Influence of implant design and bone quality on stress/strain distribution in bone around implants: a 3-dimensional finite element analysis

PURPOSE: A 3-dimensional finite element analysis was performed to evaluate the influence of implant type and length, as well as that of bone quality, on the stress/strain in bone and implant. MATERIALS AND METHODS: Two types (screw and cylinder) and 4 lengths (9.2, 10.8, 12.4, and 14.0 mm) of titanium implants were buried in 4 types of bone modeled by varying the elastic modulus for cancellous bone. Axial and buccolingual forces were applied to the occlusal node at the center of the abutment. RESULTS: Regardless of load direction, maximum equivalent stress/strain in bone increased with a decrease in cancellous bone density. Under axial load, especially in the low-density bone models, maximum equivalent strain in cancellous bone was lower with the screw-type implant than with the cylinder-type implant. It was also lower with the longer implants than with the shorter implants. Under buccolingual load, equivalent stress/strain was influenced mainly by bone density. DISCUSSION: This study confirms the importance of bone quality and its presurgical diagnosis for implant long-term prognosis. Implant length and type can also influence bone strain, especially in low-density bone. CONCLUSIONS: The results of this study suggest that cancellous bone of higher rather than lower density might ensure a better biomechanical environment for implants. Moreover, longer screw-type implants could be a better choice in a jaw with cancellous bone of low density.     

Two dental implants designed for immediate loading: a finite element analysis

PURPOSE: The aim of this study was to evaluate by finite element analysis the influence of the design of 3 different dental implants on micromovements, cervical shearing stress intensity, and stress distribution after occlusal loading. MATERIALS AND METHODS: The first investigated implant was a classical cylinder, the second was reinforced by 2 bicortical locking pins, and the third was an expanding dental implant. The parameters analyzed were the implant's geometry, the quality of the cancellous bone, and the orientation of occlusal loading. RESULTS: It was found that initial stability of the locking pin implant was greater than the initial stability of the other investigated implant designs, regardless of the quality of cancellous bone and orientation of occlusal loading; in low-rigidity cancellous bone, under a horizontal load (500 N), decreasing displacement compared to those of the other investigated implants was 16 microm. The apical expansion and locking pin implants exhibited favorable behavior regarding the distribution and intensity of cervical shearing stresses; in low-rigidity cancellous bone, under horizontal load, decreasing cervical stresses compared with those of the cylindric implant were 10 MPa for the apical expansion implant and 150 MPa for the locking pin implant. DISCUSSION: For the cylindric implant, stresses were concentrated in the neck region; for the apical expansion implant, stresses were evenly distributed from the neck to the apex of the implant. For the locking pin implant, stresses around the neck were moderate and appeared concentrated around the pins. CONCLUSIONS: Initial stability of the pin implant was greater than that of the expanding implant, but the expanding implant showed the most favorable stress distribution.     

Finite element analysis of non-axial versus axial loading of oral implants in the mandible of the dog

The influence of axial and non-axial occlusal loads on the bone remodelling phenomena around oral implants in an animal experiment is simulated in a finite element analysis. The axial and non-axial loading conditions were introduced by inserting a bilaterally supported fixed partial prosthesis and a cantilever fixed partial prosthesis on two IMZ^® implants in the mandible of beagle dogs. Earlier quantitative and qualitative histological analyses revealed a statistically significant different remodelling response between both loading conditions. Two-dimensional and three-dimensional models are built to analyse and compare von Mises equivalent stress, maximum principal stress, maximum principal strain and strain energy density distributions, first around a free-standing implant and subsequently around the implants of the two prosthesis designs under the respective resultant in vivo loads. Strong correlations between the calculated stress distributions in the surrounding bone tissue and the remodelling phenomena in the comparative animal model are observed. It is concluded that the highest bone remodelling events coincide with the regions of highest equivalent stress and that the major remodelling differences between axial and non-axial loading are largely determined by the horizontal stress component of the engendered stresses.     

Factorial analysis of variables influencing mechanical characteristics of a single tooth implant placed in the maxilla using finite element analysis and the statistics-based Taguchi method

The aim of this study was to determine the relative contribution of changes (design factors) in implant system, position, bone classification, and loading condition on the biomechanical response of a single-unit implant-supported restoration. Non-linear finite-element analysis was used to simulate the mechanical responses in an implant placed in the maxillary posterior region. The Taguchi method was employed to identify the significance of each design factor in controlling the strain/stress. Increased strain values were noted in the cortical bone with lateral force and an implant with a retaining-screw connection. Cancellous bone strain was affected primarily by bone type and increased with decreasing bone density. Implant stress was influenced mainly by implant type and position. The combined use of finite-element analysis and the Taguchi method facilitated effective evaluation of the mechanical characteristics of a single-unit implant-supported restoration. Implants placed along the axis of loading exhibit improved stress/strain distribution. The reduction of lateral stress through implant placement and selective occlusal adjustment is recommended. An implant with a tapered interference fit connection performed better as a force-transmission mechanism than other configurations.     

Effect of abutment angulation on the strain on the bone around an implant in the anterior maxilla: a finite element study

STATEMENT OF PROBLEM: Angled abutments are often used to restore dental implants placed in the anterior maxilla due to esthetic or spatial needs. The effect of abutment angulation on bone strain is unknown. PURPOSE: The purpose of the current study was to measure and compare the strain distribution on the bone around an implant in the anterior maxilla using 2 different abutments by means of finite element analysis. MATERIAL AND METHODS: Two-dimensional finite element models were designed using software (ANSYS) for 2 situations: (1) an implant with a straight abutment in the anterior maxilla, and (2) an implant with an angled abutment in the anterior maxilla. The implant used was 4x13 mm (MicroThread). The maxillary bone was modeled as type 3 bone with a cortical layer thickness of 0.5 mm. Oblique loads of 178 N were applied on the cingulum area of both models. Seven consecutive iterations of mesh refinement were performed in each model to observe the convergence of the results. RESULTS: The greatest strain was found on the cancellous bone, adjacent to the 3 most apical microthreads on the palatal side of the implant where tensile forces were created. The same strain distribution was observed around both the straight and angled abutments. After several iterations, the results converged to a value for the maximum first principal strain on the bone of both models, which was independent of element size. Most of the deformation occurred in the cancellous bone and ranged between 1000 and 3500 microstrain. Small areas of cancellous bone experienced strain above the physiologic limit (4000 microstrain). CONCLUSIONS: The model predicted a 15% higher maximum bone strain for the straight abutment compared with the angled abutment. The results converged after several iterations of mesh refinement, which confirmed the lack of dependence of the maximum strain at the implant-bone interface on mesh density. Most of the strain produced on the cancellous and cortical bone was within the range that has been reported to increase bone mass and mineralization.     

全下颌牙种植义齿及支持组织应力的三维有限元分析──Ⅱ． 固定式种植义齿在三种加载方式下应力分析比较

采用三维有限元法考察全下颌种植固定义齿在正中均布加载、集中加载，前伸加载下，其种植体－支架、人工牙、皮质骨、松质骨的应力分布变化规律。结果显示：①三种加载方式的种植体颈部及周围骨界面应力增高，以叶状种植体最明显，但种植体－支架、支持骨应力分布趋于均匀，分布规律近似，提示临床设计具有力学可行性；②全下颌牙种值固定义齿由刚性较好的支架能有效地分散载荷。     

Transmission of bone strain in the craniofacial bones of edentulous human skulls upon dental implant loading

STATEMENT OF PROBLEM: Little is known about how craniofacial bones that are distant from dental implants are loaded. Whether bone experiences different strain when implants of different diameters are loaded is unknown. PURPOSE: This study was designed to (1) characterize bone strain both adjacent to and distant from dental implants and (2) compare bone strain in response to the same loads on small-diameter and large-diameter implants. MATERIAL AND METHODS: On 4 edentulous, dry adult human skulls, the buccopalatal midpoint of the edentulous occlusal surface was marked unilaterally in the maxillary first molar area with a round bur. A hole for implant placement was prepared, and 2 self-tapping titanium implants (3.75 x 7 mm and 4 x 7 mm) were placed in the same location and at the same orientation, one after the other. A 4-mm-long titanium abutment was connected to the implant. Each implant was loaded 10 degrees lateral to its longitudinal axis, simulating a lateral occlusal force in 3 of the skulls. In skull 2, loading was along the longitudinal axis of the implant and simulated a vertical occlusal force. The magnitude of the ramp forces was 0 to 100 N. Uniaxial strain gages and/or 3-element strain rosettes were implanted in the supramolar cortical bone, the supraincisor cortical bone, the zygomaticomaxillary suture, and the zygomaticotemporal suture. All strain gages/rosettes were excited with 500 mV DC, and the output signals were recorded with a strain conditioner. Tensile strain was expressed as positive values and compressive strain as negative values. Student t tests were used to test for normal distribution of bone strain within each skull; Wilcoxon tests were applied for skewed distribution between small- and large-diameter implants and between 50-N and 100-N loads (P相似文献   

植入位点及轴向对不同牙槽窝形态上中切牙即刻种植即刻负重应力影响的三维有限元分析

目的 基于三维有限元法,分析并探讨不同牙槽窝形态下,上颌中切行牙即刻种植即刻负重时,植入位点及轴向对种植体、基台、中央螺丝、牙冠应力分布的影响。方法 参照1名健康成年人的口腔CBCT影像资料;建立偏唇型、中间型、偏腭型三种牙槽窝形态的上颌中切牙即刻种植即刻负重的三维有限元模型;模拟不同植入位点(根尖位点、偏腭/唇侧位点)及轴向(牙长轴、牙槽骨长轴);对已建立的模型以100 N的力进行应力加载;应用ANSYS软件分析种植体、基台、中央螺丝、牙冠的应力值。结果 成功建立12个不同牙槽窝形态的上颌中切牙即刻种植即刻负重三维有限元模型;牙槽窝偏唇型及偏腭型的上颌中切牙行即刻种植即刻负重时,沿牙槽骨长轴偏腭/唇位点进行植入,种植体及其上部结构所受应力最小;中央型上颌中切牙行即刻种植即刻负重时,沿牙长轴偏腭位点进行植入,种植体及其上部结构所受应力最小。结论 不同牙槽窝形态、植入位点及轴向,都会对上颌中切牙即刻种植即刻负重种植体及其上部结构生物力学特点产生影响。医生应针对不同牙槽窝形态制定不同植入轴向及植入位点的手术方案。     

不同种植体外形设计对上颌窦提升术后种植体周围应力分布的影响

目的：比较不同种植体外形设计对上颌窦提升术后种植体周围生物力学的影响。方法：在D3型上颌骨简化模型上利用三维有限元法分析3种不同外形设计的种植体在植骨与不植骨条件下的应力分布情况。假设所有材料都是线弹性、连续材料,向种植体施加150 N的倾斜力,测量种植体周围骨组织的最大等效力（equivalent von-Mises,EQV）。采用Ansys Workbench 14.5软件包对数据进行测量分析,采用SPSS 17.0软件包对数据进行统计学分析。结果：各组应力集中区域均位于种植体颈部皮质骨区域。不同种植体外形设计对种植体周围皮质骨最大EQV值无显著影响,但锥形种植体较其他种植体的周围松质骨最大EQV值显著上升,上颌窦提升术后植骨可以降低各组种植体周围最大EQV值。结论：锥形种植体用于上颌后牙区种植修复时,可能引起种植体周围松质骨应力变大,增加种植体周围骨吸收的风险。上颌窦提升后植骨,可降低种植体周围压力负载。     

A Three-Dimensional Finite Element Stress Analysis of Angled Abutments for an Implant Placed in the Anterior Maxilla

Purpose A three-dimensional mathematical model of the maxilla was developed that was used to analyze the stresses and strains produced by an abutment system capable of three abutment angulations. Materials and Methods Computed tomography was used to derive the geometry and density values used for the maxillary model. A 3.8 × 10–mm cylindrical implant was embedded in the right central incisor position at a 35° angle to the horizontal plane and parallel to the angulation of the bone site. All geometric and elastic properties for the fixture and the surrounding bone were included in the model. A simulated occlusal load of 178 N was applied along the long axis of 0°, 15°, and 20° abutments. The mathematical models were solved by the Cray Y/MP Ohio Supercomputer (Cray, Eagan, MN) using the ABAQUS software program (Hibbitt, Karlsson, and Sorenson, Providence, RI). Results Numerical and graphic results were generated for the maximum (tensile) and minimum (compressive) stresses and strains. Principal stresses occurred predominantly in the cortical bone layers, whereas strains occurred mostly in the cancellous bone. Conclusions In general, there was an increase in the magnitude of stress and strain as the abutment angulation increased. Reported stresses and strains for all three angles were within or slightly above the physiological zone derived from animal studies. A need to investigate the response of human bone to stress and strain was indicated.     

上切牙区双端悬臂梁种植固定桥的应力分析

目的：通过分析双端悬臂梁种植义齿修复上颌切牙区牙列缺损的种植体在不同加载条件下的周围骨应力分布及位移量,进而探讨临床修复的可行性。方法：应用CT断层扫描技术对上颌骨及上颌牙列的大致轮廓进行三维重建,后于上中切牙区植入种植体,完成牙冠修复并建立模型。通过三维有限元技术模拟载荷,比较不同加载条件下种植体的周围骨组织应力分布及位移量。结果：经统计学分析,种植体-骨界面的皮质骨唇侧、舌侧、近中、远中、根尖部五个部位应力值的差异有统计学意义（P〈0.001）,五个部位的位移量的差异也有统计学意义（P〈0.001）。模型在各种加载条件下的应力分布及位移量的特征大致相同,且变化趋势相似,种植体颈部及周围骨皮质为应力集中区。在各种不同的加载条件中,30°加载角度时种植体周围骨应力分布更为科学。结论：在适当的负重条件下,双端悬臂梁种植义齿是临床修复切牙区缺失可供选择的一种设计方案。     

上颌前牙区种植方案中角度设计的三维有限元分析

目的 采用有限元法观察分析不同种植体植入角度与不同角度基台联合运用时种植体周骨组织的应力分布及种植体的位移情况,为上颌前牙区种植修复方案的设计提供依据。方法利用锥形束CT（cone beam computed tomography, CBCT）建立包含部分上颌骨、种植体（4.3 mm×11.5 mm）、基台及上部修复体（氧化锆全瓷冠）的三维有限元模型,以种植体植入角度A,即种植体长轴与理想长轴之间的夹角 (0°、5°、10°、15°、20°、25°)和基台角度B,即基台长轴与种植体长轴之间的夹角(0°、5°、10°、15°、20°、25°)建立有限元模型。在模型上与牙冠长轴呈130°、舌侧切端下2 mm,模拟大小为178 N的力加载,采用Ansys13.0软件观察种植体周围皮质骨、松质骨的最大主应力值、分布情况和种植体的位移。结果建立了16个符合实际情况的不同种植修复方案的上颌中切牙种植义齿的三维有限元模型;各种修复方案的种植体—骨界面应力分布特点相同,应力集中在种植体颈部及根部;在相同的植入角度下,基台角度越大,种植体周围皮质骨、松质骨的最大主应力峰值及种植体位移峰值均越大。在相同的基台角度下,种植体的植入角度越大,种植体周围皮质骨、松质骨的最大主应力峰值及种植体位移峰值均越大;植入角度或基台角度大于20°时,种植体周围皮质骨、松质骨的最大主应力峰值及种植体位移峰值增加幅度较大。结论种植体的植入角度和基台角度均与种植体周围皮质骨、松质骨的最大主应力峰值及种植体位移峰值呈正相关关系,应尽量减小种植体的植入角度和基台角度,尤其是需要严格掌握种植体的植入角度。从应力、位移考虑,前牙区种植体植入角度和基台角度在20°以内为佳。大于20°时,应力有明显升高趋势,增加种植成功的风险。     

氧化锆瓷基台与钛种植体联合应用中不同连接体设计的有限元分析

目的：分析不同氧化锆基台对基台自身及钛种植体周围骨组织应力的影响,为氧化锆基台设计提供理论依据。方法：采用计算机辅助设计建立5种不同设计的氧化锆基台模型,并根据不同的基台模型设计了与之对应的种植体、牙槽骨及全瓷冠模型。用三维有限元方法对每个模型进行100N的斜向加载,分析不同氧化锆基台的设计对基台自身及牙槽骨应力分布及应力峰值的影响。结果：5种设计的等效应力的分布基本一致,基台的应力主集中在基台颈部连接体上方,皮质骨及松质骨的应力主集中于骨与种植体连接的最上方。5种设计等效应力的峰值不同,圆形连接体设计时氧化锆基台,皮质骨及松质骨的等效应力峰值均小于其他各设计组。结论：圆形连接体设计是本研究5种设计中氧化锆基台与钛种植体相连的最佳设计形式。     

上颌前牙倾斜角度对种植治疗设计的影响

目的 利用锥形束CT（CBCT）研究上颌前牙与牙槽骨的相对位置关系。方法 选取上颌恒牙牙列完整的患者150例（年龄19~48岁,男性和女性各75例）,按性别和牙位分为6个组。以牙槽骨长轴为基准,在CBCT影像上测量上颌前牙牙体长轴的相对倾斜角度（偏向腭侧为正,偏向唇侧为负）。使用SPSS 19.0软件对数据进行统计分析。结果 所有研究对象的上颌前牙的牙体长轴均偏向牙槽骨长轴的腭侧。男性上颌中切牙、侧切牙、尖牙的牙体长轴与牙槽骨长轴所成角度α的平均值分别为16.22°（2.50°~28.80°）、17.50°（3.80°~29.50°）、16.27°（1.00°~31.50°）,而女性的相应测量结果平均值分别为15.20°（2.20°~27.20°）、15.99°（4.10°~33.30°）、15.01°（3.50°~27.40°）。结论上颌前牙与牙槽骨的倾斜方向不一致,所有上颌前牙牙体长轴均偏向于牙槽骨长轴腭侧。通过CBCT观察上颌前牙与牙槽骨的位置关系,可以指导种植时机,种植体植入位置以及骨增量方案的选择。     

Stress distribution around maxillary implants in anatomic photoelastic models of varying geometry. Part II

STATEMENT OF PROBLEM: Insufficient buccal bone volume can be a significant problem when loading dental implants in the maxilla. Increased potential for buccal fenestration and dehiscence can result in an exposed implant surface, mucosal irritation, decreased support, and potential implant failure. PURPOSE: The objective of this study was to model the stress distribution around maxillary implants by comparing simulated occlusal loading of maxillary implants in a 2-dimensional photoelastic anatomic model and a dry skull model. MATERIAL AND METHODS: Two model systems were used. First, a 2-dimensional photoelastic anatomic frontal skull sectional model was prepared in the first molar region. Left and right maxillary metal cylinder implant analogues inclined at 0 and 25 degrees to the sagittal plane were loaded in simulated intercuspation. Second, a dry skull lined with a photoelastic coating on the buccal aspect over an embedded cylinder implant was prepared in the first molar region. Principal stress concentration was photographed on axial and nonaxial implant loading. RESULTS: On simulated intercuspal loading, maximum stress concentration occurred at the buccal concavity in both the 2-dimensional anatomic photoelastic and skull models. There was no stress concentration at the apices of the maxillary implants in the 2-dimensional model. On lateral loading of the skull model, stress was distributed along the entire buccal aspect of bone adjacent to the implant, with a higher concentration at the buccal concavity. CONCLUSION: Preservation of buccal supporting bone volume is desirable to obtain a physiological modeling response and to enhance the facial plate. Insufficient bone volume may result in buccal fenestration or dehiscence, which can precipitate mucosal irritation, decreased support, and potential implant failure.     

Influence of bone quality on the stress distribution

Adequate bone quality and stress distribution to the bone are of decisive importance for implant success. The purpose of this in vitro study was to investigate the influence of bone quality on the stress distribution using 2 implant-bone mimicking models, simulating compact and cancellous bone quality. The resin model was made of an acrylic resin only simulating compact bone quality. The hybrid model was made of 2 kinds of materials, acrylic resin covered with a 1-mm layer of urethane to simulate cancellous bone quality. An implant was embedded in each model, and the abutment and suprastructures were connected to the implant. A strain gauge was placed perpendicular to the implant on the surface of the model and a small accelerometer was attached to the abutment. When an impact load was applied to the suprastructure, both strain and acceleration were measured. Both abutment acceleration and surface strain in the hybrid model decreased rapidly as time progressed when compared to the resin model. Abutment accelerations in the resin model were significantly lower than those in the hybrid model. In the hybrid model, the strain increased as the loading site was moved closer to the strain gauge. The influence of loading sites on strain in the resin model was greater than in the hybrid model. Therefore, the occlusal stress was distributed more widely in the hybrid model than in the resin model. This may indicate that occiusal stress in compact bone may have a tendency to concentrate in particular regions.     

A three-dimensional finite element analysis of a passive and friction fit implant abutment interface and the influence of occlusal table dimension on the stress distribution pattern on the implant and surrounding bone

Aims:

The aim of the study was to evaluate the stress distribution pattern in the implant and the surrounding bone for a passive and a friction fit implant abutment interface and to analyze the influence of occlusal table dimension on the stress generated.

Materials and Methods:

CAD models of two different types of implant abutment connections, the passive fit or the slip-fit represented by the Nobel Replace Tri-lobe connection and the friction fit or active fit represented by the Nobel active conical connection were made. The stress distribution pattern was studied at different occlusal dimension. Six models were constructed in PRO-ENGINEER 05 of the two implant abutment connection for three different occlusal dimensions each. The implant and abutment complex was placed in cortical and cancellous bone modeled using a computed tomography scan. This complex was subjected to a force of 100 N in the axial and oblique direction. The amount of stress and the pattern of stress generated were recorded on a color scale using ANSYS 13 software.

Results:

The results showed that overall maximum Von Misses stress on the bone is significantly less for friction fit than the passive fit in any loading conditions stresses on the implant were significantly higher for the friction fit than the passive fit. The narrow occlusal table models generated the least amount of stress on the implant abutment interface.

Conclusion:

It can thus be concluded that the conical connection distributes more stress to the implant body and dissipates less stress to the surrounding bone. A narrow occlusal table considerably reduces the occlusal overload.Key Words: Conical connection, friction fit interface, implant abutment interface, occlusal table dimension, passive fit interface, Tri-lobe connection     

无牙颌一侧上颌骨缺损种植修复后的有限元应力分析

目的:探讨无牙颌一侧上颌骨缺损种植修复后在力作用下支持组织中的应力分布特点。方法:建立无牙颌一侧上颌骨缺损种植修复的三维有限元模型,观察计算机模拟的不同修复方式以及不同加载方式作用下骨组织中的应力分布情况。结果:无论何种加载方式,在单纯健侧种植修复时,1位种植体周围骨皮质应力值均很高;双侧种植修复后无论何种加载方式1位种植体周围骨皮质的应力值都大大降低。结论:患侧植入种植体能够降低单纯健侧种植时邻近缺损处的种植体周围骨皮质应力,使支持组织中应力分布均匀合理,提高修复成功率。     

Influence of bone parameters on peri-implant bone strain distribution in the posterior mandible

Objectives: The success rate of dental implants depends on the type of bone at the implant site. The purpose of the present study was to investigate the effects of the bone parameters at the implant-placement site on peri-implant bone strain distributions. Study Design: The morphologies and bone densities of seventy-five potential implant sites in the posterior mandible were measured using computed tomography (CT). Based on the CT data, we defined bone parameters (low and high in terms of cancellous-bone density and crestal-cortical bone density, and thin and thick in terms of crestal-cortical bone thickness), and we constructed finite-element models simulating the various bone types. A buccolingual oblique load of 200 N was applied to the top of the abutment. The von Mises equivalent (EQV) strains in the crestal-cortical bone and in the cancellous bone around the implant were calculated. Results: Cancellous-bone density greatly affected the maximum EQV strain regardless of the density and thickness of the crestal cortical-bone. The maximum EQV strains in the crestal cortical-bone and the cancellous bone in the low-density cancellous-bone models (of 150 Hounsfield units (HU) were 1.56 to 2.62-fold and 3.49 to 5.31-fold higher than those in the high-density cancellous-bone models (of 850 HU), respectively. The crestal cortical-bone density affected the maximum EQV strains in the crestal cortical-bone and in the cancellous bone in the low-density cancellous-bone models. The crestal cortical-bone thickness affected the maximum EQV strains in the cancellous bone and in the crestal cortical-bone in the low-density cancellous-bone models. Conclusions: Our results confirm the importance of bone types for the peri-implant bone strain distribution. Cancellous-bone density may be a critical factor for peri-implant bone strain. Key words:Dental implant, bone density, finite-element analysis.     

The influence of implant location and length on stress distribution for three-unit implant-supported posterior cantilever fixed partial dentures

STATEMENT OF THE PROBLEM: The influence of implant location for an implant-supported cantilever fixed partial denture (FPD) on stress distribution in the bone has not been sufficiently assessed. PURPOSE: This study examined the influence of location and length of implants on stress distribution for 3-unit posterior FPDs in the posterior mandibular bone. MATERIAL AND METHODS: Each 3-D finite element model included an FPD, mesial and distal implants, and supporting bone. The mesial implant with a length of 10 mm or 12 mm was placed in locations where its long axis was 3 mm to 11 mm posterior to the remaining first premolar. The distal implant with a length of 10 mm was fixed at the same distance from the premolar on each model. A buccally-oriented oblique occlusal force of 100 N was placed on each occlusal surface of the FPD. RESULTS: The maximum equivalent stresses were shown at the cervical region in the cortical bone adjacent to the mesial or the distal implants. Relatively high stresses of up to 73 MPa were shown adjacent to the mesial implant located 9 mm or more posterior to the first premolar. The use of a 12-mm-long mesial implant demonstrated a relatively weak influence on stress reduction. CONCLUSION: The implant location in the cantilever FPDs was a significant factor influencing the stress created in the bone.