Influence of Orbital Implant Length and Diameter on Stress Distribution: A Finite Element Analysis

Abstract

Purpose:

A mathematical simulation of stress distribution around orbital implants was used to determine which length and diameter of implants would be best to dissipate stress.

Methods:

An integrated system for computed tomography data was utilized to create a 3-dimensional model of craniofacial structures. The model simulated implants placed in the 7, 11, and 12 o’clock positions of the orbital rim. A load of 2 N was applied to the model along the long axis of the implant (model 1) and an angle of 45° with the long axis of the implant (model 2). A model simulating an implant with a diameter of 3.75 mm and lengths of 3, 4, 6, 8, and 10 mm was developed to investigate the influence of the length factor. The influence of different diameters was modeled using implants with a length of 6 mm and diameters of 3.0, 3.75, 4.2, 5.0, and 6.0 mm. Values of von Mises equivalent stress at the implant–bone interface were computed using the finite element analysis for all variations.

Results:

The elements exposed to the maximum stress were located around the root of the orbital implant in model 1 or between the neck and the first thread of the orbital implant in model 2. An increase in the orbital implant diameter led to a decrease in the maximum von Mises equivalent stress values. In model 1, the reductions were 45.2% (diameter of 3.0–3.75 mm), 25.3% (diameter of 3.75–4.2 mm), 17.2% (diameter of 4.2–5.0 mm), and 5.4% (diameter of 5.0–6.0 mm). In model 2, the reductions of the maximum stress values were 51.9%, 35.4%, 19.7%, and 8.1% respectively. However, the influence of orbital implant length was not as pronounced as that of diameter. In model 1, the reductions were 28.8% (length of 3–4 mm), 19.2% (length of 4–6 mm), 9.6% (length of 6–8 mm), and 4.3% (length of 8–10 mm). In model 2, the reductions of the maximum stress values were 35.5%, 21.1%, 10.9%, and 5.4% respectively.

Conclusions:

An increase in the implant diameter decreased the maximum von Mises equivalent stress around the orbital implant more than an increase in the implant length. From a biomechanical perspective, the optimum choice was an orbital implant with no less than 4.2 mm diameter allowed by the anatomy.

Surgical reconstruction of the orbital after tumor resection and exenteration is challenging. Orbital osseointegrated implants can be surgically installed to guarantee secure retention of the prosthesis.^1–4 However, success rate of orbital implants between 35% and 75% after 3 to 14 years observation depends on the sites of insertion and the dimension of the orbital implants.^5–8 Failure takes place after orbital implant loading and is associated primarily with bone loss around the implant neck. Stress distribution created in the bone depends on the dimension of the orbital implants. Clinicians must determine the most appropriate dimensions of orbital implants in developing treatment plans to minimize hazardous stress concentration in the supporting bone.^9,10 However, the influence of the orbital implant length and diameter on stress distributions in craniofacial bones has not yet been described.

An integrated system for three-dimensional (3D) data utilization in craniofacial applications that allows 3D scanning, solid modeling, and finite element analysis has been developed by the authors. In this study, a digital biomechanical model of the craniofacial skeleton, created from computed tomography (CT) scanning data, was used to analyze the influence of orbital implant diameter and length on stress distribution around the implant.

METHODS

Craniofacial Model Construction

A 3D, finite element, solid model of the human skull was constructed based on CT data.¹¹ A 24-year-old healthy volunteer without orbital bone deossification was arbitrarily chosen. The craniofacial part of the skull was scanned with a spiral CT scanner at an axial plane (120 kV, 25 mA, 1 mm slice thickness, 1 mm slice distance, voxel size 0.3 × 0.3 × 2 mm³) from below the zygomatic bone to 4 cm above of the supraorbital margin. The CT Digital Imaging and Communications in Medicine data were analyzed with 3D scanning software (RapidFormTM, INUS Technology Inc, Seoul, Korea). This generated a polygonal isosurface and shell and fit nonuniform rational Bspline surfaces. Three-dimensional reconstructions of these parts were edited and optimized polygonal surfaces were exported to the downstream application. The orbital bone consists of both trabecular and cortical bone, and correct representation of the mechanical properties of these different bone types in finite element models is important for accurate results. The output data were transferred to 3D computer-aided design software (ANSYS Workbench, ANSYS Inc, Canonsburg, PA) for finite element solid model conversion (Fig. 1A).

FIGURE 1.

Three-dimensional finite elemental meshing model. (A) Craniofacial model. (B) Orbital implant model with length of 3 mm, diameter of 3.75 mm, and an abutment 7 mm in height.

Implant Model Construction

The craniofacial Vistafix System implant (Entific Medical Systems, Göteberg, Sweden) and titanium abutment 7 mm in height were constructed using 3D computer-aided design software. The 3D implant models represented commonly available submerged titanium solid cylinder-shaped craniofacial implant with 0.5 mm thread pitch (Fig. 1B). The implants were placed into the 7, 11, and 12 o’clock positions of the right orbital rim in the vertical position. Implant models with a diameter of 3.75 mm and lengths of 3, 4, 6, 8, 10 mm were used to investigate the influence of length as a factor. The influence of diameter was modeled by implants with a length of 6 mm and diameters of 3.0, 3.75, 4.2, 5.0, and 6.0 mm.

Material Properties and Meshing

All materials used in the models were considered homogeneous, isotropic, and linearly elastic. Poisson ratio (μ) and Young modulus (E) were 0.3 and 14.7 GPa for the cortical bone, 0.3 and 0.49 GPa for the cancellous bone, and 0.33 and 117 GPa for the implants, respectively. All interfaces between the materials were assumed to be bonded or osseointegrated. These models were read into a finite elemental program (COSMOS/Works, Structural Research & Analysis Corp, Los Angeles, CA) for mesh generation. Each model was meshed by elements defined by 8 nodes with 3 degrees of freedom in tetrahedral bodies (Solid 45). Each model consisted of approximately 190,000 elements and 290,000 nodes.

Loading and Boundary Conditions

Usually, the orbital prostheses was fixed by magnetic attachments, the average of force (including the weight of prostheses and magnetic retentive force) was approximately 2 N.⁴ Therefore, a load of 2 N was applied to the model along the long axis of the implant (model 1) and an angle of 45° with the long axis of the implant (model 2). With regard to boundary conditions, movement was restricted to the zygomatic bone plane and 4 cm above the supraorbital margin. The von Mises equivalent stress distribution in the orbital bone for each model was calculated by the finite elemental program.

RESULTS

The mathematical analysis demonstrated an uneven stress distribution inside the bony socket around the loaded implants. The elements exposed to the maximum stress were located around the root of the orbital implant in model 1 (Fig. 2A and B) or between the neck and the first thread of the orbital implant in model 2 (Fig. 2C and D). These maximum stress locations were identical for all implant lengths and diameters.

FIGURE 2.

Distribution of von Mises equivalent stress around implants with different diameters and lengths. View is from inside bony socket. The maximum stress was located around the root of the orbital implant in model 1 or between the neck and the first thread in model 2. (A) Model computed for implant with diameter of 4.2 mm and length of 6 mm in model 1. (B) Implant with diameter of 3.75 mm and length 3 mm. (C) Implant with diameter of 4 mm and length of 3 mm in model 2. (D) Implant with diameter of 5 mm and length 10 mm in model 2.

A comparison with maximum stress for implants of the same length but different diameters showed distinct variances. The plotting of maximum stress for implant diameters, varying from 3.0 to 6.0 mm, indicates a marked influence of the implant diameter on stress in the orbital bone (Fig. 3A and B). In model 1, the maximum stress value in the bone around the orbital implant with a diameter of 3.75 mm was 45.2% smaller than the diameter of 3.0 mm implant. Stress reduction continued to decrease for larger diameters. The reductions of the maximum stress values were 25.3% (diameter of 3.75–4.2 mm), 17.2% (diameter of 4.2–5.0 mm), and 5.4% (diameter of 5.0–6.0 mm), respectively. In model 2, the reductions of the maximum stress values in the bone around the orbital implant were 51.9% (diameter of 3.0–3.75 mm), 35.4% (diameter of 3.75–4.2 mm), 19.7% (diameter of 4.2–5.0 mm), and 8.1% (diameter of 5.0–6.0 mm) respectively.

FIGURE 3.

The influence of implant diameter and length on the orbital bone maximum stress values. (A) In model 1, the reductions of the maximum stress values were 45.2% (diameter of 3.0–3.75 mm), 25.3% (diameter of 3.75–4.2 mm), 17.2% (diameter of 4.2–5.0 mm), and 5.4% (diameter of 5.0–6.0 mm) respectively. (B) In model 2, the reductions of the maximum stress values in the bone around the orbital implant were 51.9% (diameter of 3.0–3.75 mm), 35.4% (diameter of 3.75–4.2 mm), 19.7% (diameter of 4.2–5.0 mm), and 8.1% (diameter of 5.0–6.0 mm) respectively. (C) In model 1, the reductions of the maximum stress values were 28.8% (length of 3–4 mm), 19.2% (length of 4–6 mm), 9.6% (length of 6–8 mm), and 4.3% (length of 8–10 mm), respectively. (D) In model 2, the reductions of the maximum stress values in the bone around the orbital implant were 35.5% (length of 3–4 mm), 21.1% (length of 4–6 mm), 10.9% (length of 6–8 mm), and 5.4% (length of 8–10 mm), respectively.

The relation between maximum stress values and implant length showed a similar trend as for the variable diameters (Fig. 3C and D). However, compared with the results for varying implant diameter, there was a smaller effect of implant length on stress in the orbital bone. In model 1, the maximum stress value in the bone around the orbital implant with a length of 4 mm was 28.8% smaller than the length of 3 mm implant. The reductions of the maximum stress values were 19.2% (length of 4–6 mm), 9.6% (length of 6–8 mm), and 4.3% (length of 8–10 mm) respectively. In model 2, the reductions of the maximum stress values in the bone around the orbital implant were 35.5% (length of 3–4 mm), 21.1% (length of 4–6 mm), 10.9% (length of 6–8 mm), and 5.4% (length of 8–10 mm) respectively.

DISCUSSION

Three-dimensional finite element analysis is a numerical stress analysis technique that is widely used to study engineering and biomechanical problems.¹² This technique has the following advantages: it is noninvasive; the amount of stress experienced at any given point can be theoretically measured; the material properties of craniofacial structures can be assigned to the nearest one that possibly can simulate this environment in vitro; the point of application, magnitude, and direction of a force may easily be varied to simulate a clinical situation; reproducibility does not affect the physical properties of the material involved; and the study can be repeated as many times as the operator wishes. The results of the finite element analysis computation depend on many individual factors, including material properties, boundary conditions, interface definition, and also on the overall approach to the model.

The orbital implant failure rate is high (between 35% and 75% after 3–14 years of follow-up). In general, bone sites in the orbital region are thin and irregular. They are often heavily compacted, with little or no marrow, and may lack the blood supply necessary to maintain an adequate bone–implant interface.^5–8 Therefore, it is the guarantee for long-term success rate of orbital implant to choose an appropriate orbital implant, provide a reasonable biomechanical environment for orbital implant osseointegration, and ensure stable bone–tissue interface around the implant. In which length and diameter of implant are very important factors.

At present, there are still no reports about 3D finite element mechanical analysis of orbital implant in craniofacial structures. Orbital implant material, surgical operation, and implant osseointegration are almost the same with dental implantation. As for the differences between these 2: the orbital implants have different length and diameter; the external loading of implants has different intensity and direction.

Literatures possess different viewpoints about the influence of diameter and length on stress distribution of bone around the dental implant. According to some researches, bone interface stress will be greatly affected by jaw height rather than the dental implant length.¹³ There is no significant difference in the maximum stress between the short implant and the long implant.¹⁴ However, according to some other studies, the peak value of implantation torsion and bearing capacity for lateral force have obvious correlation with implant length and diameter.¹⁵ Length and diameter of implant is closely related to long-term success rate of implant and short implant has a higher failure rate.¹⁶ According to this study, with the increase of implant length and diameter, maximum stress value at 2 models reduces, but the decrease value has a difference among different implant lengths and diameters. When the implant length rises from 3 to 4 mm or diameter rises from 3 to 3.75 mm, the maximum stress value reduces obviously at 2 models; when the length increases from 6 to 8 mm and 10 mm or diameter increases from 4.2 to 5.0 mm and 6.0 mm, the maximum stress value does not decrease obviously. As for the reason, the increased length and diameter of implant are mostly located in cancellous bone and it does not bear much stress distribution; stress distribution of orbital implant is mainly in cortical bone.

This research result also shows that in selection of orbital implant, there is no need to deliberately increase the implant length and diameter. Meanwhile, it is feasible to apply short orbital implant, but implant of 3 mm possesses a high stress, so the orbital rim with thick compact bone (1, 4, and 5 o’clock positions for a left eye and 7, 8, and 11 o’clock positions for a right) should be selected according to the circumstances. The results of this simulation study have shown that orbital implant diameter was more important for improved stress distribution than length. These likely result from the fact that stress distribution inside the bony socket is uneven, the elements exposed to maximum stress are located around the neck,¹⁷ and therefore, the wider area in the cervical portion of the implant may better dissipate the external forces.

In clinical operation, orbital implant is often inserted perpendicular to the orbital rim, the directions of multiple implants parallel are not necessary. The presented study shows that maximum stress was located around the root of the orbital implant when the loading along the long axis of the implant or between the neck and the first thread of the orbital implant when the loading along an angle of 45° with the long axis of the implant. This result indicated that the direction of orbital implant can be adjusted to reduce implants neck stress concentration, and gain a reasonable stress distribution. In this way, long-term success rate of the orbital implant should be improved.

According to this research result, there are significant differences in the maximum stress in orbital bone when the loading with different directions on the implants of the same length and diameter. This result shows that loading directions have obvious effect on stress distribution of the interface. Further study is required as for the specific influence of orbital implant loading directions on stress distribution.

Matsuura et al¹⁸ reported on cadavers that at the sites corresponding to potential placement sites for implants as the fixation source for ocular epitheses, the mean length of bone was 7.8 mm and the mean width was 8.3 mm, allowing the insertion of orbital implants as described in this study.

Once orbital implants are successfully placed, 3 basic retentive systems can be used: the magnet and keeper, the ball and keeper, and the bar and clip. In clinical treatment, the magnetic retention system is more popular than the others, primarily because of the ease with which the patient can position a magnetically retained prosthesis and also because they offer better access for hygiene procedures. In this study, magnetic retention system was used. Further research to assess the behavior and stress distribution of 3 retention systems associated with implant for orbital prosthesis may be the subject of future research.

CONCLUSIONS

This finite elemental analysis of loading on orbital implant to craniofacial model should contribute to optimal orbital implant choice and placement to achieve better long-term success rate of the orbital implant. This finite element study showed that increased orbital implant diameter better decreased the stress around the implant. From a biomechanical perspective, the optimum choice was an orbital implant with no less than 4.2 mm diameter allowed by the anatomy. In this study, the effect of implant length was less notable.