Journal of Orofacial Sciences

: 2020  |  Volume : 12  |  Issue : 1  |  Page : 41--46

A Finite Element Analysis of Biomechanics in Distraction Osteogenesis of Ascending Ramus Lengthening between Males and Females—A Comparative Study

Ali R Al-Khatib1, Lamiaa A Hasan1, Mohammed Najeeb Abdullah Alrawi2, Emad Hazim Kasim Alhajar2,  
1 Department of Pedodontics, Orthodontics and Preventive Dentistry, College of Dentistry, University of Mosul, Mosul, Iraq
2 Department of Mechanical Engineering, College of Engineering, University of Mosul, Mosul, Iraq

Correspondence Address:
Ali R Al-Khatib
Department of Pedodontics Orthodontics and Preventive Dentistry, College of Dentistry, University of Mosul, Mosul


Introduction: The asymmetry of mandibular ascending ramus leads to serious orthodontic problems in the dentofacial complex. This study was aimed to assess the effects of gender bone properties difference on biomechanics of distraction osteogenesis that used for ascending ramus lengthening with different forces. Materials and Methods: A 3D mandibular model was constructed and an oblique osteotomy line was made. The force was applied perpendicular to the osteotomy line in a bidirectional manner with three different distraction rates (5 mm, 10 mm and 15 mm). Results: Male and female models showed the same maximum Von Mises stress value and the same distribution with the same force, the maximum stress value for 5mm, 10mm and 15mm rates were greater than the ultimate tensile stress for the human bone. The displacement within the three rates in X, Y and Z directions was higher for male than female. The displacements in all three directions were more prominent in the mandibular chin area. Conclusion: No gender difference in stress values and distribution with more anterior displacement in male than female. This site of distraction results in forward and anti-clockwise rotation of the mandible resulting in reducing anterior facial height.

How to cite this article:
Al-Khatib AR, Hasan LA, Alrawi MN, Alhajar EH. A Finite Element Analysis of Biomechanics in Distraction Osteogenesis of Ascending Ramus Lengthening between Males and Females—A Comparative Study.J Orofac Sci 2020;12:41-46

How to cite this URL:
Al-Khatib AR, Hasan LA, Alrawi MN, Alhajar EH. A Finite Element Analysis of Biomechanics in Distraction Osteogenesis of Ascending Ramus Lengthening between Males and Females—A Comparative Study. J Orofac Sci [serial online] 2020 [cited 2020 Oct 29 ];12:41-46
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The facial asymmetry that occurs due to unilateral hypoplasia of mandibluar ascending ramus is congenital or acquired condition that leads to sever orthodontic and craniofacial problems.[1] The reduction in vertical mandibular ramus length leads to chin deviation towards the affected side and oblique maxillary occlusal plane. This phenomenon worsens as growth continues and lead to severe malocclusion. [2] Distraction osteogenesis (DO) is a procedure that involves gradual, controlled bony movement in a surgically created fracture that results in the expansion of soft tissue and rebuilding of bone deformities.[3],[4]

The mean extent of hypoplastic ascending ramus lengthening ranged between 10 and 16 mm.[2],[5] Marquez et al. [5] recorded that 15 mm or more of ramus lengthening lead to relapse by about 100% in hemifacial microsomia due to the action of the pterygomasseteric muscles which was elongated and then returned to their original lengths. This may be accompanied by condylar head resorption due to permanent muscle pressure.

Distraction osteogenesis for ascending ramus hypoplasia is usually conducted during the growth period. However, severe asymmetries should be treated at an earlier age than those with mild conditions.[2] Jansma et al.[2] treated seven patients complained of facial asymmetry caused by unilateral hypoplasia of the mandibular ramus by ramus lengthening with intraoral DO. The treatment accomplished with mean lengthening of 13 mm, however, the lengthening measured on the apparatus differed from lengthening that occurs at distraction space. They concluded that the main cause is the difference in the bone property which defiantly governs the treatment outcome.

Stress analysis of dental structures becomes a topic of attention in recent years. Finite Element Analysis (FEA) is a modern mathematical tool for stress analysis, with the advantage of being appropriate for the irregular model.[6] Finite element models can be a designer for the variations of specific individual properties such as sex and age which improved understanding of biomechanical response for different dental treatment procedures. [7] Sensoy et al.[8] emphasized on the necessity for specific 3D model for each patient to construct the osteotomy line in a way that maximized advantages of conventional DO protocols. Tehranchi et al.[9] used the FEA to assess the biomechanical effect of different surgical cut directions during unilateral mandibular lengthening by DO. They presented specific guidelines to be used to treat asymmetric mandible.

Bone is a natural composite anisotropic material, mainly composed of three materials organic, inorganic and water. [10]

The mechanical properties of the bone consistently differed between gender. Havaldar et al.[11] mentioned that the mechanical behavior of bone is gender and age-dependent. According to our best knowledge, no study was conducted to assess the gender variation effect on the DO result by FEA. Thus, the aim of this study was to test the effect of gender difference in bone properies on the biomechanics of distraction osteogenesis of mandibular ramus lengthening conducted with different force rates in a non-invasive manner.

 Materials and Methods

Ethical approval for this study (4S/51) was provided by the Authorized Committee of College of Dentistry, University of Mosul, Mosul, Iraq on 14 March 2019.

Modeling process

In this study, dry normal mandible was used to construct 3D mandiblar model with mandibular teeth[12] by AutoCAD (2010) Program. All linear measurements that obtained from the mandible were measured by digital vernia. At the osteotomy site the fracture line was detected in the model. According to Sethi et al.,[13] different osteotomy lines were presented [Figure 1]. In this study, we used the oblique cut at gonial angle distal to the last available molar. This site was used for mandibular body and ramus lengthening. The constructed model was exported to the FE program Autodesk® Inventor® Professional Computer Program version (2012) and the right side of mandible was used for the FEA.[14]{Figure 1}

Material properties

In this study, Young’s modulus (Ym), and Poisson ratio represented the elementary input variables that used to run the program. Young’s modulus defined as the relationship between stress and strain in the elasticity region of uniaxial deformation.[15] Whereas, Poisson ratio represents the ratio of transverse contraction (for expansion) strain to longitudinal extension strain in the direction of stretching force. [15] The materials properties are considered being isotropic, homogenous and linear elastic. [16] In this study, Ym of cortical bone for male and for the female was (338.3±179.74 and 404.7±314 MPa) respectively[11] while Ym for sponge bone and teeth characterized according to Boccaccio et al.,[17] (1.37, 18.6 GPa) respectively. Poissons ratio were considered for cortical bone, sponge bone and teeth (0.3,0.3 and 0.31) correspondingly.[17] According to that, we constructed two informatics models, one for the male the other for the female.

Boundary conditions

The boundary condition is a restraint applied to the model, from which potential energy and solutions are derived. [16] The false results can be associated with the areas adjacent to the constraints. [16] Boundary conditions in our model designed so that the mandible was fixed to prevent bodily movement of model by supporting the outer surface of the condyle and molars buccal cusps and fossa.[9],[14]


The mandible under analysis was discretized to many parts named as elements. Each element had a specific number of apexes called nodes. The network of elements and nodes was called the finite element mesh. Using auto mesh option for meshing the design of interest. In this study, the final mesh comprised 654104 nodes, 450018 elements.


The static loading was applied in bidirectional manner perpendicular to the line of osteotomy as shown in [Figure 2] with three different distraction rates for both models (5 mm, 10 mm and 15 mm). Robinson et al.[18] mentioned that 1mm of distance between osteotomized bone, need a force of 35.6 Newton, so that, 35.6 multiplied by 5 to obtain the necessary force to open the osteotomized site by 5 mm. In a similar way, the force was estimated to obtain the 10 and 15 mm of distraction.{Figure 2}


The results of Von-Mises stress (VMs) and translation in all three directions (X,Y, and Z) were evaluated. A pseudo-color scale with 12 color code and 13 values were used for magnitude visualization of the stress scattering and displacement along the mandible [Figure 3]. These values differ according to the range of variable, the blue colour code represented the minimum variable value, whereas, the red colour coderepresented the maximum value regions. The maximum values for VMs and displacement were showed in [Table 1].{Figure 3}{Table 1}

In this study, the maximum VMs values were the same for male and female at the same force with the same pattern of stress distribution, the maximum stress value was seen adjacent to the area of fixation and area of the force application. The maximum stress values for 5 mm, 10 mm and 15 mm distraction was higher than the ultimate tensile stress for bone tissue [Figure 4].{Figure 4}

The X axis displacement represented anterio-posterior movement (sagittal plane) and the positive value indicated an anterior movement. Whereas, Y axis displacement represented the movement in transverse plane (horizontal) and the positive range mean an expansion was occured. The Z axis displacement represented up-down rotation of the mandible and the positive value indicated anti-clockwise rotation of the mandible. In this study, the displacement for all three directions is more in male than female.

For X axis displacement, anterior movement with direction of force was observed. The maximum range of displacement was observed in the chin area and along the lower border of the body of the mandible, smaller range was also seen along the osteotomized site within ascending ramus [Figure 5].{Figure 5}

For Y axis displacement maximum value was seen along the osteotomized site within ascending ramus and with less than that of ascending ramus was seen along the inferior border of the body of the mandible and central region [Figure 6].{Figure 6}

For Z displacement as appeared in [Figure 7] maximum value was seen within gonial angle and central area and along the anterior part of the mandible, nearly zero movement in the condyle and coronoid for X and Z axes with little movement in the coronoid notch in Y axis direction. Z axis displacement (upward movement) was more obvious than in X and Y axes displacement, but it was higher in male than female.{Figure 7}


Mandibular DO is often a sophisticated procedure than other alternative long bone lengthening; this is due to the complicated 3D distraction needed to alter each the size and shape of a mandible. It is clear that the mechanical bone properties are affected by its mineral content, the higher mineralization makes the bone is stiffer with a high modulus of elasticity.[10] Studies have found that mechanical behavior of bone is gender and age-dependent.[7],[11],[19] This variation mainly affects the outcome of surgical and orthodontic treatment that should be clearly understood by the clinicians.

Different methods for mandibular modeling and analysis were presented such as radiography and CT scan.[6],[16],[20]These methods have some limitations such as the 2D illustration of a 3D subject. [16],[21] Also, the risk of radiation and cost in case of Computed Tomography.[21] In this research, dry normal mandible was utilized to create 3D model with mandibular teeth using Autocad (2010) Program.[12]

In this study, Young’s modulus variation for each gender has no effect on either stress values or form of distribution. However, displacement in all three directionsis more in male than female. Havaldar et al.[11] tested human femur cortical samples and determined that Young’s modulus for male was constant until the age of 55 years, minimal increase was recorded until 75 years with a significant increase after the 75 years of age.Whereas, In the female, until 55 years no significant change was observed, however,a significant increase after the 55 years was recorded. The degree of bone mass is ruled by a variety of factors such as the hormonal, nutritional and mechanical one. Female usually have a lower bone mass than male and with an increasing age, this gap becomes wider. Regarding cortical bone, losing of bone mass begins in female at 40 years but in males starts at 50 years of age.[11]

Additionally, women experience an accelerated period of bone loss around the menopause. This accelerated loss is associated with the reduction of estrogen. The role of estrogen deficiency appears to involve an increase in bone resorption and a reduction of bone formation. Thus in males and females, estrogen has both a catabolic and an anabolic effect on bone throughout life. In older men, osteoporosis is more closely related to low estrogen than to low androgen levels. [11]

Subit et al.[7] studied tibiae and femora forms for males aged 15, 37, 40, 72 and 75 years. They recorded that the subject with 15 years exhibited an elasto‐plastic behavior with lower Ym compared with the other subjects. However, McCalden et al.[22] showed that there is no age dependence observed for the Ym.

In this study, Von Mises stress was the same for male and female at the same force.It is important to know that the stress is the ratio between the force and the area upon which it acts; so stress is depended on the force amount and the surface area on which the force applied only [15] since the model was standardized with different property to investigate the effect of mechanical bone property on distraction result.The stress values of 5 mm, 10 mm and 15 mm distraction were more than the ultimate tensile stress for the human bone 12.000 psi[23], when the bone tissue cannot withstand such stress, this damage would trigger the formation of a new mesenchymal tissue.[23]

High stress is seen within posterior mandibular condyle and anterior mandibular condylar because these are next to area of fixation when the reaction force will appear resulting in high-stress level that agreed with Basciftci et al.[24] who found stress accumulation appear at mandibular condyle, Basciftci et al. thought that the reason for this stress accumulation was the restraining of the mandibular condyles in the simulation and this considered to be representative finding because the mandibular condyle is connected to the cranium by several ligaments and muscles that limit the movement of the mandible.

Zero stress values seen in Pogonion, Menton, Infradental, Supramemtale,Central incisor edge and Coronoid this consider hypothetically true because they are far from restriction area and point of force application,this in agree with Basciftci et al.[24] who mentioned that no stress accumulation was occurred in symphysis region because they are distant from the fixation point.

The displacement represents the strain which defines as the change in the linear dimensions of a body as the result of the application of a force.[15] The Young’s modulus (E) was calculated by the following equation:[15] E= σ max/ε max where σ max is the maximum stress and ε max are maximum strain at failure; so Young’s Modulus is reversely related to the strain while strain is express as the ratio of the total change in length ΔL per unit of the original length L[17], so Young’s modulus will equal to E= result in Young’s Modulus is reversely related to the displacement, this gives explanation of why the displacement for male in all three directions are more than female.

This site of osteotomy gave an anti-clockwise rotation of mandible and this is in agreement with Tehranchi et al.[9] who studied three spatial planes for osteotomy site (vertical, horizontal and oblique) within the right side of mandible; measure the proximal and distal segments movement after simulation of 15mm distraction. Tehranchi et al.[9] found that oblique osteotomy line result in an anti-clockwise rotation of mandible and make the gonial angle more prominent and can be used in patient with long anterior facial height and this in agreement within this study. Moreover, Hasan et al.[25] studied the vertical surgical cut within different orientations to lengthen the body of mandible in patient within hemifacial microsomia. They stated that vertical osteotomy line resulted in an anti-colockwise rotation of mandible. So that, both vertical and oblique directions can be used to lengthen the body of mandible with reduction in anterior facial height. Authors advised to use this approach with caution in patient within short face. Moreover, both planes vertical and oblique for osteotomy site result in more anteroposterior lengthening than transverse expansion of mandible.

In current investigation, the applied force was measured in newton units and the results were in mm overlapped with those of Robinson et al.,[18], enhance our results. In addition to that, FEA did not show tooth movement resulted from distraction force because teeth and bone are expanded as one unit. Moreover, facial Soft tissues including the masticatory muscle couldn’t simulate, because finite element programs present rigid fixation while these muscles in reality allow expansion to some extent and this is the main difficulties in modeling natural boundary condition in all finite element study. Other limitation, that the researchers cannot found asymmetric mandible to be modeled.


Young’s modulus variation for both genders will not affect either stress values or distribution, Young’s modulus is reversely related to the displacement, for male the displacement in all three directions is more than for female. This site of distraction result in an upward rotation of mandible. This osteotomy site could give more lengthening of mandible than the expansion.


Authors wish to acknowledge College of Dentistry and College of Engineering, University of Mosul, for the given support.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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