Optimum Degree of Bone-Implant Contact in Bone Remodelling Induced by Dental Implant

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1 Optmum Degree of Bone-Implant Contact n Bone Remodellng Induced by Dental Implant Author Lan, Z., Guan, Hong, Loo, Yew-Chaye Publshed 2011 Journal Ttle Proceda Engneerng DOI Copyrght Statement 2011 Elsever. Ths s the author-manuscrpt verson of ths paper. Reproduced n accordance wth the copyrght polcy of the publsher. Please refer to the journal's webste for access to the defntve, publshed verson. Downloaded from Grffth Research Onlne

2 (Proceda Engneerng, 14 (2011) ) OPTIMUM DEGREE OF BONE-IMPLANT CONTACT IN BONE REMODELLING INDUCED BY DENTAL IMPLANT Z. Q. LIAN 1*, H. GUAN 2, and Y. C. LOO 2 1 Department of Engneerng Mechancs, Dalan Unversty of Technology, Chna 2 Grffth School of Engneerng, Grffth Unversty Gold Coast Campus, Australa ABSTRACT Dental mplants are an effectve, safe and predctable soluton for patents sufferng from tooth loss. An deal level of bone-mplant contact (osseontegraton) s of drect mpact on the success of an mplant surgery. Ths leads to a queston as whether hgher degree of bone-mplant contact would yeld better surgcal outcome. Ths study ams to determne an optmum degree of bone-mplant contact usng the newly developed bone remodellng algorthm through 2D fnte element analyss. Four dfferent degrees of bone-mplant ntal contact (25, 50, 75 and 100%) are consdered and ther nfluences on the resultng densty dstrbuton of jawbone are evaluated. Results ndcate that, under 100N mastcatory force, dfferent ntal bone-mplant contacts lead to a smlar and optmum degree of contact when an equlbrum state s reached. Ths result s consstent wth clncal observatons and fndngs. To account for normal to traumatc loadng condtons, practcal mastcatory forces rangng from 100N to 400N are also consdered, for ntal contact of 50 and 75%, to evaluate the optmum degrees of bone-mplant contact under dfferent loadng scenaros. Keywords: Dental mplant, bone remodellng, bone-mplant contact percentage, optmzaton. 1. INTRODUCTION A dental mplant s a bocompatble ttanum devce that s surgcally placed nto the mandbular or maxllary bone to support a prosthetc tooth crown n order to replace mssng teeth. Dental mplants are an effectve, safe and predctable soluton for those who have lost a tooth or teeth due to dental cares, perodontal dsease, njures or other reasons. Despte hgh success rate of mplantaton when mplants are correctly desgned, manufactured and nserted n bone of good qualty and quantty, falures do exst, especally n compromsed stes and patents (Neukam and Flemmg 2006). As a lvng tssue, bone s capable of optmzng ts nternal structure by redstrbutng ts apparent densty under external loads to fulfll ts maxmum functon. Ths s known as the Wolff s law (1892). The process of bone redstrbutng ts apparent densty s termed as bone remodellng. Snce the early publcaton of Wolff, many theores descrbng bone remodellng process have been proposed. * Correspondng author: Emal: lanzq75@dlut.edu.cn 1

3 Frost (1964) suggested that nternal and external remodellng should be dstngushed, where nternal remodellng refers to the alteraton of densty of bone tssue and external remodellng s the apposton and removal of bone tssue on the bone surface. Frost also suggested a trgger crteron for remodellng based on the stran magntude. Ths concept was formally developed later by Cown and Hegedus (1976) and Cown and Nachlnger (1978) usng the concept of adaptve elastcty under small strans, whch was the frst mathematcally rgorous theory for adaptve growth and remodellng of bone. Carter (1984) proposed the concept of lazy zone, a threshold value, ndcatng that bone remodellng takes place only when the external stmul exceed the lazy zone. Ths concept was ncorporated by Huskes et al. (1987, 1992) who used the stran energy densty as the stmulus sgnal to control bone remodellng. Mullender et al. (1994) and Mullender and Huskes (1995) developed a physologcal approach to smulate bone remodellng whch assumed that osteocytes are senstve to mechancal loadng and are actve n controllng the adaptaton of bone mass n ther envronment. Although many applcatons of bone remodellng theores are documented, majorty of them focused on the predcton of densty dstrbuton n per-mplant bone tssues (Chou et al. 2008; Grup et al. 2004; L et al. 2007; Mellal et al. 2004). Lttle or no consderaton was taken on the effect of bone-mplant contact on bone remodellng outcomes. A full contact (100%) between the bone and mplant s often assumed n exstng bomechancal research. Ths s however nconsstent wth clncal observatons, whch show that bone-mplant contact s dependent on a varety of factors such as mplant surface topography and bone qualty. The present study ams to evaluate through 2D fnte element analyss the optmum degrees of bone to mplant contact under a range of mastcatory forces. 2. METHODS Lan et al. (2010) proposed a new bone remodellng algorthm whch s a combnaton and further development of two exstng and wdely accepted bone remodellng theores. In ths algorthm, the bone s assumed to have N sensor cells dstrbuted unformly over ts volume (Mullender et al. 1994). An arbtrary sensor measures a sgnal S, whch s gven as: S (1) U/ρ where U s the stran energy densty and ρ s the densty at the locaton of the sensor. The densty ρ(x,t) at the locaton x s regulated by the stmulus value Ф(x,t), to whch all sensor cells contrbute, relatve to ther dstance from x. Hence, ( x, t) N N f ( x)( S f ( x)( S 0 (1 s) K) (1 s) K) f f f S (1 s) K (1 s) K S (1 s) K S (1 s) K (2) where N s the total number of sensors; α s the order of non-lnear remodellng equaton; K s a reference sgnal of stran energy densty per unt bone mass; s s n percentage denotng the lazy zone regon around the threshold value K. f (x) s a spatal nfluence functon n the followng form: 2

4 f ( ) [ d ( x)/ D] x e where d (x) s the dstance between sensor and locaton x; D s the rate of the spatal nfluence reducton. The densty ρ(x,t) s now governed by: d( x, t) ( x, t), wth 0 ( x) max (4) dt where ρ max s the maxmum densty equvalent to that of a cortcal bone, and τ s a tme constant regulatng the rate of the remodellng process. As the apparent densty of bone tssue changes durng the process of remodellng, Young s modulus of bone changes accordngly. Carter and Hayes (1977) suggested a specfc relatonshp between the elastc modulus (E) and densty (ρ),.e: (3) 3 E ( x, t) 3790 (5) The applcablty of the proposed algorthm on densty dstrbuton of bone has been verfed usng Mullender et al s 2D plate model as well as a 2D bone-mplant model (Lan et al. 2010). 3. FINITE ELEMENT ANALYSIS SIMULATION To evaluate the effect of dfferent bone-mplant contact on the densty dstrbuton of jawbone and the optmum degree of such contact under dfferent loadng scenaros, a 2D slce at the poston of frst premolar s taken from the entre mandbular bone. The system of crown, abutment, abutment screw, mplant and bone are modeled usng 2D plane stran elements. The cortcal and cancellous bones are dentfed based on CT scan mages. The mplant dmensons are based on those of Neoss (2006). Fg. 1(a) shows an mplant of dameter 4.5mm and length 11mm, and a mandble secton wth a cortcal bone thckness of 1 mm. The mplant s concal wth 2 taper and has a helcal thread. A small area of bone surroundng the mplant (0.2mm from tp of mplant thread) s desgnated as connectve tssue, consttutng a mx of hard and soft tssue to smulate varyng degrees of bone to mplant contact (see Fg. 1(a)). Based on the work of Chou et al. (2008), the mplant system s loaded wth an occlusal load of 100N on the crown at an angle of 11 and a unformly dstrbuted pressure of 500kPa on the outer surface of the cortcal bone wth the latter representng forces due to jaw flexure. In the present study, typcal values of Young s modulus (E) of bone, mplant components as well as crown are selected based on the work of Mencucc et al. (2002). The Posson s rato for all components s taken as 0.3. The load and boundary condtons, and the materal propertes are detaled n Fg. 1(b). When an mplant s surgcally placed nto jawbone, the bone-mplant nterface can be dvded nto regons wth and wthout drect contact (Smmons et al. 2001). To smulate dfferent degrees of bone-mplant contact, a certan percentage of connectve tssue elements s randomly selected and assgned the propertes of bony tssue. The remanng elements wthn the connectve tssue are assgned the propertes of soft tssue. Accordng to Lu et al. (2005) and Xng et al. (2002), Young s modul of the bony and soft tssues are taken as 2.4GPa and 70MPa, respectvely. In ths study, four 3

5 bone-mplant contacts (.e. 25, 50, 75 and 100%) are consdered to evaluate ther effect on the densty dstrbuton of jawbone. Note that 25% contact represents 25% bony tssue and 75% soft tssue. 4.5mm N 1mm 500kPa Crown E=172GPa 0.2mm Abutment E=105GPa 11mm Abutment Screw E=93GPa Connectve tssue 21mm Lngual Implant E=105GPa Cancellous Bone E=7.93GPa Cortcal Bone E=13.7GPa Buccal (a) Fxed Constrant Fgure 1:Fnte element model of mplant and jawbone: (a) Dmensons; (b) Load, boundary condtons and materal propertes. Cancellous bone s often more metabolcally actve and responsve to stmul than cortcal bone (Jacobs 2000). Therefore n the remodellng process, densty dstrbuton of cortcal bone s assumed to be unchanged. However the rato of bony-soft tssue does not reman constant durng the process. Hence the connectve tssue s also remodelled together wth cancellous bone to represent a clncal realty. The cancellous bone has a unform ntal densty dstrbuton of ρ=1.279 g/cm 3 and the correspondng Young s modulus s 7.93GPa (Eq. (5)). It s worthwhle notng that there are no standard rules n the determnaton of bone remodellng parameters as specfed n Eqs. (2) and (4). Such parameters as K, the reference sgnal of SED, s, the lazy zone effect and τ, the tme constant regulatng the remodellng rate are found to be qute dfferent n the lterature (see Table 1). Table 1: Bone remodellng parameters used n publshed lterature K s τ or τδt Chou et al. (2008) 25 Nm/kg 65% kg 4 /Nm 4 (τδt) L et al. (2007) J/g (4 Nm/kg) 1.0 (g/cm 3 ) 2 (τ) Mellar et al. (2004) J/g (4 Nm/kg) 10% 1.0 (g/cm 3 ) 2 (τ) In order to compare the effect of four dfferent bone-mplant contacts, the followng bone remodellng parameters are kept constant for all scenaros. Accordng to Chou et al. (2008), the maxmum and mnmum denstes are assumed to be ρ max = g/cm 3 and ρ mn =0.064g/cm 3 respectvely whch corresponds to Young s modul of 13.7GPa and 1kPa respectvely; the sensor cell dstrbuton s assumed to be unform and s located at the centre of each element; the nfluence reducton parameter s taken as D=0.2mm. Usng Table 1 as a gudelne, other parameters are chosen as: s= 20%, τ=1 (g/cm 3 ) 2 /(MPa tme-unt) and K=16 Nm/kg. It should be noted that mastcatory force s not a constant value. To account for normal to traumatc loadng condtons, practcal mastcatory forces rangng from 100N to 400N are also consdered, for (b) 4

6 ntal contact of 50 and 75%, to evaluate the optmum degrees of bone-mplant contact under dfferent loadng scenaros. Note also that the angle of the mastcatory forces reman unchanged. 4. RESULTS AND DISCUSSION Presented n Fg. 2 are the predcted results of densty dstrbutons n cancellous bone and connectve tssue for four dfferent bone-mplant contact scenaros under 100N mastcatory force. As can be seen the fnal densty dstrbutons are almost dentcal for ths four cases. The only notceable dfference s the area located on the buccal sde of the mplant where the bone tssue demonstrates an average densty. Ths s partcularly true for 50%-100% bone-mplant contact scenaros. For the 25% contact, ths area s a mx between bone resorpton and formaton g/cm g/cm 3 (a) 25% (b) 50% (c) 75% (d) 100% Fgure 2: Densty dstrbuton under dfferent ntal bone-mplant contact. Fg. 3 presents a comparson of the predcted densty dstrbuton results (for 75% contact) wth publshed numercal predcton (Chou et al. 2008) and clncal observatons on a baboon s jawbone surroundng a dental mplant (Watzak et al. 2005). The overall densty dstrbutons n the three fgures are qute smlar n the followng aspects: (1) trabecular-lke pattern surroundng the mplant as hghlghted by regon A; (2) lower densty area (bone resorpton) below the mplant as hghlghted by regon B. It should be noted that Chou et al. s algorthm s based on Huskes et al. s (1992) theory wth a consderaton of hgh-order effect. However, the lazy-zone effect was gnored. In addton, wth a focus on the nfluence of dfferent types of mplant systems on the densty dstrbuton, ther studes dd not cover varyng bone-mplant contact percentages. A B (a) (b) (c) Fgure 3: Bone remodelng comparson: (a) Predcted result (75% contact); (b) Chou et al. s (2008) predcton; (c) Watzak et al. s (2005) clncal observaton. 5

7 Mass (g) Shown n Fg. 4 s the relatonshp between bone-mplant contact percentage and bone mass after remodellng s complete. As ndcated, the bone mass reaches ts maxmum value for 100% contact and a smlar bone mass s acheved for 50% and 75% contact. Furthermore, the dfference between the maxmum (100% contact) and mnmum (25% contact) bone mass s less than 0.5%. Ths suggests that the assumed ntal contact percentage has lttle nfluence on the bone mass upon completon of bone remodellng. Fg. 5 further compares the bone-mplant contact percentage before and after bone remodellng. Agan ntally assumed dfferent contact percentages result n a rather constant (about 58%) percentage of contact after bone remodellng. Fgs. 2, 4 and 5 all demonstrate that the ntal bone-mplant percentages have lttle mpact on the fnal densty dstrbuton and bone mass. Upon reachng a balanced bone resorpton and formaton throughout bone remodellng process, the bone-mplant contact remans almost constant at about 58%. Testor et al. (2002) found a bone-mplant contact of 64.2% for an mmedately loaded mplant. Through a hstology study, Degde et al. (2003) also dscovered about 65% to 70% contact for two mmedately loaded mplants. Ths further verfes that the fndngs of the present study are n a good agreement wth those of the publshed lterature Percentage of bone-mplant contact (100%) Fgure 4: Bone mass versus contact percentage after remodellng. Fgure 5: Bone-mplant contact percentage before and after bone remodellng. Fgure 6: Bone-mplant contact percentage under dfferent mastcatory forces. Based on the above fndng, t becomes nterestng to examne the mpact of dfferent mastcatory forces on bone densty dstrbuton based on two selected bone-mplant contact percentages (.e. 50% and 75%). As llustrated n Fg. 6, ncreased mastcatory forces (from 100N to 400N) result n a slght decrease n the fnal but agan stable bone-mplant contact percentage (from about 58% to about 52-53%). Fg. 7 also demonstrates that the fnal bone densty dstrbuton changes accordngly when the mastcatory force ncreases. Not only more bone resorpton takes place around the mplant, but also more bone formaton on the buccal sde under the mplant. The ncreased bone formaton s hghlghted by the decreased area of regon A (shown n Fg. 7(a)), whch mples that more bone s formed n order to resst the ncreasng mastcatory force. Ths outcome s true for all three dfferent bone-mplant contacts. Further, despte the changes n the overall densty dstrbuton patterns for dfferent contacts and dfferent forces, the total areas of bone resorpton and formaton seem to balance each other out, thereby resultng n lttle or no change n the total mass of bone tssue. 6

8 0.064 g/cm g/cm 3 A (a) (b) (c) (d) 100 N (50% contact) 200 N (50% contact) 300 N (50% contact) 400 N (50% contact) (e) (f) (g) (h) 100 N (75% contact) 200 N (75% contact) 300 N (75% contact) 400 N (75% contact) Fgure 7: Densty dstrbuton under dfferent bone-mplant contacts and mastcatory forces. 5. CONCLUSION Usng a newly proposed remodellng algorthm, ths study evaluates the nfluence of dfferent degrees of bone-mplant contact and dfferent levels of mastcatory forces on bone remodellng nduced by dental mplant. The present 2D fnte element study demonstrates that the ntal contact percentage (25-100%) has lttle nfluence on the ultmate densty dstrbuton n the bone. Increased mastcatory forces nfluence the overall pattern of densty dstrbuton n terms of areas of bone resorpton and formaton. However the total mass of bone tssue does not change sgnfcantly. Further, ncreased mastcatory forces result n a slght decrease n the fnal but agan stable bone-mplant contact percentage when an equlbrum state s reached by bone remodelng. The results are consstent wth the clncal observatons and fndngs. REFERENCES [1] Carter DR and Hayes WC (1977). The compressve behavor of bone as a two-phase porous structure. The Journal of Bone and Jont Surgery. 59(7), pp [2] Carter DR (1984). Mechancal loadng hstores and cortcal bone remodellng. Calcfed Tssue Internatonal. 36 (Suppl 1), pp. S19 S24. [3] Chou HY, Jagodnk JJ, and Muftu S (2008). Predctons of bone remodellng around dental mplant systems. Journal of Bomechancs. 41(6), pp [4] Cown SC and Hegedus D (1976). Bone remodellng I: theory of adaptve elastcty. Journal of Elastcty. 6(3), pp [5] Cown SC and Nachlnger RR (1978). Bone remodellng III: unqueness and stablty n adaptve elastcty theory. Journal of Elastcty. 8(3), pp

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