Quasi-linear viscoelastic behavior of the human periodontal ligament

Inverse finite element analysis for an axisymmetric model of vertical tooth extraction

BACKGROUND AND OBJECTIVE

Tooth extraction is a common clinical procedure with biomechanical factors that can directly influence patient outcomes. Recent development in atraumatic extraction techniques have endeavoured to improve treatment outcomes, but the characterization of extraction biomechanics is sparse. An axisymmetric inverse finite element (FE) approach is presented to represent the biomechanics of vertical atraumatic tooth extraction in an ex-vivo swine model.

METHODS

Geometry and boundary conditions from the model are determined to match the extraction of swine incisors in a self-aligning ex vivo extraction experiment. Material parameters for the periodontal ligament (PDL) model are determined by solving an inverse FE problem using clusters of data obtained from 10 highly-controlled mechanical experiments. A seven-parameter visco-hyperelastic damage model, based on an Arruda-Boyce framework, is used for curve fitting. Three loading schemes were fit to obtain a common set of material parameters.

RESULTS

The inverse FE results demonstrate good predictions for overall force-time curve shape, peak force, and time to peak force. The fit model parameters are sufficiently consistent across all three cases that a coefficient-averaged model was taken that compares well to all three cases. Notably, the initial modulus ,u, converged across trials to an average value of 0.472 MPa with an average viscoelastic constant g of 0.561.

CONCLUSIONS

The presented model is found to have consistent parameters across loading cases. The capability of this model to represent the fundamental mechanical characteristics of the dental complex during vertical extraction loading is a significant advancement in the modelling of extraction procedures. Future work will focus on verifying the model as a predictive design tool for assessing new loading schemes in addition to investigating its applications to subject-specific problems.

An in vivo evaluation of clear aligners for optimal orthodontic force and movement to determine high-efficacy and periodontal-friendly aligner staging

Objectives

To investigate the effect of aligner displacement on tooth movement and periodontal health to improve the efficiency of aligner treatment and explore the mechanism in vivo.

Methods

A two-tooth site was established by a finite element (FE) model to virtually evaluate aligner staging. A randomized controlled experiment was conducted when the tooth sites in beagles were treated with fixed or aligner appliances with different movement and force, and tooth movement and internal structure were recorded during the alignment. After sacrificing five dogs, bone-periodontal ligament (PDL)-tooth specimens were removed and processed to conduct uniaxial compression and tensile tests as well as micro-CT imaging and histological analysis.

Results

Three displacements of 0.25, 0.35 and 0.45 mm were obtained from FE analysis and applied in beagles. In general, aligners had poorer performance on movement compared to fixed systems in vivo, but the aligner with a staging of 0.35 mm had the highest accuracy (67.46%) (P < 0.01). Loaded with severe force, fixed sites exhibited tissue damage due to excess force and rapid movement, while aligners showed better safety. The PDL under a 0.35-mm aligner treatment had the highest elastic modulus in the biomechanical test (551.4275 and 1298.305 kPa) (P < 0.05).

Conclusions

Compared to fixed appliances, aligners achieve slightly slower movement but better periodontal condition. Aligners with an interval of 0.35 mm have the highest accuracy and best PDL biomechanical and biological capacities, achieving the most effective and safest movement. Even with complexity of oral cavity and lack of evaluation of other factors, these results provide insight into faster displacement as a method to improve the efficacy of aligners.

Identification of the periodontal ligament material parameters using response surface method

The orthodontic treatment can be guided by the finite element (FE) simulation of periodontal ligament (PDL) mechanical properties, and the biomimetic degree of FE simulation can be primarily affected by the material properties of the PDL. According to the principle of parameter inverse, a method: response surface (RS) method and FE inverse method were proposed to identify the material parameters of PDL. The Prony series viscoelastic FE model was established based on the relaxation experiment. With root mean square error of simulation results and experimental results as the objective function, the optimal parameter combination was obtained by RS method, and the FE simulation result were compared with the experimental result. The result showed that the optimal parameters of the PDL were elastic modulus: 3.791 MPa, Poisson's ratio: 0.42, temperature: 29.294°C separately, and the simulation result of optimal combination maintained consistency with experiment with the correlation coefficient of 0.97258, indicating that the method proposed in this paper could well identify of PDL material parameters. The parameter identification method used in this paper can significantly improve the calculation efficiency, and reduce the parameter identification error compared with the simple FE inverse method, which has scientific significance and theoretical value.

Determination of the compressive modulus of elasticity of periodontal ligament derived from human first premolars

Purpose

There are two commonly cited modulus of elasticity of the human periodontal ligament (EPDL), i.e., 6.89 ✕ 10-5 GPa (E1) and 6.89 ✕ 10-2 GPa (E2), which are exactly 1000-fold different from each other. This study aims to clarify the ambiguity of the two EPDL used for simulations and determine a more accurate EPDL value of human first premolars using experimental and simulation approaches.

Methods

Numerical simulations using finite element analysis were performed to analyze PDL deformation under an average Asian occlusal force. To confirm the results, simple and multi-component, true-scale 3D models of a human first premolar were used in the simulations. Finally, a compression test using a universal testing machine on PDL specimens was conducted to identify the compressive EPDL of human first premolars.

Results

The simulation results from both models revealed that E1 was inaccurate, because it resulted in excessive PDL deformation under the average occlusal force, which should not occur during mastication. Although the E2 did not lead to excessive PDL deformation, it was obtained by an error in unit conversion with no scientific backing. In contrast, the compression test results indicated that the compressive EPDL was 9.64 ✕ 10-4 GPa (E3). In the simulation, E3 did not cause excessive PDL deformation.

Conclusion

The simulation results demonstrated that both commonly cited EPDL values (E1 and E2) were incorrect. Based on the experimental and simulation results, the average compressive EPDL of 9.64 ✕ 10-4 GPa is proposed as a more accurate value for human first premolars.

Clinical significance

The proposed more accurate EPDL would contribute to more precise and reliable FEA simulation results and provide a better understanding of the stress distribution and deformation of dental materials, which will be beneficial to precision dentistry, orthodontics and restoration designs.

Biomechanical evaluation of bridge span with three implant abutment designs and two connectors for tooth-implant supported prosthesis: A finite element analysis

Background/purpose

Bridge stability under loading was influenced by bridge span with the connector and implant abutment design. Thus, the purpose of this study was to evaluate the effects of rigid and non-rigid connector designs and pontic connections of different abutment systems in the tooth-implant supported prosthesis (TISP) at different span distances on the biomechanical stress distribution of the overall system components.

Materials and methods

For comparative analysis, rigid and non-rigid bridge connections were fitted with three implant abutment systems (one-piece, two-piece and three-piece), and five implant-to-natural tooth distance configurations (12 mm, 14 mm, 16 mm, 18 mm, and 20 mm) were provided.

Results

The maximum stress between TISP components occurred at the distal side of crown margin of cement1 in rigid connector with one-piece group and the bottom of the crown3 in non-rigid connector with one-piece group, while the other groups were more concentrated at the junction between the mesial side of the implant collar and the abutment. In addition, neither the rigid nor non-rigid connector model showed that stress distribution increased proportionally with the bridge span distance.

Conclusion

It was clinically recommended that if the implant with a shorter bridge distance of 12 mm from the natural tooth, the rigid connection of the three-piece abutment can be used as the TISP design. If the bridge distance was 18 mm longer, the non-rigid connection of the three-piece abutment could maintain the physiological movement of the natural tooth and avoid the excessive stress on the bone crest around the implant.

The effects of different types of periodontal ligament material models on stresses computed using finite element models

INTRODUCTION

Finite element (FE) method has been used to calculate stress in the periodontal ligament (PDL), which is crucial in orthodontic tooth movement. The stress depends on the PDL material property, which varies significantly in previous studies. This study aimed to determine the effects of different PDL properties on stress in PDL using FE analysis.

METHODS

A 3-dimensional FE model was created consisting of a maxillary canine, its surrounding PDL, and alveolar bone obtained from cone-beam computed tomography scans. One Newton of intrusion force was applied vertically to the crown. Then, the hydrostatic stress and the von Mises stress in the PDL were computed using different PDL material properties, including linear elastic, viscoelastic, hyperelastic, and fiber matrix. Young's modulus (E), used previously from 0.01 to 1000 MPa, and 3 Poisson's ratios, 0.28, 0.45, and 0.49, were simulated for the linear elastic model.

RESULTS

The FE analyses showed consistent patterns of stress distribution. The high stresses are mostly concentrated at the apical area, except for the linear elastic models with high E (E >15 MPa). However, the magnitude varied significantly from -14.77 to -127.58 kPa among the analyzed patients. The E-stress relationship was not linear. The Poisson's ratio did not affect the stress distribution but significantly influenced the stress value. The hydrostatic stress varied from -14.61 to -95.48 kPa.

CONCLUSIONS

Different PDL material properties in the FE modeling of dentition do not alter the stress distributions. However, the magnitudes of the stress significantly differ among the patients with the tested material properties.

Strain Measurement within an Intact Swine Periodontal Ligament

The periodontal ligament (PDL) provides support, proprioception, nutrition, and protection within the tooth–PDL–bone complex (TPBC). While understanding the mechanical behavior of the PDL is critical, current research has inferred PDL mechanics from finite element models, from experimental measures on complete TPBCs, or through direct measurement of isolated PDL sections. Here, transducers are used in an attempt to quantify ex vivo PDL strain. In-fiber Bragg grating (FBG) sensors are small flexible sensors that can be placed within an intact TPBC and yield repeatable strain measurements from within the PDL space. The objective of this study was to determine: 1) if the FBG strain measured from the PDL space of intact swine premolars ex vivo was equivalent to physical PDL strains estimated through finite element analysis and 2) if a change in FBG strain could be linearly related to a change in finite element strain under variable tooth displacement, applied to an intact swine TPBC. Experimentally, individual TPBCs were subjected to 2 displacements (n = 14). The location of the FBG was determined from representative micro–computed tomography images. From a linear elastic finite element model of a TPBC, the strain magnitudes at the sensor locations were recorded. An experimental ratio (i.e., FBG strain at the first displacement divided by the FBG strain at the second displacement) and a finite element ratio (i.e., finite element strain at the first displacement divided by the finite element strain at the second displacement) were calculated. A linear regression model indicated a statistically significant relationship between the experimental and finite element ratio (P = 0.017) with a correlation coefficient (R²) of 0.448. It was concluded that the FBG sensor could be used as a measure for a change in strain and thus could be implemented in applications where the mechanical properties of an intact PDL are monitored over time.

Quasi-linear viscoelastic behavior of fresh porcine ureter

PURPOSE

To evaluate the viscoelastic properties of the fresh porcine ureter. Prove the QLV theory can sufficiently model the stress relaxation function of porcine ureters, and determine the QLV model constants which may provide insight into the synthesis of ureteral scaffolds with biomimetic viscoelastic properties in tissue engineering.

METHODS

Hysteresis tests were applied to study the differences in dissipated energy ratio for each different strain group. In stress relaxation tests, samples were sub-grouped and quickly ramping up to 5%, 20%, and 30% strain in each group and gradually relaxed to a corresponding level. Bringing together the quasi-linear viscoelasticity (QLV) theory and stress relaxation function to determine the eight constants of the ureteral tissue, and fitting the raw data with the model via MATLAB.

RESULTS

The hysteresis response measurement results revealed that the porcine ureter was a highly dissipative material and there were differences between toe and linear region in stress-stain curve. The stress relaxation results revealed ureters responded with time-dependent decay of stress. The eight constants of the ureteral QLV model were determined for three different strain groups, and we proved that the QLV model can sufficiently adapt the experimental data of the ureter stress relaxation.

CONCLUSION

This study investigated the time-dependent properties of the porcine ureter, and demonstrated the QLV theory could be used to evaluate the viscoelastic properties of the porcine ureteral tissue.

A hyperelastic model to capture the mechanical behaviour and histological aspects of the soft tissues

It is well established that the soft connective tissues show a nonlinear elastic response that comes from their microstructural arrangement. Tissues' microstructure alters with various physiological conditions and may affect their mechanical responses. Therefore, the accurate prediction of tissue's mechanical response is crucial for clinical diagnosis and treatments. Thus, a physically motivated and mathematically simplified model is required for the accurate prediction of tissues' mechanical and structural responses. This study explored the 'Exp-Ln' hyperelastic model (Khajehsaeid et al., 2013) to capture soft tissues' mechanical and histological behaviour. In this work, uniaxial tensile test data for the belly and back pig skin were extracted from the experiments performed in our laboratory, whereas uniaxial test data for other soft tissues (human skin, tendon, ligament, and aorta) were extracted from the literature. The 'Exp-Ln; and other hyperelastic models (e.g. Money Rivlin, Ogden, Yeoh, and Gent models) were fitted with these experimental data, and obtained results were compared between the models. These results show that the 'Exp-Ln' model could capture the mechanical behaviour of soft tissues more accurately than other hyperelastic models. This model was also found numerically stable for all modes and ranges of deformation. This study also investigated the link between 'Exp-Ln' material parameters and tissue's histological parameters. The histological parameters such as collagen content, fibre free length, crosslink density, and collagen arrangement were measured using staining and ATR-FTIR techniques. The material parameters were found statistically correlated with the histological parameters. Further, 'Exp-Ln' model was implemented in ABAQUS through the VUMAT subroutine, where the mechanical behaviour of various soft tissues was simulated for different modes of deformation. The finite element analysis results obtained using the 'Exp-Ln' model agreed with the experiments and were more accurate than other hyperelastic models. Overall, these results demonstrate the capability of 'Exp-Ln' model to predict the mechanical and structural responses of the soft tissues.

Development and verification of a constitutive model for human periodontal ligament based on finite element analysis

This study aimed to develop a constitutive model for human periodontal ligament (PDL) by combining the hyperelastic and viscosity models. We performed the finite element analysis (FEA) to simulate the experimental processes of the PDL in vitro and in vivo tests to verify the developed model. The FEA results indicated that the simulative curves were consistent with the experimental curves in the PDL in vitro tests. Moreover, for the in vivo measurements, the simulative result of 0.6258 N was similar to the experimental value of 0.65 N. The study results can help orthodontists better understand the biomechanical characteristics of PDL.

In-vitro stress relaxation response of neonatal peripheral nerves

Characterizing the viscoelastic behavior of neonatal peripheral nerves is critical in understanding stretch-related peripheral nerve injuries (PNIs) in neonates. This study investigated the in-vitro viscoelastic stress relaxation response of neonatal piglet brachial plexus (BP) and tibial nerves at two different strain levels (10% and 20%) and stress relaxation testing durations (90- and 300-seconds). BP and tibial nerves from 20 neonatal piglets were harvested and pre-stretched to either 10% or 20% strain at a dynamic rate of 100 mm/min to simulate conditions, such as shoulder dystocia, that may lead to stretch-related PNIs in neonates. At constant strain, the reduction in stress was recorded for 90- or 300-seconds. The biomechanical data were then fit to a viscoelastic model to acquire the short- and long-term stress relaxation time-constants. Though no significant differences in the degree of stress relaxation were found between the two tested strain levels after 90 seconds in both nerve types, reduction in stress was moderately greater (p = 0.056) at 10% strain than at 20% for BP after 300 seconds. The reduction in stress was significantly higher in nerves subjected to a 300 second testing duration than 90 second for both strain levels and nerve types. When comparing BP and tibial nerve stress relaxation response, BP nerve relaxed significantly more than tibial at both strain levels after 90 seconds, but no significant differences were observed after 300 seconds. Our results confirm that neonatal peripheral nerve tissue is highly viscoelastic. These novel biomechanical data can be incorporated into finite element and computational models studying neonatal PNIs.

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.

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."

Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: a case study

OBJECTIVES

The objective of this study was to investigate the optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar to determine tooth movements during orthodontic treatment using hydrostatic stress and logarithmic strain on the periodontal ligament (PDL) as indicators by numerical simulations.

MATERIAL AND METHODS

Teeth, PDL and alveolar bone numerical models were constructed as analytical objects based on computed tomography (CT) images. Teeth were assumed to be rigid bodies, and rotational moments ranging from 1.0 to 4.0 Nmm were exerted on the crowns. PDL was defined as a hyperelastic-viscoelastic material with a uniform thickness of 0.25 mm. The alveolar bone model was constructed using a non-uniform material with varied mechanical properties determined based on Hounsfield unit (HU) values calculated using CT images, and its bottom was fixed completely. The optimal range values of PDL compressive and tensile stress were set as 0.47-12.8 and 18.8-51.2 kPa, respectively, whereas that of PDL logarithmic strain was set as 0.15-0.3%.

RESULTS

The rotational tendency of PDL was around the long axis of teeth when loaded. The optimal range values of rotational moment for the mandibular lateral incisor, canine and first premolar were 2.2-2.3, 3.0-3.1 and 2.8-2.9 Nmm, respectively, referring to the biomechanical responses of loaded PDL. Primarily, the optimal range of rotational moment was quadratically dependent on the area of PDL internal surface (i.e. area of PDL internal surface was used to indicate PDL size), as described by the fitting formula.

CONCLUSIONS

Biomechanical responses of PDL can be used to estimate the optimal range of rotational moment for teeth. These rotational moments were not consistent for all teeth, as demonstrated by numerical simulations.

CLINICAL RELEVANCE

The quantitative relationship between the area of PDL internal surface and the optimal orthodontic moment can help orthodontists to determine a more reasonable moment and further optimise clinical treatment.

A one-dimensional collagen-based biomechanical model of passive soft tissue with viscoelasticity and failure

INTRODUCTION

Strains and sprains of soft tissues, including tendons and ligaments, are frequently occurring injuries. Musculoskeletal models show great promise in prediction and prevention of these injuries. However, these models rarely account for the viscoelastic properties of ligaments and tendons, much less their failure properties. The purpose of this project was to develop, simplify, and analyze a collagen-distribution model to address these limitations.

MODEL DEVELOPMENT

A distribution-moment approximation was applied to an existing partial differential equation model to reduce its computational complexity. The resulting model was equipped with a Voigt model in series, which endowed it with viscoelastic properties in addition to failure properties.

RESULTS

The model was able to reproduce the characteristic toe, linear, and failure regions ubiquitous throughout in-vitro tests on tissue specimens. In addition, it was able to reproduce a tri-phasic creep test consisting of an initial deformation, a steady-state, and failure. Stress-relaxation and hysteresis were also reproducible by the model.

DISCUSSION AND CONCLUSION

The ability to reproduce so many characteristics of biological tissues suggests more bio-fidelity was achieved by the reduced model was other currently available models. Future work to further improve its bio-fidelity is proposed for specific tendons and ligaments.

The Effect of Strain Rate on the Stress Relaxation of the Pig Dermis: A Hyper-Viscoelastic Approach

The understanding of strain rate-dependent mechanical properties of the skin is important for accurate prediction of its biomechanics under different loading conditions. This study investigated the effect of strain rate, i.e., 0.025/s (low), 0.5/s (medium), and 1.25/s (high), ranging in the physiological loading rate of connective tissue, on the stress-relaxation response of the porcine dermis. Results show that in the initial phase of the relaxation, the value of stress relaxation (extent of relaxation) was found higher for high strain rate. However, the equilibrium stress was found strain rate independent. A Mooney-Rivlin-based five-term quasi-linear viscoelastic (QLV) model was proposed to determine the effect of strain rate on the stress-relaxation behavior of the porcine dermis. The value of relaxation modulus G1 and G2 were found higher for the high strain rate, whereas the reverse trend was observed for G3, G4, and G5. Moreover, the value of time constants τ1,τ2,τ3τ4, and τ5 were found higher for low strain rate. Statistical analysis shows no significant difference in the values of G5, τ4, and τ5 among the three strain rates. The proposed model was found capable to fit the stress-relaxation response of skin with great accuracy, e.g., root-mean-squared-error (RMSE) value equal to 0.015 ± 0.00012 MPa. Moreover, this hyper-viscoelastic model can be utilized: to quantify the effects of age and diseases on the skin; to simulate the stresses on sutures during large wound closure and impact loading.

In situ AFM-based nanoscale rheology reveals regional non-uniformity in viscoporoelastic mechanical behavior of the murine periodontal ligament

The periodontal ligament (PDL) is a critical player in the maintenance of tooth health, acting as the primary stabilizer of tooth position. Recent studies have identified two unique regions within the PDL, the 'dense collar' region and the 'furcation' region, which exhibit distinct structural and compositional differences. However, specific functional differences between these regions have yet to be investigated. We adapted an AFM-based nanoscale rheology method to regionally assess mechanical properties and poroelasticity in the mouse PDL while minimizing the disruption of the 3-dimensional native boundary conditions, and then explored tissue mechanical function in four different regions within the dense collar as well as in the furcation region. We found significant differences between the collar and furcation regions, with the collar acting as a stabilizing ligamentous structure and the furcation acting as both a compressive cushion for vertical forces and a conduit for nutrient transport. While this finding supports our hypothesis, based on previous studies investigating structural and compositional differences, we also found surprising inhomogeneity within the collar region itself. This inhomogeneity supports previous findings of a tilting movement in the buccal direction of mandibular molar teeth and the structural adaptation to prevent lingual movement. Future work will aim to understand how different regions of the PDL change functionally during biological or mechanical perturbations, such as orthodontic tooth movement, development, or aging, with the ultimate goal of better understanding the mechanobiology of the PDL function in health and disease.

Stress-Relaxation and Cyclic Behavior of Human Carotid Plaque Tissue

Atherosclerotic plaque rupture is a catastrophic event that contributes to mortality and long-term disability. A better understanding of the plaque mechanical behavior is essential for the identification of vulnerable plaques pre-rupture. Plaque is subjected to a natural dynamic mechanical environment under hemodynamic loading. Therefore, it is important to understand the mechanical response of plaque tissue under cyclic loading conditions. Moreover, experimental data of such mechanical properties are fundamental for more clinically relevant biomechanical modeling and numerical simulations for risk stratification. This study aims to experimentally and numerically characterize the stress-relaxation and cyclic mechanical behavior of carotid plaque tissue. Instron microtester equipped with a custom-developed setup was used for the experiments. Carotid plaque samples excised at endarterectomy were subjected to uniaxial tensile, stress-relaxation, and cyclic loading protocols. Thirty percent of the underlying load level obtained from the uniaxial tensile test results was used to determine the change in mechanical properties of the tissue over time under a controlled testing environment (Control tests). The stress-relaxation test data was used to calibrate the hyperelastic (neo-Hookean, Ogden, Yeoh) and linear viscoelastic (Prony series) material parameters. The normalized relaxation force increased initially and slowly stabilized toward the end of relaxation phase, highlighting the viscoelastic behavior. During the cyclic tests, there was a decrease in the peak force as a function of the cycle number indicating mechanical distension due to repeated loading that varied with different frequencies. The material also accumulated residual deformation, which increased with the cycle number. This trend showed softening behavior of the samples. The results of this preliminary study provide an enhanced understanding of in vivo stress-relaxation and cyclic behavior of the human atherosclerotic plaque tissue.

Influence of Different Implants on the Biomechanical Behavior of a Tooth-Implant Fixed Partial Dentures: A Three-Dimensional Finite Element Analysis

This study analyzed the biomechanical behavior of rigid and nonrigid tooth-implant supported fixed partial dentures. Different implants were used to observe the load distribution over teeth, implants, and adjacent bone using three-dimensional finite element analysis. A simulation of tooth loss of the first and second right molars was created with an implant placed in the second right molar and a prepared tooth with simulated periodontal ligament (PDL) in the second right premolar. Configurations of two types of implants and their respective abutments-external hexagon (EX) and Morse taper (MT)-were transformed into a 3D format. Metal-ceramic fixed partial dentures were constructed with rigid and nonrigid connections. Mesh generation and data processing were performed on the 3D finite element analysis (FEA) results. Static loading of 50 N (premolar) and 100 N (implant) were applied. When an EX implant was used, with a rigid or nonrigid connection, there was intrusion of the tooth in the distal direction with flexion of the periodontal ligament. Tooth intrusion did not occur when the MT implant was used independent of a rigid or nonrigid connection. The rigid or nonrigid connection resulted in a higher incidence of compressive forces at the cortical bone as well as stress in the abutment/pontic area, regardless of whether EX or MT implants were used. MT implants have a superior biomechanical performance in tooth-implant supported fixed partial dentures. This prevents intrusion of the tooth independent of the connection. Both types of implants studied caused a greater tendency of compressive forces at the crestal area.

Finite element modeling of the periodontal ligament under a realistic kinetic loading of the jaw system

Purpose

The stresses and deformations in the periodontal ligament (PDL) under the realistic kinetic loading of the jaw system, i.e., chewing, are difficult to be determined numerically as the mechanical properties of the PDL is variably present in different finite element (FE) models. This study was aimed to conduct a dynamic finite element (FE) simulation to investigate the role of the PDL (PDL) material models in the induced stresses and deformations using a simplified patient-specific FE model of a human jaw system.

Methods

To do that, a realistic kinetic loading of chewing was applied to the incisor point, contralateral, and ipsilateral condyles, through the experimentally proven trajectory approach. Three different material models, including the elasto-plastic, hyperelastic, and viscoelastic, were assigned to the PDL, and the resulted stresses of the tooth FE model were computed and compared.

Results

The results revealed the highest von Mises stress of 620.14 kPa and the lowest deformation of 0.16 mm in the PDL when using the hyperelastic model. The concentration of the stress in the elastoplastic and viscoelastic models was in the mid-root and apex of the PDL, while for the hyperelastic model, it was concentrated in the cervical margin. The highest deformation in the PDL regardless of the employed material model was located in the caudal direction of the tooth. The viscoelastic PDL absorbed the transmitted energy from the dentine and led to lower stress in the cancellous bone compared to the elastoplastic and hyperelastic material models.

Conclusion

These results have implications not only for understanding the stresses and deformations in the PDL under chewing but also for providing comprehensive information for the medical and biomechanical experts in regard of the role of the material models being used to address the mechanical behavior of the PDL in other components of the tooth.

A porous fibrous hyperelastic damage model for human periodontal ligament: Application of a microcomputerized tomography finite element model

The periodontal ligament (PDL) is a soft biological tissue that connects the tooth with the trabecular bone of the mandible. It plays a key role in load transmission and is primarily responsible for bone resorption and most common periodontal diseases. Although several numerical studies have analysed the biomechanical response of the PDL, most did not consider its porous fibrous structure, and only a few analysed damage to the PDL. This study presents an innovative numerical formulation of a porous fibrous hyperelastic damage material model for the PDL. The model considers two separate softening phenomena: fibre alignment during loading and fibre rupture. The parameters for the material model characterization were fitted using experimental data from the literature. Furthermore, the experimental tests used for characterization were computationally modelled to verify the material parameters. A finite element model of a portion of a human mandible, obtained by microcomputerized tomography, was developed, and the proposed constitutive model was implemented for the PDL. Our results confirm that damage to the PDL may occur mainly because of overpressure of the interstitial fluid, while large forces must be applied to damage the PDL fibrous network. Moreover, this study clarifies some aspects of the relationship between PDL damage and the bone remodelling process.

A numerical-experimental study on thermal evaluation of orthodontic tooth movement during initial phase of treatment

The most desired target of orthodontic treatment is tooth movement as a result of application of efficient force system. In this study, effect of tooth loading is studied on temperature profile around the tooth at early stages of treatment. The basis of temperature variation is increase of cell number and activities in periodontium as a result of compression and tension of this layer. Highest cellular activities occur in the beginning of loading procedure and aim to reduce mechanical stress in the periodontium which finally ends up with orthodontic tooth movement during couple of years. To find out the correlation between temperature variation and the applied force, in vivo experiments are conducted on ten rats and temperature is measured in specific time periods. It is observed that temperature is higher in direction of the net force about 0.3℃. Next, numerical finite element analysis is carried out on the rat tooth model. Mechanical stress results show that regions with compressive stress have rather high temperature in the experiments. Mechanical stress on periodontium-bone interface is multiplied by a coefficient to simulate cellular activities on this boundary as a heat source and thermal analysis is carried out to obtain temperature profile. The thermo-mechanical coefficient is identified for each rat by imposing the experimental temperatures on numerical outputs. For assessment of a treatment efficiency and deduction of the applied force, temperatures could be measured experimentally and compared with the corresponding numerical analysis temperature result obtained by employing the thermo-mechanical coefficient found earlier for each rat.

Extruded upper first molar intrusion: Comparison between unilateral and bilateral miniscrew anchorage

Objective:

The aim of his study was to evaluate the stress on tooth and alveolar bone caused by orthodontic intrusion forces in a supraerupted upper molar, by using a three-dimensional Finite Element Method (FEM).

Methods:

A superior maxillary segment was modeled in the software SolidWorks 2010 (SolidWorks Corporation, Waltham, MA, USA) containing: cortical and cancellous bone, supraerupted first molar, periodontal tissue and orthodontic components. A finite element model has simulated intrusion forces of 4N onto a tooth, directed to different mini-screw locations. Three different intrusion mechanics vectors were simulated: anchoring on a buccal mini-implant; anchoring on a palatal mini-implant and the association of both anchorage systems. All analyses were performed considering the minimum principal stress and total deformation. Qualitative analyses exhibited stress distribution by color maps. Quantitative analysis was performed with a specific software for reading and solving numerical equations (ANSYS Workbench 14, Ansys, Canonsburg, Pennsylvania, USA).

Results:

Intrusion forces applied from both sides (buccal and palatal) resulted in a more homogeneous stress distribution; no high peak of stress was detected and it has allowed a vertical resultant movement. Buccal or palatal single-sided forces resulted in concentrated stress zones with higher values and tooth tipping to respective force side.

Conclusion:

Unilateral forces promoted higher stress in root apex and higher dental tipping. The bilateral forces promoted better distribution without evidence of dental tipping. Bilateral intrusion technique suggested lower probability of root apex resorption.

Non-invasive evaluation of periodontal ligament stiffness during orthodontic tooth movement

OBJECTIVES

To evaluate the longitudinal changes in periodontal ligament (PDL) stiffness during orthodontic tooth movement using the Advanced System for Implant Stability Testing (ASIST).

MATERIALS AND METHODS

ASIST measurements of maxillary canines that were actively retracted into an extraction space were collected approximately once per month for 12 adolescent female patients. The ASIST Stability Coefficient (ASC) values, which are directly related to PDL stiffness, were determined for each visit to examine longitudinal changes for individual canines as they were exposed to different forces (approximately 80 and 150 g) during retraction.

RESULTS

The pattern of longitudinal changes in ASC was similar for both canines (regardless of the two force levels applied) in individual patients and across patients. All patients showed some decrease in ASC, with an average maximum reduction in stiffness of 73.4 ± 7.7%. Some recovery was observed for most patients; however, none of the patients had the PDL stiffness return to the pre-treatment value at the final measurement appointment which was some time close after space closure was completed. On average, the ASC value at the final measured visit was 48.1 ± 12.2% of the initial value. No measurements are available after removal of orthodontic appliances and during retention.

CONCLUSIONS

The ASIST was able to detect changes in PDL stiffness during orthodontic treatment, providing some insight into the mechanical changes that occur at the tooth root interface.

A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis

Excessive forces may cause root resorption and insufficient forces would introduce no effect in orthodontics. The objective of this study was to investigate the optimal orthodontic forces on a maxillary canine, using hydrostatic stress and logarithmic strain of the periodontal ligament (PDL) as indicators. Finite element models of a maxillary canine and surrounding tissues were developed. Distal translation/tipping forces, labial translation/tipping forces, and extrusion forces ranging from 0 to 300 g (100 g=0.98 N) were applied to the canine, as well as the force moment around the canine long axis ranging from 0 to 300 g·mm. The stress/strain of the PDL was quantified by nonlinear finite element analysis, and an absolute stress range between 0.47 kPa (capillary pressure) and 12.8 kPa (80% of human systolic blood pressure) was considered to be optimal, whereas an absolute strain exceeding 0.24% (80% of peak strain during canine maximal moving velocity) was considered optimal strain. The stress/strain distributions within the PDL were acquired for various canine movements, and the optimal orthodontic forces were calculated. As a result the optimal tipping forces (40-44 g for distal-direction and 28-32 g for labial-direction) were smaller than the translation forces (130-137 g for distal-direction and 110-124 g for labial-direction). In addition, the optimal forces for labial-direction motion (110-124 g for translation and 28-32 g for tipping) were smaller than those for distal-direction motion (130-137 g for translation and 40-44 g for tipping). Compared with previous results, the force interval was smaller than before and was therefore more conducive to the guidance of clinical treatment. The finite element analysis results provide new insights into orthodontic biomechanics and could help to optimize orthodontic treatment plans.

Inclusion of periodontal ligament fibres in mandibular finite element models leads to an increase in alveolar bone strains

Alveolar bone remodelling is vital for the success of dental implants and orthodontic treatments. However, the underlying biomechanical mechanisms, in particular the function of the periodontal ligament (PDL) in bone loading and remodelling, are not well understood. The PDL is a soft fibrous connective tissue that joins the tooth root to the alveolar bone and plays a critical role in the transmission of loads from the tooth to the surrounding bone. However, due to its complex structure, small size and location within the tooth socket it is difficult to study in vivo. Finite element analysis (FEA) is an ideal tool with which to investigate the role of the PDL, however inclusion of the PDL in FE models is complex and time consuming, therefore consideration must be given to how it is included. The aim of this study was to investigate the effects of including the PDL and its fibrous structure in mandibular finite element models. A high-resolution model of a human molar region was created from micro-computed tomography scans. This is the first time that the fibrous structure of the PDL has been included in a model with realistic tooth and bone geometry. The results show that omission of the PDL creates a more rigid model, reducing the strains observed in the mandibular corpus which are of interest when considering mandibular functional morphology. How the PDL is modelled also affects the strains. The inclusion of PDL fibres alters the strains in the mandibular bone, increasing the strains in the tooth socket compared to PDL modelled without fibres. As strains in the alveolar bone are thought to play a key role in bone remodelling during orthodontic tooth movement, future FE analyses aimed at improving our understanding and management of orthodontic treatment should include the fibrous structure of the PDL.

Biomechanical Effects of Various Bone-Implant Interfaces on the Stability of Orthodontic Miniscrews: A Finite Element Study

INTRODUCTION

Osseointegration is required for prosthetic implant, but the various bone-implant interfaces of orthodontic miniscrews would be a great interest for the orthodontist. There is no clear consensus regarding the minimum amount of bone-implant osseointegration required for a stable miniscrew. The objective of this study was to investigate the influence of different bone-implant interfaces on the miniscrew and its surrounding tissue.

METHODS

Using finite element analysis, an advanced approach representing the bone-implant interface is adopted herein, and different degrees of bone-implant osseointegration were implemented in the FE models. A total of 26 different FE analyses were performed. The stress/strain patterns were calculated and compared, and the displacement of miniscrews was also evaluated.

RESULTS

The stress/strain distributions are changing with the various bone-implant interfaces. In the scenario of 0% osseointegration, a rather homogeneous distribution was predicted. After 15% osseointegration, the stress/strains were gradually concentrated on the cortical bone region. The miniscrew experienced the largest displacement under the no osseointegra condition. The maximum displacement decreases sharply from 0% to 3% and tends to become stable.

CONCLUSION

From a biomechanical perspective, it can be suggested that orthodontic loading could be applied on miniscrews after about 15% osseointegration without any loss of stability.

Development of a fast curing tissue adhesive for meniscus tear repair

Isocyanate-terminated adhesive amphiphilic block copolymers are attractive materials to treat meniscus tears due to their tuneable mechanical properties and good adhesive characteristics. However, a drawback of this class of materials is their relatively long curing time. In this study, we evaluate the use of an amine cross-linker and addition of catalysts as two strategies to accelerate the curing rates of a recently developed biodegradable reactive isocyanate-terminated hyper-branched adhesive block copolymer prepared from polyethylene glycol (PEG), trimethylene carbonate, citric acid and hexamethylene diisocyanate. The curing kinetics of the hyper-branched adhesive alone and in combination with different concentrations of spermidine solutions, and after addition of 2,2-dimorpholinodiethylether (DMDEE) or 1,4-diazabicyclo [2.2.2] octane (DABCO) were determined using FTIR. Additionally, lap-shear adhesion tests using all compositions at various time points were performed. The two most promising compositions of the fast curing adhesives were evaluated in a meniscus bucket handle lesion model and their performance was compared with that of fibrin glue. The results showed that addition of both spermidine and catalysts to the adhesive copolymer can accelerate the curing rate and that firm adhesion can already be achieved after 2 h. The adhesive strength to meniscus tissue of 3.2-3.7 N was considerably higher for the newly developed compositions than for fibrin glue (0.3 N). The proposed combination of an adhesive component and a cross-linking component or catalyst is a promising way to accelerate curing rates of isocyanate-terminated tissue adhesives.

Fatigue responses of the human cervical spine intervertebral discs

Numerous studies have been conducted since more than fifty years to understand the behavior of the human lumbar spine under fatigue loading. Applications have been largely driven by low back pain and human body vibration problems. The human neck also sustains fatigue loading in certain type of civilian occupational and military operational activities, and research is very limited in this area. Being a visco-elastic structure, it is important to determine the stress-relaxation properties of the human cervical spine intervertebral discs to enable accurate simulations of these structures in stress-analysis models. While finite element models have the ability to incorporate viscoelastic material definitions, data specific to the cervical spine are limited. The present study was conducted to determine these properties and understand the responses of the human lower cervical spine discs under large number of cyclic loads in the axial compression mode. Eight disc segments consisting of the adjacent vertebral bodies along with the longitudinal ligaments were subjected to compression, followed by 10,000 cycles of loading at 2 or 4Hz frequency by limiting the axial load to approximately 150 N, and subsequent to resting period, subjected to compression to extract the stress-relaxation properties using the quasi-linear viscoelastic (QLV) material model. The coefficients of the model and disc displacements as a function of cycles and loading frequency are presented. The disc responses demonstrated a plateauing effect after the first 2000 to 4000 cycles, which were highly nonlinear. The paper compares these responses with the "work hardening" phenomenon proposed in clinical literature for the lumbar spine to explain the fatigue behavior of the discs. The quantitative results in terms of QLV coefficients can serve as inputs to complex finite element models of the cervical spine to delineate the local and internal load-sharing responses of the disc segment.

Mechanical Integrity of a Decellularized and Laser Drilled Medial Meniscus

Since the meniscus has limited capacity to self-repair, creating a long-lasting meniscus replacement may help reduce the incidence of osteoarthritis (OA) after meniscus damage. As a first step toward this goal, this study evaluated the mechanical integrity of a decellularized, laser drilled (LD) meniscus as a potential scaffold for meniscal engineering. To evaluate the decellularization process, 24 porcine menisci were processed such that one half remained native tissue, while the other half was decellularized in sodium dodecyl sulphate (SDS). To evaluate the laser drilling process, 24 additional menisci were decellularized, with one half remaining intact while the other half was LD. Decellularization did not affect the tensile properties, but had significant effects on the cyclic compressive hysteresis and unconfined compressive stress relaxation. Laser drilling decreased the Young's modulus and instantaneous stress during unconfined stress relaxation and the circumferential ultimate strength during tensile testing. However, the losses in mechanical integrity in the LD menisci were generally smaller than the variance observed between samples, and thus, the material properties for the LD tissue remained within a physiological range. In the future, optimization of laser drilling patterns may improve these material properties. Moreover, reseeding the construct with cells may further improve the mechanical properties prior to implantation. As such, this work serves as a proof of concept for generating decellularized, LD menisci scaffolds for the purposes of meniscal engineering.

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.

Viscoelasticity of periodontal ligament: an analytical model

BACKGROUND

Understanding of viscoelastic behaviour of a periodontal membrane under physiological conditions is important for many orthodontic problems. A new analytic model of a nearly incompressible viscoelastic periodontal ligament is suggested, employing symmetrical paraboloids to describe its internal and external surfaces.

METHODS

In the model, a tooth root is assumed to be a rigid body, with perfect bonding between its external surface and an internal surface of the ligament. An assumption of almost incompressible material is used to formulate kinematic relationships for a periodontal ligament; a viscoelastic constitutive equation with a fractional exponential kernel is suggested for its description.

RESULTS

Translational and rotational equations of motion are derived for ligament's points and special cases of translational displacements of the tooth root are analysed. Material parameters of the fractional viscoelastic function are assessed on the basis of experimental data for response of the periodontal ligament to tooth translation. A character of distribution of hydrostatic stresses in the ligament caused by vertical and horizontal translations of the tooth root is defined.

CONCLUSIONS

The proposed model allows generalization of the known analytical models of the viscoelastic periodontal ligament by introduction of instantaneous and relaxed elastic moduli, as well as the fractional parameter. The latter makes it possible to take into account different behaviours of the periodontal tissue under short- and long-term loads. The obtained results can be used to determine loads required for orthodontic tooth movements corresponding to optimal stresses, as well as to simulate bone remodelling on the basis of changes in stresses and strains in the periodontal ligament caused by such movements.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures.

Predicting the holistic force-displacement relation of the periodontal ligament: in-vitro experiments and finite element analysis

BACKGROUND

The biomechanical property of the periodontal ligament (PDL) is important in orthodontics and prosthodontics. The objective of this study was to evaluate the feasibility of measuring the biomechanical behavior of the periodontal ligament using micro-computed tomography (micro-CT).

METHODS

A custom-made apparatus measured the force and displacement of a porcine PDL specimen within the micro-CT environment. Synchronized computed tomography (CT) images were used to obtain the deformation and displacement of the entire specimen and to reconstruct the three-dimensional mesh model. To match the experimental results, finite element analysis was then applied to simulate the biomechanical response of the PDL. The mechanical model of the PDL was assumed as the hyperelastic material in this study.

RESULTS

The volume variations of the tooth and the alveolar bone were less than 1%, which implies that tooth displacement was caused mostly by displacement of the PDL. Only translational displacement was observed with each load step because the transformation matrix acquired from the CT image registration was identical. The force-displacement curve revealed the nonlinear behavior of the PDL. There was a high correlation between the experimental displacement results and the simulation displacement results. The numerical results (based on the assumption that the PDL is the hyperelastic material) showed good agreement with the experimental results.

CONCLUSIONS

Nondestructive measurements by micro-CT obtained the biomechanical behavior of the PDL. Using the hyperelastic characteristic as the constitutive model can properly predict the force-displacement relation of the PDL after loading. This study provided a feasible approach for measuring the biomechanical behavior of the PDL for further dental application.

Adaptive properties of human cementum and cementum dentin junction with age

OBJECTIVES

The objective of this study was to evaluate age related changes in physical (structure/mechanical properties) and chemical (elemental/inorganic mineral content) properties of cementum layers interfacing dentin.

METHODS

Human mandibular molars (N=43) were collected and sorted by age (younger=19-39, middle=40-60, older=61-81 years). The structures of primary and secondary cementum (PC, SC) types were evaluated using light and atomic force microscopy (AFM) techniques. Chemical composition of cementum layers were characterized through gravimetric analysis by estimating ash weight and concentrations of Ca, Mn, and Zn trace elements in the analytes through inductively coupled plasma mass spectroscopy. The hardness of PC and SC was determined using microindentation and site-specific reduced elastic modulus properties were determined using nanoindentation techniques.

RESULTS

PC contained fibrous 1-3 µm wide hygroscopic radial PDL-inserts. SC illustrated PC-like structure adjacent to a multilayered architecture composing of regions that contained mineral dominant lamellae. The width of the cementum dentin junction (CDJ) decreased as measured from the cementum enamel junction (CEJ) to the tooth apex (49-21 µm), and significantly decreased with age (44-23 µm; p<0.05). The inorganic ratio defined as the ratio of post-burn to pre-burn weight increased with age within primary cementum (PC) and secondary cementum (SC). Cementum showed an increase in hardness with age (PC (0.40-0.46 GPa), SC (0.37-0.43 GPa)), while dentin showed a decreasing trend (coronal dentin (0.70-0.72 GPa); apical dentin (0.63-0.73 GPa)).

SIGNIFICANCE

The observed physicochemical changes are indicative of increased mineralization of cementum and CDJ over time. Changes in tissue properties of teeth can alter overall tooth biomechanics and in turn the entire bone-tooth complex including the periodontal ligament. This study provides baseline information about the changes in physicochemical properties of cementum with age, which can be identified as adaptive in nature.