Breaking crown dentine in whole teeth: 3D observations of prevalent fracture patterns following overload.

Teeth with intact crowns rarely split or fracture, despite decades of cyclic loading and occasional unexpected overload. This is largely attributed to the presence of dentine, since cracking and fracture of enamel have been frequently reported. Dentine is similar to bone, comprising mineralised collagen fibres as a main constituent. Unlike cortical bone, however, where microcracking and damage arrest are essential for re/modelling and healing, dentine can neither remodel nor regenerate. This raises questions regarding the evolutionary benefits of toughening, leading to uncertainty whether cracks actually appear in dentine in situ. Here we study the notion that circumpulpal dentine is usually protected against, rather than damaged by severe overloads, even though it is not much more massive or stronger than it needs to be. To address this, we examined hydrated teeth still within whole jawbones of freshly-slaughtered skeletally mature pigs, mechanically loaded until fracture. Force displacement curves, optical and electron microscopy combined with 3D microstructural analysis by conventional micro-computed tomography (µCT) revealed mostly brittle fracture paths in circumpulpal crown dentine. Once overload cracks reach this mass of dentine they propagate rapidly along straight paths often parallel to the enamel flanks of the oblong shovel shaped premolars. We find infrequent signs of active toughening mechanisms with minimal crack diversion, ligament bridging and microcracking. When such toughening is seen, it mainly appears in softer dentine in the root, or near the dentine-enamel-junction (DEJ) in mantle dentine. We observed shear bands in overloaded circumpulpal dentine, due to mutual gliding of upper and lower segments. These shear bands are formed as periodic arrays of rotated dentine fragments. The 3D data consistently demonstrate the importance of the layered tooth structure, containing a stiff outer enamel shell, a soft sub-DEJ interlayer and a stiff circumpulpal dentine bulk, for deflecting cracks from splitting the tooth.

Revisiting the links between bone remodelling and osteocytes: insights from across phyla.

We question two major tenets of bone biology: that the primary role of remodelling is to remove damage in the bone (so-called damage-driven remodelling) and that osteocytes are the only strain-sensing orchestrators of this process. These concepts are distilled largely from research on model mammal species, but in fact, there are a number of features of various bones, from mammalian and non-mammalian species, that do not accord with these 'rules'. Here, we assemble a variety of examples, ranging from species that lack osteocytes but that still seem capable of remodelling their bones, to species with osteocytic bones that do not remodel, and to instances of inter-species, inter-bone and/or intra-bone variation in bone remodelling that show that this purported repair process is not always where the 'rules' tell us it should be. This collection of points argues that our understanding of the advantages, roles and primary drivers of remodelling are inadequate and biased to quite a small phylogenetic cross section of the species that possess bone. We suggest a variety of new directions for bone research that would provide us with a better understanding of bone remodelling, tying together the interests of comparative biologists, palaeontologists and medical researchers.

Importance of the variable periodontal ligament geometry for whole tooth mechanical function: A validated numerical study.

When mammalian teeth breakdown food, several juxtaposed dental tissues work mechanically together, while balancing requirements of food comminution and avoiding damage to the oral tissues. One important way to achieve this is by channeling mastication forces into the surrounding jaw bone through a thin and compliant soft tissue, the periodontal ligament (PDL). As a result, during a typical chewing stroke, each tooth moves quite substantially in its anchor-site. Here we report a series of experiments, where we study the reaction of three-rooted teeth to a single chewing event by finite element (FE) modelling. The nonlinear behaviour of the PDL is simulated by a hyperelastic material model and the in silico results are validated by our own in vitro experiments. We examine the displacement response of the complete tooth-PDL-bone complex to increasing chewing loads. We observe that small spatially-varying geometric adjustments to the thickness of the PDL lead to strong changes in observed tooth reaction movement, as well as PDL strain and bone stress. When reproducing the regionally varying thickness of the PDL observed in vivo, FE simulations reveal subtle but significant tooth motion that leads to an even distribution of the stresses in the jaw bone, and to lower strains in the PDL. Our in silico experiments also reproduce the results of experiments performed by others on different animal models and are therefore useful for overcoming the difficulties of obtaining tooth-PDL-bone loading estimates in vivo. This data thus enhances our understanding of the role the variable PDL geometry plays in the tooth-PDL-bone complex during mastication.

Learning from evolutionary optimisation: what are toughening mechanisms good for in dentine, a nonrepairing bone tissue?

The main mass of material found in teeth is dentine, a bone-like tissue, riddled with micron-sized tubules and devoid of living cells. It provides support to the outer wear-resistant layer of enamel, and exhibits toughening mechanisms which contribute to crack resistance. And yet unlike most bone tissues, dentine does not remodel and consequently any accumulated damage does not 'self repair'. Because damage containment followed by tissue replacement is a prime reason for the crack-arresting microstructures found in most bones, the occurrence of toughening mechanisms without the biological capability to repair is puzzling. Here we consider the notion that dentine might be overdesigned for strength, because it has to compensate for the lack of cell-mediated healing mechanisms. Based on our own and on literature-reported observations, including quasistatic and fatigue properties, dentine design principles are discussed in light of the functional conditions under which teeth evolved. We conclude that dentine is only slightly overdesigned for everyday cyclic loading because usual mastication stresses may come close to its endurance strength. The in-built toughening mechanisms constitute an evolutionary benefit because they prevent catastrophic failure during rare overload events, which was probably very advantageous in our hunter gatherer ancestor times. From a bio-inspired perspective, understanding the extent of evolutionary overdesign might be useful for optimising biomimetic structures used for load bearing.

Remodeling in bone without osteocytes: billfish challenge bone structure-function paradigms.

A remarkable property of tetrapod bone is its ability to detect and remodel areas where damage has accumulated through prolonged use. This process, believed vital to the long-term health of bone, is considered to be initiated and orchestrated by osteocytes, cells within the bone matrix. It is therefore surprising that most extant fishes (neoteleosts) lack osteocytes, suggesting their bones are not constantly repaired, although many species exhibit long lives and high activity levels, factors that should induce considerable fatigue damage with time. Here, we show evidence for active and intense remodeling occurring in the anosteocytic, elongated rostral bones of billfishes (e.g., swordfish, marlins). Despite lacking osteocytes, this tissue exhibits a striking resemblance to the mature bone of large mammals, bearing structural features (overlapping secondary osteons) indicating intensive tissue repair, particularly in areas where high loads are expected. Billfish osteons are an order of magnitude smaller in diameter than mammalian osteons, however, implying that the nature of damage in this bone may be different. Whereas billfish bone material is as stiff as mammalian bone (unlike the bone of other fishes), it is able to withstand much greater strains (relative deformations) before failing. Our data show that fish bone can exhibit far more complex structure and physiology than previously known, and is apparently capable of localized repair even without the osteocytes believed essential for this process. These findings challenge the unique and primary role of osteocytes in bone remodeling, a basic tenet of bone biology, raising the possibility of an alternative mechanism driving this process.

Cavities in the compact bone in tetrapods and fish and their effect on mechanical properties.

Bone includes cavities in various length scales, from nanoporosities occurring between the collagen fibrils and the mineral crystals all the way to macrocavities like the medullary cavity. In particular, bone is permeated by a vast number of channels (the lacunar-canalicular system), that reduce the stiffness and, more importantly, the strength of the bone that they permeate. These consequences are presumably a price worth paying for the ability of the lacunar-canalicular system to detect changes in the strain environment within the bone material and, when deleterious, to trigger processes like modeling or remodeling which 'rectify' it. Here we review the size and density of the various types of cavities in bone, and discuss their effect on the mechanical properties of cortical bone. In this respect the bones of advanced teleost fish species (probably the majority of all vertebrate species) are an unsolved conundrum because they lack bone cells (and therefore lacunae and canaliculi) in their skeleton. Yet, despite being acellular, some of these fish can undergo considerable remodeling in at least some parts of their skeleton. We address, but do not solve this mystery.

Tubular frameworks guiding orderly bone formation in the antler of the red deer (Cervus elaphus).

Deer antler is a bony tissue which re-grows every year after shedding. Growth speed and material properties of this tissue are truly remarkable, making it an interesting model for bone regeneration. Surprisingly, not much is known about the ultrastructure of the calcified tissues and the temporal sequence of their development during antler growth. We use a combination of imaging tools based on light and electron microscopy to characterize antler tissue at various stages of development. We observe that mineralized cartilage is first transformed into a bone framework with low degree of collagen fibril ordering at the micron level. This framework has a honeycomb-like appearance with the cylindrical pores oriented along the main antler axis. Later, this tissue is filled with primary osteons, whose collagen fibrils are mainly oriented along the pores, thus improving the antler's mechanical properties. This strongly suggests that to achieve very fast organ growth it is advantageous to have a longitudinal porous framework as an intermediate step in bone formation. The example of antler shows that geometric features of this framework are crucial, and a tubular geometry with a diameter in the order of hundred micrometers seems to be a good solution for fast framework-mediated bone formation.

Significance and importance: some common misapprehensions about statistics.

There are many common misapprehensions about statistics that occur in the literature. We are sure that the three misapprehensions we deal with in this short review are widespread. They concern: 1)what P values mean;2)what an insignificant result means, and what it does not mean; the question of the 'power' of a statistical test;3)the difference between importance and statistical significance.We produce no formulae or recipes for dealing with particular situations, instead we concentrate on the commonsense use of simple statistics. We emphasise that if the use of any but the simplest statistics is intended, it is much better to get proper statistical help before starting experiments, rather than afterwards.

Are tensile and compressive Young's moduli of compact bone different?

This study examines the question of whether the stiffness (Young's modulus) of secondary osteonal cortical bone is different in compression and tension. Electronic speckle pattern interferometry (ESPI) is used to measure concurrently the compressive and tensile strains in cortical bone beams tested in bending. ESPI is a non-contact method of measuring surface deformations over the entire region of interest of a specimen, tested wet. The measured strain distributions across the beam, and the determination of the location of the neutral axis, demonstrate in a statistically-robust way that the tensile Young's modulus is slightly (6%), but significantly greater than that of the compressive Young's modulus. It is also shown that within a relatively small bone specimen there are considerable variations in the modulus, presumably caused by structural inhomogeneities.

Inhomogeneous fibril stretching in antler starts after macroscopic yielding: indication for a nanoscale toughening mechanism.

Antler is a unique mineralized tissue, with extraordinary toughness as well as an ability to annually regenerate itself in its entirety. The high fracture resistance enables it to fulfill its biological function as a weapon and defensive guard during combats between deer stags in the rutting season. However, very little is quantitatively understood about the structural origin of the antler's high toughness. We used a unique combination of time-resolved synchrotron small angle X-ray diffraction together with tensile testing of antler cortical tissue under physiologically wet conditions. We measured the deformation at the nanoscale from changes in the meridional diffraction pattern during macroscopic stretch-to-failure tests. Our results show that on average fibrils are strained only half as much as the whole tissue and the fibril strain increases linearly with tissue strain, both during elastic and inelastic deformation. Most remarkably, following macroscopic yielding we observe a straining of some fibrils equal to the macroscopic tissue strain while others are hardly stretched at all, indicating an inhomogeneous fibrillar strain pattern at the nanoscale. This behavior is unlike what occurs in plexiform bovine bone and may explain the extreme toughness of antler compared to normal bone.

Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure.

It is difficult to define the 'physiological' mechanical properties of bone. Traumatic failures in-vivo are more likely to be orders of magnitude faster than the quasistatic tests usually employed in-vitro. We have reported recently [Hansen, U., Zioupos, P., Simpson, R., Currey, J.D., Hynd, D., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering/Transactions of the ASME 130, 011011-1-8] results from tests on specimens of human femoral cortical bone loaded in tension at strain rates (epsilon ) ranging from low (0.08s(-1)) to high (18s(-1)). Across this strain rate range the modulus of elasticity generally increased, stress at yield and failure and strain at failure decreased for rates higher than 1s(-1), while strain at yield was invariant for most strain rates and only decreased at rates higher than 10s(-1). The results showed that strain rate has a stronger effect on post-yield deformation than on initiation of macroscopic yielding. In general, specimens loaded at high strain rates were brittle, while those loaded at low strain rates were much tougher. Here, a post-test examination of the microcracking damage reveals that microcracking was inversely related to the strain rate. Specimens loaded at low strain rates showed considerable post-yield strain and also much more microcracking. Partial correlation and regression analysis suggested that the development of post-yield strain was a function of the amount of microcracking incurred (the cause), rather than being a direct result of the strain rate (the excitation). Presumably low strain rates allow time for microcracking to develop, which increases the compliance of the specimen, making them tougher. This behaviour confirms a more general rule that the degree to which bone is brittle or tough depends on the amount of microcracking damage it is able to sustain. More importantly, the key to bone toughness is its ability to avoid a ductile-to-brittle transition for as long as possible during the deformation. The key to bone's brittleness, on the other hand, is the strain and damage localisation early on in the process, which leads to low post-yield strains and low-energy absorption to failure.

The effect of strain rate on the mechanical properties of human cortical bone.

Bone mechanical properties are typically evaluated at relatively low strain rates. However, the strain rate related to traumatic failure is likely to be orders of magnitude higher and this higher strain rate is likely to affect the mechanical properties. Previous work reporting on the effect of strain rate on the mechanical properties of bone predominantly used nonhuman bone. In the work reported here, the effect of strain rate on the tensile and compressive properties of human bone was investigated. Human femoral cortical bone was tested longitudinally at strain rates ranging between 0.14-29.1 s(-1) in compression and 0.08-17 s(-1) in tension. Young's modulus generally increased, across this strain rate range, for both tension and compression. Strength and strain (at maximum load) increased slightly in compression and decreased (for strain rates beyond 1 s(-1)) in tension. Stress and strain at yield decreased (for strain rates beyond 1 s(-1)) for both tension and compression. In general, there seemed to be a relatively simple linear relationship between yield properties and strain rate, but the relationships between postyield properties and strain rate were more complicated and indicated that strain rate has a stronger effect on postyield deformation than on initiation of yielding. The behavior seen in compression is broadly in agreement with past literature, while the behavior observed in tension may be explained by a ductile to brittle transition of bone at moderate to high strain rates.

Variability of the mechanical properties of bone, and its evolutionary consequences.

The relative variabilities (coefficient of variation (CV)) of 10 different mechanical properties of compact bone were determined from 2166 measurements. All measures of variability were made on a minimum of four specimens from any bone. Three pre-yield properties had a CV of about 12%. Six post-yield properties had CVs varying from 24 to 46%. Pre-yield properties increase as a function of mineral content, whereas post-yield properties decrease. These differences give insight into mechanical phenomena occurring at different stages during loading. Furthermore, the fact that some properties are more tightly determined than others has implications for the optimum values set by natural selection. This assertion is made more rigorous using a simple mathematical model for the evolutionarily optimal allocation in a trade-off where one property is imprecisely determined. It is argued that in general the optimum will be biased in favour of the more tightly determined properties than would be the case if all properties had the same CV.

Leaf mechanical properties modulate feeding movements and ingestive success of the pond snail, Lymnaea stagnalis.

We examined the mechanical properties of Butterhead and Iceberg lettuce leaves, and the rate at which they were eaten by the pond snail Lymnaea stagnalis. The outer part of Butterhead leaves were less robust than either the inner Butterhead or outer Iceberg leaves (Young's modulus 2.8, 5.2, 7.7 MPa respectively; ultimate tensile stress 0.18, 0.34 0.51 MPa) which were also thicker. Snails ingested inner Butterhead and Iceberg strips more slowly (36 and 32%) than outer Butterhead. This was not due to differences in latency to first bite or biting rate. Rather, the drop was due to a decrease in the proportion of successful bites (inner Butterhead 84%; Iceberg 86%), to a shorter length ingested per bite (inner Butterhead 55%; Iceberg 45%) and to increased handling time (inner Butterhead 30%). We conclude that sensory input from the mechanically more robust lettuce slows the buccal central pattern generator.

Bone architecture and fracture.

Bones are designed to carry out their requirements effectively. One of these requirements is to resist fracture. Two other important requirements are to be stiff and to be light. Few theories of adaptive modeling distinguish modeling for adequate stiffness from modeling for adequate strength. Bones achieve their architecture partially through genetics, the rough form of the bone being laid down in the genes, and partially through response to normal loading. Normal loading rarely includes traumatic loading and bones are not usually well adapted to resist trauma, though they are probably well adapted to fatigue loading. Some aspects of architectural function, such as hollowness, are well understood. Some aspects, such as the need for uniform loading in impact, are less understood, and some, such as size effects, are only now beginning to be investigated.

Phase shifting speckle interferometry for determination of strain and Young's modulus of mineralized biological materials: a study of tooth dentin compression in water.

Mineralized biological materials have complex hierarchical graded structures. It is therefore difficult to understand the relations between their structure and mechanical properties. We report the use of electronic speckle pattern-correlation interferometry (ESPI) combined with a mechanical compression apparatus to measure the strain and Young's modulus of root dentin compressed under water. We describe the optomechanical instrumentation, experimental techniques and procedures needed to measure cubes as small as 1 x 1 x 2 mm. Calibration of the method is performed using aluminum, which shows that the measurements are accurate within 3% of the compression modulus reported for standard aluminum 6061. Our results reveal that the compression moduli of root dentin from the buccal and lingual sides of the root are quite different from the moduli of the interproximal sides. Root dentin from interproximal locations is found to have an average modulus of 21.3 GPa, which is about 40% stiffer than root dentin from the buccal and lingual locations, found to have a modulus of 15.0 GPa. Our approach can be used to map deformations on irregular surfaces, and measure strain on wet samples of varying sizes. This can be extended to the study of other biological materials including bone and synthetic biomaterials.

Notch sensitivity of mammalian mineralized tissues in impact.

The toughness of bone is an important feature in preventing it from fracturing. We consider the notch sensitivity in impact, and the associations between brittleness, notch sensitivity and post-yield energy absorption of mammalian mineralized tissues. Specimens of bone-like tissues covering a wide range of mineralization were broken, either notched or un-notched, in impact. The greater the mineral content, the greater was the notch sensitivity. Also, the more brittle tissues dissipated the least post-yield energy and were the most notch sensitive. It is suggested that since antler bone, the least mineralized of all known mammalian mineralized tissues, seems to be notch insensitive in impact, no adaptive purpose would be served by having mineralized tissues of a lower mineralization than antler. This may explain the lower cut-off in mineralization seen in mammals.

Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content.

Compact bone specimens from many species were examined to determine the relationships, in tension, between mineral content, Young's modulus, yield stress, yield strain, post-yield stress, post-yield strain, ultimate stress, ultimate strain and work under the stress-strain curve. Yield strain varied much less than the post-yield strain, and yield stress was strongly dependent on Young's modulus. Mineral content was a rather poor predictor of yield stress. However, post-yield events were predicted better by mineral (calcium) content than by Young's modulus. The greater the mineral content the less the post-yield work under the curve and the less the increase in post-yield stress and strain. The findings are compared with those of Les et al. who compressed specimens from equine metacarpals. Where they can be compared, the results are consistent with each other.

How well are bones designed to resist fracture?

Because bone is obviously in some way adapted to the loads falling on it and because fracture is usually the failure of mechanical competence of main clinical importance, it is often thought that bones are adapted to resist fracture. In this perspective, I consider that this may not be the case. Bones may be designed to be very stiff, and therefore highly mineralized, and therefore brittle; they may be adapted to normal loads, but not to the characteristic loads occurring in falls, or may be very poorly designed to stop cracks traveling once they have started. Bones may also potentially fail in completely contrasting modes, and therefore their design has to be a compromise that does not resist either mode completely successfully. The greatly differing fracture incidences in different bones seen in pre-senile adults suggest that safety factors have been adapted, over evolutionary time, to produce the best compromise for a host of different design constraints.