A comparison of salivary pH in sympatric wild lemurs (Lemur catta and Propithecus verreauxi) at Beza Mahafaly Special Reserve, Madagascar

Chemical deterioration of teeth is common among modern humans, and has been suggested for some extinct primates. Dental erosion caused by acidic foods may also obscure microwear signals of mechanical food properties. Ring-tailed lemurs at the Beza Mahafaly Special Reserve (BMSR), Madagascar, display frequent severe tooth wear and subsequent tooth loss. In contrast, sympatric Verreaux's sifaka display far less tooth wear and infrequent tooth loss, despite both species regularly consuming acidic tamarind fruit. We investigated the potential impact of dietary acidity on tooth wear, collecting data on salivary pH from both species, as well as salivary pH from ring-tailed lemurs at Tsimanampesotse National Park, Madagascar. We also collected salivary pH data from ring-tailed lemurs at the Indianapolis Zoo, none of which had eaten for at least 12 hr before data collection. Mean salivary pH for the BMSR ring-tailed lemurs (8.098, n=41, SD=0.550) was significantly more alkaline than Verreaux's sifaka (7.481, n=26, SD=0.458). The mean salivary pH of BMSR (8.098) and Tsimanampesotse (8.080, n=25, SD=0.746) ring-tailed lemurs did not differ significantly. Salivary pH for the Indianapolis Zoo sample (8.125, n=16, SD=0.289) did not differ significantly from either the BMSR or Tsimanampesotse ring-tailed lemurs, but was significantly more alkaline than the BMSR Verreaux's sifaka sample. Regardless of the time between feeding and collection of pH data (from several minutes to nearly 1 hr), salivary pH for each wild lemur was above the "critical" pH of 5.5, below which enamel demineralization occurs. Thus, the high pH of lemur saliva suggests a strong buffering capacity, indicating the impact of acidic foods on dental wear is short-lived, likely having a limited effect. However, tannins in tamarind fruit may increase friction between teeth, thereby increasing attrition and wear in lemurs. These data also suggest that salivary pH varies between lemur species, corresponding to broad dietary categories.     

The impact of fallback foods on wild ring-tailed lemur biology: A comparison of intact and anthropogenically disturbed habitats

Fallback foods are often viewed as central in shaping primate morphology, and influencing adaptive shifts in hominin and other primate evolution. Here we argue that fruit of the tamarind tree (Tamarindus indica) qualifies as a fallback food of ring-tailed lemurs (Lemur catta) at the Beza Mahafaly Special Reserve (BMSR), Madagascar. Contrary to predictions that fallback foods may select for dental and masticatory morphologies adapted to processing these foods, consumption of tamarind fruit by these lemurs leaves a distinct pattern of dental pathology among ring-tailed lemurs at BMSR. Specifically, the physical and mechanical properties of tamarind fruit likely result in a high frequency of severe tooth wear, and subsequent antemortem tooth loss, in this lemur population. This pattern of dental pathology is amplified among lemurs living in disturbed areas at Beza Mahafaly, resulting from a disproportionate emphasis on challenging tamarind fruit, due to few other fruits being available. This is in part caused by a reduction in ground cover and other plants due to livestock grazing. As such, tamarind trees remain one of the few food resources in many areas. Dental pathologies are also associated with the use of a nonendemic leaf resource Argemone mexicana, an important food during the latter part of the dry season when overall food availability is reduced. Such dental pathologies at Beza Mahafaly, resulting from the use or overemphasis of fallback foods for which they are not biologically adapted, indicate that anthropogenic factors must be considered when examining fallback foods. Am J Phys Anthropol 140:671–686, 2009. © 2009 Wiley-Liss, Inc.     

Severe wear and tooth loss in wild ring-tailed lemurs (Lemur catta): a function of feeding ecology, dental structure, and individual life history

The ring-tailed lemurs at Beza Mahafaly Special Reserve, Madagascar, exhibit a high frequency of severe wear and antemortem tooth loss. As part of a long-term study, we collected dental data on 83 living adult ring-tailed lemurs during 2003 and 2004. Among these individuals, 192 teeth were scored as absent. The most frequently missing tooth position is M1 (24%). As M1 is the first tooth to erupt, its high frequency of absence (primarily a result of wear) is not remarkable. However, the remaining pattern of tooth loss does not correlate with the sequence of eruption. We suggest that this pattern is a function of 1) feeding ecology, as hard, tough tamarind fruit is a key fallback food of ring-tailed lemurs living in gallery forests; 2) food processing, as tamarind fruit is primarily processed in the P3-M1 region of the mouth; and 3) tooth structure, as ring-tailed lemurs possess thin dental enamel. The incongruity between thin enamel and use of a hard, tough fallback food suggests that ring-tailed lemurs living in riverine gallery forests may rely on resources not used in the past. When comparing dental health in the same individuals (n=50) between 2003 and 2004, we found that individual tooth loss can show a rapid increase over the span of one year, increasing by as much as 20%. Despite this rapid loss, individuals are able to survive, sometimes benefiting from unintentional assistance from conspecifics, from which partially processed tamarind fruit is obtained. Although less frequent in this population, these longitudinal data also illustrate that ring-tailed lemurs lose teeth due to damage and disease, similar to other nonhuman primates. The relationship between tooth loss, feeding ecology, dental structure, and individual life history in this population has implications for interpreting behavior based on tooth loss in the hominid fossil record.     

Interpreting food processing through dietary mechanical properties: a Lemur catta case study

Knowledge of dietary mechanical properties can be informative about physical consequences to consumers during ingestion and mastication. In this article, we examine how Tamarindus indica fruits can affect dental morphology in a population of ring-tailed lemurs (Lemur catta) at Beza Mahafaly special reserve in southwestern Madagascar. Ring-tailed lemurs in tamarind dominated gallery forests exhibit extreme wear and tooth loss on their postcanine dentition that has been related to processing T. indica fruits. We measured and compared mechanical properties of individual food parts in the diet of ring-tailed lemurs in different seasons in 1999-2000, 2008, and 2010. Fracture toughness, hardness, and modulus of foods were measured with a portable mechanical tester. The ripe fruits of T. indica are indeed the toughest and hardest foods ingested by the lemurs. In addition, they are among the largest foods consumed, require high numbers of ingestive bites to process, and are the most frequently eaten by volume. During controlled cutting tests of the ripe fruit shell, multiple runaway side cracks form alongside the cut. Similarly, the lemurs repeatedly bite the ripe shell during feeding and thereby introduce multiple cracks that eventually fragment the shell. Studies of enamel microstructure (e.g., Lucas et al.: BioEssays 30 (2008) 374-385; Campbell et al., 2011) advance the idea that the thin enamel of ring-tailed lemur teeth is susceptible to substantial micro-cracking that rapidly erodes the teeth. We conclude that micro-cracking from repeated loads, in combination with the mechanical and physical properties of the fruit, is primarily responsible for the observed dental damage.     

The impact of dental impairment on ring-tailed lemur food processing performance

During mastication, foods are reduced into particles suitable for swallowing and digestion. Smaller particles possess a greater surface area per unit of volume on which digestive enzymes and bacteria may work than relatively larger particles, and are thus more readily digested. As dental morphology facilitates the breakdown of diets with specific mechanical properties, extensive dental wear and/or tooth loss may impede an individual's ability to break down and exploit foods. We present data demonstrating a relationship between dental impairment and particle size in 43 fecal samples from 33 ring-tailed lemurs at the Beza Mahafaly Special Reserve (BMSR), Madagascar. All fecal samples were sifted through three sieves of decreasing size (11.2 mm, 4.75 mm, and 1.0 mm). The resulting fraction in each sieve was then weighed and assessed in relation to individual dental impairment status. With increasing wear, the percentage of each sample within the 1.0 mm sieve decreases, whereas that in the 11.2 mm sieve increases with increasing postcanine wear, although these effects are not present when limited to individuals without tooth loss. Individuals with tooth loss also demonstrate larger proportions of fecal material 1.0-4.75 mm in size. Dental impairment results in larger food particles and potentially less efficient utilization of foods. When fecal material was examined by leaf vs. fruit content, individuals with tooth loss demonstrated reduced proportions of fruit in the 1.0 mm and 11.2 mm sieves. These data suggest individuals with tooth loss consume less fruit than those without loss, potentially reflecting a reduced ability to process tamarind fruit, a key fallback resource at BMSR.     

The role of tooth enamel mechanical properties in primate dietary adaptation

Primate teeth adapt to the physical properties of foods in a variety of ways including changes in occlusal morphology, enamel thickness, and overall size. We conducted a comparative study of extant primates to examine whether their teeth also adapt to foods through variation in the mechanical properties of the enamel. Nanoindentation techniques were used to map profiles of elastic modulus and hardness across tooth sections from the enamel-dentin junction to the outer enamel surface in a broad sample of primates including apes, Old World monkeys, New World monkeys, and lemurs. The measured data profiles feature considerable overlap among species, indicating a high degree of commonality in mechanical properties. These results suggest that differences in the load-bearing capacity of primate molar teeth are more a function of morphology-particularly tooth size and enamel thickness-than of underlying mechanical properties.     

Morphology is not Destiny: Discrepancy between Form,Function and Dietary Adaptation in Bovid Cheek Teeth

Mammal teeth have evolved morphologies that allow for the efficient mechanical processing of different foods, therefore increasing dietary energy uptake for maintenance of high metabolic demands. However, individuals masticate foods with biomechanical properties at odds with the optimal function of a given tooth morphology. Here, we investigate tooth form and function using two quantitative 3D methods at different scales on the same individuals of nine bovid species. Dental topometry quantifies the gross morphology, and therefore, reflects evolutionary adaptive patterns. Surface texture analysis infers mechanical occlusal events, which reflect the actual tooth function, and is free from the influence of morphology. We found that tough foods can be satisfactorily exploited by grazing species with enamel ridge morphologies not more complex than those found in intermediate feeders and browsers. Thus, the evolution of enamel complexity is likely determined by a balance between adaptation and constraints. Wider enamel ridges seem to be a common functional trait in bovids to compensate for severe wear from abrasive foods and/or chipping from hard foods. Our results demonstrate that supposedly essential functional adaptations in tooth morphology may not be required to process food efficiently. This emphasizes the large plasticity between “optimal” morphology and the potential function of the tooth, and underscores the need to appreciate (apparently) maladaptive structures in mammalian evolution as nevertheless effective functioning units.     

Dietary adaptations of South African australopiths: inference from enamel prism attitude

The angle at which enamel prisms approach the wear surface holds information with regard to the stiffness of the tissue, as well as its wear resistance. Hence, analyses of prism orientation may shed light on questions of whether the thick enamel in hominins has evolved to confer stiffness or wear resistance to the teeth and may thus inform about the diet and behavioural ecology of these species. This was explored for Paranthropus robustus and Australopithecus africanus, whereby a distinction was made between prisms at the Phase I and Phase II facets. The results were compared with those obtained for Theropithecus, Macaca, and Potamochoerus for whom behavioural and/or experimental data are available, and were interpreted against simple mechanical principles. The South African hominins differ significantly in their relationships between wear facets and prism angulations. Teeth of P. robustus are better adapted to more vertical loads during mastication (Phase I), whereas those of A. africanus are better adapted to cope with more laterally-directed loads (Phase II) commonly associated with roll-crush and mastication. Overall, teeth of P. robustus appear stiffer, while those of A. africanus seem more wear resistant.     

Sauropod teeth from the Upper Cretaceous Bissekty Formation of Uzbekistan

The isolated adult teeth of titanosaurian sauropods from the Upper Cretaceous Bissekty Formation at Dzharakuduk, Uzbekistan, differ little in overall structure but show considerable variation in enamel sculpturing and wear patterns. The crown shape of unworn juvenile teeth ranges from lanceolate to conical. Most specimens have enamel texture resembling crumpled paper or completely smooth enamel. Longitudinal grooves along the mesial and distal edges are present on only a few tooth crowns and might be developed on both the labial and lingual sides. Among 252 worn tooth crowns there are eight variants of wear patterns, all possible combinations of 0–2 apical and 0–2 lateral wear facets. The most common is wear pattern A1L0 (one apical facet, no lateral facets; 62.7%). The next most common variant has two apical and no lateral facets (A2L0, 12.3%). These apical wear facets include the primary wear facets, which are produced by an opposing functional tooth, and secondary wear facets, which are produced by a replacing upper tooth coming into contact with the functional lower tooth at a late wear stage. The relative abundance of tooth crowns with two apical wear facets possibly suggests incipient development of a tooth battery in the Bissekty titanosaur.     

Functional implications of primate enamel thickness.

Recent evolutionary interpretations of Hominoidea have postulated functional relationships between tooth form, diet and masticatory biomechanics. A major consideration is the durability of the tooth under certain dietary conditions. Teeth with low cusps and thicker enamel are able to withstand heavy mastication of abrasive food bolus for a longer period. When comparisons are made between species of higher primates the variables of tooth size, cusp morphology, and enamel thickness appear to be related but until now no systematic analysis has been made to determine the functional relevance of several dental dimensions. This study provides data gained from comparisons of dentition of nine species of primates. Histological sections were made of the post canine teeth and 21 dimensions were compared. The relevant dimensions identified serve to withstand dental wear. The distribution of thicker enamel corresponded to the observed wear planes. Humans had thicker enamel than pongids while the macaque had the thinnest. These preliminary results tend to support theories which explain low, thick, enameled cusps in hominids.     

Nanoindentation and storage of teeth

This study determined changes in nanomechanical properties of dentin and enamel during storage in deionized water, calcium chloride buffered saline solution and Hank's balanced salts solution (HBSS). Atomic force microscopy based nanoindentation showed that storing teeth in deionized water or CaCl(2)-solution resulted in a large decrease in elastic modulus and hardness. At 1 day a decrease in the mechanical properties values of up to 20% and 30% was observed for enamel and dentin, respectively. After 1 week, mechanical properties dropped below 50% of their starting values, which is attributed to a demineralization process during storage. In contrast, storing teeth in HBSS did not significantly alter the mechanical properties for a time interval of 2 weeks. The use of HBSS for storage of samples from teeth is recommended.     

Enamel ultrastructure and masticatory function in molars of the American opossum, Didelphis virginiana

Maxillary and mandibular molars of the American opossum, Didelphis virginiana L., were viewed in the scanning electron microscope (SEM) after acid-etching or after cutting and acid-etching. Observations were made on enamel prism patterns as they relate to functional properties of the tooth at a particular site. Molars at different stages of wear were also observed under a dissecting microscope; worn surfaces were correlated with function and enamel ultrastructure. Pounding surfaces of molar cusps wear more rapidly than near-vertical shearing surfaces or crushing basins (i.e. the trigon and talonid basin). Pounding surfaces are subjected to abrasion by food and arc not normally involved in tooth-tooth contact. Near-vertical shearing surfaces and basins used for crushing do experience tooth-tooth contact, but are surprisingly more resistant to wear. Prisms at pounding sites approach the occlusal surface at a near 90° angle and are surrounded with very thick interprismatic (IP) enamel parallel to the occlusal surface of the tooth. The pounding pattern is present at tips of cusps and at occlusal surfaces of ridges of the tooth. At near-vertical shearing surfaces, the prisms approach the outer surface obliquely and are surrounded with IP crystals which are perpendicular to the vertical surface. The angle between prismatic and IP enamel in these patterns is 60–90° in a cervical to occlusal direction. In basins of the tooth used principally for crushing and some shearing, IP enamel is perpendicular to the changing slope of the basin and the prisms are usually at a 55–65° angle to the IP enamel. When the pounding and shearing-crushing patterns meet at a ridge, a distinct seam is observed. Pounding forces occur parallel to the long axis of the prisms and perpendicular to the thick IP enamel (i.e. perpendicular to the long axis of the IP crystals) lying on either side of the prisms. Shearing and crushing forces occur at an oblique angle to the prism, and interprismatic enamel is more evenly distributed about the prism. A spiral pattern is found at the bottoms of the trigon and talonid basins, but not at the bottom of the trigonid which is a non-occluding basin. It is concluded that the differential rates of wear of the enamel surfaces are necessary in maintaining the sharp cutting edges and effective crushing basins of the tribosphenic molar, and the ultrastructural arrangements of the enamel prisms are of functional significance.     

A Systematic Study on Tooth Enamel Microstructures of Lambdopsalis bulla (Multituberculate,Mammalia) - Implications for Multituberculate Biology and Phylogeny

Tooth enamel microstructure is a reliable and widely used indicator of dietary interpretations and data for phylogenetic reconstruction, if all levels of variability are investigated. It is usually difficult to have a thorough examination at all levels of enamel structures for any mammals, especially for the early mammals, which are commonly represented by sparse specimens. Because of the random preservation of specimens, enamel microstructures from different teeth in various species are often compared. There are few examples that convincingly show intraspecific variation of tooth enamel microstructure in full dentition of a species, including multituberculates. Here we present a systematic survey of tooth enamel microstructures of Lambdopsalis bulla, a taeniolabidoid multituberculate from the Late Paleocene Nomogen Formation, Inner Mongolia. We examined enamel structures at all hierarchical levels. The samples are treated differently in section orientations and acid preparation and examined using different imaging methods. The results show that, except for preparation artifacts, the crystallites, enamel types, Schmelzmuster and dentition types of Lambdopsalis are relatively consistent in all permanent teeth, but the prism type, including the prism shape, size and density, may vary in different portions of a single tooth or among different teeth of an individual animal. The most common Schmelzmuster of the permanent teeth in Lambdopsalis is a combination of radial enamel in the inner and middle layers, aprismatic enamel in the outer layer, and irregular decussations in tooth crown area with great curvature. The prism seam is another comparably stable characteristic that may be a useful feature for multituberculate taxonomy. The systematic documentation of enamel structures in Lambdopsalis may be generalized for the enamel microstructure study, and thus for taxonomy and phylogenetic reconstruction, of multituberculates and even informative for the enamel study of other early mammals.     

Nanoindentation study of human premolars subjected to bleaching agent

Bleaching of teeth is gaining popularity due to cosmetic reasons. However, the effect it has on teeth is still largely unknown. This paper seeks to evaluate the effect of a bleaching agent, 30% hydrogen peroxide, on the nanomechanical properties of dentin and enamel using the nanoindentation technique. The Young's modulus and hardness obtained from nanoindentation before and after bleaching were compared. Five newly extracted human premolars were used. Nanoindentation was first done on the sliced enamel and dentin regions to determine their mechanical properties. One batch of samples was kept in Hank's balanced salt solution as control while the other was bleached in 30% hydrogen peroxide for 24h. The same number of nanoindentations was then done near the previously indented regions for both the control and bleached samples and the results compared. Using paired sample t-tests with alpha=0.05, it was found that there were no significant differences in both the Young's modulus and hardness of dentin and enamel kept in control. However, the mechanical properties of the bleached dentin were significantly decreased. For intertubular dentin, the mean hardness decreased by 29-55% and the mean Young's modulus decreased by 19-43%. For enamel, the mean hardness decreased by 13-32% while the mean Young's modulus decreased by 18-32%. The exact mechanism by which hydrogen peroxide affects the dentin and enamel has yet to be fully elucidated. However, it is observed to have an undermining effect on the nanomechanical properties of teeth.     

湖北郧西黄龙洞更新世晚期人类牙齿磨耗与使用痕迹

对2004—2006年在黄龙洞发现的7枚人类牙齿磨耗与使用痕迹的观察显示: 除具有正常牙齿相互接触造成的磨耗外, 黄龙洞人类牙齿还呈现出一些特殊的使用痕迹, 包括明显的前部牙齿釉质破损与崩裂、上颌侧门齿齿冠唇面釉质破损、上颌前部牙齿齿间邻接面沟等。根据这些牙齿使用痕迹集中在前部牙齿, 釉质破损与崩裂主要分布在靠近切缘的上颌门齿唇面及下颌门齿舌面的情况, 推测生活在黄龙洞的更新世晚期人类经常使用前部牙齿从事啃咬、叼衔、或剥离等动作, 并可能将前部牙齿作为工具使用。分布在前部牙齿的齿间邻接面沟提示当时人类经常从事剔牙活动。黄龙洞人类前部牙齿的使用痕迹与当时人类获取、处理及食用附着在骨骼上的筋或肉的动作密切相关, 当时人类的食物构成中可能包含有较多的肉类及粗纤维植物。     

Measurements of tooth wear among Australian Aborigines: I. Serial loss of the enamel crown

The dental casts made from Aboriginal children during the course of a longitudinal growth study in Central Australia provided material for analyzing tooth wear under known environmental conditions. The wear facets produced on the occlusal surfaces were clearly preserved on the dental stone casts and recorded the progress of enamel attrition from ages 6 to 18. These casts were photographed and traced by electronic planimetric methods that automatically recorded the location and size of wear facets on the first and second permanent molars. These areas of worn tooth surface were compared to the total tooth surface. The worn surface was regressed on age to calculate wear rates of each tooth. Discriminant analyses were also performed to determine the significance of dental attrition differences between the sexes at each age group. The total wear on each tooth was highly correlated with age as expected but females wore their teeth at a significantly higher rate than males. The mandibular molars wore more rapidly than maxillary teeth in both sexes. The discriminant analysis successfully grouped 91% of the cases according to age and sex. Pattern of wear, the location, and size of wear facets also differed between age groups and sex. The questions of why there is a difference between male and female wear or why there is greater wear on one arch or arch region have no ready answers. The differing rates and pattern of dental wear do suggest that arch shape and growth rates may be the answer though it has yet to be tested. However, the occlusal surface wear is useful for age estimation in a population and provides a record of shifting masticatory forces during growth.     

Effect of prism orientation and loading direction on contact stresses in prismatic enamel of primates: implications for interpreting wear patterns

The ability of prisms to effectively dissipate contact stress at the surface will influence wear rates in teeth. The aim of this investigation was to begin to quantify the effect of prism orientation on surface stresses. Seven finite element models of enamel microstructure were created, each model differing in the angulation of prism orientation with regard to the wear surface. For validation purposes, the mechanical behavior of the model was compared with published experimental data. In order to test the enamel under lateral loads, a compressed food particle was dragged across the surface from the dentino-enamel junction (DEJ) towards the outer enamel surface (OES). Under these conditions, tensile stresses in the enamel model increased with increases in the coefficient of friction. More importantly, stresses were found to be lowest in models in which the prisms approach the surface at lower angles (i.e., more obliquely cut prisms), and highest when the prisms approached the surface at 60 degrees (i.e., less obliquely cut). Finally, the direction of travel of the simulated food particle was reversed, allowing comparison of the difference in behavior between trailing and leading edge enamels (i.e., when the food particle was dragged either towards or away from the DEJ). Stresses at the trailing edge were usually lower than stresses at the leading edge. Taken together with what is known about prism orientation in primate teeth, such findings imply greater wear resistance at the intercuspal region and less wear resistance at the lateral enamel at midcrown. Such findings appear to be supported by archeological evidence.     

Functional ecology and evolution of hominoid molar enamel thickness: Pan troglodytes schweinfurthii and Pongo pygmaeus wurmbii

The divergent molar characteristics of Pan troglodytes and Pongo pygmaeus provide an instructive paradigm for examining the adaptive form-function relationship between molar enamel thickness and food hardness. Although both species exhibit a categorical preference for ripe fruit over other food objects, the thick enamel and crenulated occlusal surface of Pongo molar teeth predict a diet that is more resistant to deformation (hard) and fracture (tough) than the diet of Pan. We confirm these predictions with behavioral observations of Pan troglodytes schweinfurthii and Pongo pygmaeus wurmbii in the wild and describe the mechanical properties of foods utilized during periods when preferred foods are scarce. Such fallback foods may have exerted a selective pressure on tooth evolution, particularly molar enamel thinness, which is interpreted as a functional adaptation to seasonal folivory and a derived character trait within the hominoid clade. The thick enamel and crenulated occlusal surface of Pongo molars is interpreted as a functional adaptation to the routine consumption of relatively tough and hard foods. We discuss the implications of these interpretations for inferring the diet of hominin species, which possessed varying degrees of thick molar enamel. These data, which are among the first reported for hominoid primates, fill an important empirical void for evaluating the mechanical plausibility of putative hominin food objects.     

Regulated fracture in tooth enamel: A nanotechnological strategy from nature

Tooth enamel is a very brittle material; however it has the ability to sustain cracks without suffering catastrophic failure throughout the lifetime of mechanical function. We propose that the nanostructure of enamel can play a significant role in defining its unique mechanical properties. Accordingly we analyzed the nanostructure and chemical composition of a group of teeth, and correlated it with the crack resistance of the same teeth. Here we show how the dimensions of apatite nanocrystals in enamel can affect its resistance to crack propagation. We conclude that the aspect ratio of apatite nanocrystals in enamel determines its resistance to crack propagation. According to this finding, we proposed a new model based on the Hall–Petch theory that accurately predicts crack propagation in enamel. Our new biomechanical model of enamel is the first model that can successfully explain the observed variations in the behavior of crack propagation of tooth enamel among different humans.