Four implants of the multiunit abutment-implant connection system (Oxy Implant by Biomec S.r.l, Colico, Italy) [group A] and four monoblock implants (Oxy Implant by Biomec S.r.l, Colico, Italy) [group B] were installed in the interforaminal area of the edentulous mandible, and two different 3-D finite element models were prepared and rehabilitated with an acrylic fixed prosthesis. The anterior implants used in the models were placed straight, and the posterior implants at 30° angles (Fig. 1 and Fig. 2). A total of 6 models were obtained from each system using implants with 3.5 mm, 4.0 mm, and 4.5 mm diameters.
Dental volumetric tomography of the edentulous mandible was used to get finite element models. To optimize the 3-dimension (3-D) network structure and make it more homogeneous, generate the 3-D solid model, and the FEM analysis; Intel Xeon ® R CPU 3,30 GHz processor, 500 GB Hard disk, a computer equipped with 14 GB RAM and Windows 7 Ultimate Version Service Pack 1 operating system, Activity 880 (smart optics Sensortechnik GmbH, Bochum, Germany), an optical scanner and 3-D scanner, Rhinoceros 4.0 (Seattle, WA 98103 USA), 3-D modeling software, VRMesh Studio (VirtualGrid Inc, Bellevue City, WA, USA), and Algor Fempro (ALGOR, Inc., PA 152382932 USA) analysis program were used to model cortical bone, trabecular bone, body of implant, abutment, and prosthetic materials.
All the materials used in the program and models were considered linear elastic, homogeneous, and isotropic. As the biological properties of the materials used in the models do not have accepted universal values, the average values were obtained from the literature (Table 1).
Table 1
Properties of materials in models
|
Modulus of elasticity (GPa)
|
Poisson’s ratio
|
Acrlic resin (prosthesis)
|
2.7
|
0.35
|
Cortical bone
|
13.0
|
0.3
|
Trabecular bone
|
5.5
|
0.3
|
Titanium implant and abutment (Grade 4 titanium)
|
102.0
|
0.35
|
Titanium substructure in prosthesis (Ti-6Al-4V)
|
110.0
|
0.28
|
2.1 Bone
The edentulous mandible bone was modeled with a height of 15 mm, a thickness of 7 mm, and an interforamina range of 46 mm. The cortical bone heights in the upper and lower layers of the model were 3 mm and 2 mm, respectively. The trabecular bone height modeled between the two cortical layers was 10 mm.
2.2 Dental implants and abutments
In the multiunit abutment-implant connection system groups, conical connection implants with 3.5 mm, 4.0 mm, 4.5 mm diameters, and 11.5 mm length were used in the anterior area. The same diameter implants with 13 mm length were used in the posterior region. Also, 30° angulated multiunit abutments were used for tilted posterior implants, and straight multiunit abutments were used for anterior implants.
In the monoblock implant system groups, straight monoblock implants with 3.5 mm, 4.0 mm, 4.5 mm diameters, and 11.5 mm length were used in the anterior region. Monoblock implants with the same implant diameters, 13 mm length, and a 30° tilt were used in the posterior area.
Implants in the anterior area were installed as far as possible from each other, with a confident distance of 12 mm between implants in the posterior region. As cited by Malhotra et al. [12], the bone-implant contact given in this study was 65% to imitate immediate loading status.
2.3 Prosthesis
A minimum total prosthesis thickness of 1.5 mm is suggested for resistance to fracture [13]. In this study, a 2.2 mm thick homogeneous acrylic resin block with a 10 mm cantilever on both ends and a titanium substructure was created.
2.4 Loading procedure
A 100 N force was carried out to the anterior implants, and a 250 N force was carried out to the mesiobuccal and distobuccal ends of the cantilever in the posterior region (Fig. 3). Both axial and oblique forces angled at 30° to the long axis were applied to the force zones in each model.
2.5 Meshed models
These finite element analysis models were transferred to Algor Fempro (Algor Inc., USA) software in STL format for analysis. They were created geometrically using VRMesh software for meshing (Fig. 4).
In the meshing process, models were made of 10 node (brick type) elements as far as possible. In the regions close to the center, fewer nodes were used to complete the structure when necessary. The models were converted into solid bricks and tetrahedral elements. In bricks and tetrahedral modeling, Fempro uses 8-noded elements as much as it can and 7-node, 6-node, 5-node, and 4-node elements where 8-node elements cannot reach the required details. To obtain realistic results, considering the dimensions of the mandible bone model, we selected as many elements as possible. A total of six mathematical models were created with implants of different diameters and categorized into two main groups: the multiunit abutment-implant connection implants group (group A) and the monoblock implants group (group B). Group A implants were classified according to their diameter as follows: 3.5 mm (model-1A [M1A]), 4.0 mm (model-2A [M2A]), and 4.5 mm (model-3A [M3A]). Group B implants were classified as follows: 3.5 mm (model-1B [M1B]), 4.0 mm (model-2B [M2B]), and 4.5 mm (model-3B [M3B]). The number of elements and knots used in the created mathematical models are presented in Table 2.
Table 2
Number of nodes and number of elements in models
Models in Groups
|
Number of Nodes
|
Number of Elements
|
M1A
|
281407
|
1329234
|
M2A
|
261731
|
1286671
|
M3A
|
266199
|
1313308
|
M1B
|
320877
|
1317592
|
M2B
|
314863
|
1357176
|
M3B
|
320458
|
1396542
|
2.6 Comparative groups
The stress rates in the implants and prosthesis screws of the same diameter in the same area were compared to the stress rates in the bone under axial and oblique loading. The determined forces were applied to the force regions of the six models concurrently.
2.7 Measurements of stress and strain values
In loadings using the FEM program, von Mises standard were used to assess the tension in the implants and prosthesis screws, and maximum principal stresses were used to evaluate the tension in the cortical and trabecular bone.