1  +  17±2 (N=5)  0.44±0.05 (N=5)  7.5±1.3 (N= 5)  9.5±0.5 (N=7)  23±2  0.44±0.06 (N=5)  3  78  (N=7) §t  (N=5)  Figure 2.12: Representative tensile stress-strain curves for inner, middle and outer regions of fully hydrated equine hoof wall. The initial stiffness increased progressing from the inner to outer region of the wall, although curves were similar beyond the 'yield' region.  79  3.0xl0  7  Inner  _| 0.0  I  I  I  I  I  0.1  0.2  0.3  0.4  0.5  Strain  80  |_ 0.6  Figure 2.13: Double-logarithmic scatterplot of initial longitudinal modulus E versus water content W . Open circles are estimated from Bertram and Gosline (1987),filledcircles are data from this study. Average water content at 100% RH was estimated from an absorption isotherm for each region (data not shown). The regression line is for the Bertram and Gosline (1987) data;E = 2.84xl0 W; . iL  Q  u  xli  iL  81  82  Bertram, personal communication). To determine water content at 100% RH, data were extrapolated from absorption isotherms (data not shown) for each of the three regions. Estimated water contents at 100% RH were 48%, 41% and 35% for inner, middle and outer samples, respectively. Data from the present study fell very close to the regression line for Bertram and Gosline's (1987) data, suggesting that water content alone could account for the differences in initial longitudinal stiffness.  2.2. Fractography. Scanning electron micrographs of CT fracture surfaces from representative specimens are shown in Fig. 2.14. Fracture patterns from the three wall regions agreed with the pattern observed for specimens of the entire wall thickness. Fig. 2.14A shows the fracture surface of an inner CT test specimen. A notch was introduced up the radial-longitudinal plane and is visible in the lower left of the specimen (notch surfaces in all specimens are indicated by asterisks). The advancing crack deviated in two distinct directions (towards the upper right) in this specimen; one along the tubule axis (inner-most portion) and the other along a path at an angle to the tubule axis (outer-most portion). This fracture path is more easily seen in the illustration in Fig. 2.15, in which each test specimen is shown in a sample location within the hoof wall and then enlarged to show detail. The upper specimen in Fig. 2.15B illustrates thefracturepath observed in the inner region sample. The specimens in Fig. 2.15B are illustrated in their correct positions through the wall thickness. In Fig. 2.14B, the notched surface of a specimen from the middle region is barely visible on the lower right side of the micrograph. Here, the crack deviated towards the circumferential axis of the wall (towards the upper left hand side of the micrograph), passing through tubules as it progressed. This crack reorientation is seen as a twist of the fracture surface illustrated for clarity in Fig. 2.15B. Fig. 2.14C shows thefracturesurface of an outer hoof wall specimen. Here, the crack propagated from the upper left to lower right of the specimen, along the tubule axis (see Fig. 2.15B). 83  Figure 2.14: Scanning electron micrographs of compact tension test specimen fracture surfaces. (A) Inner, (B) middle and outer. Notches were applied parallel to the tubule axis and run through the thickness of the wall sample; they appear as the smooth surface marked with an asterisk in each photograph. In A, the innermost portion is on the upper left, the outermost portion is on the lower right. In B, the outermost portion is on the upper right, the innermost portion is on the lower left; the notch surface is not clearly visible on the lower right. Here, the notch was redirected circumferentially and radially. In C, the innermost portion is on the lower left, the outermost portion is on the upper right. Scale bars equal 1 mm.  84  85  Figure 2.15: (A) Illustration of the equine hoof wall and sample compact tension (CT) specimens of the toe region photographed in Fig. 2.14. In B, notch surfaces are indicated by white areas, and fracture surfaces by dark gray areas. (B) Inner, middle and outer specimens from Fig. 2.14A, B, and C, respectively. Stars indicate portions shown in Fig. 2.14. Fracture paths were determined by alignment and quantity of the dominant material (tubular or intertubular) in the respective regions. The illustration for the inner region is the mirror of that shown in Fig. 2.14A since the latter was obtained from the other side of the midline.  86  87  2.3. Fracture parameters. The ./-integral parameter suggested decreasing toughness progressing outwardly (Table 2.4). The inner region of the hoof wall showed a statistically significant higher toughness than the middle and outer regions (Student-Neuman-Keuls test, P<0.05). Using the stress intensity factor K measure of fracture toughness, the inner and outer regions were statistically similar, but the middle region of the wall was significantly tougher than the inner and outer regions (Student-Newman-Keuls test; PO.05). No decline in fracture toughness is evident with the gradual softening of the tissue towards the inner regions of the wall. Furthermore, differences between the toughest and weakest regions of the wall using J and K are relatively small (29 and 31%, respectively). These differences may not exist at in situ hydration levels since, if optimal hydration levels for fracture toughness exists for the outer and inner regions (as it does for the middle region; Bertram and Gosline, 1987), then the in situ J for each region could be higher and more similar.  88  Table 2.4: Fracture toughness datafromcompact tension tests of the equine hoof wall notched in the radial-longitudinal plane. Data are presented as mean ±1 S.E.M. Values with similar symbols are statistically different from one another (P<0.05, Student-Newman-Keuls test).  J-integral (kJ m")  Stress intensity factor, K (MN irf )  Inner SM  7.8±0.4 * (N=22)  0.47±0.03 (N=22)  Middle SM  6.4±0.2 (N=31)  0.68±0.02** (N=31)  Outer SM  5.5±0.4* (N=12)  0.55±0.04* (N=12)  Region  2  §  §  89  3/2  +  DISCUSSION 1. Initial stiffness.  The observed rise in E with increasing strain rate is indicative of a viscous or viscoelastic x  material. As strain rate increases, the time for molecular movement is limited, thereby requiring a higher stress for a given strain. This stiffening will offer the hoof wall increased resistance to deformation during higher speed gaits. E^ values were generated from CT tests to verify the trend of tensile test E with increasing c  iL  strain rate and to check the validity of fracture toughness calculations using parameters obtained from CT tests. Although data were not directly comparable, the plateau in CT E data for impact tests iC  made further testing necessary. Dynamic bending tests were therefore conducted to resolve this issue. These tests also show a trend of continuing stiffness increase with increasing strain rate, further suggesting that a plateau does not exist. Therefore, impact E from CT tests are probably uC  underestimates of the true values, possibly as a result of data over-smoothing. The effect of strain rate on E over the range tested is not nearly as great as the effect of {  dehydration. Bertram (1984) found a 36-fold increase in E for equine hoof wall tested from 100% {  to 0% relative humidity; this study shows only a threefold increase over five orders of magnitude of strain rate. Bertram's (1984) findings of a continued trend of increasing E-, provides further confidence that a plateau does not exist over the range of test rates. To act effectively as a load transfer element, the hoof wall must be stiff enough to routinely withstand large loads without undergoing large-scale or irreversible deformation. It has been documented here and in other studies (Leach, 1980; Douglas et al. 1996) that a gradient of stiffness exists through the wall thickness. This gradient is due to the proximity of the different regions to the source of moisture (the vascularized tissues adjacent to the stratum internum and coronary border) and, as seen in this study, to the properties of the keratin in each region. 90  Although the hoof wall must be stiff enough to support incurred loads, differential mechanical demands on the tissue through the wall thickness may require particular mechanical properties in specific regions. The outer wall likely encounters a variety of mechanical insults from many directions. To resist crack initiation and minimize abrasion, this region must be both strong and stiff (i.e. hard). Loading of the inner wall, however, is more predictable since loads become diffuse before reaching this region. Here, loads are ultimately transferred (primarily by shear and tension) to the collagenous, dermal suspension system, which links the hoof wall to the bony skeleton. To minimize the strain differential (and potentially high stresses) which resultsfroman abrupt transition in modulus from one load-bearing element to another, the two stiffnesses must be similar. Consequently, the inner wall tissue is highly hydrated, to approach the stiffness of the dermis. A stiffness gradient is also necessary through the hoof wall thickness, because high stresses would result at the interface between the stiff outer wall and the soft inner wall. Note that the stiffness values for fully hydrated specimens are underestimates of the true in situ stiffnesses. Bertram and Gosline (1987) noted a 36-fold increase m£ ffom fully hydrated to completely dehydrated specimens of middle equine hoof wall. To fully tL  appreciate the magnitude of this stiffness gradient, we may estimate the in situ wall stiffnesses. Since specimens from inner, middle and outer wall placed in environments with the same relative humidity differ in water content, the proportion of IFs to IF-associated proteins (non-ordered molecules) changesfromone region to the next, the protein constituents may vary, or both of these may occur. Although protein constituents vary between the SI and SM (Grosenbaugh and Hood, 1992), it is unknown whether these differences exist through the SM thickness. Fig. 2.13 suggests that differences in E through the wall thickness are due to water content {  and not morphological or biochemical differences. Assuming that this is true, we may use estimates of water content from Leach's (1980) data and the curve from Bertram and Gosline's (1987) data to predict the in situ E . From Leach (1980), water content estimates for inner, middle and outer iL  91  specimens are 33.1%, 23.5% and 13.9%, respectively. Using the equation from Bertram and Gosline's (1987) data, E will increasefrom0.30 to 0.66 GPa (a 2.2-fold increase), from 0.43 to 1.2 x  GPa (a 2.8-fold increase) andfrom0.56 to 3.0 GPa (a 5.4-fold increase) for inner, middle, and outer regions, respectively. This predicts an in situ stiffness differential of about 2.3 GPa through the wall thickness. Stiffness differences measured for the three wall regions are contrary to expectations based on current knowledge of hoof wall design, as tubule morphology does not correlate with initial longitudinal stiffness. The inner region, which has relatively large tubules with IF aligned close to the tubule axis (Nickel, 1938a,Z>) should be considerably stiffer than the middle region, which has smaller tubules with IFs aligned at steeper angles to the tubule axis. This is not the case. These results show that the innermost third of the SM is almost half as stiff as the outer third at the same RH and would probably be equally stiff at the same water content (refer to Fig. 2.13). Note, however, that initial stiffnesses across the tubule axis are considerably lower than those along the tubule axis (Table 2.3) and also show a tendency towards higher stiffness progressing outwards. Although ultimate properties are also expected to correlate with tubule morphology, no significant differences were found in maximum stress and maximum strain between regions of the wall (refer to Table 2.3). Yield stress data further show that tubule morphology and mechanical properties are unrelated in the wall; the yield stress of the inner region was lower than that of the middle region.  2. Ultimate tensile properties and hoof wall viscoelasticity.  The maximum strain, e , is unaffected by strain rate as the material apparently fails when u  molecules become fully extended and covalent bonds are broken. The extension to maximum alignment will therefore be strain-rate-independent. The observed increase in strength (o ) with u  increasing strain rate is characteristic of viscoelastic materials. As strain rate increases, viscous 92  resistance rises, resulting in a higher stress for a given strain. A larger number of molecular interactions of the viscous, protein-matrix component leads to an increase in the energy absorption of the system. The rise in stiffness and in maximum stress consequently lead to an increase in the total energy input. Using total energy as a measure of toughness, equine hoof wall material appears to become tougher with increasing loading rate; so as a horse accelerates, increased skeletal loading (Pratt and O'Connor, 1976; Bartel et al. 1978; Schryver et al. 1978) is met with a concomitant rise in tensile properties, allowing the hoof to absorb more energy before failure. It is likely that the evolution of the equine hoof wall involved exploitation of the natural mechanical behaviour of viscoelastic solids; the abundance of lipids in the stratum externum probably reflects a need to maintain a certain level of viscosity through hydration. Hoof wall material was fully hydrated during all tests, an unusual condition for hoof wall. In situ, a gradient of hydration exists in the hoof wall: high to lowfrominner to outer hoof, and high to low from proximal to distal regions (Leach, 1980). In this study, the outer region of the wall was hydrated to a greater extent above its in situ level than the inner region (data not shown), and it should be noted that the mechanical effects of viscoelasticity in equine hoof wall peak at an intermediate level of hydration (Bertram and Gosline, 1987). Mechanical strain-rate sensitivity observed here for hoof wall keratin, has been noted in many other biological materials including wool (Danilatos and Feughelman, 1979), feather (Bonser and Purslow, 1995), compact bone (Crowninshield and Pope, 1974; Currey, 1975; Carter and Hayes, 1976; Wright and Hayes, 1976; Behiri and Bonfield, 1984; Fisher et al. 1986; Evans et al. 1992) cranial bone (Wood, 1971), antler (Currey, 1989) and wood (Nadeau et al. 1982). The conserved biochemical attributes of hard a-keratin tissues allow generalizations from small-scale mechanical properties obtained from wool. The viscous components of wool are likely the matrix proteins (Chapman, 1975) intimately associated with water molecules; the fibrous phase appears to contribute 93  initial elasticity. A mechanical yield region of declining stiffness precedes a post-yield region characterised by a gradual rise. Microfibrils (the fibrous phase) are likely responsible for the initial (up to a few percent strain) linear or Hookean behavior. Further extension induces a yield resulting from an apparent molecular breakdown of the fibrous phase, whereby a portion of the a-helical fibers are transformed to P-sheet structures (Bendit, 1960). On the basis of data from wool, Feughelman (1994) suggested that this transition is concomitant with a movement of microfibrils closer to one another. Microfibrils eventually displace water molecules such that globular matrix proteins are squeezed by approaching microfibrils. Extension of matrix proteins is believed to be responsible for the increase in stiffness in the post-yield region, irrespective of water content. As with bone, equine hoof wall consists of numerous levels of morphological hierarchy and should not be considered as a simple composite. Comparisons with the mechanical behavior of simpler keratins (such as wool) must therefore be done with caution. In addition, the tubuleintertubular matrix relationship is not quite analogous to a hollow-fiber reinforced composite, as the materials composing both tubule and intertubular matrix are presumably similar, with only intercellular fiber orientation differing between the two components. Further studies are necessary to determine the mechanical properties of each component and its possible contribution to the hoof.  3. Hoof wall fracture toughness.  To obtain consistent estimates of fracture toughness for a particular material, the sample must be subjected to plane strain (as opposed to plane stress) conditions. Plane strain is a state in which principle strains are confined to one plane (i.e. minimal contraction across the thickness of the specimen). Plane strain conditions occur when specimen thickness / is greater than 2.5(K I o ) (see 2  lc  y  Broek, 1988) where the subscripts lc represent the critical value of AT in mode I loading and_y signifies yield. Yield is usually defined as the point of intersection of the stress-strain curve and a line 94  representing some deviationfromthe initial slope of the curve. Using this criterion for a viscoelastic material is non-sensical because deviationfroman initial slope in these materials does not necessarily represent irreversible material change. We may, however, define a yield point for these tests as the stress corresponding to the lowest instantaneous E value. Using this method, the minimum thickness for plane strain conditions in equine hoof wall ranges from approximately 10-11 mm for the highest and slowest strain rates, respectively. Although merely an estimate, this result implies that the condition for plane strain has not been violated in this study. Plane strain conditions are required for testing because toughness values will represent a minimum, conservative estimate of toughness for a particular material (plane stress conditions will inflate fracture toughness). It could, however, benefit an animal to utilize a structure which is thin enough that plane stress conditions exist, yet thick enough to withstand large loads; the equine hoof wall and hoof walls from smaller animals may be designed such that plane stress conditions exist in vivo to exploit this phenomenon. Although wall specimens appear to have met the thickness requirement of plane strain conditions, estimates of the stress intensity factor K must be considered as candidate values, K , and Q  not K . A non-Hookean stress-strain curve eliminates the possibility of determining a reliable lc  representative ofK and also excludes the use ofK = (EG)' (see Broek, 1988) to confirm the LEFM A  lc  results, since an appropriate value of E cannot be determined. However, since K values were determined using the same procedure on all cross-head rates, relative values of K are still useful. Bertram (1984) reported a value for K of 1.74 MN m' for hoof wall tissue tested under m  similar conditions. This is over twice the values of 0.71 MN m' for larger specimens tested at a 3/2  comparable rate, and 0.68 MN m for middle SM specimens tested at the same rate. This difference m  is not due to a violation of the conditions for plane strain since middle SM samples were of similar dimensions to their specimens. The increase in stress intensity as a function of cross-head rate (Fig. 2.10B) is expected since K is directly proportional to the critical load P. Since P is sensitive to over95  smoothing, as with E^ , K values at impact are also likely to be underestimates. A linear regression c  fitted to data that excludes impact values provides a coefficient of0.0903, suggesting that K at impact in CT tests should average approx. 2.0 MN m" . Using AT as a fracture toughness parameter, it 3/2  appears that equine hoof wall becomes tougher as loading rate increases, a favourable attribute to the horse, since increasing loading rate in vivo resulting from a change in gait would probably be concomitant with a rise in load. Large-scale extensibility coupled with gross crack tip rounding (data not shown), suggests that crack propagation is accompanied by extensive plastic deformation in equine hoof wall. For such materials, the use of a LEFM parameter such as G to represent the strain energy release rate is inappropriate. The ./-integral technique employed here overcomes limitations of LEFM in characterising fracture toughness and is therefore a more suitable parameter than G. In addition, J values are probably insensitive to possible errors resulting from over smoothing, as these values were obtained from relative changes in energy. There are, however, limitations with the use of J and although it is widely accepted as the most versatile single-parameter measure of fracture toughness, these values must still be considered to be estimates. The method in which J was determined used energy differences from specimens with varying notch lengths at the point just prior to stable crack growth. This method assumes selfsimilarity, whereby the applied notch resembles the cracked surface in both orientation and texture. In wall specimens, stable fracture proceeded at an angle to the tubule axis in the middle SM. Fortunately, this pattern was generally observed in specimens at all test rates such that although absolute values of toughness may not be as accurate as desired, relative values are still valid. Another required condition which was unavoidably violated with the use of this material was isotropy. Examination of the fracture surfaces in Fig. 2.11 reveals a 'recognition' of the tubular and intertubular components of the hoof wall by the propagating crack and that, at the micro scale, crack 96  progression seems to be sensitive to test rate. That is, the smoother surfaces of impact test specimens imply a less pseudo-ductile and a more brittle behaviour of failure. On the micro scale, path shortcutting should reduce the energy input during fracture as less surface area is created. However, no reduction in energy was statistically evident in these tests; the rise in energy absorption with increasing strain rate (seen in tensile tests) may counter a slightly less pseudo-ductile mode of fracture at higher strain rates, resulting in a constant J value over the range of strain rates tested in this study. Confidence in J may be found with the notch length insensitivity of J over the a/W range used (t-test; P>0.05 for all tests). This is of paramount importance since if J is to be a valid material parameter, it must represent the toughness of materials regardless of size or shape (within the size limitations discussed earlier). Bertram and Gosline's (1987) J value of 11.9 KJ irf for middle SM hoof samples 2  tested in a similar manner agrees well with the slower test, verifying the repeatability of these tests. Using J, these results suggest that there is no effect of strain rate on fracture toughness. In contrast, K implies an increase in fracture toughness with increasing test rate. Recall, however, that K is an LEFM parameter. In linear elastic materials, the stress intensity factor and strain energy release rate will be more tightly coupled, since changes in ultimate stresses will reflect a concomitant change in energy. In viscoelastic materials where the stress-strain curve may be far from linear, the relationship between ultimate load and energy input is often decoupled. By simply representing the critical stress intensity at the crack tip, K ignores the large energy absorption capacity characteristic of many viscoelastic materials. Consequently, the contribution of crack tip plasticity to fracture toughness (which may be ignored when quantifying the fracture toughness of generally linear elastic materials such as bone), is not recognized by quantifying toughness using K. The J-integral method is more sensitive to the mechanical behavior of the material, and is therefore likely to be a more suitable representation of fracture toughness. Regardless of which parameter is accepted as representing fracture toughness, these results show that toughness is not compromised by the 97  viscoelastic nature of the material at high strain rates.  4. Functional significance offractography.  Recall that, in all but the outer-wall specimens, cracks were redirected away from the initial notch plane. Therefore, the K and J values presented here (Table 2.4) are not accurate representations of fracture toughness along the initial notch plane, but rather more closely reflect the toughness of the relative planes of weakness along which the cracks followed. It must be stressed that the favored planes of crack growth are only relative planes of weakness, and that favored planes of crack growth are only relative planes of weakness, and these results suggest that the energy required to propagate cracks along these planes is much higher than the fracture toughness of bone to which the hoof wall is indirectly attached (Behiri and Bonfield, 1984). It may be assumed that the resistance to crack propagation along the initial notch plane will be much higher. To understand the significance of the mechanical properties of a biomaterial, one must consider the use of that material by the organism. Since it is virtually impossible for an organism to produce indestructible materials or structures, some means of repair or replacement is necessary. Unlike bone, which is a living tissue that can undergo adaptive remodelling and repair, the hoof wall is composed of non-living tissue which cannot be repaired. Instead, tissue is continuously generated at the proximal end at a rate of about 1 cm per month (Butler and Hintz, 1977; Buffa et al, 1992) to replace an equal amount of material lost distally. The wall must therefore continuously abrade from the distal surface in order to maintain proper hoof shape. It appears that a plane of relative weakness exists parallel with the ground contact surface to provide a crack diverting mechanism and to allow for necessary wear (Bertram and Gosline, 1986). Fractography of CT specimens agrees with the findings of Bertram and Gosline (1986) for the middle region of the stratum medium, with cracks following a path along the grain of the intertubular material instead of along tubules as one would 98  expect based on the loading conditions of the fracture test. The deviation from this pattern in inner and outer regions is surprising and difficult to explain functionally, although a few possibilities exist. Recall that three morphologically distinct types of tubules have been identified in the equine hoof wall SM: inner type I, middle type II and outer type III tubules (Nickel, 1938a; see also Leach, 1980). Fracture results suggest that cellular orientation of the intertubular material in inner and outer  regions may differ from that previously found for the type middle region (Bertram and Gosline, 1986). Alternately, these regions may have a higher density of tubules, the intracellular fiber  orientation of which may determine the fracture path. It may simply be that a plane of weakness is  either non-existent in inner and outer regions or that it is not as prevalent as that in the middle region. Tests conducted on specimens isolatedfromeach of these three regions (data not shown) suggest that the observed pattern of fracture is not the result of plane stress conditions on the lateral surfaces at the notch front. Further investigation is required to determine if a plane of weakness exists in inner and outer hoof wall SM. The overall pattern of crack propagation in CT tests suggest that the hoof wall is designed as a unidirectionally, hollow-tubule reinforced ply with no obvious lamellae per se. This design forces the crack to follow a more tortuous route than if the crack were to travel in one plane. This process presumably utilizes substantially more energy, making the hoof tougher. Hooves often show surface (outer) cracks running up the hoof, parallel to the tubule axis. At present, there is no information about the precise three-dimensional orientation of keratinfibersin any region of the hoof wall, the knowledge of which is required for a full understanding of the mechanical properties of this material. The following chapter is directed towards the development of a more complete model to explain the mechanical behavior of this complex, biological composite.  99  CHAPTER 3: DESIGN COMPLEXITY AND FRACTURE CONTROL  100  INTRODUCTION In chapter 2, it was found that hoof wall test pieces fractured in a manner that was inconsistent with our current knowledge of hoof wall morphology. Specimens which incorporated most of the thickness of the wall and were notched along the hoof radial-longitudinal plane, fractured like a trilaminar ply. Unlike man-made plies, however, distinct lamellar boundaries were not evident in fractured hoof wall specimens. As noted previously (Bertram & Gosline, 1986), the fracture path in the middle region was redirected across hollow tubules, the dominant components of the SM microstructure. Thus, in the middle region, the intertubular material forms a barrier to the propagation of cracks up the hoof wall. However, crack propagation in the inner and outer regions of the wall did appear to be controlled by tubules. In these regions, a notch initiated in the radial-longitudinal plane formed cracks which generally continued running in the plane along the tubule axis, suggesting that the function of the tubules may vary depending on their position through the wall thickness. Morphological over-simplification of tubule morphology by Nickel (1938a) Wilkens (1964) has led to a present knowledge of wall microstructure which is insufficient to provide a satisfactory explanation of hoof wall mechanics. Using microscopy, it is possible to develop a complete model of the hoof wall which may aid in the understanding of the mechanisms that confer the wall's favorable mechanical properties. Composite theory predicts that the stiffness of afiber-reinforcedcomposite will depend upon the orientation of the fibers relative to an applied stress, and upon the mechanical properties and volume fractions of the fiber and matrix phases (Wainwright et al. 1976). Therefore, knowledge of keratin fiber orientation is of paramount importance in understanding the mechanics of the wall, and should predict tensile and fracture behavior. It is hypothesized that IF orientation is correlated with fracture properties of hoof wall and, based on fracture results from chapter 2, it is predicted that overall IF orientation should vary across the wall. Polarized light microscopy is used here to determine the 101  orientation and degree of order of IF molecules, and CT tests are used to determine the fracture behavior of the wall. The following study is the first three-dimensional documentation of the IF organization in cells of both the tubule cortex and the surrounding intertubular material of the equine hoof wall toe region. It also documents all aspects of tubule morphology and combines findings with mechanical data from tests conducted on isolated regions of the hoof wall in order to link form and function. These results suggest that the complex design of the structure is a reflection of an equally complex loading pattern. The intertubular material appears to play a major role in crack redirection and skeletal load transfer, while the roles of the tubular components is dependent on their position through the thickness of the wall.  102  MATERIALS AND METHODS 1. Tissue acquisition and preparation.  Equine hooves were obtained from 4 freshly killed horses of unknown age and mass (destroyed for reasons other than this study) and disinfected in 0.02% benzalkonium chloride for approximately 1 h. Wall tissue was roughly sectioned using a bandsaw and refrigerated at 4°C in distilled water with 0.02% sodium azide to prevent bacterial growth. Keratinous tissues are highly resistant to microbial attack, so histological specimens could be stored in this manner for months without degradation. Samples were used within 90 days after the death of the animal.  2. Mechanical tests.  Procedures for mechanical tests followed those described in chapter 2, with the following modifications. Blocks of hoof tissue from the toe region running the full length of the hoof wall and spanning the entire SM (Fig. 3.1), were sectioned as shown in Fig. 3.1 A, B using the water-cooled thin-sectioning machine. Material loss was minimized by using very thin (0.35 mm) circular saw blades. CT and tensile tests utilized hooves from one animal.  2.1. Compact tension tests. Strips of hoof wall were cut to appropriate dimensions for CT tests (Fig. 3.1C) using the thinsectioning machine and were notched using a razor blade affixed to an attachment on a drill press. Fourty-two test pieces were produced from the rightfronthoof of one animal. To test for inter-animal variability and thereby permit comparisons with test results from chapter 2, seven pieces were obtained from the middle hoof wall region and were notched upward along the radial-longitudinal plane (a/W=0.23-0.60). Thirty-five pieces were produced that spanned the wall thickness from an adjacent block to test for possible crack diversion mechanisms. Twelve specimens were notched 103  Figure 3.1: (A) Front view of the equine hoof wall showing example positions from where columns of tissue were obtained. (B) A column of hoof wall with portions removed to display relative sizes and orientations of compact tension (CT) specimens. (C) CT specimen. All dimensions are in mm. a, notch length; W, specimen width.  104  105  upwards along the circumferential-longitudinal plane along the circumferential-radial plane  (a/W=0.20-0.65),  (a/W=0.26r0.61)  eleven were notched inwards  and twelve were notched inwards along the  radial-longitudinal plane (o/W=0.23-0.59). All tests were performed at room temperature with samples immersed in distilled water using the test apparatus described by Bertram and Gosline (1987).  Samples were tested at a cross-head speed of 8.3  x 10"  5  m s" using an Instron mechanical 1  testing machine (model 1122) with a 50 kg load cell. Data were collected at 10 Hz using Labtech Notebook and were processed with spreadsheet software. For a full explanation of CT specimen preparation, refer to chapter 2. The procedures for determining the stress intensity factor K, the J-integral, the initial circumferential modulusE and the initial radial modulus E are outlined in chapter 2. A Poisson's ic  lK  ratio of 0.45 was used for CT specimens which spanned the wall thickness, since the notch was introduced along the middle region. The critical displacement was defined as the point on the loaddisplacement curve where the first decrease in load was observed. Used CT test specimens were prepared for the scanning electron microscope (SEM) as described in chapter 2.  3. Histology.  The majority of specimens used for microscopy were taken from the lateral toe region of the right front foot of three horses. The wall was arbitrarily sectioned distally into three levels of equal length: a, b and c (Fig. 3.2). It was also divided radially (through the wall thickness) into six arbitrary regions of equal thickness: la, Ib, Ha, lib, Ilia and Illb. Strips of tissue were sectioned perpendicular to the tubule longitudinal axis (i.e. perpendicular to the outer wall surface) approximately 5-8 pm thick using a microtome. Specimens were also obtained from the heels and quarters of one hoof, to qualitatively document the morphology around the wall. All sections for light microscopy were observed without staining. 106  Figure 3.2: Axes and angles as defined in this study. (A) Illustration of the hoof wall showing the three levels defined in the text (a, b and c). Samples used for determination of the orientation of intermediatefilaments(IFs) were obtained from the lateral toe region of the right front foot, whereas longitudinal sections were obtainedfromthe medial toe region of the right front foot. (B) Illustration of a block of hoof wall defining the stationary tubule longitudinal axis, L, and the two non-stationary axes, R (radial) and C (circumferential). Angles 0 (in the C-R plane) and (p (in the illustrated hemisphere) are also shown with positive and negative assignments as indicated, and the C-R plane is cp = ±90°. (C) Scanned 20pm thick ToluidineBlue-stained section (sectioned orthogonal to the tubule longitudinal axis) of the hoof wall showing the lamellar, inner stratum internum with associated dermal tissue and the stratum medium (SM), which was subdivided into six regions (la to Illb) of equal wall thickness from the inside to the outside of the wall. The stratum externum is an extremely thin layer and is usually not present in samples. The scanned image was slightly altered in a small area at the lower left corner of the section using software to remove a microtome knife mark. (D) Side view of the hoof wall from the front foot, illustrating the rearward tilt of the wall.  107  108  4. Definitions of axes and angles.  The axes as defined in this study are illustrated in Fig. 3.2: the stationary, longitudinal, tubule axis L, and two non-stationary orthogonal axes, the radial axis R, and the tangential or circumferential axis, C. Tubules run along the length of the wall, parallel to the outer surface. Since the wall tilts back by approximately 40° from vertical in the toe region (of the front foot), the L axis here lies approximately 40°fromvertical (Fig. 3.2D). The R axis represents the radial axis of the foot, running perpendicular to the outer surface of the wall, and is non-stationary since there is more than one radial axis; the C axis lies tangential to the outer surface of the wall (and is therefore also non-stationary). The azimuthal angle theta, 0, is measured from the R-L plane and is in the plane of section (C-R plane). If observed along the R axis from the inside to the outside of the wall, fibers oriented to the left of the R-L plane are considered positive andfibersangled to the right are considered negative. In this manner,fiberorientations from -90° to +90° encompass all possible values of 0. An angle cj) defines the deviation from the L axis. When observed radially from the inside to the outside of the wall,fiberstilting upwards are defined as negative whereas those tilting downwards are positive; the C-R plane is at (p=90° (a 1 ° slope upwards from this plane is -89°, 1 downwards is 89°; refer to 0  Fig. 3.2B).  5. Three-dimensional orientation determination using the universal stage.  A universal rotating stage is a high-precision accessory for light microscopes equipped with plane-polarized light optics and is used to determine the three-dimensional orientation of ordered molecules without requiring sectioning in orthogonal planes. Positioning was determined by rotating a specimen within and out of the plane of the microscope stage tofindthe angle of extinction. This occurred when the primary axis of ordered molecules was oriented parallel to microscope axis. In this study, a Leitz UT 5 universal stage (angular resolution ± 1 °) was mounted to the rotating stage of 109  a Leitz Orthoplan-Pol polarizing microscope (see Canham et al. 1991). Extinction angles were determined on specimens magnified 400 times, allowing resolution of IF orientation in areas approximately 1pm. 2  The universal stage was capable of rotating through an arc of ±58°, so that fiber angles in some areas were not measurable. Therefore, sections were also cut at 45° to the C-R plane (i.e. d>=45°), and the orientation found in these sections was converted to the aforementioned angular references by first finding cp using: cp = arccos (sinT sinA)  Eq. 3.1.  T = arccos {[ tan(A - [ 0' - (90 - A)])]/tanA} + 45  Eq. 3.2.  where  A = arccos(sin0'sincp')  Eq. 3.3.  and 0' and cp' are analogous to 0 and cp, but 0' is the angle from the N-S axis (the N-S axis extends from the observer towards the back of the microscope) and cp' is the angle relative to the microscope axis. 0 was then found by: 0 = arcsin [( sincp' sin0')/sincp]  Eq. 3.4.  Sections along the R-L plane that did not require angular corrections were also produced.  6. Circularly polarized light microscopy.  Plane-polarized light is useful in determining the axial alignment of ordered molecules; however, there are drawbacks to using this illumination technique. Regions where molecules are aligned parallel or perpendicular to the plane of polarization appear dark. Therefore, to produce images that show only orientation of molecules relative to the plane of section, photographs of hoof wall samples were taken with circularly polarized light. This technique produced images in which the lightest areas indicate molecules close to the plane of section and darker areas show molecules 110  oriented more towards the axis of the microscope; areas which were not birefringent (such as the background) appeared black using both circularly and plane-polarized light optics.  7. Scanned images.  Pixilated images were produced by scanning photographic negatives of histological samples with a Kodak RFS 2035 Plus film scanner at 1000 dots per inch (dpi). Digital images were processed using a Macintosh PC and arranged using Adobe Photoshop 3.0 software. One image of the entire SM and SI was obtained by producing a 20 pm thick specimen that was stained with toluidine blue (in distilled water with 1% sodium borate) for 3 min, placed in 100% ethanol overnight and then mounted in a projector slide. The slide was then scanned at 2000 d.p.i. with the Kodak scanner and the image processed by the PC (see Figs 3.2C, 3.4A). Tubule dimensions were measured from hoof wall specimens sectioned along the C-R plane, by digitizing pixilated images with a PC videoframe-capturingprogram (V'for Windows 3.0) and then processing point coordinates using a spreadsheet. Images were generated using a video camera (Panasonic model WV-BL200) mounted on the polarizing microscope and interfaced with a Matrox PIP-1024framegrabber. Tubules were approximated as elliptical in cross section, so that only major and minor axes dimensions were necessary to estimate cross-sectional area. The dimensions of tubules from different regions were tested for significant differences using an ANOVA.  Ill  RESULTS 1. Morphology of the hoof wall toe.  Circularly polarized light optics proved very useful in characterizing both general and specific aspects of hoof wall morphology. This illumination technique revealed not only gross morphological changes through the hoof wall thickness, but also fine-scale design at the cellular level. Fig. 3.3 is an image of a non-stained cross-sectional sample from region Ilia illuminated using this technique. Medullary cavities appeared dark in the centers of the tubules and were usually devoid of cellular material, but occasionally they contained irregularly positioned cellular matter incapable of supporting load. Overlaid in Fig. 3.3 are tracings of cell boundaries identified from a second image of the same section illuminated with bright-field optics. Inner, middle and outer cortical lamellae types are labeled as a, b and c, respectively. There are clearly differences in shape and size between the cells of the tubule cortex and thosefromthe intertubular material. These differences are probably due both to the orientation of the pancake-shaped cells within the wall and to slight changes in cell morphology. Also visible is the intimate relationship between cells of the tubule and intertubular material. Note the brightness of the intertubular cells above and below the tubules (indicated by asterisks in Fig. 3.3) contrasted with the mottled appearance of the intertubular material on either side (indicating a less regular pattern of IF organization). Tubule morphology, intertubular material organization, and the relationship between the tubule and intertubular material were dependent on the position through the wall thickness. Complexity and variability in design, however, were best exemplified in tubule morphology.  1.1. Tubule morphology. Cells of the tubular cortex were organized generally into concentrically arranged lamellae, where each lamella was composed of one layer of cells (see Fig. 3.3). In cross-sectional samples 112  Figure 3.3: Circularly polarized light photograph of a tubule and associated intertubular material from region Ilia (see Fig. 3.2C). Overlaid are cell boundaries traced from a second image of an unstained section which was illuminated with non-polarized light. Inner, middle and outer tubule cortical lamellae types are indicated as a, b and c, respectively. The arrow indicates a cell in which there is a change in helix direction; asterisks show general areas of ordered intermediate filament (IF) alignment closer to the plane of section. For clarity, not all cell boundaries are shown. Scale bar, 50 pm.  113  114  Figure 3.4: Hoof wall tubule composite diagram. (A) High-magnification image of Fig. 3.2C; (B) pixilated circularly polarized light microscope photographs. Areas with intermediate filaments (IFs) oriented out of the plane of section appear dark, light areas havefibersoriented closer to the plane of section. (C) Schematic illustration of cross-sections of tubules showing average size and shape of tubules, and the number and relative thicknesses of cortical lamellae of the tubules from each region. Each cell layer is represented by one lamella. (D) Threedimensional reconstructions of tubules showing IF orientations of each cortical lamella. Each layer of helical cylinders represents one cell layer and, although relative lamella thicknesses are correct, the cylinders merely serve to represent the helical direction of IF molecules.  115  Dermal Tissoe  Stra Int&rriu  )  C  100 microns  US flegiop II  in  Region-Ilia  Region  116  D  viewed under circularly polarized light, these lamellae were characterized as one of three types: bright, innermost cortical lamellae which were usually one or two cell layers thick (a in Fig. 3.3), more numerous middle lamellae which appeared dark (b in Fig. 3.3), and outer, bright cortical lamellae consisting of approximately 2-3 cell layers (c in Fig. 3.3). In Fig. 3.3, the inner cortex has two lamellae, the middle cortex has approximatelyfivelamellae and the outer cortex is composed of approximately four lamellae. To avoid confusion, the inner, middle and outer tubule lamellae will be referred to as inner, middle and outer type, thereby distinguishing these areas of the tubule cortex from the inner, middle and outer regions of the SM. An outer cortex was not clearly distinguishable in tubulesfromregions la and Ib. Although this outer cortex appeared to be present in these regions, its extensive association with the adjacent intertubular material implied that this material was not generated by dermal papillae, but instead was probably formed by cells at the coronary border. Cortical lamellae differed not only in appearance under circularly polarized light, but also in cross-sectional thickness (Table 3.1). Inner-type mean lamellar thickness ranged from 5.1 to 7.5 pm depending on wall region, and showed statistical differences in thickness between tubules through the thickness of the wall (PO.00T, ANOVA). The thicknesses of middle- (9.9 pm) and outer-type (13.5pm) lamellae were not statistically different between tubules from different regions (P>0.05, ANOVA). Although lamellar thicknesses were generally constant, tubule size was dependent on position in the wall. This resulted from a change in the number of cortical lamellae in tubules from different regions (Table 3.2). Tubulesfromregion Ib were largest, averaging 0.046 mm in whole-tubule (i.e. 2  cortex plus medullary cavity) cross-sectional area; the smallest tubules averaged 0.018 mm and were 2  found in region Ha near the middle of the wall. Tubule shape was also dependent on position through the wall thickness. A weak trend towards relative widening along the C axis was evident within the tubule cortex of one animal, whereas the medullary cavity consistently increased along the 117  Table 3.1: Average tubule cortical lamellae thicknesses from the six regions of the equine hoof wall defined in this study. Based on appearance under polarized light, cortical lamellae were defined as either inner, middle or outer type. Data are presented as mean ± 1 S.E.M. Values in each column with similar symbols are statistically different from one another (ANOVA; P<0.001, Dunn's method).  Tubule Cortical Lamellae Type Outer (pm)  Inner (pm)  Middle (pm)  la (inner)  6.0±0.4 (7V=28)  9.5±0.5 (AK30)  Ib  6.4±0.3 (7V=27)  f  9.8±0.5 (7V=27)  -  Ila  6.9±0.3 (7V=25)  9.9±0.5 (/V=26)  15.2±1.1 (7V=4)  lib  5.1±0.3 (7V=33)  10.5±0.7 (/V=32)  11.9±0.7 (7V=8)  Ilia  5.5±0.3* (yV=32)  9.6±0.5  14.5±0.6 (yV=14)  Region  Illb (outer) Mean  t§  t§  (N=32)  9.9±0.7  7.5±0.7 (7V=51) _  (N=S\)  13.3±1.3 (7V=51)  9.9±0.3  13.5±0.9  (N=\9S)  118  _  (N=ll)  Table 3.2: Average number of tubule cortical lamellae from samples from the six regions of the equine hoof wall defined in this study. Based on appearance under polarized light, cortical lamellae were defined as either inner, middle or outer type. Data are presented as mean ±1 S.E.M.  Tubule Cortical Lamellae Type Inner  Middle  Outer  la  1.8±0.1 (N=3l)  7.2±0.5  _  lb  1.4±0.1  8.2±0.5  (#=30)  (#=30)  1.2±0.1  4.4±0.3  2.3±0.1  (#=35)  (#=35)  (#=35)  lib  1.2±0.1 (#=41)  3.4±0.2 (#=42)  2.4±0.1 (#=42)  Ilia  1.3±0.1 (AMI)  4.4±0.2 (#=41)  2.5±0.1 (#=41)  Illb  2.8±0.2  3.3±0.2  3.2±0.2  (#=55)  (#=55)  (#=55)  Region  Ha  (#=33)  119  -  circumferential axis from 37.1 um in the innermost region to 69.0 um in the outermost region of another animal (Table 3.3). Innermost tubules from region la were the most circular in cross-section, with an average major axis to minor axis ratio of 1.15 (Table 3.3). Progressing outwards, tubules became more elliptical in cross-section; the outermost Illb tubules had an average ratio of 1.57. Note, however, that the axis ratio is higher than the CIR ratio in tubules from regions la, lb, and Illb. This indicates that the major axis of a tubule was occasionally oriented radially, not circumferentially. In regions where the values were equal, tubules were always oriented with their major axis oriented circumferentially. Tubule morphology is summarized in Fig. 3.4. Fig. 3.4A is a photograph of a Toluidine-Bluestained section of the entire hoof wall, including the lamellar stratum internum. Gross changes in tubule morphology are visible, as are the differential staining patterns of each hoof wall region. Higher-magnification images produced using circularly polarized light further indicate the dependence of tubule morphology on position through the wall thickness (Fig. 3.4B). To the right of these images are illustrations based on average cross-sectional dimensions and the shapes of tubules from each region (Fig. 3.4C). Molecular alignment in each lamellar type, relative tubule sizes and shapes are generalized in three-dimensional tubule renderings in Fig. 3.4D. To show inter-animal variability, cross-sectional areas for two animals are plotted in Fig. 3.5A; these curves revealed similar trends. Tubule density (Fig. 3.5B) increased radially from approximately 10 to 25 tubules mm". The ratio of cortex to medulla cross-sectional area shows that, 2  although tubules in some regions may take up considerable space, the medullary cavity contributes more of the tubule space progressing outwardly (Fig. 3.5C). Therefore, in order to determine the material contributed by the tubule cortex to the tissue, a ratio of cortex cross-sectional area to total SM area (discounting the medullary space) was calculated. A U-shaped curve resulted, with tubule cortex area as a proportion of total SM area starting near 50% in the inner region, declining to 25120  Table 3.3: Average tubule dimensions from the six regions of the equine hoof wall thickness as defined in this study. Data are presented as mean ±1 S.E.M. C, circumferential; R, radial. For definitions of axes, see Fig. 3.2B.  Tubule  Region  Medullary Cavity  C axis (pm)  R axis (pm)  C axis (pm)  Tubule C/R Axis Ratio  Tubule Major to Minor Axis Ratio  WholeTubule crosssectional Area (mm) 2  la  27  199±15  193±14  37.1±1.4 (7V=21)  1.03±0.03 1.15±0.02 0.034±0.005  Ib  25 240±17  218±16  38.2±1.0 (7V=25)  1.10±0.04 1.19±0.04 0.046±0.006  Ila  32  181±9  121±5  45.1±1.3 (yV=26)  1.50±0.03 1.50±0.03 0.018±0.002  lib  39 204±10  125±5  47.3±2.2 (yV=19)  1.63±0.04 1.62±0.04 0.021±0.002  Ilia  42  237±7  160±5  54.3±1.4 (/V=30)  1.48±0.03 1.50±0.03 0.031±0.002  Illb  48  249±9  161±5  69.0±2.4 (7V=48)  1.54±0.05 1.57±0.04 0.033±0.002  121  Figure 3.5: Hoof wall morphology plotted as a function of position through wall thickness for two animals; solid lines are for one animal, dotted lines are for the other. Graphs progress from the inside to the outside of the wall along the x-axis. (A) Mean whole-tubule (tubule cortex plus medullary cavity) and tubule medullary cavity cross-sectional areas. The medullary cavity (bold lines) of both specimens increases in size progressing outwards, whereas tubule crosssectional area peaks in the inner region. (B) Tubule density increases progressing outwards. (C) The ratio of whole-tubule (tubule cortex plus medullary cavity) to medullary cavity crosssectional area reveals the declining contribution of the tubule cortex to the total tubule crosssectional area from the middle to outer regions. (D) A plot of tubule cortex cross-sectional area as a percentage of total stratum medium area (not including medullary space) indicates that whereas tubules contribute about 50% of the wall in the inner region and more than 55% in the outer region, the stratum medium is dominated by the intertubular material in the middle region. Medul. = medullary, cross-sect. = cross-sectional, avg. = average.  122  123  30% in the middle regions and increasing to over 50% in the outer region (Fig. 3.5D). This suggests that tubular material plays a large role in determining the mechanical properties of the outer and inner regions of the wall, whereas intertubular material likely dominates the mechanics of the mid-wall.  1.2. IF orientation in the tubule cortex. The entire SM of the equine hoof wall was intensely birefringent, indicating a high degree of molecular order (see Fig. 3.4B). IF alignment in hoof tubules did not have a significant radial component (with respect to an individual tubule), so that the 'pine-cone' arrangement of cells (and therefore, of IFs) noted by Wilkens (1964) in bovine hoof tubules does not exist in the equine hoof wall. Rather, the lamellar-like design offered by Nickel (193 8a, b) is more appropriate. Tubule cortex IFs were usually aligned in the cell plane and wound helically around the central medullary cavity. Since a helical formation was generally found in lamellae of tubules from all regions, the term helical angle (measured from the tubule axis) will be used in place of cp. It should be noted, however, that  in lamellae with very small cp angles, regular helices were not always evident. In addition, helices were observed to change direction through the thickness of a single cell (see arrow in Fig. 3.3), such that in one instance a single cell contained three helices with complimentary angles. IF helical orientation also changed periodically around a lamella and continued across adjacent lamellae. These findings suggest that, although cellular lamellae are an obvious morphological scale of order, the lamellar structure may also exist at a smaller scale, at the level of IF organization within cells. In general, helices of adjacent cells of inner-type and outer-type lamellae were crossed (Fig. 3.4D). Tubule IF helical angles changed progressively from the inner la region to the outer Illb region of the wall (Table 3.4, Fig. 3.4D). Throughout most of the wall, this change occurred as a gradual morphological gradient. Tubules from regions la and lb were similar in IF orientation. Often, inner-type lamellae of la tubules had cross-helical IF orientations, usually with helical angles between 124  ro ro CO  ro "H „ o *> in .  co  ro -H ro in in  4.  -H  ro in  -*—»  o .5  -H  Jl  3 ^  m in -H  4.  3  o  CO TO  •s »-  £ <a O  -H  o JS '5b co co c  m  4  5? ^ ~H II ^ 2"  5  ^  "H  II  i Jl  ro 4)  CO  X)  o  +1  m  8  eg I  c t ^ c O c .S3 u  u  CO  5 3  +->  2  CO  3  "5  a> cs C  r~- 2; "2 in ro —-  VO  CO  E <-> —- to .&> b 0 • -C » fa  v  ~H II  E  ro  HJ "TO  O  T3  -H  •a  J  '77 oo ~H  2  o  II  2  S:  -H  CN  2;  "H II  u  co  2  S;  VO  r--  II  2  2;  £ CN o\ 2; ro O  3  x> 3  H  -H  2  „  2:  il Ji  ro f S  SlJ ll)  -  f  a  CO  .  CO  —i  MiC  "H II O >>  3 3  "H  ||  co  1 e&  c c  § 1 2  £ S .2 *  ^  >S  P.  8  §  CO  11 C  G CO  ro  Q  W  -H  CN  IT)  -H  4.  VO  II  s  -H 00  in  ||  s  m -H ro m  +1  c o  s  '5b I  CO  Pi  u  s  VO  ro  c/5  vO* ||  CO  II  m in  I  ro  ro  ro' co  1 H  -H  o  55±11  S r t  125  4  40° and 60° (the innermost lamella usually had a right-handed helix). Adjacent lamellae from middletype lamellae of tubules from regions la and lb usually did not cross, however, crossing was observed in these lamellae in tubules from outer regions. Tubules from outer regions were characterized by crossed helices of all adjacent lamellae. Cells forming middle-type lamellae of region la and lb tubules were not as flattened as those of inner and outer-type lamellae of these tubules, or as those of middletype lamellae of tubules from other regions. Helical angles of middle-type lamellae in regions la and lb rangedfrom0° to 12°, and adjacent lamellae were usually wound in register with a right-handed helix (see Fig. 3.4D); left-handed, in-register winding of adjacent lamellae was not observed. A particularly abrupt transitionfromone tubule type to another was evident in the zone between lb and Ila (see Fig. 3.4A). This transition region has been previously recognized and named the intermediate zone (Leach, 1980). Here, wall dominance changed from tubules that primarily reinforced the L axis, to intertubular material. Vast tubule size and overall design changes occurred over such a short distance that the contrast was observed in stained sections with the unaided eye. Samplesfromall other animals showed this same pattern, suggesting a unique function for this region of the wall. Helical angles of the inner-type tubule lamella of region Ila were similar to those of la and lb; however, both left-handed and right-handed helices were observed. Ila tubules had reduced numbers of middle-type lamellae. In a sectionfromone animal, helical angles in these lamellae ranged from 0° to 33°. In region Ila, distinct outer-type lamellae became apparent, although middle-type lamellae were still predominant. Similar helical angles were observed in region lib (Table 3.4). A second major transition was apparent in region Illb. Here, tubules were characterized by increased numbers of inner- and outer-type cortical lamellae (Table 3.2). These lamellae retained the same helical orientations as tubulesfrommore inner regions, but helical angles in middle-type lamellae in tubules from region Illb appeared greater (from 0° to approximately 50°). Here again, although helices of adjacent lamellae tended to cross, no consistent pattern was observed. As with tubules from 126  more inner regions, helical angles were quite variable between samples and amongst animals.  1.3. IF organization in the intertubular material. Intertubular IFs from specimens sectioned in the C-R plane formed a static pattern which resembled a 'flow' around the wall circumference, with tubules acting in a manner analogous to pillars, obstructing the 'flow' and causing 'turbulence'. In contrast to normal flow, this 'turbulence' is formed immediately behind and in front (with respect to the flow) of the tubules (refer to Figs 3.3, 3.4B). In these areas of'turbulence', IF organization was unpredictable and appeared as areas of mixed light and dark patterns as seen under circularly polarized light, whereas IF organization in areas outside of these turbulent zones was consistent. As with cells of the tubule cortex, IFs lay parallel to the cell plane of the intertubular material. However, most of the SM cells of the intertubular material lay in a plane at a large angle relative to the tubule axis, and this angle varied through the wall thickness. Intertubular IF pattern of organization is summarized in Fig. 3.6. The top photograph (Fig. 3.6A) is a cross-section (C-R plane) of the entire hoof wall SM illuminated with circularly polarized light; afirst-orderredfilterprovided coloration. Areas withfibersgenerally aligned radially appear yellow and those running circumferentially are illuminated blue (non-birefringent areas such as the background, and areas withfibersoriented longitudinally appear purple). Fig. 3.6B.C show threedimensional renderings of the intertubular material, based on a tracing of a portion of Fig. 3.4A. Fig 3.6D shows a longitudinal section (R-L plane) of the SM, illuminated as in Fig. 3.6 A. Here, areas with fibers oriented approximately radially are yellow and those running approximately longitudinally appear blue (non-birefringent areas and areas withfibersoriented circumferentially appear purple). Intertubular organization is clearly discernable in the cross section (Fig. 3.6A). In the innermost la region, intertubular IFs tended to follow the longitudinal axis of cells and generally formed a 127  Figure 3.6: Hoof wall intertubular material composite diagram. (A) a pixilated image of a 10pm thick hoof wall sample cross-sectioned along the C-R plane (see Fig. 3.2B) and illuminated with circularly polarized light and a first-order red filter. Blue areas indicate circumferential molecular axial alignment, yellow areas reveal radial orientation. Purple areas in the hoof wall indicate axial alignment out of or perpendicular to the plane of section. Surrounding tubules are areas of alternating blue and yellow intertubular material, indicating a strong concentric organization of intertubular intermediatefilaments(IFs) around the tubule cortex. (B) A three-dimensional representation of the intertubular material extruded from a tracing of Fig. 3.4A. (C) Three-dimensional models of intertubular material IF organization from each representative region. The plane of intertubular material varies depending on position through the thickness of the hoof wall. Standard deviation bars are shown below each illustration, the scale is to the far left. No regular IF organization was apparent in region lb, as indicated by the large standard deviation (bar) of IF angles. (D) A 10pm thick specimen sectioned along the R-L plane (see Fig. 3.2B) of the toe region and viewed with circularly polarized light. Blue areas indicate longitudinal molecular axial alignment, yellow areas reveal radial orientation. In A and D, two photographs were necessary to capture the entire wall thickness; these images were combined using computer software. A and D are correctly aligned with respect to one another. Scale bars in A and D, 1 mm. The angle superimposed on D shows the intertubular IF angle.  128  129  concentric path around the tubules. Note that this region appeared mostly blue, indicating that more fibers were running circumferentially than radially. In the adjacent lb region, radial and circumferential orientations became apparent, with the presence of blue and yellow areas. Intertubular cortex of the middle (Ila and lib) regions accounted for approximately 70% of the total hoof wall material in that region. Intertubular cells immediately adjacent to tubule cortex still conformed to the concentric orientation, but in the large intertubular space, a predominantly circumferential IF alignment was apparent (note the predominance of blue in this region). This dominance of circumferentially aligned fibers continued towards the outermost regions (Ilia, Illb), although overall birefringence appeared to decrease as intertubular IFs became aligned further and further out of the C-R plane. The innermost la region was the only part of the intertubular SM that lay predictably in or close to the C-R plane (cp = -83 °; 7v=38); most of the intertubular material of the SM lay at an angle to the C-R plane as illustrated in Fig. 3.6C. Middle regions showed planar intertubular IF angles decreasing (approaching the tubule axis) outwardly, ranging from cp = -81° (Ila; N=4S) to -62° (lib; JV=58; see Fig. 3.6D). These regularly aligned intertubular IFs of the middle region comprise approximately 70% of the mid-wall SM (Fig. 3.5D), and lie in planes like unidirectional 'mats' which are stacked and tilted relative to the tubule axis such that, when a foot is placed on the ground, the 'mats' planes would orient nearly vertically. Within each mat, IFs were generally aligned circumferentially (around the hoof) within these planes and appeared to flow around tubules. This arrangement is analogous to a forest situated on a surface that is predominantly tilted at about 60°; the lower side represents the inside, and the higher side the outside of the wall. The lower side tapers off to a flat surface perpendicular to the tree axis, and near the end of the upper side it slopes quickly higher to almost 90°. Now imagine a current of a fibrous liquid defying gravity and flowing along the slope (not down the slope); this flow direction would be circumferential with respect to the hoof wall. The flow is generally laminar, but turbulence develops in front of and behind the trees (with 130  respect to the flow direction). If one of these layers represented a cell plane in the wall, then numerous layers of'currents' would be stacked on top of one another. These intertubular 'mats' form the crack propagation barrier whose function was first recognized by Bertram and Gosline (1986). Towards the periphery of the wall, intertubular material was aligned close to the tubule L axis; although this is not easily seen in Fig. 3.6D, it is visible as the progressive change to purple towards the outer wall in Fig. 3.6A. This progression is also seen as the darkening of the intertubular material towards the outermost region in Fig. 3.4B. In one section, (j) changed from -55° (#=64) in region Ilia to -38° (#=45) in Illb, and rapidly approached the tubule axis in the outer part of region Illb. The pattern of intertubular IF orientation close to the tubule axis and the prevalence of tubules (Fig. 3.5D) in the outer wall, suggests that this region inhibits inward crack propagation across the tubule axis. In contrast to all other areas of the SM, intertubular IF planar alignment in region lb was highly variable and unpredictable. Here, although uniformity in planar IF angles was observed occasionally in localized areas (see top of region lb in Fig. 3.6D), angles were measured through a 180° arc (#=46). Therefore, no mean intertubular IF plane angle was assigned to this region. However, to show relative angular variability, standard deviations are shown below each illustration in Fig. 3.6C. The standard deviation in region lb was about seven times that of region Ilia. To ensure that this variability was not unique to the specimen, the observation was verified by examining sections from three different animals. In all cases, although a general concentric order around tubules was discernabje (see Fig. 3.6A), no regular pattern of (j> could be quantified. Random IF order, coupled with the large tubules in this region whose IFs are generally aligned longitudinally, could form an inner-wall crack diversion mechanism. This hypothesis is tested in fracture tests that follow.  2. Morphology of the wall heels and cptarters.  The most obvious changes in wall morphology that occur progressing towards the back of 131  the wall (Fig. 3.7) are changes in wall thickness and alterations of the proportion of the three regions defined here as inner, middle and outer. The thickness of the inner region seems conserved around the wall, with little qualitative change in tubule and intertubular matrix morphology. Middle and outer regions, however, undergo marked changes progressing posteriorly. Reductions in the thicknesses of both these regions are evident; in addition, the 'flow' of intertubular material around tubules deviatesfromcircumferential (tangential to the outer wall surface) towards a more interior-exterior alignment in the quarters. Intertubular IF orientation tangential to the wall surface is again visible at the heels. The general shape of tubules from all three regions appears consistent around the wall, however, it is not possible to ascertain from these photographs whether tubule cortex IF alignment changes. The degree of birefringence remains constant in all sections, suggesting the same degree of IF order exists around the wall. Intertubular IF slope is relatively constant around the wall (Fig. 3.8). Inner IF orientation approximately perpendicular to the tubule axis, and intertubular IF of the mid-wall is oriented approximately 60° to the tubule axis. In sections m5 and m6 (see Fig. 3.8), however, it appears that the aforementioned pattern is disrupted. This trend was not confirmed in other sections from the same tissue, and therefore probably represent anomalies. The decreasing slope of intertubular IF (towards the tubule axis) progressing outwards that was observed in sections from the toe region (Fig. 3.6C,D), is also visible in sections from the quarters and heels. As in Fig. 3.7, the same degree of birefringence is apparent in all sections from around the wall.  3. Hoof wall mechanics.  Mechanical tests were performed primarily to test functional hypotheses generated after the collection of morphological data. Mechanical tests on mid-wall specimens (which incorporated regions Ila and lib) tested for the existence of a crack diversion mechanism for cracks generated up 132  Figure 3.7: From top to bottom: A model of the equine hoof wall with a slice removed; a crosssectional slice of the wall showing the positions which define lateral segments 11-16 and medial segments ml-m6; circularly-polarized light photographs of the different segments showing the changes in morphology around the wall. Two photographs were necessary to capture the entire wall thickness; the images were then combined using computer software. The dark areas near the middle of the wall are artifacts of this procedure. The upper and lower parts of each photograph are the inner and outer regions, respectively. Scale bar, 1mm for all photographs.  133  134  Figure 3.8: From top to bottom: A model of the equine hoof wall with slits illustrated to show the positions around the wallfromwhere lateral (11-16) and medial (ml-m6) longitudinal sections were obtained; circularly-polarized light photographs of the different segments showing changes in morphology around the wall. Two photographs were necessary to capture the entire wall thickness; the images were then combined using computer software. The dark areas near the middle of the wall are artifacts of this procedure. The left and right parts of each photograph are the inner and outer regions, respectively. Scale bar, 1mm for all photographs.  135  136  the R-L plane in the mid-wall. By incorporating more than one region (as defined in this study), data from CT tests represent average mechanical properties for the middle region of the SM thickness. The remainder of CT experiments tested the effectiveness of possible fracture control mechanisms that became apparent after morphological data and results from chapter 2 were obtained. All CT specimens fractured stably, with the exception of several specimens which failed at a clevis hole. Scanning electron micrographs of CT fracture surfaces from representative specimens are shown in Fig. 3.9. A-C in Fig. 3.9 are from chapter 2, and show the fracture surfaces of inner (regions la and lb), middle (regions Ila and lib) and outer (regions Ilia and Illb) CT test specimens, respectively, notched up the R-L plane (notch surfaces in all specimens are indicated by asterisks). These results are included here for comparison, and may now be explained on the basis of morphological results obtained in this study. In Fig. 3.9A, differences in micro structure between regions la and lb (left and right sides, respectively) caused the advancing crack to deviate in two directions; one along the tubule axis (region lb) and the other along the intertubular IF plane (region la). This fracture path is illustrated in Fig. 3.10 (reproduced from Fig. 2.15). In Fig. 3.9B, the crack deviated towards the circumferential axis of the wall and also began to follow the forward slope of the intertubular IF plane (refer to Fig. 3.6), passing through tubules as it progressed. This crack reorientation is seen as a twist of the fracture surface (see Fig. 3.10B) and results from the mid-wall crack diversion mechanism described previously. In Fig. 3.9C, the crack propagated along the tubule axis (see Fig. 3.10B). Although region Ilia was structurally similar to the middle region, the strong L axis orientation of the outer (Illb) tubular and intertubular components caused the crack to progress along the favored path parallel to the tubule axis. In general, regions with a high proportion of tubules showed fracture paths which followed the tubule axis (see Fig. 3.9A,C), whereas cracks initiated in regions dominated by intertubular material, primarily followed the intertubular IF plane (Fig. 3.9A.B).  137  Figure 3.9: Scanning electron micrographs of compact tension test specimen fracture surfaces. (A) Inner (region I), (B) middle (region II), (C) outer (region III), and (D-F) whole-thickness equine hoof wall stratum medium. A-C are reproduced from Fig. 2.14 and notches were applied parallel to the tubule axis and run through the thickness of the wall sample (i.e. are applied upwards along the R-L plane; see Fig. 3.2); they appear as the smooth surface marked with an asterisk in each photograph. In A, the innermost portion is on the upper left, the outer is on the lower right. In B, the outermost portion is on the upper right, the innermost portion is on the lower left; the notch surface is not clearly visible on the lower right. Here, the notch was redirected along the intertubular intermediatefilament(IF) plane circumferentially and radially. In C, the innermost portion is on the lower left, the outermost portion is on the upper right. In D, a notch was applied upwards along the C-L plane, but the propagating crack was redirected across the tubules towards the outer wall surface, following the plane of the intertubular material. (E) The radical crack deviation by the inner tubule 'barrier' in a specimen with a notch directed inwards along the C-R plane. (F) An example of the circumferential redirection of cracks initiated inwards along the R-L plane by the intertubular material. All specimens were tested in distilled water at a cross-head speed of 8.3><10" m s". Scale bars, 1 mm. 5  138  1  139  Figure 3.10: (A) Illustration of the equine hoof wall and sample compact tension (CT) specimens of the toe region photographed in Fig. 3.9. In B-D, notch surfaces are indicated by white areas, and fracture surfaces by dark gray areas. (B) Inner, middle and outer specimens from Fig. 3.9A, B, and C, respectively. (C) Illustration of specimens from Fig. 3.9D,E. (D) Illustration of the notch and crack path of the specimen in Fig. 3.9F. Stars indicate portions shown in Fig. 3.9. Fracture paths were determined by alignment and quantity of the dominant material (tubular or intertubular) in the respective regions. The illustration for region I is the mirror of that shown in Fig. 3.9 A since the latter was obtained from the other side of the midline. Notes adjacent to specimens refer to notch plane.  140  141  Data from CT tests also provided initial modulus values for the middle region in the circumferential (E ) and radial (E ) directions. E of the middle region from CT tests in this study uC  iR  lC  (0.38±0.02 GPa; mean± 1 S.E.M.) was significantly higher (PO.01; /-test) than that obtained from CT samples in chapter 2 (see Table 2.3). This implies that inter-animal variability could contribute significantly to the differences between E^ and E^ observed in chapter 2. E (0.23±0.01 GPa; mean c  L  iR  ± 1 S.E.M.) was significantly lower than E (P<0.0001; Mest), and is probably the effect of the lC  circumferential alignment of intertubular IFs in this region. Inter-animal variability is not a factor here, since both parameters were obtained from the same hoof. Representative samples from CT tests are also shown in Fig. 3.9D-F. Cracks in seven of the twelve CT specimens notched in the middle region up the C-L plane were redirected, as expected by the mid-wall crack diversion mechanism, along the intertubular IF plane towards the outer wall surface (Fig. 3.9D; Fig. 3.9C, bottom). At the outermost wall, cracks continued along the intertubular IF plane, deviating closer to the tubule axis as the crack progressed further outwards. In two specimens, the crack continued generally in the original notch plane, but showed tendencies to deviate along the intertubular IF plane. Three specimens failed at the clevis hole in the outer wall, with cracks that followed the intertubular IF plane and indicated a considerable weakness of the outer wall relative to the mid wall, along which the notch was applied. Clevis-hole failure was not observed in any of the middle region specimens notched up the R-L plane. To test the effectiveness of the structural discontinuity at the intermediate zone and region Ib tubules in stopping cracks propagating inwards across tubules, 11 specimens were produced that spanned the entire SM thickness and were notched inwards along the C-R plane. Four samples failed along the intertubular IF plane at a clevis hole in region III. In all others, the notch was redirected downwards. In specimens with short notches (through the outer and middle regions), the crack deviated downwards and inwards along the intertubular IF plane until it met the large inner tubules 142  of region la. Upon encountering these structures, the crack then continued straight downwards along the tubule axis. In specimens with long notches which entered region lb, cracks were immediately redirected perpendicular to the notch surface along the tubule axis (see Figs 3.9E and 3. IOC). These results clearly establish the existence of an inner-wall crack diversion mechanism. The effectiveness of the mid-wall crack diversion mechanism in redirecting cracks initiated inwards along the R-L plane was tested by notching 12 specimens from the lateral toe region in this plane (see Fig. 3.10D). In specimens in which the notch front terminated in the middle regions, the crack was redirected circumferentially (following the predominant, intertubular IF 'grain' of the middle region), twisting into the intertubular IF plane (Fig. 3.6A). All of these specimens were cut to the right (lateral) of the mid-line and in all cases cracks were redirected towards the back of the hoof. In specimens with notches that extended into the inner region, cracks were only weakly redirected. Fig. 3.9F shows a micrograph of a fracture surface, and an illustration is also provided in Fig. 3.10D. In four specimens, failure occurred at the clevis holes in region III by crack propagation between tubules. J and AT values obtained from the middle region of CT samples notched up the R-L plane (see Table 3.5) were statistically similar those obtained from similar specimens in chapter 2 (Table 2.4), indicating that inter-animal variability was not a factor affecting this parameter and that toughness is not compromised by storing specimens in this manner over a period of 3 months. J values from specimens notched in the C-L plane (in the middle region) were significantly higher (Table 3.5; P<0.001; Mest). Results for the parameter K, however, suggested that these specimens were less tough than specimens notched in the R-L plane. Fracture data for specimens notched inwards along the C-R and L-R planes (see Fig. 3.9E,F, respectively) are not presented because in these tests fracture toughness was dependent on notch length (since cracks were initiated in different regions, depending on the original notch length). This violated a critical assumption necessary for determining 143  a single, representative value of fracture toughness.  144  Table 3.5: Fracture toughness datafromCT tests of the equine hoof wall. Data are presented as mean ±1 S.E.M. Values with similar symbols are statistically different from one another (P<0.05, Student-Newman-Keuls test). SM, stratum medium; C-L and R-L planes are defined in Fig. 3.2B.  J-integral (kJ m")  Stress intensity factor, K (MN m")  Middle SM (notched in R-L plane)  5.8±0.4  0.64±0.04  (N=l)  (N=l)  Entire SM thickness (notched in C-L plane)  10.7±0.9  0.46±0.04  Region  2  (N=9)  145  32 /  (N=9)  DISCUSSION The primary mechanical function of the equine hoof wall is to transfer ground-reaction loads to the bony skeleton. While doing so, it must resist the formation and propagation of cracks yet also allow for the necessary process of wear. The transfer of loads is a relatively simple task; fracture control and wear management are more complex. Although load transfer and wear management are functionally important issues, fracture control appears to be the major driving force in the development of morphological complexity in this tissue. Therefore, the following discussion considers all issues, but weighs most heavily on crack control.  1. The uncoupling of IF alignment and mechanical properties on a large scale.  Locally, IF appear to increase stiffness along their axis of orientation. In the middle wall region, which is dominated by circumferentially-aligned intertubular IFs, circumferential stiffness (0.38 GPa) is significantly higher than radial stiffness (0.23 Gpa). However, through the wall thickness, IF alignment does not correlate with stiffness (see chapter 2). The inner region, which has a large proportion of SM cortex with IFs aligned nearly parallel to the L axis, should be considerably stiffer than the middle region, which is dominated by intertubular material with IFs aligned at relatively large angles to the L axis (large tp). This is not the case. In addition, although ultimate properties are also expected to correlate with IF alignment, no significant differences were found in maximum stress and maximum strain between regions of the wall (refer to Table 2.3). Yield stress data further show that IF orientation and mechanical properties are unrelated in the wall; the yield stress of the inner region, which had a high proportion of IFs aligned close to the axis of applied stress, was lower than that of the middle region, which was dominated by intertubular material with IFs aligned at a steep angle to the stress axis. It may therefore be concluded that the primary function of IFs is not to increase stiffness in 146  the axis of orientation. This has major implications for the tubular components of the wall whose primary mechanical role was believed to involve offering reinforcement along the wall L axis (Nickel, 1938 a,b; Bertram and Gosline, 1986). The function of tubules and the role of IF orientation within both the tubule cortex and intertubular material are more complex than previously imagined. These results suggest that these elements are not expressions of demands for rigidity in the hoof wall, but rather they arise from the need to control fracture processes and increase fracture toughness.  2. Functional design for crack control.  2.1. Tubules. Recall that tubules are also present in other keratinous, non-homologous (developmentally non-related) structures such as rhinoceros horn (Ryder, 1962) and bovine horn (Kitchener, 1987; Kitchener and Vincent, 1987), but are absent in homologous structures such as human nail (Hashimoto, 1971 a, b). Although the exact functions of tubules are still under debate, current dogma holds that they facilitate hydration of the wall (Evans et al. 1990) and/or provide mechanical reinforcement along the wall length. Kitchener (1987) suggested that tubules in bovine horn have functions analogous to fibers of composites. This analogy may not be appropriate for horn or hoof wall. The fibers of composites are usually stiffer than the matrix and provide rigidity and strength to the composite along the axis of orientation. The matrix is normally made from a more flexible material and aids in transferring stresses to the fibers via shear. In horn and hoof, however, there is no indication of a difference in stiffness between tubules and the intertubular 'matrix'. Tubule 'pull-out' observed in fracture tests (see Fig. 3.9) indicates that tubules reinforce the hoof wall along the longitudinal axis to some extent. Even as cracks produced in the middle (Ila and lib) region find a new route along the intertubular IF plane (Fig. 3.9B), tubules (which form about 147  30% of the material in this region) retard crack propagation by acting as mechanical barriers. These reinforcements offer just enough resistance to cause the advancing crack to deviate part-way along its surface (and between tubular lamellae), thereby dissipating energy and retarding crack growth in the process (see Broek, 1986). But tubules do not just reinforce along the tubule axis. Tubules from different regions are morphologically distinct, differing in IF helical angles and in quantity of lamellae with similar helical angles. Nickel (1938Z>) recognized the morphological gradient of equine hoof wall tubules, but simplified the wall model by characterizing tubules into one of two extreme classes: those with predominantly 'steeply-angled spirals' (low cp) and those with predominantly 'low-angled spirals' (high cp). Illustrations of tubules with 'spirals at high angles' and those with 'spirals at low angles' correspond best to tubulesfromregions la and Illb, respectively (see Fig. 3.4D). This study generally agrees with Nickel's (1938Z>). Unfortunately, by representing averages of morphologies from more than one of the regions investigated here, they are not directly comparable. In this study, adjacent lamellae from similar tubule cortex zones also had alternate IF helical directions. However, unlike Nickel (19386) I did not observe alternating helices in the middle-type cortical zone of inner tubules (regions la and Ib); rather, fibers in lamellae of this zone were in register and aligned to the right. An outer cortical zone for these tubules was also not defined in this study (hence the term 'middle-type' for the outer cortical zone of these tubules), as it was impossible to locate a distinct tubuleintertubular material interface in these inner regions. Note, however, that tubule-forming papillae are continuous with the coronary epidermis that is responsible for generating intertubular cortex. It is therefore not surprising tofindregions where a distinction between the two wall components is not clearly evident, suggesting a tight coupling between the two wall components in this region. A satisfactory explanation of tubule function must also rationalize the complexity of tubule design. In this study the wall has been arbitrarily divided into six regions through the thickness of the 148  tissue and have offered illustrations of representative tubules by averaging morphological dimensions of tubules within each region. Recall that a gradient of tubule morphology exists, and that no abrupt morphological transition exist in the equine hoof wall. For convenience, I shall refer to an average or 'typical' tubule from each region at the toe. Generally, tubules from all regions share two elements: a medullary cavity incapable of supporting loads and at least one abrupt transitionfromlamellae with low helical angles to those with high helical angles. This transition may play an analogous role to the tubules in the intertubular material by leading the crack through a more tortuous route and absorbing fracture energy in the process. The alternation of helical angles between lamellae of similar cortical zones (recall that there are three tubule cortical zones: inner, middle and outer) may also serve the same purpose. Note that lamellaefrommiddle cortical zones of tubules from regions la, lb, and Ila do not alternate like those from other tubules and other cortical zones. The reason for this is unclear. Kitchener (1987) also found extensive delamination of the layers of keratinocytes after fracture, implying that relatively weak lamellar interfaces may serve as energy-dissipation and crack-blunting mechanisms. Progressing outwards, the intertubular IF plane changes from approximately perpendicular, to nearly parallel to the tubule axis in all areas around the wall. In contrast, tubules progress from structures dominated by lamellae with low helical angles, to those with primarily high helical angles, so that most tubular IFs lie approximately perpendicular to the intertubular IF axis. This could create extensive strain-transition interfaces that will promote separation of tubules from the intertubular material during fracture (tubule pull-out), and absorb energy in the process. The elliptical cross-sectional shape of outer tubules may be a response to the bending mechanics observed in the hoof wall. It has been observed that expansion at the heels occurs during loading of the equine hoof wall (Lungwitz and Adams, 1966). In combination with loading along the tubule axis, compressive loading from this expansion translates into a particular pattern of surface 149  strains which includes large circumferential surface compression at the hoof toe (Thomason et al. 1992). Orientation of the major ellipse axis of these outer tubules along the circumference of the wall could offer tubules increased resistance to collapse along this axis. Equine hoof wall is clearly not designed as a simple, hollow fiber-reinforced composite. Differentiated tubules and changing planar orientation of intertubular material signify changing mechanical demands through the wall thickness. But what are these mechanical demands? Unfortunately, the specific demands are still unknown. However, the following discussion considers the morphological features of the hoof wall that control the growth of cracks initiated at the groundcontact surface propagating up the wall and at the outer surface propagating inwards.  2.2. Crack propagation up the wall. The most extreme mechanical demands placed on the hoof wall are loads generated at the distal, ground-contact surface upwards towards the coronary border. Whereas on flat surfaces these loads pose no threat to the structure, very high stresses resulting from localized loading (such as stepping on a small rock) during high-speed locomotion pose serious threats of injury to the animal. Any crack that contacts the vascularized (dermal) tissue will create the potential for infection, subsequent lameness and possible death. Bertram and Gosline (1986) showed that the intertubular material creates a mid-wall crack diversion mechanism that prevents cracks from propagating up the wall, and they suggested that this mechanism would reorient cracks into the plane of the ground contact surface, thus facilitating the necessary process of wear. Morphological and fracture results for the mid-wall region at the toe confirm the existence of this mechanism. It was observed that cracks initiated up the hoof wall are redirected parallel to intertubular IFs, and this redirection likely occurs because the intertubular material occupies 70-80% of the load-bearing cross-sectional area in the middle SM (Fig. 3.5D). However, these results clearly indicate that the intertubular IF plane and the 150  direction of crack propagation run upwards towards the outer surface of the hoof, not parallel to the ground contact surface. Since the intertubular material slopes at approximately cp=-60°, and the hoof wall at the toe region of forehooves is sloped backwards by approximately 40° from vertical (Sack and Habel, 1977), the intertubular IF plane at the toe region follows a path at an angle of approximately 20° from vertical (Fig. 3.1 IC). The intertubular IF plane orientation is probably a direct consequence of the orientation of the generative tissue at the coronary border (see Stump, 1967; Banks, 1993; Fig. 3.1 ID) and continues around the wall (Fig. 3.8). Although the intertubular IF plane runs upwards and outwards, IFs are strongly aligned circumferentially within this plane (Fig. 3.6A). Therefore, the mid-wall crack diversion mechanism is capable of redirecting cracks initiated at the ground contact surface in any orientation. For example, cracks initiated in the C-L plane in specimens from the toe (Figs 3.9D, 3.10C) are always redirected along the intertubular IF plane and will, if they continue, emerge at the outer wall surface (Fig. 3.11C). Longitudinal sections from the quarters and heels (Fig. 3.8) suggest that this redirection should occur around the wall. Alternately, cracks initiated in the R-L plane are initially diverted circumferentially by the IF fibers, but as the crack progresses the fracture path twists towards the plane of intertubular IFs (Figs 3.9B, 3.1 OB). This tendency to twist redirects the circumferentially diverted cracks, forcing them to emerge at the hoof surface. Thus, irrespective of initial crack orientation, the mid-wall crack diversion mechanism redirects cracks initiated upwards between regions lb (outer) and Ilia outwards towards the wall surface (Fig. 3.1 IC), away from the living tissues of the foot. Such crack redirection is visible in Fig. 3.1 IE. Here, a naturally formed notch shows the circumferential and forward redirection of cracks initiated in the toe region.  2.3. Crack propagation inwards. Potentially destructive mechanical insults may be received by the outer surface of the wall 151  Figure 3.11: Summary diagram of crack redirection in the hoof wall. (A) Circumferential redirection of cracks by the intertubular intermediate filaments (IFs). The black arrow indicates the direction of crack initiation and the red arrow shows the likely route of crack propagation. (B) Side view of the hoof wall with a portion of the toe and quarter removed. The circled portion in B is magnified in C to show two other example directions of crack initiation (indicated by black arrows) and the likely routes of crack redirection (in red). Green dashed lines approximate the intertubular IF orientation; tubule positioning is represented by three lines which fade distally. A block of hoof tissue from the toe region of an animal not used in this study is shown in D. The coronary border is at the upper right, the stratum externum is to the left and the stratum internum is to the right. A flaw is visible in the material which follows the predicted path of inward-oriented cracks along the intertubular IF plane; the flaw stopped at the inner-wall fracture barrier. (E) An actual notch from the toe region of an animal not used in this study. Note the upward continuation of the crack path in the outer region, the general circumferential redirection of the crack and the forward slope of the wall tissue at the notch top.  152  153  which will tend to drive cracks inwards. As in previous studies (Nickel, 1938a; Bolliger and Geyer, 1992), it was found that the outer SM (Illb) region is characterized by a high density of elliptical tubules which are surrounded by intertubular material with IFs aligned generally parallel to the tubule axis. This combination of tubules and parallel-oriented intertubular IFs appears to form an outer-wall fracture barrier that should be effective in inhibiting the inward propagation of cracks initiated perpendicular to the tubule axis (e.g. in the C-R plane). For cracks initiated inwards in a plane parallel to the tubule axis, a degree of reinforcement may be offered by the morphology and organization of the tubules. The staggering of tubules, their elliptical shape and the prevalence of tubular lamellae with fibers aligned at high cp may offer a degree of resistance to these cracks. Unfortunately, it was not possible to construct CT specimens to test for the existence of an outer-wall fracture barrier. However, results from these tests show how the mid-wall crack diversion mechanism and other aspects of hoof wall morphology control the growth of cracks that pass into the hoof wall from the outside. In tests which simulated the initiation of cracks propagating inwards along the R-L plane, cracks were redirected circumferentially and twisted towards the intertubular IF plane by the mid-wall crack diversion mechanism (Figs 3.9F, 3.10D). The predominantly circumferential orientation of the mid-wall intertubular IF effectively eliminates the possibility of cracks initiated from the outside in the R-L plane from reaching the inner living tissues of the foot. In addition, cracks were always redirected laterally towards the back of the hoof (recall that these specimens were taken lateral to the hoof mid-line). The deviation of middle region intertubular IFs away from a circumferential orientation in the quarters (Fig. 3.7) suggests that cracks initiated in the R-L plane in this area will be diverted at an angle to the hoof surface. Intertubular IF orientation in the quarters implies that inwards-oriented insults in the R-L plane usually encountered in this area are not perpendicular to the wall surface, but are instead directed slightly towards the toe since these resulting cracks would be 154  directed circumferentially and outwards. However, further mechanical tests are necessary to test this hypothesis. The results of tests which simulated the initiation of cracks propagating inwards along the C-R plane were dependent on initial notch length. In specimens with notches that terminated in the midwall (region II) crack growth progressed downwards along the intertubular IF plane. Upon encountering the morphological discontinuity at the Ib-IIa boundary, these cracks were abruptly redirected downwards along tubules (towards the ground-contact surface). In specimens with notches that terminated in the inner wall, cracks always progressed downwards along the tubule axis (Fig. 3.9E, 3.IOC). This behavior indicates a new fracture control strategy that shall be referred to as the inner-wall crack diversion mechanism. This mechanism is important because, without it, cracks initiated from the outside in the C-R plane could propagate downwards and inwards along the intertubular IF plane (see Fig. 3.11C,D) and enter the living tissues of the foot. Conservation of inner wall morphology around the wall (Fig. 3.7), even as the other regions become thinner, suggests that this crack diversion mechanism is important in all areas of the wall. An inadvertent consequence of this mechanism is that cracks in this region along the L axis will tend to propagate up towards the coronary border (Fig. 3.9A). This predisposition, however, is countered by the propensity for circumferential crack redirection of cracks by the mid-wall crack diversion mechanism.  2.4. Principles of crack diversion mechanisms. Typical uniaxially aligned syntheticfiber-reinforcedcomposites strongly resist crack growth perpendicular to thefiberaxis, but they allow relatively easy crack propagation along thefiberaxis. To resist crack growth in more than one direction, sheets or laminae may be adhered such that the fiber axes of adjacent laminae are crossed. Alternatively,fibersmay be incorporated in a random orientation throughout the matrix; this offers equal fracture toughness in any direction, but 155  compromises toughness in any single direction. In the hoof wall, where the potential directions of crack initiation are numerous but predictable, evolution has apparently produced a complex composite tissue with highly organized, specialized crack diversion mechanisms to control cracks initiated in specific directions. These mechanisms involve the incorporation of planes of relative weakness, which redirect cracks from an initial dangerous route to a more benign path. The predictability of these fracture paths ensures a particular mode of failure depending on the initial crack orientation, without seriously compromising the mechanical integrity of the structure. This design strategy works, however, only if crack propagation along these planes requires a high energy cost which is reflected in high fracture toughnesses. As with fracture tests in chapter 2, cracks in these tests were redirected away from the initial notch plane. Therefore, the J and K values presented here are also not accurate representations of fracture toughness along the initial notch plane, but rather more closely reflect the toughness of the relative planes of weakness along which the cracks were redirected. Again, it must be stressed that the favored planes of crack growth are only relative planes of weakness. It may be assumed that the resistance to crack propagation across a crack diversion mechanism will be much higher. Several mechanisms are incorporated into hoof wall design which maintain high fracture toughness along a crack diversion mechanism. The mid-wall crack diversion mechanism is reinforced periodically with tubules which run through its planes of weakness, providing a more effective bond between planes. These tubules also act as small-scale crack deviation structures and further confound crack progression by directing the crack along a more tortuous route across its complex, lamellar structure. Additionally, unlike traditional homogenous matrix phases of synthetic composites, intertubular material is formed by the adhesion of cells which are filled with a molecular composite, a-keratin. Effective bonding of these cells makes crack propagation between cells difficult, so that cracks propagate between and within cells. Propagation along the IF axis within cells is inhibited by 156  intimate associations of the IFs and the globular IF-associated proteins. The inner-wall crack diversion mechanism is reinforced only by intertubular material whose IF are less ordered. This offers an advancing crack minimal resistance and implies that it acts as afinalsafety mechanism to ensure the redirection of cracks (which have penetrated deep into the wall) away from the very sensitive mechanical junction of the wall and the skeleton. The production of these crack diversion mechanisms is not without limitations. In hoof wall, planes of preferred crack propagation are formed by substructures whose IFs are predominantly organized in one axis or plane, and IF orientation seems to be restricted to a direction within the cell plane. Thus, crack diversion design is coupled to the surface plane of the generative tissue. This restriction may be responsible for the difference in morphology between the inner-wall crack diversion mechanism and the (hypothesized) outer-wall fracture barrier which apparently have the same functions. These difference are likely because it is functionally impossible to produce intertubular IF along the tubule axis in the inner region. In the outer region, this was achieved by curving the generative tissue at the outer coronary border to a plane almost parallel with the tubule axis; this design may be impossible to repeat in the inner-wall region. Instead the inner coronary border lies at a plane approximately perpendicular to the tubule axis. All resources for reinforcing the L axis are therefore invested in tubule cortex, which is a dominant feature of this region. In contrast to the intertubular IF of the outer-wall, inner-wall intertubular IFs are suitably disorganized (see Fig. 3.6C, D), since any intertubular IF order except along the tubule axis would tend to divert a crack along a plane across these tubules. It has been known for some time that the equine hoof wall is a multi-level composite material. This study has revealed that, in addition to the advantages in increased fracture toughness resulting from its hierarchical design, mechanisms have been incorporated to control the direction of crack growth. By recruiting the intertubular component into a fracture toughness and direction control 157  mechanism, the hoof wall has become one of the most fracture-resistant biological structures known and, upon failure, is capable of modulating crack direction along predetermined routes which are dependent on initial crack orientation. From this study, it is now apparent that equine hoof wall tubules have important mechanical functions. There are, however, still other possible roles for tubules. The following chapter investigates hypotheses for both mechanical and non-mechanical functions of their hollow form. The results are discussed in relation to tubule function in overall design of the equine hoof wall.  158  CHAPTER 4: THE FUNCTIONS OF TUBULES  159  INTRODUCTION From the results of chapters 2 and 3, it is now apparent that equine hoof wall tubules have important functions in fracture control. Non-mechanical roles, however, are also possible for hoof wall tubules. For example, proper hydration is of paramount importance in maintaining a sound foot (see Lambert, 1966, 1968). In addition, Bertram and Gosline (1987) found an optimal hydration level for maximal fracture toughness and a trend towards brittle failure with excessive dehydration. It has been suggested the hollow form of tubules facilitates conduction of water from the contact surface proximally (aided by cells within the medullary cavity; Evans et al. 1990), and could also facilitate the movement of water in its vapor phase (evaporated from dermal papillae) distally. If tubules facilitate the conduction of water vapor along the wall, then the rate of tissue hydration vertically (along the tubule axis) should be greater than the hydration rate in any other direction. The purpose of this study is to test the hypothesis that tubules facilitate the conduction of water vapor down the wall, and to discuss other possible roles of these enigmatic components of hoof wall substructure; the hypothesis is tested by conducting hydration experiments on blocks of hoof wall tissue.  160  MATERIALS AND METHODS 1.1. Sample preparation and test methodology for hydration/dehydration tests  Hoof wall samplesfroma single horse (killed for reasons other than this study) were obtained from the heels and quarters of fore and hind hooves. Specimens were shaped into approximately 1 cm cubes with the Gillings Hamco water-cooled cut-off machine. The SI was removed by using the cutoff machine as a water-cooled grinder; the outer wall was not processed. All samples were stored in a sealed hydration chamber above a saturated solution (in distilled water) which provided a constant RH of 75% at room temperature (approximately 22° C) until equilibration (at least thirty days). Immediately prior to use, specimens were weighed to the nearest 0.1 mg, impaled with a syringe needle (250%) and then sealed by painting with melted Tackiwax (Cenco Softseal; Central Scientific Co.). All faces were coated except for the test surface which lay on the opposite side to the impaled surface. Four surfaces were investigated: Vertical, the face on which tubule ends are exposed, Inner, the face of the SM block that is adjacent to the inner SI, Outer, the outer surface of the hoof wall, and Lateral, the face which is approximately parallel to the radial axis of the foot (Fig. 4.1). No distinction was made between the two Lateral sides or the two Vertical sides. Each cube was used to test either the hydration or dehydration rate through one surface only. An air-tight mounting device was inserted into the needle base, and the whole assembly was then placed onto a test chamber (Fig. 4.2). In hydration tests, the chamber contained a saturated solution of K S0 (in distilled water) that maintained the chamber at a constant RH of 97%. For 2  4  dehydration tests, a saturated solution of MgCl provided a constant RH of 33%. The system was 2  attached to a Mettler balance (model H31) such that specimens could be weighed without removal from the chamber. To weigh specimens during a test, the chamber was lowered so that the mounting assembly was suspended above the chamber by the balance arm. The total weight of the apparatus was recorded and the device was then lowered back onto the mouth of the chamber, resealing it. 161  Figure 4.1: Illustration showing the faces of a hoof wall block as defined in this study: Inner (adjacent to the stratum internum), Outer, Lateral and Vertical faces (the face of exposed tubule ends). Tissue was obtainedfromthe quarters and heels of equine hooves and cut into approximately lcm blocks. 3  162  Vertical  163  Figure 4.2: Illustration of the hydration/dehydration chamber. The chamber contained a saturated salt solution which maintained the chamber at a constant relative humidity. Specimens were coated with wax on all but one side and suspended in the chamber by a mounting apparatus. The chamber could be lowered and raised to weigh the specimen and seal the chamber, respectively.  164  Balance arm  Pin Lead washer Rubber washer  A To weigh specimen  Plastic chamber  To seal chamber  Waxed specimen Exposed face  165  Weights were recorded periodically over four days. All tests were conducted at room temperature. After test completion, specimen dimensions were measured with Vernier calipers to the nearest 0.01 mm. Weight versus time data were fit to a polynomial function using software (Tablecurve 2.11; Jandel Scientific). The hydration or dehydration rates (in g H20 m" hr ) at two 2  1  arbitrary times (1500 min. and 4000 min. after start of the experiment) were then determined by finding the derivative of the function at each time and dividing by the exposed area of the test surface.  1.2. Methodology for morphometries  Histological samples were obtained from the toe region of two animals and processed as described in chapter 3. Two 20pm thick specimens were cut (one from each animal) transverse to the tubule axis and stained with Toluidine blue (in distilled water with 1% sodium borate). Pixilated images were produced by mounting the sections in a projector slide. The slide was then scanned at 2000 dpi with a Kodak RFS 2035 Plusfilmscanner. Images were divided into nine regions of approximately equal areas (Fig. 4.3), point coordinates marked with a PC video frame capturing program (Vfor Windows 3.0) and processed on a spreadsheet (Quatt.ro Pro 5.0). Medullary cavities were approximated as elliptical in cross-section; therefore only 4 points representing the ends of the major and minor axes were necessary to quantify the cross-sectional area. In cases where tubules overlapped two regions, the tubule center determined in which area it was counted.  166  Figure 4.3: An image of a cross-section of an equine hoof wall specimen. The stratum medium was divided into nine regions of approximately equal thickness for the collection of morphometric data.  167  Stratum internum  Stratum medium  168  RESULTS 1.1. Hydration rates  If tubules facilitate the transfer of water vapor distally, hydration rates through the vertical surfaces should be greatest. These data indicate that this is not the case. The Outer face was the slowest to hydrate through (3.11 g H 0 irf h ) at the 1500th min., and the rate was significantly 2  _1  2  slower than that recorded by hydrating through either the Inner or Lateral faces (Table 4.1). No significant differences in hydration rates were found between any of the other block faces. At the 4500th min., the Outer face allowed the entrance of water at a rate of 1.99 g H 0 irf h", a value that 2  1  2  was significantly lower than for hydration through any other block face. There were no significant differences in hydration rates between any of the other exposed faces at this time.  1.2. Dehydration rates  Dehydration results closely mirrored hydration data, with the Outer face showing a dehydration rate of-1.32 g H 0 irf h' at the 1500th min (Table 4.1) that was significantly lower than 2  1  2  the dehydration rate through the Vertical surface (-1.70 g H 0 irf h'). At the 4500th min. there were 2  1  2  no significant differences in dehydration rates among any of the exposed surfaces. Since hoof wall treatment history (with externally applied moisture sealants) could not be obtained for the animals from which samples were obtained, Outer face hydration rates are purely suggestive. Although it appears that the outer face acts as a barrier to water, further testing is necessary to properly determine the effectiveness of the outer face in this role. These data do, however, suggest that tubules allow for higher water loss through their exposed ends at the distal surface of the wall.  169  Table 4.1: Hoof wall hydration and dehydration rates in various directions. Data are presented as mean±l S.E.M. Values within a column with similar symbols are statistically different from one another (P<0.05, Student-Newman-Keuls).  Hydration rates (gH 0 m" h") 2  Dehydration rates (g H 0 rn h") 2  1  2  Exposed face Inner Outer Lateral Vertical  1  2  1500th min. 4500th min.  1500th min.  4500th min.  5.08±0.44 (#=7)  3.72±0.31  -1.59±0.08  -0.939+0.101  (N=7)  (N=7)  (N=7)  r  3.1 l±0.15  t  n  1.99+0.14™ -1.32+0.06* -0.787+0.043 (N=7)  (N=7)  (N=7)  5.16+0.68*  3.91±0.53  (N=7)  (N=7)  4.04±0.08  3.00±0.09  (N=7)  (N=7)  J  170  -1.46+0.11 -0.846+0.117 (N=7)  §  (N=7) (N=7)  -1.70+0.07* -0.989+0.096 (N=7)  (N=7)  1.3. Morphometries  From the two histological specimens used in this study, it was determined that the medullary cavities occupied about 2% of the total hoof wall cross-sectional area. In Fig. 4.4A, the percentage of the SM cross-sectional area occupied by medullary space is plotted against region through wall thickness for the two samples. A 9-fold increase in percent of area occupied by medullary space progressing outwardly is accompanied by a 4-fold increase in mean medullary cavity cross-sectional area (Fig. 4.4B). These trends are the reflection of an increase in tubule density progressing outwards.  171  Figure 4.4: (A) Percent of area occupied by tubule medullary cavity and (B); mean medullary cavity cross-sectional area, plotted against region through hoof wall thickness. The proportion of space occupied by the medullary space rose about 9-fold progressing outwardly, whereas the average medullary cross-sectional size only increased 4-fold.  172  10  • .2  o •  ro =3 <U <•  3  •  CO  B  8 o  Q _L_ 0.004 ro o  3  O  J  L  _J  I  L_  B  S B ^ co  0.003  ro  CO  s I  o  • 0.002  CO  •  c/3  <u g  o  0.001  • • o o J  0.000  L  D  o  • o J  Inner  • o  O  L  Outer Region through wall thickness  173  DISCUSSION Hoof wall tubules may serve one or more functions. They may 1) act as water conduits (in either the fluid or vapor phase, or both) to facilitate hydration of distal and outer regions of the wall, 2) serve an indirect mechanical function by providing high flexural stiffness while minimizing hoof wall weight (thereby saving energy during locomotion by decreasing the wall density), 3) lower the thermal conductivity of the wall tissue (insulating the foot), 4) serve direct mechanical functions (e.g., reinforce the wall along their longitudinal axes). Each of these issues is discussed below. Currently dogma suggests that hoof wall tubules are hollow to facilitate hydration of distal portions of the wall. This could be achieved by: 1) The drawing up of water by tubules via capillary action 2) The conduction of water vapor down the tubule length. The former would require that the hoof be placed on or into liquid water. Water vapor in the latter case would be the result of evaporative loss from dermal papillae which form the tubules. If hydration through capillary action was a significant hydration mechanism, then a gradient of hydration should exist from the distal end upwards. Leach (1980), however, found that hydration gradients extend downwards (from the dermal papillae) and outwards, and he noted that the most highly hydrated areas of the wall are adjacent to dermal tissue. This indicates that the drawing up of water via capillary action does not contribute significantly in equine hoof wall hydration. In addition, results from this study indicate that tubules do not facilitate the conduction of water vapor down the hoof wall. The hydration rate through the Vertical face (along the tubule axis) was not significantly different than the rates through either the Lateral or Inner faces. Rather, these data suggests that tubules may facilitate the dehydration of the wall at the distal surface, since dehydration rate was highest through the vertical surface (Table 4.1). This result is surprising since the apparent increase in conductive surface area (offered by the walls of the medullary cavities) should affect the hydration rate. It does, however, agree with the comment by Feughelman (1959) that the hydration rate is faster 174  across keratin fibers than along them; the more longitudinally-arranged fibers of the tubule cortex should have retarded water conduction. Since proper hoof wall hydration is crucial in maintaining high fracture toughness (Bertram and Gosline, 1987) and the relatively thin stratum externum is thought to be produced solely to restrict water loss through the outer wall, the dehydrative effect of tubules is likely inadvertent. The presence of hollow tubules is therefore likely the reflection of a compromise resulting from some other hoof wall function. Surface strain recordings of the equine hoof wall during locomotion (Colles, 1989; Thomason et al. 1992) and hoof wall deformation (Lambert, 1968) suggest that two bending moments could result at the toe from both weight bearing, and expansion at the heels. Therefore, we may consider the possibility that the incorporation of tubules in the wall (particularly at the toe) is an attempt to reduce the overall weight of the wall while maintaining high resistance to bending. This idea appears to have merit sinceflexuralstiffness, EI, is a product of both the stiffness of the material, E, and the second moment of area, /. Whereas £ is a material constant, / is dependent on the shape of the structure. For example, a Styrofoam board is quite stiff considering the stiffness of the material of which it is made. By creating many air pockets within the board, much of the foam material lies away from the central bending plane of the board. Since / « / W (where t is the foam thickness and W is 3  the width), the bending stiffness rises quickly with an increase in thickness. If the same board is compressed so as to reduce the size of the air cells, its bending stiffness decreases dramatically. In the case of the hoof wall, a bending plane (or neutral axis) may exist along the middle of the wall thickness. Air spaces within the medullary cavity of the hoof wall could act in the same manner. However, data from this study (see Fig. 4.4A) indicate that the tubule medullary cavity only comprises about 2% of the total volume of the equine hoof wall at the toe. If we consider a bending  plane in the middle of the hoof wall thickness at the toe region, then an increase in area of about 2% from the inclusion of voids (although in the equine hoof wall, medullary spaces are not completely 175  empty) would increase / by about 4% and therefore increase the overall flexural stiffness EI by only 4%. This increase in bending stiffness is hardly significant, and would not likely have been the singular evolutionary driving force towards the development of hollow hoof wall tubules. Since the hoof wall interfaces directly with the environment, the incorporation of medullary spaces should aid in insulating the wall. Using equation 9 provided by Springer and Tsai (1967), it is possible to estimate the effect on thermal conductivity with the inclusion of these columns of air (assuming they are void of debris). Estimating the thermal conductivities of keratin and air as 0.2 and 0.023, respectively, the medullary spaces would only decrease the thermal conductivity of the wall by about 7%. Indeed, Moog and Pollitt (1992) recorded equine hoof surface temperatures about 8°C above ambient and 8.5°C below core temperature (37.5°C), suggesting that heat loss through the wall surface occurs at a significant rate and is not greatly retarded by the wall thermal conductivity. A mechanical role for hoof wall tubules is now widely accepted; however, their specific mechanical role (or roles) is still under debate. Nickel (1938a) originally suggested that they are the primary compressive load-bearing elements of the wall. Later, Bertram and Gosline (1986) proposed that tubules act as fibers of a fiber-reinforced composite, reinforcing the wall against crack propagation perpendicular to their primary axis. It is now believed that their presence in the wall is not easily rationalized, and that their functions are nearly as diverse as their morphology is complex Recallfromchapter 3 that in addition to increasing fracture toughness by causing a crack to deviate along a more tortuous route, tubules also serve to redirect cracks away from the sensitive dermis of the foot. Therefore, differential tubule morphology through the wall thickness may be rationalized in terms of crack resistance and redirection. However, discussion of the mechanical function of tubules must also justify the presence of hollow tubules, rather than solid fibers. Here, two possible explanations which are not mutually exclusive are offered. It appears that a high degree of molecular order is achieved by laying fibers down in the plane 176  of any flattened, keratinized cells. It may be impossible to achieve this degree of order through the thickness of a cell, such that keratin fiber axes can only be produced parallel to the plane of the generative tissue (Fig. 4.5). This rule also appears to be observed in the generation of fibers in intertubular material. Therefore, in order to produce material with keratin fibers orientated along the length of the wall (to reinforce the longitudinal axis), generative tissue must lay down cells in planes along this axis. The resulting structures are papillae which extend part way into the wall, producing hollow tubules with cortical material containing concentrically aligned IF molecules. One may argue that fiber alignment along the wall length could also be achieved by the production of solid columns rather than tubules. Solid columns may not be found because the process of their production would likely exclude the possibility of effective bonding with inter-column cells (in all tissues, tubules are bonded with intertubular cells). Column-like structures such as hairs are normally produced in an invagination below the surface of the skin, and by the time they reach the surface, they have become mature shafts. Since inter-cellular bonds of keratinous tissues appear to be formed before complete maturation of the cells, an inability to form strong bonding between the mature column and adjacent inter-column cells at the skin surface may have made it impossible to adapt these structures into the hoof wall during evolution. In addition, although solid structures would increase the amount of load-bearing material per unit of cross-sectional area, hollow fibers appear to prevent cooperative buckling and are presently being used in artificial polymer-matrix composites (see Baer et al. 1992). Therefore, hollow fibers may actually increase resistance to compressive failure of the wall. However, the production of columns, would also be mechanically advantageous since they would offer greater strength and toughness. In addition, fracture tests (Bertram and Gosline, 1986, 1987; Kasapi and Gosline, 1996, 1997) do not suggest any significant contribution of voids (medullary cavity) to Cook and Gordon crack stopping mechanisms (for an explanation, see Cook and Gordon, 1964). 177  Figure 4.5: (A) Illustration of a longitudinal section of the equine foot. (B) A low magnification illustration of the coronary border and cells of the hoof and (C) a high magnification illustration of the tubule and intertubular wall components illustrate the planar orientation of stratum medium cells with respects to their generative surfaces, and the planar orientation of fibers within cells, respectively.  178  c  179  If the production of hollow tubes is merely a manufacturing constraint, then why should medullary size and density increase progressing outwardly (see Figs. 4.3 and 4.4)? Tubules size does not correlate with the increase in medullary cavity cross-sectional area (see chapter 3). It may be simply that an increase in papillary size is required to produce the progressively more ellipticallyshaped tubules towards the outer wall. These results show that equine hoof wall tubules do not appear to have non-mechanical functions; their hollow form does not significantly increase the hoof wall hydration rate or flexural stiffness, and would have only a minor effect on decreasing the thermal conductivity of the wall. Therefore, equine hoof wall tubules appear to serve primarily mechanical functions such as crack redirection mechanisms (see chapter 3). Clearly, information about the mechanical properties of both the tubules and the intertubular material would aid in understanding the mechanical role of these wall components. In addition, an understanding of the form and function of the hoof wall is not complete without mechanical information on the primary building material, keratin, of which they are formed. The final experimental chapter of this thesis therefore documents the micro mechanics of the wall in order to couple form and function at the smaller scales of morphological hierarchy.  180  CHAPTER 5: OPTIMIZATION OF CRACK CONTROL AND MATERIAL STIFFNESS THROUGH THE MODULATION OF THE PROPERTIES OF KERATIN  181  INTRODUCTION Through the processes of selection there has been a remarkable convergence of both the designs and materials used in natural and synthetic structural systems. This is not surprising, as biological systems experience mechanical demands similar to those imposed on man-made systems. Biological structural elements, which often show high fracture toughness, have been used in manmade systems for millennia but have only recently been recognized as model designs for crack growth resistance. These elements are now known to be formed from nano-scale composites which are fundamental in providing high fracture toughness. Most structural biomaterials are composites of two or more nano-scale elements which usually include polymeric fibers embedded in either a globular or amorphous matrix. When combined, the two components, or phases, synergistically raise the fracture toughness beyond that of the individual elements. However, although this observation has been made in synthetic materials, it has yet to be shown empirically in biomaterials, and even in a highly-studied natural composite such as keratin, the mechanical contributions of each phase are still speculative. As described in chapter 1, keratin is a protein-based nano-scale composite with filamentous (IFs) and matrix phases (globular proteins) that are believed to have analogous roles to those of phases of fiber-reinforced composites. Beyond the composite nature of a-keratin at the nano-scale, tubules and intertubular material form what has been suggested to be a macro-scale composite (refer to Fig. 2.1B; Nickel, 1938a; Ryder, 1962), and the hoof wall may therefore be considered as a multilevel, or hierarchical composite. The mechanical functions of hoof wall tubules appear to be more complex than that of a simplefiberof afiber-reinforcedcomposite; design complexity in both the tubular and intertubular components facilitates the control of crack growth (chapter 3) and appears to increase fracture toughness. However, two fundamental, long-standing hypotheses of tubule function have yet to be 182  tested: that 1) tubules reinforce the wall along their axis of orientation and therefore, to some degree, are analogous to fibers offiber-reinforcedcomposites at the macro-scale and 2) the IFs and globular proteins of keratin form a composite at the nano-scale. Results from chapters 2 and 3 indicate that IF alignment does not correlate with mechanical stiffness and so appear to refute the analogy of keratin as a typical composite. However, since IFs appear to increase wall strength along their axes of orientation (chapters 2 and 3), it may be that the properties of keratin change through the hoof wall thickness, and that the functions of the phases are still conserved. If so, then on a local scale (within a small area of the wall) IF orientation should correlate with tensile stiffness, and each hoof wall cell should behave mechanically as a fiberreinforced composite. The structures that they comprise should therefore behave according to the alignment of their IFs and the mechanical properties of the keratin in that region. From the morphological results of chapter 3, it was determined that the innermost region of the hoof wall is morphologically ideal for determining the mechanical functions of the wall micro and macro components. It contains large (over 300 pm diameter), easily isolated tubules with IFs organized primarily along the tubule axis (see Fig. 3.4). In this region, most of the IFs in the surrounding intertubular material are aligned nearly perpendicular to the tubule axis. Simple tensile tests on isolated samples of tubules and intertubular material from this region may provide insight into the mechanical role of these substructures on a local scale, and may suggest roles of their constituent phases. Mechanical testing at a veryfinescale may be conducted to determine the mechanical properties of the phases, since the exact orientation of IFs within cells is now known (see chapter 3). Using the morphological map,finestrands of hoof wall material may now be obtained in which the precise IF orientation is known. By testing rows of cells from specific regions in orthogonal directions and with known IF alignment, estimates of the tensile stiffness of the nano-scalefiberand matrix phases may be obtained. This procedure would be more representative of the true keratin 183  phases than results from previous studies which utilized material (usually wool hairs) that were composed of many cells joined in series and in parallel. Hoof wall substructures are probably of paramount importance in providing high fracture toughness and controlling crack growth (see chapters 2 and 3). The mechanism by which they accomplish this, however, is still speculative since the mechanical properties of tubules and intertubular material are still unknown. Without information about the mechanical properties of these components, a complete understanding of the relationship between form and function is not possible. This study attempts to ascertain the functions of these substructures by quantifying the mechanical properties of isolated tubules and intertubular material specimens of equine hoof wall, and it also presents estimates of the properties of the nano-scale phases of a-keratin.  184  MATERIALS AND METHODS Hoof wall materialfromthe right front hoof of one animal (destroyed for reasons other than this study) was used here. It was decided that data from a single hoof was appropriate for this study to avoid inter-animal variability that may have added to the variance in the data, making small differences more difficult to distinguish statistically. The conserved wall morphology previously observed between animals (see chapter 3) indicated that data obtained from one animal may be generalized. The hoof was roughly cut with a bandsaw, and the hoof wall separated from the third phalanx with a scalpel. Care was taken not to remove any of the stratum medium. Tissues were then sealed in plastic bags (to retain moisture) and refrigerated at 4° C until used. Specific methodologies used in each type of test follow.  Tests on samples of tubule dimension.  Tests to determine the mechanical properties of tubules and intertubular material were conducted by first sectioning hoof wall blocks in the R-L plane. Sections approximately 300pm thick were produced using a water-cooled Gillings-Hamco thin sectioning machine equipped with a circular saw blade and then placed in distilled water with 0.2% sodium azide (to prevent bacterial growth). Under a dissecting microscope, individual tubules or strips of intertubular material were dissected out with a single-edge razor blade. Final test specimen size was approximately 300pm x 300pm x 25mm. Individual samples were placed on a wet paper towel (to minimize tissue dehydration), and the top surface of the specimen was blotted dry. A fine-tipped permanent black felt pen (Staedtler lumocolor) was used to mark a segment (mean 4.0 mm) near the center of the specimen. Sample ends were adhered to a cardboard frame using cyanoacrylate glue, and the frame was clamped to an apparatus designed for tensile testing of specimens under water (Fig. 5.1). The marking and adhesion steps were performed quickly (<2 min.) in order to minimize dehydration. Tests 185  Figure 5.1: The chamber used in the tensile testing of specimens of tubule dimensions. Specimens were adhered to a cardboard frame using cyanoacrylate glue and then clamped to the test apparatus. During tests, the chamber wasfilledwith distilled water and two O-ring oil seals mounted in the floor of the chamber permitted vertical sliding of the chamber while a specimen was mounted. Scale bar, 1cm.  186  187  were conducted at room temperature (approximately 20°C). An Instron 1122 testing machine was employed to provide a constant cross-head displacement rate of 2 mm min' (corresponding to a mean strain rate of approximately 3.33* 10' s"). Specimen 1  3  1  extension, however, was directly determined by tracking the change in length of the marked reference segment using a Panasonic video camera (model CL-350) which interfaced with a video dimension analyzer (VDA). A custom-made force transducer provided load data. Outputs from both devices interfaced with a PC and were sampled at 5 Hz using PC software (Labtech Notebook). Force (N) and VDA (m) data were processed on a spreadsheet to convert these parameters to stress, a (N m') and strain, e (AL/L , where L is the length of the marked reference segment), 2  0  0  respectively. Cross-sectional areas of specimens were required to convert forces to stresses, and were also necessary to ensure that the correct substructure was isolated. Used specimens were thinsectioned immediately adjacent to either end of the marked segment using a razor blade. Sections were viewed under a compound microscope at 40 times total magnification, and the images captured using a Panasonic (model WV-BL600) video camera which interfaced with a Matrox PIP frame grabber; an inner wall tubule cross-sectional sample is shown in Fig. 5.2. Vfor Windows software was utilized to digitize points necessary for the determination of cross-sectional areas. Extension data occasionally contained periods of noisy or otherwise unusable data as the result of VDA tracking difficulties. Therefore, a polynomial function was fit to extension data (Fig. 5.3) using Tablecurve software (Jandel Scientific), and this function was used to calculate specimen strain. The initial longitudinal modulus (or stiffness), E-^ , was defined as the slope of a linear L  regression which ran through the initial part of the stress-strain curve. A yield stress was determined with the offset method described in ASTM E8M-94a (ASTM, 1994a), using an offset strain of 0.5%. Total energy was found by determining the area under the stress-strain curve. The above procedures with the following modifications were also used to determine the 188  Figure 5.2: A video captured cross-sectional image of a tubule test specimen from the inner hoof wall. Inclusion of intertubular material with tubule specimens was unavoidable; the reverse was also occasionally the case. Scale bar, 100 pm.  189  190  Figure 5.3: A sample of raw strain data plotted as a function of time. A polynomial function was fit to each set of strain data, and the function used instead of the raw data.  191  192  hysteresis of wall macro-scale components. Specimen dimensions and strain data were not recorded since force-extension curves provide the energies necessary to determine energy loss or hysteresis. Extension was provided by the cross-head movement. Each test involved a single tensile cycle to either 2 % or 4 0 % extension.  Mechanical tests on horse hair.  It has been suggested that hoof wall tubules are hollow simply due to manufacturing constraints and that solid rods would be better reinforcing elements (chapter 3). Determination of the mechanical properties of body hairs immediately proximal to the hoof wall could therefore help to ascertain a possible compromise which may have occurred in hoof wall evolution. Ten body hairs were collected from the region just proximal to the hoof wall used in this study. The full length of the shaft was obtained by allowing the skin to degenerate for a few weeks at 4 ° C before removal. Hairs were then stored at 4 ° C in distilled water with 0.2% sodium azide until use. Specimens were mounted and marked using the aforementioned methods; however, it was not possible to track the marked segment with the video dimension analyzer. Instead, video output was routed through a Panasonic digital timer (0.01 sec resolution; model W J - 8 1 0 ) and recorded on a Panasonic (model AG-1960)  VCR. Strain data were obtained from taped sequences by digitizing each end of the  marked reference segment using V software. The initial 20 s period was digitized at 0.5 s intervals to obtain high resolution data for accurate determination of the initial stiffness, and 4 s interval for the remainder of the test. A polynomial function was fit to extension data using Tablecurve software (Jandel Scientific), and this function was used to calculate specimen strain. Four samples of fully hydrated horse hair tail hair approximately 2 0 0 mm long were tested at a strain rate of 4 . 2 x 1 0 " s" 3  using the cross-head displacement to determine strain.  193  1  Cell strand production and mechanical testing.  Threads of hoof wall tissue containing a single row of cells (Fig. 5.4) were produced by first shaping the wall tissue into approximately 1 cm blocks that encompassed the entire wall thickness. 3  Seven micron thick sections were produced with a microtome (American Optical, model 820 with a stainless steel blade), and then placed in distilled water. Specimens were then sectioned perpendicular to the plane of the section to produce narrow strips. To do this, wet sections were first sandwiched between two Teflon sheets (0.8 mm thick). A water-soluble embedding medium (TissueTek OCT. Compound) was applied to afreezingmicrotome stage, and a section was placed into the solution on one end. The stage was then cooled to approximately -10° C, thereby adhering the specimen perpendicular to the stage surface. The Teflon sheets were then removed and additional mounting solution applied to fully secure the sections. The freezing microtome was equipped with a disposable stainless steel blade and was set to produce 7.5 pm thick sections. This procedure produced single rows of cells measuring approx. 7pm><7.5pmx 10mm. To produce rows of cells from inner wall tubules the first section was made in the C-L plane; the second, orthogonal section was along the R-L plane (Fig. 5.4A). Single rows of cells from the inner and middle intertubular material were produced by first sectioning blocks along the circumferential-radial (C-R) plane and then along the C-L plane (Fig. 5.4B). Test specimens were carefully removed from the blade by gently rolling the end of a glass rod in the melted embedding medium containing the strands. The rod was dipped into a petri dish containing distilled water to dissolve the mounting solution and free the specimens. Strands were removed from the distilled water using a 2-pronged miniature fork constructed from insect pins. Dehydration of specimens occurred almost immediately after removal from the water. Dehydrated strands were then transferred to a mechanical test system. A micro mechanical test apparatus (Fig. 5.5) was constructed to test the mechanical properties of hoof wall cell strands at room temperature. The body of the test system was a milled 194  Figure 5.4: Illustrations of cell strand specimen preparation. 7 pm sections were produced from a hoof wall block that was approximately 1 cm. Specimens were then sectioned 7.5 pm wide perpendicular to the first plane of section by freezing onto a freezing microtome stage in an upright position using mounting medium. Test specimens were either produced by (A) first sectioning in the C-L plane and then the R-L plane or C-R plane, or (B) byfirstsectioning in the C-R plane and then the C-L plane or R-L plane. Captured images from actual tests on midwall samples tested parallel to (on-fiber) and perpendicular to (across-fiber) the IF axis are shown in C and D, respectively. Cell boundaries are clearly visible and were used as landmarks for strain measurements. Scale bars, 10 pm. 3  195  196  Figure 5.5: Micro mechanical test system. The test system consisted of a very sensitive force transducer and a motor-controlled micrometer that provided a constant displacement rate. Dry cell strand test specimens were adhered to the surface of stainless steel rods which were adhered to the force transducer and micrometer arms. The instrument armsfitinto a well so that the tests could be conducted under water. The entire apparatusfiton the stage of a Leitz compound microscope was constructed to permit stage rotation of about 180 degrees. Tests were observed with a 40x water immersion objective lens.  197  198  plexiglass block that fit onto the stage of a Leitz Orthoplan Polarizing compound microscope. A custom-made force transducerfitinto the well such that it was submerged in distilled water during an experiment, allowing experiments to be conducted under water. A stainless steel wire extension wasfixedto the end of the transducer beam, and another was attached to the end of a micrometer. A drive system consisting of a small motor provided a constant displacement rate (2.37 mm min ). -1  A mounting apparatus was constructed for precise mounting of the strands. Specimens were fixed to the apparatus and slowly lowered across the wire extensions onto two drops of adhesive (Devcon 5 minute epoxy). During an experiment, force data were collected at 5Hz using a PC with an analogue-todigital board and Labtech Notebook software. Specimens were illuminated with plane polarized light and viewed with a 40x water immersion objective lens (total magnification = 400 times). Tests were recorded using a Panasonic (model WV-BL600) video camera attached to the microscope; the former interfaced with the digital timer and the VCR. Strain data were obtained from taped sequences by digitizing selected points of a single cell using V software. Strain measurements were synchronized with force traces by determining the time of failure on the video tape and in the force record (failure occurred in a single frame). Taped sequences of the initial 10 s period were digitized at 0.25 s intervals, and at 0.5 s intervals for the remainder of the test. It was determined that for these sequences a linear regression would best describe the strain data. Captured images from taped sequences were then used to determine one dimension (that visible on the monitor) of the cell strands and it was estimated that the second dimension was 7 pm.  Determination of the effects of dehydration andfreezing.  To determine the possible effect of dehydration (which occurred during test specimen preparation) on the stiffness of wall tissue, three-point bend tests were conducted on fully-hydrated 199  specimens before and after dehydration at room temperature. Dynamic tests were conducted because this methodology does not require mounting and thereby avoids material dehydration. The dynamic test system was not sensitive enough to determine the properties of single cell strands or specimens the dimensions of individual tubules; consequently, specimens for this series of experiments were thicker, measuring approximately 12><lxl mm. The three-point bend apparatus (described previously in Katz and Gosline, 1992) ultimately provides the storage modulus parameter E' as a function of frequency. However, since only the relative changes in mechanical properties were investigated, quantification of specimen dimensions was not required and data are therefore reported as magnitude (the ratio of the input load to the output load) and phase (the phase difference between the force and displacement recording) as a function of frequency. Small-amplitude vibrations at frequencies ranging  from 0.04-100 Hz were applied to the beams and a pre-load of approximately 9 g was applied to each beam. To determine if freezing affected the initial modulus of tissue samples, three point bend tests were also conducted on hoof wall beams before and after freezing on the microtome stage. Specimens of the same approximate dimensions as those listed above were produced, and a preload ranging from 2-4 g was applied to each beam. Samples were tested before and after being frozen for approximately 10 min. Mechanical properties were characterized over the same frequency range mentioned above.  Birefringence measurements and the determination of IF volume fraction.  The volume fractions of each phase of the keratin composite was determined by converting birefringence measurements to % IF content. To do this, a calibration was needed that related IF volume fraction to birefringence. Tissue birefringence is easily determined; however, IF content is more difficult to ascertain. Therefore, a previously reported value of IF volume fraction for another hard cc-keratin was used. Bendit (1980) determined the total matrix phase volume fractions for 200  various hard a-keratin tissues. His value for horse hair was chosen for the birefringence calibration, since this tissue was felt to be most closely related to the hoof wall. Although it was not specified in the study, it is assumed here that tail hair was used since these specimens are largest and easily accessible. The birefringence B of dry horse tail hair was first determined with green light (\-546 nm) following the A/4-plate Senarmont method and using the relationship:  B=-  Eq. 5.1.  t  where the specimen retardation jP(in nm) is 3.033 nm degree" x 0(the extinction angle in degrees) 1  and t is specimen thickness (in nm). The volume fraction of horse hair a-keratin matrix (high sulfur and high glycine-tyrosine) and IF proteins are 2 4 % and 7 6 % , respectively (Bendit,  1980). The  assumption was made that all birefringence was due to IFs. Normalizing % IF content for mean horse hair birefringence  (2.19xl0" ±0.08xl0" 2  2  degrees nm"; mean±l S.E.M.), provided the calibration 1  factor necessary to convert birefringence to IF volume fraction (3.48x IO" %IF B' ). However, since 3  x  birefringence is dependent on specimen thickness, the accuracy of the microtome sectioning procedure was quantified. Using the light microscope, sixteen thickness measurements were made on each of three hoof wall sections (produced from a dry hoof block with a microtome setting of 10pm). The pooled mean from the 48 measurements was 1 0 . 2 ± 0 . 2 pm (mean±l S.E.M.).  Birefringence measurements were made on 10 pm sections produced from a dry hoof block. Both cross-sectional (C-R plane) and longitudinal (R-L plane) sections were necessary to determine the birefringence of tubules and intertubular material. Three R-L plane sections were used to determine birefringence of inner tubules, and three sections were produced to determine the birefringence of the intertubular material from inner, middle and outer regions. Samples were 201  mounted in immersion oil, and 20 birefringence measurements were made from each section (i.e. 60 measurements for each of the inner tubules, and inner, middle and outer intertubular material).  202  RESULTS  The effects offreezing / dehydration.  Neither the freezing nor the dehydration method produced a measurable effect on the initial modulus of hoof wall specimens over the frequency range tested. Fig. 5.6A compares properties from a sample before and after complete dehydration. The shapes of all curves were very similar before and after treatment, and differences in both magnitude and phase could be attributed to mounting error. Fig. 5.6B shows the mechanical response of a specimen before and after removal and remounting without treatment, and it exemplifies the apparent changes in mechanical properties due simply to the remounting procedure. These artifacts were also apparent in tests to determine the effect of freezing. In these tests, the differences in the curves (Fig. 5.6C) could be accounted for as the manifestation of mounting artifacts. These results agree with those of Landeau el al. (1983) who found no effect of repeated rehydration on the compressive mechanical behavior of equine hoof wall but disagree with Leach (1980) who found that freezing of equine hoof wall specimens at -20 °C lowered the initial longitudinal compressive modulus by 13%. The differences are probably due to dissimilarities in methodology (his specimens were frozen for 2 days, whereas specimens in this study were frozen for only a few minutes; his freezing temperature was about 10°C colder than that of the sample preparation and he measured compressive stiffness, not tensile stiffness).  The tensile properties of specimens of tubule dimension.  The shapes of stress-strain curves from both hoof wall macro-scale components and body hairs were similar to those obtained from mechanical tests of specimens of a much larger scale (see chapters 2 and 3). Representative stress-strain curves for tubules and intertubular material from the inner and middle regions are compared in Fig. 5.7A,B with horse body hair samples. In all tensile tests, stress-strain curves showed an initially stiff, near linear region followed by a rapid decline in 203  Figure 5.6. Storage magnitude (analogous to E) plotted against test frequency. (A) The effects of dehydration and (C) the effects of freezing were negligible; artifacts resulting from mounting inconsistencies (B) were sufficient to explain slight differences before and after treatment.  204  Hydrated Rehydrated Dry  B  First mount Second mount  Before freezing After freezing  o o o  20  _L  J_  40  60  Frequency (Hz)  205  80  100  Figure 5.7. (A) Tubule and (B) intertubular material stress-strain curves for inner, mid-wall and horse body hair specimens. Only samples are given and may not necessarily represent the average mechanical behavior of the specimens.  206  2.5e+7 \ -  2.0e+7 h  ^ fe  1.5e+7  v>  in <U  £  1.0e+7  Inner wall tubules Mid-wall tubules Horse hair  5.0e+6  O.Oe+0 0.6  2.5e+7  B  Inner wall intertubular material Mid-wall intertubular material  2.0e+7 h  y fe  1.5e+7  cn Vi  &  1.0e+7  5.0e+6  0.0e+0 0.0  0.1  0.2  0.3  Strain  207  0.4  0.5  0.6  instantaneous modulus. After a period of relatively low resistance to extension, the sample stiffness gradually rose until failure. Initial longitudinal tensile stiffness or modulus E of wall macro-scale components was iL  dependent on region through the wall thickness and correlated locally with IF orientation. £  iL  of  tubulesfromthe inner third of the wall was highest (0.47 GPa; Table 5.1) and about six-fold higher than that of the adjacent intertubular material (0.080 GPa). The stiffnesses recorded for these tubules ranged almost one order of magnitude, from 0.12-1.14 GPa; a 3-fold range of-Ej was recorded for the intertubular material in this region (from 0.04-0.12 GPa). Tubules from the mid-wall and body hairs obtained just proximal to the hoof wall, however, showed a mean initial tensile stiffness similar to that of the inner region tubules (0.36 and 0.45 GPa, respectively). Horse tail hair E was 2.3±0.1 t  GPa (mean±l S.E.M.). As with inner wall tubules, a large range of stiffness values was recorded for mid-wall tubules, with values ranging from 0.14-0.57 GPa. Although E of the intertubular material iL  from the middle region (0.14 GPa) was approximately 2-fold less stiff than tubules from the same region, this difference was not statistically significant; the range in stiffness for these samples was over 6-fold (0.04-0.27 GPa). Horse body hair specimens yielded at stresses (6.6 MPa) considerably higher than any hoof wall macro-scale component, and their mean yield stress was over 2-fold higher than that of the inner wall intertubular samples. Surprisingly, inner wall tubules yielded at a stress (4.2 MPa) that was not significantly different than that of mid-wall tubules (4.8 GPa) and was very similar to that of mid-wall intertubular samples (4.1 MPa). Yield stresses of inner (2.9 MPa) and mid-wall (4.1 MPa) intertubular materials were statistically similar. Failure appeared to occur randomly along the specimen length and was therefore not likely influenced by the grips or marking of the specimen. Since ultimate properties from specimens that failed near the grips were often higher than those that failed away from them, they were included in 208  Table 5.1: Mean longitudinal mechanical properties for hoof wall macro-scale components of tubule dimension and horse body hairs obtained just proximal to the hoof wall. Data are presented as mean ± 1 S.E.M. Values in columns with similar symbols are statistically different from one another (ANOVA; P<0.05). The number of specimens used is indicated under the specimen type, unless otherwise indicated. E from one horse body hair tensile test was omitted due to an irregular stress-strain curve at the beginning of the experiment. SNK - StudentNewman-Keuls. lL  Inner  Middle  Maximum Maximum stress strain (MPa)  Initial modulus (GPa)  Total energy (MJ m")  Yield stress (MPa)  Tubule (/V=7)  0.47±0.17 t  8.3±2.9 t  4.2±0.4  22±2  0.56±0.04  Intertubular (AN 10)  0.08±0.01 t§  4.4±0.5  2.9±0.3 t  15±2 §J  0.60±0.01 t  Tubule  0.29±0.09  2.8±0.8 t  4.8±1.0  11±1 JV  0.36±0.10  Intertubular  0.14±0.05  3.0±1.0  4.1±0.4  10±2  0.43±0.13  Horse body hair  0.45±0.06 (N=9)§  4.7±0.4  6.6±0.2 t  20±1  m  0.44±0.02 t  Dunn's  Dunn's  Dunn's  SNK  Dunn's  (N=4)  3  (N=\0)  209  ttJ  n  the data analysis. Ultimate stress was highly dependent on specimen type (ranging from 10 MPa in mid-wall intertubular specimens to 22 MPa in inner wall tubules; Table 5.1), whereas maximum strain was independent (pooled mean = 0.52). Total energy was not highly dependent on specimen type, however, inner wall tubules were 3-fold tougher than mid-wall tubules (8.3 MJ m' and 2.8 MJ m", 3  3  respectively). Due to the low sample sizes, statistical analyses were neither performed on hysteresis nor extension resistance data; however, large, unexpected differences were observed that are worth noting. Hysteresis in tests conducted to 40% extension were at least 2-fold higher than those found in tests conducted to 2% extension (Table 5.2). In the latter tests, lowest hysteresis was found in inner wall intertubular samples (7.8%) and highest values were found in mid-wall intertubular specimens (23.8%). Inner and mid-wall tubules had similar mean hysteresis values (16.4% and 19.1%, respectively). When strained to 40% extension, the hysteresis of inner wall tubules and intertubular samples were similar (40.0% and 37.6%, respectively), as were those of the mid-wall tubules and the intertubular material (50.8% and 49.9%, respectively). After a 30 min. recovery period, inner wall tubules showed a 2.5-fold reduction in hysteresis  in tests conducted to 2% strain. There was also a marked decline in inner and mid-wall tubules tested to 40% extension. This phenomenon was also observed in intertubular samples from the inner and mid-wall extended by 40%, with hysteresis values dropping 2.3% and 4.6%, respectively, after a 30 min. recovery period. In contrast, the hysteresis of inner wall intertubular material tested to 2% extension rosefrom7.8 to 16.5%. There were no exceptions to these trends in any of these tests. In tubule samplesfromthe mid-wall tested to 2% extension, a slight increase in hysteresis was observed; however, this rise did not always occur (in one of the samples, the hysteresis was lower after 30 min). The hysteresis of intertubular samplesfromthis region tested to 2% extension was slightly lower after the recovery period, although this behavior was also inconsistent (the hysteresis of one sample was 210  Table 5.2: Hysteresis data for tensile loading of hoof wall macro-scale components. Data are presented as mean ± 1 S.E.M.  Hysteresis (%) 2% extension Tubule  0 min  30 min  16.4±3.8  6.4±2.5  (N=3)  Inner  Intertubular  Middle  0 min  30 min  40.0±1.3 38.8±0.1 (N=2)  7.8±4.5 (N=2)  Tubule  40% extension  16.5±2.3 37.6±1.5 34.3±1.0 (N=2) (7V=2) (tf=2)  19.1±2.4 20.1±1.3 50.8±0.6 46.6±0.6 (N=4) (N=3) (/V=4) (N=3)  Intertubular 23.8±2.6 21.8±2.2 49.9±0.8 45.3±0.7 (N=3) (N=3) (N=3) (/V=3)  211  higher after the 30 min. recovery period). Since the dimensions of samples subjected to hysteresis tests were not determined, extension resistances (force/extension) of the initial portion of the curve were measured instead of the normalized modulus parameter E. The extension resistance, however, is analogous toE. In all tests conducted to 2% strain, extension resistance increased after the 30 min. recovery period; in tests conducted to 40% strain, extension resistance was considerably lower after the recovery period (Table 5.3).  The mechanical properties of cells from tubules and intertubular material.  Tests on specimens of this dimension were extremely difficult to conduct; of all the samples sectioned, only a small fraction were successfully mounted on the test system. Of the 45 samples that were successfully mounted, only data from 20 tests could be analyzed. Specimens were rejected as a result of either premature failure or unsuitable video recordings (due to excessive movement of specimens, or unsuitable strain markers). Fig. 5.8 shows data from mid-wall cell strand experiments; Fig. 5.8A shows a sample of raw force and digitized strain data of an on-fiber tensile specimen from the middle region. In Fig. 5.8B, the data from Fig. 5.8A has been converted into stress and strain and the data plotted as open circles. For comparison, an across-fiber specimen is also plotted (solid triangles). In all cell strand specimens, the mean initial tensile modulus E of cells was much higher x  along thefiberaxis than across (Table 5.4). Although an analysis of variance (ANOVA) found a statistically significant difference between means, the pairwise multiple comparison procedure (Student-Newman-Keuls method) could not determine any differences, probably as a result of the low sample sizes. It is worth noting, however, that mean on-fiber E- (range=0.17-0.85 GPa) was t  approximately 10-fold higher than the across-fiber E (range=0.020-0.080 GPa) of tubule cells from {  the inner region, and intertubular on-fiber E values were 24 and 12-fold higher than the across-fiber t  E for inner and mid-wall cells, respectively. On-fiber E for inner wall intertubular cells ranged from {  {  212  Table 5.3: Change in initial extension resistance after 30 minutes. Note: Positive values indicate increase in extension resistance, negative values denote a decrease.  Change in initial extension resistance after 30 minutes (%) Tubule Inner  Intertubular Tubule Intertubular  2% extension  40% extension  2.0±1.3  -9.4±2.5  (N=3)  (#=2)  3.0±1.8  -8.99±0.01  (N=2)  (N=2)  2.6±1.6 (/V=3)  -18.9±0.9  29±19 (/V=3)  -20±1  213  (tf=4) (N=3)  Table 5.4: Initial nano-scale tensile modulus values of cells from different wall macro-scale components and regions. Data are presented as mean±l S.E.M.  Initial tensile modulus, E (GPa) {  Tubule Inner Middle  Intertubular Intertubular  On-fiber  Across-fiber  0.42±0.21 (N=3)  0.036±O.OT5 (#=4)  0.51±0.17  0.021±0.009  (N=3)  (N=3)  0.91±0.34  0.077±0.018  (N=4)  (N=3)  214  Figure 5.8. (A) Raw force and strain data for an on-fiber cell strand specimen from the mid-wall. The raw force data and strain data regression line were used to produce the stress-strain curve in B (open circles). The initial modulus E was determined by running a linear regression through the initial portion of the curve. A mid-wall across-fiber test (filled circle) is included in B for comparison. (C) stress-strain regression lines for all mid-wall on-fiber and across-fiber specimens used in this study. Although statistical analyzes could not distinguish a significant difference between mean initial stiffnesses, the data lines are clearly clustered in separate areas of the graph, and there is no overlap between curves from on- and across-fiber tests. x  215  0.0  0.1  0.2  0.3  0.4  Strain 1.2e+7 1.0e+7 ^ 8.0e+6 03  8 6.0e+6 M  4.0e+6 2.0e+6 0.0e+0 0.00  0.05  0.10 0.15 Strain  216  0.20  0.5  0.17-0.69 GPa; across-fiber E for cells from this material ranged from 0.012-0.039 GPa. On-fiber {  and across-fiber E were similar between tubules and intertubular material of the inner region. Mid{  wall intertubular on- and across-fiber E values (ranges=0.47-1.90 GPa and 0.056-0.11 GPa, {  respectively), however, were approximately double those of the inner wall samples.  IF volume fraction.  There was no significant difference in IF volume fraction between cells of tubules (22%) and the intertubular material of the inner wall (23%; Table 5.5); however, the pooled volume fraction of IFs in these cells (23%) was significantly lower than those of the intertubular material from the middle (31%) and outer wall (30%). No difference in IF volume fraction was found between middle and outer wall intertubular cells.  217  Table 5.5: Birefringence data (top) and corresponding intermediate filament volume fractions (below) of cellsfromtubules and intertubular material. Data are presented as mean ± 1 S.E.M. Values with similar symbols are statistically different from one another (Student-Newman-Keuls; P<0.05); only statistics for IF volume fraction are shown. N=60 for each.  Birefringence and IF volume fraction (%) Region Inner  Middle  Intertubular  6.6±0.2xl0" 23±lfJ  Tubular  6.4±0.1xlfj  9.0±0.1xl0" 31±lf§  3  3  22±1§V  218  Outer 3  8.8±0.2xlfj 30±1JV  3  DISCUSSION Modulation of the wall properties through modification of the properties of keratin.  A gradual change in stiffness through the wall thickness has been noted by Leach (1980) and has also been documented in chapter 2. This progression to a stiffer material proceeding outwards appears to be necessary to provide for a more gentle transfer of loads to the collagenous suspensory elements of the dermis, and arises partly due to the relative proximity of the tissue to the source of moisture (see Leach, 1980). This gradation of stiffness has been correlated with water content (Leach, 1980; chapter 2), and it has been suggested that the change in water content alone could account for these differences (chapter 2); however, results from this study offer an additional explanation. Current findings suggest that the IF volume fraction changes through the wall thickness. IF contents in the outer and mid-wall are higher than that of the inner wall by 30% and 35%, respectively, (see Table 5.5). Since IFs are believed to provide most of the stiffness in a-keratins, this reduction in IF content would explain the low E of the inner wall relative to the middle and outer iL  wall found in chapter 2, even though IFs of the inner wall are more strongly aligned along the tubule axis (the test axis) than in either the mid-wall or outer wall (see chapter 3). Within the inner region, the IF volume fractions of cells from tubules and the intertubular material are similar, implying that locally IF volume fraction is constant. Modulation of the wall stiffness through variation in IF volume fraction may be necessary since IFs in tubules and intertubular material of the mid-wall are generally  aligned at a large angle to the tubule axis, and much of those in the inner wall are organized along the tubule axis (see Figs 3.4, 3.6). If the LF volume fraction was constant across the wall, the strong axial IF orientation of the inner wall would result in a higher tensile stiffness than has been observed in this region (see chapter 2). An increase in IF volume fraction is not necessary to raise the longitudinal stiffness from the middle to outer wall, since intertubular IF alignment is closer to the tubule axis 219  towards the outer wall (for the formation of another crack diversion mechanism; see chapter 3), and this alignment alone should increase E . In this manner, although the IF volume fractions of the mid lL  and outer wall are similar (see Table 5.5), the stiffness increases towards the outer wall. Therefore, findings from this study suggest that the mechanical properties of hoof wall material are also modulated by varying both the IF organization and volume fraction. Variation in the mechanical properties of hard a-keratins by modification of IF volume fraction also appears to have occurred between different tissue types (Bendit and Gillespie, 1978; Bendit, 1980; also see Fraser and MacRae, 1980). Bendit (1980) found a strong correlation between matrix protein content and transverse compressive E for various hard a-keratins. His findings suggest x  that the modulation of hard a-keratin mechanical properties between tissues of different animals has been achieved through the variation of the ratio of matrix proteins to IF proteins. Differences also exist in the protein constituents of the hoof wall. Grosenbaugh and Hood (1992) found variations in both matrix and IF protein constituents between the stratum internum and stratum medium of the equine hoof wall. It is not known, however, whether these differences exist within the stratum medium, and if this would affect the mechanical properties of the tissue. If modulation of IF content in the hoof wall serves to control the wall stiffness, then one must also explain why modulation of the properties of keratin is necessary to counter the effects of IF orientation in a particular region. Clearly, IF organization must serve a role other than to affect the material stiffness, or the desired stiffness would simply be achieved with the appropriate IF alignment. It is suggested in chapter 3 that the evolution of hoof wall design may be explained in terms of fracture control. In the inner wall where material stiffness must be relatively low for safe load transfer, a possible crack diversion mechanism has been identified that prevents cracks from propagating inwards. The inner wall mechanism has been formed with the production of relatively large tubules (up to 385 pm diameter; data not shown) with IFs oriented primarily along the tubule axis (see Fig. 220  3.4). This particular morphology redirects cracks initiated inwards to a path along the tubule axis, since mechanical tests show that cracks apparentlyfindpropagation across the IF axis more difficult than along the IF axis (see chapters 2 and 3). In addition to associating with most of the cellular water (see Fueghelman, 1994), matrix proteins appear to have a much lower tensile stiffness than IF proteins (Feughelman, 1959). Due to the low sample sizes of these tests, however, it was not possible to provide statistical confirmation of the effects of IF volume fraction on the mechanical properties. The results shown in Fig. 5.8B,C suggest large differences in mechanical properties between IF and matrix proteins. Therefore, results from this study agree with those of Feughelman (1959). Using resultsfromthis study, rough estimates for the tensile stiffnesses of the matrix and IF proteins may be obtained. If the transverse (across-fiber) modulus is assumed to be roughly equal to the matrix stiffness, then E of the fully hydrated matrix protein is approximately 0.03 GPa (the t  average of the two inner wall across-fiber values; see Table 5.4). This value is similar to that obtained for the matrix compressive E from fully hydrated horse hair specimens (0.06-0.13 GPa; Bendit, {  1980). By rearranging Eq. 1.2 and approximating the volumefractionsof the phases at full hydration, we may estimate E for the IF proteins. The water contents of fully hydrated inner and mid-wall iL  specimens are approximately 48% and 41%, respectively (chapter 2). Using an average dry hoof wall (ignoring the medullary cavity) density of 1200 kg m" (data not shown), these values equal 37% and 3  33% water volume fraction for inner and mid-wall, respectively. If we assume that the water associates exclusively with the matrix proteins, then the inner and mid-wall fully hydrated matrix volume fractions equal 85% and 79%, respectively. Assuming that the mechanical properties of matrix proteins are isotropic, and assigning V = 0.85 for the inner wall, wefindthat inner wall E is n  {  approximately 3 GPa, approximately 100-fold higher than that of the wet matrix E,. Using E -0.03 m  for the mid-wall (the inner wall estimate is better than the mid-wall across-fiber value, since the inner 221  wall wet matrix volume fraction is higher), an estimate of Ef=4 GPa for the mid-wall is obtained. These estimates agree reasonably well with a previous estimate of E (4.6 GPa) obtained by f  Feughelman (1959). The differences in IF volume fraction do not correlate well with the gradation in water content. In chapter 2, inner, middle and outer wall water contents (at 100% relative humidity) were estimated to be 48, 41 and 35%, respectively. The inner wall is expected to be more hydrated than the middle and outer wall at the same relative humidity; however, according to IF volume fraction, middle and outer wall samples should have the same water content. This discrepancy may be due, at least in part, to differences in tubule morphology. Using data from chapter 3, the medullary cavities of mid- and outer wall tubules occupy 1.5% and 4.5% of the hoof wall area, respectively. There is therefore correspondingly less stratum medium material in the outer wall to absorb water and hence the lower water content. Possible differences in protein type and content could also contribute to the discrepancy.  Mechanical properties of the macro-scale components of the hoof wall.  Hysteresis represents the energy loss of a system during loading. The hysteresis even at a low extension (2%), which is thought to be within the linear range of this material, suggests that viscoelastic behavior is a significant factor in the mechanical properties of this material even at low strains (see Table 5.2). It further suggests that pre-straining of this material in mechanical tests is not recommended, as the material properties will change even with low pre-strains. It should also be noted that in situ hysteresis is expected to be higher for all tests, since specimens were tested at hydration levels beyond their normal states, and viscous energy loss of polymeric systems decreases as water content increases. The increase in extension resistance after the initial cycle suggests that some molecular 222  reordering has occurred along the test axis and that full reversion has not occurred even after 30 min. (see Table 5.3); re-zeroing of the crosshead was necessary, even after the recovery period, to take up the slack that resulted after the first cycle. It is not possible to determine if the increase in resistance is due to IF or matrix proteins movement; however, results in Table 5.2 suggest that matrix proteins are not the primary source of the energy loss. In most tests, lowest hysteresis is observed in inner wall intertubular samples which have IFs aligned primarily perpendicular to the test axis. If matrix proteins were the primary viscoelastic components of a-keratin, then inner wall intertubular specimens should display the highest loss, since IFs of these samples will generally bear load perpendicular to, not along their primary axis and would therefore not likely contribute significantly to the process. Instead, higher hysteresis is observed in samples where the loading direction is along the IF axis, suggesting that IFs are viscoelastic. In the mid-wall, intertubular and tubular hysteresis are very similar due to the general similarities in IF orientation relative to the tubule axis. With a large extension (40%), samples showed high mean energy losses ranging from 3851%. The hysteresis was slightly lower after the recovery period, suggesting some molecular reordering of the composite. However, in these tests the extension resistance was generally lower in the second cycle, suggesting a number of possibilities. Some reordering may have occurred that resulted in a loss of molecular alignment along the test axis. Sliding of molecules appears to have occurred to cause specimens to remain in an extended state; consequently they became narrower. Since specimen dimensions were not corrected after the first cycle, extension resistances would be underestimates of the true material properties. Molecular disruption may have also occurred at this extension, resulting in inferior mechanical properties after the first cycle. Birefringence measurements on wool tested to a strain of 60% suggest that specimens will revert to their original conformation when provided with a sufficient recovery period (Gupta and Rao, 1991). The higher hysteresis in mid-wall samples is unexpected and impossible to rationalize on the 223  basis of molecular order. In inner wall tubule and intertubular samples where the general IF alignment is parallel and perpendicular to the test axis, respectively, hysteresis values are similar and considerably lower than those of the mid-wall where IFs are generally at intermediate angles. This result is also contrary to that expected based on the differences in IF volume fraction. Clearly some other variable component of the a-keratin composite is responsible for this observation, and further testing is necessary to understand this behavior. It has been suggested recently that tubules are hollow simply due to a manufacturing constraint and that the incorporation of solid fibers would be mechanically advantageous (chapter 3). If this is true, then this compromise may be reflected in a difference in mechanical properties between tubules and hair. Apart from possibly offering resistance to cooperative buckling, no other justification for the incorporation of hollowfibersinto a composite has been provided, as they offer only minor improvements in bending stiffness, decreased thermal conductivity, and their hollow form does not serve to facilitate hydration of distal portions of the wall to maintain optimal fracture properties (see chapter 4). Interestingly, the mechanical properties of horse body hairs obtained from the area just proximal to the coronary band are similar to those of the inner wall tubules. Although this finding shows that the tensile properties have not been compromised in the formation of hollow tubules, tubules do not appear to confer any advantage to the tensile properties of the wall over that which would be conferred by the incorporation of horse hairs. They would still, however, act as localized stress raisers and may therefore reduce the relative fracture toughness. The similarity in E- between inner equine hoof wall tubules and body hair is not in conflict with t  the difference in IF volume fraction (23% and 76%, respectively). E-^ of fully hydrated horse tail hairs L  (2.3 GPa) is 4.8-fold higher than that of inner wall tubules and horse body hair (0.47 and 0.45 GPa, respectively). This suggests that the IF content of equine body hair is much lower than that of tail hair, and similar to that of inner wall tubules. The 3.3-fold higher IF content of tail hair explains most 224  of the observed differences in E^ , and suggests that this is indeed the hair type examined by Bendit L  (1980). Findings from chapters 2 and 3 suggest that although the mechanical functions of tubules depend on their position through the wall, all tubules provide some degree of mechanical reinforcement along their longitudinal axes. Tubules of the inner wall appeared to provide the highest degree of reinforcement along the primary axis, probably as the result of a high degree of IF organization along the axis. Results of this study show that these tubules, which occupy up to 50% of the stratum medium material in the inner wall (see chapter 3), are the high (longitudinal) stiffness elements of this region. In this sense, this region of the wall functions as a macro-scale composite, however, it must be noted that the intertubular material may not be considered a 'matrix', since it is formed from highly ordered IFs and would therefore not likely be isotropic. Inner wall tubules are capable of withstanding a 1.4-fold higher stress before yielding (Table 5.1), and a 1.9-fold higher stress before failure than the adjacent intertubular material. These findings suggest that the high degree of IF alignment along the tubule axis offers relatively high resistance to deformation, and delays any permanent or temporary molecular re-ordering such as a partial transition from a-helices to P-sheets (see Bendit, 1960), relative to the intertubular material. It should be noted here that perfect isolation of wall macro-scale components was not possible, and therefore tubule specimens contained a portion of the intertubular material (Fig. 5.2) and occasionally, vice versa. If the true ultimate (failure) properties of one component is higher than that of the other, then the ultimate properties will be compromised by the weaker, component. Since perfect isolation of a desired wall macro-scale component was virtually impossible, this may explain the similarity in this parameter between tubules and the intertubular material from both regions (see Table 5.1), and this would result in an underestimation of the ultimate properties of the stronger, tougher component. In the mid-wall, all material properties determined here are statistically similar between the 225  tubules and intertubular material. Based on the E  U L  values obtained here and a whole tubule volume  fraction of 29% (data not shown), the averageE for fully hydrated mid-wall should be 0.18 GPa. IL  This is considerably lower than the mean mid-wall E  of 0.43 GPa determined in chapter 2. If,  L L  however, highest recorded values for the tubules (0.57 GPa) and intertubular material (0.27 GPa) are considered, the resulting average mid-wall E- (0.36 GPa) would be much closer to that previously KL  recorded. This suggests that the mean mid-wall E-^ data presented here are underestimates of the L  actual  and that highest recorded values are probably closer to the true E^ of these macro-scale L  wall components. Based on this and the similarities of all other parameters between mid-wall tubules and intertubular material (see Table 5.1), mid-wall tubules would not act to reinforce the longitudinal stiffness to a great extent. This explains why only minor crack deviation occurs as a propagating crack encounters tubules in this region (see chapters 2 and 3). The-E^L values presented here for inner wall tubules agree with the on-fiber tensile modulus of cellsfrominner wall tubules (compare Tables 1 and 4). This result suggests that the methodologies for these tests are reliable, and confirms that most of the inner wall tubular IF alignment is along the tubule axis. However, the true material E of these tubules is approximately 10-13% higher than the IL  values presented here, since the cross-sectional areas included the medullary space which does not support load. Areas were not corrected to permit direct comparisons with previous tensile tests. Since tubule samples contained some intertubular material (see Fig. 5.2), E for these structures are again X  underestimated; the highest values (~ 1 GPa) are probably more representative of the true E of these {  structures. Using Eq. 1.2, an average whole inner wall E of 0.30 GPa (chapter 2) and an intertubular {  E of 0.08 GPa, inner tubules should constitute about 56% of the inner hoof wall; however, the actual T  average area occupied by these tubules is approximately 32%. The underestimation of tubule stiffness is probably responsible for this discrepancy since, based on the data presented here, the average tubule stiffness should be 1 GPa. This suggests that the mean on-fiber E- for cells from this region is T  226  also an underestimate, and the highest value (0.85 GPa) is probably closer to the true on-fiber E for {  these cells. This discrepancy could result from the necessary assumption of one of the cell strand dimensions (recall that only one dimension could be verified).  Other levels of the mechanical hierarchy.  Two levels of equine hoof wall morphological hierarchy have been studied here, the nanoscale (a-keratin phases) and the macro-scale (tubules and intertubular components). There is, however, the possibility of another, intermediate scale. The extracellular glycoprotein adhesive (Matoltsy, 1975) and cornified cell envelope that lines the inside of these cells (Steven and Steinert, 1994) may form an additional level of functional hierarchy. Although the inter-cellular space and the cell envelope are only approximately 30 and 15 nm thick, respectively, extensive plasma membrane interdigitation may increase the effective thickness of this cell interface complex to approximately 750 nm wide. Unfortunately, little is known about the mechanical properties of this complex, except that it appears to conform to strains elastically (Fraser and MacRae, 1980; present study). If we hypothesize that the intracellular blocks of a-keratin (i.e. the nano-scale composite) act as short-fibers that are surrounded and connected by a 'matrix' formed by cell interface complexes, forming a microscale composite (see Fig. 5.9), then we may make inferences about the mechanical behavior of the cell interface complex. If the stiffness of the matrix for this short-fiber composite is significantly less than the stiffness of the fiber, then the stiffness of the bulk material in the on-fiber direction (inner wall whole tubules) should be less than the on-fiber stiffness of the a-keratin within individual cells (see Fig. 5.9A). The agreement in stiffness between inner wall on-fiber specimens (£^=0.42 and 0.51 GPa; Table 5.4) and whole tubule stiffness (£ =0.47 GPa; Table 5.1) suggests that the stiffness of the iL  complex is near the stiffness of the combined matrix and fibrous phases tested on-fiber. As a first approximation, an estimation of the stiffness of the complex is 0.5 GPa. 227  Figure 5.9: Diagram of the hypothesized micro-scale composite that illustrates the possible contributions of the cell interface complex to the mechanical properties of hoof wall tissue. Macro-scale tensile tests recorded strains of the cell interface complex and the contents of cells (intermediatefilamentsand matrix proteins). In nano-scale tensile tests, a marker within a cell was followed so that in these tests followed strain of the a-keratin and did not include deformation of the cell interface complex. (A) A block of tissue a few cells wide that is shown in tension on-fiber. The stiffness for on-fiber loading of the intracellular a-keratin was similar to that of whole inner wall tubules (in which the fibers within cells are primarily aligned along the tubule axis), suggesting that the stiffness of the cell interface complex and the on-fiber stiffness of a-keratin are similar. (B). A block of tissue loaded across-fiber. If the cell interface stiffness is much higher than that of the intracellular a-keratin composite tested across-fiber, then the stiffness of the tissue block would be considerably higher than that observed at the nano-scale (a-keratin within one cell).  228  229  (  If the stiffness of the interface complex is indeed similar to the on-fiber stiffness of a-keratin, it could account for the apparent difference in inner wall across-fiber intertubular stiffness (E-, is approximately 0.03 GPa; Table 5.4) and the stiffness of the macro-scale intertubular material (0.08 GPa; Table 5.1). For tests in this direction (see Fig. 5.9B), the cell interface complex forms the higher stiffness element that reinforces the 'composite', raising its modulus above that of the a-keratin measured across-fiber. Low sample sizes prevented statistical confirmation of this apparent difference in stiffness, therefore further testing is necessary to verify these inferences about the mechanical properties of the hypothesized micro-scale composite. The formation of hoof wall tissue through the adhesion of hardened cells forms an additional level of the morphological hierarchy, but it remains to be demonstrated if the micro-scale composite is merely a reflection of a manufacturing limitation, or if any functional properties of the hoof wall arisefromit. Preliminary examination offracturesurfaces indicate that cracks propagate through cells (along the IF axis) and also along cell interfaces (data not shown). This suggests that the cell interface complex may play a role in the deviation of cracks away from their initial route to a path following cell interfaces, and this may constitute afracturetoughening mechanism whereby energy is consumed through increasing the crack path complexity. If this is true, the hoof wall would contain at least 3 levels of functional hierarchy, and that the micro-scale composite is not merely a reflection of a manufacturing limitation. This hypothesis of a functional role for the cell interface complex, however, requires further investigation. The results presented here suggest that the mechanical properties of the equine hoof wall are modulated by varying both the LF orientation and the volumefraction,in addition to varying the water content. LF volumefractionvariability is necessary to uncouple IF orientation and E through the wall {  thickness, while still maintaining the LF orientation effect at a local scale. This allows for the presence of possible crack diversion mechanisms formed from specific IF alignments which would otherwise 230  alter the wall stiffness gradient that is necessary for the proper transfer of loads to the bony skeleton. Findings here also suggest the presence of an additional scale of functional hierarchy at the cellular level, the interfacial complex. Hysteresis data from this study are contrary to expectations based on current dogma and suggests that further research be conducted to elucidate the cause of this enigmatic behavior.  231  CHAPTER 6: GENERAL CONCLUSIONS  232  The path of investigation followed in this thesis is reverse to that normally taken by mechanical engineers. Whereas an engineer normally starts with materials of known properties and combines them to optimize or maximize one or more parameters, studies of biomaterials usually start with a structure or material that represents a solution to a problem. At the onset of an investigation, the biomaterials scientist often has only an intuitive feel for the mechanical properties of the material, and may know few details of its function. The exact parameters that are of issue in the structural design may also be unknown. Such has been the case with the hoof wall. The equine hoof wall clearly functions well as a skeletal element that interfaces directly with the environment. It is also obvious that the wall is routinely subjected to high compressive loads. At the inception of this thesis, the hoof wall literature consisted of a variety of manuscripts dealing with aspects of hoof wall morphology and mechanics. Information, however, was patchy, and although an understanding of the relationship between form and function was developing, it was far from complete. This thesis was therefore devised to gain an understanding of the parameters involved in the hoof wall design, and to do so required a more extensive investigation of the wall morphology. A major objective of this research was to determine what levels of the morphological hierarchy were structurally important and what levels, if any, were simply the expressions of manufacturing constraints. Before analyzing the numerous scales of the hoof wall, however, the gross mechanics of the tissue needed to be ascertained.  The equine hoof wall is fracture tough at all gaits.  At the commencement of this thesis, there was surprisingly no data available on the mechanical properties of the whole wall tissue. In addition, the mechanical consequence of hoof wall viscoelasticity was unknown. This latter point was of primary concern since ductile or pseudo-ductile viscoelastic materials usually experience a transition to brittle behavior with increasing strain rate. 233  Therefore, the first goal was to determine the behavior of the whole-wall tissue, and how it would be affected by a change in locomotor speed. Fracture results from chapter 2 suggest that the fracture toughness is high and it is not compromised with increasing loading rate; tensile results indicate that the wall becomes slightly stronger and tougher (an increase in the total energy to break, not fracture toughness) and considerably stiffer as the loading rate increases. Pseudo-static (very slow) loading rates from chapters 2 and 3 confirm the high fracture toughness of the equine hoof wall first observed by Bertram and Gosline (1986). In addition, they offer new information on large-scale tensile and fracture properties which questioned our understanding of equine hoof wall design. Although the longitudinal stiffness of fully hydrated wall samples decreased proceeding inwardly, ultimate properties were constant; fracture toughness parameters indicated that no compromise results from the declining stiffness. The paths of crack propagation, however, were unexpected. Inner and outer wall specimens fractured along a path parallel to the tubule axis, whereas the propagating crack in mid-wall samples followed a path across the tubule axis. Based on the current hoof wall morphological literature and the assumptions of the roles of hoof wall tubules and intertubular material, the fracture patterns observed were impossible to explain, and this warranted a more thorough investigation of the wall morphology to elucidate the reason for and the function of this behavior.  Equine hoof wall design.  In chapter 3, the detailed three-dimensional morphology of the hoof wall toe is presented by describing the IF organization of tubules and intertubular material throughout the wall thickness. The findings indicate a dependence of tubule size, shape and helical arrangement of IFs within the lamellae on position through the wall thickness. The plane of intertubular IFs was not parallel to the ground contact surface, as had been previously assumed (Bertram and Gosline, 1986), but instead changed 234  from perpendicular to the tubule axis in the inner wall to almost parallel to the axis in the outer wa Characterization of the intertubular organization proved crucial in the understanding of the preceding fracture tests of chapter 2 and those that accompanied the morphological study. As a result of this new data, it was suggested that the intertubular material plays a major role in the formation of crack diversion mechanisms that serve to redirect cracks away from paths that are potentially dangerous to the animal. Three possible crack diversion mechanisms were identified including 1) a mid-wall crack diversion mechanism which is formed primarily from intertubular material, that redirects upwards oriented cracks outwards and towards the quarters, and inwards oriented cracks towards  the quarters 2) an inner wall mechanism that diverts cracks that have reached the inner wall to a path along the tubule axis towards the ground and 3) an outer wall mechanism that appears to form the first line of defense against crack propagation inwards. Fracture patterns also imply that morphological complexity at a finer scale causes propagating cracks to follow a more tortuous route, thereby consuming more energy and retarding crack growth.  The sum of its components.  The gradient of stiffness observed through the wall in chapter 2 has been justified as a means to gradually transfer loads to the bony skeleton (Leach, 1980; Kasapi and Gosline, 1996), and it is explained on the basis of water content and IF orientation in chapter 3. Chapter 5 provides additional rationale for this behavior with new findings of varying IF volume fraction through the wall. This appears necessary to counter the effects that the IF orientations (that are necessary for crack diversion mechanisms) would otherwise have on the wall stiffness. Without this modulation, the relative stiffnesses of the different regions of the wall would not allow proper load transfer. The above suggestions assume that the IFs are considerably stiffer than the matrix proteins and therefore provide the majority of the tissue stiffness. To test this assumption, the tensile 235  stiffnesses of IF and matrix proteins are estimated in chapter 5; longitudinal tensile stiffnesses for the IF and matrix proteins are estimated at 3-4 GPa and 0.03 GPa, respectively. Although the mechanical properties of tubules suggest primarily mechanical roles for these structures, other functions are still possible. In chapter 4, various possible functions of tubules are investigated in an attempt to resolve the long-standing debate over the role of these structures in the equine hoof wall.  The final word on tubule function.  Chapter 4 addressed a variety of possible roles for hoof wall tubules. It examined the possibility that their hollow form serves to increase the structural flexural stiffness, and/or decreases the thermal conductivity to retard heat loss. It was concluded that any benefits relating to these issues are not likely great enough to be the driving force for the evolution of hollow, rather than solid fibers. The hypothesis that their hollow form serves to conduct water vapor to more distal portions of the wall is tested empirically, and the hypothesis is rejected. Their hollow form, which could have detrimental mechanical consequences, is justified as a manufacturing constraint. It is suggested that the large-scale production of intermediate filaments in the hoof wall longitudinal axis is only possible through the construction of these structures, since the production of planes of IFs in hardened, akeratinized cells has only been observed parallel with the germinative tissue surface. To produce IFs at large angles to the coronary border (which forms the intertubular material), germinative tissue must lay at an angle to the coronary border; this is accomplished with the formation of dermal papillae.  Future directions.  This thesis has investigated numerous levels of morphological hierarchy in the equine hoof wall including the nano-scale (molecular), macro-scale (tubule and intertubular components) and large-scale (wall regions and whole hoof wall). Results presented here have suggested that each of 236  these levels is a crucial component of a structural hierarchy. The investigation of tubule function, however, has led to the postulation that although tubules have structural functions in the wall, their specific morphology may be the result of a manufacturing constraint. Another manufacturing issue is also addressed in chapter 5. Formation of the hoof wall through the adhesion of solid cell 'bricks' may also be the expression of a manufacturing constraint. Preliminary findings and results from chapter 5, however, suggest that this is not the case and imply that a micro-scale component of the mechanical hierarchy may exist. Disagreements in results from nano-scale and macro-scale tests suggest that the cellular interface complex (formed from the cell envelope, plasma membrane and intercellular 'glue'), may have unique mechanical properties that result in a high degree of fracture surface complexity. Further research is necessary to quantify the mechanical properties of this complex, and to verify its possible role as an additional crack deviation mechanism at the micro-level.  237  BIBLIOGRAPHY  238  Agarwal, B. D. and Broutman, L. J. (1990). Analysis and performance offiber composites. Toronto: John Wiley and Sons. ASTM Standard E 8M-94a. (1994a). Standard test methods for tension testing of metallic materials (metric). Annual Book of ASTM Standards 03.01. ASTM Standard E 399-90 . (19946). Standard test methods for plane-strain fracture toughness of metallic materials. Annual Book of ASTM Standards 03.01. el  ASTM Standard E 813-89. (1994c). 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Eng. 14, 671-679. Wright, T. M. and Hayes, W. C. (1977). Fracture mechanics parameters for compact bone-effects of density and specimen thickness. J. Biomechanics 10, 419-430.  246  APPENDIX  247  1. Impact tensile test strain determination.  To determine strain from impact tensile tests, a pseudo-strain was calculated as cross-head movement divided by the length of the parallel segment, L (refer to Fig. 2.1). Pseudo-strain values x  were then converted to an estimate of the actual strain by applying a correction factor that was obtainedfromInstron tests on identical samples in which we measured both pseudo-strain and actual strain. The correction factor from the Instron was applicable to the impact apparatus because their compliances were very similar and because more than 99% of the total system compliance resulted from deformation of the specimen. Since the slope of thefirstpart of the strain-time curve often differed considerably from that of the rest of the curve, a separate line wasfitthrough those points used to calculate the initial modulus, E , in Instron experiments. This strain correction factor was used t  only in calculating E for impact tests. t  2. Data correction procedure  Thefirststep in load data correction was characterization of the Instronfiltersystem. A dual channel digital spectrum analyzer (SA; Wavetek model 5830a) was employed to generate a sinusoidal sweep function from 0 to 10 Hz. This signal was delivered to a Ling V456 electrodynamic vibrator system which acted to load the Instron system through a custom-built reference force transducer. The outputs of the reference transducer and the Instron load cell/electronics were compared by a SA (Wavetek model 5820a) which produced a transfer function for both magnitude and phase between 0 and 10 Hz. 10 Hz was taken as the cutoff frequency since the Instron system acted as a 2 Hz filter and it was decided thatfivetimes thefiltercut-off frequency would represent the limit of our ability to reconstruct the curve accurately. A PC program was written to accept a time series and compute its Fourier transform using the Fast Fourier Transform (FFT) algorithm (Press et al. 1984). Sensitivity of this procedure to the 248  rapid drop in load in tensile tests necessitated the addition of padding to the end of tensile tests. Padding of curves for the 3.2x10" s" tests involved the addition of the mirror image of the entire 2  1  curve to the end of the trace; a portion of a sine wave approximating the shape of the force curve was added to the end of 0.33 s" tests. The transfer function correction factors were applied to the power 1  spectrum and the curve was then reassembled using an inverse FFT. Corrected data was smoothed using a fourth order digital Butterworth filter (Winter, 1990). A similar method was used to determine and correct for the frequency response of the VDA system in Instron tensile tests. Noise was fed into a vibrator motor to which a displacement transducer was affixed. The VDA system was used to follow a marker on the vibrating motor shaft; the outputs of the VDA and displacement transducer were compared by the SA and the transfer function magnitude and phase were generated. Frequency distortion of displacement data generated from the VDA system was much less than that in force data from the Instron system. Only data from 0.33 s" experiments required correction, as the result of a minor phase shift. 1  To test our correction program, we chose an analogous system with controllable parameters. Thefilterfunction of a 40 Hz single-pole, low-pass, analogfilterwas characterized by generating a noise output from a SA and passing it through the filter. The noise generated by the SA was compared with the output of thefilterby the SA and the transfer function magnitude and phase were generated over 200 Hz (i.e. aboutfivetimes thefilterfrequency, analogous to our previous method). The reconstruction of a triangle wave was used as a test of the technique, as it was thought to pose a more difficult challenge to the correcting system than the force curves; a 9.77 Hz wave was chosen since this would provide the correction program with about 20 harmonics, the same number of harmonics available for reconstruction of force curves. The triangle wave data was entered into the program and a corrected wave very similar to the original triangle wave was generated (see Fig. A.1A). 249  Figure A.1: (A) Test of the data correction program. A 9.77 Hz triangle wave (dashed line) was run through a 40 Hz low-pass filter; the output signal was distorted and phase shifted (thick, solid line). Data representing the filtered wave was then entered into the PC program which generated a corrected output (thin line). (B) A typical tensile test conducted at 0.33 s" (thick line). This curve was corrected (thin line) and then smoothed (dashed line) to produce a reliable estimate of the actual event. 1  250  Time (s)  Time (s)  251  The FFT technique used in the correction program required thatfiltereddata encompass an entire cycle, or some multiple thereof. Fig. A.l A shows how well data can be reconstructed when these conditions are met. The data, however, was not a complete 'cycle' and consequently a corrected trace was susceptible to artifacts generated by the program. Force data from 0.33 s" tensile tests 1  posed the most difficult challenge to the program. A typical force-time curve generated from a 0.33 s" tensile test is shown in Fig. A. IB before and after correction. Here, a low amplitude, high 1  frequency ripple is visible on the corrected trace. Addition of the aforementioned padding greatly reduced the amplitude of the ripple generated at the end of the trace such that it was easily filtered out using the Butterworth digital filter.  252  

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