Brief communication: Comparing loading scenarios in lower first molar supporting bone structure using 3D finite element analysis

Brief Communication: Comparing Loading Scenarios inLower First Molar Supporting Bone Structure Using 3DFinite Element Analysis

Stefano Benazzi,1* Ottmar Kullmer,2 Ian R. Grosse,3 and Gerhard W. Weber1

1Department of Anthropology, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria2Department of Palaeoanthropology and Messel Research, Senckenberg Research Institute—Senckenberganlage 25,D-60325 Frankfurt am Main, Germany3Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA

KEY WORDS mandible; biomechanics; loading conditions; three-dimensional finite-elementanalysis (3D FEA); occlusal fingerprint analyzer (OFA)

ABSTRACT Finite element analysis (FEA) is a wide-spread technique to evaluate the stress/strain distribu-tions in teeth or dental supporting tissues. However, inmost studies occlusal forces are usually simplified using asingle vector (i.e., point load) either parallel to the longtooth axis or oblique to this axis. In this pilot study weshow how lower first molar occlusal information can beused to investigate the stress distribution with 3D FEA inthe supporting bone structure. The LM1 and the LP2-LM1

of a dried modern human skull were scanned by lCT inmaximum intercuspation contact. A kinematic analysis ofthe surface contacts between LM1 and LP2-LM1 duringthe power stroke was carried out in the occlusal finger-print analyzer (OFA) software to visualize contact areasduring maximum intercuspation contact. This informa-

tion was used for setting the occlusal molar loading toevaluate the stress distribution in the supporting bonestructure using FEA. The output was compared to thatobtained when a point force parallel to the long axis of thetooth was loaded in the occlusal basin. For the point loadcase, our results indicate that the buccal and lingual cort-ical plates do not experience notable stresses. However,when the occlusal contact areas are considered, the disto-lingual superior third of the mandible experiences hightensile stresses, while the medio-lingual cortical bone issubjected to high compressive stresses. Developing amore realistic loading scenario leads to better models tounderstand the relationship between masticatory func-tion and mandibular shape and structures. Am J PhysAnthropol 000:000–000, 2011. VVC 2011 Wiley-Liss, Inc.

The investigation of the distribution of stress/strainduring biting and chewing is a major topic in compara-tive anthropology, as well as in dentistry and maxillofa-cial surgery. Several authors have studied this topic fordifferent reasons: for acquiring functional biomechanicsinformation about anthropoid mandibles (Daegling andHylander, 1998; Daegling and Hotzman, 2003), toimprove the design of fixed partial dentures (in pros-thetic dentistry; Field et al., 2010), or to test varioustype of mandibular reconstruction after resection proce-dures due to tumors, osteomyelitis and trauma (in ortho-dontics and maxillofacial surgery; Tie et al., 2006). In allcases, finite element analysis (FEA) has gained increas-ing interest because a virtual simulation prevents dam-ages to the original specimen (Cheng et al., 2010a; Fuet al., 2010). At the same time FEA offers the possibilityto test various scenarios beginning from the same model.However, the biomechanics of mastication is very com-

plex both for the number of structures and tissuesinvolved and for the kinds of forces generated. For a re-alistic simulation of functional biomechanics, severalforces engendered during mastication or other feedingbehaviors should be simultaneously considered (Daeglingand Hotzman, 2003). Based on the facilities and techni-ques currently available to researchers, all these param-eters cannot be considered virtually at once. Thereforeloading simplifications at different levels have beenintroduced to create experimental models. In particular,previous studies have recognized two main kinds ofstress in the postcanine portion of the mandibular cor-

pus: 1) torsional loads, the primary source of stress, and2) occlusal loads (Daegling and Hotzman, 2003). None-theless, when only a limited portion of the mandible isinvestigated, researchers have usually considered onlythe latter. Accordingly, occlusal load was applied to eval-uate both the stress and strain distribution in teeth ordentures under loading conditions (De Jager et al., 2006;Fu et al., 2010; Jiang et al., 2010; Rafferty et al., 2010)and the biomechanical response of the underlying den-ture supporting tissues (periodontal ligament—PDL, tra-becular and cortical bone; Kondo and Wakabayashi,2009; Field et al., 2010; Hasegawa et al., 2010). In theaforementioned studies, forces were applied in the cen-tral basin of the occlusal surface or, alternatively, on thetip of the dental cusps by means of vectors parallel tothe long axis of the tooth crown or oblique to it (Ichimet al., 2007; Coelho et al., 2009; Motoyoshi et al., 2009;Field et al., 2010; Hasegawa et al., 2010; Jiang et al.,

Grant sponsor: NSF (Hominid Grant 2007); Grant number: 01-120. Grant sponsor: Deutsche Forschungsgemeinschaft (DFG).

*Correspondence to: Dr. Stefano Benazzi, Althanstrabe 14, 1090Vienna, Austria. E-mail: [email protected]

Received 8 April 2011; accepted 31 July 2011

DOI 10.1002/ajpa.21607Published online in Wiley Online Library

(wileyonlinelibrary.com).

VVC 2011 WILEY-LISS, INC.

AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 000:000–000 (2011)

2010). This approach does not take into considerationthe individual wear pattern of the crown. Some research-ers have already emphasized that during maximumintercuspation contact several wear facets should be con-sidered and loaded in different direction and to variousextents (Hattori et al. 2009; Kondo and Wakabayashi,2009; Benazzi et al., 2011) to correctly estimate how thechewing forces are distributed in the structures support-ing the teeth (DeLong, 2006).In this article we use 3D FEA to compare the stress

distributions produced in the supporting bone structureof a lower first molar (M1) under two different occlusalloading conditions: 1) the molar is loaded by a vectorparallel to the long axis of the tooth and placed in thecentre of the occlusal basin of the crown (Case 1); 2) theforces are applied onto the occlusal contact areasdetected during two-body interactions in maximumintercuspation contact; the vectors are perpendicular tothe wear facets (Case 2). In so doing we seek to under-stand the fidelity needed in modeling intercuspation con-tact in terms of the biomechanical response of the tooth’ssupporting structure.

MATERIALS AND METHODS

A dried modern human skull collected at the Depart-ment of Anthropology, University of Vienna, was selectedfor the simulation. The individual (ID 5 S138) is anadult male (30- to 40-years old) from Europe. The sexand age at death were assessed by the examination ofthe cranial and postcranial characters (Acsadi and Nem-

eskeri, 1970; Ferenbach et al., 1980; Buikstra and Ube-laker, 1994).This specimen was selected because of its M1 wear

stage 3 (after Smith, 1984), thus showing a well estab-lished pattern of wear facets. The lower left first molar(LM1) and the antagonistic upper left second premolar(LP2) and first molar (LM1) were taken into account forthe analysis.

Micro-CT scan, segmentation, and 3Dreconstruction

A micro-CT (lCT) scan of the skull with upper andlower dentition in maximum intercuspation contact wascarried out at the Vienna Micro-CT Lab, Department ofAnthropology, University of Vienna, with a ViscomX8060 lCT scanner using the following scan parameters:130 kV, 100 mA, voxel size 5 55 lm.The half-maximum height protocol (Spoor et al., 1993)

was used to reconstruct 3D digital models for the LM1,LP2, and LM1 using the software package Amira 5.2(Mercury Computer Systems, Chelmsford, MA). Thisprotocol samples the Hounsfield values on either side ofthe transition between two adjacent tissues and takesthe value halfway between them as the threshold value.To segment the voxels with similar Hounsfield valueslocated at the boundary between two tissues a manualcorrection was conducted.A complete segmentation of the LM1 dental tissues

(enamel, root and pulp chamber) and its supporting tis-sues (PDL, trabecular, and cortical bone) was carried out(Fig. 1a).

Fig. 1. a) Dental tissues and supporting structures for S138. PDL 5 periodontal ligament. b) The FE mesh consisting of536,769 10-noded tetrahedral elements. c) The restrained nodes in the medial and distal surfaces (the latter only partially visible)of the mandible are displayed in pink/white colors. B 5 buccal; D 5 distal; L 5 lingual; M 5 mesial. [Color figure can be viewed inthe online issue, which is available at wileyonlinelibrary.com.]

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Because the LP2-LM1 complex was used only to assessthe occlusal contact areas with LM1, only the externalsurface of the teeth was segmented. The final refinementof the digital models was carried out in Rapidform XOR2(INUS Technology, Seoul, Korea).

Case 1: Single point loading

The long axis of the LM1 was computed in RapidformXOR2. This axis informs about the loading direction forthe first test, applied onto a single point (i.e., node) atthe central groove area of the occlusal basin.

Case 2: Load distributed onto the contact areas

To recognize the contact areas on the LM1 during max-imum intercuspation contact with the antagonistic teeth,both dental surface models (LM1 and LP2-LM1) wereimported into the occlusal fingerprint analyzer (OFA)software. The software allows moving one model towardthe other along a defined pathway to analyze the colli-sion of crown contacts. OFA software prevents the pene-tration of the models into one another thanks to collisiondetection, deflection and break free algorithms (Fig. 2a).The tolerance distance for collision detection was set to0.2 mm, a distance slightly larger than the averagelength of the surface model triangles edge length. Thecolliding triangles of the two models are automaticallyselected by the software and highlighted in a user-defined color (Fig. 2b). The OFA contact results provideinformation about the loading position, but does notinform about the loading direction. For maximum inter-cuspation contact we can assume that a compressiveforce acts between complementary wear facet pairs,which could ultimately be represented as perpendicularloads to these facets (Hattori et al., 2009; Benazzi et al.,2011). Therefore, the occlusal wear facets of the LM1

were manually marked in Rapidform XOR2 by placingcurves onto the models surface (Kullmer et al., 2009).Then, we created the best-fit planes for each wear facet,and we computed the normal vectors (i.e., the line ofaction of the normal force) of each facet’s plane (Fig. 2c).Each contact area was loaded by the wear facet’s vectorto which the contact area belongs to. Obviously, there isnot an exact correspondence between the pattern of con-

tact areas obtained by the OFA software and the patternof wear facets identified on the occlusal surface of themolar. Some spots, e.g., such as the worn protoconid tip,are not developed through attrition due to tooth-to-toothcontacts, but through tooth-food-tooth abrasion (Kayand Hiiemae, 1974). Those areas probably do not experi-ence direct chewing loads, and they are maybe activeduring initial moments of chewing, such as tip puncture-crushing.

Finite element mesh generation and FEA

The surface models were then imported into Strand7Software (G1D Computing, Sydney, Australia), wherevolumetric meshes (including PDL, cortical and trabecu-lar bone shown in Fig. 1a) were created using 10-nodestetrahedral elements. The specimen was meshed with atotal of 775,442 nodes and 536,769 tetrahedral elements(Fig. 1b). Information for material properties such as theelastic modulus—E, and the Poisson’s ratio were col-lected from the literature and summarized in Table 1.All the biological materials represented in the modelswere considered homogeneous, linearly elastic and iso-tropic, assumptions that are regularly applied with sim-pler continuum mechanics models (e.g., Coelho et al.,2009; Fu et al., 2010; Jiang et al., 2010).Boundary constraints were applied to the medial and

distal cut surfaces of the mandible section (Fig. 1c). Themedial nodes were restrained only in x-axis translation(linguo-buccally) to prevent the mandible from twistingand were free along the y- and z-axes (supero-inferiorlyand medio-distally, respectively). The distal nodes wererestrained both in the y- and z-axes. Accordingly, we areasserting that the function of the balancing masticatingforces is to keep the mandible from twisting, and theworking side forces are producing the superior–inferiorbite force. These boundary constraints, while not per-fectly realistic, are much more consistent with mandibu-lar biomechanics than the nonphysical boundary con-straints employed in other studies (e.g., Hasegawa et al.,2010).In both cases the model was subjected to 150N occlu-

sal load, which is an average force among the loadingconditions found in the literature (e.g., Dejak et al.,

Fig. 2. a) Maximum intercuspation contact between LM1 and the antagonistic teeth LP2-LM1. b) Occlusal contacts (dark grey)detected by the occlusal fingerprint analyzer software in the occlusal surface of S138-LM1 specimen. c) S138-LM1 shows the wearfacet pattern (dark grey) and the normal vectors (arrows) computed for each facet’s plane.

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2003; Cheng et al., 2010b; Fu et al., 2010). As mentionedabove, for Case 1 a single point load was used. For Case2, the load was distributed proportionally in relation tothe area of the wear facets involved during maximumintercuspation contact, thus simulating the case of uni-form contact pressure. Because loads applied in Case 2on each facet are not collinear, a total applied load of150N will not conserve the 150N load acting in the direc-tion of force applied in Case 1. Thus, we scaled up themagnitude of load which we distributed to the facets inproportion to their surface area such that the net compo-nent of Case 2 loading acting in the Case 1 load direc-tion was equal to 150N (scale factor 5 1.42). The totalmagnitude of force that was distributed over the facetsin proportional to their surface areas was equal to 1.423 150N 5 213N. In essences, we designed the Case 2loading to conserve the value of load applied in the Case1 direction, while at the same time applying loads nor-mal to each facet and in proportion to their contact area.The stress state patterns were qualitatively and quan-

titatively compared according to the von Mises stressesand the maximum principal stresses criterion (Chenget al., 2010a; Field et al., 2010; Hasegawa et al., 2010).At any material point the square of the von Mises stressis directly proportional to distortional strain energy den-sity, while the first and the third principal stressesinform respectively about tensile and compressive behav-ior in specific sites of the 3D model (Field et al., 2010).

RESULTS

The von Mises stresses of higher magnitude observedin Case 1 (load in the occlusal basin) occurred in thedisto-superior border of the model, in correspondence tothe constrained area (this area is subjected to tensilestresses), and in the lingual and buccal mid-corpus ofthe model due to compressive stresses (see Fig. 3).Regarding the latter, the maximum third principalstresses show negative values of low magnitude. Accord-ingly, we assume that only a slight compression charac-terizes this area. These results suggest that the load istransferred directly from the molar to the bottom of themandible, and does not affect considerable the buccal orlingual cortical bone.In Case 2 (maximum intercuspation contact) elevated

von Mises stresses occurred in the cortical bone in thedisto-lingual superior third of the mandible and in thelingual cortical bone (see Fig. 3). The former highlightsthe high tensile stresses increased during maximumintercuspation contact in the alveolar cortical bone,mainly disto-lingually. The latter corresponds to the highcompressive stresses in the medio-lingual aspect of themandible. Compressive stresses occur also in the distaland mainly in the medio-buccal cortical bone around thecervical region of the LM1, and in the distal bottom of

the mandible (see Fig. 3). It is noteworthy that the lin-gual side, which shows high tensile stresses in the mid-dle and distal superior third of the mandible and com-pressive stresses in the mid-corpus and mainly in themedio-lingual surface, is characterized by thinner corti-cal bone compared to the buccal side.

DISCUSSION AND CONCLUSIONS

Virtual simulation by means of 3D FEA allows investi-gating stress/strain distributions in loaded mandible togather more information about its functional morphol-ogy. Most of the simulations done so far for the sake ofprosthetic dentistry, biomaterial testing and maxillofa-cial surgery involve single teeth (De Jager et al., 2006;Fu et al., 2010; Jiang et al., 2010; Rafferty et al., 2010)or portions of the human mandible (Kondo and Waka-bayashi, 2009; Field et al., 2010; Hasegawa et al., 2010),where the loading scenario is simplified and limited tothe occlusal loads. This simplification is a compromiseowing to technical limitations in evaluating the effect ofmultiple loading regimes (i.e., torsional loading, sagittalbending) in a section of the mandible when the wholemandible and the masticatory muscle force informationare not available. Nevertheless, compared with previousworks (see also Ichim et al., 2007; Coelho et al., 2009;Motoyoshi et al., 2009; Field et al., 2010; Hasegawaet al., 2010; Jiang et al., 2010), we believe that the loadsettings can be usefully enhanced with the facilities andtechniques that are now available. Hitherto, the loadingconditions have been oversimplified by using for instanceonly point vectors placed in the middle of the occlusalsurface. However, while the magnitude of the load doesnot affect the pattern of stress distribution (Dejak et al.,2003; Jiang et al., 2010), loading direction and positionare expected to affect patterns of stress distribution con-siderably (De Jager et al., 2005; Fu et al., 2010).Our simulation focused on the occlusal loading, to

show the different pattern of stress distributions in thesupporting bone structure (mainly the cortical bone) thatare obtained under different occlusal loading directionsand locations. By doing so, we used a new approach todetect the occlusal contacts between upper and lowerdentition (i.e., the LM1 and LP2-LM1 complex) experienc-ing two-body interactions during maximum intercuspa-tion. According to the results of our pilot study, the load-ing of the LM1 resulting from a point force applied atthe central groove area of the occlusal basin results in adifferent stress distribution compared with a loading sce-nario based on the occlusal contact areas. In the formerinstance (Case 1), buccal and lingual cortical plates donot experience notable stress and the load is basicallydirected toward the bottom of the mandible. Conversely,in Case 2 the medio-lingual cortical bone of the mid-cor-pus is subjected to high compressive stresses while thedisto-lingual superior third shows high tensile stresses.More comprehensive analyses following the outline of

our preliminary study here could lead to quite differentinterpretations of the mandibular biomechanics andlikely influence clinical choices in prosthetic dentistryand mandibular reconstruction.For example, in Demes at al. (1984; but see also Dae-

gling and Hotzman, 2003), the occlusal force (directshear loading) was represented as straight parallelarrows, affecting similarly the buccal and lingual corticalbone. When the occlusal force is summed up algebrai-cally to the torsional load, the two sources neutralize

TABLE 1. Elastic properties of isotropic materials

Material Ea (Gpa) Poisson’s ratio Reference

Enamel 84.10 0.30 Magne, 2007Dentine 18.60 0.31 Ko et al., 1992Pulp 0.002 0.45 Rubin et al., 1983PDLb 0.0689 0.45 Holmes et al., 1996Alveolar bone 11.50 0.30 Dejak et al., 2007Cortical bone 13.70 0.30 Ko et al., 1992

a elastic modulus.b Periodontal ligament.

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each other lingually but they add on the buccal side.This eventuality has been put forward to account for thethinnest cortical bone usually observed lingually (Demesat al., 1984). It is noteworthy that the pattern of occlusalstress distribution (direct shear stress) used by theseauthors basically reflects the results we obtained forCase 1. There is still uncertainty about the functional

meaning of this asymmetry in the cortical bone thick-ness (Daegling and Hotzman, 2003). We suggest to useour Case 20 load settings instead of Case 10 to tackle thisproblem of local variation in cortical bone thickness inthe mandibular corpus. This issue is of relevant interestin dentistry and orthodontics. To plan customized man-dibular scaffolds to reproduce the resection created in a

Fig. 3. Von Mises stresses (first row), the first principal stresses (second row; tensile stress) and the third principal stresses(third row; compressive stress) distributions observed when the tooth is loaded 1) onto a single contact point of the occlusal basin(Case 1), 2) in the contact areas (Case 2).

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surgical environment or to produce a positive mold thatis subsequently casted with biomaterials (Yoshikawaet al., 2009; Xu et al., 2010), a correct evaluation of thestress distribution due to the occlusal force is required.Some researchers have emphasized this problem, point-ing out that the occlusal contact areas should be consid-ered and loaded to their whole extent (e.g., Hattoriet al., 2009) because it might be inaccurate and unrealis-tic to reduce the wear facets to point contacts (De Jageret al., 2006).A better approximation of a realistic dental loading

scenario as we introduce it here can also be applied toexamine the functional relationships between both themandible and tooth morphology in extant and extinctprimates, and to investigate whether directional evolu-tionary change was involved to guarantee masticatoryefficacy. This is particularly relevant for fossil remainswhere biomechanical considerations cannot be supportedby in vitro analysis. In such cases, more realistic occlusalloading conditions can lead to better interpretations ofevolutionary changes in dental arch form, mandibularshape, and tooth relief. Such models undoubtedly alsoimprove our understanding of bone remodeling in alveo-lar bone, since it has been suggested that masticatoryfunction might affect cortical bone density and thickness(Sato et al., 2005).Moreover, the medio-lingual compression in the man-

dible that we mentioned above suggests a medio-lingualdisplacement of the M1 during maximum intercuspation.In a recent contribution (Benazzi et al., 2011) we haveemphasized the bucco-lingual displacement of the M1

during Phase II, when forces were applied in the lingualslope of the buccal cusps. The combination of medio-lin-gual (during maximum intercuspation) and bucco-lingual(during Phase II) displacements might explain the crea-tion of interproximal wear facets. Nevertheless, we notethat results of our relatively simple model could changeif bending and twisting moments are integrated. Thus,further studies that consider also the neighboring teethand the effect of multiple loading regimes (i.e., torsionalloading, sagittal bending) are required to better eluci-date the dynamic involved in the tooth displacement andto understand the relationship between masticatoryfunction and mandibular shape and structures.Even though our pilot study could of course not pro-

vide a comprehensive picture of the stress distributionexperienced in a particular portion of the mandible, itclearly demonstrates that results between the usualapproach and one that considers more realistic loadingsdiffer indeed markedly. We point out here the implica-tions this has and hope that this first step will stimulatefurther work with increased complexity and sample size.

ACKNOWLEDGMENTS

The authors thank Cinzia Fornai for her help and val-uable advices. This research is publication no. 25 of theDFG Research Unit 771 ‘‘Function and performanceenhancement in the mammalian dentition—phylogeneticand ontogenetic impact on the masticatory apparatus.’’

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