Effect of Bone to Implant Contact Percentage on Bone Remodelling Surrounding a Dental Implant

Transcription

1 Effect of Bone to Implant Contact Percentage on Bone Remodellng Surroundng a Dental Implant Author Lan, Z., Guan, Hong, Ivanovsk, Saso, Loo, Yew-Chaye, Johnson, Newell, Zhang, H. Publshed 2010 Journal Ttle Internatonal Journal of Oral & Maxllofacal Surgery DOI Copyrght Statement 2010 Internatonal Assocaton of Oral and Maxllofacal Surgeons. Publshed by Elsever Ltd. 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 * Manuscrpt (Manuscrpt prepared for Internatonal Journal of Oral and Maxllofacal Surgery) Effect of Bone to Implant Contact Percentage on Bone Remodelng Surroundng a Dental Implant Zhqang Lan a, Hong Guan b, Saso Ivanovsk c, Yew-Chaye Loo b, Newell W. Johnson c, Hongwu Zhang a a State Key Laboratory of Structural Analyss for Industral Equpment, Dept. of Engneerng Mechancs, Dalan Unversty of Technology, Dalan, , Chna b Grffth School of Engneerng, Grffth Unversty Gold Coast Campus, Queensland 4222, Australa c School of Dentstry and Oral Health, Grffth Unversty Gold Coast Campus, Queensland 4222, Australa Dec 16, 2008 Word count of abstract = 190 words Word count of man text = 4859 words Address correspondence to Mr. Zhqang Lan. State Key Laboratory of Structural Analyss for Industral Equpment, Dept. of Engneerng Mechancs, Dalan Unversty of Technology, Dalan, , Chna. Telephone number: +86 (0) Fax number: +86 (0) Emal: lanzq75@dlut.edu.cn or lanzq75@gmal.com. 1

3 Abstract Dental mplants are an effectve, safe and predctable soluton for patents sufferng from tooth loss. However mplant placement changes the normal mechancal envronment of the jawbone leadng to bone densty redstrbuton and remodelng, n order to to adapt to the new envronment. Many bone remodelng theores assume the presence of 100% contact between bone and mplant, whch s nconsstent wth clncal realty that s about 50%~80% bone-mplant contact s commonly seen n clncally successful mplant treatment. The nfluence of dfferent percentages of bone-mplant contact on bone remodelng has not been nvestgated adequately n lterature. Ths study ams to evaluate such an nfluence usng a newly proposed remodelng algorthm through a 2D fnte element model. Four dfferent degrees of bone-mplant contact (25, 50, 75 and 100%) are consdered and ther nfluences on the densty dstrbuton of jawbone s evaluated. The predcted results ndcate that no matter what the ntal percentages of bone-mplant contact (25-100%) are, the fnal outcome s about 58%-60% contact when an equlbrum state s reached by bone remodelng. The results are consstent wth clncal observatons and fndngs. Keywords: Dental mplant, Bone-mplant contact, Bone remodelng, Fnte element analyss 2

4 Introducton 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 the mplants are correctly desgned, manufactured and nserted n bone of good qualty and quantty, mplant falures do exst, especally n compromsed stes and patents 25. Bone, as a lvng tssue, s capable of optmzng ts nternal structure by redstrbutng ts apparent densty under the nfluence of external loads to fulfll ts maxmum functon. Ths paradgm s known as the Wolff s law 38. The process of bone redstrbutng ts apparent densty s termed as bone remodelng. Snce the early publcaton of Wolff 38, many theores descrbng the bone remodelng process have been proposed. Frost 12 suggested that nternal and external remodelng should be dstngushed, where nternal remodelng refers to the alteraton of densty of bone tssue and external remodelng s the apposton and removal of bone tssue on the bone surface. Pauwels 27 concluded that changes n the magntude of the habtual mechancal stmulaton lead to an atrophy or hypertrophy of the osseous structure. Frost 12 also suggested a trgger crteron for remodelng based on the stran magntude. Ths concept was formally developed later by Cown and hs co-workers 5,6 usng the concept of adaptve elastcty under small strans, whch was the frst mathematcally rgorous theory for adaptve growth and remodelng of bone. Cown and Froozbakhsh 7, Froozbakhsh and Cown 11, and Cown et al. 8 used the stran tensor as the stmul of bone remodelng and assumed a quadratc relatonshp between the stran and the rate of adaptaton. Carter 3 proposed the concept of lazy zone, a threshold value, ndcatng that bone remodelng takes place only when the external stmul exceed the lazy zone. Ths concept was ncorporated by Huskes et al. 14,15 who used the stran energy densty as the stmulus sgnal to control bone remodelng. Mullender et al. 22 and Mullender and Huskes 23 developed a physologcal approach to smulate bone remodelng whch assumed that osteocytes are senstve to mechancal loadng and are actve n controllng the adaptaton of bone mass n ther envronment. When an mplant or mplants are surgcally placed nto the jawbone, the mechancal envronment s altered. Accordng to Wolff s law, bone rearranges ts nternal structure by remodelng n response to mplant placement and loadng. Although many applcatons of bone remodelng theores are documented on the predcton of densty dstrbuton n per-mplant bone tssues 4,13,17,20, no 3

5 consderaton was taken on the effect of percentage of bone-mplant contact on bone remodelng outcomes. A full contact between the bone and mplant s often assumed n exstng bomechancal research, whch assumes that 100% bone-mplant contact s acheved. Ths s nconsstent wth clncal observatons, whch show that bone-mplant contact s dependant on a varety of factors such as mplant surface topography and bone qualty. The present study, based on a newly proposed bone remodelng algorthm, ams to evaluate the effect of percentage of bone to mplant contact on densty dstrbuton of jawbone through a two-dmensonal fnte element model. Methods The bone remodelng theory Amongst the exstng bone remodelng theores 14-16,22,23,37,40, some popular yet dstnctve ones are summarzed n the followng subsectons. Wenans and Huskes theory A popular bone remodelng theory suggested by Huskes et al. 15 s expressed as U U B (1 s) K f (1 s) K d U 0 f (1 s) K (1 s) K dt (1) U U B 1 sk f (1 s) K where ρ s the apparent densty of bone tssue; dρ/dt s the rate of change n densty; B s a constant regulatng the rate of the remodelng process; U s the stran energy densty (SED); s s n percentage denotng the regon of the lazy zone around the threshold value K, whch s a reference value of SED (Fgure 1); and the lazy zone descrbes the bone not havng a net change n apparent densty. In Eq. (1), U can be expressed as: 1 U (2) 2 where and are respectvely the stress and stran tensors of the bone tssue. For multple-load cases, the SED can be expressed as: n 1 U U (3) n 1 where n s the number of load cases and U s the SED under load case. 4

6 [Insert Fgure 1 about here] Smlar to Huskes et al. theory, Wenans et al. 37 adopted the stran energy per unt of bone mass,.e. U/ρ as the bone remodelng stmul and proposed a tme-dependent remodelng equaton: d U a B k,0 cb dt (4) where ρ=ρ(x,y,z) s the apparent densty of bone tssue at poston (x,y,z); U a s n the same form as Eq.(3) and ρ cb s the maxmum apparent densty whch s equvalent to that of a cortcal bone. Wenans et al. s algorthm was appled to predct densty dstrbuton n a normal proxmal femur wth results showng a dscontnuous pattern 37. The algorthm showed an unstable condton n ts mathematcal operaton. Due to the nature of the dfferental equatons used n the algorthm to descrbe the adaptve remodelng process, the smulaton produces dscontnuous confguratons, a phenomenon called checker-board. As dscussed by Rumerman and Huskes 32, the resultng densty dstrbutons correlate well wth those n a real proxmal femur, only when the densty dstrbutons were locally averaged from dscontnuous densty patterns n the femoral head where the trabecular bone s located. Mullender et al. and Mullender and Huskes theory Not havng ntrnscally dfferent bologcal nature from the theory of Huskes et al. 15 and Wenans et al. 37, Mullender et al. 22 and Mullender and Huskes 23 suggested a new algorthm whch smulated bone remodelng as a self-organzatonal control process. In ther theory, bone s assumed to have N sensor cells dstrbuted unformly over ts volume. An arbtrary sensor measures a sgnal S, whch s gven as: S U (5) where U s the SED and ρ s the apparent densty at the locaton of the sensor. The densty ρ(x,t) at locaton x s regulated by the stmulus value Ф(x,t), to whch all sensor cells contrbute, relatve to ther dstance from x. Hence, N ( x, t ) f ( x)( - ) S K 1 where N s the total number of sensors; K s a reference sgnal of SED and f (x) s a spatal nfluence functon gven as: (6) 5

7 f [ d ( x)/ D] ( x) e (7) where d (x) s the dstance between sensor and locaton x; D s the rate of the spatal nfluence reducton. Note that D represents the dstance from a sensor at whch locaton ts effect s reduced to e -1,.e. 36.8%. Ths s llustrated n Fgure 2. [Insert Fgure 2 about here] The densty ρ(x,t) s now governed by: d( x, t) ( x, t), wth 0 ( x) max (8) 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 remodelng process. Ths algorthm was used to predct the densty dstrbuton of a 2D plate model prevously studed by Mullender et al. 22. The model produced trabecular-lke structures wthout the checker-board patterns. It should be noted that the checker-board problem produced by the phenomenologcal models lke the one of Wenans et al. 37 has been completely solved by dfferent technques ncludng non-local stmul 22,23 or usng extrapolaton method to the nodal ponts 16. The checker-board phenomenon s beleved to be attrbutable to the softenng nduced by resorpton rather than remodelng tself. When usng the non-local defnton of the stmulus as a sum of the sgnal of dfferent osteocytes near the pont concerned, Mullender et al.'s model 22,23 does not produce checker-board patterns. Based on the theores of Wenans et al. 37 and Mullender et al. 22, Zhu et al. 40 proposed a new bone remodelng theory whch ncludes a hgh-order non-lnear effect. The governng equaton s: d x, t) B( dt N ( f ( x)( 1 1), wth 0 ( x) cb (9) U a ( ) (10) K where β s a comparatve coeffcent descrbng the comparson of mechancal stmulus U a ()/ρ n each sensor cell wth reference value K; α s the order of non-lnear remodelng equaton. Zhu et al. s remodelng algorthm s able to control the remodelng process more effectvely due to 6

8 the consderaton of non-lnear effect. However, smlar to Mullender s theory, the lzay zone effect was not ncluded n ther equatons. The proposed algorthm The abovementoned two types of theores have both shown to exhbt advantages and dsadvantages. Huskes s theory takes nto account the lazy zone effect but s unstable n ts mathematcal operaton leadng to a dscontnuous and an nevtable checker board pattern. Mullender and Zhu et al. s theores, on the other hand, are physologcally and mechancally more consstent and the checker board phenomena can be effectvely elmnated. However the effect of lazy zone was not consdered. The lazy zone effect, ntally proposed by Carter 3 based on expermental nvestgaton, has been verfed by Rubn and Lanyon 31 to be an mportant factor whch should be consdered n the smulaton of the remodelng process. To overcome the shortcomngs of the above theores, a new algorthm combng these theores s proposed heren. In the proposed algorthm, the bone s assumed to have N sensor cells dstrbuted unformly over ts volume 22. An arbtrary sensor measures a sgnal S, whch s gven as: S U (11) where U s the stran energy densty; and ρ s the densty at the locaton of the sensor. For multple-load cases, the stran energy densty can be expressed as: 1 n U n 1 U (12) where n s the number of load cases and U s the stran energy densty under load case. 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 S S (1 s) K (1 s) K (13) (1 s) K where N s the total number of sensors; α s the order of non-lnear remodelng equaton; K s a reference sgnal of stran energy densty per unt bone mass; s s n percentage denotng the regon of the lazy zone around the threshold value K. The densty ρ(x,t) s governed by the remodelng rate as expressed n Eq. (8) and f (x) s a spatal nfluence functon as gven n Eq. (7). 7

9 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 smplfed mplant model 18. The fnte element procedure As the apparent densty of bone tssue changes durng the process of remodelng, Young s modulus of bone changes accordngly. Some emprcal relatonshps between the apparent densty and the mechancal propertes of bone have been establshed expermentally 2,9,29. Young s modulus E of bone tssue at locaton x s calculated accordng to Currey 9 and Rce et al. 29 as E( x, t) C( x, t) (14) where s the apparent densty of bone tssue; C and γ are the constants whch can be determned through experment 2,9,29. In the teratve fnte element analyss process, the governng equaton (Eq. (8)) s necessary to be re-wrtten as: ( t t) ( t) t ( t) (15) where Δt s the tme step n the teraton process and Ф (t) s n the form of Eq. (13). The teraton s contnued untl no more sgnfcant changes take place n densty dstrbuton. The remodelng procedure s outlned as follows: (1) Create a fnte element model of mplant-bone system. Apply load and boundary condtons. Assgn unformly dstrbuted ntal values of Young s modulus and densty to the bone. (2) Perform a lnear statc fnte element analyss. (3) For each element, a sensor s located at the centre of the element. For an arbtrary sensor, calculate the stmulus Ф (x,t) based on Eq. (13) and the densty value based on Eq. (15). Such calculaton s done for all sensors (elements) and some of whch may have ther orgnal denstes changed to new values. (4) Is a densty convergence reached? f YES, the procedure of remodelng s termnated. If NOT, then contnue to the next step. (5) Update the values of Young s modulus based on Eq. (14) whch n turn updates the fnte element model. (6) Go to step 2. 8

10 Fnte Element Analyss Smulaton To evaluate the effect of dfferent bone-mplant contact on the densty dstrbuton of jawbone surroundng a dental mplant, 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. Two dfferent types of bone,.e. cortcal and cancellous bone, are dentfed n the model based on CT scan mages. The mplant dmensons are based on those of Neoss 24. Fg. 3(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 degrees of 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. Ths s also detaled n Fg. 3(a). In ths partcular fnte element model, the total numbers of elements are respectvely 759 for the crown,147 for the abutment, 312 for the abutment screw, 1335 for the mplant, 1274 for the cortcal bone, 2897 for the cancellous bone, and 408 for the connectve tssue. Based on the work of Chou et al. 4, 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. The pressure load s to more realstcally smulate the boundary condtons. The load and boundary condtons are detaled n Fg. 3(b). [Insert Fgure 3 about here] It s commonly known that bone s an orthotropc or ansotropc materal. However, n most fnte element smulaton of bone tssues, an sotropc materal behavor of bone s often assumed. Ths s manly due to the followng consderatons: (1) It s dffcult to determne the materal orentaton of bone; (2) Peng et al. 28 conducted a fnte element comparatve study on a femur wth two dfferent materal propertes (.e. sotropc and orthotropc materals). Lttle dfference was found n the results due to the two dfferent materal assumptons; (3) the relatonshps between Young s modulus and apparent densty of bone are mostly establshed based on the sotropc assumpton. For the above reasons, an sotropc materal behavor s also assumed n the present study. An extensve lterature revew by van Staden et al. 35 ndcates that the assumed range of Young s modulus for the cortcal bone vares from 5.57 to 22.8GPa and that for the cancellous bone vares from 0.08 to 7.93GPa. 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. 21. They are also 9

11 ndcated n Fg. 3(b). The Posson s rato for all components s taken as 0.3. When an mplant s surgcally placed nto jawbone, the nterface between bone and mplant can be dvded nto two regons,.e. regons wth drect bone-mplant contact and those wthout drect contact 33. To smulate dfferent degrees of bone-mplant contact, a certan percentage of connectve tssue elements are randomly selected and assgned the propertes of bony tssue. The remanng elements wthn the connectve tssue are assgned the propertes of soft tssue (Fg. 4). Accordng to Lu et al. 19 and Xng et al. 39, Young s modul of the bony and soft are taken as 2.4GPa and 70MPa, respectvely. In ths study, four dfferent degrees of bone-mplant contact (.e. 25, 50, 75 and 100%) are consdered to evaluate ther effect on the densty dstrbuton of jawbone. Note that 25% bone-mplant contact represents 25% bony tssue and 75% soft tssue. [Insert Fgure 4 about here] In the remodellng process, the densty dstrbuton of cortcal bone s assumed to be unchanged. However the rato of bony-soft tssue keeps changng 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. Ths corresponds to a Young s modulus of 7.93GPa, whch s calculated by a specfc relatonshp between the elastc modulus and densty as suggested by Carter and Hayes 2,.e: 3 E ( x, t) 3790 (16) where E s Young s modulus; x s the locaton of sensors; t s the remodelng tme and ρ s the apparent densty of bone tssue. It s worthwhle notng that there are no standard rules n the determnaton of bone remodelng parameters as specfed n Eqs. (13) and (15). Such parameters as K, the reference sgnal of SED; s, the lazy zone effect and τ, the tme constant regulatng the remodelng rate are found to be qute dfferent n the lterature. They are enumerated n Table 1. [Insert Table 1 about here] In order to compare the effect of four dfferent bone-mplant contact, the followng bone remodelng parameters are kept constant for all four scenaros. Accordng to Chou et al. 4, the maxmum and 10

12 mnmum denstes are assumed to be ρ max = g/cm 3 and ρ mn =0.064g/cm 3 respectvely whch corresponds to Young s modulus 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 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. Results and Dscusson To evaluate the effect of dfferent bone-mplant contact on the densty dstrbuton of jawbone surroundng a dental mplant, a 2D representaton of the mplant and mandble s studed. Ths s a prelmnary study dealng wth a new bone remodelng algorthm amed at overcomng the lmtatons of the exstng methodologes. For the purpose of ntal verfcaton, a 2D analyss s undertaken to obtan fundamental understandng of the remodelng process. A more sophstcated 3D analyss wll be conducted n the future so that detaled mplant geometry can be consdered and more accurate solutons be obtaned. Fg. 5 presents the outcome of a progressve remodelng process for a 50% bone-mplant contact scenaro. The densty dstrbutons n the cancellous bone and connectve tssue vary from the orgnal to the converged stages, correspondng to teratons 0, 50, 200, 300, 800 as shown n Fgs. 5(a) to (e)). As evdent n Fg. 5 that large areas of bone resorpton and surroundng formaton take place drectly under the mplant at early teraton (around 50 th ) stages. Ths morphology remans almost unchanged throughout the remanng remodelng process. At approxmately 200 th teraton, further resorpton and formaton occur at around both sdes of the mplant. Agan ths morphology changes very lttle untl the converged stage. Between teratons 200 and 800, the overall changes n the densty dstrbuton are mnor. However the total area of bone resorpton ncreseas. [Insert Fgure 5 about here] The predcted results of densty dstrbutons n the cancellous bone and connectve tssue for four dfferent bone-mplant contact scenaros are shown n Fg. 6. As can be seen the fnal densty dstrbutons are almost dentcal for four dfferent bone-mplant contact percentages. The only notceable dfference s the area located at the bottom rght sde of the mplant where the bone tssue demonstrates an average densty. Ths s partcularly true for 50%-100% bone-mplant contact 11

13 scenaros. For the 25% contact, ths area s a mx between bone resorpton and formaton. [Insert Fgure 6 about here] Fg. 7 presents a comparson of the predcted densty dstrbuton results wth clncal observatons. Shown n Fg. 7(a) s the predcted result due to the present study for 50% bone-mplant contact scenaro. Fg. 7(b) s the predcton of Chou et al. 4 and Fg. 7(c) dsplays the densty dstrbuton on a baboon s jawbone surroundng a dental mplant 36. The overall densty dstrbutons n the three fgures are qute smlar n the followng aspects: (1) the trabecular-lke pattern surroundng the mplant as hghlghted by regon A; (2) the lower densty area (bone resorpton) below the mplant as hghlghted by regon B. It should be noted that Chou et al. s 4 algorthm s based on Huskes et al. s 15 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 analyss dd not cover varyng bone-mplant contact percentages. [Insert Fgure 7 about here] Shown n Fg. 8 s the relatonshp between bone-mplant contact percentage and bone mass after remodelng s complete. As can be seen, 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 contact percentage has lttle nfluence on the bone mass upon completon of bone remodelng. Fg. 9 further compares the bone-mplant contact percentage before and after bone remodelng. Agan ntally assumed dfferent percentages result n a rather constant (between 58-60%) percentage of contact after bone remodelng. Fgs. 6, 8 and 9 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 the process of bone remodelng, the bone-mplant contact percentages reman almost constant at about 59%. Testr et al. 34 found a bone-mplant contact percentage of 64.2% for an 12

14 mmedately loaded mplant. Through a hstology study, Degde et al. 10 also dscovered a contact percentage of about 65% to 70% 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. [Insert Fgure 8 about here] [Insert Fgure 9 about here] Other smlar nvestgatons on bone-mplant contact nclude that of Papavaslou et al. 26 who ponted out that an mplant never acheves 100% contact wth surroundng bone. Roberts 30 also stated that even clncally successful mplants have less than half of drect contact wth bone. In addton, Block et al. 1 found smlar levels of bone-mplant contact n dogs. All these nvestgatons suggested a range of 50% to 80% bone-mplant contact n clncally successful mplants, whch are consstent wth our predcted results. In ths study, the nfluence of dfferent degrees of bone-mplant contact on bone remodelng followng dental mplantaton s evaluated usng a newly proposed remodelng algorthm. A two-dmensonal fnte element model s establshed and four representatve percentages of bone-mplant contact are consdered n the bone remodelng smulaton. The study demonstrates that the ntal percentages of bone-mplant contact (25-100%) have lttle nfluence on the fnal densty dstrbuton n the bone. Further, a fnal contact percentage of about 58%-60% s resulted when an equlbrum state s reached by bone remodelng. The results are consstent wth the clncal observatons and fndngs. Declaratons Fundng: Ths work was funded by the Natonal Scence Nature Foundaton (No , ) and 2006 Grffth Unversty Research Grant scheme Competng Interests: We, the authors of the manuscrpt, declare that we have no dsclose any fnancal and personal relatonshps wth other people or organzatons that could napproprately nfluence (bas) ther work. Ethcal Approval: Not requred 13

15 References 1. Block MS, Fnger IM, Fontenot MG, Kent JN. Loaded hydroxylapatte-coated and grt-blasted ttanum mplants n dogs. Int J Oral Maxllofac Implants 1989: 4: Carter DR, Hayes WC. The compressve behavor of bone as a two-phase porous structure. J Bone Jont Surg Am 1977: 59: Carter DR. Mechancal loadng hstores and cortcal bone remodelng. Calcf Tssue Int 1984; 36: S19-S Chou HY, Jagodnk JJ, Muftu S. Predctons of bone remodellng around dental mplant systems. J Bomech 2008: 41, Cown SC, Hegedus D. Bone remodellng I: theory of adaptve elastcty. J Elastcty 1976: 6: Cown SC, Nachlnger RR. Bone remodellng III: unqueness and stablty n adaptve elastcty theory. J Elastcty 1978: 8: Cown SC, Froozbakhsh K. Bone remodellng of daphysal surfaces under constant load: theoretcal predctons. J Bomech 1981: 14: Cown SC, Hart RT, Baber JR, Kohn DH. Functonal adaptaton n long bones: establshng n vvo values for surface remodellng rate coeffcents. J Bomech 1985: 18: Currey JD. The effect of porosty and mneral content on the Young s modulus of elastcty of compact bone. J Bomech 1988: 21: Degde M, Petrone G, Lezz G, Pattell A. Hstologc evaluaton of 2 human mmedately loaded and 1 ttanum mplants nserted n the posteror mandble and submerged retreved after 6 months. J Oral Implantol 2003: 29(5): Froozbakhsh K, Cown SC. An analytcal model of Pauwels functonal adaptaton mechansm n bone. J Bomech Eng 1981: 103: Frost HM. The laws of bone structure. Sprngfeld: Thomas C C, Grup V, Guglelmno E, La Rosa G, Vander Sloten J, Van Oosterwyck H. Numercal analyss of bone adaptaton around an oral mplant due to overload stress. Proc Inst Mech Eng [H] 2004: 218: Huskes R, Wenans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. Adaptve bone-remodelng theory appled to prosthetc desgn analyss. J Bomech 1987: 20: Huskes R, Wenans H, van Retbergen B. The relatonshp between stress sheldng and bone resorpton around total hp stems and the effects of flexble materals. Cln Orthop Relat Res 1992: 274: Jacobs CR, Smo JC, Bearpre GS, Carter DR. Adaptve bone remodelng ncorporatng smultaneous densty and ansotropy consderatons. J Bomech 1997: 30: L JY, L HY, Sh L, Foa AS, Ucer C, Devln H, Horner K, Slkas N. A mathematcal model for smulatng the bone remodelng process under mechancal stmulus. Dent Mater 2007: 23: Lan ZQ, Guan H, Ivanovsk S, Loo YC, Johnson NW. Bone remodelng smulaton n human jawbone surroundng dental mplant. Int J Oral Maxllofac Implants 2008(submtted) 19. Lu J, Pan KF, Xu XL, Qu HT. Influence of dfferent bone contact rato to stress dstrbuton n bone around dental mplant (n Chnese). J Oral Maxllofac Surg 2005: 15: Mellal A, Wskott HWA, Scherrer SS, Belser UC. Stmulatng effect of mplant loadng on surroundng bone. 14

16 Comparson of three numercal models and valdaton by n vvo data. Cln Oral Implants Res 2004: 15: Mencucc G, Mossolov A, Mozzat M, Lorenzett M, Pret G. Tooth-mplant connecton: some bomechancal aspects based on fnte element analyses. Cln Oral Implants Res 2002: 13: Mullender MG, Huskes R, Wenans H. A physologcal approach to smulaton of bone remodellng as a self-organzatonal control process. J Bomech 1994: 27: Mullender M G, Huskes R. Proposal for the regulatory mechansm of Wolff s law. J Orthop Res 1995: 13: Neoss Lmted. Neoss Implant System Surgcal Gudelnes, UK, Neukam FW, Flemmg TF, Workng Group 3. Local and systemc condtons potentally compromsng osseontegraton. Consensus report of Workng Group 3. Cln Oral Implants Res :17: Papavaslou G, Kamposora P, Bayne SC, Felton DA. 3D-FEA of bone-mplant contact percentages and patterns on mplant-bone nterfacal stresses. J Dent 1997: 25: Pauwels F. Bomechancs of the locomotor apparatus. Berln: Sprnger, Peng L, Ba J, Zeng X, Zhou Y. Comparson of sotropc and orthotropc materal property assgnments on femoral fnte element models under two loadng condtons. Med Eng Phys 2006: 28: Rce JC, Cown SC, Bowman JA. On the dependence of the elastcty and strength of cancellous bone on apparent densty. J Bomech 1988: 21: Roberts WE. Bone tssue nterface. J Dent Educ 1988: 52: Rubn CT, Lanyon LE. Regulaton of bone mass by mechancal stran magntude. Calcf Tssue Int 1985: 37: Rumerman R, Huskes R. Development of a unfyng theory for mechancal adaptaton and mantenance of trabecular bone. Theor Issues Ergon Sc 2005: 6: Smmons CA, Megud SA, Pllar RM. Mechancal regulaton of localzed and appostonal bone formaton around bone-nterfacng mplants. J Bomed Mater Res 2001: 55: Testor T, Szmukler-Moncler S, Francett L, Del Fabbro M, Trs P, Wensten RL. Healng of Osseotte mplants under submerged and mmedate loadng condtons n a sngle patent: a case report and nterface analyss after 2 months. Int J Perodontcs Restoratve Dent 2002: 22: van Staden RC, Guan H, Loo YC. Applcaton of the fnte element method n dental mplant research. Comput Methods Bomech Bomed Engn 2006: 9: Watzak G, Zechner W, Ulm C, Tangl S, Tepper G, Watzek G. Hstologc and hstomorphometrc analyss of three types of dental mplants followng 18 months of occlusal loadng: a prelmary study n baboons. Cln Oral Implants Res 2005: 16: Wenans H, Huskes R, Grootenboer HJ. The behavor of adaptve bone-remodelng smulaton models. J Bomech 1992: 25: Wolff JL. The law of bone remodellng. Translated by Maquet P, Furlong R, n Berln: Sprnger-Verlag, Xng XJ, Lu BL, Lu L. The nfluence of osseontegraton percentage on mplant-bone nterfacal stresses (n 15

17 Chnese). J X an Jaotong Unv (Med Sc) 2002: 23: Zhu XH, Gong H, Zhu D, Gao BZ. A study of the effect of non-lneartes n the equaton of bone remodellng. J Bomech 2002: 35:

18 Fgure Legends Fgure 1. The assumed local adaptaton as a functon of the SED wth the effect of lazy zone. Fgure 2. Relatonshp between f(x) and d(x). Fgure 3. Fnte element model of mplant and jawbone: (a) Dmensons; (b) Load, boundary condtons and materal propertes. Fgure 4. Illustraton of dfferent bone-mplant contact n connectve tssue. Fgure 5. Progressve alteraton of densty dstrbuton n mandble (50% bone-mplant contact). Fgure 6. Densty dstrbuton n cancellous bone and connectve tssue under dfferent bone-mplant contact. Fgure 7. Comparson between predcted results and clncal observatons. (a) Predcted result wth 75% bone-mplant contact; (b) Predcted result by Chou et al. 4 ; (c) Densty dstrbuton n baboons jaw 36 Fgure 8. Relatonshp between bone-mplant contact percentage and bone mass after bone remodelng. Fgure 9. Comparson of bone-mplant contact percentage before and after bone remodelng. Table 1. Bone remodellng parameters used n publshed lterature 17

19 Fgures d dt Lazy Zone Resorpton K (1 s) K (1 s) K Formaton U Fg. 1. The assumed local adaptaton as a functon of the SED wth the effect of lazy zone. Fg. 2. Relatonshp between f(x) and d(x). 18

20 4.5mm N 1mm Crown E=172GPa 0.2mm Abutment E=105GPa Connectve tssue 11mm 21mm 500kPa Abutment Screw E=93GPa Implant E=105GPa Cancellous Bone E=7.93GPa Cortcal Bone E=13.7GPa a Fxed Constrant Fg. 3. Fnte element model of mplant and jawbone: (a) Dmensons; (b) Load, boundary condtons and materal propertes. b --Bony tssue; --Soft tssue (a) 25% (b) 50% (c) 75% (d) 100% Fg. 4. Illustraton of dfferent bone-mplant contact n connectve tssue. 19

21 0.064 g/cm g/cm 3 (a) Orgnal stage (b) Iteraton 50 (c) Iteraton 200 (d) Iteraton 300 (e) Iteraton 800 Fg. 5 Progressve alteraton of densty dstrbuton n mandble (50% bone-mplant contact) 20

22 g/cm g/cm 3 (a) 25% (b) 50% (c) 75% (d) 100% Fg. 6. Densty dstrbuton n cancellous bone and connectve tssue under dfferent bone-mplant contact 21

23 A B (a) (b) (c) Fg. 7. Comparson between predcted results and clncal observatons. (a) Predcted result wth 75% bone-mplant contact; (b) Predcted result by Chou et al. 4 ; (c) Densty dstrbuton n baboons jaw 36 M ass (g) Percentage of bone-mplant contact (100%) Before Remodelng After Remodelng Fg. 8 Relatonshp between bone-mplant contact percentage and bone mass after bone remodelng. Fg. 9 Comparson of bone-mplant contact percentage before and after bone remodelng. 22

24 Tables Table 1. Bone remodellng parameters used n publshed lterature K s τ or τδt Chou et al Nm/kg 65% kg 4 /Nm 4 (τδt) L et al J/g (4 Nm/kg) N/A 1.0 (g/cm 3 ) 2 (τ) Mellar et al J/g (4 Nm/kg) 10% 1.0 (g/cm 3 ) 2 (τ) *N/A-Not Avalable 23