Three-dimensional Stress Distribution Around a Dental Implant at Different Stagesof Interface Development

L. BORCHERS and P. REICHART

Zentrum Zahn-, Mund-, und Kieferheilkunde der Medizinischen Hochschule Hannover, Karl-Wiechert-Allee 9, D-3000 Hannover 61, FederalRepublic of Germany

An anchor-type ceramic dental implant contained in a section of themandibular molar region was modeled for finite element stressanalysis. The distributions of stresses in the bone around theimplant due to axial and transverse loading were calculated fordifferent stages of normal and pathological development of theimplant-bone interface. Highest stress concentrations are observed inthe crestal region with transverse loading when spongy bone sur-rounds the implant immediately after surgery. Development of alamina dura around the implant slightly reduces severe stress peaks,whereas ingrowth of connective tissue almost eliminates them.

J Dent Res 62(2):155-159, February 1983

Introduction.

Anchor-type endosteal implants made of aluminum oxideceramic (Al203-ceramic) were used to replace teeth in themolar region of the mandible.1 The occasional clinical andexperimental failures of this type of implant were partly dueto connective tissue formation at the implant-bone inter-face2-3 and showed the need for a detailed stress analysis.Since the finite element method (FEM) has proved to be auseful tool in estimating stresses around implants ofdifferent designs,46 this method was adopted to analyzea loaded implant in situ. The objective of the present in-vestigation was to simulate different stages of normal andpathological interface development, and to calculate stressdistributions in the bone surrounding the implant. Resultsfrom such a study will improve the understanding of themechanisms of tissue reaction and failure in endostealdental implantation.

Materials and methods.For this study, an anchor-type endosteal implant,

which was made of Al203-ceramic, was chosen. The crownof the implant is at an angle of 150 to the stem's axis to allowfor the run of the inferior alveolar nerve (Figs. 1 and 2a).A section of the molar region of the mandible, 50 mm inlength and containing the implant, was modeled for stressanalysis by means of the FEM.7 The Structural AnalysisProgram, SAP IV, was chosen for the computations. Thisprogram requires that a three-dimensional structure bedivided into hexahedral elements; adjacent elements areconnected to each other at their common corners ornodes. Each element is defined by eight such nodes.8

The mandibular region to be analyzed is representedby its cross-section in Fig. 1. The whole structure wasdivided into a series of horizontal, vertical, and inclinedsections, which, in turn, were subdivided into quadranglesin such a way that a three-dimensional network formed byhexahedrons developed. The finite element models of theimplant and layers of surrounding tissues are shown in theseries of computer-drawn Figs. 2a-d. In total, the modelconsists of 1129 elements, with 1473 nodes. The

Received for publication January 19, 1982Accepted for publication August 12, 1982

mandibular section has been regarded as symmetrical to theplane in Fig. 1, which allowed modeling of only one of thesymmetrical halves, with the other half simulated by appro-priate boundary conditions. The slight curvature of themandible in the anterior-posterior direction has beenneglected for ease of modeling.

Four possible stages of implant-bone interface develop-ment (Fig. 3) were simulated in the model by varyinginput data for the mechanical properties of the layers in theinterface region shown in Fig. 2b. In Fig. 3, model con-figuration A represents the situation immediately afterimplantation, when the implant is totally surrounded bycancellous bone. Brinkmann2 observed development of acortical bone-like lamina dura around the implant in about50% of all cases of successful implantation. This situation isrepresented by configuration B. Proliferation of connectivetissue into the gap between implant and spongy bone,increasing implant mobility and causing subsequentfailure,3'9 is reflected in configuration C. Finally, it mighthappen that, after successful implantation and formation ofa lamina dura, connective tissue migrates along the implantstem as represented by configuration D.

ling

2mm_-~

Fig. 1 - Buccolingual section through mandible in the region ofthe first molar with implant in situ (buc: buccal side, ling: lingualside). The 15° angle between crown and shaft of the implant allowsfor the run of the inferior alveolar nerve.

155

156 BORCHERS & REICHART

In the model, the tissues and ceramic were regarded ashomogeneous, isotropic, and linearly elastic materials. Theirmechanical properties listed in the Table were selected fromthe literature. No slip between the implant and surroundingtissue was allowed to occur in the model.

Two load cases were taken into account for each of thefour model configurations. A force of 200 N was chosen toact: first, occlusally, i.e., parallel to the axis of the

2 mm

C

implant's crown; and second, in the lingual direction,perpendicular to the crown's axis. For convenient com-parison of the results, and due to lack of data in the litera-ture, the forces were taken as equal in both cases, eventhough the lateral forces are most probably smaller inreality. Force was applied at the top center node of theimplant crown. The reaction force was generated by con-straining the bottom nodes of the model.

B

j,i

D

Fig. 2 - 3-D view of finite element model parts, seen from the lingual side (only one of the symmetrical halves shown). In the appropriatescale, the model parts fit into each other: the implant wing and stem into the cavity of the surrounding layers, and those parts into the hollowed-out spongy bone, etc.(a) Model of implant.(b) Model of two tissue layers surrounding the implant. Thickness of the layers is 0.4 mm and 0.8 mm, respectively.(c) Model of spongy bone around two layers of Fig. 2b.(d) Model of enclosing cortical bone layer.In b-d, the lingual portions facing the viewer have been removed for clarity.

J Dent Res February 1 983

STRESS DISTRIBUTIONAROUND A DENTAL IMPLANT

buccalside

CONFIGURATION A CONFIGURATION B CONFIGURATION C CONFIGURATION D

_ A1203-ceramic spongy bone

cortical bone/ lamina dura = connective tissue

Fig. 3 - Illustration of different possible stages of interfacedevelopment around the implant in the buccolingual section.

Results.The computations resulted in values of a stress tensor for

each element of the model. For clarity, only distributionsof maximum and minimum principal stresses are presented.These may be regarded as the maximum and minimumstresses acting at a given point in any direction. A positivesign indicates tensile stress; a negative sign indicates com-pressive stress.

In Figs. 4 and 5, the principal stresses vs. location areplotted, as indicated by the bold lines around the implantin the sketches. Fig. 4 applies to the bone layer directlyadjacent to the implant. Since stresses within the connec-tive tissue are not of interest in this study, configurationsC and D do not appear in this Fig. They are, however,included in Fig. 5, which refers to the model sheath ofbone being farther away from the implant surface.

Most evident in the buccolingual section for axial load(Fig. 4a) are the strong compressive stress peaks near thelingual upper portion of the implant stem for the cancellousbone (configuration A) and the lamina dura (configurationB) as well. In the latter, the stress level, in general, appearsto be slightly higher. Minor compressive stress peaks existunder the lingual part of the stem's bottom in both cases.

With a transverse load of equal magnitude (Fig. 4b),

the lingual portion exhibits stress distributions similar tothose obtained with axial loading. Remarkably, however,stress levels are about five times as high as with the axialload. Furthermore, tensile stress peaks of about 40 N/mm2occur near the buccal part of the stem.

Since the longitudinal sections are symmetrical, onlyhalf of the stress distributions are shown in Figs. 4c and 4d.They are exceptionally smooth and of low magnitudearound the implant wing (note the enlarged scale). In theprotruding part of the stem, major stress concentrationsare compressive with axial loading, and they are bothcompressive and tensile with transverse loading. Thesestress peaks are less marked within the lamina dura (con-figuration B), which is more rigid, and, hence, distributesthe load more evenly than does spongy bone (configura-tion A).

The stress distributions in the outer portion of the twomodel layers surrounding the implant are shown in Fig. 5.The distribution for configurations A and B exhibits nosignificant changes in shape with the increased distancefrom the implant surface (compare Figs. 4a and 5a, 4b and

ib.ccal \ In aI

WIE-E

-j

zlciL

A

200\

"~'OIc \

LOCATION [mm]B

TABLEMECHANICAL PROPERTIES ASSIGNED TO THEDIFFERENT MATERIAL COMPOUNDS OF THE

FINITE ELEMENT MODEL

ElasticModulus Poisson's Reference

Material N/mm2 Ratio Nos.

A120 3-ceramic 380,000 0.26 10Cortical Bone 13,700 0.30 4,6Lamina Dura 13,700 0.30 4,6#Spongy Bone 1,370 0.30 4,6Connective Tissue 2 0.45 4,11###The properties of the lamina dura consisting of dense bone were

assumed to be the same as those of cortical bone,##There is a wide range of values given in the literature for the elasticmodulus of connective tissue.4'6'11'13 The value chosen for thisstudy is close to that determined for human periodontal ligament ina rotation experiment with central incisors in vivo.11 Poisson'sratio is taken from reference no. 4.

2

0

S

a.

C

[/"- !I5 10 iS 20 25 30

LOCATION [mm]

S r iL

z2

L I

5

10 15 20 25 30

LOCATION [mFAN

DFig. 4- Principal stresses in alveolar bone vs. location (distance

from implant surface, 0.2 mm).(a) Axial load, buccolingual section.(b) Transverse load, buccolingual section.(c) Axial load, mesiodistal section.(d) Transverse load, mesiodistal section.

t

Vol. 62 No. 2 157

158 BORCHERS & REICHART

200C\

4 .

CO#NFP K;RATXN

0

12

2 CONFIGURATIN

E -0

-J CONFtURAUT NC C

11

0

0 5 10 1s 20 25

ALOCATION [Min

E,E

A-

I-

E

Zt

US

0.0

2\ ~~~~~CONFIGURATION a1'O ~~~~~~~~~~~~~~~~~~~~~~~-2 §,

2 ~ ~~~~~~CONFlaURAr10iN C:

-2COWFIGt)RAN 0 D

_2o/' o==A~~~~~~~~~1

20b U,

o 5 10 15 20 25 30 0 5 10 15 20 25 30

LOCATIONUmm*1D LOCATION (mm]

Fig. 5 - Principal stresses in alveolar bone vs. location (distancefrom implant surface, 0.8 mm).(a) Axial load, buccolingual section.(b) Transverse load, buccolingual section.(c) Axial load, mesiodistal section.(d) Transverse load, mesiodistal section.

5b, 4c and 5c, 4d and 5d; note different scales). In general,intermediate connective tissue layers cause considerablysmoother stress distributions without critical concentra-tions in the crestal region, as may be derived from compari-son of the results for configurations A vs. C and B vs.D. In the case of an occlusally acting force, however (Figs.S a and 5c), compressive stresses are slightly increasedunder the stem base. Load transmission via the wings tothe bone is also enhanced (Fig. 5c, configurations C and D),probably due to less stress taken by the soft surroundingsof the post than by the bone surrounding the implant inconfigurations A and B.

For the longitudinal section (Figs. Sc and Sd), the highstress concentrations which occur in the crestal regiondirectly after implantation (configuration A) are markedlydiminished by the development of a lamina dura (configura-tion B). They are almost completely eliminated by connec-

JDent Res February 1983

tive tissue layered between the implant and bone, withslightly elevated stress levels occurring in the other parts ofthe distributions (configurations C and D).

Discussion.Our results are in the same range as those of a similar

investigation by Cook et al.,5 and, qualitatively, theycompare closely to those obtained by Soltesz et al.12 in aphoto-elastic study of an implant of the same type underload.

Consistently, the most prominent stress peaks occur inthe bone (either cancellous or compact) near the protrudingpart of the stem. Maximum compressive stresses on thelingual side are about 10 N/mm2 with axial loading andabout 50 N/mm2 with transverse loading. These valueswere probably underestimated, since slip might occurbetween implant and tissue - contrary to the model'sassumptions -thus at the least reducing the amount of loadtransmitted by shear and tension. For the same reason, thehigh tensile stresses of about 45 N/mm2, which resulted onthe buccal side from transverse loading, are unlikely to betransmitted by the interface. However, even if it is assumedthat the transverse load of 200 N is too high by a factor oftwo or three, the resulting compressive stresses in themandible are still locally approaching the upper limit oftemporarily-acting physiological stresses. This limit isbelieved to be about 25 N/mm2 , as indicated by FEManalysis of a loaded natural tooth.13 Hence, we concludefrom our results that bone resorption in the crestal regionaround this type of implant might occur due to stressconcentrations during transverse loading. In case of noresorption, however, the observed stresses could be highenough to prevent the bone from proper apposition to theimplant, since they locally exceed the level of constantstress favorable to induced bone formation. This level hasbeen determined, in a rabbit experiment,14 to be about 3-4N/mm2, and is thought to be of the same order ofmagnitude for humans.A lamina dura commonly formed around the implant in

a clinically favorable course of healing tends to distributestresses more evenly than does spongy bone. The timeimmediately after insertion of the implant - while itssurroundings still consist of spongy bone and exhibitthe most distinct stress concentrations - is likely to bemost critical for the success of the implantation. Theformation of a lamina dura, however, might be interpretedas an adaptation of the biological system to the actingloads. Since connective tissue ingrowth considerablyreduces critical stress peaks in the adjacent bone, this wayseems to be the most effective and the ultimate means forthe body to respond to injuriously high stresses.

Conclusions.From the results of FEM stress analysis of an anchor

type A1203-ceramic dental implant, the following conclu-sions may be drawn:1. High stress peaks which were calculated in the crestal

region of the alveolar bone, especially with transverseloading, might cause bone resorption, connective tissueingrowth, and subsequent implant failure. Stress concen-trations were most distinct with the implant's surround-ings consisting of cancellous bone.

2. Presence in the model of a lamina dura or a connectivetissue layer around the implant was found to reducestress peaks.

29.8CORFIGURATIONA

Q,4. = z-==.-

1-1

- 2

STRESS DISTRIBUTIONAROUND A DENTAL IMPLANT

3. Further analysis should be done to evaluate designimprovements in order to increase the share of loadtransmitted by the implant wings, thus unburdening thestem region.

Acknowledgments.Calculations in this study were carried out with the

support of the Regional Computation Center for LowerSaxony at the University of Hannover (RRZN). We wish tothank Mrs. Katharina Schmidt for her help with the datapreparation and illustrations.

REFERENCES1. MUTSCHELKNAUS, E. and DORRE, E.: Extensions-

Implantate aus Aluminiumoxidkeramik (I), Die Quintessenz28(7):21-28, 1977.

2. BRINKMANN, E.: Enossale Implantate aus Aluminiumoxid-keramik, Zahndrztl Prax 31(8):328-330, 1980.

3. REICHART, P. and BORCHERS, L.: TierexperimentelleUntersuchungen tell- und unbelasteter A1203-extensions-implantate, Dtsch Z Mund-Kiefer-Gesichts-Chir 4:22-26,1980.

4. WIDERA, G.E.O.; TESK, J.A.; and PRIVITZER, E.: Interac-tion Effects among Cortical Bone, Cancellous Bone, andPeriodontal Membrane of Natural Teeth and Implants, JBiomed Mater Res Symp 7:613-6 23, 1976.

5. COOK, S.D.; KLAWITTER, J.J.; WEINSTEIN, A.M.; andLAVERNIA, C.J.: The Design and Evaluation of DentalImplants with Finite Element Analysis. In: InternationalConference Proceedings, Finite Elements in Biomechanics,

Simon, B.R., Ed., Tucson: The University of Arizona, 1980,pp. 169-178.

6. LAVERNIA, C.J.; COOK, S.D.; KLAWITTER, J.J.; WEIN-STEIN, A.M.; and DAS, S.C.: The Effect of Implant ElasticModulus on the Stress Distribution Surrounding DentalImplants. In: International Conference Proceedings, FiniteElements in Biomechanics, Simon, B.R., Ed., Tucson: TheUniversity of Arizona, 1980, pp. 179-182.

7. ZIENKIEWICZ, O.C.: The Finite Element Method inEngineering Science, London: McGraw-Hill, 1971, pp. 1-102.

8. BATHE, K.J.; WILSON, E.L.; and PETERSON, F.E.: SAPIV - A Structural Analysis Program for Static and DynamicAnalysis of Linear Structural Systems. In: EERC Report No.73-11, Berkeley: The University of California, June, 1973,rev. April, 1974, pp. IV.5.1-IV.5.8.

9. GRENOBLE, D.E. and VOSS, R.D.: Materials and Designs forImplant Dentistry, Biomater Med Devices Artif Organs 4(2):133-169, 1976.

10. DORRE, E.: Aluminiumoxidkeramik als Implantatwerkstoff,MOT 96:104-105, 1976.

11. NICHOLLS, J.I.; DALY, C.H.; WILSON, B.D.; and KYDD,W.L.: A Mathematical and Experimental Investigation ofTooth Mobility, Proc Ann Conf Eng Med Biol 25:289, 1972.

12. SOLT.SZ, U.; RIEDMULLER, J.; and DORRE, E.: Modellun-tersuchung zur Spannungsverteilung um Extensionsimplantate,ZahndrztlPrax 31(8):357-361, 1980.

13. ATMARAM, G.H. and MOHAMMED, H.: Estimation ofPhysiologic Stresses with a Natural Tooth Considering FibrousPDL Structure, JDent Res 60:873-877, 1981.

14. HASSLER, C.R.; RYBICKI, E.F.; CUMMINGS, K.D.; andCLARK, L.C.: Quantification of Bone Stresses DuringRemodeling,JBiomech 13:185-190, 1980.

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