A biomechanical analysis of titanium miniplates used fortreatment of mandibular symphyseal fractures with thefinite element methodBaohui Ji,a Chun Wang,a Lei Liu, PhD, MD,b Jie Long, PhD, MD,b Weidong Tian, PhD, MD,b

and Hang Wang, PhD, MD,a Chengdu, PR ChinaSICHUAN UNIVERSITY

Objective. This study aimed to evaluate the stress distribution and stress shielding effect of titanium miniplates usedfor the treatment of symphyseal fractures using finite element (FE) analysis.Study design. Two 3-D FE models of symphyseal fractured mandibles reduced by technique 1, reduction with a singleminiplate, and technique 2, reduction with 2 miniplates, respectively, were developed. Three basic loading conditionswere simulated.Results. The ratios of stress shielding of miniplates were different. Ratios of the lower miniplates in technique 2 weremuch higher than the upper miniplates and the miniplates in technique 1 during all conditions, and that value of thelower miniplate gained a maximum value of 83.34% during left unilateral molar clenching. The stress areas wereconcentrated on the central section of the miniplates. However, the stress distribution varied with masticatoryconditions.Conclusion. The study demonstrated that miniplate stress distribution and stress shielding effect ratio were affected notonly by the way in which the mandible was loaded but also by the number of the miniplates fixing the fracture. (Oral

Surg Oral Med Oral Pathol Oral Radiol Endod 2010;109:e21-e27)

The symphysis is one of the most frequently fracturedregions after traumatic events involving the mandible,with a frequency of 9% to 57%.1,2 Rigid internal fixa-tion is now routinely used for surgical management ofmandible fractures.3-8 The stability of the mandibleduring functional activities takes the premier place inthis technique. Indeed, movement at a fracture line is aknown predisposing factor for both infection and non-union.9 Thereby, the ideal plate-screw system must bestrong and rigid enough to withstand the functionalloads and enable undisturbed fracture healing. In addi-tion, the concept of “stress shielding” should also betaken into account. A too rigid plate will lead to boneloss.10 Given these facts, optimized internal fixationshould attain a balance between the stability of thefragments and the stress shield effect of the miniplates.In past decades, finite element (FE) analysis, which isbased on material properties to determine the distribu-

This work was supported by the National Natural Science Foundationof China (10702046).aState Key Laboratory of Oral Disease, Sichuan University, Chengdu,PR China.bDepartment of Oral and Maxillofacial Surgery, West China Hospitalof Stomatology, Sichuan University, Chengdu, PR China.Received for publication May 11, 2009; returned for revision Oct 17,2009; accepted for publication Nov 8, 2009.1079-2104/$ - see front matter© 2010 Published by Mosby, Inc.

doi:10.1016/j.tripleo.2009.11.003

tion of stress and strain when the structures are sub-jected to force, was applied to stress-strain analysis forcomplex structures. Previous research7,11-13 has alreadydescribed the biomechanical distribution of a mandiblethat fractured at the angle or condylar process afterreduction with miniplates using FE analysis. However,the symphyseal fracture has not yet been explored. Forthese reasons, in the present study, we proposed andanalyzed two 3-dimensional (3-D) FE models simulat-ing the behavior of symphyseal fractured mandiblesafter reduction with titanium miniplates. We then usedthese models to study the response to 3 different mas-ticatory conditions of the mandible that were treatedwith 1 or 2 miniplates in the symphysis region.

MATERIALS AND METHODSThe mandible model and its mechanicalproperties

A human mandible of a 25-year-old man, whoshowed no craniofacial abnormalities, was scanned bydual-slice spiral computed tomography (CT) (SiemensSomatom DR2, Siemens GmbH, Munchen, Germany)in the axial direction at 0.75-mm intervals. After beingdigitized with MIMICS 11(Materialise, Leuven, Bel-gium), the data were exported to the Ansys 7.0 pro-gram, which created a model from bottom to top. Mesh-ing was performed with the use of Solid 92 finiteelement. Finally, we assumed that the mandible had

linearly elastic behavior, and its mechanical properties

e21

OOOOEe22 Ji et al. March 2010

could therefore be described by the Young’s modulus(E) and Poisson’s ratio (�). As in previous work,7,14 weassumed the mandible to be elastic and isotropic withelastic constants E � 13,700 MPa and � � 0.3 for thecortical bone and E � 7930 MPa and � � 0.3 for thecancellous bone. The teeth were assumed to be part ofthe mandible with the same mechanical properties. Inthis way, the real anisotropic properties of the mandiblewere simplified, which means the bone material wasassumed the same in every plane and would not exhibitany nonlinear stress-strain characteristics or plasticity.

As for the fracture site, we assumed a clear symphy-sis fracture in the middle sagittal plane. Contact be-tween the 2 bone segments was assumed nonexistent.

Fixation hardware and its mechanical propertiesThe computer models of the titanium miniplates and

monocortical screws were set by the Pro/E program,based on physical specimens of the 4-hole, 2.4-mmthickness maxillofacial miniplate (SYNTHES, WestChester, PA), and a 2.4-mm-diameter monocorticalscrew, respectively. The miniplates and screws in-volved in this study were assumed to be composed ofan isotropic elastic material, whose elastic coefficientsare E � 1.15 � 105 MPa and � � 0.34. Each miniplatewas fixed to the mandible by 4 monocortical screws.

Two different surgical fixation techniques, whichwere commonly used in symphyseal fracture fixation,were then developed (Fig. 1). In technique 1, a singleminiplate was fixed horizontally in the middle of thesymphysis. In technique 2, 2 miniplates parallel to eachother were used. One miniplate was fixed onto thelower part and the second one was fixed immediatelybelow the dental roots and above the lower dentalnerve, in accordance with the work of Champy et al.15

Each screw was determined to be in perfect contact andfirmly fixed with the cortical and trabecular bone sur-rounding it and the miniplate (no slip and no clearance)as the design of Uni-locking plating system. Further-more, the miniplates were assumed not to receive ortransmit any force directly from the bone segments,rather, the chain of force transfer was defined as pro-gressing from bone to screw, from screw to plate, andfinally returning via the screws back to the bone.

Contact and boundary conditionTo prevent the rigid corpus translation and/or rota-

tion during biting on an object, the top of the 2 condyleswere fixed in space for the boundary condition and onlyrotational movement was allowed. The effect of theintermediate articular disk, which acts as a cushionbetween the condyle and temporal bone, was neglectedin this study. The area of concern was well away from

the condyle and should not be much affected by ignor-

ing the disk. Restriction of the teeth will be detailed inthe following section.

Biting and muscle forcesIn the present investigation, 3 static biting tasks,

namely clenching in the intercuspal position (ICP),

Fig. 1. A, Location of miniplate in technique 1. B, Locationof miniplates in technique 2.

incisal clenching (INC), and left unilateral molar

nt ma

OOOOEVolume 109, Number 3 Ji et al. e23

clenching (L-MOL) were simulated. In ICP, the pre-molars and molars were restrained bilaterally and ver-tically from movement (excluding the third molar,which was partially erupted). During INC and L-MOL,the 4 incisors and the first molar, respectively, were notallowed to translate upward. These restraints acted per-pendicularly to the occlusal plane (y-direction) at thelower supporting cusps, allowing freedom of displace-ment in the horizontal plane.

Aiming at simulating realistic muscle forces exertedon the bone when clenching, we used pairs of parallelvectors to simulate 9 pairs of masticatory muscles in-volved in the 3 static biting tasks (superficial and deepmasseter; anterior, middle, and posterior temporalis;medial pterygoid; superior and inferior lateral tempo-ralis; and anterior digastric). The origin and direction ofeach muscle force was defined from anatomical mea-surements.16 Their directions were derived algebra-ically as unit vectors (ie, direction cosines). The singlevectors of the muscular attachment were available inthe literature.17 The magnitude of each muscle forcewas assigned according to its physiological cross sec-tion and the scaling factor.18,19 With a well-definedgeometry and mesh, material properties, and appropri-ate bite and muscle forces loading, the Ansys 7.0 finiteelement solver software was used to compute stress inthe models. After fixation, miniplate and bone directlyunder it form one mechanical system, and the stress thatthe miniplate bears accounts for a certain proportion tothe bone stress when there is no miniplate. This pro-

Fig. 2. Ratios of stress shielding of miniplates during differe

portion was defined as the stress shielding ratio in our

study. A local stress shielding ratio of the miniplate wasalso calculated according to the formula

� � (1 � � ⁄ �0) � 100%,

where � is the stress of the bone directly under theminiplate after fixation, and �0 is the stress of the boneof the same site before fixation.

RESULTSThe Von Mises stress’s scalar running from minimum

stress value (blue) to the maximum value (red) repre-sented the general effective stress of the miniplates. Allstress values were given in MPa.

The ratios of stress shielding in both of the modelsare shown in Fig. 2. When the mandible was fixed with1 miniplate, the ratios during ICP and INC were both50%, but the ratio was smaller during L-MOL. Whenthe mandible was fixed with 2 miniplates, the valueschanged. As shown in Fig. 2, the ratios of the 2miniplates in technique 2 not only differed from eachother, but also differed from that of the single miniplateof technique 1. In general, the value of the lowerminiplate was much higher than that of the upperminiplate and the single miniplate in technique 1 duringeach condition, and it gained a maximum value of83.34% during L-MOL. For the upper miniplate, thevalue during INC was higher than its value duringthe other 2 conditions, and the value during ICP was thelowest. In contrast with the upper miniplate, the lower

sticatory conditions.

miniplate gained its minimum value during INC.

ry con

OOOOEe24 Ji et al. March 2010

The maximum stress values of different miniplatesare shown in Fig. 3. The stress distributions of differentminiplates are shown in Fig. 4. In general, the stressareas were concentrated in the central part of theminiplates. The magnitude of the stress on the upperminiplates in technique 2 was smaller than that on thelower miniplates during all conditions. The superiorand inferior boundaries covering the fracture linegained the maximum stress in every miniplate; how-ever, the stress distribution varied with masticatoryconditions. During ICP, the stress of the 2 holes closeto the fracture line concentrated on the part farthestaway from the fracture line, whereas for the other 2holes, the stress concentrated on the part closest to thefracture line. During INC, the stress concentrated on the2 holes just alongside the fracture line. We also wouldlike to point out that the maximum stress values of thescrews were uniformly higher than those of theminiplates. Moreover, the 2 screws farthest away fromthe fracture line gained the maximum value.

DISCUSSIONPrevious authors20,21 have reported a reduction in

bite force occurring for several weeks post injury.However, a uniform agreement of the magnitude of thebite forces has not been arrived at. In our study, themuscle forces were consistent with the values of anintact mandible. Of course, these models were still farfrom being realistic. Our simulations, like most finiteelement simulations, were based on an idealized model

Fig. 3. Stress values of miniplates during different masticato

to which idealized properties (Young’s modulus and

Poisson’s ratios) were assigned. As described in theMethods section, weaknesses in the model included thelack of information on teeth, the lack of detailed knowl-edge regarding the material properties of the cancellousbone, the uncertainty of how to realistically distributethe muscle loading, and the difficulty of knowing howto model the boundary conditions of the condyles.However, as we only aimed at investigating stressdistribution and variation rather than predicting thebiological reaction, these models were completely qual-ified for the work. In the future, great importanceshould be attached to overcoming the shortcomings ofthe model.

The effect of stress shielding is well known in longbones. The scientific evidence to date strongly suggeststhat bone loss in plated long bone is caused by stressshielding, and not interference with cortical perfusionsecondary to bone–plate contact.22 Kennady et al.23,24

documented decreased mandibular bone volume as wellas smaller interlable width on the plate side, suggestinga stress shielding effect as a result of the rigid internalfixation plate. Dechow et al.25 stated that bone straininferior to the plates was reduced by 34% to 53% afterattachment of the plates. However, long-term place-ment of bone plates, and the resulting stress shieldingwere not found to result in structural changes in themandibular corpus. Because of their different methodsand goals, the results are different. Nevertheless, weshould point out that neither of them revealed the stressshielding effects when a load shearing plate was used to

ditions.

plate the fracture fragments. To our knowledge, no

OOOOEVolume 109, Number 3 Ji et al. e25

study has been published providing definite data revealingthe stress shielding effects when titanium miniplates areused to immobilize mandibular symphyseal fractures.

The results of our study indicate that mandibles fixedwith titanium plates also experience stress shielding as

Fig. 4. A, The Von Mises stress of the miniplate in technique1 during INC. C, The Von Mises stress of the miniplate in tecin technique 2 during ICP. E, The Von Mises stress of the miminiplates in technique 2 during L-MOL.

long bones. Moreover, the value varies with fixation

sites even though the mandible is under the same loads.It also varies with masticatory conditions even thoughthe miniplate is fixed in the same place (Fig. 2). In ourprevious study,26 we found that under a certain masti-catory condition the mandible gained different values at

g ICP. B, The Von Mises stress of the miniplate in technique1 during L-MOL. D, The Von Mises stress of the miniplatess in technique 2 during INC. F, The Von Mises stress of the

1 durinhniqueniplate

different sites, and the same area gained different val-

OOOOEe26 Ji et al. March 2010

ues when the load was changed. Therefore, based onthese studies, we can draw the conclusion that the ratioof stress shielding correlates with the way in which themandible is burdened and the number of miniplatesfixing the fracture. The important question, however, iswhether the amount of stress shielding observed isbiologically significant. It will therefore be necessary infuture studies to determine whether the amount of stressshielding found in this study is a clinically significantproblem after the fixation of symphyseal fractures.

It is well known that a mandible is normally sub-jected to bending forces at its upper boundary part andto compression forces at its lower boundary, and thesymphyseal region is the very area bearing torsionforces as well as tension forces.10,15 In a mandiblefracture, there is a discontinuous change of the stresstrajectory, and miniplates were designed to regain thestress trajectory continuity and counteract the forces.Therefore, they must be well tolerated, adaptable, andstrong enough to counter forces up to 600 to 1000MPa—their elastic limit of flexibility is 700 to 800 MPaand the rupture point is 950 to 1100 MPa.27 As theresults showed, miniplate stress in each configurationwas below the static yield limit for titanium. In addi-tion, the value of each miniplate varied with mastica-tory conditions. All miniplates presented the same pat-tern: that the magnitudes during L-MOL were higherthan the corresponding values during the other 2 con-ditions and the values during ICP were the lowestamong the 3 conditions. Moreover, in each condition,the stress value of the miniplate in technique 1 wassuperior to the other 2 plates and the upper miniplate intechnique 2 was inferior to the other 2 plates.

In summary, the present study evaluated the biome-chanical behavior of 2 different techniques used inplating the fractured mandibular symphysis. Three-di-mensional FE methods were used to calculate the stressvalue in Von Mises form and the stress shielding effectof the miniplates. Our results demonstrated that stressdistribution and miniplate stress shielding effect ratioare affected not only by the way in which the mandibleis burdened, but also by the number of the miniplatesfixing the fracture.

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Reprint requests:

Hang Wang, PhD, MDState Key Laboratory of Oral DiseaseSichuan UniversityChengdu 610041, PR China

dentistwh@gmail.com