口腔内における支台歯荷重の三次元解析に基づく部分床義歯設計の検討

口腔内における支台歯荷重の三次元解析に基づく部

分床義歯設計の検討

著者

佐々木 啓一

口腔内における支台歯荷重の三次元解析に基づく

部分床義歯設計の検討

課題番号 15390583

平成15年度∼平成17年度科学研究費補助金(基盤研究(B) )

研究成果報告書

平成18年5月

研究代表者 佐々木啓一

(東北大学 大学院歯学研究科 教授)

目次

1.はしがき

2.研究組織

3.交付決定額

4.研究発表

5.研究成果

6.謝辞

7.研究成果資料

1) In vivo 3-D force measurement on the abutment tooth of removable partial denture

2)歯に加わる荷重の生体内三次元測定

3) In vivo 3-Dimensional force measurement in teeth during functions

4) Three-dimensional load on a tooth during function

5) Invivo 3-Dimensional measurement of the force exerted on a tooth during clenching

6) Behavior of 3-dimensional loads exerted on a tooth during RlnCtion

7) Behaviors of 3-dimensional compressive and tensile fわrces exerted on a tooth during function

1.はしがき

部分床義歯の予後を決定する要素の一つとして,支台歯に加わる荷重があげられる.

支台歯-の負担過重は支台歯周組織に障害を及ぼし,義歯の予後を悪化させると考え

られる.したがって,岨噂や嚇下など機能時に義歯に加わる力の支台歯-の伝播,およ

び負担すべき荷重について知ることは,支台歯の選択を含めた義歯の設計や付与する

嘆合様式などを検討する上で極めて重要である.

今日までこの課題について数多くの研究が行われているが,その多くは光弾性模型

や有限要素津による解析であり,患者個々の口腔内条件,すなわち支台歯や歯周組織

の条件を詳細に反映する解析までは到達していない.また,口腔内において支台歯に加

わる荷重を測定した研究はほとんどなく,三次元的に解析した研究は皆無であった.さら

に,支台歯に加わる荷重に対しての支台装置の違いによる影響などについては未だ不

明な点が多い.これらのことに結論を出すには,口腔内における荷重の実測が必要不可

欠である.

最近,我々は精密加工と精密計測を専門とする工学分野との共同研究により,圧電性超

小型荷重センサを歯の内部に組み込むことにより,機能時に歯-作用する荷重を三次元

的に実測し,機能力の口腔内分布をリアルタイムで解析可能な三次元荷重測定システムを

開発した.

本研究では,このセンサを用いて種々の設計,形態の部分床義歯を装着した際の,機

能時に支台歯-作用する荷重とその変化を実測することにより,部分床義歯の設計,支

台装置の種類ならびにP交合様式と支台歯に加わる荷重の関係を明らかにする.

さらに本システムを部分歯欠損患者に用いて､部分床義歯の設計や嘆合の違いによる

支台歯に作用する荷重の変化を検索し,支台歯に加わる機能力から見た義歯の設計に

ついて検討を加える｡

本研究の結果は,これまでの部分床義歯における支台歯選択やクラスプの種類など支

台装置の決定等に関する認識を変えうる可能性が高く,部分床義歯治療の予知性の向

上に多大な貢献をもたらすものと考える.

2.研究組織

研究代表者    佐々木啓一 研究分担者    厨川常元

稲井哲司

小山重人

川田哲男

研究協力者    川口威史

依田信裕

3.交付決定額

(東北大学大学院歯学研究科･教授)

(東北大学大学院歯学研究科･教授)

(東北大学病院･講師)

(東北大学病院･講師)

(東北大学大学院歯学研究科･助手)

(東北大学大学院歯学研究科･大学院生)

(東北大学大学院歯学研究科･大学院生)

(金額単位:千円)

直接経費 亊I

ｨﾆ

N

合計

平成15年度 釘ﾃc 0 釘ﾃc 平成16年度 釘ﾃ 0 釘ﾃ 8 ﾂ 平成17年度 ﾃ3 0 ﾃ3 総計 免ﾂﾃs 0 免ﾂﾃs ﾂ 3

4.研究発表

1)川口威史,川田哲男,佐々木啓一,厨川常元

小型水晶圧電式センサによる部分床義歯支台歯の荷重測定 第109回日本補綴歯科学会学術大会

品川区立総合区民会館｢きゆりあん｣ (東京:平成15年5月11日)

2) Kawaguchi T, Kawata T, Sasaki K, Kuriyagawa T

Invivo 3-D force measurement on the abutment tooth of removable partial denture The loth meeting of the intemational college of prosthodontists

Hotel Nova scotia ( Halifax: 2003年7月12日)

3)川田哲男,依田信裕, ′州徹末永華子,厨川常元,佐々木啓一 歯に加わる荷重の生体内三次元測定

第38回日本エム･イ-学会東北支部大会

東北大学大学院工学研究科電子情報システム･応物系(仙台:平成16年11月27

日)

4) N Yoda, T Kawata, H Suenaga, T Kuriyagawa, K Sasaki

Invivo 3-Dimensional force measurementinteeth during functions 83rd General Session & Exhibition of the IADR

Baltimore Convention Center (Baltimore, 2005年3月10日)

5) N Yoda, T Kawata, T Kawaguchi, H Suenaga, T Kuriyagawa, K Sasaki

Three-dimensional load on a tooth during触1Ction

lnternational Symposium fb∫ lnte脆ce Oral Health Science in SENDAI

Sendai lntemational Center (Sendai, 2005年2月2,3日)

6) Kawata T, Yoda N, Suenaga H, Ogawa T, Kuriyagawa T and Sasaki K

Tractive force exerted on a tooth during chewing measured with 3-D transducer in vivo

The l lth meeting of the intemationalCollege of prosthodontists

Creta Maris Resort (Crete: 2005年5月23日)

7) N Yoda, T Kawata, T. Ogawa, T Kuriyagawa, K Sasaki

Behavior of 3-dimensionalloads exerted on a tooth during function The 4th Biemial Congress of Asian Academy of Prosthodontics

5.研究成果

1. IntI10duction

Functionalocclusalforces transmitted onto teethare detemined bythe biomechanical

properties of the stomatognathic system, includingthe masticatory muscle forces,the position of the teeth,andthe condition of the periodontal tissue･ The transmitted force vectors arethus very complex･ Numerousin vitroand in vivo studies have investigated thefunctionalforces exertedin

the mouthin order to identifythe force magnitudesand directions related tothe biomechamiCal

Conditions.

Ln vitro model simulationshave been done using photoelastic models (Ralphand Caputo,

1975; Assif etal･, 1989; Asundiand A血l, 2000)and two- orthree-dimensionalfimite element

models (Takahashi etal･, 1980; Rees, 2001; Lee etal･, 2002)and by means of strain gauges

(Anderson, 1953; Craig and Peyton, 1966; Asundiand Anl1, 2000). Photoelastic models havealso

beenused to estimatethe intemalstress patterns･ A major disadvantage of using such models is that the mechamiCalproperties of plastic differfromthose ofperiodontaltissueandjawbone. Finite

element models canbeused to estimatethe rangesand distributions of stressand strain in a

subject,althoughthis requires using modules for the appliedforcesand knowingthe propedy

distributionsofthe muscles, jawbone,andperiodontaltissue. In addition,the variouspower

resources provided bythe muscles ofmasticationare very difficult to reproduce.

Straingauges have beenused to register the directionand magnitude of strains under loading･ However, becausethe toothsu血ce does not deformunder normal physiological loads, attaching

the points of a straingauge tothe surface of the toothis not a suitable method for measunng

imperceptible changes intheforce magmitudeand directions･ As mentioned above, the transmitted

force vectors are very complex･ Since modeling results depend onthe input data, in vivo data on the behavior of the forces should beused inthe models. These forces have been measuredwith stmin gaugesinmost in vivo studies. However, Sincethe criteria fbrand definition of the toothelxis is vagueandthe shapes of the teethcrowns vary'it is difficult to conformthe position of a strain

gauge on a toothsurface tothe other teeth･ Therefore,few in vivo measu托mentS have actually

been camied out.

Since die SPOntaneOusPOlarizationthat occurSinpleZOelectric materialcorresponds tothe load, a pleZOelectric force transducer canaccurately measure loads rangingfromminute tointense.

Such transducers havethus been usedwithmany applicationsinthe biomechanicsfield, which

requires accurate measurements (Collins and De Luca, 1994; Mitchell et a1., 1995; Shiba et a1.,

1995; Goldie etal., 1996). Althoughapplication intothe mouth has been attempted (Graf etal.,

1974; Palla etal., 1981), measurement where the transducer is directly inserted intoanabutment too仇crown has not yet been unde血en.

Fumctional forces transmitted tothe abutment teethof removable partialdenturesare critical factors innuenclng the clinlCalresults. TherPfore, it is important to elucidatethefunctionalfbrces ontothe abutment tooth. There have been numerous studies discusslng forces ontothe abutment tooth･ However, in vivo measurements have seldom been carried out, because of the difficultyof

direct fわrce senslng On a tooth during丘lnCtion.

The aim of this study was toinsert a pleZOelectric transducerinto a toothcrownin vivo to

meastuethe load applied tothe toothand toanalyzethe fわrce magnitudesand directionswith

respect tothe biomechamiCalconditions. We first Clarified the characteristics of the piezoelectric

force transducer to be used. Then we developed a measuring device for applyingthe transducer to

a tooth･ Finally, We measuredthe magnltudesand directions of a force applied toanabutment toothofRPDand a toothinnaturaldentition during function

2. Materials and Method 2. 1. Measuring device

The血ICtional load onthe toothwas recordeduslng a 3-dimensionalpiezoelectric force

transducer (Z 1 8400,Kistler Instruments AG Winterthur, Switzerland). It was anlmproved version

of the piezoelectric force transducer usedinstudies of 31dimensionalforce measurement on oral endosseous implants (Mericske-Stem et al. 1996a, 1996b, 1997, 1998)and was also

water-resistant･ It contained three crystals in a steel housingwitha diameter of 7 rr汀nand a height

of3･5 mm (Fig. la) for measuringthe loadalongthe x-, y-,and z-axes. The load couldthus be simultaneouslyand independently measured inthree dimensions,includingthe horizontaland

perpendicular directions,inrealtime (Fig. lb). The three dlmensions were defined as vertical

(Z-axis), antero-posterior (y-axis),and mediolateral(X-axis). The transducer preloaded to 750 N

had a horizontal measuring range of土150 N (X-axisand y-axis) and a vertiCalone of土500 N

(Z-axis). The measurement threshold was 0.01 N. Crosstalkalongthe x-axis was 0.1% in the direction of the z-aD(isand ｣).6% inthe direction of the y-axis. Alongthe y-axis, it was 1.1% in

the direction of the x-批isand 1.7%inthe direction of the z-axis.Alongthe z-axis, it was ｣). 1%in

the direcdon 10fthe y-axisand 10･6% inthe direction of the x-axis･ These transducer specifications were provided bythe manufacturer･ The transducer charge wasamplifiedusing a 4-channel charge amplifier (501 9B,Kistler Instruments AG Winterthur, Switzerland), which was cornected tothe transducerwitha multicore-shielded cable･ Theamplified signals were jVD converted usingan

〟D converter PR-2000, Keyence Corporation, Osaka, Japan)witha sampling rate of 100 Hz

and recorded on a personalcomputer. I

2 ･2･ Proofreading apparatus

The丘ame of the proofreading apparatus (Fig･ 2a)used for benclmarking was manufactu,ed &om steel plate (15 mmthick)and had foursteel pillars (15 mm square) so as not to be disto,ted bythe applied load･ A vise was attached tothe血ne･ The angle of the vise could be shifted

around one axis in O･05o steps･ Loading was done by placing weights, one by one, on a ball spline.

The bottom end of the spline had a specialprobe sothat the load transfer area was a polnt COntaCt

(Fig･ 2b)･ A steel cap was secured tothe brassjig atthe end of the transducerusing a steel screw to ensurethatthe pressure was distributed evenly overthe pressure receiver of the transducer, which

was the upper surface of the transducer (Fig･ la)･ During horizontalmeasurement,the tip was set

as close as possible tothe pressure receiver (Fig. 2C).

2･3･ Prookeading

The proofreading apparatus wasused to clarifythe characteristics of the piezoelectriCfo,ce

transducerunderthe asst-ption of oralConditions･ The characteristics included 1 )the relationship betweenthe actualload and transducer output, 2)the effect of hysteresis on transducer output,and

3)the effect of temperature on transducer output.

The transducer was tightenedwitha 20-Ncm load to obtain a preload of about 680 Nusingan

electric torque controller (DEA 055-0, Nobel Biocare, G6teborg, Sweden). The preload de丘ned

the measurement llmitationsintheperpendicular direction,pemittingusto measurethe tensile

force･ Moreover, lt PreVentedthe丘xed transducerfrom sliding when horizontalshearing force was

applied･ The load whenthe tip of the ball spline contactedthe cap onthe transducer was defined as

zero･ Loads of up to 148, 148,and 297 N were applied tothe x-, y-'and z-axes, respectively･ To 7

measurethe relationship betweenthe actualloadand transducer output, we appliedthe loads sequentially to each axis individually from zero to maximumineach trial. The number of different sequentialloads applied tothe x-, y-,and x-axes was 5, 5,and 8, respectively, ln each of 10 trials.

To measurethe effTect of hysteresis on transducer OUQ)ut, we apPliedthe loads sequentially to each

axis individually from zero to maximumandthen sequentially removedthem to reach zero agaln･ The number of different sequentialloads again applied tothe x-, y-,and x-axes was 5, 5,and 8, respectively, ln each of 10 trials, andthe numbers were the same when removingthem. The room temperature was 26o whenthe relationship betweenthe actualloadand transducer outputand the effects of hysteresis on output were measured. The room temperature was changed from 26 to 3 8o in 21degreeincrements whenthe effect of temperature on transdtlCer Output Was meaSured･ The loads were sequentially applied at each temperatureinthe same way as whenthe relationship

betweenthe actualloadand transducer output was measured, The temperature of the transducer was maintained at each temperature for 10 minutes before measurement,and ten trials were

carried out for each measurement condition. A thermocouplemicro-probe (IT-21, Physitemp Instruments, Inc., NJ, USA) was attached tothe transducer to measurethe temperature･ The temperature data were displayed on a microprobethermometer (BAT-2 1 , Physitemp Instruments,

Inc., NJ, USA)and recorded on a personalcomputer.

2.4.Analysis

The data wereanalyzed uslng SO氏Ware for biological signalmeasurementand processlng

(Signal Basic Light 2100, MedicalTry System Co.). Linear regressionanalysis wasused to

determinethe relationship betweenthe loadand transducer output (STATISTICA, Stat So允 Inc, OK, USA).

2.5. Application into mou血

2.5. 1. Device丘)∫ 3-D fわrce measurement

The piezoelectric force transducer was manufactured tofitinto a commercialdentallmplant

fixture (043. 1 3 1 S ITI standard implant, Stratmann, Wddenburg, Switzerland). A custom-made

component wasused to a氏Xthe transducer to a natural tooth･ The measuring device comprisedan

irmer part formlng a metalcore, the force transducer,andanouter part formlng a metaltooth crown･ The innerand outer parts were made of platinumgold castalloy (Fig. 3a). These three parts were joined together witha steel screw (Fig. 3b). The implant fixture was embedded in the

core to enablethe transducer to be tightlyfixed.

2.5.2 In vivo measurement

2.5.2. 1 Natural dとntition

The subject was a 26-year old healthy manhaving no abnormalitiesinthe stomatognathic

system･ Informed consent was obtained a鮎rfull explanation of this study･ The load-measunng

device was set over the maxillary leR second molar, which had three roots and a root canalfllling

and was suitable for afnxing the transducer･ The palatalroot was 7･8 mm long･ The measunng

device was inserted intothe tooth rootand held by temporary dentalcement (Figs･ 4aand b).

Figure 4c showsthe occlusal contact at the time of intercuspation･

Thethermocouple micro-probe was attached to the metaltooth crownsurface to measurethe

temperature･ The temperature data were displayed on the microprobethermometerand recorded

on a personalcomputer.

The force magnitudes and directions in three dlmensions were recorded during (MVC). The

task was repeated five times･ The 3-D load calculatedfromthe outputs of the transducer was expressed as a vector of the coordinates based onthe Frankfort horizontalplane (F-H plane)and

sagiualplane･ The starting polnt Of the vector wasthe center of the pressure receiver. The transducer outputs were transformedusingtheangles calCulated from posteroanteriorand lateral

cephalogramSand a study cast･ The palatalroot was positioned at 29･Oo to the perpendicular line

of the F-H planeand 4･Oo tothe sagi他l plane.

2.5.2.2 Partialedentulousdentition: abutment tooth

The subject was a sixtyyears old femalewithpardaledentulousmandible･ Theright second

premolarwas needed for restoration aRer root canaltreatmentand it was adequate for settingthe

transducer (Fig. 5). Her opposing dentition was a complete denture･

Figure 6 showsthe arti丘cialmetalcrownwiththe transducer･Anexperimentalpartialdenture

was providedthe removable medialand distalrests (Fig･ 7)･ The transmitted loads ontothe abutment tooth were measuredand compared amongthree different pattems of rest design, i･e･

withmedial rest,withthe distalrestand bothofthe medialand distalrests･ Experimentaltask

employed in this study was maximum voldntary clenching (MVC)･ The task was repeated five

times.

2.6･ Transducer output transformation

The transducer outputs were based onthe particular axis of the transducer (Fig･ lb)･ They

needed to be transfわrmed based onthe reference axes deflned in this study to clarifythe

relationship to the stomatognathic morphology･ Theanteroposterior axis (AIP)and mediolateral

axis (MIL) were detemined bythe FH plane inthe subject (Figs･ 8aand b)･ The superior-inferior

axis (S-I) was determined by a line perpendiculartothe FH plane･ The transformation regime was to first calculatetheangle of the partiCularaxes of the transducer tothe reference axes atthe first

setout. The transducer output wasthen rotated three-dimensionally based on theangles calculated below

Rotationangles αand β were estimated from the posteroanteriorand lateralcephalogramS

(Figs. 8aand b). Rotationangle y was estimatedfromthe study cast, on whichthe transducer had been aFIXed (Fig. 8C).

The unit vector of the particular axis of the transducer (Figs･ 8a, b, C) is given by

u-【x y z].

Whenthe transformed output is ull it canbe writteninmatrix formas

u, -u α α 0.帆 os S C o a.那 C 一 1 0 0 β  β ･m o o ら S 一  C O 1 0 β,  β os 0 n o  .a γー γー 0 0 1 .m os 0 S C 叩.叩o C 一 (2) (1)

Figures 9aand b show examples of the raw output data obtained during MVCandthe

5 1 ･50, respectively.

3. Results

3. 1. Proo&eading

3･ 1 ･ 1 Relationship between transducer outp,utand load (Fig･ 1 0)

We applied linear regressionanalysis tothe relationship betweenthe transducer outputand load･ The correlation coeFICients forthe x-, y-'and z-axes were O･99999, 0･99999, and 0.99996,

respectively.

3･ 1 ･2 Effect ofhysteresis on transducer output

The effect of hysteresis on transducer output was used to evaluate the reliabilityof transducer output when measunng dynamic loads, such as during mastication･ The effects were 0.9%, 1.1%, and 1 ･7%, respectively, forthe x-, y-, Z-axes at maximum for ten trials･ The effect ofhysteresis on

trans血cer output was thus negligible.

3･ I ･3･ Effect of temperature on transducer output

A change inthe temperature had little effect on transducer output･Asthe temperature was

increased,the emitted charge increased･ Most of the difference in transducer output occurred between 26and 380･ The output at 380 increased O･5%, 0･46%,and O･45%, respectively, alongthe x-, y-,and z-axes, comparedwith that at 260･ The effect of temperature on transducer output was

血us negligible.

3･2. Application into mouth

3.2. 1 Natural dentition

As shownin Fig･ lla, during MVC,the compressive force exerted onthe toothincreased

rapidly舟omthe start ofclenchingand reached a plateau. The rate of increase was 0. 144土0.034

N/msec,andthe maxlmumforce was 1 73･29士15･32 N･ Each axis,s curve has a different point of

therising edge･AsshowninFig･ I 1b, during Caramel chewing'the force rhythmically increased

and decreased. The rate of increase was 0.977 A: 0.168 N/msec,andthe maximum force was 146.3

土14.7 N. As shownin Fig. llC, during peanut chewing,the force rhytlmical1y increasedand

decreased,the same as during Caramel chewing. The duration of the chewing cycle was slightly

longerthanduring Cammel chewing. The rate of increase was O･363 ± 0･145 N/msec,andthe maxlmumforce was 57.7土35.7 N. The maximummagnltude recorded during Peanut chewing was signl丘Cantly smal1erthanthat during MVCand Caramel chewing (〟 < 0･001, Dun)･ There

were no signi丘Cant diFerences between MVCand Caramel chewing.

As the magnitude of the compressive force wasincreased,the vector tended towardthe

medial and posterior directions (Fig. 12). Viewed丘om血e coronaュ plane,血e maximum fわrce

vector was directedfromthe crowntothe root medially atan'angle of 10.27土1･000 to the perpendicularline of the FIH plane (Fig. 12a). Viewedfromthe sagi他l plane,the maximum force vector was directedfromthe crownto the root posteriorly atanangle of 3.18土0.85o to the

perpendicular line of the F-H plane (Fig. 12C). These directions were approximate to the direction of the palatal root, but not coincidentwith it, particularlyanteroposteriorly. Compared tothe palatal root, the maximumCompressive force was directed posteriorlyand laterally･

As血e magn血de of the compressive fわrce was increased,血e fわrce vector direction changed

bothinthe coronaland sagittal plane for each type of chewing. For example, during Caramel

chewing,the vector tended towardthe medial (-ll.4土1.10)and posterior (-3･7士1･Oo) directions

(Fig. I 3). The force vector direction at maximum magnitude in each cycle during Peanut chewing

was significantly more laterallyandwidely scatteredthanthat during MVCand Caramel chewing b < 0.01, Dumm) (Fig. 14). There were no significant differences between MVCand Caramel

chewing･ The range of the force vector direction dming the force-increaslng Phase of MVC was

significantly smallerthanthat during Caramel chewingand Peanut chewing, bothinthe coronal

and sagittal planes (〟 < 0.01, Dun) (Fig. 15).

The tensile force was recorded throughoutthe second half of Caramel chewing but not during

MVC and peanut chewing (Figs. 13 and 16). It reached a maximum (on average) 0･161土0･034

msec aRerthe compressive force reached a maximumduring each chewing cycle (Fig. 16)･ The

maximummagnltude of the tensile force was 4.05士0.98 N (range: 2.05-塙.37 N). The direction

was 45.7 j= 1 1.50anteriorlyand 1 1.6 j= 17.3o laterally. me tensile force was dispersed significantly

widerthanthe compressive force (P < 0.001, Mann-Whitney) (Fig･ 17)･

The directionand amplitude of the transmitted forces onto the abutment toothinthe sagittal planeand projected onthe lateralcephalogram(Fig. 1 8a). The mean values of the directionand amplitude of the loads measured at four directions i･e･without denture, wearingthe experimental

denture withthe medialand distalrests,withthe medialrestandwiththe distalrest are shownin

Table 1 ･ The force vectorwithout denture directed more posteriorlythanthe vectors at wearingthe

denture･AmOng three different conditions 6f rest design,the force vectorwiththe distalrest was

towardsthe most posterior direction･ Theangles decreased in descending order when measured

withthe medialand distalrest,andwiththe medialrest. There was significant difference between

theangleswiththe medialrestandwiththe distal rest. As forthe maximumload, highest force

was recorded when not wearingthe denture. Meanwhile,the smallest force was recorded whenthe denturewiththe distal rest was wom･ Force vectors of the transmitted forces are projected onthe P-A cephalogram(Fig･ 1 8b). The meanValues of dhectionandamplitude of the force vectorsin

thefrontalplane at fourdifferent conditionsare showninTable 2. The force vectorwiththe

medialand distalrests directed most laterally, andthat withthe medialrest directed most

downward･ There was not sigmiflCant diFerenceamongthe directions of fわur different conditions

inthefrontal plane.

4. Discussion

Many measurements ofa load applied to teethhave been done in vivoand in vitro. Because in

vivo measurements are problematic due tothe transducer size, in vitrlO meaSurementS have been

done more often･ Sincethe phenomena canbeinterpreted very easily, in vitro measurements can simplifythe experimentalconditions. The results derived from in vivo measurements are

complicated due to血母 many power resources pmvided by血e muscles of mastication and也e

nexibilityofthe constituent elements, includingthe periodontalmembraneand jaw bone (Korioth and Ha-am, 1994; Koolstraand vanEijden, 2001). While in vit710 meaSurementS havethusbeen

more common,thoroughanalysis of the results requiresknowledge of the originaltransmission

adtudes of the loads in vivo･ Furthermore,the 3-D loads, bothmagnitudeand direction, need to be

measl∬ed･ Since we were able to insertthe transducer directly into a tooth, we could directly

measurethe 3-D load applied to it･ We still need to measurethe in vivo accuracy of this transducer. Asthe correlation coefhcients between the loadsand transducer output were 0.99999for the x-axis, 0･99999 forthe y-axis,and O･99996 forthe z-axis,the relationship for each axis showed

vety good linearity. The slightly worse coefficient forthe z-axis was becausethe z-axis had twice

as much load applied asthe other axes･ These linearities forthe transducer outputs demonstrate

thatthe data output bythe transducer were valid. The correlation coeFICients were higherthanfor

results obtainedwitha similar transducer (Mericske-Stem etal., 1 996a)that used half the preload weused. Inthe latter study,the authors needed to applythe preload whenthe transducer was inthe mouth, consequentlythey had touse a lower preload･ 0urabilityto preloadthe transducer when it was outsidethe mouthresulted in better correlation betweenthe loadand output

Hysteresis of the transducer outputalo喝eaCh axis had very lime effect･ The pnncipalfactor

responsible for hysteresis was apparently the use of a houslng made of steel ratherthanone made of crystal, which isthe main part of the transducer･ The results demonstratedthe reliabilityofthe transducer outputwitha variable load･ The findingthatthe output was little affected by hysteresis meanSthatthe trqnsducer is well suited for measuring dynamic loads･

A piezoelectric element emits electric charges due to loading･Anincrease inthe temperature

increasesthe electric charge. The higher the temperature,the more easily electric charges are

emitted. We initially thought that this transducermight be greatly affected by temperature･ The

outer crownwhere the transducer wasinstal1ed experienced temperatLu:e Changes whenthe subject's mouthwas open. Wethusmeasuredthe difference in transducer output between room temperatureand mouth temperature･ We foundthat changes in temperature hadaninsignlficant effect on outputunder measurement conditions that were consistentwith use inthe mouth･

To the best of ourknowledge, this study is the first to establish a method for in viv0 3_dimensional measurement of the force exerted on a toothduringfunction. Whileanother group (Mericske-Stem etal. 1996a, 1996b, 1997, 1998) applied a similar transducer to implzmt-bome dentalprostheses, we applied our transducer to a toothhaving a vitalperiOdontal ligamentand viable periodontium. Moreover, we transformed the transducer output to clarifythe force direction relative to a skeletally based coordinate system･ The clinical situation differs greatlyfromthat of

anendosseousimplant becausethe periodontalligament isknownto beanimportant component

of neurosensOry systems for detecting forces exerted on humanteeth(Trulssonand Johansson, 1994, 1996). Weusedthe FH plane asthe coordinate basis inthis study･ Theuse of this basis should help elucidatethe biomechanics of the stomatognathic systeminrelation to cranio-facial

morphologyand help clarifythefunctionalmeanings of force exerted onthe toothin relation to

stomatognathic血nction･ Inthefuture, die force vectors for different teeth need to be compared,

andthe interindividualdifferences need to be clarified using the skeletalreference･

while this transducer cannot be used onall teeth, it canbeinserted into any tooththat has had

endodontic treatment, has a crown morethan5 rrm highand morethan7 mmwide,and has a root

canalmorethan2mmwide.Whenthese conditionsare met,this transducer canbe used to

meastwethe load applied tothe toothin vivo･ Having succeeded in applying this transducer to

in-mouthmeasurement, wewill next test its abilityto dynamically measure a load applied to a toothunderfunction.

Applyingthis measunng system tothe subjects, numerousRndings as tothe transmitted

forces ontothe subject teethcould be obtained, which wereunable to be demonstrated before. The change inthe compressive force vector daring bothchewingand clenching is explained as follows. During clenching attheintercuspalposition,forces generated bythe masticatory muscles are exerted onthe upperand lower dentitions as well as onthe bilateraltemporomandibularjolntS

(Koriothand Hannam, 1994a, 1994b)･ The force vector on a toothis a component of the forces

exerted onthe totaldentition･ Thus,the changesinthe force vector onthe subject tooth would reflectthe balanceand changes inthe force vectors onthe totaldentition based onthe muscle function (Eriksson etal., 1984, Blanksma etal･, 1992, Hannamand McMillan, 1994, Ogawa etal, 2006)･ Masticatory muscles'activities naturally change during clenching. However, Since the rate of increaseinboththe masseter (Devlinand Wastell, 1985) and temporalis (Mao et a1., 1996)

activityis not coincidentwiththat of the occlusalforce magnitude,there must beanother

explanation･ Becausethe timing of the medial pterygoid does not coincidewiththat of the

masseterand temporalis for several jaw functions (Hamamand Wood, 1981, Wood, 1981 , Plesh et al, 1996),the medialpterygoid may have contributed tothe changeinthe compressive force

vector･ The change during clenching might be related tothe movement of the tooth, which

depends onthe viscoelastic character of the periodontiumandthe distortion ofthealveolar bone (Koriothand Ha-am, 1994a, 1994b)･ The upper molarapparently displacesinthe root direction and tilts towardthe palataldirection during clenching (Kato, H., 1982, Miura et a1., 1995). Kato reportedthatthe measurement point onthe toothcrown moved 6111 16 micrometersinthe palatal direction during clenching whenthe compressive force was 2046 kgf, sothe changes inthe

aligrment angle of the tooth axis are not clear intheir results. In contrast,the direction of the

changes inthe compressive force inthe present study was largely coincidentwiththe direction of the toothmovement･ The change inthe toothalignmentandthe forces and movements caused by adjacent contacted toothduring clenching mighttherefore partly contribute tothe force vector

changes we recorded･ The di飴rence inthe vector direction betweenthe force-increaslng Phase

andthe force-decreaslng Phase of MVC may be related to the mechanlCalproperties of the periodontalmembraneand thealveolar, asthe periodontalmembrane has viscoelastic conformlng compressionand decompressionandthealveolar bones distorted during function.

Asthe magnitude of the compressive force increased during bothMVCand caramel chewing,

the vector direction of the fわrce at maximummagmitude concentrated,andthe mediolateral

direction of the force tended to correspond tothe direction of the palatalroot of the tooth. This supportsthe generalconcept of the relationship betweenthe toothaxisandanocclusalforce (Kato, H., 1982, Miura etal., 1995). In contrast,the vector direction at maximumtensileforce during caramel chewing was dispersed. This might be related tothe position of the item to be chewed on

the toothbefore openingthe mouth. ,

Compressive force was apparently applied tothe toothkom variousdirectionsduring chewing. As a result, the range of the force vector direction during caramel chewingand peanut

chewing was significantly largerthanthat during MVC dmingtheforce-increaslng Phase.

Since the maximumcompressive force during peanut chJewing was smal1erand more dispersedthanduring Cammel chewing ln most Chewing cycles,the mandibular position during peanut chewingmight have been dispersed. Additionally, for hard foods like peanuts,the

compressive force applied to a toothduring chewing might vary due to food remnants betweenthe

occlusalsurfaces of the maxillaryand mandibularteeth. These remnants might account for our

finding thatthe range of the vector direction at maximum magnitude duringpeanut chewing was widerthanthat during Caramel chewing.

Tothe best of ourknowledge,this study isthe first to measurethe tensile force exerted on a toothduringfunction, i.e., Caramel chewing; this force was not recorded during MVCand peanut chewing. It goes without sayingthat the characteristics of the food item, such as stickiness, affect

血e tensile fわrce generated. As tensile fわrce can lead to血e loss or a restoration or pros血esis,仙is

data should be helpful for researchinthose areas.

The actualtensile fわrce was probably morethan4 N because large tensile force isusually felt

when chewing sticky food. This speculation is supported by our findingthatthe rate of decrease in the compressive force during the opening phase of Caramel chewing (0.958 j= 0. 147 N/msec) was

significantly largerthanduring slmply opening the mouth(0.443士0.084 N/msec). This indicates

that force was applied tothe toothduring Caramel chewing;that is,the tensile force developed soon aRer maximum compressive force occurred. Giventhatthe tensile force started atthe onset

of the maximumcompressive force (① in Fig. 7a),the fわrce was larger, possibly greaterthan150

N (roughly 4+146 N), thanthe value recorded (4.05土0.98 N)inthis study.

Weusedthe F-H plane asthe coordinate basis, which should help elucidatethe biomechanics

of the stomatognathic system in relation to crami0-facialmorphologyand help clarifythe

functional meamngs offorce exerted onthe toothinrelation to stomatognathic mnction. We still need to comparethe force vectors for different teethand clarifythe interindividualdifferences

usingthe skeletalreference.

0urfindingthatthe compressive force direction atthe maxlmummagmitude was approximate tothe direction of the palatalroot but not coincidentwithit is probably related tothe biomechanics of the stomatognathic system･ h particular,the characteristics of the facialskeleton,the lines of action of the muscles,and the physiology of the muscles, includingthat withinthe muscles (Eriksson etal･, 1984, Blanksma etal･, 1992, Hamamand McMillan, 1994, Ogawa etal, 2006), probably affectthe direction･ Furtherinvestigation is needed to clarifythe differences in direction.

The magnitude of tranSmitted force ontothe abutment toothwas higher in measurement

without the RPD thanwiththe RPDwithanytypes of rest design. The direction of force vector

withoutthe RPD was more posteriorlythanwith the RPD･AmOng three different rest designs, the

vectorwiththe distalrest was towardthe most posterior direction, followedwiththe medialand

distalrest,andwiththe medialrest, in order･ Regardingthe force direction inthe &ontalplane,

significant differences were not observedamongthe conditions.

When applying RPD for restoration inthe distalfree-ending edentulousridges like as the case

inthe subject, design of RPD, especially the rest setting ontothe abutment toothis considered as one of the criticalpoints of discussion in order to protect the abutment toothand supportlng tlSSueS･ Numerous s山dies have been,血erefbre, made discusslng RPD design and也e fわrce onto the

abutment toothand residualridges,and movement of the abutment toothandthe denture base (Matsumoto, 1970, Thompson, 1977, McCartney, 1980, Firtell, 1985, Bazirgan, 1986, Ogata,

1992, Igarashi, 1999)･ Althoughthe idealtheories of RPD designing for protectingthe abutment

teethand residualtissues have been proposed (Boucher, 1982, McGivney, 1995), the direct measurement of the transmitted forces ontothe abutment toothinvivo has not been camied out yet･ The findingsinthis studyarethe first descriptionsas tothe forces ontothe abutment toothin vivo. Inthe results, it is indicatedthat weanng RPD decreasedthe force, which would be related to shearing the occlusalforce onto the residualridge viathe denture base as describedinthe textbooks･ The differences of the force vector ontothe abutment toothrelating tothe rest designs

arealso coincidentwiththe descriptionsinthe textbooks (Boucher, 1982, McGivney, 1995).

However, this study could revealthe actual measurement values of magnltudesand directionsof forces･ It would be distinctly valuable for establishing RPD designing based on biomechanicsand

biology.

0urforce-measuring device canbeused to measure in vivo both the compressiveand tensile 3-D force exerted on a toothduring血nction over time･ Application of this device to a greater

number of subjectswill providelmportant basic data for clarification of stomatognathicfunctions

17

and foranalysisus1ng computer Simulation, such as丘血te elementanalysis･

5. Conclusions

The 3-D force-measuring device we developedwitha piezoelectric transducer has high

responsibilityandthermalstabilityin the mouth･ Using the device, We recordedthe 3-D

compressiveand tensile forces exerted on a toothduringfunction,althoughonly for one subject･

We foundthat the direction of the fわrces changed during function, both dming chewingand

maximalvoluntary clenching. There were sigmificant differencesinthe behavior of the forcesI The characteristics of the item chewed affectedthe force vector. The force transmitted tothe abutment toothofRPD differedwithin rest resign.

The device enabled time series measurement of the dynamic load on a toothduringfunction in vivo. Its use should help clarifythe biomechanicalcharacteristics of the stomatognathic system and establishthe design of the RPD.

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Plesh, 0., Bishop, B., McCal1, W.D., 1996. Pattems of jaw muscle activityduring voluntary chewing. 23; Joumalof OralRehabilitation 262-269･

Ralph, J.P., Caputo, A.A., 1975.Analysis of stress pattems in the humanmandible･ Joumalof

Rees, J･S･, 2001 ･Aninvestigation into the importmce of the periodontalligamentandalveolar

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Shiba, N･,Kitaoka, H･B･, Cahalan, T･D･, Chao, Y･S･E･, 1995･ Shock-absorbing effect of shoe insert materials corrmonly used in management of lower extremitydisorders･ ClinicalOrthopaedicsand

Related Research 3 10, 130-136.

Tbkahashi, N･,Kitagami, T･, Komori, T･, 1980･ Behaviourof teethunder variousloading

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Thompson, W･D･, Kratchvil F･J･, Caputo, A･A･, 1977･ Evaluation of photoelastic stress pattems produced by various designs of bilateraldistal extension removable partialdentures. Joumalof

Prosthetic Dentistry 38; 261 1273.

Trulssonand Johansson, 1994･ Encoding ofamplitudeand rate of forces applied to the teethby humanperiodontal mechanoreceptive afferents･ Joumalof Neurophysiology 74, 1 734- I 744. Trulssonand Johansson, 1996･ Encoding of tooth loads by humanperiodontalafferentsand their

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Kato, H･, 1982 The function of toothsupportlng StruCtureS･ Part II･ The dynamics of molars in functionand at rest･ The JoumalofJapanProsthodontic Society(in Japanese) 26; 1 33-1 47. Miura, H･, Hasegawa, S･, Kato, H･, Furuki, Y., Masuda, T･, 1995･ A measunng method of the three dimensional toothdisplacement･ The Joumalof Japanese Societyof Stomatognathic Function (in

Japanese) 2; 1-10.

Figure

(b)

Fig. 1 Structure ofpiezoelectriC 3 -component force transducer:

(a) diameter is 7 mm,and height is 3.5 rrm; O)) three crystals in steel housing enable loads to be

simultmeouslyand independently measured in three directions (along x-, y-,and z-axes). Upper surface oftransducer is pressure receiver (diameter 5mm).

泳  芳 ぎ 志1芸穿つ?aOpbe l I●  一  ■ 一-1--■一･L-I j vertical f.roe

Fig･ 2 (a) Prookeading apparatus: (1) ball splinewithprobeand (2) visewith variableangle (115

to 1 300)･ O') Close-up during loadingfor verticalmeasurement; load point becomes point contact.

(C) Close-up during loading for horizontal measurement.

Fig. 3 (a) (b) (1)  (2)  (3) J/

#

･･ト

Fig. 3 Device fわr 3-D force measurement･

(a) Inner part (1) was similar to metal core,and fTorce transducer (2)and outer part (3) were similar to metaltoothcrown. 03) Photograph of measuring deviceinuse. Outer part, force transducer,and irmer part were joinedwith a steel screw･

Fig. 4 Placement oftransducer on tooth

(a) view丘om occlusalplane, 0,) view from le氏 sidewithmouthclosed,and (C) view of ｡cclusal

contact (made of silicon rubber)with mouth closed as viewed kom mandibular sidewith

transmitted light･ Measured tooth (white arrow) was equaltoall other premolarsand molarsin

terms of area of contactwithopposing tooth.

Fig･ 5 Status of the mandible befTore settingthe force measming deviceinthe RPD wearer

Fig. 6 Device f♭r 3-Dforce measurement of the abutment tooth

Fig･ 7 Experimentalpartialdenturewith removable medialand distalrests

Fig. 8 MaterialS for transducer output transformation

(a) lateralcephalogram, @) posteroanterior cephalogram,and (C) study cast. Rotationangles Band

β were estimated from cephalograms;that of † was estimated五･om study cast, on whichthe transducer had been a氏xed. The superior-inferior axis (S-I) was determined by a line

perpendicularto the Frankfort-horizontal QTH) plane. The mediolateralaxis (M-L)and

anteroposterior axis (A-P) were determined bythe FH plane. @lack dashed line: FH plane. White

叫00 5｡g LDOt｡5｡州紬ー rL 2  1  1       l

100

50 0 50 ｢▲-X 一店トY ー __.____礼 -.ムー.M⊥ 1:トA-P -OS-I G e ら 1

M AS   …   州

Fig･ 9 Transformation of output data dming maximumvoluntary clenching

(a) example of raw output data; 0,) example of transformed output data. Transducer output was

transformedthree-dlmensionally usingthe rotationangles (oL, β, and †). After transformation, the

dataindicatedthe supenor, posterior,and lateraldirections.

150 J-三100 ･■■ コ 白一 ･●■ 蔓｣ 0 50 0

十

150 1 (XI 50 0 (b)

./

/

/

/

0   50  1m  150 0   50  100 Load lN] 300 200 100 0 1 50  0   1 00   200   300

Fig･ 10 Relationship between transducer outputand actualload.

Correlation coefrlCients f♭r (a) X-axis,仲) y-axis,and (C) Z-axis were 0.99999, 0.99999,and

0.99996. Ten trials were camied out for each measurement condition.

(b) ー________A I;i.,､J 1:T=t'.L:-{ ( C) ､一′′J-I).'J

-Compression(+),tension(-)

A...-...-..anteri9r(+),POSterior(-) ｢ lat○ral(巾,m○dialO

Fig･ll Example of calculated 3-Dforces data for (a) MVC; 0,) chewing caramel; (C) chewing

peanut･ MVC showed compressive, medial,and posterior directedforceswithanapparent

mediolateralovershoot･ Caramel chewing showed mostly compressive forcewithtensile force at

the endand medialand posterior directed forceswithanapparent mediolateralovershoot atthe

end･ Peanut chewing showed compressive,anterior,and medialforces･ The plus slgnsindicate compressionandanteriorand lateraldirectedforces,and the minus slgnSindicate tension and

posterior        and medial        directed

forces.

(a)

_(C)

Fig･12 Vector locus during MVC

(a) coronalplaneview; (b) 3-D view kom medial-anterior position; (C) sagittal plane view. 3D

force was convertedinto two 2-dimensionalfbrces (coronaland sagittalplane). Top surface of

each graphindicates F-H plane･ White dashed lineindicates direction perpendicular to F-H plme.

Yellow arrow indicates palatalroot of tooth･ Orange locusand blue locusindicate closing and

opening phases of vector, respeanut chewingtively･ M: medialdirection. L: lateraldirection. P:

(a)

_(b)

_(C)

Fig･13 Vector locus for caramel chewing

(a) coronal plane view; 0,) 3-D view丘om medial-anterior position; (C) sagi他l plane view. Data

expressionand abbreviations arethe same asinFig. 12.

** 4R ﾆ｢ ﾘ " e2 ﾃﾔ **

｢｢

蘭k:.D霊二 や替増.肝_ひ 200誓｡耳 Cl I FVw&R # FVw&VW2 +MVC @CaC Opec

A   (** p<o･01: Dunn test)

Fig.14 Meanvector directions fTor compressive force at maximm magnitude onthe F-H plane.

The number of sample data points f♭r MVC, Caramel chewing,and Peanut chewing were 7, 35,

and 1 0, respeanut chewingtively. Abbreviations arethe same asinFig. 12.

5

4

(aaL6ap)uo!733]!q

MVC CaC PeC _{MVC CaC PeC}

('* p<0･01.'p<0.05. Dunntest)

Fig･ 15 Range of vector direcdons for compressive force during force-increasing

phase.

①②

③ 凵 ◆■ 十㌧,i. 凵｡▲暮 .I-*I>- ∼:I iu三. ･ゝ■乞 .′紙 ちLL.すけ二 kti､.- ･1./i ■榛等ミー 考有数,. ∼⊆-.もーはtl ､満ちて…- pt,i : L/{も ち", ＼ ′1 '1∼ 1.■､.< L::.?蕎建】J

Fig･ 16 (a) Example tensileand compressive forces measured during caramel chewin

(compressive-tensile direction); (b) close-up of circled area in (a). ①: average maximw

magnitude of compressive force, @: maximummagnitude oftensile force, @: 0. 1 61iO.034 mse

Fig･17 Vector directions at maximum magnitude during caramel chewing･ Abbreviationsarethe same as in Fig. 12.

Fig,18Forcevectorofthetransmittedloadsontotheabutmenttooth.

(a)ForcevectorsonthesagiWplane,projectedonthetateralcephaloglam(b)Forcevectors

Medi0-1ateral an91e Load(N)

Without denture

Mesial ･ distal rest

Mesial rest

ni史I只I rpqI i  1

- -1 "  ■  ■ ー1- -21.0

16.8

′

12.8

1q_q

o･9 0･9 1 ･6 0･3 ±  ±  ± ± _112.9±8.1

93.5±15.3

87.6±13.8

7Lq.?+1 a

■  - ■ -       - ■ -(A; p<0105. ''; p<0.01, Dunn test)

(∩ =4)

Table 1 the meanvalues of the directionandamplitude of the loads measired at four different

conditions inthe sagittal plane.

Medio-lateral ang一e Load(N)

Without denture

MesiaI. distal rest

Mesial rest

Distal rest

9.9 ±0.9  112.9±8.1 ll.2 ±1.4   93.5±15.3 10.2 ±0.8   87.6±13.8 9.0 ±1.0   76_3±3_9 ('; p<0.05, Dunn test ) (n=4)

Table 2the meanValues of the directionandamplitude of the loads measired at fourdifferent conditionsinthefrontalplane･

6.謝辞

本研究の遂行にあたり,ご協力を頂いた被験者各位ならびに東北大学大学院歯学研究

科口腔システム補綴学分野教室員に,心から感謝し御礼を申し上げます.

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