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Research Article Comparison of Three Different Types of Two-Implant-Supported Magnetic Attachments on the Stress Distribution in Edentulous Mandible Fengling Hu, 1,2 Yiming Gong, 2 Zhen Bian, 1 Xiaoying Zhang, 1 Bin Xu, 1 Jianguo Zhang, 3 Xiaojun Shi, 1 Youcheng Yu , 2 and Liang Song 1 1 Department of Stomatology, e Fifth People’s Hospital of Shanghai, Fudan University, 801 Heqing Road, Shanghai 200240, China 2 Department of Stomatology, Zhongshan Hospital of Fudan University, 180 Fenglin Road, Shanghai 200032, China 3 School of Mechanical Engineering, Shanghai Institute of Technology, Haiquan Road 100, Shanghai 201418, China Correspondence should be addressed to Youcheng Yu; [email protected] and Liang Song; sky_songliang@ hotmail.com Received 23 September 2018; Accepted 21 January 2019; Published 8 April 2019 Academic Editor: Maria E. Fantacci Copyright © 2019 Fengling Hu et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Two-implant-retained mandibular overdentures with magnetic attachments can provide an effective treatment modality for edentulous patients. In this study, a three-dimensional finite element analysis was used to compare the biomechanical char- acteristics of three different types of magnetic attachments in two-implant-retained mandibular overdentures. Flat-type, dome- type, and cushion-type of the magnetic attachments were designed to retain the overdenture. Four types of load were applied to the overdenture in each model: 100 N vertical and oblique loads on the right first molar and a 100 N vertical load on the right canine and the lower incisors. e biomechanical behaviors of peri-implant bone, abutment, and mucosa were recorded. In vertical incisors, vertical right canine, and oblique molar loading condition, the flat-type group exhibited the highest levels of maximum equivalent strain/stress in the peri-implant bone. e total deformation of mucosa and the maximum equivalent strain/ stress in the oblique molar loading condition are about two times as the vertical molar loading condition. ese results suggested that both cushion-type and dome-type of the magnetic attachments are better choices in two-implant-retained mandibular overdentures, and oblique loading is more harmful than vertical loading. 1. Introduction e mandibular bone resorption is significantly greater than the maxilla. Complete mandibular dentures always have the poor retention problem. Overdenture is a good choice for the mandibular edentulous patients. Dental implants with removable prosthesis are helpful way for rehabilitation of edentulous patients [1]. Magnetic at- tachments, which have been used to maintain the stability of denture since the 1950s, presented several advantages including long-lasting constant retentive force, reduced lateral forces, and simplicity in installation for patients with dexterity problems [2–4]. ey were widely applied in both dental prostheses and implants [5, 6] and have shown high levels of clinical success [7]. Two-implant-retained man- dibular magnetic overdentures are stable, cost-effective, and less invasion and have achieved good patient satis- faction [8, 9]. ree types of the magnetic attachments, such as flat- type, dome-type, and cushion-type, are commercially available for implant-retained overdenture. e flat-type is a conventional magnetic attachment that has larger retentive force and greater stress. As new generation of magnetic attachments, the dome-type and cushion-type attachments have the function to allow displacement or rotation of the overdenture during function [10]. Hindawi Computational and Mathematical Methods in Medicine Volume 2019, Article ID 6839517, 10 pages https://doi.org/10.1155/2019/6839517

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Page 1: Comparison of Three Different Types of Two-Implant

Research ArticleComparison of Three Different Types of Two-Implant-SupportedMagnetic Attachments on the Stress Distribution inEdentulous Mandible

Fengling Hu,1,2 Yiming Gong,2 Zhen Bian,1 Xiaoying Zhang,1 Bin Xu,1 Jianguo Zhang,3

Xiaojun Shi,1 Youcheng Yu ,2 and Liang Song 1

1Department of Stomatology, �e Fifth People’s Hospital of Shanghai, Fudan University, 801 Heqing Road,Shanghai 200240, China2Department of Stomatology, Zhongshan Hospital of Fudan University, 180 Fenglin Road, Shanghai 200032, China3School of Mechanical Engineering, Shanghai Institute of Technology, Haiquan Road 100, Shanghai 201418, China

Correspondence should be addressed to Youcheng Yu; [email protected] and Liang Song; [email protected]

Received 23 September 2018; Accepted 21 January 2019; Published 8 April 2019

Academic Editor: Maria E. Fantacci

Copyright © 2019 Fengling Hu et al. .is is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Two-implant-retained mandibular overdentures with magnetic attachments can provide an effective treatment modality foredentulous patients. In this study, a three-dimensional finite element analysis was used to compare the biomechanical char-acteristics of three different types of magnetic attachments in two-implant-retained mandibular overdentures. Flat-type, dome-type, and cushion-type of the magnetic attachments were designed to retain the overdenture. Four types of load were applied tothe overdenture in each model: 100N vertical and oblique loads on the right first molar and a 100N vertical load on the rightcanine and the lower incisors. .e biomechanical behaviors of peri-implant bone, abutment, and mucosa were recorded. Invertical incisors, vertical right canine, and oblique molar loading condition, the flat-type group exhibited the highest levels ofmaximum equivalent strain/stress in the peri-implant bone..e total deformation of mucosa and the maximum equivalent strain/stress in the oblique molar loading condition are about two times as the vertical molar loading condition. .ese results suggestedthat both cushion-type and dome-type of the magnetic attachments are better choices in two-implant-retained mandibularoverdentures, and oblique loading is more harmful than vertical loading.

1. Introduction

.e mandibular bone resorption is significantly greaterthan the maxilla. Complete mandibular dentures alwayshave the poor retention problem. Overdenture is a goodchoice for the mandibular edentulous patients. Dentalimplants with removable prosthesis are helpful way forrehabilitation of edentulous patients [1]. Magnetic at-tachments, which have been used to maintain the stabilityof denture since the 1950s, presented several advantagesincluding long-lasting constant retentive force, reducedlateral forces, and simplicity in installation for patients withdexterity problems [2–4]. .ey were widely applied in both

dental prostheses and implants [5, 6] and have shown highlevels of clinical success [7]. Two-implant-retained man-dibular magnetic overdentures are stable, cost-effective,and less invasion and have achieved good patient satis-faction [8, 9].

.ree types of the magnetic attachments, such as flat-type, dome-type, and cushion-type, are commerciallyavailable for implant-retained overdenture. .e flat-type is aconventional magnetic attachment that has larger retentiveforce and greater stress. As new generation of magneticattachments, the dome-type and cushion-type attachmentshave the function to allow displacement or rotation of theoverdenture during function [10].

HindawiComputational and Mathematical Methods in MedicineVolume 2019, Article ID 6839517, 10 pageshttps://doi.org/10.1155/2019/6839517

Page 2: Comparison of Three Different Types of Two-Implant

Bioengineering tools have been shown to be useful toevaluate the performance of implants and the dentures.Previous studies using strain gauge analyses displayed lowerlateral stress distribution for overdentures retained bycushion-type magnetic attachment than did the flat-type[11], while others showed similar effect on the denturemovement and lateral stresses between the three types ofmagnetic attachments [3]. Based on these inconsistent re-sults, it may be better to use other engineering tools toevaluate the biomechanical behaviors of the three magneticattachment systems.

.ree-dimensional finite element method is consideredas a precise and effective research approach for investigatingstress/strain distribution in the study of prosthodontics[12, 13], which provide precious representation of complexgeometries, and the model modification is convenient.When loaded appropriately, the three-dimensional finiteelement method can reveal the stresses/strains distributionthroughout the whole structure [14].

.e aim of this study was to evaluate the biomechanicalbehaviors of three different types of magnetic attachments intwo-implant-supported overdentures by three-dimensionalfinite element analysis methods.

2. Materials and Methods

2.1. Model Design. .e three-dimensional geometry wasobtained and acquired through the edentulous mandible,the overdenture, the implant, and the magnetic attachment.Mandibular bone and overdenture computerized tomog-raphy (CT) data were obtained from a 63-year-old femalevolunteer with a complete edentulous mandible covered bya resin complete denture which can provide the preciserelationship between the denture and mandible. .e CTwas done through the KaVo 3D exam (KaVo DentalGmbH, Bismabring, Germany) CBCTscanner, to make thepreoperative examination after obtaining the agreement ofpatient through signing a consent form according to ourlocal Human Research Ethics Committee (#2015EC099)before the surgery. .e Digital Imaging and Communi-cations in Medicine (DICOM) data obtained from CTwereprocessed using three-dimensional image processing andediting software (Mimics 10.01, Materialise, Leuven, Bel-gium). .e point cloud data of overdenture, cortical, andcancellous bones were extracted and performed from CTHounsfield value, using the threshold value and regiongrowth function. .en, modeling software (SolidWorksrelease 2010, SolidWorks Corporation) was used totransform the reference model subject data into the FEMsolid model of the mandibular and the overdenture..e 3Dgeometry (Figure 1) was exported to FE preprocessingsoftware ANSYS14.1 (ANSYS Inc., Canonsburg, PA, USA)and discretized in linear tetrahedral elements (Figure 2)..e mandible surface is assumed a 2mm constant corticalbone layer wrapped around the cancellous bone surface[15]. Based on the precise location between the mandibularand the overdenture on the CT, the precise geometry ofmucosa closely contacted with the inner surface of thedenture was obtained [16]. .e average thickness of the

mucosa covered on the edentulous mandibular was about2mm.

.e models of two implants (4.3mm in diameter,10.0mm in length; Nobel Replace, Sweden) and three dif-ferent magnetic attachments were constructed according tothe manufacturer’s product data. Two implants were ver-tically oriented, mutually parallel, and 20mm away fromeach other inserted in the bilateral mandibular canine re-gion. .e magnetic attachments consisted of a magnet, akeeper, and an abutment cylinder. .e keeper (K) wasscrewed onto the abutment cylinder (A) and inserted intothe implant, and the magnet (M) was embedded in thedenture. .ree different magnetic attachments were used inthis research: flat-type (IP-DXFL; Aichi Steel Co., Japan),dome-type (IP-MCD; Aichi Steel Co., Japan), and cushion-type (IP-MCS; Aichi Steel Co., Japan) (Figure 3), divided asFM group, DM group, and CM group. .e total numbers ofelements and nodes of three models are listed in Table 1.

2.2. Material Properties and Interface Condition. .e me-chanical properties of the materials are presented in Table 2..e interface between implants and the bone was assumed tobe absolute osseointegration [23]. .e implant, the keeper,and the abutment cylinder were considered as a combinationso that no motion among these structures occurs under ap-plied loading [23]. To simulate the clinical situation that theoverdenture was able to generate rotation and slide on thebottom mucosa in different directions when functioning,sliding friction contact was applied at the overdenture-mucosainterface, and the friction coefficient μ was set at 0.334 [15].

2.3. Constraints and Loading Conditions. .e models wererestrained at the nodes on the mandible within all directionsin all degrees of freedom. To simulate the clinical masti-catory loading, four types of 100N load strength fromdifferent directions and positions were applied to theoverdenture, namely, 100N vertical load on the lower in-cisors, 100N vertical load on the right canine, and 100Nvertical and oblique loads on the right first molar..e choiceof a load with a magnitude of 100N was based on theviewpoints that both the moderate level of biting force onimplant overdentures and the average maximum occlusalforce in complete denture patients were 100N [24, 25]. .efour loading conditions have been abbreviated as VI (vertical

Figure 1: .ree-dimensional solid geometric models of mandible,mucosa, overdenture, implants, and magnetic.

2 Computational and Mathematical Methods in Medicine

Page 3: Comparison of Three Different Types of Two-Implant

load on the lower incisors) (Figure 4(a)), VC (vertical loadon the right canine) (Figure 4(b)), VM (vertical load on theright first molar) (Figure 4(c)), and OM (oblique load on theright first molar) (Figure 4(d)). OM refers to a 45° angledforce buccolingually applied at the centre of the right firstmolar [15].

3. Results

3.1. Stress Distribution in Peri-Implant Cortical Bone.Among the attachment types and loading conditions, thestress areas were mainly distributed around the loading side(Figure 5).

Figure 2: Meshed modeling of jaw, mucosa, and implant magnetic overdenture (flat-type).

M

A

K

Implant

(a) (b) (c)

Figure 3: Combination models of the implants and magnetic attachments. .e keeper (K) is screwed onto the abutment cylinder (A) andinserted into the implant, and the magnet (M) is assembled in the denture. (a) Flat-type. (b) Dome-type. (c) Cushion-type.

Table 1: Total number of elements and nodes.

Elements NodesFlat-type model 29,989 54,547Dome-type model 30,429 55,211Cushion-type model 50,487 90,314

Table 2: Material properties.

Material Structure Young’s modulus (Mpa) Poisson’s ratio ReferencePOM Cushing pad 5000 0.36 Manufacture∗AUM20 .e keeper (K) 200,000 0.28 Manufacture∗Ti-6Al-4V Implant 110,000 0.33 Colling [17]NdFeB (magnet) .e magnet (M) 160,000 0.24 John et al. [18]Pure titanium .e abutment cylinder (A) 117,000 0.30 Sakaguchi and Borgersen [19]Acrylic resin Artificial teeth and denture base 8300 0.28 Darbar et al. [20]

Cortical bone 13,700 0.3 Barbier et al. [21]Trabecular bone 1370 0.3 Barbier et al. [21]Oral mucosa 680 0.45 Barao et al. [22]

∗Personal communication.

Computational and Mathematical Methods in Medicine 3

Page 4: Comparison of Three Different Types of Two-Implant

100N

(a)

100N

(b)

100N

(c)

100N

(d)

Figure 4: Four loading conditions. (a) Vertical load on the lower incisors (VI). (b) Vertical load on the right canine (VC). (c) Vertical loadon the right first molar (VM). (d) Oblique load, 45° angled force buccolingually applied at the centre of the right first molar (OM).

7.01016.56536.06045.55555.05064.54574.04083.53593.0312.52612.02121.51631.01140.506540.0016458

10.5389.78539.03278.287.52746.77476.02215.26944.51673.76413.01142.25881.50610.753450.00079119

3.64493.38453.12422.86392.60352.34322.08281.82251.56221.30181.04150.781160.520820.260490.00014978

7.20166.68736.17295.65855.14424.62984.11543.6013.08672.57232.05791.54361.02920.514830.00045829

6.80546.31945.83345.34744.86154.37553.88953.40352.91752.43161.94561.45960.973610.487630.0016449

10.5079.75689.00638.25597.50546.75496.00455.2544.50363.75313.00262.25221.50170.751240.00077563

3.6183.35963.10122.84272.58432.32592.06751.80911.55071.29231.03380.775430.517020.25860.00018777

7.12636.61736.10835.59935.09034.58134.07243.56343.05442.54542.03641.52741.01840.509460.00047495

6.61136.13925.66715.1954.72284.25073.77863.30653.83442.36222.89011.4180.945890.473770.0016494

9.64438.95558.26677.57796.8896.20025.51144.82264.13373.44492.75612.06731.37840.689610.00078686

3.6183.35963.10122.84272.58432.32592.06751.80911.55071.29231.03380.775430.517020.25860.00018777

6.73226.25145.77055.28975.80894.3283.84723.36632.88552.40471.92381.4430.962130.481290.00044732

VI

VC

VM

OM

(a) (b) (c)

Figure 5: Maximum equivalent stress in the peri-implant bone of the flat-type model, dome-type model, and cushion-type model in fourloading situations. Colors indicate level of stress from dark blue (lowest) to red (highest) (MPa). (a) Flat-type. (b) Dome-type. (c) Cushion-type.

4 Computational and Mathematical Methods in Medicine

Page 5: Comparison of Three Different Types of Two-Implant

.e FM group exhibited the highest levels of maximumequivalent stress in the peri-implant bone under VI, VC, andOM loading conditions, and the peak stress values in thecortical bone were shown in VC loading condition.

When the vertical load was applied on the right firstmolar, the maximum equivalent stress in the peri-implantcortical bone was much less than the vertical load applied onthe incisor or on the canine. But when the vertical loadchanged to be oblique load, the maximum equivalent stressin the peri-implant cortical bone is about two times as theVM loading condition (Table 3).

3.2. Stress Distribution in Dental Implant. .e stress distri-bution in the dental implant showed a similar trend as in theperi-implant cortical bone (Figure 6). .e peak maximumequivalents stress is in VC loading condition in the FMgroup. .e lowest levels of maximum equivalents stress arein VM loading condition (Table 4).

3.3.�ePressure on theMucosa. .emaximum pressures onthe mucosa were higher in VI, VC, and OM loading con-dition than in VM loading condition (Figure 7). In VMloading condition, the maximum pressure on the mucosa ofFM group, DM group, and CM group was almost the same.When the vertical load changed to be oblique load, themaximum pressure on the mucosa is about two times as theVM loading condition. In the same loading condition, theCM group mostly showed the highest maximum mucosapressures, and the peak maximum pressure was observed inthe CM group in VI loading condition (Table 5).

3.4. �e Deformation of the Mucosa. .e maximum de-formation of the mucosa showed a similar trend as thepressure on the mucosa (Figure 8). .e lowest levels ofmaximum mucosa deformation are in VM loading condi-tion. When the vertical load changed to be oblique load, themaximum mucosa deformation is about two times as theVM loading condition. .e peak maximum deformation ofthe mucosa is in VI loading condition in the CM group. Inthe OM group, the peak deformation was concentrated inthe distal border seal area (Table 6).

4. Discussion

Dental implants are used to stabilize complete mandibulardentures, and the two-implant-supported mandibularoverdentures are considered to be the most economical andeffective treatment for edentulous patients [26]. Previousstudies have demonstrated that the retentive force ofmagnets is adequate to aid denture retention and providepatients with great satisfaction [27, 28]. Magnetic attach-ments which are shorter and do not follow a particular pathof insertion compared to mechanical attachments can beused in edentulous patients, especially the cases of reducedinterarch space or in moderately nonparallel abutments [29]or patients with physical disabilities for they are easy to placeand remove [30]. .e clinical study of Ellis et al. [27]

indicated that more than 30% of patients prefer the magneticattachment as the retention system within implant-supported mandibular overdentures for comfortable feel-ing and ease of cleaning. Meanwhile, Cheng et al. showedthat implant-retained magnetic attachment can significantlyimprove the masticatory efficiency of mandibular over-denture, improve the comfort level, and greatly improve thesatisfaction [28].

In VI, VC, and OM loading conditions, the flat-typemodel exhibited higher maximum equivalent stress in theperi-implant bone than dome-type and cushion-typemodels, which can be explained by the difference in theload transfer mechanism of various attachments. .e flat-type attachment can provide the strongest retentive force,but the stress is easy to concentrate with a lack of resilience[31]. .e dome-shaped type is manufactured to reduce thestress level by allowing the denture movement to a certainextent, while the cushion-shaped type is primary through thestress distributor effect of the elastic cushion pad [3]. Ourdata showed that the peak maximum deformation of themucosa is in VI loading condition in the CM group. Itdemonstrated that under vertical force in the upward-downward direction, flexible cushion is helpful for trans-ferring the force to oral mucosa to reduce the vertical forceon the dental implant. Our data are highly consistent withthe results of Takeshita et al. [14] that the characteristics ofdifferent attachment systems will affect the stresses gener-ated in the peri-implant bone of mandibular overdenture. Interms of stress distribution, dome-type and cushion-typeattachments may be a better choice to reduce the stressgenerated in the peri-implant bone during vertical loadingcondition.

.e oblique force was applied buccolingually on the rightfirst molar to simulate the chewing forces. It can be seen thatthe maximum stress on the peri-implant bone under obliqueloading was approximately two times as those under verticalloading. Oblique load is thought to be harmful for stressdistribution on the implants [32]. Our results indicated thatthe peri-implant bone damage is more likely happenedunder oblique loading than vertical loading. Compared withthe flat-type attachment, dome-type and cushion-type at-tachments exhibit less stress on the peri-implant bone underoblique loading condition. .is is due to the stress-breakingability of these two attachments [33, 34]..e study by Gondaet al. [3] has demonstrated that the magnetic attachmentwith stress breaker caused lower lateral stress than con-ventional magnetic attachment. .e effect of the cushionmaterials and allowance in rotational movement of thedome-shaped configuration are beneficial for mitigating thelateral stresses on the peri-implant bone, which may min-imize traumatic loads towards the implant fixture.

In the implant-retained overdenture, the movement ofthe denture should also be considered [35]. Retention of theoverdenture results from the type of the attachment system,and the pressure on the denture border sealing area affectsthe denture base coordination. In oblique molar loadingcondition, the highest maximum deformation of the mucosawas approximately two times as high as in VM loadingconditions, and the deformations of the mucosa were mainly

Computational and Mathematical Methods in Medicine 5

Page 6: Comparison of Three Different Types of Two-Implant

Table 3: Maximum equivalent stress in the peri-implant bone (MPa).

Loading condition Flat-type model Dome-type model Cushion-type modelVI 7.0701 6.8054 6.6113VC 10.538 10.507 9.6443VM 3.644 3.618 3.688OM 7.202 7.127 6.7322

20.51119.05717.60216.14814.69313.23911.78410.3298.87497.42035.96584.51123.05674.60210.14757

37.51634.86732.21829.56926.92124.27221.62318.97416.32613.67711.0288.37955.73073.0820.43321

5.77555.36464.95384.54294.13213.72123.31042.89962.48872.07791.6671.25620.845320.434470.023626

15.26114.17313.08611.99810.9119.82328.73577.64826.56075.47334.38583.29832.21081.12330.035802

19.59318.20316.81415.42414.03412.64411.2559.86498.47527.08545.69574.3062.91621.52650.13678

35.48832.98530.48327.9825.47722.97420.47117.96815.46612.96310.467.95735.45442.95160.44883

5.43635.04954.66274.27593.88923.50243.11562.72882.3421.95521.56841.18160.794840.408060.021267

15.02413.95312.88211.81210.7419.67048.59977.52916.45845.38784.31713.24652.17581.10520.034541

18.89717.55616.21514.87413.53312.19310.8529.51088.16996.8295.48814.14722.80631.46540.12452

32.83830.52428.20925.89423.57921.26418.9516.63514.3212.0059.69037.37555.06072.74590.43113

5.43635.04954.66274.27593.88923.50243.11562.72882.3421.95521.56841.18160.794840.408060.021267

14.02713.02812.02811.02910.0299.02968.03017.03066.03115.03164.03213.03262.03311.03360.034056

VI

VC

VM

OM

(a) (b) (c)

Figure 6: Maximum equivalent stress in dental implant of the flat-type model, dome-type model, and cushion-type model in four loadingsituations. Colors indicate level of stress from dark blue (lowest) to red (highest) (MPa). (a) Flat-type. (b) Dome-type. (c) Cushion-type.

6 Computational and Mathematical Methods in Medicine

Page 7: Comparison of Three Different Types of Two-Implant

concentrated in the distal border seal area. It inferred thatthe oblique force leads to the largest deformation of themucosa, which may ultimately destroy the denture border

sealing effects. A previous report compared the stress dis-tribution around implant and movement of overdenturesretained with ball and three different types of magneticattachments [11]. .e authors concluded that magneticattachments could be a better choice based on lower stresson peri-implant bone and better denture stability. Mean-while, they also indicated that when the dentures were undertoo much lateral loads, the magnetic attachment was notstable. It is generally accepted that the low resistance tolateral forces is one of the greatest advantages of magneticattachment, and the loss of retention under excessive obliqueloading may help to protect the implant against unfavorable

Table 4: Maximum equivalent stress in dental implant (MPa).

Loading condition Flat-type model Dome-type model Cushion-type modelVI 20.511 19.593 18.897VC 37.516 35.488 32.838VM 5.775 5.436 5.726OM 15.261 15.026 14.027

1.98771.84611.70461.56311.42161.281.13850.9970.855480.713960.572440.430910.289390.147870.0063484

1.97711.83641.69561.55491.41411.27341.13260.991880.851130.710390.569640.428890.288150.14740.0066532

2.02971.88521.74071.59621.45171.30721.16271.01820.873750.729260.584760.440260.295770.151270.0067751

VI

1.0520.977020.902080.827140.75220.677260.602330.527390.452450.377510.302570.227640.15270.0777590.0028208

1.0620.98640.910770.835140.759520.683890.608260.532640.457010.381380.305750.230130.15450.0788730.0032457

1.38431.28561.18691.08820.989480.890770.792060.693350.594640.495930.397210.29850.199790.101080.0023678

VC

0.683190.634410.585630.536840.488060.439280.390490.341710.292930.244140.195360.146580.0977950.0490120.00022947

0.673980.625860.577730.529610.481490.433370.385250.337130.289010.240890.192770.144650.0965290.0484090.00028825

0.676020.627750.579480.531220.482950.434690.386420.338150.289890.241620.193360.145090.0968240.0485580.00029216

VM

1.62351.50771.39191.27611.16031.04440.928640.812820.697010.58120.465380.349570.233760.117950.0021336

1.58211.46931.35641.24361.13071.01790.905030.792180.679330.566480.453630.340780.227930.115080.0022286

1.63641.51971.4031.28621.16951.05280.936020.819290.702560.585830.46910.352360.235630.11890.0021676

OM

(a) (b) (c)

Figure 7: Maximum equivalent stress on the mucosa of the flat-type model, dome-type model, and cushion-type model in four loadingsituations. Colors indicate level of stress from dark blue (lowest) to red (highest) (MPa). (a) Flat-type. (b) Dome-type. (c) Cushion-type.

Table 5: Maximum equivalent stress on the mucosa (MPa).

Loadingcondition

Flat-typemodel Dome-type model Cushion-type model

VI 1.987 1.9771 2.0297VC 1.052 1.062 1.3843VM 0.683 0.673 0.676OM 1.623 1.582 1.6364

Computational and Mathematical Methods in Medicine 7

Page 8: Comparison of Three Different Types of Two-Implant

lateral forces, especially for patients with osteoporosis orwhen a shorter or smaller diameter implant has to be useddue to bony deficiency.

Based on these results, it can be suggested that the se-lection of a magnetic attachment system for two-implant-retained overdentures should be carried with caution. Inpatients with osteoporosis or bony deficiency, dome-type orcushion-type attachments should be better choices than theflat-type attachment. From the official website of Aichi Steel

Company (http://www.aichi-steel.co.jp), the flat-type mag-netic attachment is indicated only for four-implant-supported overdentures. .e limited usage of this systemfor two-implant-retained overdentures can be attributed tothe relatively higher levels of lateral forces and strain/stressdistribution when compared with the other two magneticsystems, which has been demonstrated by our FEA analysis.

.ree-dimensional finite element method used in thisstudy has some limitation in predicting the response ofapplied loadings [36–38]. First, the structures were con-sidered isotropic, homogeneous, and linearly elastic, andperfect osseointegration between implants and bone was alsohypothesized. Secondly, only one oblique force on the rightfirst molar was applied to the model. In fact, the occlusalforces are multidirectional, so it is hard to simulate thecomplicate stress distribution. However, our data mayprovide a deeper understanding about the biomechanicalbehaviors of magnetic attachment. Long-term clinical

0.00295910.00274880.00253850.00232820.0021180.00190770.00169740.00148710.00127680.00106650.000856160.000645860.000435570.000225271.4969e – 5

VI

0.00294330.00273410.0025250.00231580.00210670.00189750.00168840.00147920.00127010.00106090.00085180.000642650.000433510.000224361.5209e – 5

0.00302170.0028070.00259230.00237760.00216290.00194820.00173360.00151890.00130420.00108950.000874820.000660140.000445460.000230771.6086e – 5

0.00167690.00155780.00143860.00131950.00120030.00108120.000962010.000842860.000723710.000604550.00048540.000366250.00024710.000127948.7915e – 6

VC

0.00169320.00157290.00145260.00133220.00121190.00109160.000971330.000851020.000730710.00061040.000490090.000369790.000249480.000129178.8644e – 6

0.00223870.00207940.00192020.00176090.00160170.00144240.00128320.00112390.000964640.000805380.000646120.000486870.000327610.000168359.0972e – 6

0.0010080.000936070.000864110.000792150.000720190.000648240.000576280.000504320.000432360.00036040.000288440.000216480.000144527.2558e – 55.9789e – 7

VM

0.000999640.000928270.000856910.000785540.000714170.00064280.000571440.000500070.00042870.000357340.000285970.00021460.000143237.1867e – 55.0026e – 7

0.000997480.000926270.000855060.000783850.000712640.000641420.000570210.0004990.000427790.000356580.000285370.000214160.000142957.1734e – 55.2254e – 7

0.00246960.00229380.00211790.0019420.00176610.00159030.00141440.00123850.00106270.000886810.000710940.000535070.000359210.000183347.4697e – 6

OM

0.00245220.00227750.00210290.00192820.00175360.0015790.00140430.00122970.00105510.000880440.00070580.000531170.000356530.00018197.2632e – 6

0.00249320.00231560.00213810.00196050.0017830.00160540.00142790.00125040.00107280.000895280.000717730.000540190.000362650.00018517.5613e – 6

(a) (b) (c)

Figure 8: Distribution of the mucosa deformation of the flat-type model, dome-type model, and cushion-type model in four loadingconditions. Colors indicate level of strain from dark blue (lowest) to red (highest) (10−3 μm/μm). (a) Flat-type. (b) Dome-type. (c) Cushion-type.

Table 6: .e maximum deformation of the mucosa (10−3μm/μm).

Loadingcondition

Flat-typemodel Dome-type model Cushion-type model

VI 5.72 5.55 5.62VC 6.66 6.49 6.58VM 4.40 4.16 4.16OM 18.05 17.83 16.59

8 Computational and Mathematical Methods in Medicine

Page 9: Comparison of Three Different Types of Two-Implant

studies are needed to assess the effects of different types ofmagnetic attachment on mandibular injuries and denturefunction.

5. Conclusions

Within the limitations of the study, the following conclu-sions were drawn:

(1) Flat-type magnetic attachment exhibited higherlevels of maximum equivalent strain/stress in theperi-implant bone compared to dome-type andcushion-type attachments under vertical and obliqueloading conditions

(2) Oblique loading may play a detrimental role for allmagnetic attachments in strain/stress distributionand denture stability

(3) Cushion-type and dome-type attachments are betterchoices in two-implant-retained mandibular over-dentures, especially for patients with bad boneconditions such as osteoporosis or when a shorter orsmaller diameter implant has to be used

Abbreviations

VM: 100N vertical load applied on the right first molarVC: 100N vertical load applied on the right canineVI: 100N vertical load applied on the lower incisorsOM: 100N oblique load applied on the right first molar.

Data Availability

.e data used to support the findings of this study are in-cluded within the article.

Conflicts of Interest

.e authors declare that they have no conflicts of interest.

Authors’ Contributions

Fengling Hu and Yiming Gong contributed equally to thiswork.

Acknowledgments

.is work was supported by Shanghai Cooperative In-ternational Project (Grant no. 12410710500), ShanghaiMunicipal Natural Science Foundation (Grant no.13ZR1441400), Shanghai Municipal Planning Commissionof Science and Research Fund (Grant no. 201740230),Talent Development Plan funded by the Fifth People’s Hos-pital of Shanghai, Fudan University (no. 2017WYRCJY02),and Shanghai Minhang District Health and Family PlanningCommission (Grant no. 2015MW05).

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