In vitro time-dependent response of periodontal ligament to mechanical loading

Dynamic tensile viscoelastic properties of porcine periodontal ligament

The periodontal ligament plays a significant role in orthodontic and masticatory processes. To explicitly investigate the effects of dynamic force amplitude and frequency on the dynamic tensile properties of the periodontal ligament, in vitro tensile experiments were conducted using a dynamic mechanical analysis at various dynamic force amplitudes across a wide frequency range. Storage modulus, loss modulus, and loss factor values were measured. A Maxwell constitutive model based on modulus was established to describe the dynamic mechanical properties of the periodontal ligament. The results showed that the storage modulus ranged from 29.53 MPa to 158.24 MPa, the loss modulus ranged from 3.26 MPa to 76.16 MPa, and the loss factor values all increased with higher frequencies and higher dynamic force amplitudes. Based on the parameters obtained from the fitting results, it is evident that the short-term response has a more pronounced impact on the elastic response of the periodontal ligament than the long-term response. Increasing the dynamic force amplitude and its frequency amplified the viscous effects of the periodontal ligament and enhanced energy dissipation. The proposed constitutive model further demonstrated that the periodontal ligament acts as a viscoelastic biomaterial. These findings have implications for future research on the periodontal ligament.

Tensile forces in the neurovascular bundle: A contributor to orthodontic relapse?

OBJECTIVES

The aim of this study is to investigate the neurovascular bundle (NVB) as a potential orthodontic relapse factor. The mechanical properties and the forces generated in the NVB after orthodontic extrusion are explored.

MATERIALS AND METHODS

Six NVBs branching from the inferior alveolar nerve to the apices of the mandibular canines and premolars of mature pigs were harvested. Stress relaxation tests were conducted. A standard linear solid model (SLS) was utilized to simulate the orthodontic extrusion of a single rooted tooth with NVB length and cross-sectional diameter of 3.6 and 0.5 mm, respectively, so the NVB was stretched 10% and 20% of its original length. The maximum force within the NVB was then calculated.

RESULTS

Based on our data, the average Young's modulus before relaxation (E 0 ), after relaxation (E P ) and the difference between Young's moduli before and after relaxation (E S ) were 324 ± 123, 173 ± 73 and 151 ± 52 kPa, respectively. The theoretical force within the NVB stretched to 10% and 20% strain was 3 and 5 mN, respectively.

CONCLUSION

The data from our study indicate that the NVB exhibits stress relaxation, a characteristic trait of viscoelastic materials. SLS model simulation predicted residual forces around 5 mN for elongation up to 20%. We observed strain hardening with additional elongation, which has the potential to cause forces to increase exponentially. Therefore, tensile forces in the NVB should not be ruled out as a contributor to orthodontic relapse, especially in adult patients who may have decreased adaptability of their NVB. Further preclinical and clinical models should be developed to further clarify what is the contribution of the NVB to orthodontic relapse.

Rational design of viscoelastic hydrogels for periodontal ligament remodeling and repair

The periodontal ligament (PDL) is a distinctive yet critical connective tissue vital for maintaining the integrity and functionality of tooth-supporting structures. However, PDL repair poses significant challenges due to the complexity of its mechanical microenvironment encompassing hard-soft-hard tissues, with the viscoelastic properties of the PDL being of particular interest. This review delves into the significant role of viscoelastic hydrogels in PDL regeneration, underscoring their utility in simulating biomimetic three-dimensional microenvironments. We review the intricate relationship between PDL and viscoelastic mechanical properties, emphasizing the role of tissue viscoelasticity in maintaining mechanical functionality. Moreover, we summarize the techniques for characterizing PDL's viscoelastic behavior. From a chemical bonding perspective, we explore various crosslinking methods and characteristics of viscoelastic hydrogels, along with engineering strategies to construct viscoelastic cell microenvironments. We present a detailed analysis of the influence of the viscoelastic microenvironment on cellular mechanobiological behavior and fate. Furthermore, we review the applications of diverse viscoelastic hydrogels in PDL repair and address current challenges in the field of viscoelastic tissue repair. Lastly, we propose future directions for the development of innovative hydrogels that will facilitate not only PDL but also systemic ligament tissue repair. STATEMENT OF SIGNIFICANCE.

Effect of temperature on dynamic compressive behavior of periodontal ligament

Periodontal ligament (PDL) attaches tooth root to the surrounding bone. Its existence between tooth and jaw bone is of utmost importance due to its significant role in absorbing and distributing physiological and para-physiological loading. According to the previous studies, various mechanical tests have been performed to characterize the mechanical properties of the PDL; however, all of them have been done at room temperature. To the best of our knowledge, this is the first study in which the testing was performed at body temperature. The present research was planned to measure the dependency of PDL's viscoelastic behavior on temperature and frequency. Three different temperatures, including body and room temperature, were opted to perform the dynamic compressive tests of the bovine PDL. In addition, a Generalized Maxwell model (GMM) was presented based on empirical outcomes. At 37 °C, amounts of loss factor were found to be greater than those in 25 °C, which demonstrates that the viscous phase of the PDL in higher temperatures plays a critical role. Likewise, by raising the temperature from 25 °C to 37 °C, the model parameters show an enlargement in the viscous part and lessening in the elastic part. It was concluded that the PDL's viscosity in body temperature is much higher than that in room temperature. This model would be functional for a more accurate computational analysis of the PDL at the body temperature (37 °C) in various loading conditions such as orthodontic simulations, mastication, and impact.

Three-dimensional finite element analysis of the effect of alveolar cleft bone graft on the maxillofacial biomechanical stabilities of unilateral complete cleft lip and palate

BACKGROUND

The objective is to clarify the effect of alveolar cleft bone graft on maxillofacial biomechanical stabilities, the key areas when bone grafting and in which should be supplemented with bone graft once bone resorption occurred in UCCLP (unilateral complete cleft lip and palate).

METHODS

Maxillofacial CAD (computer aided design) models of non-bone graft and full maxilla cleft, full alveolar cleft bone graft, bone graft in other sites of the alveolar cleft were acquired by processing the UCCLP maxillofacial CT data in three-dimensional modeling software. The maxillofacial bone EQV (equivalent) stresses and bone suture EQV strains under occlusal states were obtained in the finite element analysis software.

RESULTS

Under corresponding occlusal states, the EQV stresses of maxilla, pterygoid process of sphenoid bone on the corresponding side and anterior alveolar arch on the non-cleft side were higher than other maxillofacial bones, the EQV strains of nasomaxillary, zygomaticomaxillary and pterygomaxillary suture on the corresponding side were higher than other maxillofacial bone sutures. The mean EQV strains of nasal raphe, the maximum EQV stresses of posterior alveolar arch on the non-cleft side, the mean and maximum EQV strains of nasomaxillary suture on the non-cleft side in full alveolar cleft bone graft model were all significantly lower than those in non-bone graft model. The mean EQV stresses of bilateral anterior alveolar arches, the maximum EQV stresses of maxilla and its alveolar arch on the cleft side in the model with bone graft in lower 1/3 of the alveolar cleft were significantly higher than those in full alveolar cleft bone graft model.

CONCLUSIONS

For UCCLP, bilateral maxillae, pterygoid processes of sphenoid bones and bilateral nasomaxillary, zygomaticomaxillary, pterygomaxillary sutures, anterior alveolar arch on the non-cleft side are the main occlusal load-bearing structures before and after alveolar cleft bone graft. Alveolar cleft bone graft mainly affects biomechanical stabilities of nasal raphe and posterior alveolar arch, nasomaxillary suture on the non-cleft side. The areas near nasal floor and in the middle of the alveolar cleft are the key sites when bone grafting, and should be supplemented with bone graft when the bone resorbed in these areas.

Food hardness can regulate orthodontic tooth movement in mice

BACKGROUND AND OBJECTIVES

Orthodontic treatment is often accompanied with prescription of softer foods to patients. The question to ask is, is this prescribed load regimen congruent with Wolff's law, and does it provide an adequate mechanical stimulus to maintain the functional health of periodontal complex? This question was answered by studying the effects of mice chewing on soft food (SF) and hard food (HF) while undergoing experimental tooth movement (ETM).

METHODS

Three-week-old C57BL/6 mice (n = 18) were fed either hard pellet (HF; n = 9) or soft-chow food (SF; n = 9). ETM was performed on mice at 8 weeks of age, and mice were euthanized at 1 min, 2 weeks, and 4 weeks (8, 10, and 12 weeks old, respectively). A logistic regression model was applied to the experimental data to extrapolate the prolonged effects of ETM on the physical features of the dentoalveolar joint (DAJ).

RESULTS

By 12 weeks, mice that chewed on SF expressed wider periodontal ligament space than those that chewed on HF. Mice that chewed on SF demonstrated increased alveolar socket roughness with larger alveoli and decreased bone volume fraction but with significantly lower bone mineral density and reduced overall tooth movement.

CONCLUSIONS

These altered physical features when contextualized within the DAJ illustrated that (a) the regions farther away from the "site of insult" also undergo significant adaptation, and (b) these adaptations vary between mesial and distal sides of the periodontal complex and topographically differentiate in the direction of the ETM. These insights underpin the main conclusion, in that there is a need to "regulate chewing loads" as a therapeutic dose following ETM to encourage regeneration of periodontal complex as an effective clinical outcome. The discussed multiscale image analyses also can be used on patient cone beam computed tomography data to identify the effectiveness of orthodontic treatment within the realm of masticatory function.

A multi-patient analysis of the center of rotation trajectories using finite element models of the human mandible

Studying different types of tooth movements can help us to better understand the force systems used for tooth position correction in orthodontic treatments. This study considers a more realistic force system in tooth movement modeling across different patients and investigates the effect of the couple force direction on the position of the center of rotation (CRot). The finite-element (FE) models of human mandibles from three patients are used to investigate the position of the CRots for different patients’ teeth in 3D space. The CRot is considered a single point in a 3D coordinate system and is obtained by choosing the closest point on the axis of rotation to the center of resistance (CRes). A force system, consisting of a constant load and a couple (pair of forces), is applied to each tooth, and the corresponding CRot trajectories are examined across different patients. To perform a consistent inter-patient analysis, different patients’ teeth are registered to the corresponding reference teeth using an affine transformation. The selected directions and applied points of force on the reference teeth are then transformed into the registered teeth domains. The effect of the direction of the couple on the location of the CRot is also studied by rotating the couples about the three principal axes of a patient’s premolar. Our results indicate that similar patterns can be obtained for the CRot positions of different patients and teeth if the same load conditions are used. Moreover, equally rotating the direction of the couple about the three principal axes results in different patterns for the CRot positions, especially in labiolingual direction. The CRot trajectories follow similar patterns in the corresponding teeth, but any changes in the direction of the force and couple cause misalignment of the CRot trajectories, seen as rotations about the long axis of the tooth.

Residual stress and osmotic swelling of the periodontal ligament

Osmotic swelling and residual stress are increasingly recognized as important factors in soft tissue biomechanics. Little attention has been given to residual stress in periodontal ligament (PDL) biomechanics despite its rapid growth and remodeling potential. Those tissues that bear compressive loads, e.g., articular cartilage, intervertebral disk, have received much attention related to their capacities for osmotic swelling. To understand residual stress and osmotic swelling in the PDL, it must be asked (1) to what extent, if any, does the PDL exhibit residual stress and osmotic swelling, and (2) if so, whether residual stress and osmotic swelling are mechanically significant to the PDL's stress/strain behavior under external loading. Here, we incrementally built a series of computer models that were fit to uniaxial loading, osmotic swelling and residual stretch data. The models were validated with in vitro shear tests and in vivo tooth-tipping data. Residual stress and osmotic swelling models were used to analyze tension and compression stress (principal stress) effects in PDL specimens under external loads. Shear-to-failure experiments under osmotic conditions were performed and modeled to determine differences in mechanics and failure of swollen periodontal ligament. Significantly higher failure shear stresses in swollen PDL suggested that osmotic swelling reduced tension and thus had a strengthening effect. The in vivo model's first and third principal stresses were both higher with residual stress and osmotic swelling, but smooth stress gradients prevailed throughout the three-dimensional PDL anatomy. The addition of PDL stresses from residual stress and osmotic swelling represents a unique concept in dental biomechanics.

Tensile creep mechanical behavior of periodontal ligament: A hyper-viscoelastic constitutive model

OBJECTIVE

In orthodontic treatment, the biomechanical response of periodontal ligament (PDL) induces tooth movement. Coupling modeling of PDL can effectively reflect its biomechanical response. The nonlinear creep mechanical behavior of PDL was studied by uniaxial tensile creep test and a new hyper-viscoelastic constitutive model. Two coupling modeling methods with limitations were excluded.

METHODS

PDL specimens were prepared from the central incisors of pig mandible. The theoretical step function was replaced by static loading with a total loading time of 1 s. The creep loading with the constant stresses of 0.05, 0.1, and 0.15 MPa was selected and kept unchanged for 1000 s. The instantaneous hyperelastic mechanical behavior and time-dependent nonlinear viscoelastic mechanical behavior of PDL were characterized by coupled instantaneous third-order Ogden hyperelastic and time-dependent nonlinear creep models.

RESULTS

The results showed that the instantaneous elastic curve of PDL increases in the form of hyperelastic index. The creep strain and creep compliance curves increase rapidly before 200s, and then increase slowly in steady state. The creep strain increased with an increase in the constant stress; conversely, the creep compliance decreased with an increase in the constant stress. The results showed that the experimental data were highly consistent with the hyper-viscoelastic constitutive model (R²>0.97).

SIGNIFICANCE

We normalize the framework of hyper-viscoelastic coupling modeling (Instantaneous hyperelastic model + time-dependent nonlinear viscoelastic model). Which can be extended to other nonlinear viscoelastic biomaterials.

Biomechanical Properties of Bone and Mucosa for Design and Application of Dental Implants

Dental implants’ success comprises their proper stability and adherence to different oral tissues (integration). The implant is exposed to different mechanical stresses from swallowing, mastication and parafunctions for a normal tooth, leading to the simultaneous mechanical movement and deformation of the whole structure. The knowledge of the mechanical properties of the bone and gingival tissues in normal and pathological conditions is very important for the successful conception of dental implants and for clinical practice to access and prevent potential failures and complications originating from incorrect mechanical factors’ combinations. The challenge is that many reported biomechanical properties of these tissues are substantially scattered. This study carries out a critical analysis of known data on mechanical properties of bone and oral soft tissues, suggests more convenient computation methods incorporating invariant parameters and non-linearity with tissues anisotropy, and applies a consistent use of these properties for in silico design and the application of dental implants. Results show the advantages of this approach in analysis and visualization of stress and strain components with potential translation to dental implantology.

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.

Enhancement of Gingival Tissue Adherence of Zirconia Implant Posts: In Vitro Study

Prevention of bacterial inflammation around dental implants (peri-implantitis) is one of the keys to success of the implantation and can be achieved by securing the gingival tissue-abutment interface preventing penetration of bacteria. Modern dental practice has adopted zirconia abutments in place of titanium, but the adhesion of gingival tissue to zirconia is inferior to titanium. The aim of this study was to assess and improve the adhesion of mucosal tissues to zirconia posts using sol-gel derived TiO₂ coating following dynamic mechanical testing. The posts were cultivated with porcine bone-gingival tissue specimens in vitro for 7 and 14 days and then subjected to dynamic mechanical analysis simulating physiological loading at 1 Hz up to 50 μm amplitude. In parallel in silico analysis of stresses and strains have been made simulating "the worst case" when the fixture fails in osseointegration while the abutment still holds. Results show treatment of zirconia can lead to double interface stiffness (static shear stiffness values from 5-10 to 17-23 kPa and dynamic from 20-50 to 60-125 kPa), invariant viscostiffness (from 5-35 to 45-90 kPa·s^α) and material memory values (increased from 0.06-0.10 to 0.17-0.25), which is beneficial in preventing bacterial contamination in dental implants. This suggests TiO₂-coated zirconia abutments may have a significant clinical benefit for prevention of the bacterial contamination.

A new perspective: Periodontal ligament is a viscoelastic fluid biomaterial as evidenced by dynamic shear creep experiment

Currently, Periodontal ligament (PDL) is considered as a viscoelastic solid biomaterial. However, we observed the steady-state rheological behavior of PDL through long time loading experiments, and suggested the theoretical definition of PDL as a viscoelastic fluid biomaterial. PDL specimens were prepared from the middle area of the mandibular central incisors in pigs. Dynamic force loading with frequencies of 0 (static load), 2, 5, and 10 Hz and amplitudes of 0.01, 0.02, and 0.03 MPa was adopted. The shear strain-time curve at the equilibrium position of PDL was obtained by a dynamic shear creep experiment. The results showed that the shear strain increased exponentially at first and then inclined toward an oblique line. The results showed that the PDL has viscoelastic fluid characteristics, independent of frequency and amplitude. The shear strain decreased with an increase in frequency and amplitude. To further analyze the viscoelastic characteristics of PDL, a 50000-s static shear creep experiment was re-designed. PDL exhibited viscoelastic fluid biomaterial characteristics according to the three aspects of the algebraic fitting, geometric characteristics, and physical results. For the first time, a viscoelastic fluid constitutive model was established to characterize the mechanical properties of PDL with high fitting accuracy. Furthermore, the shear viscosity coefficient of the dynamic load was larger than that of the static load, increasing with an increase in frequency and amplitude; compared with the static force, the dynamic force improved the viscosity of PDL, enhancing its function of fixing teeth, and introducing the new medical knowledge of "No tooth extraction after a meal."

Frequency-related viscoelastic properties of the human incisor periodontal ligament under dynamic compressive loading

Studies concerning the mechanical properties of the human periodontal ligament under dynamic compression are rare. This study aimed to determine the viscoelastic properties of the human periodontal ligament under dynamic compressive loading. Ten human incisor specimens containing 5 maxillary central incisors and 5 maxillary lateral incisors were used in a dynamic mechanical analysis. Frequency sweep tests were performed under the selected frequencies between 0.05 Hz and 5 Hz with a compression amplitude that was 2% of the PDL's initial width. The compressive strain varied over a range of 4%-8% of the PDL's initial width. The storage modulus, ranging from 28.61 MPa to 250.21 MPa, increased with the increase in frequency. The loss modulus (from 6.00 MPa to 49.28 MPa) also increased with frequency from 0.05 Hz- 0.5 Hz but remained constant when the frequency was higher than 0.5 Hz. The tanδ showed a negative logarithmic correlation with frequency. The dynamic moduli and the loss tangent of the central incisor were higher than those of the lateral incisor. This study concluded that the human PDL exhibits viscoelastic behavior under compressive loadings within the range of the used frequency, 0.05 Hz- 5 Hz. The tooth position and testing frequency may have effects on the viscoelastic properties of PDL.

Numerical simulation of hydro-mechanical coupling of periodontal ligament

Orthodontic tooth movement in the alveolar bone is due to the mechanical response of periodontal ligament to applied forces. Definition of a proper constitutive model of the periodontal ligament to investigate its response to orthodontic loading is required. For this purpose, a three-dimensional finite element model of incisor tooth, periodontal ligament, and bone was built utilizing the hydro-mechanical coupling theory. Tooth displacement in response to orthodontic loading was then investigated, and the effect of different mechanical behaviors assigned to the solid phase of the periodontal ligament was compared. Results showed that where the periodontal ligament was placed in tension, pore volume was filled with fluid intake from the bone, but fluid flow direction was from the periodontal ligament toward the bone where the periodontal ligament was placed in compression. Because of the existence of interaction between solid and fluid phases of the periodontal ligament, considering biphasic material formulation was capable to address its microscopic behavior as well as time-dependent and large deformation behaviors. This article provides beneficial biomechanical data for future dental studies in determination of optimal orthodontic force.

Quantitative/qualitative analysis of adhesive-dentin interface in the presence of 10-methacryloyloxydecyl dihydrogen phosphate

Dental adhesive provides effective retention of filling materials via adhesive-dentin hybridization. The use of co-monomers, such as 10-methacryloyloxydecyl dihydrogen phosphate (10-MDP), is thought to be crucial for hybridization owing to their ionic-binding to calcium and co-polymerization in the polymerizable adhesives. Optimal hybridization partly depends on the mechanical properties of polymerized adhesives, which are likely to be proportional to the degree of conversion ratio. This study assessed the correlation between polymerization quality and mechanical properties at the adhesive-dentin interfaces in the presence or absence of 10-MDP. In situ Raman microspectroscopy and nanoindentation tests were used concurrently to quantify the degree of conversion ratio and dynamic mechanical properties across the adhesive-dentin interfaces. Despite the excellent diffusion and apparent higher degree of co-polymerization, 10-MDP reduced the elastic modulus of the interface. The higher viscoelastic properties of the adhesive are suggestive of poor polymerization, namely polymerization linearity related to the long carboxyl chain of 10-MDP. Such reduced mechanical integrity of hybridization could also be associated with the inhibition of nano-layering between 10-MDP and mineralized tissue in the presence of hydroxyethyl methacrylate (HEMA). This potential drawback of HEMA necessitates further qualitative/quantitative characterization of adhesive-dentin hybridization using a HEMA-free/low concentration experimental 10-MDP monomer, which theoretically possesses superior chemical bonding potential to the current HEMA-rich protocol.

Mechanical Considerations for Electrospun Nanofibers in Tendon and Ligament Repair

Electrospun nanofibers possess unique qualities such as nanodiameter, high surface area to volume ratio, biomimetic architecture, and tunable chemical and electrical properties. Numerous studies have demonstrated the potential of nanofibrous architecture to direct cell morphology, migration, and more complex biological processes such as differentiation and extracellular matrix (ECM) deposition through topographical guidance cues. These advantages have created great interest in electrospun fibers for biomedical applications, including tendon and ligament repair. Electrospun nanofibers, despite their nanoscale size, generally exhibit poor mechanical properties compared to larger conventionally manufactured polymer fiber materials. This invites the question of what role electrospun polymer nanofibers can play in tendon and ligament repair applications that have both biological and mechanical requirements. At first glance, the strength and stiffness of electrospun nanofiber grafts appear to be too low to fill the rigorous loading conditions of these tissues. However, there are a number of strategies to enhance and tune the mechanical properties of electrospun nanofiber grafts. As researchers design the next-generation electrospun tendon and ligament grafts, it is critical to consider numerous physiologically relevant mechanical criteria and to evaluate graft mechanical performance in conditions and loading environments that reflect in vivo conditions and surgical fixation methods.

Mechanical properties of the airway tree: heterogeneous and anisotropic pseudoelastic and viscoelastic tissue responses

Airway obstruction and pulmonary mechanics remain understudied despite lung disease being the third cause of death in the United States. Lack of relevant data has led computational pulmonary models to infer mechanical properties from available material data for the trachea. Additionally, the time-dependent, viscoelastic behaviors of airways have been largely overlooked, despite their potential physiological relevance and utility as metrics of tissue remodeling and disease progression. Here, we address the clear need for airway-specific material characterization to inform biophysical studies of the bronchial tree. Specimens from three airway levels (trachea, large bronchi, and small bronchi) and two orientations (axial and circumferential) were prepared from five fresh pig lungs. Uniaxial tensile tests revealed substantial heterogeneity and anisotropy. Overall, the linear pseudoelastic modulus was significantly higher axially than circumferentially (30.5 ± 3.1 vs. 8.4 ± 1.1 kPa) and significantly higher among circumferential samples for small bronchi than for the trachea and large bronchi (12.5 ± 1.9 vs. 6.0 ± 0.6 and 6.6 ± 0.9 kPa). Circumferential samples exhibited greater percent stress relaxation over 300 s than their axial counterparts (38.0 ± 1.4 vs. 23.1 ± 1.5%). Axial and circumferential trachea samples displayed greater percent stress relaxation (26.4 ± 1.6 and 42.5 ± 1.7%) than corresponding large and small bronchi. This ex vivo pseudoelastic and viscoelastic characterization reveals novel anisotropic and heterogeneous behaviors and equips us to construct airway-specific constitutive relations. Our results establish necessary fundamentals for airway mechanics, laying the groundwork for future studies to extend to clinical questions surrounding lung injury, and further directly enables computational tools for lung disease obstruction predictions. NEW & NOTEWORTHY Understanding the mechanics of the lung is necessary for investigating disease progression. Trachea mechanics comprises the vast majority of ex vivo airway tissue characterization despite distal airways being the site of disease manifestation and occlusion. Furthermore, viscoelastic studies are scarce, whereas time-dependent behaviors could be potential physiological metrics of tissue remodeling. In this study, the critical need for airway-specific material properties is addressed, reporting bronchial tree anisotropic and heterogeneous material properties.

A novel approach for early evaluation of orthodontic process by a numerical thermomechanical analysis

The main objective of this paper is to propose a novel method that provides an opportunity to evaluate an orthodontic process at early phase of the treatment. This was accomplished by finding out a correlation between the applied orthodontic force and thermal variations in the tooth structure. To this end, geometry of the human tooth surrounded by the connective soft tissue called the periodontal ligament and the bone was constructed by employing dental CT scan images of a specific case. The periodontal ligament was modeled by finite strain viscoelastic model through a nonlinear stress-strain relation (hyperelasticity) and nonlinear stress-time relation (viscoelasticity). The tooth structure was loaded by a lateral force with 15 different quantities applied to 20 different locations, along the midedge of the tooth crown. The resultant compressive stress in the periodontal ligament was considered as the cause of elevated cell activity that was modeled by a transient heat flux in the thermal analysis. The heat flux value was estimated by conducting an experiment on a pair of rats. The numerical results showed that by applying an orthodontic force to the tooth structure, a significant temperature rise was observed. By measuring the temperature rise, the orthodontic process can be evaluated.

In-vivo determination of critical force levels using an intraoral electromechanical device to measure nonpathologic tooth mobility

INTRODUCTION

An electromechanical device was used to experimentally characterize the movement of a single tooth within the periodontal ligament space. The force magnitude leading to the complete compression of the periodontal ligament is considered a critical force and is designated Fc. We investigated the effectiveness of the electromechanical device to repeatedly determine the critical force magnitude Fc.

METHODS

The study comprised 12 tests conducted on 11 subjects. Alternating labial and lingual forces were applied to a maxillary incisor by the device. The resulting immediate intra-alveolar tooth displacement was recorded in real time. Data processing was used to determine the tooth mobility curve for 193 push-pull cycles. The critical force Fc was mathematically determined for both the labial and lingual displacements of the tooth.

RESULTS

The tooth mobility curve could be characterized for all 12 tests. A total of 386 values of Fc were calculated for the 12 different teeth. Values of Fc for each test ranged from 10.47 to 20.18 g in the lingual direction, and from 12.56 to 21.72 g in the labial direction.

CONCLUSIONS

The electromechanical appliance was successful in repeatedly determining Fc in vivo. The ability to experimentally determine the extent of periodontal ligament compression at a given force magnitude could shed new light on the question of an optimal orthodontic force and open new avenues of orthodontic research and treatment.

DETERMINATION OF VISCOELASTIC PROPERTIES OF THE PERIODONTAL LIGAMENT USING NANOINDENTATION TESTING AND NUMERICAL MODELING

Viscoelasticity of the periodontal ligament (PDL) plays an important role in load transmission between tooth and alveolar bone, as well as tooth movement. This paper provides a novel nanoindentation experiment in combination with a rheological model to characterize the viscoelastic mechanical properties of the PDL. Two creep models of the indentation experiments with a Berkovich and a spherical indenter based on Zener model were developed. The hardness and reduced modulus were determined by using the Berkovich indenter. The parameters were identified through curve fittings. The fitting results show that the creep models are both in good agreement with the experimental data. Meanwhile, the models were both validated by comparing the numerical curves for load–depth relationship in loading segment with the corresponding experimental data. It is found that the spherical indenter is more suitable for testing the viscoelastic mechanical properties of the PDL than Berkovich indenter. Hence, the nanoindentation experiment with spherical indenter was simulated to further evaluate the Zener model by finite element analysis. The good agreement between the simulated results and experimental data demonstrates that the Zener model is capable of describing the viscoelastic mechanical behavior of the PDL.

Biomechanical characterization of the periodontal ligament: Orthodontic tooth movement

OBJECTIVE

To quantify the biomechanical properties of the bovine periodontal ligament (PDL) in postmortem sections and to apply these properties to study orthodontic tooth intrusion using finite element analysis (FEA). We hypothesized that PDL's property inherited heterogeneous (anatomical dependency) and nonlinear stress-strain behavior that could aid FEA to delineate force vectors with various rectangular archwires.

MATERIALS AND METHODS

A dynamic mechanical analyzer was used to quantify the stress-strain behavior of bovine PDL. Uniaxial tension tests using three force levels (0.5, 1, and 3 N) and samples from two anatomical locations (circumferential and longitudinal) were performed to calculate modulus. The Mooney-Rivlin hyperelastic (MRH) model was applied to the experimental data and used in an FEA of orthodontic intrusion rebounded via a 0.45-mm step bend with three archwire configurations of two materials (stainless steel and TMA).

RESULTS

Force levels and anatomical location were statistically significant in their effects on modulus (P < .05). The apical part had a greater stiffness than did the middle part. The MRH model was found to approximate the experimental data well (r = 0.99), and it demonstrated a reasonable stress-strain outcome within the PDL and bone for FEA intrusion simulation. The force acting on the tooth increased five times from the 0.016 × 0.022-inch TMA to the 0.019 × 0.025-inch stainless steel.

CONCLUSIONS

The PDL is a nonhomogeneous tissue in which the modulus changed in relation to location. PDL nonlinear constitutive model estimated quantitative force vectors for the first time to compare intrusive tooth movement in 3-D space in response to various rectangular archwires.

Combined microcomputed tomography, biomechanical and histomorphometric analysis of the peri-implant bone: a pilot study in minipig model

OBJECTIVES

To present a practical approach that combines biomechanical tests, microcomputed tomography (μCT) and histomorphometry, providing quantitative results on bone structure and mechanical properties in a minipig model, in order to investigate the specific response to an innovative dental biomaterial.

METHODS

Titanium implants with innovative three-dimensional scaffolds were inserted in the tibias of 4 minipigs. Primary stability and osseointegration were investigated by means of insertion torque (IT) values, resonance frequency analysis (RFA), bone-to-implant contact (BIC), bone mineral density (BMD) and stereological measures of trabecular bone.

RESULTS

A significant positive correlation was found between IT and RFA (r=0.980, p=0.0001). BMD at the implant sites was 18% less than the reference values (p=0.0156). Peri-implant Tb.Th was 50% higher, while Tb.N was 50% lower than the reference zone (p<0.003) and they were negatively correlated (r=-0.897, p=0.006).

SIGNIFICANCE

μCT increases evaluation throughput and offers the possibility for qualitative three-dimensional recording of the bone-implant system as well as for non-destructive evaluation of bone architecture and mineral density, in combination with conventional analysis methods. The proposed multimodal approach allows to improve accuracy and reproducibility for peri-implant bone measurements and could support future investigations.

Bone Aging by Advanced Glycation End Products

The quality and quantity of mandibular bone are essential prerequisites for osseointegrated implants. Only the Hounsfield unit on preoperative computed tomography is currently used as a clinical index. Nevertheless, a considerable mismatch occurs between bone quality and the Hounsfield unit. Loss of bone toughness during aging has been accepted based on empirical evidence, but this concept is unlikely evidence based at the level of mechanical properties. Nonenzymatic bone matrix cross-links associated with advanced glycation end products predominate as a consequence of aging. Thus, loss of tissue integrity could diminish the bone toughening mechanism. Here, we demonstrate an impaired bone toughening mechanism caused by mimicking aging in rabbits on a methionine-rich diet, which enabled an enhanced nonenzymatically cross-linked bone matrix. A 3-point bending test revealed a greater reduction in femoral fracture resistance in rabbits on a methionine-rich diet, despite higher maximum and normalized breaking forces (287.3 N and 88.1%, respectively), than in rabbits on a normal diet (262.2 N and 79.7%, respectively). In situ nanoindentation on mandibular cortical bone obtained from rabbits on a methionine-rich diet did not enable strain rate–dependent stiffening and consequent large-dimensional recovery during rapid loading following constant displacement after a rapid-load indentation test as compared with those in rabbits on a normal diet. Such nanoscale structure-function relationships dictate resistance to cracking propagation at the material level and allow for the overall bone toughening mechanism to operate under large external stressors. The strain-dependent stiffening was likely associated with strain-energy transfer to the superior cross-linked bone matrix network of the normal diet, while the reduction in the enzymatically cross-linked matrix in bone samples from rabbits on a methionine-rich diet likely diminished the intrinsic bone toughening mechanism. The present study also provides a precise protocol for evaluating bone mechanical properties at the material level based on observations from a series of nanoindentation experiments.

In situ quasi-static and dynamic nanoindentation tests on calcified nodules formed by osteoblasts: Implication of glucocorticoids responsible for osteoblast calcification

The functional requirements of regenerated calcified tissues are that they enable the tissues to bear a variety of imposed stress and consequent contact-induced strain without substantial fracture. Here we demonstrate the effects of glucocorticoid hormones such as dexamethasone and hydrocortisone on the nanomechanical properties of calcified nodules formed by mouse osteoblastic MC3T3-E1 cells in differentiation-inducing medium containing ascorbic acid and β-glycerophosphate. Neither cell proliferation nor calcium deposition, evaluated using alizarin red and von Kossa staining, was affected by dexamethasone. On the other hand, calcified nodules formed in the presence of dexamethasone were significantly harder and stiffer than those formed in their absence. In particular, a series of nanoindentation tests revealed that the calcified nodules formed in the presence of dexamethasone showed enhanced stiffness against dynamic strain as compared to a quasi-static load. Furthermore, Raman spectroscopy revealed that dexamethasone and hydrocortisone increased the apatite/matrix ratio and lowered that of carbonate in the nodules. Our results suggest that glucocorticoids are required for in vitro formation by osteoblasts of more mature calcified nodules containing apatite/phosphate.

Strain-rate stiffening of cortical bone: observations and implications from nanoindentation experiments

While bone mineralization is considered to be responsible for its stiffness, bone durability partially associated with the time-dependent viscoelasticity of matrix proteins is still poorly elucidated. Here we demonstrate a novel mechanism of highly mineralized bone durability almost independent of inherent viscoelastic behaviour along with a protocol for measuring the mechanical properties of mineralized tissues. Strain-rate nanoindentation tests showed substantial stiffening of the highly mineralized calvarial bone, whereas large creep or stress relaxation was observed during constant load or displacement tests, respectively. Based on the lower viscoelasticity of the highly mineralized structure, such large time-dependent response appears to be associated with nanoscale dimensional recovery, rather than viscoelastic behaviour, implying the inverse namely strain-rate dependent dilatant behaviour. This dilatant expansion increased the indenter penetration resistance into the surface, enhancing instantaneous stiffness. The associated stiffening and higher effective elastic modulus were highly strain-rate dependent and more readily observed in more highly mineralized tissues such as the calvarial bone. Such strain-rate stiffening and consequent dimensional recovery may be vital responses of bone tissues against excessive deformation to maintain tissue integrity.

Variation of the mineral density in cortical bone may serve to keep strain amplitudes within a physiological range

Within-bone variation in mineral density could be functional. A heterogeneous mineral-density distribution might serve to maintain habitual amplitudes of bone strain within a non-harmful, i.e., physiological range. Regions of a bone that would be strained the most on the basis of architecture alone might have a higher mineral density to make them more stiff and resistant to strain. We hypothesised that the cortical bone of the rabbit mandible contains such a functional distribution of mineral density. We thereby expected similar mineral-density patterns in the mandibles of different individuals due to the shared masticatory function. Secondly, we hypothesised that the highest mineral densities occur in mandibular regions predicted to be exposed to the largest amplitudes of strain-when taking into account bone architecture only. Mineral-density maps of the cortical bone of rabbit mandibles were obtained using micro-computed tomography (μCT). The μCT scans of two rabbits were converted into finite-element models (FEMs). To predict mandibular deformation during biting, these models were loaded by muscle forces and reaction forces. The forces acted on the condyles and on either the incisal or molar bite point. The FEMs were assigned a homogeneous material stiffness to calculate the strain amplitudes that would occur when only the architecture of the mandibular bone would be of influence. We found the cortical bone-mineral density patterns to be similar in all six mandibles. The mineral density of the corpus was higher than that of the ramus. A second consistent feature of the mandibular mineral-density distribution was that the medial ridge of the temporal-muscle insertion groove contained more mineral than its surrounding regions. The strain amplitudes calculated with the FEMs were variable and did not feature clear corpo-ramal differences. However, specific mandibular bone sites calculated to be exposed to the largest amplitudes of strain, including the medial ridge of the temporal-muscle insertion groove, did correspond with high-mineral-density regions. We conclude that, in the rabbit mandible, the heterogeneous mineral-density distribution might serve to suppress bone-strain amplitudes in regions architecturally susceptible to the largest deformations during loading.

Alveolar ridge resorption after tooth extraction: A consequence of a fundamental principle of bone physiology

It is well established that tooth extraction is followed by a reduction of the buccolingual as well as the apicocoronal dimension of the alveolar ridge. Different measures have been taken to avoid this bone modelling process, such as immediate implant placement and bone grafting, but in most cases with disappointing results. One fundamental principle of bone physiology is the adaptation of bone mass and bone structure to the levels and frequencies of strain. In the present article, it is shown that the reduction of the alveolar ridge dimensions after tooth extraction is a natural consequence of this physiological principle.

Correlations between photogrammetric measurements of tooth mobility and the Periotest method

OBJECTIVE

The purpose of the present study was to investigate whether or not the quantitative Periotest values of anterior teeth correlate with quantitative metric values of tooth mobility under vertical (VL) and horizontal load (HL) in periodontally healthy subjects.

MATERIALS AND METHODS

Thirty-one subjects with good periodontal conditions were included and subjected to two different tooth mobility measurement techniques. Periotest values were measured at reproducible measurement points in the vertical (vPT) and horizontal (hPT) dimensions of upper central and lateral incisors and canine teeth. Using the optical measurement technique (photogrammetry), tooth mobility was measured under load in the horizontal (HL) and vertical loading directions (VL) at different load forces. Pearson's correlation coefficients were used to determine exploratory associations.

RESULTS

The comparison between hPT and HL showed no correlations between the two measurements except for 'weak' and 'moderate' correlations for teeth 21 and 23. The analysis of correlations between vPT and VL data showed statistically significant correlations for both the left and right canine teeth that ranged from 'weak' to 'high'. Comparisons between hPT values and VL and between vPT and HL showed significant correlations at a few loading forces only.

CONCLUSION

Quantitative Periotest values cannot be used to draw conclusions about the metric assessment of tooth mobility. For this purpose, the photogrammetric technique could be an additional tool for scientific questions.

Measurement of tooth and implant mobility under physiological loading conditions

In vivo measurement of the mobility of teeth under physiological loading has been subject of research for years. Comparing the deflection under load of dental implants with teeth provides valuable input for designing restorations spanning both teeth and implants. Physiological force rise time of about 50-100 ms and displacement of 10-100 μm requires high spatial and temporal resolution of the measurement set-up. Using an optical system attached to the teeth/implants to be measured and a light source attached to a point of reference, displacement of teeth and implants under axial and lateral loading was measured on a series of volunteers. Axial displacement of teeth shows strong time dependence consistent with (hydraulic) damping not observed for lateral loads. Displacement under lateral loading was found to be about one order of magnitude higher than under axial load. For dental implants elastic deflection was observed in axial and lateral direction without measurable influence of the load rise time. For purely axial loading, dental implants and teeth show similar deflection under physiological force rise time but for lateral loading the considerably difference between teeth and implant may put some restrictions on the construction of tooth-implant-bridges, especially for teeth in the anterior region.

Appropriateness of viscoelastic soft materials as in vitro simulators of the periodontal ligament

The periodontal ligament is a viscoelastic soft tissue that connects the tooth to the alveolar bone. This tissue should be simulated in numerical as well as in laboratory models. The mechanical properties of this tissue were previously determined ex vivo and in vivo. The aim of the study was to analyse the appropriateness of impression and reline materials used in dentistry to simulate viscoelastic behaviour of the periodontal ligament. Two reline [Durabase (Reliance Dental MFG, Co.) and Soft Liner (GC Corporation)] and two impression [President Plus (Coltene) and Prestige L (Vanini Dental Industry)] materials were examined in recovery and tensile relaxation tests. Recovery: This experiment simulated in vivo test. Roots of a pair of plastic maxillary premolar teeth were covered with each test material and embedded in acryl while maintaining the contact point. A 0·1-mm stainless steel strip, inserted at the contact point and maintained for 10 s, was used to tip the teeth. After removal, the tightness of dental contact point was measured over 30 min by determining the force needed to insert a 0·05-mm metal strip. Tensile relaxation: strips were elongated to 120%, 140% and 160% of their initial length and maintained at that length for 30 min. Two-phase decay function was applied. The results showed that elastic modulus and relaxation behaviour were significantly different between materials. Elastic modulus values were in the same range of those reported in the literature. However, the recovery values and behaviour showed that impression materials, especially President, are the materials of choice for this purpose because they simulated better the in vivo test.

Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature

Introduction. This review is intended to highlight and discuss discrepancies in the literature of the periodontal ligament's (PDL) mechanical properties and the various experimental approaches used to measure them. Methods. Searches were performed on biomechanical and orthodontic publications (in databases: Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, and Scopus). Results. The review revealed that significant variations exist, some on the order of six orders of magnitude, in the PDL's elastic constants and mechanical properties. Possible explanations may be attributable to different experimental approaches and assumptions. Conclusions. The discrepancies highlight the need for further research into PDL properties under various clinical and experimental loading conditions. Better understanding of the PDL's biomechanical behavior under physiologic and traumatic loading conditions might enhance the understanding of the PDL's biologic reaction in health and disease. Providing a greater insight into the response of the PDL would be instrumental to orthodontists and engineers for designing more predictable, and therefore more efficacious, orthodontic appliances.

Photogrammetric measurement of initial tooth displacement under tensile force

The purpose of this study was to quantitatively measure tooth displacement under low horizontal tensile force (≤18 N) and to test the reproducibility of measurements. Anterior tooth mobility was measured using a photogrammetric measurement technique in 23 periodontally healthy subjects. While slowly increasing the tension on each tooth, an automated software program recorded three-dimensional tooth displacement at 3 N intervals, up to 18 N. Measurements were repeated three-times for each tooth. The vector of absolute tooth mobility in the buccal direction was calculated. Intra-class correlations of the three repeated measurements of each tooth were calculated and ranged between "good" and "optimal". The agreement of measurements was significant (p≤0.05). The analysis of differences between the deviation vectors of contralateral teeth revealed that most differences emerged to be statistically non-significant. The combination of a mechanical loading approach with the optoelectronic system allowed the measurement of three-dimensional tooth mobility in vivo.

Three-dimensional morphometry of strained bovine periodontal ligament using synchrotron radiation-based tomography

The periodontal ligament (PDL) is a highly vascularized soft connective tissue. Previous studies suggest that the viscous component of the mechanical response may be explained by the deformation-induced collapse and expansion of internal voids (i.e. chiefly blood vessels) interacting with liquids (i.e. blood and interstitial fluids) flowing through the pores. In the present work we propose a methodology by means of which the morphology of the PDL vascular plexus can be monitored at different levels of compressive and tensile strains. To this end, 4-mm-diameter cylindrical specimens, comprising layers of bone, PDL and dentin covered by cementum, were strained at stretch ratios ranging from lambda = 0.6 to lambda = 1.4 and scanned using synchrotron radiation-based computer tomography. It was concluded that: (1) the PDL vascular network is layered in two distinct planes of blood vessels (BVs): an inner layer (close to the tooth), in which the BVs run in apico-coronal direction, and an outer layer (close to the alveolar bone), in which the BVs distribution is more diffuse; (2) during tension and compression, the porosity tissue is kept fairly constant; (3) mechanical straining induces important changes in BV diameters, possibly modifying the permeability of the PDL and thus contributing to the viscous component of the viscoelastic response observed under compressive forces.