1

Introduction

Tooth loss is a crucial measure of oral health, particularly for the elderly, and is followed internationally as a population oral health indicator [ ]. In Canada, a notable proportion of persons aged 60–79 years, namely 14.2 %, have self-reported experiencing suboptimal oral health [ ]. This finding is of particular significance due to the demographic trend of an aging population. It is projected that the demographic group including those aged 65 and above will have a 70 % increase in its share over the course of the next two decades [ ] (see Tables 9–12 , Figs. 23–38 ).

By 2050, China will have 400 million individuals aged 65 and older due to population aging [ ]. In the country of Japan, those who are 65 years of age or older now constitute 23 % of the total population. It is projected that this proportion will increase to 38 % by the year 2050 [ ]. In the US, Canada, Australia, and the UK, the prevalence of edentulism ranges from 6 % to 8 % for adults, increasing to 20 %–26 % for those over 65 [ ]. In India, Brazil, and Turkey, edentulism ranges from 48 % to 60 % among the elderly in low- and middle-income nations [ ].

In the US, 9.7 % of older persons became edentulous between 2006 and 2018 [ ]. From 2013 to 2018, there was a statistically significant rise in the rate of edentulism among Korean people aged 75 and above [ ]. According to the 2017–2018 Australian national adult oral health study, 8.1 % of adults between the ages of 55 and 74 were toothless [ ]. According to the WHO study on global ageing and adult health wave says, the rates of edentulism in India (16.3 %) and Russia (18 %) are quite comparable [ ]. The prevalence of severe tooth loss, as measured by age standardization, is substantially greater in Iran than it is everywhere else in the world, approximately half of Iran’s senior population is toothless [ ].

Bony changes and abnormalities in the alveolar ridge may result from periodontitis, injury, missing teeth, or agenesis [ ]. Indeed, the loss or extraction of teeth initiates a cascade of biological processes that result in the deterioration of the alveolar process, thus leading to a gradual atrophy [ ]. Research conducted on tooth loss caused by periodontitis has shown that maxillary molars are the tooth category that is most often affected [ , ].

The observed horizontal changes exhibit a range of 29 %–63 %, while the vertical changes demonstrate a range of 11 %–22 % [ ]. Loss of posterior molar roots on the maxillary sinus floor leads to increased osteoclastic activity and bone resorption, leading to additional development of the inferior side of the sinus [ ]. Resorption of alveolar bone and sinus cavity pneumatization might cause insufficient bone height for dental implant surgery [ ]. The rehabilitation of edentulous subjects with extreme bone resorption with fixed dentures can be a challenge due to inadequate bone volume to anchor standard implants [ ].

Various options documented such as bone grafting techniques, specifically block bone grafts and sinus lifting through crestal or lateral approaches [ ]. Additionally, there are non-grafting techniques available, which involve modifications of the traditional implant procedure, These modifications include implant placement in the zygomatic bone, the pterygoid process, or the maxillary tuberosity, as well as the utilization of short or tilted implants [ ].

The definition of pterygoid implant is “implant placement through the maxillary tuberosity and into the pterygoid plate [ ], which are designed to be inserted into the dense cortical bone formed by the posterior wall of the maxillary tuberosity, the horizontal process of the palatine bone, and the pterygoid process of the sphenoid bone [ ]. The pterygoid process is usually denser than the maxillary tuberosity, the utilization of this technique is recommended for the purpose of anchoring implants in maxilla with atrophic conditions [ ].

One of the most frequent complications that was recorded was bleeding that occurred during the operation, it is likely that the pterygoid muscles were injured during the implantation process, or that the pterygoid bone plate was drilled through, both of which may lead to intraoperative bleeding [ ].

Valeron et al. study reported mild venous hemorrhage occurred due to the placement of the drill a few millimeters into the retropterygoid region. The issue was resolved with the use of local hemostatic techniques [ ]. Contraindications for this treatment include a smaller mouth opening, the lack of tuberosity, and third molars that are impacted [ , ].

Wilkirson et al. study presented findings about the biomechanical characteristics of pterygoid implants in individuals with total edentulism [ ]. By doing a biomechanical analysis on pterygoid implants, enhanced treatment strategies and prospective investigations can be facilitated [ ].

Tulasne et al. first introduced the concept of pterygoid implants, which was later adopted and used by several researchers [ ]. The establishment of anchorage in the posterior atrophied maxilla is facilitated, hence promoting stability and achieving high rates of long-term success, without necessitating sinus lifts or bone transplants, the elimination of posterior cantilevers and the improvement of axial loading may be seen [ ]. The analysis of stress and strain distribution in the bone around the implant, together with biological parameters such as oral hygiene, are crucial aspects to consider in the failure process [ ]. Finite element study (FEA) is a three-dimensional numerical simulation approach often used in engineering study [ ]. The finite element method has been used to predict the stress and strain distributions in the bone surrounding a dental implant [ ]. The study aimed to determine the angle of pterygoid implant that have minimum equivalent stress and minimum equivalent strain in 10 models using the finite element analysis (FEA) technique. Three distinct load scenarios were investigated: 150- N axial loading, 50-N lateral loading, and simultaneous 150-N axial loading with 50-N lateral loading, each applied for a duration of 1 s.

The ten models, evaluated from various angles, were analyzed using finite element methodology in accordance with the Frankfort Horizontal Plane. It is a craniometric plane, defined as the horizontal plane that is established by identifying, the apex of the upper border of each external auditory canal and the inferior margin of the orbit. This plane serves as a reference for the orientation of a human skull or head [ ]. No articles studies were discovered that provide a comprehensive examination of the biomechanical characteristics, despite the existence of clinical case evaluations [ ].

2

Material and methods

This study was conducted by the approval of Non-Interventional Clinical Research Ethics Board at Yeditepe University in Istanbul under Application Number 202304Y0599.

The present study involves the reconstruction of a three-dimensional (3D) model of the human maxilla, which encompasses both cancellous and cortical bone. This model is derived from computed tomography (CT) images obtained from individuals who are edentulous, and it is used for the determination of the best angle to be the least harmful to the surrounding bone.

The study aimed to determine the angle of pterygoid implant that have minimum equivalent stress and minimum equivalent strain using the finite element analysis (FEA) technique.

In our study, we evaluated the effect of axial and lateral forces on a pterygoid dental implant placed at 5 different angle degrees (45,55,65,75,and 85), according to the Frankfort Horizontal Plane are evaluated. The implant is secured within the pterygoid plate of the sphenoid bone, passing through the maxillary and palatine bones. The angulation of the implant is determined by the inclination of the maxillary sinus floor and the height of the tuberosity bone, ranging between 45° and 85°. The anchorage of the implant is achieved using both monocortical and bicortical fixation, which was determined by the finite element analysis method (FEA). A computer equipped with an Intel(R) Core(TM) i5-1035G1 CPU @ 1.00 GHz 1.19 GHz processor, 250 GB SSD (Solid State Drive), 8 GB RAM, and a Windows 11 professional 64-bit operating system was used for arranging and making the 3D network structure more homogeneous, creating the 3D solid model, and FEA operation. The facial region of a 58-year-old male patient with atrophic maxilla was planned to be treated only with an angled pterygoid implant and was imaged in DICOM format with CT. Raw DICOM data with a section thickness of 0.3 mm was loaded.

The maxilla in millimetric sections of a completely edentulous patient was imaged in DICOM format with cone beam tomography. The DICOM file, which was obtained with 536 x 536 resolution and 0.3 mm thick sections of the raw data, was loaded into MIMICS Research 21.0 software (Materialise, Leuven, Belgium), a software with which images can be reconstructed in a computer environment. Simplification and reformatting operations were performed on the images reconstructed with the software. In MIMICS software, a 3D models of the bone tissues, separated on the sections, were created.

The 3D model was generated symmetrically using simplification techniques in the MIMICS software. Asymmetrical regions were introduced, and the model was then converted into a smooth surface composed of elements with consistent proportions. The modeling of the upper jawbone was successfully finalized and saved in the “.step” format. With the help of the 3-matic Research 13.0 program, a 3D computer-aided design model (CAD) of the pterygoid maxilla complex was obtained. ( Fig. 1 ). A pterygoid dental implant with a diameter of 3.5 mm and a length of 16 mm, conical form, and special thread design was placed with the SOLIDWORKS software (Dassault Systèmes, Vélizy-Villacoublay, France). After the modeling process was completed, a three-dimensional computer-aided design model (CAD) was obtained ( Fig. 1 ) (see Fig. 2 ).

The Frankfort Horizontal Plane is to be determined above the model.

(a) Horizontal view of pterygoid implant model image, (b) Vertical view of pterygoid implant model image

Model 1-A : Pterygoid dental implant placed with 45 angle degree monocortically in the right pterygomaxillary region ( Fig. 3 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 45° monocortically in the right pterygomaxillary region.

Model 1-B : Pterygoid dental implant placed with 45 angle degree bicortically in the pterygomaxillary region( Fig. 4 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, pterygoid dental implant placed angled with 45° bicortically in the right pterygomaxillary region.

Model 2-A : Pterygoid dental implant placed with 55 angle degree monocortically in the right pterygomaxillary region ( Fig. 5 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 55° monocortically in the right pterygomaxillary region.

Model 2-B : Pterygoid dental implant placed with 55 angle degree bicortically in the right pterygomaxillary region ( Fig. 6 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 55° bicortically in the right pterygomaxillary region.

Model 3-A : Pterygoid dental implant placed with 65 angle degree monocortically in the right pterygomaxillary region ( Fig. 7 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 65° monocortically in the right pterygomaxillary region.

Model 3-B : Pterygoid dental implant placed with 65 angle degree bicortically in the right pterygomaxillary region ( Fig. 8 ).

The elastic modulus and poisson ratio values of the materials are shown in Table 1 used in the study [ ] (see Table 2 ).

Ten models designed with the SOLIDWORKS program, 5 models monocortical pterygoid dental implant (end border of crest and cancellous bone) and 5 models bicortical (between crest and basal bone, 1 mm outside the pterygoid process) were placed at 45, 55, 65, 75, and 85 angled degrees according to the Frankfort Horizontal Plane.

The Frankfort Horizontal Plane is defined as the plane that intersects the most superior section of the “Porion” on both sides and the most inferior piece of the “Orbitale” on both sides [ ].

2.1

Created models

Implants are placed at 45, 55, 65, 75, and 85 angled degrees according to the Frankfort Horizontal Plane, monocortically in 5 models and bicortically in 5 models, as follow.

Model 1-A has an angle of 45° according to the Frankfort Horizontal Plane and is monocortical.

Model 1-B has an angle of 45° according to the Frankfort Horizontal Plane and is bicortical.

Model 2-A has an angle of 55° according to the Frankfort Horizontal Plane and is monocortical.

Model 2-B has an angle of 55° according to the Frankfort Horizontal Plane and is bicortical.

Model 3-A has an angle of 65° according to the Frankfort Horizontal Plane and is monocortical.

Model 3-B has an angle of 65° according to the Frankfort Horizontal Plane and is bicortical.

Model 4-A has an angle of 75° according to the Frankfort Horizontal Plane and is monocortical.

Model 4-B has an angle of 75° according to the Frankfort Horizontal Plane and is bicortical.

Model 5-A has an angle of 85° according to the Frankfort Horizontal Plane and is monocortical.

Model 5-B has an angle of 85° according to the Frankfort Horizontal Plane and is bicortical.

The CAD models were imported to the FEA software ANSYS program for the purpose of creating loading conditions (Workbench 19.2; ANSYS Inc., Providence, RI, USA). The network structure with this software (mesh) is formed, pterygoid implant and bone contact surfaces have an edge length of 0.5 mm, the rest of the model was divided into a 2 mm tetrahedral structure ( Fig. 14 ). The average number of elements in the models was determined as 59044, and the number of nodes was determined as 102132. This helps to avoid errors and ensures that the model accurately represents the physical system being analyzed (see Fig. 13 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 65° bicortically in the right pterygomaxillary region.

Model 4-A : Pterygoid dental implant placed with 75 angle degree monocortically in the right pterygomaxillary region ( Fig. 9 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 75° monocortically in the right pterygomaxillary region.

Model 4-B : Pterygoid dental implant placed with 75 angle degree bicortically in the right pterygomaxillary region ( Fig. 10 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 75° bicortically in the right pterygomaxillary region.

Model 5-A : Pterygoid dental implant placed with 85 angle degree monocortically in the right pterygomaxillary region ( Fig. 11 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 85° monocortically in the right pterygomaxillary region.

Model 5-B : Pterygoid dental implant placed with 85 angle degree bicortically in the right pterygomaxillary region ( Fig. 12 ).

(a) Frontal view, (b) Lateral view, (c) Occipital view, Pterygoid dental implant placed angled with 85° bicortically in the right pterygomaxillary region.

The CAD models were imported to the FEA software ANSYS program for the purpose of creating loading conditions (Workbench 19.2; ANSYS Inc., Providence, RI, USA). The network structure with this software (mesh) is formed, pterygoid implant and bone contact surfaces have an edge length of 0.5 mm, the rest of the model was divided into a 2 mm tetrahedral structure ( Fig. 14 ). The average number of elements in the models was determined as 59044, and the number of nodes was determined as 102132. This helps to avoid errors and ensures that the model accurately represents the physical system being analyzed.

(a) Edentulous maxilla and surrounding bone model image with network structure (b) Pterygoid implant model image with network structure.

Image of the regions where the model is fixed

Three different load scenarios were explored to simulate stress and strain with the following conditions [ ]: 150-N axial loading and [ ] 50-N lateral loading and [ ] 150-N axial loading with simultaneous 50-N lateral loading. The loadings were evenly applied to the occlusal surface over the abutment ( Fig. 15 ) ( Fig. 16 ).

The Ti-6Al-4V alloy was selected as the implant material for the pterygoid implant. The elastic modulus of that alloy was determined as 110,000 MPa and the Poisson ratio was determined as 0.33 [ ]. The contact surfaces between the implant body and bone were deemed to have connected, indicating osseointegration [ ]. Each DOF (degree of freedom) from the lower and lateral regions of cortical and trabecular bone, fixed to have ‘0′ motion, creates direct boundary conditions. Prior to applying force, the boundary conditions of the maxilla are established. The maxilla is a bone in the human skull that forms the upper jaw and contains the upper teeth. Due to its elastic nature, both the cortical and cancellous bones exhibit linear and homogenous characteristics [ ]. So the fixation was performed on the zygomatic region. ( Fig. 15 ).

(a) Lateral view of axial direction, (b) Lateral view of lateral direction, the application direction and the image of the implant relationship with the application area.

The analysis of monocortical vs. bicortical fixation of implants was performed using the ANSYS FEA software to create loading conditions (Workbench 19.2; ANSYS Inc., Providence, RI, USA). The monocortical pterygoid dental implant is located at the end border of the crest and cancellous bone, while the bicortical implant is situated between the crest and basal bone, 1 mm outside the pterygoid process. Three different load scenarios were explored to simulate stress and strain with the following conditions [ ]: 150-N axial loading and [ ] 50-N lateral loading and [ ] 150-N axial loading with simultaneous 50-N lateral loading ( Fig. 16 ) ( Fig. 17 ) [ ]. The loadings were evenly applied to the occlusal surface over the abutment [ , ].

(a) Frontal view of axial direction, (b) Frontal view of lateral direction, the application direction and the image of the implant relationship with the application area.

Maximum stress in the implant and surrounding bone for each model under 150N axial loading.

The operator personally inputted data for all angles in our study. We consistently applied the same dataset across all six angles, ensuring uniformity in the analysis. The only variable was the angle itself, while all other input parameters remained identical.

We evaluated each of the six angles in our study using two different placement methods: monocortical and bicortical. This approach means that each angle was effectively replicated twice. We applied the loads separately to each angle in both placement methods. We assessed each angle in two configurations, applying the loads 12 times in total to ensure comprehensive evaluation across all conditions (see Table 3 ).

Table 3

Von Mises Stress and location under 150N axial loading.

Models	Maximum stress in implant MPa	Maximum stress in implant location	Maximum stress in bone MPa	Maximum stress in bone location
1-A	515.64	Abutment connection area of the pterygoid implant	125.81	Crestal bone at pterygoid implant
1-B	672.82	Abutment connection area of the pterygoid implant	137.97	Crestal bone at pterygoid implant
2-A	278.35	Abutment connection area of the pterygoid implant	92.282	Crestal bone at pterygoid implant
2-B	321.86	Abutment connection area of the pterygoid implant	88.64	Crestal bone at pterygoid implant
3-A	248.8	Abutment connection area of the pterygoid implant	60.799	Crestal bone at pterygoid implant
3-B	240.02	Abutment connection area of the pterygoid implant	54.578	Crestal bone at pterygoid implant
4-A	148.97	Abutment connection area of the pterygoid implant	43.028	Crestal bone at pterygoid implant
4-B	164.57	Abutment connection area of the pterygoid implant	116.19	Crestal bone at pterygoid implant
5-A	75.898	Abutment connection area of the pterygoid implant	110.52	Crestal bone at pterygoid implant
5-B	89.163	Abutment connection area of the pterygoid implant	29.927	Crestal bone at pterygoid implant

 

The ethical approval documentation is attached as supplementary material.

No funding was received for this study.

3

Results

• A.

  Maximum and minimum stress values on surrounding bone

Von Mises Stress values on the surrounding bone of all models under three forces are shown in Table 4 , ( Fig. 18 ).

Table 4

Von Mises Stress and location under 50N lateral loading.

Models	Maximum stress in implant MPa	Maximum stress in implant location	Maximum stress in bone MPa	Maximum stress in bone location
1A	211.79	Abutment connection area of the pterygoid abutment	58.154	Crestal bone at pterygoid implant
1B	348.69	Abutment connection area of the pterygoid abutment	82.317	Crestal bone at pterygoid implant
2A	159.59	Abutment connection area of the pterygoid abutment	62.027	Crestal bone at pterygoid implant
2B	175.74	Abutment connection area of the pterygoid abutment	59.884	Crestal bone at pterygoid implant
3A	172.77	Abutment connection area of the pterygoid abutment	51.187	Crestal bone at pterygoid implant
3B	225.03	Abutment connection area of the pterygoid abutment	43.378	Crestal bone at pterygoid implant
4A	158.18	Abutment connection area of the pterygoid abutment	48.522	Crestal bone at pterygoid implant
4B	184.49	Abutment connection area of the pterygoid abutment	51.019	Crestal bone at pterygoid implant
5A	222.43	Abutment connection area of the pterygoid abutment	53.076	Crestal bone at pterygoid implant
5B	278.52	Abutment connection area of the pterygoid abutment	51.888	Crestal bone at pterygoid implant

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