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ORIGINAL ARTICLE
Year : 2011  |  Volume : 1  |  Issue : 1  |  Page : 19-25

Stress distribution analysis during an intermaxillary dysjunction: A 3-D FEM study of an adult human skull


1 Department of Orthodontics and Dentofacial Orthopedics, Rural Dental College, Loni - 413 736, Tal. Rahata, Dist. Ahmednagar, India
2 Department of Orthodontics and Dentofacial Orthopedics, Government Dental College and Hospital, Nagpur - 440 003, India

Date of Web Publication26-Jul-2011

Correspondence Address:
Rahul Shyamsunder Baldawa
302, Department of Orthodontics and Dentofacial Orthopedics, Rural Dental College, Loni-413 736, Tal. Rahata, Dist. Ahmednagar
India
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DOI: 10.4103/2231-0746.83148

PMID: 23482925

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  Abstract 

Background: With the increased interest in adult orthodontics, maxillary width problems in the nongrowing patients have been encountered with greater frequency. In view of the negative outlook for successful nonsurgical palatal expansion in adult patients it seemed appropriate to evaluate the biomechanical effects of nonsurgical rapid maxillary expansion (RME) in adults using the finite element method (FEM). Objectives: To evaluate the biomechanical effects of RME on the craniofacial complex as applied to three-dimensional (3D) model of an adult human skull using the finite element method. Settings and Design: The Department of Orthodontics and Dentofacial Orthopedics at Government Dental College and Hospital, Nagpur. The study was done on an analytical model developed from a dry human skull of an adult female with an approximate age of 20 years. Materials and Methods: A 3D finite element analysis of the craniofacial complex was developed from sequential computed tomography scan images. Known transversal (X) displacement with magnitudes of 1, 3, and 5 mm were applied and the displacement and Von-Mises stresses in different planes were studied on different nodes located at various structures of the craniofacial complex. Results: Transverse orthopedic forces not only produced an expansive force at the intermaxillary suture but also high forces on various structures of the craniofacial complex, particularly at the base of the sphenoid bone and frontal process of the zygomatic bone. Lateral bending of the free ends of the pterygoid plates were noted. Conclusion: RME must be used judiciously in adults because of its far-reaching effects involving heavy stresses being noted at the sphenoid bone, zygomatic bone, nasal bone, and their adjacent sutures.

Keywords: Adult, biomechanical effect, craniofacial complex, finite element method, rapid maxillary expansion


How to cite this article:
Baldawa RS, Bhad WA. Stress distribution analysis during an intermaxillary dysjunction: A 3-D FEM study of an adult human skull. Ann Maxillofac Surg 2011;1:19-25

How to cite this URL:
Baldawa RS, Bhad WA. Stress distribution analysis during an intermaxillary dysjunction: A 3-D FEM study of an adult human skull. Ann Maxillofac Surg [serial online] 2011 [cited 2019 Oct 22];1:19-25. Available from: http://www.amsjournal.com/text.asp?2011/1/1/19/83148


  Introduction Top


Interest in the use of rapid maxillary expansion (RME) in adult patients has increased markedly during the past 2 decades. The correction of transverse discrepancies and the gain in arch perimeter as a potential nonextraction technique appear to be the most important reasons underlying this increased interest. [1] Although the major treatment effect is noticed clinically in the area of the dentition, transverse enlargement of the apical base or the skeletal structures throughout the nasomaxillary complex occur simultaneously.

The review by Bishara and Staley [2] and the orthodontic texts by Proffit [3] as well as by McNamara and Brudon, [4] all state that the feasibility of palatal expansion beyond the late teens and early twenties is questionable.

This pessimistic view of RME in adults is based in part on anatomic studies of the maturing face, which show the midpalatal suture and adjacent circum-maxillary articulations becoming more rigid and beginning to fuse by the mid-twenties.

In order to overcome the resistance of the adult sutures to expansion, "surgically-assisted" rapid maxillary expansion (SA-RME) has been advocated. SA-RME procedures have traditionally been thought to have a low morbidity, but this surgery is not free of risks, and surgeons need to be aware of its potential complications.

In view of the negative outlook for successful nonsurgical palatal expansion in adult patients and concerns about the potential complications and hazards of surgical procedure, it seemed appropriate to evaluate the biomechanical effects of nonsurgical RME in adults.

The aim of the present study was to make use of the state-of-the-art finite element method to evaluate the biomechanical effects of RME on the craniofacial complex as applied to three-dimensional (3D) model of an adult human skull. The present research also aimed to evaluate the pattern of stress accumulation and distribution among different bones.


  Material and Methods Top


The analytical model in this study was developed from a dry human skull of an adult female [Figure 1] with an approximate age of 20 years, selected from the anatomic collection of Government Medical College, Nagpur.
Figure 1: Dried adult human skull used in this study

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Previous studies [5] have used photographs of cross-sections of skull. In the present study, computed tomography (CT) scan images of the skull excluding the mandible were taken in the axial direction, parallel to the Frankfort horizontal plane. Sequential CT images were taken at 1 mm intervals to reproduce finer and detailed aspects of the geometry [Figure 2]. This spacing of CT images enabled a higher geometric accuracy than that used by Jafari et al, [6] Iseri et al, [7] and Tanne et al. [5]
Figure 2: Sample CT slices

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The CT scan images were read into visualization software Materialise's Interactive Medical Image Control System (MIMICS). This is an interactive tool for visualization and segmentation of CT images as well as MRI images and 3D rendering of objects [Figure 3]a, b. In this model, Tet 10 solid elements (10 noded) were used. The model consisted of 7,13,009 nodes and 3,57,425 Tet 10 elements [Figure 4].
Figure 3: (a,b) Different views of 3D reconstruction of CT scans of skull

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Figure 4: Lateral view of the final 3D fi nite element model constructed using Tet 10 solid elements

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The materials in the analysis were assumed to be linearly elastic and isotropic. The material properties of the compact and cancellous bones and teeth in the model were defined according to the experimental data in previous studies [5],[6],[7] as shown in [Table 1]. All sutures were assumed to have the same mechanical properties as the surrounding bone material except at the palatine bone.
Table 1: Material properties

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The two parts of the palatinal bone that are separated by the vertical plane of symmetry were assumed to be unconnected, so that they moved freely in lateral directions with respect to the vertical plane of symmetry. This was done to investigate the stress distribution and deformation of the craniofacial complex after splitting of the midpalatal suture.

All other points of the cranium lying on the symmetry plane were constrained to have no motion perpendicular to this plane. In addition, a zero-displacement and zero-rotation boundary condition was imposed on the nodes along the superior and posterior surface of the skull and along the foramen magnum.

Eventhough application of a known force is possible with FEM, known transversal (X) displacement with magnitudes of 1, 3, and 5 mm were applied on the maxillary canine and first permanent molar crown. It was assumed that the two plates of transversal orthopedic appliance moved apart by a total of 2, 6, and 10 mm, respectively.

The displacements and Von-Mises stresses in different planes were studied on different nodes located at various structures of the craniofacial complex. The stress distribution patterns were analyzed; the results were tabulated and graphically represented.


  Results Top


The biomechanical changes observed in this study were evaluated under the headings:

  1. Displacement of different bones of the craniofacial complex with varying amounts of transverse expansion.
  2. Stress distribution observed at different bones of the craniofacial complex with varying amounts of transverse expansion.
Displacements of the craniofacial structures were studied in 3 dimensions: transversal-(X) plane, sagittal-(Y) plane, and vertical-(Z) plane. Positive value (+) indicated an anterior movement in a sagittal (Y) plane and an upward movement in the vertical (Z) plane. Negative value (−) indicated a posterior movement in a sagittal (Y) plane and a downward movement in the vertical (Z) plane.

Displacement in the transverse plane: (X-displacement)

Maximum X-displacement (lateral displacement) was 4.45 mm at node corresponding to the incisal edge of upper central incisor. Displacements in the dentoalveolar region were noted more than the skeletal changes [Table 2].
Table 2: Comparison of the computational result of transversal (X) displacement of the various structures of the craniofacial complex with varying amounts of expansion

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With 1 mm of separation of expansion device on each side, changes were evident only in the dentoalveolar region and anterior maxillary region. As the expansion device was further separated, displacements of the adjacent structures were noticeable.

Expansion was more in anterior maxillary area compared to the posterior. From the frontal view, pyramidal displacement of maxilla away from the midline was evident.

The width of the nasal cavity at the floor of the nose increased markedly, whereas the posterosuperior part of the nasal cavity had moved minimally in the lateral direction. No significant lateral displacement was observed at the temporal, frontal, and sphenoid bone. The inferior parts of the pterygoid plates, however, demonstrated lateral displacement or bending. But minimum displacement was observed in the region close to the cranial base, where the plates were more rigid.

Displacement in the anteroposterior plane: (Y-displacement)

Maximum positive Y-displacement (forward displacement) was 1.21 mm at node representing the anterior aspect of palate followed by 1.09 mm at posterior aspect. All the dentoalveolar structures, maxillary structures, and structures on nasal cavity wall demonstrated forward displacement to varying extent. These changes were evident when the expansion was beyond 3 mm on each side [Table 3].
Table 3: Comparison of the computational result of sagittal (Y) displacement of the various structures of the craniofacial complex with varying amounts of expansion

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Maximum negative Y-displacement (backward displacement) of 0.82 mm was noted at the node representing the anterior region of zygomatic arch. Overall, the zygomatic bone displayed a backward displacement.

Displacement in the vertical plane: (Z-displacement)

Maximum positive Z-displacement (upward displacement) was 0.98 mm at node representing the frontal process of the zygomatic bone. Maximum negative Z-displacement (downward displacement) was 1.02 mm of point "A," indicating a downward displacement of maxilla. Considering both these points, it is evident that the nasomaxillary complex rotated in such a manner that the lateral structures had moved upward and midline structures downward. The anterior part of the maxillary bone (point A and ANS) and maxillary central incisors were displaced downward [Table 4].
Table 4: Comparison of the computational result of vertical (Z) displacement of the various structures of the craniofacial complex with varying amounts of expansion

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[Table 5] shows the comparison of maximum Von-Mises stresses on the various craniofacial structures with varying amounts of expansion. The findings show that the stresses at the nodes varied linearly for the given displacement boundary conditions due to RME.
Table 5: Comparison of maximum Von-Mises stresses on the various structures of the craniofacial complex with varying amounts of transverse expansion

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Initial stress images of the 3D model of skull are as shown in [Figure 5]a-c. The areas of stress are shown with the help of different colors. The pellets of colors representing the tensile and compressive stresses are shown on the right-hand side of the diagram. Using the computer-generated color diagrams the following results were obtained.
Figure 5: Contour plots for stress distribution in craniofacial complex with (a) 1 mm, (b) 3 mm, and (c) 5 mm of expansion

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In the dentoalveolar region, the stresses were high in apical region of canine and first molar and they continued to increase as the expansion progressed. In the maxilla, zygomatic buttress demonstrated high stress values compared to the other areas evaluated. The posterior region of the palate demonstrated higher stress values compared to the anterior region. The anteroinferior region of the nasal cavity demonstrated stresses in range of 5.24-20.42 kg/mm 2 , which were highest for the areas assessed.

Highest stress levels were observed in the pterygoid plates of sphenoid bone. The findings indicated that high stresses produced by RME are especially located in the superior parts of the pterygoid processes of the sphenoid bone (74.24 kg/mm 2 at medial and 68.17 kg/mm 2 at lateral pterygoid). The greater wing of sphenoid also demonstrated high stress levels (51.24 kg/mm 2 ).


  Discussion Top


Finite element analysis is a mathematical method in which the shape of complex geometric objects and their physical properties are computer constructed. Interactions of various components of the model are then calculated for stress, strain, and deformation. This method was first used in orthodontics by Thresher and Saito [8] to study stresses on human teeth. Ever since, this method has proved effective in many dental fields such as simulation of tooth movement and optimization of orthodontic mechanics. Such an extensive use is primarily because of its advantages. The method is noninvasive; the actual amount of stress experienced at any given point can be theoretically measured; the tooth, alveolar bone, periodontal ligament, and craniofacial bones can be simulated; the displacement of the tooth and the craniofacial complex can be visualized graphically; the point of application, magnitude, and direction of a force may easily be varied to simulate the clinical situation; reproducibility does not affect the physical properties of the involved material; and the study can be repeated as many times as the operator wishes.

The 3D FEM used in the present study provided the freedom to simulate orthodontic force systems applied clinically and allowed analysis of response of the craniofacial skeleton to the orthodontic loads in 3D space.

The experimental method employed in this study permitted the visualization of bone reactions, even with the lowest loading degree. One should be aware that the structural and spatial relationships of various craniofacial components vary among individuals. It is important to realize that these factors may contribute to the varied responses of the craniofacial components on loading in vivo. Thus, the results of this study are valid only for a single specific human skull.

This can be seen as a problem in generalizing the findings obtained in this study. On the other hand, studies done by Iseri et al[7] and Jafari et al[6] yielded same results in spite of the differences in method used and the variation in skull geometry. Iseri et al[7] used CT images of a 12-year-old patient, whereas Jafari et al[6] constructed the model from CT images of dry human skull with an approximate age of 12 years. They showed that, although there were differences in the craniofacial structures between subjects, the responses to the same mechanical forces were same in the FEM.

So, although there were quantitative differences [Table 6], qualitatively, the mechanical response was predicted in the same manner, which is a positive indication for the validity of the qualitative conclusions.
Table 6: Comparison of transversal (X), sagittal (Y), and vertical (Z) displacement of the various structures of the craniofacial complex with previous studies

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Although we used an adult human skull to develop the finite element model, the displacements of the various craniofacial structures were compared with similar corresponding structures of the previous studies [Table 6]. [6],[7]

Overall pattern of displacement

The pattern of displacement revealed that the greatest widening was observed in the dentoalveolar structures, with the expansion effect gradually decreasing toward the superior structures. The results of the present study support those of the previous studies, [6],[7] which reported the maxillary suture to separate superoinferiorly in a nonparallel manner, the separation being pyramidal in shape with base of the pyramid located at the oral side of the bone and the center of rotation located near the frontonasal suture.

In the sagittal (Y) plane, the structures along the midline showed an anterior displacement, whereas the lateral structures demonstrated a posterior displacement.

In the vertical (Z) plane, the entire maxillary complex descended downward more or less in a parallel manner, whereas the lateral structures demonstrated an upward displacement.

Overall pattern of stress distribution

Stresses produced by the expansion appliance were concentrated in the anterior region of the palate. The initial effects of the expansion were observed in the central incisor region.

With increased activations, stresses radiated from the midpalatine area superiorly along the perpendicular plates of the palatine bone to deeper anatomic structures. The buttressing of the maxillary tuberosity with the pterygoid plates of the sphenoid bone allowed the forces to then radiate to the base of the medial pterygoid plate. From this region, the stresses then spread further superiorly toward the malar and the zygomatic bones.

Heavy stresses were observed in the area of the base of pterygoid plates of sphenoid bone. These areas of stress concentration indicate regions of potential weakness or regions where major biologic responses may be expected.

If the maxilla is fused to the pterygoid plates, as is the probable case in adult patients, intermaxillary expansion would be difficult to obtain, regardless of how much the suture between the two halves of maxilla are affected by the orthopedic forces.

Unlike the maxillae, the pterygoid processes are not individual bones, but parts of the same cranial bone-the sphenoid. So, even if SA-RME is advocated, the osteotomized maxillae and palatine bones would move apart on application of expansion forces, but the fused pterygoid processes which cannot separate, tend to splay outward.

In children and adolescents, the midpalatal and circum-maxillary sutures generate less resistance to expansion forces, thus limiting the development of internal stresses in the dentoalveolar region. Consequently, maxillary expansion is accompanied by sutural adjustments in the craniofacial complex in remote regions, rather than by alveolar remodelling or tipping. However, these adaptive changes cannot be exploited following skeletal maturation because the sutures are no longer patent and the expansion forces are now resisted by the reinforcing buttresses of the midfacial skeleton. The heavy stresses at the pterygoid plates can radiate across to deeper anatomic structures, including the body and greater wings of sphenoid bone thereby denoting far-reaching effects of orthopedic expansion of maxilla in adults.

Contrary to conventional perception, this study along with the previous studies [6],[7],[9],[10] disclosed that resistance provided by the pterygomaxillary articulations was greater than that of the zygomaticomaxillary buttresses.

The results of the present study using the 3D FEM of an adult human skull provided explanation about the mechanical reactions of the bony tissues, which are the first steps in the complex and dynamic process of tissue response to maxillary expansion.

However, as stated previously, FE method has certain limitations, most important being the results applicable only to the FE model created. It may not necessarily apply to all individuals quantitatively. However, what is important is that most of them, would give QUALITATIVELY THE SAME RESULTS as were obtained in the present study, which can prove useful if employed judiciously.

The present study is precisely for the purpose of highlighting the qualitative differences in biomechanical effects of RME employed in an adult. Simulation models that are being used for diagnostic, operational planning, or rehearsal purposes in the field of medical sciences can be effectively and efficiently employed in the field of orthodontics and maxillofacial surgery.


  Conclusion Top


It can be thus concluded from the present study that:

  • Finite element analysis is a valid, reliable, and fairly accurate method of analysis of stresses generated in the craniofacial complex.
  • Accurate geometric model of craniofacial skeleton should be created to study the displacement and stresses in the craniofacial complex and skeleton.
  • Although expansion can be achieved in adults, displacements are noted more in the structures located anteriorly and along the midline, while the posterior and lateral structures demonstrate minimal displacement but high stresses.
  • RME must be used judiciously in adults, because of its far-reaching effects involving heavy stresses being noted at the sphenoid bone, zygomatic bone, nasal bone, and their adjacent sutures.
  • Specific responses in individual cases, especially in adults, can be predetermined with the use of simulation models and the design of treatment mechanics, accordingly tailored.
  • It is hoped that this further exploration of the skeletal and dental effects of transverse orthopedic forces better defines the parameters of clinical expectations from this orthopedic procedure when employed in adults.


 
  References Top

1.Cameron CG, Franchi L, Baccetti T, McNamara JA. Long-term effects of rapid maxillary expansion: A posteroanterior cephalometric evaluation. Am J Orthod Dentofac Orthop 2002;121:129-35.   Back to cited text no. 1
    
2.Bishara SE, Staley RN. Maxillary expansion: Clinical implications. Am J Orthod Dentofac Orthop 1987;91:3-14.  Back to cited text no. 2
    
3.Proffit WR, Fields HW, Ackerman JL, Bailey LT, Tulloch JF. Contemporary Orthodontics. 3 rd Ed. St. Louis: Mosby Inc. 2000.  Back to cited text no. 3
    
4.McNamara JA Jr, Brudon WL. Orthodontic and orthopedic treatment in the mixed dentition. Ann Arbor, MI: Needham Press; 1993.  Back to cited text no. 4
    
5.Tanne K, Harage J, Kakiuchi K, Uamagat Y, Sakuda M. Biomechanical effect of anteriorly directed extraoral forces on the craniofacial complex: A study using the finite element method. Am J Orthod Dentofac Orthop 1989;95:200-7.  Back to cited text no. 5
    
6.Jafari A, Shetty KS, Kumar M. Study of stress distribution and displacement of various craniofacial structures following application of transverse orthopedic forces: A three-dimensional FEM study. Angle Orthod 2003;73:12-20.  Back to cited text no. 6
    
7.Iseri H, Tekkaya AE, Oztano, Bilgic S. Biomechanical effects of rapid maxillary expansion on the craniofacial skeleton, studied by the finite element method. Eur J Orthod 1998;20:347-56.  Back to cited text no. 7
    
8.Thresher RW, Saito GE. The stress analysis of human teeth. J Biomech 1973;6:443-9. Cited in Tanne K, Sakuda M, Burstone CJ. Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces. Am J Orthod Dentofac Orthop 1987;92:499-505.  Back to cited text no. 8
    
9.Chaconas SJ, Caputo AA. Observation of orthopedic force distribution produced by maxillary orthodontic appliances. Am J Orthod 1982;82:492-501.  Back to cited text no. 9
    
10.Shetty V, Mendoca Caridad J, Caputo AA, Chaconas SJ. Biomechanical rationale for surgical-orthodontic expansion of the adult maxilla. J Oral Maxillofac Surg 1994;52:742-9.  Back to cited text no. 10
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
 
 
    Tables

  [Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]


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