Three-Dimensional Finite Element Analysis of Fixed Complete-Arch Prostheses Supported by 4 Immediate-Loaded Implants in the Completely Edentulous Maxilla Using Clinical Computerized Tomography Data

Previous osseointegration-type implants typically required 3–6 months for healing after implant placement to achieve strong osseointegration.1 In the classic protocol of implant treatment, this healing period prolongs the treatment period and involves inconvenience to patients having to use a temporary prosthesis. To overcome these problems, immediate loading on implants has recently been reported,2–4 but fewer reports have described immediate loading on conventional implants, particularly in the maxilla.5 No reported study has clarified the basis of immediate loading and conditions by mechanical analysis, and investigations of treatment and indication are lacking.

Recently, computer-based simulation of oral implant treatment is a great step ahead, allowing for the precise prognosis and optimization of the performance of oral implants, with all the flexibility of a computerized model: changing dimensions, materials, and loads without the necessity of using a real patient or creating a real model. One other great advantage, besides the flexibility of computer-based prototyping, is the ability to evaluate the design's response in anatomical features of each patient using X-ray computerized tomography (CT) data. In this study, we prepared a computer-based 3-dimensional finite element analysis (FEA) model based on preoperative CT data and constructed a stress analysis system in a maxillary edentulous patient who underwent the placement of 4 implants, followed by provisional restoration for immediate connected loading. We then investigated the effect of connected fixation and the utility of this method through its application in a clinical case. Mechanical simulation by loading an occlusal force (load), assumed to be that loaded under clinical conditions, was performed in the CT data-based implant placement simulation. Then stresses on and displacements of the implants and surrounding bone tissue were mechanically analyzed using 3-dimensional FEA to investigate the possibility of practical preoperative design, its evaluation, and assessment of the effects of connected fixation.

A flowchart of the method is shown in Figure 1. First, a 3-dimensional simulation model of the bone shape was prepared from CT data, following current procedures.6,7 X-ray CT images of the head were acquired from a 69-year-old woman under standard X-ray CT acquisition conditions (tube voltage, 120 kV; tube current, 200 mV; slice width, 1 mm; stored in digital imaging and communication in medicine [DICOM] format) at the Department of Radiology, Kyushu Dental College. The target hard tissue alone was extracted from the CT data using Simplant Pro (Materialise Dental Japan, Chiba, Japan), and a 3-dimensional bone model was prepared.

The CT data of the human head were handled anonymously, with appropriate ethical considerations. The study was explained to the subject, and consent was obtained for the use of the CT data in this study.

Implant placement was simulated using the 3-dimensional bone model prepared above. Implants were placed in the bilateral upper incisor and premolar regions, with 4 implants in total. The implants used were Branemark System Mk IV TiU (Nobel Biocare AB, Göteborg, Sweden): 11.5 mm long and 4.0 mm in diameter for the bilateral upper incisor regions (the left and right sides were designated as #22 and #12, respectively) and 13 mm length and 4.0 mm in diameter for the premolar regions (the left and right sides were designated as #25 and #15, respectively). The placement angles were decided by the standard method, referring to the maxillary bone morphology and mass. The angle from the occlusal surface in the sagittal plane was 89° for #15 and #12, 66° for #22, and 114° for #25, and that in the frontal plane was 85° for #15, 76° for #12, 97° for #22, and 104° for #25 (Figures 2–4; Table 1).

The material properties and loading conditions are shown in Figure 5 and Tables 2 and 3. Implant placement was simulated in a maxilla model prepared from the CT data, and this simulation model was divided into the maxillary region (cortical and cancellous bones and soft tissue) and implant region (implants and connector) to prepare a 3-dimensional finite element model.

A 3-dimensional model was constructed from the placement simulation model designed in Simplant Pro and the CT DICOM data using 3D Bon (Ratoc, Tokyo, Japan) and Mimics (Materialise Japan, Yokohama, Japan), from which a 3-dimensional FEA voxel model was prepared using Voxelcon (Quint, Tokyo, Japan). The voxel size was 0.5 mm, and the number of voxels was about 720 000. The material properties of the cancellous and cortical bones, soft tissue, implants, and connector are shown in Table 2. Regarding the loading condition, the 4 implants undergoing individual loading were regarded as the control group (individual loading), and those undergoing connected loading were the test group (connected loading). A 100-N vertical force was loaded on each implant on individual loading (400 N in total; control group). On connected loading (test group), a 400-N vertical force was loaded on all connected implants, and the whole upper skull was restrained.8 On analysis, the von Mises stresses on the implants and surrounding tissue were determined, with the stress distribution presented using contours. The distance of displacement in the region with maximum stress loading is presented as the maximum displacement.

The results of the 3-dimensional FEA are given in Figures 6–9. As indicated in the color legend bar, 10-MPa or greater von Mises stresses are shown in red, 0-MPa in blue, and intermediate values as gradations in color between the two.

In the #15 right premolar region, large stresses were loaded on the implant fixture, mesial cortical bone region, and maxillary sinus wall on connected loading (test group). In proximity to the implant and maxillary sinus base, stress was widely distributed. On individual loading (control group), large stresses were concentrated in narrow regions in the implant fixture, mesial cortical bone region, and part of the mesial maxillary sinus wall compared with those in the test group.

In the #12 right incisor region, large stresses were distributed in the implant fixture, with weak stresses around the implant in both the test and control groups. Stress was more markedly concentrated in the implant region corresponding to the root apex in the control than in the test group.

In the #25 left incisor region, a large stress was loaded on the implant fixture, while weaker stresses were distributed in the medial cortical bone region and entire maxillary sinus wall in the test group. In the control group, large stresses were distributed along the placement direction on the implant fixture, mesial cortical bone, and the whole maxillary sinus wall. The distribution of high stress was marked compared with that in the test group.

In the #22 left premolar region, a large stress was loaded on the implant fixture, while weaker stresses were distributed around the implant in both groups.

The maximum displacements of the individual implants are shown in Figure 10 and Table 4. In the control group (individual loading), the maximum displacements of #15, #12, #22, and #25 were 185, 180, 145, and 60 µm, respectively. The largest maximum displacement was noted in the #15 upper incisor region, and the smallest in the #25 premolar region, which was about one-third of the largest value.

In the test group (connected loading), the maximum displacements of #15, #12, #22, and #25 were 30, 40, 25, and 20 µm, respectively. The largest maximum displacement was noted in the #12 upper incisor region and the smallest in the #25 premolar region. These were about one-ninth and one-third of the largest and smallest displacements, respectively, in the control group.

The spread of X-ray CT instruments and their application has recently progressed in the medical and dental treatment fields. Under current dental treatment conditions, the current preoperative planning and designing of implant placement based on bone morphology and mass by X-ray CT are important methods, considering the anatomical morphology of individual cases, and they are essential for achieving safe, reliable implant placement and favorable outcomes.

This method started with the evaluation of 2-dimensional X-ray CT data of the jaw bones and has progressed to 3-dimensional image construction and placement simulation. Placement simulation facilitates the selection of implants and investigations on the direction and depth of placement corresponding to the specific anatomical morphology, which varies by individual. Its usefulness for various applications has been acknowledged, such as clarification of the application range, the design and establishment of a preoperative plan, and sharing of consensus conditions.

However, although this procedure has become routine, evaluation and investigation of an important factor of implant treatment, functional ability (ie, mechanical factors), are lacking. Thus, although a preoperative plan and design meeting anatomical and morphological conditions can be simulated, whether the design is actually sufficiently functional, both mechanically and in terms of safety, has not been investigated, which may lead to an unfavorable outcome in cases with possible overloading, such as a large occlusal force and the presence of many defective regions.

The implant placement simulation model constructed from the CT data by our method and mechanical assessment of this model using a 3-dimensional FEA may facilitate the planning, design, and evaluation of preoperative implant placement simulation for individual bone morphologies from not only an anatomical but also a mechanical viewpoint.9 

All processes, from the acquisition of bone morphology data to mechanical analysis, can be performed without contact or destruction, which is clinically useful.10,11 Generally, mechanical measurements are performed under conditions in which the test material is damaged or destroyed because a force is actually loaded on the test material to measure stress and strain; such a destructive mechanical evaluation, however, is clinically impossible. Moreover, the measurement of internal stress in tissue is difficult and analysis impossible because bone tissue has a complex morphology (as noted in cancellous bone), and the addition of properties of multiple materials such as hard and soft tissues is necessary for analysis.

However, mechanical assessment of the bone model constructed from CT data using the 3-dimensional FEA overcame these problems, suggesting that this method may be useful for the preoperative simulation of custom-made implants corresponding to individual cases. We acquired X-ray CT images of the human maxilla prepared for a preoperative plan and designed an implant placement using this method in an actual clinical case. We then analyzed these from both anatomical and mechanical viewpoints to investigate its usefulness.

Duyck et al12 reported that for prostheses of the entire dentition, an arrangement to support the prosthesis at the 4 corners, the frontal tooth, and molar regions achieved the highest success rate. In the design for the present case, 2 mesial and distal implants, 4 in total, were arranged as cornerstones and connected to support a fixed-type implant bridge.13 In this design, the implants act structurally as a cantilever in the labio-bucco-lingual direction because they are placed on the medial side of the prosthetic arch. Ninety percent and 10% of the force loaded on the cantilever are transmitted to the implant closest to the defective region and its adjacent implants, respectively, and no force is loaded on implants apart from these. Accordingly, 2 implants are sufficient to support the cantilever, and increasing the number of implants is useless. Thus, we simulated the placement of 4 implants.5,14 

By presenting stresses as contours, the levels, sites, directions, and distribution or concentration of stresses on implants and the surrounding tissues can be judged and evaluated at a glance, indicating that this method is simple and objective for clinical evaluation.8,15 

The von Mises stresses were determined as stresses produced by loading. An occlusal force loads various stresses on implants and their surrounding tissue, such as compressive, tensile, and shear stresses. Thus, which stress is adopted for the evaluation is important. von Mises stress is useful for the relative comparison of multiple mechanical conditions because its values reflect the influences of various stresses.16 

The angle between the placement and loading directions was large at #25. On individual loading (control group), the placement condition was directly reflected in the stress distribution, resulting in large stresses along the placement direction. In contrast, on connected loading (test group), stress was distributed widely over the entire maxillary sinus wall. This may have resulted from the connection, which fixed the implant placement and loading in different directions and dispersed the stress (dispersion of load vector).

The angle from the occlusal plane was almost vertical (ie, the angle difference was small between the placement and loading directions) at #15, #12, and #22, and large stresses were loaded on the implant and cortical bone region on individual loading (control group). No marked difference was observed in the stress distribution at #12 and #22 between the test and control groups. The effect of load dispersion may have been small due to the influence of the placement angle (ie, the placement and loading directions were close).

What is an acceptable level of microdisplacement (micromovement) for osseointegrating implants? It varies among reports from 30 µm17 to 50–150 µm18 or 100 µm.19 Microdisplacement is also reported to be affected by factors such as implant surface properties,20 suggesting that no limit or numerical index exists regarding the distance of displacement. Because the direct measurement of displacement in clinical cases is impossible, it may be necessary to propose some method to prevent or reduce micro displacement and a numerical index for immediate loading.21 Vandamme et al22 reported that immediate loading was effective for tissue differentiation and bone formation around implants in vitro and that a microdisplacement of 50 µm or less was important for bone formation at the implant interface.

The maximum (40 µm at #12) and minimum (20 µm at #25) implant displacements on immediate loading after placement were smaller than the minimum displacement (50 µm) assumed to be required for interfering with osseointegration, indicating that bone formation around the implants can be expected. The angle formed by the implant placement and loading directions in the connected fixation was small at #15 and large at #25. In a comparison between #15 and #25, the displacement of #15 was greater, but it was only about one-sixth to one-third of that in the control group (individual loading). The connective fixation reduced the influence of the angle formed by the loading and placement directions, which may have dispersed the stress and displacement, reducing the displacement distance and its variation (SD  =  8.5). However, the difference in the placement direction may have some influence, resulting in the difference between #15 and #25.

In contrast, in the control group (individual loading), the minimum and maximum displacements were 70 µm at #25 and 185 µm at #15, respectively. These were greater than the minimum displacement (50 µm) required to interfere with osseointegration, and so bone formation would not be expected. The angle formed by the implant placement and individual loading direction was small at #15 and large at #25, and the displacement at #15 was larger than that at #25. Because forces were individually loaded on the implants, the resulting displacement might have been markedly influenced when the vector of the implant placement direction was close to that of the loading direction. When the implant placement angle was fixed, the stress and displacement may have been dispersed within the angle formed by the vectors, reducing the displacement, compared with the former for which no angle was formed. The large variation (SD  =  58.88) in the displacement distance in the individual loading group may have been due to differences in the placement angle.

On comparison of #25 on connected loading, at which a large angle difference was formed between the placement and loading directions, and #15 on individual loading, at which the angle difference was small, the displacements were 20 and 185 µm, respectively, about a 9-fold difference. Based on these findings, a condition yielding a large angle difference between the placements and loading directions on connected loading may reduce implant displacement on immediate loading in cases requiring oblique placement, while avoiding anatomical structures and the maxillary sinus such as in this model. The microdisplacement under this condition was less than the critical value (50 µm) for osseointegration, suggesting successful immediate-loaded implant treatment.

We improved the current preoperative planning and designing of implant placement by X-ray CT and placement simulation using FEA by considering anatomical bone morphology and mass from CT data, designed a preoperative evaluation method for implant placement by mechanical simulation, which was not possible employing the current method, and investigated their utility. The conclusions are as follows:

In the test group, established on the assumption of connected fixation for provisional restoration to achieve immediate loading, the maximum stress and displacement were reduced in the bone around the implants, as compared with those on individual loading (control group). In the control group, the displacement decreased as the difference between the implant placement and loading directions increased.

Maximum stress was loaded around the cortical bone in the implant neck region in the test and control groups. A large stress was loaded on the implant and in the placement direction on individual loading (control group), but stress was widely distributed around the implants on connected loading (test group).

The findings suggest that the distance of implant displacement may serve as a numerical prognostic index for osseointegration of immediate loaded implants.

This preoperative implant placement simulation using the FEA method is immediately applicable, with no additional tests, in clinical practice because X-ray CT and results of an implant placement simulation based on CT data generated in current clinical practice can be adopted with no modification.

CT

computerized tomography

FEA

finite element analysis