Geometrical effects of orthodontic miniscrew implants and resulting distortion stresses in a simulated bone model for different applied forces: An FEM study

Om Prakash Kharbanda, Naresh Bhatnagar, Vilas D. Samrit, Avinash Kumar, Sumit Yadav, Sneh Anand

1.Chief, Centre for Dental Education and Research, Professor and Head, Division of Orthodontics and Dentofacial Deformities, Centre for Dental Education and Research

2.Professor, Department of Mechanical Engineering, Indian Institute of Technology Delhi

3. Associate Professor, Division of Orthodontics and Dentofacial Deformities, Centre for Dental Education and Research, New Delhi, India

4. Trainee, Shalya Medical Technologies, Indian Institute of Technology Delhi, New Delhi, India
5. Assistant Professor, Department of Orthodontics, Dental School, Connecticut Health Sciences Centre, Connecticut, USA 
6.Professor and Head, Department of Biomedical Engineering, All India Institute of Medical Sciences, 
 New Delhi, India
ABSTRACT

Introduction: This study investigated the influence of orthodontic miniscrew implant (MSI) design and diameter on stresses in MSI and peri-implant bone with application of varying the amount of tangential orthodontic force, using finite element method (FEM). 

Materials and Methods: Three dimensional, finite element models of bone with four MSIs (6 mm in length, with diameters 1.2 mm and 1.4 mm each, cylindrical and tapered in shape) were created. The effect of four forces 50 cN, 75 cN, 100 cN and 150 cN were evaluated by applying them in the head region perpendicular to the MSI axes. 

Results:  On loading the MSI, highest von Mises stress levels were seen in the neck region of the MSI. The cortical bone in contact with the neck of the MSI showed high von Misses stresses while cancellous bone around the body of the MSI showed the least. Alteration in diameter from 1.2 mm to 1.4 mm or shape (cylindrical vs taper) of the MSI did not affect the stress levels with the range of forces 50, 75, 100 and 150 cN. 

Conclusions: The cortical bone around MSI at the neck region, and MSI at the neck is subjected to maximum von Mises stresses on loading with orthodontic forces in the range of 50 to 150 cN force levels. Keywords: MSI, peri-implant bone, von Mises stress, FEM, Orthodontic force

Keywords: MSI, peri-implant bone, von Mises stress, FEM, Orthodontic force 

INTRODUCTION

In the last two decades, clinical and laboratory research has evolved the successful use of orthodontic miniscrew implants (MSIs) as a significant addition to orthodontic armamentarium. MSIs have been advocated for use as absolute anchorage savers in the treatment of various malocclusions. With an effectual foundation of laboratory and clinical research on anatomical limitations posed by the dentate mouth, tactical implant sites in the mouth, the intended mechanical advantages desired, a variety of MSIs in combinations of varying length, diameter, and shapes have been designed. More so, these are commercially available for use by the orthodontists. 

The excellence of anchorage provided by the MSI primarily depends upon its stability and the biomechanical leverage provided by it to the orthodontic appliances in use. When mechanical force is applied on the MSI, it produces stress in the surrounding bone causing deformation of their structural arrangement.The process of insertion of MSI and its loading also produces a mechanical and biological reaction in the surrounding bone.The clinical success of the MSI depends on the manner in which mechanical stresses are transferred to the surrounding bone after loading the MSI. Also, the technique of MSI placement and the amount of bone necrosis produced during insertion greatly influences the biological response of the host to MSI. Moreover, the loading protocol and the amount of force applied in specific directions also influences these responses greatly. Hence, it becomes necessary to understand that after loading how does the geometry of the MSI influence stress distribution or concentration of stresses, both on the MSI and the surrounding bone.

Finite element method (FEM) has been extensively used as an analytical tool to study the pattern of stress in and around prosthetic implants. Lately, this tool is also being used with respect to orthodontic MSIs. Studies have been performed to assess force distribution following load application to dental implants of different design configurations and dimensions. Findings of various authors on stress 

around implants with tapered and cylindrical geometries are contentious.Similarly, views regarding the effect of cortical bone thickness on stresses generated are discordant. Many authors found stress distribution in the bone to be more sensitive to implant diameter than the implant length. While a larger diameter can efficiently reinforce the initial stability of the MSI, the proximity of the roots at the implant site limits the possible increase in diameter in clinical use.

Unlike prosthetic implants, MSIs are designed to serve as non-osseointegrated devices for only a limited term during orthodontic treatment. Orthodontists commonly use either tapered or cylindrical MSIs, ranging from 1.0 mm to 2.3 mm in diameter and 6 mm-12 mm in length. Research suggests that MSIs of 1.2 mm-1.6 mm diameter in the length of 7-8 mm are generally successful in interdental areas. Though many investigators studied the stress pattern around the MSI,[18-21] only a few studies have investigated the stress distribution at the MSI itself. Therefore, in the present study, the influence of MSI shape and diameter on stresses in MSI and peri-implant bone was investigated by varying the amount of tangential orthodontic force, using finite element method (FEM).  Also, the location and pattern of stress distribution in MSI and the peri-implant bone was studied.

 
MATERIAL AND METHODS

Orthodontic MSIs (AbsoanchorTM, Dentos Inc, Korea) of 6 mm length and 1.2 mm and 1.4 mm in diameters were used for this study. These MSIs were tapered and cylindrical in shape and were made of titanium alloy (Ti6Al4V). The tapered and cylindrical MSIs were converted into a solid model with the ProEngineer Wildfire software version 4.0. The model was then imported into the finite element environment.

A model of cortical and cancellous bone (10X10X10mm) was created for the finite element analyses. In the bone model, cortical bone was 1 mm thick, and rest of the bone had a property of cancellous bone to simulate the maxillary bone. The tapered and cylindrical MSIs were placed in the middle of the bone models, aligned at 90 degrees and were superimposed to form the assembly (Figure 1). A hole was created in each bone block using Boolean subtraction. The assembly was imported into ANSYS 12.0 and the material properties of cortical bone, cancellous bone and MSI were assigned. The elastic modulus of the cortical bone, cancellous bone and MSI was 14.7 GPa, 1.3 GPa and 110 GPa, whereas the Poisson’s ratio was 0.3, 0.3 and 0.33 respectively. All material properties used in creating the model in this study were homogeneous, isotropic and linearly elastic. Miniscrew and bone block models were meshed using tetrahedral elements. There were 19577 elements for cortical bone and 91341 for cancellous bone. Furthermore, there were 32639 nodes in the cortical bone and 133981 nodes in the cancellous bone. The total number of elements ranged from 164778 to 207945, and the number of nodes ranged from 245767 to 310783, depending on the size of the miniscrew model. The mesh was refined, and the element size in the region of interest was reduced. The relationship between miniscrew and bone models were defined as bonded assuming 100% bone to miniscrew contact. Fixed boundary conditions were applied to immobilize all sides and the bottom surface of the bone blocks. The four forces of increasing magnitude (50 cN, 75 cN, 100 cN and 150 cN) were applied to the head region of the MSIs perpendicular to their long axes and the effects were analyzed. 

Geometrical-effects_figure-1
Figure 1: MSI-bone assembly. The MSI is placed perpendicular to the cortical bone surface and force applied perpendicular to its long axis.
RESULTS

The stress appeared to be distributed around the neck of the MSI, at the cortical bone and cancellous bone. Regardless of diameter and shape of MSI, increase in applied force magnitude, resulted in the increase in von Mises stress values of the cortical bone, cancellous bone and the neck of the MSI. Highest von Mises stresses were focused in the neck region of MSI adjacent to the cortical bone, followed by cortical bone. (Table 1). 

von-Mises-stress-in-MSIs-cortical-bone-and-cancellous-bone-at-different-level-of-forces
Table 1: von Mises stress in MSIs, cortical bone and cancellous bone at different level of forces (values in MPa)
Stress distribution in bone

Within the same shape of the MSI, von Mises stress in cortical bone was greater with 1.4 mm diameter miniscrew as compared to the 1.2 mm diameter MSI; however, von Mises stress in cancellous bone was greater with 1.2 mm diameter in comparison to 1.4 mm diameter MSI. When cylindrical and tapered MSIs of the same diameter were compared, both shapes generated the similar amount of von Mises stresses in the cortical bone. von Mises stresses in cancellous bone were also similar with 1.2mm and 1.4mm cylindrical and tapered MSIs. von Mises stress distribution pattern in the bone was similar for all types of MSIs used in this study. In all models, maximum von Mises stress occurred around the MSI neck at the cortical bone- MSI interface (Figures 2A, 2B).

Geometrical-effects_figure-2a
Figure 2a: Stresses in bone around tapered MSI for 150cN
Geometrical-effects_figure-3b
Figure 2b: Stresses in bone around cylindrical MSI for 150cN
Stress distribution in MSI

In MSIs, von Mises stresses were more in 1.4 mm diameter MSIs of both cylindrical and tapered shapes. When shapes were compared, von Mises stresses were more in tapered MSIs of the same diameter. Similarly, an identical pattern of stress distribution was observed in all the four MSI models.(Figures 3A, 3B). Maximum von Mises stress occurred at MSI neck adjacent to the cortical bone. Irrespective of diameter or shape of MSIs, the location of peak stress was in the groove of the thread (Figure 4 and 5).

Geometrical-effects_figure-3a
Figure 3a: Von Mises stress in tapered MSI for 150cN
Geometrical-effects_figure-3b
Figure 3b: Von Mises stress in cylindrical MSI for 150cN
Geometrical effects_figure 4
Figure 4: The location of zones with higher stress around the MSI neck for 150cN
Geometrical-effects_figure-5
Figure 5: Bending of the MSI for the different loads
DISCUSSION

For the purpose of finite element analysis, all materials were considered homogeneous, isotropic and linearly elastic, although bone is neither homogeneous nor isotropic. For simplicity and to represent the best possible relation between the bone and the MSI, 100% bone MSI contact was assumed. Previous studies on orthodontic MSIs have reported that the stresses are not generated beyond 4.2 mm from the site of MSI placement, therefore a finite element model of dimensions 10x10x10 mm was considered suitable for this experiment. In this finite element model, the cortical bone thickness was maintained as 1 mm to ensure MSI stability.

Elevated von Mises stress levels were located at the MSI neck for the studied MSIs at four levels of force applied. This phenomenon is supported by various studies, which concluded that the regions of bone exposed to maximum stresses are located around the MSI neck which is in close proximity to the cortical bone. Also, the stress in MSI is mostly concentrated around the part adjacent to the cortical bone.[10,19,21,25-30] Cortical bone with high elastic modulus compared to cancellous bone and in contact with the neck of the MSI serves as a fulcrum for the MSI at neck region. Higher distortion stresses are therefore induced in this neck region of MSI resulting in bending pattern at the neck of MSI (Figure 5). Similarly, in the cortical bone, highest stress concentration was observed in the area in contact with the MSI neck, near the fulcrum of MSI bending. Since the cortical bone had a much higher elastic modulus than the cancellous bone, most of the stress is expected to be cushioned /absorbed by the cortical bone. Therefore we postulate that the differences in MSI length and shape in its lower part should not influence the stress distribution pattern. Previous finite element studies have also proved that change in length of the MSI does not influence the bone stress location. The major role of cortical bone for the stress distribution has also been explored. The higher stress around the MSI neck may indicate a danger of overloading and breakage of MSI at the neck region. Yun et al. found that the stress of about 2 MPa in  peri

implant bone had a positive effect on new bone formation, osseointegration and bone-implant interface of immediately loaded dental implants while bone loss was noticed in some specimen with stress exceeding 4 MPa. In contrast to this, Sugiura et al. reported the critical threshold of compressive stress of ~50 MPa to induce bone resorption around screws by measuring the changes in stress-bearing bone of mini plates and simulation of stresses loading the bone around the screws using 3D FEM. However, in our study the stresses in the cortical and cancellous bone are of low magnitudes and seemingly direct comparison with either dental implants or bone plate screws may not be a truly reflected in terms of its biological effects on alveolar bone. In the present study, the stress distribution pattern for the cylindrical and tapered MSIs was similar. Hence it can be concluded that the MSI shape, i.e., tapered or cylindrical, for similar thread design did not greatly influence the von Mises stress distribution probably because the MSI neck had the same shape and the diameter along with the similar pattern of stress transfer to the surrounding bone. In a similar study, Duaibis et al. found that the taper had minimal effect on the stresses in the bone, though the cylindrical MSI had caused less stresses in cortical bone than the tapered MSIs. It has been reported that by increasing the diameter of the MSI, stress on the cortex has been decreased. This is based on the second moment of inertia of a cylinder which states that under bending, the peak stress is inversely proportional to the third power of the diameter. However, this work substantiates that the diameter considered in the range of experiments (i.e. 1.2 mm to 1.4 mm) does not yield substantial differences in the von Mises stress values as well as the site of the failure. 

One interesting phenomenon observed in this study was the location of maximum distortion stress in the MSI. The maximum distortion stresses are constantly observed in the groove of the threads of the MSI, adjacent to cortical bone. The stress distribution of this nature also indicates the possibility of future failure of the MSI. It is suggested that the modification in thread structure in the part of MSI, which assumes contact with cortical bone, are warranted for effective load transfer. This information can be applied in designing MSI in future.

The results are based only on FEM on a bone stimulated model,that does represent the actual behaviour of MSI in vivo; however, these findings do enhance understanding of the accumulation of the stresses in the miniscrew and surrounding bone. The results need to be validated by other mechanical or biological findings before extrapolating to the human alveolar bone.


CONCLUSIONS

1. The cortical bone around MSI at the neck region, and MSI at the neck is subjected to maximum Von misses stresses on loading with orthodontic forces in the range of 50 to 150 cN force levels.

2. The MSI in contact with cancellous bone and bone itself bear least von Misses stresses

3. Increasing the force magnitude (from 50 cN150 cN) increases the intensity of stresses in MSI and the surrounding cortical bone.

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