Introduction

The skeletal effect of functional therapy on the mandible is a highly debatable subject that is yet unresolved. Many trials and systematic reviews have been made in a quest to find whether functional appliances have a skeletal effect on the mandible or is it merely the dentoalveolar compensation that corrects the discrepancy.

Some researchers assert the presence of favorable mandibular growth represented by condylar and glenoid fossa remodeling (Ruf and Pancherz 1999; Rabie and Hägg 2003; Antonarakis and Kiliaridis 2007; Paulsen et al. 1995; McNamara Jr and Howe 1990; Franchi et al. 1999; Woodside et al. 1987). Such remodeling resulted from the acceleration of chondrocytic differentiation and the increase in the amount of cartilage matrix formation, hence enhancing growth (Rabie and Hägg 2003).

On the other hand, some researchers argue about the significance of the magnitude of such skeletal effects and point to the evidence showing the distinction of the dentoalveolar changes produced (Cozza et al. 2006; Franchi et al. 2011; Zymperdikas et al. 2016; Marsico et al. 2011; Cope et al. 1994; Darda et al. 2010; Küçükkeleş et al. 2007). However, these dentoalveolar changes may in turn have acted as a restraint to the full expression of the skeletal enhancement.

It then appears that to be able to ascertain or negate the presence of significant skeletal changes with functional therapy, it was necessary to rule out the dentoalveolar factor through modifying the appliance design.

Consequently, this finite element analysis was conducted to study the effects produced by a newly devised fixed functional appliance (EFA; Elhiny functional appliance) and hence predict its clinical effectiveness.

Materials and methods

The current finite element analysis simulated a clinical situation where the mandible was positioned forward via a new fixed functional appliance design, EFA. The appliance could be easily constructed in the laboratory.

A two-dimensional model was prepared on ANSYS GUI, to simulate the lower part of the skull. The model dimensions were taken from literature (Panigrahi and Vineeth 2009). Two types of elements were used to build the model: Shell 3D 4node 181 with 6 degrees of freedom to mesh the bone and Link 180 as spar element to represent the appliance effect (Kohnke 2013). The applied force was 2 N propulsive force, as the forces generated by fixed functional appliances range from 150 to 200 g, i.e., 1.47 to 1.98 N (Karacay et al. 2006; Nalbantgil et al. 2005). The meshing process resulted in 59,386 nodes and 30,459 elements. As presented in Fig. 1, after the model meshing, the upper line, connecting the model to the skull, was set fixed in place as boundary condition.

Fig. 1
figure 1

Simplified model after meshing

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All materials were assumed to be isotropic, homogenous, and linearly elastic, and their properties were listed in Table 1.

Table 1 Properties of materials used in the finite element model
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Linear static analysis was performed on a personal computer (Intel Core to Due processor, 2.8 GHz, 4.0 GB RAM), using commercial multipurpose finite element software package (ANSYS version 13.0). The deformation and strain results were analyzed and represented graphically.

Results

The mandible showed forward and downward deformation, in both X and Y directions (Fig. 2).

Fig. 2
figure 2

Total deformation in the mandible and its components in horizontal and vertical directions

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The mandibular symphysis showed the highest deformation in the Y direction, and the symphysis and lower border in the X direction. As illustrated in Fig. 2, the maximum horizontal deformation in the mandible was 9.3 μm, while the vertical deformation was of order 7.2 μm. The total deformation at the symphysis was 80 μm.

The maxilla showed very little deformation upwards in the Y direction (about 0.13 μm), in the area representing point A and the anterior nasal spine (ANS). While in the X direction, there was an even less backward than the upward deformation, about 0.016 μm.

The condylar strain results in Fig. 3 showed that the strain in the X direction was a compressive strain of about 1122 micro strain anterior to the condyle, and 122 tensile micro strain behind the condyle. Above the condylar head, the strain ranged from − 71 to + 191 micro strain. While in the Y direction, the strain ranged from 150 to 170 micro strain behind the condyle, from 260 to 395 micro strain in front of the condyle, and an average of 940 micro strain above the condyle. The total condylar strain was about 1520 micro strain behind the condyle.

Fig. 3
figure 3

Condylar strain in X and Y directions and total strain

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The mandibular strain increased gradually in the X direction from − 70 to + 13 micro strain and in the Y direction from − 9 to + 23 micro strain. A stress/strain concentration appeared around the point of force application, where in the X direction the strain was about 677 micro strain and in the Y direction it was approximately 86 micro strain. Hence, the total mandibular strain ranged from 0 to 166 micro strain with an average of 150 micro strain at the point of force application. On the other hand, at the tooth bearing area, the strain was approximately zero (Fig. 4).

Fig. 4
figure 4

Mandibular strain in X and Y directions and total strain

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As presented in Fig. 5, the strain in the glenoid fossa in the Y direction was around 5.3 to 6.9 micro strain, while the total glenoid fossa strain ranged from 5.6 to 11.2 micro strain whereas the strain in the X direction, in the maxillary tooth bearing area, ranged from − 9 to 16.6 micro strain and the total maxillary strain ranged from 0 to 50 micro strain.

Fig. 5
figure 5

Maxillary strain in X and Y directions and total strain

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Discussion

There has been a wide debate regarding the output of using functional appliances, removable or fixed, for mandibular advancement. In noncompliant and post pubertal patients, the fixed functional appliance was the only successful non-surgical treatment (Panigrahi and Vineeth 2009). However, the main issue was the prevalence of dentoalveolar effects over skeletal effects (Cozza et al. 2006; Franchi et al. 2011; Zymperdikas et al. 2016; Marsico et al. 2011; Cope et al. 1994; Darda et al. 2010; Küçükkeleş et al. 2007; Panigrahi and Vineeth 2009; Nalbantgil et al. 2005).

As a result, it was hypothesized, in the current study, that by modifying the fixed functional appliance design into the new Elhiny functional appliance (EFA) design, the dentoalveolar effect would be either reduced or ruled out and the presence or absence of a significant skeletal effect could be discriminated.

The deformation in finite element analysis indicates that a change in size, and accordingly movement, has occurred. In clinical practice, the desirable effects for the correction of class II skeletal malocclusion are enhancing the mandibular growth while restraining the maxillary growth (Antonarakis and Kiliaridis 2007; Vargervik and Harvold 1985; Harvold and Vargervik 1971; Pancherz 1982; Macey-Dare and Nixon 1999; Collett 2000). Similar results were reported in this study; the greatest movement occurred in the forward and downward direction at the symphysis and lower border of the mandible. This was associated with a little backward and upward deformation in the maxilla indicating that some restraining effect was demonstrated as well (Nalbantgil et al. 2005). The low deformation values observed at the condyle suggest the absence of pain during treatment.

Different studies in the literature discussed the effects of stress and stress distribution on the condyle and the glenoid fossa and how the tensile and compressive stresses created by mandibular advancement resulted in remodeling (Panigrahi and Vineeth 2009; Rabie et al. 2001; Rabie et al. 2003a; Sato et al. 2005; Hu et al. 2001; Zhou et al. 1999; Ress 1954). However, there was no known reference value for the optimal physiological range of stresses (Panigrahi and Vineeth 2009). It was apparent then, as there were reported values for strain in the literature, that it was the optimum parameter to be investigated even though there were no comparable studies considering strain. It was previously reported that the strain values that resulted in physiological bone modeling and remodeling ranged from 100 to 3000 micro strain (EL- Zawahry et al. 2016), and strains from 3600 to 4000 micro strain were considered within the physiological range in living animals (Sugiura et al. 2000).

Owtad et al. reported that the biophysical changes that occur as a result of mandibular advancement prompt cellular and molecular changes which result in bone formation and condylar growth enhancement (Owtad et al. 2011). These cellular changes could be as a result of the genetic expression of Sox 9 and type II collagen leading to merely an acceleration of the genetically predetermined growth. However, Rabie et al. demonstrated that the expression of such factors did not result in a change in the normal growth pattern; thus, functional therapy could induce true condylar growth augmentation (Rabie et al. 2003b). On analyzing the strain results in this study, it was deduced that there was physiologic adaptive remodeling in the mandibular condyle in all directions, and mandibular forward and downward movement was demonstrated.

Different growth theories that explained the mechanism of growth modification described that functional adaptation occurred harmoniously in the condyle and the glenoid fossa, yet differently, and contributed to the growth modification process (Voudouris et al. 2003). The growth relativity hypothesis explained that the viscoelastic forces applied during functional therapy resulted in growth remodeling in the TMJ complex, which depended on the balance among many factors (Voudouris et al. 2003; Voudouris and Kuftinec 2000).

On the other hand, the ratchet hypothesis proposed that the condyle was the utmost determinant of the mandibular downward and forward movement (Whetten and Johnston Jr 1985). Others also reported that the role of the condyle in the process was exceptionally higher than the glenoid fossa (Owtad et al. 2011; Barnouti et al. 2011), which conformed to the results of this study in which condylar remodeling was considerably higher, and in contrast to some studies which reported remarkable glenoid fossa adaptation (McNamara Jr et al. 2003).

Contrary to all previous clinical reports (Cozza et al. 2006; Franchi et al. 2011; Zymperdikas et al. 2016; Marsico et al. 2011; Cope et al. 1994; Darda et al. 2010; Küçükkeleş et al. 2007; Panigrahi and Vineeth 2009; Nalbantgil et al. 2005), there was no movement in the mandibular dentoalveolar area at all as the observed strain at the tooth bearing area was an average of zero. Similarly, no maxillary dentoalveolar movement was demonstrated.

Accordingly, it could be predicted that the new design would enhance mandibular forward and downward growth without resulting in any dentoalveolar compensations. The absence of such compensations provides the opportunity for observing the presence or absence of significant skeletal changes with functional therapy.

Conclusion

Within the limitations of this finite element analysis, it was concluded that the new Elhiny fixed functional appliance design (EFA) resulted in:

  • Mandibular forward and downward movement, apparent at the mandibular symphysis and the lower border of the mandible

  • Physiological remodeling at the condyle, indicative of condylar growth

  • No dentoalveolar movement

Hence, it could be predicted that the new appliance (EFA) produces pure functional skeletal results with absolutely no dentoalveolar effects. The absence of dentoalveolar effects might allow the full expression of growth.

Furthermore, it can be useful in cases with deficient mandibular growth, increased overjet, proclined lower incisors, and/or retroclined upper incisors.

Recommendations

Clinical studies should be conducted on the newly designed appliance.