The intrusion of the tooth for different loading rates

Differences in the biomechanical behaviors of natural teeth and dental implants

OBJECTIVE

The lack of a PDL, which acts as an energy absorber, is a contributor to implants' early failure; however, these discrepancies are not well understood because of limited in vivo research. This study investigated the discrepancy in biomechanical behaviors between natural teeth and dental implants by detecting micro-movements in vivo.

METHODS

We designed a device that could measure precisely mechanical behaviors such as creep, stress relaxation, and hysteresis by using load-control displacement on teeth and implants. We also compared energy dissipation between natural teeth and dental implants by subtracting the area of the hysteresis loop of natural teeth from that of dental implants.

RESULTS

Biphasic curves with an initial phase of rapid response and a subsequent phase of slow response were confirmed in creep and stress relaxation curves for the load-time relationship in natural teeth. By contrast, the behavior of creep or stress relaxation was less prominent when the dental implants were tested. We observed that the periodontal ligament under an axial intrusive load of 300g in a loading rate 3g/s could dissipate the energy of 7.35±1.18×10^-2 mJ, approximately 50 times that of the dental implants (1.47±1.22×10^-3) with statistically significant (p<0.05).

SIGNIFICANCE

We confirmed natural teeth could achieve greater energy dissipation compared to dental implants, which owe to that natural teeth exhibited fluid and viscoelastic properties.

Biomechanical considerations on tooth-implant supported fixed partial dentures

This article discusses the connection of teeth to implants, in order to restore partial edentulism. The main problem arising from this connection is tooth intrusion, which can occur in up to 7.3% of the cases. The justification of this complication is being attempted through the perspective of biomechanics of the involved anatomical structures, that is, the periodontal ligament and the bone, as well as that of the teeth- and implant-supported fixed partial dentures.

Modulus of elasticity of human periodontal ligament by optical measurement and numerical simulation

OBJECTIVE

To determine the elastic modulus of the periodontal ligament (PDL).

MATERIALS AND METHODS

This study was carried out on eight human maxillary jaw segments containing central incisors. Displacements were measured under load using a laser sensing system, electronic speckle pattern interferometry (ESPI). Subsequently, finite element models presenting the same individual geometry as the respective autopsy material were developed by the software of Mimics and Ansys, based on scanning data from micro computed tomography (micro CT), to simulate tooth mobility numerically under the same force systems as were used in the experiment. Numerical force/deflection curves obtained from the models were fitted to the experimental curves by repeatedly calculating theoretical tooth deflections and varying the elasticity parameters of the human PDL.

RESULTS

A bilinear material parameter set was assumed to simulate tooth deflections. Mean values of E₁  =  0.04 MPa, E₂  =  0.16 MPa, and ultimate strain of ε₁₂  =  7.3% were derived for the elastic behavior of the PDL.

CONCLUSION

Force/deflection curves from the measurements showed a significant nonlinear behavior of elastic stiffness of the PDL. A bilinear material parameter set was suitably assumed to be a description of nonlinear properties of the PDL.

Periodontal-Masseteric Reflexes Decrease with Tooth Pre-load

The responses of incisal periodontal mechanoreceptors to increasing mechanical stimulation are known to follow a hyperbolic-saturating course. The implications of these properties for the reflexive control of bite-force have not been examined directly. In line with the abovementioned receptor characteristics, we hypothesized that the periodontal-masseteric reflex will reduce as a function of increasing incisal pre-load. In 10 participants, a central incisor was repeatedly tapped (0.4 N). We measured the modulation by pre-load (0.2–2.0 N) of the reflex frequency-response at and between 3 and 20 Hz. The entrainment of the reflex increased with frequency up to 20 Hz and diminished with increasing pre-load. Importantly, the hyperbolic relationship shown here between the periodontal-masseteric reflex and tooth pre-load agreed with the load/response relationships predicted by single-receptor and tooth movement studies. This study demonstrated that periodontal mechano-receptors are able to contribute to the ongoing control of only small bite-forces.

In vivo measurement of the elastic modulus of the human periodontal ligament

The present study was designated to determine the elastic properties of the periodontal ligament (PDL) in human subjects. A maxillary central incisor was experimentally translated so that stress or strain could be uniformly distributed in the PDL by applying a single force passing through the center of resistance. Displacements were measured under different magnitudes of load using a magnet-magnetic sensing system. From the load-displacement relations, Young's modulus of the PDL was calculated. The values determined were approximately 0.12 MPa under load ranging from 0 to 0.5 N, 0.25 MPa within the range of 0.5-1.0 N, 0.44 MPa under load 1.0-1.5 N, and between 0.69 and 0.96 MPa with 1.5-2.0 N. The values of Young's moduli increased almost exponentially with the increment of load due to a non-linear elasticity of the PDL.

Experimental observation, theoretical models, and biomechanical inference in the study of mandibular form

Experimental studies and mathematical models are disparate approaches for inferring the stress and strain environment in mammalian jaws. Experimental designs offer accurate, although limited, characterization of biomechanical behavior, while mathematical approaches (finite element modeling in particular) offer unparalleled precision in depiction of strain magnitudes, directions, and gradients throughout the mandible. Because the empirical (experimental) and theoretical (mathematical) perspectives differ in their initial assumptions and their proximate goals, the two methods can yield divergent conclusions about how masticatory stresses are distributed in the dentary. These different sources of inference may, therefore, tangibly influence subsequent biological interpretation. In vitro observation of bone strain in primate mandibles under controlled loading conditions offers a test of finite element model predictions. Two issues which have been addressed by both finite element models and experimental approaches are: (1) the distribution of torsional shear strains in anthropoid jaws and (2) the dissipation of bite forces in the human alveolar process. Not surprisingly, the experimental data and mathematical models agree on some issues, but on others exhibit discordance. Achieving congruence between these methods is critical if the nature of the relationship of masticatory stress to mandibular form is to be intelligently assessed. A case study of functional/mechanical significance of gnathic morphology in the hominid genus Paranthropus offers insight into the potential benefit of combining theoretical and experimental approaches. Certain finite element analyses claim to have identified a biomechanical problem unrecognized in previous comparative work, which, in essence, is that the enlarged transverse dimensions of the postcanine corpus may have a less important role in resisting torsional stresses than previously thought. Experimental data have identified subperiosteal cortical thinning as a culprit in diminishing the role of cross-sectional geometry in conditioning the strain environment. These observations raise questions concerning the biomechanical significance of mandibular form in early hominids, fueling persistent arguments over whether gnathic morphology can be related to dietary specialization in the "robust" australopithecines. Nonmechanical explanations (e.g., tooth size or body size) for Paranthropus mandibular dimensions, however, are not compelling as competing hypotheses. Both theoretical and experimental models are in need of refinement before it is possible to conclude that the jaws of the "robust" australopithecines are not functionally linked to elevated masticatory loads.

Changes in the fibre arrangement of the rat incisor periodontal ligament in relation to various loading levels in vitro

The relationship between the fibre arrangement of the periodontal ligament and the load-deformation behaviour was investigated at various loading levels. Transverse sections of the rat incisor were loaded in the eruptive direction in vitro and the deformation fixed at predetermined loads. Sections were prepared at these deformation levels. The periodontal ligaments were examined by polarized-light and scanning-electron microscopy. At the initial ("toe') part of the load-deformation curve, the periodontal fibres were gradually pulled and bent towards the direction of loading; their wavy pattern and periodic dark and bright bands became indistinct. At the next, linear part of the curve, the running direction of the fibres changed gradually until they were straightened and stretched. At the yielding part of the curve, the periodontal fibres began to rupture. Ruptured fibres adhering to the bone surface returned to their original obliquity and showed periodic dark and bright bands. The fibrous components of the rat incisor periodontal ligament thus transmit forces to bone at the linear part of the curve when the tooth is axially loaded.

The effect of velocity of loading on the biomechanical responses of the periodontal ligament in transverse sections of the rat molar in vitro

Stress-strain relations of this ligament in transverse sections of the mandibular first molar were examined over a wide range of velocities of loading from 1 to 10(4) mm/24 h. With increasing velocities, the maximum shear stress, tangent modulus and failure strain-energy density increased but the maximum shear strain decreased. The mechanical responses at the highest velocity for the molar ligament were compared with those previously found for the incisor ligament. Mechanical strength, stiffness and toughness were greater for the molar than for the incisor ligament; the molar ligament therefore has more extensible fibres or a different fibre arrangement. Comparison of the mechanical responses at the slowest velocity suggests that, though the stress level was greatly reduced (presumably because of stress relaxation), the fibre components of the molar ligament still reacted at this velocity. It is also suggested that the differences in the ratios of the mechanical measures in 10(4)-1 mm/24 h between the two types of teeth are due partly to their different periodontal fibre architectures.

Mechanical responses of the periodontal ligament in the transverse section of the rat mandibular incisor at various velocities of loading in vitro

Stress-strain curves of the periodontal ligament (PDL) were obtained at various velocities of extrusive loading of 1, 10, 10(2), 10(3) and 10(4) mm/24 h in vitro. Significant increases of the maximum shear stress, tangent modulus and failure strain energy density were found with increases in the velocity of loading. The maximum shear strain increased from a velocity of 1 to 10 mm/24 h but decreased from 10 to 10(4) mm/24 h. It was shown histologically that the free surface of the PDL adhering to the cementum after mechanical testing was rough and irregular at higher velocities and rather smooth at lower velocities. These results showed that the mechanical properties and mode of failure of the rat incisor PDL were greatly dependent on the strain rate. It is possible that the PDL of the continuously erupting rat incisor has mechanical characteristics favourable for resisting weakly to slow and small eruptive forces but strongly to the fast and large occlusal forces as suggested previously [Chiba and Komatsu, The Biological Mechanisms of Tooth Eruption and Root Resorption (1988)].

A morphometric, electron microscopic analysis of tissue channels shown by ionic tracer in normal and tensioned rat molar apical periodontal ligament

A 1.0 newton continuous, extrusive load was applied to the right maxillary molar for 30 min to determine the presence of channels as shown by the distribution of tracer across the interstitial compartment of normal and tensioned PDL. Sodium ferrocyanide (1% w/v), perfused via the common carotid arteries, was the tracer probe and tris(ethylenediamine) cobalt III chloride (1% w/v) the precipitating ion. Left molar control PDL had an overall mean of 0.43 +/- 0.05/microns2 tissue channels at 0.2 microns from the vascular endothelium, and 0.15 +/- 0.04/microns2 at 7-8 microns. On the experimental side, the overall mean number of tissue channels was 0.65 +/- 0.13/microns2 at 0-2 microns and 0.19 +/- 0.07/microns2 at 7-8 microns. A significant depth effect (P less than 0.01) was present in the control and experimental interstitial tissues for tissue channels adjacent to the endothelium of different categories of vessel. Extrusion increased the tissue channel density adjacent to arterial capillaries (P less than 0.01), venous capillaries (P less than 0.01) and postcapillary-sized venules (P less than 0.01). These findings implicate these three types of vessel as being functionally important in fluid exchange across endothelial boundaries in the PDL.

Biomechanics of cross-sectional size and shape in the hominoid mandibular corpus

Mandibular cross sections of Pan, Pongo, Gorilla, Homo, and two fossil specimens of Paranthropus were examined by computed tomography (CT) to determine the biomechanical properties of the hominoid mandibular corpus. Images obtained by CT reveal that while the fossil hominids do not differ significantly from extant hominoids in the relative contribution of compact bone to total subperiosteal area, the shape of the Paranthropus corpora indicates that the mechanical design of the robust australopithecine mandible is fundamentally distinct from that of modern hominoids in terms of its ability to resist transverse bending and torsion. It is also apparent that, among the modern hominoids, interspecific and sexual differences in corpus shape are not significant from a biomechanical perspective. While ellipse models have been used previously to describe the size, shape, and subsequent biomechanical properties of the corpus, the present study shows that such models do not predict the biomechanical properties of corpus cross-sectional geometry in an accurate or reliable manner. The traditional "robusticity" index of the mandibular corpus is of limited utility for biomechanical interpretations. The relationship of compact bone distribution in the corpus to dimensions such as mandibular length and arch width may provide a more functionally meaningful definition of mandibular robusticity.

In-vitro mechanics of intrusive loading in porcine cheek teeth with intact and perforated root apices

Cyclic intrusive loads were applied to deciduous cheek teeth and monitored by radiography in dissected mandibles in three successive states: (A) intact, (B) vertically bisected in a bucco-lingual plane, (C) with perforation of the apices by lateral drilling of the mandible subsequent to (B). Loading was in a compression cage in an Instron mechanical testing-machine utilizing cross-head speeds of 0.5 and 5 mm/min, leading to loading rates of approximately 2 and approximately 20 N/s. Peak loads were approximately 100 N, causing an intrusion of approximately 200 microns. Load/recovery curves for each tooth in the three states were recorded and the data treated assuming: (a) a simple shear on the periodontal ligament, (b) tensile loading on the fibres of the collagen fraction of the ligament alone. Treatment (b) gave the best agreement with published mechanical data on isolated mammalian periodontal ligament. The small effect of apicectomy on the mechanical behaviour indicates that a mobile fluid-like support mechanism is unlikely to operate for major loads in vitro and tensile support by the collagen fibres of the periodontal ligament is the most likely dominant mechanism.

The mandibular corpus of female primates: taxonomic, dietary, and allometric correlates of interspecific variations in size and shape

Measurements were taken on skulls of 253 adult female anthropoid primates from 32 species, in order to determine patterns and possible causes for variation among species in the cross-sectional size and shape of the mandibular corpus under M1. When all 32 species are considered as a group, there is a tendency for corpus shape to become more robust with increasing body size. However, this does not hold for colobines or cercopithecines evaluated separately. When diets are classified into the general categories of folivory or frugivory, neither size-adjusted measurements of mandibular corpus breadth and height, nor estimates of the second moments of inertia or the polar moment of inertia of the mandibular cross section, show any relationship to dietary variation among species. Species reported to include hard nuts in their diets have larger mandibular cross sections than other species, and the size of the corpus is significantly correlated with size of the dentition and molar enamel thickness. A biomechanical model taking into account frictional effects of tooth-to-tooth contact indicates that mandibular corpus robusticity may not be related to a large horizontal component of force during mastication.

Influence of the rate of force application on the absolute psychophysical threshold level of periodontal mechanoreceptors in man

In seven volunteers, controlled small forces were applied in an axial direction to a maxillary central incisor. The forces were generated by a stimulating device supported by the maxillary molars. The stimuli had a symmetrical triangular shape; force-application rates were varied from 1.88 to 960 mN/s. Threshold levels of sensation were determined at the various force-application rates. The relation between force-application rate and threshold level was negative, using 1.88, 3.75 and 7.5 mN/s stimuli. This trend was interrupted as threshold levels were higher at 15 than at 7.5 mN/s. In the range of more rapidly applied forces, 15-960 mN/s, the relationship was also negative, consistently, with a slope of -0.22 of the linear regression line after logarithmic transformation. It was concluded that the periodontal mechanoreceptive unit, as far as conscious functioning is concerned, may be described as a relatively inaccurate static force-detector when small magnitude forces are applied at low rates. Some rate sensitivity appears with more rapidly-applied stimuli.

Some advances in endosseous implants

A major advance in endosseous implantology hinges on the coating of titanium implants by porous biodegradable, bioreactive tricalcium phosphate ceramic. When implanted into alveolar bone by a careful technique, the ceramic is resorbed to be replaced by bone. As a result, the endosseous implant becomes ankylosed to the bone. This represents a stable implant/bone interface as opposed to the unstable connective tissue interface that encapsulates many other implant devices.