Stress ratio contributes to fatigue crack growth in dentin

OpenMandible: An open-source framework for highly realistic numerical modelling of lower mandible physiology

OBJECTIVE

Computer modeling of lower mandible physiology remains challenging because prescribing realistic material characteristics and boundary conditions from medical scans requires advanced equipment and skill sets. The objective of this study is to provide a framework that could reduce simplifications made and inconsistency (in terms of geometry, materials, and boundary conditions) among further studies on the topic.

METHODS

The OpenMandible framework offers: 1) the first publicly available multiscale model of the mandible developed by combining cone beam computerized tomography (CBCT) and μCT imaging modalities, and 2) a C++ software tool for the generation of simulation-ready models (tet4 and hex8 elements). In addition to the application of conventional (Neumann and Dirichlet) boundary conditions, OpenMandible introduces a novel geodesic wave propagation - based approach for incorporating orthotropic micromechanical characteristics of cortical bone, and a unique algorithm for modeling muscles as uniformly directed vectors. The base intact model includes the mandible (spongy and compact bone), 14 teeth (comprising dentin, enamel, periodontal ligament, and pulp), simplified temporomandibular joints, and masticatory muscles (masseter, temporalis, medial, and lateral pterygoid).

RESULTS

The complete source code, executables, showcases, and sample data are freely available on the public repository: https://github.com/ArsoVukicevic/OpenMandible. It has been demonstrated that by slightly editing the baseline model, one can study different "virtual" treatments or diseases, including tooth restoration, placement of implants, mandible bone degradation, and others.

SIGNIFICANCE

OpenMandible eases the community to undertake a broad range of studies on the topic, while increasing their consistency and reproducibility. At the same time, the needs for dedicated equipment and skills for developing realistic simulation models are significantly reduced.

On the Mechanics of Fatigue and Fracture in Teeth

Tooth fracture is a major concern in the field of restorative dentistry. However, knowledge of the causes for tooth fracture has developed from contributions that are largely based within the field of mechanics. The present manuscript presents a technical review of advances in understanding the fracture of teeth and the fatigue and fracture behavior of their hard tissues (i.e., dentin and enamel). The importance of evaluating the fracture resistance of these materials, and the role of applied mechanics in developing this knowledge will be reviewed. In addition, the complex microstructures of tooth tissues, their roles in resisting tooth fracture, and the importance of hydration and aging on the fracture resistance of tooth tissues will be discussed. Studies in this area are essential for increasing the success of current treatments in dentistry, as well as in facilitating the development of novel bio-inspired restorative materials for the future.

Accelerated fatigue of dentin with exposure to lactic acid

Composite restorations accumulate more biofilm than other dental materials. This increases the likelihood for the hard tissues supporting a restoration (i.e. dentin and enamel) to be exposed to acidic conditions beyond that resulting from dietary variations. In this investigation the fatigue strength and fatigue crack growth resistance of human coronal dentin were characterized within a lactic acid solution (with pH = 5) and compared to that of controls evaluated in neutral conditions (pH = 7). A comparison of the fatigue life distributions showed that the lactic acid exposure resulted in a significant reduction in the fatigue strength (p ≤ 0.001), and nearly 30% reduction in the apparent endurance limit (from 44 MPa to 32 MPa). The reduction in pH also caused a significant decrease (p ≤ 0.05) in the threshold stress intensity range required for the initiation of cyclic crack growth, and significant increase in the incremental rate of crack extension. Exposure of tooth structure to lactic acid may cause demineralization, but it also increases the likelihood of restored tooth failures via fatigue, and after short time periods.

Contributions of aging to the fatigue crack growth resistance of human dentin

An evaluation of the fatigue crack resistance of human dentin was conducted to identify the degree of degradation that arises with aging and the dependency on tubule orientation. Fatigue crack growth was achieved in specimens of coronal dentin through application of Mode I cyclic loading and over clinically relevant lengths (0 ≤ a ≤ 2 mm). The study considered two directions of cyclic crack growth in which the crack was either in-plane (0°) or perpendicular (90°) to the dentin tubules. Results showed that regardless of tubule orientation, aging of dentin is accompanied by a significant reduction in the resistance to the initiation of fatigue crack growth, as well as a significant increase in the rate of incremental extension. Perpendicular to the tubules, the fatigue crack exponent increased significantly (from m=14.2 ± 1.5 to 24.1 ± 5.0), suggesting an increase in brittleness of the tissue with age. For cracks extending in-plane with the tubules, the fatigue crack growth exponent does not change significantly with patient age (from m=25.4 ± 3.03 to 22.9 ± 5.3), but there is a significant increase in the incremental crack growth rate. Regardless of age, coronal dentin exhibits the lowest resistance to fatigue crack growth perpendicular to the tubules. While there are changes in the cyclic crack growth rate and mechanisms of cyclic extension with aging, this tissue maintains its anisotropy.

Effects of simulated functional loading conditions on dentin, composite, and laminate structures

Use of composite restorations continues to increase, tempered by more potential problems when placed in posterior dentition. Thus, it is essential to understand how these materials function under stress-bearing clinical conditions. Because mastication is difficult to replicate in the laboratory, cyclic loading is frequently used within in vitro evaluations but often employs traditional fatigue testing, which typically does not simulate occlusal loading because higher stresses and loading frequencies are used, so failure mechanisms may be different. This investigation utilized relevant parameters (specimen size, loading frequency) to assess the effects of cyclic loading on flexural mechanical properties and fracture morphology of (coronal) dentin, composite, and dentin-adhesive-composite "laminate" structures. Incremental monitoring of flexural modulus on individual beams over 60,000 loading cycles revealed a gradual increase across materials; post hoc comparisons indicated statistical significance only for 1 versus 60k cycles. Paired specimens were tested (one exposed to 60k loading cycles, one to static loading only), and comparisons of flexural modulus and strength showed statistically significantly higher values for cyclically loaded specimens across materials, with no observable differences in fracture morphology. Localized reorganization of dentin collagen and polymer chains could have increased flexural modulus and strength during cyclic loading, which may have implications toward the life and failure mechanisms of clinical restorations and underlying tooth structure.

Dehydration and the dynamic dimensional changes within dentin and enamel

OBJECTIVES

The objectives of this study were to quantify the dimensional changes in dentin and enamel during dehydration, and to determine if there are differences between the responses of these tissues from young and old patients.

METHODS

Microscopic digital image correlation (DIC) was used to evaluate deformation of dentin and enamel as a function of water loss resulting from free convection in air. Dimensional changes within both tissues were quantified for two patient age groups (i.e. young 18< or =age< or =30 and old 50< or =age) and in two orthogonal directions (i.e. parallel and perpendicular to the prevailing structural feature (dentin tubules or enamel prisms)). The deformation histories were used to estimate effective dehydration coefficients that can be used in quantifying the strains induced by dehydration.

RESULTS

Both dentin and enamel underwent contraction with water loss, regardless of the patient age. There was no significant difference between responses of the two age groups or the two orthogonal directions. Over 1h of free convection, the average water loss in dentin was 6% and resulted in approximately 0.5% shrinkage. In the same time period the average water loss in the enamel was approximately 1% and resulted in 0.03% shrinkage. The estimated effective dehydration coefficients were -810microm/m/(% weight loss) and -50microm/m/(% weight loss) for dentin and enamel, respectively.

SIGNIFICANCE

The degree of deformation shrinkage resulting from dehydration is over a factor of magnitude larger in dentin than enamel.

An examination of fatigue striations in human dentin: in vitro and in vivo

Although striations are often used in evaluating fatigue crack growth in engineering materials, they have not been used in studying the mechanics of fracture in hard tissues. The primary objective of this study was to evaluate the striations resulting from fatigue crack growth in the dentin of human teeth. Compact tension (CT) specimens obtained from the coronal dentin of molars from young (17 < or = age < or = 37 years) and senior (age > or = 50 years) patients were subjected to cyclic Mode I loads. Striations evident on the fracture surfaces were examined using a scanning electron microscope (SEM) and contact profilometer. Fatigue crack growth striations that developed in vivo were also examined on fracture surfaces of restored molars. A power spectrum analysis of surface profiles from the CT specimens showed that the striation spacing ranged from 50 to 170 microm. The average spacing in the dentin of seniors (130 +/- 23 microm) was significantly larger (p < 0.001) than that in young dentin (88 +/- 13 microm). Fatigue striations in the restored teeth exhibited features that were consistent with those that developed in vitro and a spacing ranging from 59 to 95 microm. Unlike metals, the striations in dentin developed after a period of cyclic loading that ranged from 1 x 10(3) to 1 x 10(5) cycles. A quantitative evaluation of the striation spacing using the Bates-Clark equation suggested that cyclic crack growth within the restored teeth occurred at a stress intensity range near 0.7 MPa x m(0.5), and a stress range of approximately 12 MPa.

Fatigue of mineralized tissues: cortical bone and dentin

Gaining a mechanistic understanding of the mechanical properties of mineralized tissues, such as dentin and cortical bone, is important from the perspective of developing a framework for predicting and preventing failure of teeth and whole bones, particularly with regard to understanding the effects of microstructural modifications from factors such as aging, disease, or medical treatments. Accordingly, considerable research efforts have been made to determine the specific mechanisms involved in the fatigue and fracture of mineralized tissues, and to discover how these mechanisms relate to features within the respective microstructures. This article seeks to review the progress that has been made specifically in the area of fatigue, focusing on the research that moves our understanding beyond simple fatigue life (S/N) concepts and instead addresses the separate mechanisms for microdamage initiation, crack propagation, and in the case of bone, repair and remodeling.

Transition behavior in fatigue of human dentin: structure and anisotropy

The influence of tubule orientation on the transition from fatigue to fatigue crack growth in human dentin was examined. Compact tension (CT) and rectangular beam specimens were prepared from the coronal dentin of molars with three unique tubule orientations (i.e., 0 degrees , 45 degrees and 90 degrees). The CT specimens (N=25) were used to characterize fatigue crack initiation and steady-state cyclic extension, whereas the rectangular beams (N=132) were subjected to 4-pt flexure and used in quantifying the stress-life fatigue response. The transition behavior was analyzed using both the Kitagawa-Takahashi and El Haddad approaches. Results showed that both the fatigue crack growth and stress-life responses were dependent on the tubule orientation. The average Paris Law exponent for crack growth perpendicular (90 degrees) to the tubules (m=13.3+/-1.1) was significantly greater (p<0.05) than that for crack growth oblique (45 degrees) to the tubules (m=11.5+/-1.87). Similarly, the fatigue strength of dentin with 90 degrees tubule orientation was significantly lower (p<0.05) than that for the other two orientations, regardless of the range of cyclic stress. The apparent endurance strengths of specimens with 0 degrees (44MPa) and 45 degrees (53MPa) orientations were nearly twice that of the 90 degrees (24MPa) orientation. Based on these results, human dentin exhibits the largest degree of anisotropy within the stress-life regime and the transition from fatigue to fatigue crack growth occurs under the lowest cyclic stress range when the tubules are aligned with the cyclic normal stress (90 degrees orientation).

Kitagawa-Takahashi diagrams define the limiting conditions for cyclic fatigue failure in human dentin

As cyclic fatigue is considered to be a major cause of clinical tooth fractures, achieving a comprehensive understanding of the fatigue behavior of dentin is of importance. In this note, the fatigue behavior of human dentin is examined in the context of the Kitagawa-Takahashi diagram to define the limiting conditions for fatigue failure. Specifically, this approach incorporates two limiting threshold criteria for fatigue: (i) a threshold stress for fatigue failure, specifically the smooth-bar (unnotched) fatigue endurance strength, at small crack sizes and (ii) a threshold stress-intensity range for fatigue-crack growth at larger crack sizes. The approach provides a "bridge" between the traditional fatigue life and fracture mechanics based damage-tolerant approaches to fatigue-life estimation, and as such defines a "failure envelope" of applied stresses and flaw sizes where fatigue failure is likely in dentin This approach may also be applied to fatigue failure in human cortical bone (i.e. clinical "stress fractures"), which exhibits similar fatigue behavior characteristics, and in principle may aid clinicians in making quantitative evaluations of the risk of fractures in mineralized tissues.

Hydration and dynamic fatigue of dentin

An experimental investigation on the dynamic fatigue response of dentin was conducted to examine the influence of stress rate on the strength and energy to fracture. Rectangular beams were prepared from the coronal dentin of bovine maxillary molars and subjected to four-point flexure to failure. The dentin beams were examined in the fully hydrated and dehydrated condition at stress rates (sigma) ranging from 0.01 to 100 MPa/s. Results for the hydrated dentin showed that the flexure strength, energy to fracture, and flexure modulus all increased with increasing stress rate; the flexure strength increased from 100 MPa ((sigma) = 0.01 MPa/s) to 250 MPa ((sigma) = 100 MPa/s). In contrast, the elastic modulus and strength of the dehydrated dentin decreased with increasing stress rate; the flexural strength of the dehydrated dentin deceased from 170 MPa ((sigma) = 0.01 MPa/s) to 100 MPa ((sigma) = 100 MPa/s). While the hydrated dentin behaved more like a brittle material at low stress rates, the strain to fracture was found to be nearly independent of (sigma). According to the experimental results, restorative conditions that cause development of static stresses within the tooth could promote a decrease in the damage tolerance of dentin.

Age, dehydration and fatigue crack growth in dentin

A preliminary study of the effects from age and dehydration on fatigue crack growth in human dentin was conducted. Compact tension (CT) fatigue specimens of coronal dentin were prepared from extracted molars and subjected to high cycle fatigue (10(5)<N<10(6)) under Mode I loading. Young hydrated dentin (mean age=25+/-7 years), old hydrated dentin (mean age=55+/-14 years) and young dehydrated dentin (mean age=20+/-2 years) were examined. Fatigue crack growth rates were quantified according to the Paris Law in terms of the crack growth exponent (m) and coefficient (C). The average fatigue crack growth exponent for the young hydrated dentin (m=13.3+/-1.1) was significantly less than that for the hydrated old (m=21.6+/-5.2; p<0.003) and dehydrated young dentin (m=18.8+/-2.8; p<0.01). Fatigue cracks in the old dentin underwent initiation at a lower stress intensity range than in young dentin and propagated at as significantly faster rate (over 100x). Differences in the microscopic features of the fracture surfaces from the old and young dentin suggested that particular mechanisms contributing to energy dissipation and crack growth resistance in the young hydrated dentin were not present in the old dentin. Based on results of this study, the fatigue crack growth resistance of human dentin decreases with both age of the tissue and dehydration.