Experiment and hydro-mechanical coupling simulation study on the human periodontal ligament

A finite element analysis of periodontal ligament fluid mechanics response to occlusal loading based on hydro-mechanical coupling model

OBJECTIVE

Considering fluid stimulation is one of the essential biomechanical signals for periodontal tissues, this study aims to characterizing fluid mechanics response during occlusal loading by a hydro-mechanical coupling model for periodontal ligament.

DESIGN

Models simulating periodontium with normal bone height and with intraosseous defects were built with three mechanical modules: tooth, periodontal ligament and alveolar bone. Tooth was modeled as linear elastic, and periodontal ligament and alveolar bone as a hydro-mechanical coupling model. Transient analyses under dynamic occlusal loading were performed. Fluid dynamics within periodontal ligament space was simulated and visualized by post-processing module.

RESULTS

Reciprocating oscillatory flow occurred within the periodontal ligament under occlusal loading. Higher pore pressure and fluid velocity were observed in furcation and apical regions compared to mid-root and cervical regions. Intraosseous defects increased pore pressure and fluid velocity within the periodontal ligament, most significantly near the defect.

CONCLUSION

Based on the results of the hydro-mechanical coupling model, significant oscillatory fluid motion is observed within the periodontal ligament under occlusal loading. Particularly, higher fluid velocity is evident in the furcation and apical areas. Additionally, Intraosseous defects significantly enhance fluid motion within the periodontal ligament.

Evaluation of stress and displacement of maxillary canine during the single canine retraction in the maxillary first premolar extraction cases- A finite element study

OBJECTIVES

This finite element study aimed to simulate maxillary canine movement during anterior teeth retraction.

MATERIALS AND METHODS

Three methods of maxillary canine movement including miniscrew sliding with high hooks (MSH), miniscrew sliding with low hooks (MSL), and the traditional sliding method (TS) without using miniscrews were simulated using three-dimensional finite element analysis. The initial displacement of the maxillary canine, the maximum principal stress of the periodontal ligament and the Von Mises stress were calculated.

RESULTS

The distolingual tipping movements of the canine were shown in three movement modes. MSH showed a small tendency to lingual tipping movement and a extrusion movement while MSL had the largest lingual inclination. TS demonstrated a tendency toward distolingual torsion displacement. Compressive stress values were mainly concentrated in the range - 0.003 to -0.006 MPa. For tensile stress, the distribution of MSH and MSL was concentrated in the range 0.005 to 0.009 MPa, TS was mainly distributed about 0.003 MPa. Von Mises equivalent stress distribution showed no significant difference.

CONCLUSIONS

The loss of tooth torque was inevitable, irrespective of which method was used to close the extraction space. However, miniscrew application and higher hooks reduced the loss of torque and avoided lingual rotation.

CLINICAL RELEVANCE

This study shows that miniscrew implants with different hooks can better control the movement of the maxillary canines. The non-invasive nature of the finite element analysis and its good simulation of dental stress and instantaneous motion trend have a clinical advantage in the analysis of tooth movement.

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.

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.

Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations

This scoping review is intended to synthesize the techniques proposed to model the tooth-periodontal ligament-bone complex (TPBC), while also evaluating the suggested periodontal ligament (PDL) material properties. It is concentrated on the recent advancements on the PDL and TPBC models, while identifying the advantages and limitations of the proposed approaches. Systematic searches were conducted up to December 2020 for articles that proposed PDL models to assess orthodontic tooth movement in Compendex, Web of Science, EMBASE, MEDLINE, PubMed, ScienceDirect, Google Scholar and Scopus databases. Although there have been many studies focused on the evaluation of PDL material properties through numerous modelling approaches, only a handful of approaches have been identified to investigate the interface properties of the PDL as a complete dynamical system (TPBC models). Past reviews on the analytical and experimental determination of the PDL properties already show a concerning range in reported output values-some nearly six orders of magnitude in difference-that strongly suggested the need for further investigation. Surprisingly, it has not yet been possible to determine a narrower range of values for the PDL material properties. Moreover, very few scientific approaches address the TPBC as an integrated complex system model. In consequence, current methods for capturing the PDL material behaviour in a clinical setting are limited and inconclusive. This synthesis encourages more systematic, pragmatic and phenomenological research in this area.

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.

Optimal Position of Attachment for Removable Thermoplastic Aligner on the Lower Canine Using Finite Element Analysis

Malocclusion is considered as a developmental disorder rather than a disease, and it may be affected by the composition and proportions of masseter muscle fibers. Orthodontics is a specialty of dentistry that deals with diagnosis and care of various irregular bite and/or malocclusion. Recent developments of 3D scanner and 3D printing technology has led to the use of a removable thermoplastic aligner (RTA), which is widely used due to its aesthetic excellence, comfortableness, and time efficiency. However, orthodontics using only an RTA has lower treatment efficacy and accuracy due to the differing movement of teeth from the plan. In order to improve these disadvantages, attachments were used, and biomechanical analyses were performed with and without them. However, there is insufficient research on the movement of teeth and the transfer of load according to the attachment position and shape. Therefore, in our study, we aimed to identify the optimal shape and position of attachments by analyzing various shapes and positions of attachments. Through 3D finite element analysis (FEA), simple tooth shape and mandibular canine shape were extracted in order to construct the orthodontics model which took into account the various shapes and positions of attachments. The optimal shape of a cylinder was derived through the FEA of simple tooth shape and analyzing various positions of attachments on teeth revealed that fixing the attachments at the lingual side of the tooth rather than the buccal side allowed for torque control and an effective movement of the teeth. Therefore, we suggest fixing the attachments at the lingual side rather than the buccal side of the tooth to induce effective movement of teeth in orthodontic treatment with the RTA in case of canine teeth.

Increased tooth mobility after fixed orthodontic appliance treatment can be selectively utilized for case refinement via positioner therapy - a pilot study

Background

Increased tooth mobility persists after fixed orthodontic appliance removal, which is therapeutically utilized for post-treatment finishing with positioners. As such a fine adjustment is only required for selected teeth, the aim of this pilot study was to investigate tooth mobility in vivo on corrected and uncorrected subgroups under positioner therapy.

Methods

Mobility was measured on upper teeth of 10 patients (mean age 16.8) by applying loadings for 0.1, 1.0 and 10.0 s with a novel device directly after multibracket appliance debonding as much as 2d, 1, 2 and 6 weeks later. Positioners were inserted at day 2. Specimens were divided into Group C (teeth corrected via positioner), Group N (uncorrected teeth adjacent to teeth from group C), and Group U (uncorrected teeth in an anchorage block). Untreated individuals served as controls (n = 10, mean age 22.4). Statistics were performed via Kolmogorov-Smirnov test and Welch’s unequal variances t-test for comparisons between groups. P < 0.05 was considered statistically significant.

Results

After 1 week, tooth mobility in Group U almost resembled controls (13.0–15.7 N), and reached physiological values after 6 weeks (17.4 N vs. 17.3 N in controls). Group C (9.0–13.4 N) and Group N (9.2–14.7 N) maintained increased mobility after 6 weeks. Tooth mobility was generally higher by reason of long loading durations (10.0 s).

Conclusions

Positioner therapy can selectively utilized increased tooth mobility upon orthodontic fixed appliance treatment for case refinements. Here, uncorrected teeth in anchorage blocks are not entailed by unwanted side effects and recover after 6 weeks post treatment. Corrected teeth and their neighbors exhibit enhanced mobility even after 6 weeks, which represents a necessity for the proper correction of tooth position, and concurrently arouses the requirement for an adequate retention protocol.

In silico study of cuspid' periodontal ligament damage under parafunctional and traumatic conditions of whole-mouth occlusions. A patient-specific evaluation

BACKGROUND AND OBJECTIVE

Although traumatic loading has been associated with periodontal ligament (PDL) damage and therefore with several oral disorders, the damage phenomena and the traumatic loads involved are still unclear. The complex composition and extremely thin size of the PDL make experimentation difficult, requiring computational studies that consider the macroscopic loading conditions, the microscopic composition and fine detailed geometry of the tissue. In this study, a new methodology to analyse the damage phenomena in the collagen network and the extracellular matrix of the PDL caused by parafunctional and traumatic occlusal forces was proposed.

METHODS

The entire human mandible and a portion thereof containing a full cuspid tooth were separately modelled using finite element analysis based on computed tomography and micro-computed tomography images, respectively. The first model was experimentally validated by occlusion analysis and subjected to the muscle loads produced during hard and soft chewing, traumatic cuspid occlusion, grinding, clenching, and simultaneous grinding and clenching. The occlusal forces computed by the first model were subsequently applied to the single tooth model to evaluate damage to the collagen network and the extracellular matrix of the PDL.

RESULTS

Early occlusal contact on the left cuspid tooth guided the mandible to the more occluded side (16.5% greater in the right side) and absorbed most of the lateral load. The intrusive occlusal loads on the posterior teeth were 0.77-13.3% greater than those on the cuspid. According to our findings, damage to the collagen network and the extracellular matrix of the PDL could occur in traumatic and grinding conditions, mainly due to fibre overstretching (>60%) and interstitial fluid overpressure (>4.7 kPa), respectively.

CONCLUSIONS

Our findings provide important biomechanical insights into the determination of damage mechanisms which are caused by mechanical loading and the key role of the porous-fibrous behaviour of the PDL in parafunctional and traumatic loading scenarios. Besides, the 3D loading conditions computed from occlusal contacts will help future studies in the design of new orthodontics appliances and encourage the application of computing methods in medical practice.

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.

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.

Approach towards the porous fibrous structure of the periodontal ligament using micro-computerized tomography and finite element analysis

The periodontal ligament (PDL) is a porous and fibrous soft tissue situated around the tooth, which plays a key role in the transmission of loads from the tooth to the alveolar bone of the mandible. Although several studies have tried to characterize its mechanical properties, the behaviour of this tissue is not clear yet. In this study, a new simulation methodology based on a material model which considers the contribution of porous and fibrous structure with different material model formulations depending on the effort direction is proposed. The defined material model was characterized by a non-linear approximation of the porous fibrous matrix to experimental results obtained from samples of similar species and was validated by rigorous test simulations under tensile and compressive loads. The global PDL response was also validated using the parameters of the characterization in a finite element model of full human canine tooth obtained by micro-tomography. The results suggest that the porous contribution has high influence during compression because the bulk modulus of the material depends on the ability of interstitial fluid to drain. On the other hand, the collagen fibres running along the load direction are the main responsible of the ligament stiffness during tensile efforts. Thus, a material model with distinct responses depending of the load direction is proposed. Furthermore, the results suggest the importance of considering 3D finite element models based of the real morphology of human PDL for representing the irregular stress distribution caused by the coupling of complex material models and irregular morphologies.

Individual tooth segmentation from CT images scanned with contacts of maxillary and mandible teeth

BACKGROUND AND OBJECTIVE

Tooth segmentation from computed tomography (CT) images is a fundamental step in generating the three-dimensional models of tooth for computer-aided orthodontic treatment. Individual tooth segmentation from CT images scanned with contacts of maxillary and mandible teeth is especially challenging, and no method has been reported previously. This study aimed to develop a method for individual tooth segmentation from these images.

METHODS

Tooth contours of maxilla and mandible are first segmented from the volumetric CT images slice-by-slice. For each slice, a line is extracted using the Radon transform to separate neighboring teeth, and each tooth contour is then segmented by a level set model from the corresponding side of the line. Then, each maxillary tooth whose contours overlap with that of mandible ones is detected, and a mesh model is reconstructed from all the contours of these maxillary and mandible teeth with contour overlap. The reconstructed mesh model is segmented using threshold and fast marching watershed method to separate the touched maxillary and mandible teeth. Finally, the separated tooth models are restored to fill the holes to obtain complete tooth models. The proposed method was tested on CT images of ten subjects scanned with natural contacts of maxillary and mandible teeth.

RESULTS

For all the tested images, individual tooth regions are extracted successfully, and the segmentation accuracy and efficiency of the proposed method is promising.

CONCLUSIONS

The proposed method is effective to segment individual tooth from CT images scanned with contacts of maxillary and mandible teeth.