

ORIGINAL ARTICLE 



Year : 2015  Volume
: 33
 Issue : 4  Page : 302306 

Traumatic impact loading on human maxillary incisor: A Dynamic finite element analysis
K Jayasudha^{1}, M Hemanth^{2}, Raj Baswa^{3}, HP Raghuveer^{4}, B Vedavathi^{5}, Chatura Hegde^{2}
^{1} Department of Pedodontics and Preventive dentistry, Rajarajeswari Dental College and Hospital, Bengaluru, Karnataka, India ^{2} Department of Orthodontics and Dentofacial Orthopedics, Dayanand Sagar Dental College and Hospital, Bengaluru, Karnataka, India ^{3} Department of Orthodontics and Dentofacial Orthopedics, Narsinhbhai Patel Dental College, Visnagar, Gujarat, India ^{4} Department of Oral and Maxillofacial Surgery, Dayanand Sagar Dental College and Hospital, Bengaluru, Karnataka, India ^{5} Department of Conservative Dentistry, Dayanand Sagar Dental College and Hospital, Bengaluru, Karnataka, India
Date of Web Publication  18Sep2015 
Correspondence Address: Dr. K Jayasudha Manish Homes, 9th Cross, 3D Main, JP Nagar First Phase, Bengaluru  560 078, Karnataka India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09704388.165680
Abstract   
Background: The most vulnerable tooth is the maxillary incisor, which sustains 80% of dental injuries. Dynamic Finite element analysis is used to understand the biomechanics of fracture of maxillary incisor under traumatic impact loading. Aim: The aim was to investigate the stress patterns of an upper incisor in a threedimensional (3D) model under traumatic impact loading in various directions. Materials and Methods: A 3D finite element model of the upper incisor and surrounding tissues was established. A sinusoidal force of 800N was applied over a period of 4 ms. Results: Software performs a series of calculations and mathematical equations and yields the simulation results. During the horizontal impact (F1), stresses were concentrated in the cervical area of the crown, reaching peak stress of 125 MPa at 2 ms. Conclusion: A horizontal force exerted on the labial surface of the tooth tends to cause cervical crown fractures, oblique crown root fractures, and oblique root fractures.
Keywords: Dynamic force, finite element, stress distribution, traumatic impact
How to cite this article: Jayasudha K, Hemanth M, Baswa R, Raghuveer H P, Vedavathi B, Hegde C. Traumatic impact loading on human maxillary incisor: A Dynamic finite element analysis. J Indian Soc Pedod Prev Dent 2015;33:3026 
How to cite this URL: Jayasudha K, Hemanth M, Baswa R, Raghuveer H P, Vedavathi B, Hegde C. Traumatic impact loading on human maxillary incisor: A Dynamic finite element analysis. J Indian Soc Pedod Prev Dent [serial online] 2015 [cited 2019 Dec 5];33:3026. Available from: http://www.jisppd.com/text.asp?2015/33/4/302/165680 
Introduction   
Although the oral region comprises as small an area as 1% of the total body area, there is a high prevalence of maxillofacial trauma in worldwide population, that is, 933%. ^{[1]} In that, there is a high prevalence of dental injuries involving the anterior teeth, especially maxillary central incisor among children and adolescents. ^{[2]} The direction and position of fracture lines caused by frontal impacts are a horizontal crown fracture, horizontal fracture at the neck of the tooth, oblique crown fracture, and oblique crown root fracture. ^{[1]}
The theoretical studies indicate that force direction plays an important role in the propagation of fracture lines on the impacted tooth. In spite of the epidemiological importance of dentoalveolar traumatic events, little is still known about their biomechanical characteristics and their impact on adjacent tissues. ^{[3]} The intraoral environment is a complex biomechanical system. When dealing with physically and geometrically complex systems, an engineering concept that uses a numerical analysis to solve such equations becomes inevitable. ^{[4]} Finite element analysis (FEA) is a widely used numerical analysis that can be considered the most comprehensive method currently available to calculate the complex conditions of stress distributions as are encountered in dentoalveolar trauma.
Many FEA studies were done with static load applied to the tooth, assuming the applied force was constant during the impact. However, in real situations, traumatic injuries to teeth typically result from dynamic forces. The magnitude of such dynamic forces alters with time. Therefore, for traumatic analysis of the tooth, timedependent behavior should be considered for different rates of loading. ^{[5]}
A periodontal ligament (PDL), which connects the tooth root and the underlying bone, plays an important role in the mechanisms of tooth trauma. When time is taken into consideration, the effects of damping properties of PDL, the cushioning effect of pulp, affect the stress distribution in an impacted tooth. ^{[6]} The dentoalveolar articulation presents a viscoplastic behavior. ^{[3]} Therefore, any simulation that ignores the damping effect of a tooth will cause an unexpected error. In this finite element model, (FEM) studydamping ratio is incorporated from the study.
Research is limited in the area of threedimensional (3D) FEA of stress distribution in impacted teeth by various directions. A twodimensional (2D) model cannot accurately represent the clinical reality because of its simplifications that do not take into consideration some important geometric complexity of the biological structures. ^{[7],[8]} In contrast, 3D models present advantages such as images of greater and richer detail, more realistic 3D stress distributions in complex 3D geometries, the possibility of rotating in space and visualizing internal areas of the models. ^{[9]} 3D dynamic FEA was used to investigate stress concentrations and fracture line propagation in various directions.
Materials and Methods   
In this study, a 3D FEM of maxillary central incisor was created and used to calculate the fracture propagation by timedependent stress propagation using Software Design Program of SolidWorks release 2012; 3D modeling software and FEA package of ANSYS Workbench.
Steps involved in the generation of FEM:
 Construction of a geometric model.
 Conversion of the geometric model to a FEM.
 Defining the boundary condition.
 Material property data representation.
 Loading configuration.
 Analysis and Evaluation of Results.
Construction of a geometric model
The purpose of the geometric modeling phase was to represent geometry in terms of points (grids), line surfaces (patches), and volume (hyper patches). In this study, the analytical model including the length (23.5 mm) and thickness of the periodontal membrane (0.25 mm) were obtained from the textbook of dental anatomy by wheeler. The alveolar process was located 2 mm apically from the cementenamel junction. PDL was simulated as a 0.2 mm thick ring around the model of the tooth and cortical bone at 0.5 mm thick. ^{[10]} Using software SolidWorks surfaces were generated, and this data were exported in Initial Graphics Exchange Specification (IGES ) format to ANSYS Workbench [Figure 1].  Figure 1: Geometric model of maxillary central incisor and supporting structures in SolidWorks software
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Conversion of geometric model to finite element model
This geometric model in IGES format was imported into hypermesh. A FEM is created using discretization technique. The FEM approximately consisted of 35,175 tetrahedral elements 65,164 nodes and 3° of freedom [Figure 2].  Figure 2: (a and b) Finite element mesh generation nodes: 65,164 elements: 35,175
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Defining the boundary condition
The boundary condition, in the FEM, was defined at all the peripheral nodes of the bone with 3° of movement in all directions [Figure 3]. Boundary conditions were assigned to the nodes surrounding the outermost layers of the tooth, roots, and alveolar bone. The geometry of the tooth root and of the alveolus has to be kept constant during the movement.  Figure 3: (a) Boundary conditions and horizontal direction of force (F1). (b) Oblique direction (F2). (c) Vertical direction of force (F3)
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Material property data representation
The factors to be considered and included in the generated mesh are Poisson's ratio, Young's modulus and information on the density of each material [Table 1]. The structural damping factor for the model is taken from the study, which is 14.6 ± 3.7%. ^{[11]}  Table 1: Physical — Mechanical properties of the elements compromising the dentoalveolar articulation
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Loading configuration
Once the FEM model has been created and all its properties defined, it becomes possible to simulate the application of a given force, in Newtons (N), for a given time, in milliseconds (ms), to the structure. A force of 800N, equally distributed over a period of 4 ms, [Figure 4] to stimulate mild to moderate dentoalveolar traumatic events. ^{[3],[5]} Falls, collisions, frontal impacts, and being struck by an object are the most common causes for traumatic injuries to incisors, ^{[12]} hence the direction of impact is considered in three directions that is, horizontal (F1), oblique (F2), vertical (F3) [Figure 5], [Figure 6], [Figure 7].
Analysis and evaluation of results
Software performs a series of calculations and mathematical equations and yields the simulation results. These are presented according to a color scale where each shade represents a different degree of movement, tension or compression.
Results   
The Von Mise stress developed at various impact angles at various positions is depicted in the Graph 1. In each position, a horizontal impact caused the highest stresses in the incisor. With the exception of the lingual crown surface, however, the stresses caused by horizontal impact are remained below 100 MPa.
During the horizontal impact (F1), stresses were concentrated in the cervical area of the crown, reaching peak stress of 125 MPa at 2 ms. immediately after impact, stress >10 MPa was demonstrated around the lingual crown surface, with a tendency to propagate toward labial cervical. The highest stresses were demonstrated in the root apex and in the alveolar bone compared to other impact load.
When the upper incisor was subjected to an oblique impact (F2), high stresses first developed at the impact site and then progressed to root apex. At 0.5 ms with 4 MPa at the impact site, thereafter with decreasing magnitude progresses to the cervical dentin and then reaching to root apex with the same magnitude of 4 MPa. At 2 ms peak, stress of 27 MPa was demonstrated at labial cervical crown surface.
When a vertical load (F3) was applied to the model, the magnitude of concentrated stresses was higher than oblique load but lesser than horizontal load. Starting with a low stress of 3 MPa at the impact site and progresses toward the labial cervical crown area reaching a peak stress of 80 MPa at 2 ms. Continuously tracing the time profiles of the stress contours revealed that the stresses in each area were developed independently and were propagated simultaneously.
Discussion   
The FEM has been used extensively in dental biomechanics research. The method is powerful and versatile in that it can provide detailed information on stresses, strains, and displacements within complex structures such as teeth. ^{[13]}
The human tooth is neither planner nor symmetrical hence, the loading on the tooth is neither in a state of plane stress nor is symmetrical. ^{[14]} 3D models, in turn, are more complex but allow a more complete assessment of structures and loads, in any direction. The cushioning effects on strain energy dispersion by PDL and the pulp cannot be ignored for toothtrauma analysis. Therefore, the damping properties of the tooth should be considered which is taken from the previous studies. ^{[6]}
The etiology of traumatic dental injuries, today includes oral factors (e.g., over jet) environmental factors and human behavior, which can be considered along with more than 50% of injuries involving sports. ^{[12]} The most affected teeth in dental trauma are the maxillary centrals in general. It was observed that the falls or collisions were the main causes. Clinically, fractures caused by frontal impacts fall into four categories according to the direction and position of fracture lines:
 Horizontal crown fracture;
 Horizontal fractures at the neck of the teeth;
 Oblique crownroot fractures; and
 Oblique root fractures. ^{[1]}
In this study, the forces exerted horizontally to the labial side of the tooth demonstrated the highest stress on the tooth and alveolar bone than vertical and oblique forces that is in accordance with Topbasi et al. ^{[15]} was studied with the 2D photoelastic stress analysis in traumatic incisor. Various researchers compared the photoelastic study with FEA show that the numerical results of the FEM stress research tally with those of the photoelastic study. ^{[14]}
Principal stresses [Figure 6]a and b in F1 loading demonstrate a tendency to propagate toward the lingual side and reaching a peak stress at the cervical area. This phenomenon, undoubtedly result in horizontal fracture of the crown. When a crown fracture occurs, the force affecting the tooth divides into its components and causes less damage to the pulp. A fracture occurs if the effecting force exceeds the resistance against the sliding force of hard tissue. Otherwise, the resistance depending on the strength and direction of the force may cause pathological damages. ^{[15]}
It is observed that the highest stress value is obtained under F1 loading even at the root apex compared to vertical and oblique forces. This fact clearly shows that pulp dies when the effected force is transferred to the apical third of the tooth that has not been fractured after trauma. ^{[15]} When a maxillary incisor is subjected to frontal impact, if the tooth is locked into socket then the stresses will transfer to root portion of tooth, ^{[1]} that is, lingually at the cervical margin and labially at the apical portion of root. Hence, the imaginary lines joining these highstress areas will result in oblique root fracture, crown root fracture of the tooth.
When an upper incisor was subjected to a vertical force, significant stress values were obtained at the area of impact, which is propagating to the cervical part of the root on the labial side only [Figure 8]ad. Enamel fracture is a frequent injury appearing as crazing within the enamel substance that does not cross the dentinenamel junction. ^{[5]} Clinical findings show that enamel fractures are caused by direct impact, frequently occurring on the labial surface of the upper incisor. Our study shows that the occurrence of such injury is caused by vertical impact force.
Conclusion   
 A 3D dynamic FEA provides a biological simulation of mechanics of traumatic injury to teeth
 A horizontal force exerted on the labial surface of the tooth tends to cause cervical crown fractures, oblique crown root fractures, and oblique root fractures
 Vertical impact force tends to cause crazing lines limited to the cervical portion of enamel and cementum.
References   
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
[Table 1]
