research article identification of mastication organ...

Research ArticleIdentification of Mastication Organ Muscle Forces inthe Biocybernetic Perspective

Edward Kijak1 Jerzy Margielewicz2 Damian Gdska2

Danuta Lietz-Kijak3 and WBodzimierz Wiwckiewicz4

1Department of Prosthetic Dentistry Faculty of Medicine and Dentistry Pomeranian Medical UniversityRybacka 1 70-204 Szczecin Poland2Silesian University of Technology Krasinskiego 8 40-019 Katowice Poland3Department of Dental Propedeutics and Phsysiodiagnostics Pomeranian Medical University Rybacka 1 70-204 Szczecin Poland4Department of Prosthetic Dentistry Faculty of Dentistry Wroclaw Medical University 26 Krakowska Street 50425 Wroclaw Poland

Correspondence should be addressed to Edward Kijak kokakrygmailcom

Received 12 August 2014 Accepted 2 October 2014

Academic Editor Anna Paradowska-Stolarz

Copyright copy 2015 Edward Kijak et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Purpose of the Paper This paper is an attempt to mathematically describe the mastication organ muscle functioning taking intoconsideration the impact of the central nervous systemMaterial To conduct model tests three types of craniums were preparedshort normal and longThe necessary numeric data required to prepare the final calculationmodels of different craniofacial typeswere used to identify muscle and occlusion forces generated by muscles in the area of incisors and molars The mandible in modeltests was treated as a nondeformable stiff formMethods The formal basis for the formulated research problem was reached usingthe laws and principles of mechanics and control theory The proposed method treats muscles as ldquoblack boxesrdquo whose propertiesautomatically adapt to the nature of the occlusion loadThe identified values of occlusion forces referred to measurements made inclinical conditions Results The conducted verification demonstrated a very good consistency of model and clinical testsrsquo resultsThe proposed method is an alternative approach to the so far applied methods of muscle force identification Identification ofmuscle forces without taking into account the impact of the nervous system does not fully reflect the conditions of masticationorgan muscle functioning

1 Introduction

While formulating the numeric model of the masticationorgan primarily passive forces and active forces affecting themandible are defined Passive forces assume reactions in tem-poromandibular joints and occlusion force while active onesreflect muscle activity One of the methods of muscle forceidentification is the solution of the issue of masticationorgan biostatic balance Additionally the biostatic balance isdefined as a situation when the mandible loaded with anyarrangement of forces is not moved as well and does notchange its orientation that is it remains in a stable positionfor any period of time Research defined in such a way can beanalysed by both static and dynamic methods Regardless ofthe class of the formulated problem proper causal relations

are introduced by means of analytical or vector mechanicmethods From a theoretical point of view two classes ofidentification methods of mastication organ muscle forcesare distinguished The first one is represented by methodswhere active muscle forces are replaced by single resultantA detailed description of these methods is presented in thefollowing works Weijs 1989 and Erhardson et al 1993[1 2] The second group includes methods whose formalbasis is the direct identification of muscle forces which arepresented for example by Osborn and Baragar 1985 Peckand Hannam 2000 and Sellers and Crompton 2004 [3ndash5] In addition we cannot forget about methods using theMES formalism which is applicable in situations of stress anddeformations of themandible assessmentThesemethods areoften applied during analyses of any kind of biomechanic

Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 436595 11 pageshttpdxdoiorg1011552015436595

2 BioMed Research International

issues of the stomatognathic system and they are describedin works by Vollmer et al 2000 Igic et al 2001 Iwasaki etal 2003 Koolstra and Van Eijden 2004 Peck et al 2004 andHannam et al 2008 [6ndash11]

Model tests of the mastication organ are very often con-ducted on flat models Reduction of the spatial structure toa flat one each time assumes a symmetrical mandible loadwith active and passive forces Despite a number of attemptsa clear method has not yet been formulated enabling pre-cise calculation of sizes of forces generated by particularmastication organ muscles In addition there is no technol-ogy enabling direct registration of muscle forces and loadsaffecting temporomandibular joints For this reason thenumerically calculated values of muscle forces are hard to beverified However computer simulations bring the expectedeffects when the conditions of calculation model support arecorrectly defined Usually they are adopted as fixed artic-ulated supports located within temporomandibular jointsThis way of model support is particularly convenient whenstatic balance equations are used In the case of application offormalism ofmethod of finite elements themodelling personhas an available broad selection of various ways of articularreaction reflection Reactions occurring in the joints can bemodeled at least in three ways (1) as a support articulatedelastic (2) bymeans of active forces distributed along surfaceof condyloid process heads as described by Korioth et al1992 [12] (3) or by contact connection occurring betweentransport disks the acetabulum and condyloid process heads

The assessment of causal relations taking place betweenthe occlusion force and muscle forces is a difficult issue fromthe point of view of biomechanics These difficulties arecaused by the fact that spatial structure of the placement ofmuscle fibres is able to generate various ranges of staticallyequivalent forces of combinations ensuring biostatic balanceof the mandible However the advantage of this diver-sity replacing the solutions is the possibility to counteractunwanted biomechanical reactions Restrictions and difficul-ties related to identification of forces generated by muscleswere the reason to undertake activities to formulate a bio-cybernetic mastication organ model In the biocyberneticperspective muscles are considered ldquoblack boxesrdquo whoseproperties adapt automatically to the nature of the load on thedental arch of the mandible The model approach proposedin this paper is an alternative to the so-far appliedmethods ofmuscles force identificationThe formal basis for the solutiondefined in such a way as a research problem is the methodsthat can be used in mechanics and control theory

2 Methods and Material The Formulation ofthe Numerical Model

During numeric model formulation used to identify themuscle forces of the mastication organ in the biocyberneticperspective the following assumptions were adopted Amathematical model was derived for the case of symmetricaldental arch load of the mandible with occlusion forces Thecondyloid process heads assume a stable location in the artic-ular space The mandible was treated as a nondeformablerigid form Adoption of the mandible as a rigid element is

justified from the point of view of model tests as its rigid-ity in comparison to muscle stiffness is much greater Inaddition during conducting numeric experiments there isa possibility of angular movement of the mandible in rela-tion to the axis running through the centres of condyloidprocess heads The assumption is also justified because inthe initial phase of abduction mandibular movement maybe described with great accuracy as ldquoclearrdquo rotation the so-called pivoting movement Additionally limitations resultingfrom maximum force that particular muscles are able togenerate during dental arches load have been taken intoaccountThe force on the dental arch of themandible changesfrom zero to the agreed value Additionally the direction ofits operation is perpendicular to the horizontal axis of thecoordinate system in respect of which numeric calculationswere performed Bearing in mind what the work of Ideand Nakazawa [13] stated and referring to the activity ofparticular muscles when generating occlusion forces in theset zones of dental arches of the mandible additional modelassumptions were made According to the aforementionedauthors temporal muscles are inactive when occlusion forcesare generated in the zone of incisors In order to demonstratethe relevance of the information stated by the abovemen-tioned researchers measurements of masticatorrsquos functionpotentials and temporal muscles during closing dental archesin the surroundings of incisors on dynamometer covers wereconducted These preliminary tests clearly proved change infunction potentials of temporal muscles Additionally theiractivity reaches the level of ca 10 of masticators activityIn order to make a precise mapping of the biomechanicalphenomena occurring at the time of incisors loading cross-sectional area of the temporal muscle was taken at the levelof 10 of the cross-sectional area masseter muscle Such anassumption is justified from the physiological point of viewsince growth in value of the recorded activity potential of themuscle is directly proportional to the force generated by themuscle The schematic diagram constituting a formal basisfor bringing necessary analytical dependencies which at thesame time reflects the occurring relations between the skele-tal system and the muscle system is presented in Figure 1

Bearing in mind the model assessment of the value offorces generated by adduction muscles of the masticationorgan in various zones of the dental arch the possibility ofocclusion force displacement was considered 119865119874 The param-eter defining the place of the occlusion force in the formulatedmodel is dimension 119886

119885119874 Points marked with symbols 119864

119894

(Figure 1) represent immobile muscles insertions to the cra-nial bonesThe location of muscles insertion to the mandibleis defined by polar coordinates which are defined with theposition vectors 119874119860 119874119861 119874119862 and 119874119863 and angles 120593

119872 120593119875 120593119871

and 120593119879 Lengths of particular muscles included in computer

simulations are marked with symbols 119871119894 The differential

equation of the mandible movement constituting a formalbasis for muscles forces identification takes the form of

119869 +119865119872

119877119872

119871119872(ℎ119872cos (120593

119872+ 120593) + 119886

119872sin (120593

119872+ 120593))

+119865119875

119877119875

119871119875

(ℎ119875 cos (120593119875 + 120593) + 119886119875 sin (120593119875 + 120593))

BioMed Research International 3

X

Y

O

A

B

CD

S

J

hT

hZL

hZPhZM

hL

hZT

hP hM

aZL

aT

LT

ET

FT

FLLL

ELEP

EMaL

aZP

aZM

aM

LP

LM

FP

FM

aP

aZT

aZO

120572T

120572L

120572P

120572M

120593L

120593T

120593

120593O

120593P

120593M

FO

Figure 1 The schematic diagram reflecting the relations between the muscle system and the skeletal system of the mastication organ

+119865119879

119877119879

119871119879

(ℎ119879 cos (120593119879 minus 120593) minus 119886119879 sin (120593119872 minus 120593))

minus119865119871119877119871

119871119871

(ℎ119871cos (120593

minus 120593) + 119886

119871sin (120593

119871minus 120593)) = 119865

119874119886119885119874

(1)

Equation (1) is nonlinear owing to the geometry of place-ment of the muscle fibers Mass moment of mandible inertiaJ may be estimated based on research results published in thework by Zhang et al [14] From the biocybernetic perspectivethe unknown muscle forces are calculated on the basis ofthe adopted control law The basis for identification in theproposed method is comparison of the set size (control) 119904119885with the regulated size 119904119882 Additionally comparison of thesevariables is possible as a result of applying negative feedbackGeneral block diagram of muscle forces of the masticationorgan identification in the biocybernetic perspective is pre-sented in Figure 2

The effect of the central nervous system (CNS) onmuscleswas reflected by applying regulators of continuous action

types PID and PI The block diagram presented in Figure 2has an additional loop of negative feedback applied The ini-tial computer simulation based only on a single loop wouldnot provide satisfactory results Lack of the assumed resultswas connected first of all with too great angle dislocation ofthe mandible resulting from occlusion forceThe applicationof an additional speed feedback loop substantially improvedthe quality of muscle forces identification At this point itshould be mentioned that the main task of the additionalfeedback is comparing the speed of shortening or extendingmuscle fibres When formulating the final calculation modelit should be determined which variables are adjustable sizesand which are control ones In this paper regulated sizes119904119882

include changes in muscle length while control sizes 119904119885

are forces generated by particular mastication organmusclesBearing in mind the adopted model assumptions the controlcriterion was defined on the basis of diagram presented inFigure 2 whose general form is presented by the equation

intinfin

0

120576 (119905) 119889119905 = 0 997904rArr intinfin

0

(119908119885

minus Δ119897) 119889119905 = 0 (2)


The mathematical model ofstomatognathic system

RegulatorPIDreference

The nervous system Musculoskeletal system

Biocybernetic model of stomatognathic system

RegulatorPI

Variable of wZ +

minus

+

minus

120576 120576FS FM

Δl

Δl

Δl

Δl

Figure 2 The generalised block diagram of muscle forces of the mastication organ identification

The control criterion (2) demonstrates that during load-ing the mandible with occlusion force the length of themuscle cannot be changed regardless of the value of theload exerted on the dental arch If excessive occlusion loadvalue results in mandible rotation then there is no basis tostate that the mandible remains in a biostatic balance Theanalysed research task was formulated with the use of prin-ciples binding in issues concerning dynamics In the for-mulated model the mandible has the possibility of angularmovement in relation to the axis running through the centresof condyloid process heads Additionally the movementmust be compensated by regulators otherwise the analysedsystem becomes unstable A detailed block diagramof adduc-tion muscle forces of the mastication organ identificationin the biocybernetic perspective is presented in Figure 3and superscripts correspond to muscles 119872 is masticator 119875

ismedial pterygoid 119879 is temporalis and 119871 is lateral pterygoidControl laws brought out on the basis of a detailed block

diagram (Figure 3) data are then the following equations

120576119871

(119904) = 119904119871

119885(119904) minus Δ119897

119871(119904)

119865119871

119878(119904) = 119870

119871

1120576119871

(119904) +1198791198711119868

120576119871 (119904)

119904+ 119904119879119871

119863120576119871

(119904)

120576119871

1(119904) = 119865

119871

119878(119904) minus V119871

Δ119897(119904)

119865119871 (119904) = 119870

119871

2sdot 120576119871

1(119904) +

1198791198712119868

1205761198711

(119904)

119904

120576119875

(119904) = 119904119875

119885(119904) minus Δ119897

119875(119904)

119865119875

119878(119904) = 119870

119875

1120576119875

(119904) +1198791198751119868

120576119875 (119904)

119904+ 119904119879119875

119863120576119875

(119904)

120576119875

1(119904) = 119865

119875

119878(119904) minus V119875

Δ119897(119904)

119865119875 (119904) = 119870

119875

2120576119875

1(119904) +

1198791198752119868

1205761198751

(119904)

119904

120576119879

(119904) = 119904119879

119885(119904) minus Δ119897

119879(119904)

119865119879

119878(119904) = 119870

119879

1120576119879

(119904) +1198791198791119868

120576119879 (119904)

119904+ 119904119879119879

119863120576119879

(119904)

120576119879

1(119904) = 119865

119879

119878(119904) minus V119879

Δ119897(119904)

119865119879 (119904) = 119870119879

2120576119879

1(119904) +

1198791198792119868

1205761198791

(119904)

119904

120576119872

(119904) = 119904119872

119885(119904) minus Δ119897

119872(119904)

119865119872

119878(119904) = 119870

119872

1120576119872

(119904) +1198791198721119868

120576119872 (119904)

119904+ 119904119879119872

119863120576119872

(119904)

120576119872

1(119904) = 119865

119872

119878(119904) minus V119872

Δ119897(119904)

119865119872 (119904) = 119870

119872

2120576119872

1(119904) +

1198791198722119868

1205761198721

(119904)

119904

(3)

The included block diagrams and analytical dependenciesfrom (1) to (3) are the formal basis for conducting necessarycomputer simulation taking into account the effects of thecentral nervous system on forces generated by human masti-catory system adduction muscles

Identification of muscle forces was conducted for threemandible models which correspond to the following facesshort normal and long The anterior lower face height tothe anterior total face height ratio was used for assignment ofthe subjects as either SF normal or LF The rationale behindthe use of this ratio is its strong predictive power of verticalcraniofacial morphology as has been established by the use ofdiscriminant analyses Following other studies of LF and SFmorphology 79 and 80 subjects with a ratio exceeding 590were considered to have a LF whereas subjects with a ratiosmaller than 540 were labeled as SF although selection ofldquogoldenrdquo cut-off points is inevitably arbitrary Eachmodel wasanalysed for mandible load cases with force 119865

119874 in the area of

incisors andmolars Additionally the area of dental arch loadhas been obtained by changing the parameter value 119886

119885119874 The

diagram showing distribution of active forces operating onthe mandible and points describing its geometric structureis presented in Figure 4

Moments of time are marked in Figure 4 with symbolsmeaning 1199051 the moment of loading the mandibular dentalarch with force 119865119874 However time 1199052 defines the momentwhen the mandibular dental arch is relieved Model assump-tions as well as the adopted idealized profile of occlusionforce accumulation are an integral part of research in termsof muscle forces identification Such an idealized nature ofocclusion force increase was adopted for model tests because



The nervous system

Musculoskeletal system

sMZ

sPZ

sTZ

sLZ

++ +

+

+

+

+

+

+

+

+

+minus

+

minus

+

minus

+

minus

++

+

+

+

+

+

+

+

+

minus

+

minus

+

minus

+

minus

120576M

120576P

120576T

120576L

FM

FP

FT

FL

ΔlM

ΔlP

ΔlT

ΔlL

KM1

FMS

FPS

FTS

FLS

PΔl

MΔl

TΔl

LΔl

120576M1

120576P1

120576T1

120576L1

KM2

KP2

KT2

KL2

sminus1TM1I

sminus1TM2I

sminus1TP2I

sminus1TT2I

sminus1TL2I

sminus1TP1I

sminus1TT1I

sminus1TL1I

sTMD

sTPD

sTTD

sTLD

KP1

KT1

KL1


GoMe

Ar

Co

FMFP

FO

FL

FT

Ri

A

120572P

120572L

120572T

120572M

aZO

C

O

D

F (N)

t (s)

FO

t1

t2

X (cm)

Y (cm)

Figure 4 The diagram showing geometric structure of the mandible along with marked places of mandible load with muscle forces andtemporary characteristics of occlusion force accumulation


Table 1 Numeric data adopted for the need to conduct numeric calculations

Muscle name 119877119894

120593119894

Area 119865MAX 120572119894

Ar-Go Go-Me Co-Me ltGo[cm] [∘] [cm2] [N] [∘] [cm] [cm] [cm] [∘]

Short face

Masticator 597 minus77 622 2177 minus8

564 764 1206 116Medial pterygoid 597 minus77 423 148 minus13Lateral pterygoid 030 15 431 1508 minus97

Temporalis 353 4 602 2107 27

Normal face



Temporalis 364 2 507 1774 27

Long face


461 743 1215 134Medial pterygoid 537 minus83 257 899 minus18Lateral pterygoid 052 minus16 377 1319 minus99

Temporalis 385 minus8 443 155 27

it shows similarity to occlusion forces recorded with the useof an electronic dynamometer However in order to performany model test it is essential to have knowledge of specificnumeric data In this paper the required data in particularconcerning the directions ofmuscle forces operationmusclescross sections and geometrical structure of the mandiblewere taken from the works by van Spronsen 2010 and vanSpronsen et al 1996 [15 16] Table 1 compares parametersdescribing the adduction muscles and geometric construc-tion of the studied craniofacial types The numeric data arenecessary to conduct a computer simulation concerningmus-cle forces identification in the biocybernetic perspective Inaddition an extremely significant biophysical size definingthemuscle is the coefficient of unit efficiency of cross section119896 The research reportsmdashWeijs and Hillen 1985 Peck et al2000 [10 17]mdashindicate that the value of this coefficient iswithin the scope from 30 to 40Ncm2 Additionally sucha discrepancy in values has a decisive impact on the finaleffect of identification This happens because the product ofcross section A and coefficient 119896 determines the maximumvalue of force generated by a given muscle For the purposeof model tests in this paper the maximum efficiency ofparticular adduction muscles has been estimated assuming119896 = 35Ncm2

Symbols presented in Table 1 are as follows 119877119894 are theplace of muscle forces that is defined by position vectors 119874119860119874119861 119874119862 and 119874119863 (Figure 1) Parameters 120593119894 define the orienta-tion of position vectors119877119894 in an arrowplane and aremeasuredas presented in Figure 1 120572119894 defines the orientation of muscleforces identification in the arrowplane (Figure 4)WhileArearepresents cross-sectional areas of muscles 119865MAX maximumforces particular muscles can generate Change in forcesgenerated by the mastication organ muscles is characterisedby a nondimensional muscles activity coefficient 119908

119860 In this

study these coefficients are defined as the relation of forcegenerated by a given muscle to the sum of forces generatedby all the muscles Analytical dependencies characterizingactivity coefficients of particular muscles which have been

included in computer simulations are expressed by theequations

119908Masseter119860

=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

119908Temporalis119860

=119865119879

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

119908Medial pterygoid119860

=119865119875

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

119908Lateral pterygoid119860

=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

(4)

where 119865119872 is masticator 119865119879 is temporalis 119865119875 is medial ptery-

goid and 119865119871 is lateral pterygoid

3 Model Test Results

Model test results which illustrate the change in musclesactivity during loading the mandibular dental arch withocclusion forces located in the zone of incisors and molarsare presented in the charts (Figures 5 6 and 7) At this point itshould be expressly stated that the maximum values of forcesshown in the charts are identical with the end of numericcalculations namely achieving themaximumefficiency by allthe muscles included in computer simulations

The next stage of model tests was estimation ofmaximumocclusion forces in the area of incisors and molars which arecaused by the activity of mastication organ muscles Definedin such a manner research problem was solved in the waythat calculation models characterizing averaged mandiblesof three types of anatomical craniofacial construction wereloaded with force 119865

119874until achieving the border of system

stability The maximum value of forces 119865119874 which did not

cause loss of calculation model stability was consideredthe maximum occlusion force generated by the mastication


MasseterMedial pterygoid

Lateral pterygoidTemporalis

40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)

Figure 5The activity of adduction muscles of the mastication organ of short craniofacial morphology during loading the mandibular dentalarch in the area (a) of incisors and (b) of molars

06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)

Figure 6 The activity of adduction muscles of the mastication organ of normal craniofacial morphology during loading the mandibulardental arch in the area (a) of incisors and (b) of molars

10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)

Figure 7 The activity of adduction muscles of the mastication organ of long craniofacial morphology during loading the mandibular dentalarch in the area (a) of incisors and (b) of molars


LongNormal

Short

250

200

150

100

50

0

minus50M PM LP T FOMAX

F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)

Figure 8 Force generated by the adduction muscles of the mastication organ during loading the mandibular dental arch with the maximumforce in the area (a) of incisors and (b) of molars

organ muscles in the set dental arch area The results ofcomputer simulation are graphically shown in Figure 8

Symbols shown in Figure 8 represent the following mus-cles 119872 is masticator 119875 is medial pterygoid 119871 is lateral ptery-goid and 119879 is temporalis The conducted computer simula-tions assumed that the boundary value of angular mandiblemovement cannot exceed the value of 02∘ However regula-tion errors determining the change in muscles length werelower than 001mmAnatomical data concerning average val-ues of the cross-sectional areas of muscles their orientationand geometrical structure of the mandible (Table 1) were theformal basis for conducting necessary computer simulationThe numerically calculated occlusion forces loading themandibular dental arch in the area of incisors in the case ofshort face reached the value of 63661N normal 5624N andlong 45856N The calculated maximum values of occlusionforces generated in the zone of incisors amounted to 2184Nfor short face 2071 N for normal face and 1304N for longface

4 Discussion

The operation of the central nervous system is the basic ele-ment ensuring correct functioning ofmastication organmus-cles Optimum muscular action is not possible without bio-electric stimulation whose source is the nervous system Forthis reason when making attempts of numeric modelling ofliving organismrsquos movement as well as during muscle forcesidentification each time an account should be taken of causalrelations occurring between the muscular-skeletal systemand the nervous system Test results obtained this way pro-vide qualitatively new information on the functioning ofliving organismrsquos muscles An analysis of complex processestaking place within the stomatognathic system using classicalmethods is determined above all by difficulties related tomuscle forces identification One of the ways of mathematicalprojection of the impact of the central nervous system on themuscles is the use during model tests optimisation methodsOsborn and Baragar 1985 [3] and Trainor et al [18] From

the point of view of biomechanics one of the most importantparameters typical for muscles is information concerningthe maximum force generated by these muscles Final dataare required for that concerning the cross-sectional size ofthe studiedmuscle AThe confirmation of this statement is inmany publications on this issue Hsu et al 2001 Goto et al2002 Gionhaku and Lowe 1989 Kitai et al 2002 and vanSpronsen et al 1989 1992 [19ndash23] Based on data containedin works mentioned above it is possible to determine theaverage values of cross sections of the stomatognathic systemmuscles and then define their maximum efficiency

Model tests of biostatic balance of the humanmasticationorgan included in this work focused on two issues The firstonewas to determine characteristics describing the variabilityof activity coefficients 119908119860 of particular mastication organmuscles depending on the occlusion force119865

119874The second one

focused on determining the maximum occlusion force possi-ble to be generated by the stomatognathic system muscles inthe area of incisors and molars On the basis of the preparedcharacteristics describing the variability of activity coeffi-cients of muscles 119908119860 it can be stated that regardless of cran-iofacial anatomical construction as well as the place of occlu-sion forces the greatest activity in the initial phase of loadingis shown by the temporal muscles (Figures 5 to 7) Subse-quently there are medial pterygoid muscles and the lateralpterygoid muscles as the last ones Only in the case of normalcraniofacial anatomical construction domasticators generategreater forces as comparedwithmedial pterygoids In the caseof the analysed normal face model this is connected with theaverage directions of 120572

119894muscle forces actions (Table 1)

According to Ide and Nakazawa [13] occlusion load loca-ted in the area of incisors is caused mainly by simultane-ous activity of masticators medial pterygoids and lateralpterygoids Ide and Nakazawa state that during generatingloads in the area of incisors fibres of the temporal mus-cles do not operate Additionally the function potentialsmeasurements conducted by the authors of the paper thatwere recorded with surface electrodes placed above the frontfibres of the temporal muscles show almost ten times lower


activity as compared with surface masticators fibres Thegrowing occlusion load operating in the area of incisorsresults in the fact that in the first place the maximumefficiency is achieved by the temporal muscles (Figures 5(a)to 7(a)) From that moment growth is observed in masti-cators activity and medial pterygoids activity This situationlasts until medial pterygoids reach the limit value of theirefficiency After this time only the activity of masticators andlateral pterygoids increases Additionally such a condition ismaintained until masticators reach their maximum efficiencyand then rapid growth in activity of lateral pterygoids isobserved When occlusion forces are generated in the areaof molars (Figures 5(b) to 7(b)) in the initial phase ofloading the mandibular dental arch the greatest activity isobserved in the case of the temporal muscles Howevermaximum efficiency is achieved by the medial pterygoidsThemechanism of mastication organmuscles functioning atocclusion forces located in the area of molars is analogous tothe case of occlusion forces interacting in the area of incisorsThe obtained model testsrsquo results indicate that the maximumocclusion forces generated in the area of incisors are mainlythe result of masticators activity and medial pterygoids activ-ity The importance of temporal muscles becomes evidentwhen the forces loading the dental arch move towards themolars (Figure 8) In the case of craniofacial morphology ofshort anatomical construction occlusion forces generated bymasticators in the area of molars are the largest (Figure 5(b))

Achievingmaximum efficiency by one of themuscles dir-ectly causes changing the value of activity coefficients of theother muscles In other words if a givenmuscle reaches max-imum efficiency then its activity is limited at simultaneousgrowth in activity of other muscles At this point it is worthmentioning that the obtained results of the computer simula-tion indicate that regardless of the load area of the dental archand craniofacial type the lateral pterygoids demonstrate lowactivity The activity of these muscles is strictly related to therole they perform in the functioning of the stomatognathicsystemThe fact that lateral pterygoids aremainly responsiblefor pulling out themandible and they support the suprahyoidmuscles during abduction [24] is also worth mentioning Inaddition it should be remembered that ca 30ndash40 of thearea of lateral pterygoids muscle fibres insertion is located ontransport disks Therefore one of their tasks is disks move-ment in accordance with the condyloid process movementThus it is reasonable to claim that lateral pterygoids do notplay any key role in issues related to the biostatic balanceof the mastication organ The statement seems to be contra-dictory in relation to the size of lateral pterygoid cross sectionof the casement which would indicate its substantial effi-ciency However from the point of view of biomechanics andparticularly directions defining the courses of muscle fibresand location of insertions to the mandible its meaning androle are generally insignificant in issues concerning biostaticbalance of the mastication organ Clearly observations madeby Ide and Nakazawa [13] indicate that symmetrical loadof the mandibular dental arch in the area of molars is aresult of intensive activity of mostmastication organmusclesexcept the lateral pterygoids which demonstrate relativelylow activity

Regardless of the load area of the mandibular dental archit has been stated that the largest values of occlusion forcesare observed in people with short face while the lowest withlong craniofacial anatomical construction Bearing in mindthe fact that so far there has been no technology enablingdirect measurement of forces generated by muscles othermethods of verification of model testsrsquo results should beapplied One indirect way which enables result evaluation ofcomputer simulation is clinical tests inwhich occlusion forcesare recorded In these tests specialised dental dynamometersare implemented and it is possible to single out two basicconstructions of measuring devices The first group includesdynamometers where occlusion forces are determined on thebasis of plastic deformation size of the measuring sampleThis method of occlusion forces measurement was describedin detail in the work by Chladek et al 2001 [25] The secondgroup are dynamometers where the force is recorded byvarious types of sensors among others pressure Braun et al1995 Kamegai et al 2005 [26 27] or piezoresistive Flanaganet al 2012 [28] Adductionmuscles of the humanmasticationorgan in the area of molars are able to generate loads whichcan exceed the value of even 1 kN according to Braun et al1995 and Ferrario et al 2004 [26 29] However values of thisrange are found in fewpeople wherein the values of this ordercan generate a few individuals Average values of occlusionforces recorded in the area of molars are in the scope from300 up to 600N in the case of women and from 400 to 700Nin the case of men which was shown in works by Bakke et al1990 Braun et al 1995 [26 30] Alongwith relocation ofmea-surement point towards incisors decrease in the measuredocclusion forces is observed for the value of ca 100N in thecase of women and ca 200N in the case of men which isconfirmed by the following researches Paphangkorakit andOsborn 1997 1998 Regalo et al 2008 [31ndash33] It shouldalso be borne in mind that along with general ageing of thebody occlusion forces generated by adduction muscles of themastication organ are limited Bakke et al 1990 [30] It isbelieved that this phenomenon is caused mainly by loss ofmuscle fibres Faulkner et al 2007 [34]

In order to verify the model testsrsquo results obtained inthis paper the results of computer simulation referred toresults published in the work by Abu Alhaija et al 2010 [35]Average values of occlusion forces were recorded in the areaof molars in a group of 30 women and 30 men aged ca22 Among the focus group three subgroups with differentcraniofacial construction were selected Occlusion forceswere recorded bymeans of an electronic dental dynamometerGM10 obtaining average values in the area of molars forshort face 6796N normal face 59308N and long face45357N Numerically calculated by the authors of this studyocclusion forces amounted to accordingly in the case ofshort faces 63661N normal 5624N and long 45856NHighcompliance of the results obtained in the research modelrelative to the average forces recorded in the clinical trials wasfound Clearly relative errors of occlusion forces obtained inthe model tests and clinical tests were for short face 633normal face 517 and long face 110

In the event when the stomatognathic system musclesgenerated load in the area of incisors themaximumocclusion


forces amounted to 2184N for short face 2071 N for normalface and 1304N for long face It is impossible for the resultsof these model tests to relate to specific clinical tests thatwere conducted on various craniofacial types as in the caseof occlusion forces generated in the area of molars Howeverthe works by Paphangkorakit and Osborn 1997 1998 Regaloet al 2008 [31ndash33] show that occlusion forces recorded in thearea of incisors are within the scope from 120N to 225N inmen and from 64N to 185N in womenThe values are similarto the results obtained on the basis of the conduced computersimulation

This kind of numeric considerations seems to be alsoimportant from the point of view of function disorders indiagnostics of the mastication organ movement system espe-cially the temporomandibular joint dysfunctions [36ndash39] It isknown that patients suffering from bruxism [40] are able togenerate occlusion forces often exceeding the value of 1 kNFace type short normal or long may be a genetic featurebut may equally well result from orthognathic or occlusiondefects and such factors can significantly affect the lengthof the lower part of face determining its comprehensivedimension Vertical dimension of the face is important inissues of compressive forces exerted on articular structurewhich was demonstrated by van Spronsen et al [41] In otherwords elimination of occlusion defects especially in verticaldimension may contribute to change in face qualificationfrom short for example to normal which in turn affects thereductionmasticationmuscles forces which can have destru-ctive impact on particular elements of the stomatognathicsystem mainly joints The conducted research partially alsoseems to explain the importance of loss of occlusion heightQuality shortages of the dental hard tissues pathologicalabrasion untreated dental caries or iatrogenic actions canaffect normal face transformation to be short which leads toincrease in forces generated by muscles with all the negativeeffects

5 Conclusions

To sum up the method presented in this paper should beconsidered an alternative approach to identifying muscleforces and model evaluation of occlusion forces generated byadduction muscles of the mastication organ The proposedmethod treatsmuscles as ldquoblack boxesrdquo whose properties ind-ependently adapt to external conditions On the basis of theconducted computer simulation it is possible to formulate thefollowing general applications

(1) Considering the limitations of the maximum forcegenerated by particularmuscles provides qualitativelyand quantitatively new information about function-ing of the masticatory muscels

(2) Model assessment of occlusion forces generated bymuscles and identification of the mastication organadduction muscles forces may constitute an impor-tant tool in diagnostics of the mastication organdysfunctions especially related to vertical occlusiondefects

During identification of the mastication organ musclesforces it is not required to know the mathematical modelof the muscle as well as to define the degree of its activityThe conducted model tests assume the criterion of constantvalue regulation However it should be expressly pointed outthat it is possible to adopt control law reflecting the variablevalue regulation Assuming such control laws it is possibleto identify forces generated by the mastication organ musclesin operation mandible protrusion or abduction and in theaction of chewing

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] W A Weijs ldquoThe functional significance of morphologicalvariation of the human mandible and masticatory musclesrdquoActa Morphologica Neerlando-Scandinavica vol 27 no 1-2 pp149ndash162 1989

[2] S Erhardson A Sheikholeslam C M Forsberg and P Lock-owandt ldquoVertical forces developed by the jaw elevator musclesduring unilateral maximal clenching and their distribution onteeth and condylesrdquo Swedish Dental Journal vol 17 no 1-2 pp23ndash34 1993

[3] J W Osborn and F A Baragar ldquoPredicted pattern of humanmuscle activity during clenching derived from a computerassisted model symmetric vertical bite forcesrdquo Journal ofBiomechanics vol 18 no 8 pp 599ndash612 1985

[4] C C Peck and A G Hannam ldquoHuman jaw and musclemodellingrdquo Archives of Oral Biology vol 52 no 4 pp 300ndash3042007

[5] W I Sellers and R H Crompton ldquoUsing sensitivity analysis tovalidate the predictions of a biomechanicalmodel of bite forcesrdquoAnnals of Anatomy vol 186 no 1 pp 89ndash95 2004

[6] D Vollmer U Meyer U Joos A Vegh and J Piffko ldquoExperi-mental and finite element study of a human mandiblerdquo Journalof Cranio-Maxillofacial Surgery vol 28 no 2 pp 91ndash96 2000

[7] A Igic R Pavlovic and S Igic ldquoBiomechanical Analysisof forces and m o ments generated in the mandiblerdquo FactaUniversitatis Medicine and Biology vol 8 no 1 pp 39ndash45 2001

[8] L R Iwasaki B W Baird W D McCall Jr and J C NickelldquoMuscle and temporomandibular joint forces associated withchincup loading predicted by numerical modelingrdquo AmericanJournal of Orthodontics and Dentofacial Orthopedics vol 124no 5 pp 530ndash540 2003

[9] J H Koolstra and T M G J Van Eijden ldquoFunctional sig-nificance of the coupling between head and jaw movementsrdquoJournal of Biomechanics vol 37 no 9 pp 1387ndash1392 2004

[10] C C Peck G E J Langenbach and A G Hannam ldquoDynamicsimulation of muscle and articular properties during humanwide jaw openingrdquo Archives of Oral Biology vol 45 no 11 pp963ndash982 2000

[11] A G Hannam I Stavness J E Lloyd and S Fels ldquoA dynamicmodel of jaw and hyoid biomechanics during chewingrdquo Journalof Biomechanics vol 41 no 5 pp 1069ndash1076 2008

[12] T W P Korioth D P Romilly and A G Hannam ldquoThree-dimensional finite element stress analysis of the dentate human


mandiblerdquo American Journal of Physical Anthropology vol 88no 1 pp 69ndash96 1992

[13] Y Ide and K Nakazawa Anatomical Atlas of the Temporo-mandibular Joint Quintessence Chicago Ill USA 2001

[14] F Zhang C C Peck and A G Hannam ldquoMass properties ofthe humanmandiblerdquo Journal of Biomechanics vol 35 no 7 pp975ndash978 2002

[15] P H van Spronsen ldquoLong-face craniofacial morphology causeor effect of weak mast i catory musculaturerdquo Seminars inOrthodontics vol 16 no 2 pp 99ndash117 2010

[16] P H van Spronsen W A Weijs F C van Ginkel and B Prahl-Andersen ldquoJaw muscle orientation and moment arms of long-face and normal adultsrdquo Journal of Dental Research vol 75 no6 pp 1372ndash1380 1996

[17] W A Weijs and B Hillen ldquoPhysiological cross-section of thehuman jaw musclesrdquo Acta Anatomica vol 121 no 1 pp 31ndash351985

[18] P Trainor K McLachlan and W McCall ldquoModelling of forcesin the human masticatory system with optimization of theangulations of the joint loadsrdquo Journal of Biomechanics vol 28no 7 pp 829ndash843 1995

[19] C W Hsu Y Y Shiau C M Chen K C Chen and H M LiuldquoMeasurement of the size and orientation of human masseterand medial pterygoid musclesrdquo Proceedings of the NationalScience Council Republic of China B vol 25 no 1 pp 45ndash492001

[20] T K Goto K Tokumori Y Nakamura et al ldquoVolume changesin human masticatory muscles between jaw closing and open-ingrdquo Journal of Dental Research vol 81 no 6 pp 428ndash432 2002

[21] NGionhaku andAA Lowe ldquoRelationship between jawmusclevolume and craniofacial formrdquo Journal of Dental Research vol68 no 5 pp 805ndash809 1989

[22] N Kitai Y Fujii S Murakami S Furukawa S Kreiborg and KTakada ldquoHuman masticatory muscle volume and zygomatico-mandibular form in adults with mandibular prognathismrdquoJournal of Dental Research vol 81 no 11 pp 752ndash756 2002

[23] P H van SpronsenW AWeijs J Valk B Prahl-Andersen andF C van Ginkel ldquoComparison of jaw-muscle bite-force cross-sections obtained bymeans of magnetic resonance imaging andhigh-resolution CT scanningrdquo Journal of Dental Research vol68 no 12 pp 1765ndash1770 1989

[24] J P OkesonManagement of Temporomandibular Disorders andOcclusion Elsevier New York NY USA 2005

[25] W Chladek T Lipski and A Krasinski ldquoExperimental evalua-tion of occlusal forcesrdquo Acta of Bioengineering and Biomechan-ics vol 3 no 1 pp 25ndash37 2001

[26] S Braun H P Bantleon W P Hnat J W Freudenthaler MR Marcotte and B E Johnson ldquoA study of bite force part1 relationship to various physical characteristicsrdquo The AngleOrthodontist vol 65 no 5 pp 367ndash372 1995

[27] T Kamegai T Tatsuki H Nagano et al ldquoA determination ofbite force in northern Japanese childrenrdquo European Journal ofOrthodontics vol 27 no 1 pp 53ndash57 2005

[28] D Flanagan H Ilies B OrsquoBrien A McManus and B LarrowldquoJaw bite force measurement devicerdquo Journal of Oral Implantol-ogy vol 38 no 4 pp 361ndash364 2012

[29] V F Ferrario C Sforza G Zanotti and G M Tartaglia ldquoMax-imal bite forces in healthy young adults as predicted by surfaceelectromyographyrdquo Journal of Dentistry vol 32 no 6 pp 451ndash457 2004

[30] M Bakke B Holm B L Jensen L Michler and E MollerldquoUnilateral isometric bite force in 8-68-year-old women andmen related to occlusal factorsrdquo Scandinavian Journal of DentalResearch vol 98 no 2 pp 149ndash158 1990

[31] J Paphangkorakit and J W Osborn ldquoThe effect of pressure ona maximum incisal bite force in manrdquo Archives of Oral Biologyvol 42 no 1 pp 11ndash17 1997

[32] J Paphangkorakit and J W Osborn ldquoEffects on human maxi-mum bite force of biting on a softer or harder objectrdquo Archivesof Oral Biology vol 43 no 11 pp 833ndash839 1998

[33] S C H Regalo C M Santos M Vitti et al ldquoEvaluation ofmolar and incisor bite force in indigenous compared with whitepopulation in Brazilrdquo Archives of Oral Biology vol 53 no 3 pp282ndash286 2008

[34] J A Faulkner LM Larkin D R Claflin and S V Brooks ldquoAge-related changes in the structure and function of skeletal mus-clesrdquo Clinical and Experimental Pharmacology and Physiologyvol 34 no 11 pp 1091ndash1096 2007

[35] E S J Abu Alhaija I A Al ZorsquoUbi M E Al Rousan andM M Hammad ldquoMaximum occlusal bite forces in Jordanianindividuals with different dentofacial vertical skeletal patternsrdquoEuropean Journal of Orthodontics vol 32 no 1 pp 71ndash77 2010

[36] F Liu and A Steinkeler ldquoEpidemiology diagnosis and treat-ment of temporomandibular disordersrdquoDental Clinics of NorthAmerica vol 57 no 3 pp 465ndash479 2013

[37] L Guarda-Nardini F Piccotti G Mogno L Favero andD Manfredini ldquoAge-related differences in temporomandibu-lar disorder diagnosesrdquo CraniomdashJournal of CraniomandibularPractice vol 30 no 2 pp 103ndash109 2012

[38] M Wieckiewicz N Grychowska K Wojciechowski et alldquoPrevalence and correlation between TMD based on RDCTMDdiagnoses oral parafunctions and psychoemotional stressin Polish university studentsrdquo BioMed Research Internationalvol 2014 Article ID 472346 7 pages 2014

[39] M K Murphy R F MacBarb M E Wong and K A Athana-siou ldquoTemporomandibular disorders a review of etiologyclinical management and tissue engineering strategiesrdquo TheInternational Journal of Oral amp Maxilofacial Implants vol 28no 6 pp e393ndashe414 2013

[40] M Wieckiewicz A Paradowska-Stolarz and W WieckiewiczldquoPsychosocial aspects of bruxism the most paramount factorinfluencing teeth grindingrdquo BioMed Research International vol2014 Article ID 469187 7 pages 2014

[41] P H van SpronsenW AWeijs J Valk B Prahl-Andersen andF C van Ginkel ldquoA comparison of jaw muscle cross-sections oflong-face and normal adultsrdquo Journal of Dental Research vol 71no 6 pp 1279ndash1285 1992

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


issues of the stomatognathic system and they are describedin works by Vollmer et al 2000 Igic et al 2001 Iwasaki etal 2003 Koolstra and Van Eijden 2004 Peck et al 2004 andHannam et al 2008 [6ndash11]

Model tests of the mastication organ are very often con-ducted on flat models Reduction of the spatial structure toa flat one each time assumes a symmetrical mandible loadwith active and passive forces Despite a number of attemptsa clear method has not yet been formulated enabling pre-cise calculation of sizes of forces generated by particularmastication organ muscles In addition there is no technol-ogy enabling direct registration of muscle forces and loadsaffecting temporomandibular joints For this reason thenumerically calculated values of muscle forces are hard to beverified However computer simulations bring the expectedeffects when the conditions of calculation model support arecorrectly defined Usually they are adopted as fixed artic-ulated supports located within temporomandibular jointsThis way of model support is particularly convenient whenstatic balance equations are used In the case of application offormalism ofmethod of finite elements themodelling personhas an available broad selection of various ways of articularreaction reflection Reactions occurring in the joints can bemodeled at least in three ways (1) as a support articulatedelastic (2) bymeans of active forces distributed along surfaceof condyloid process heads as described by Korioth et al1992 [12] (3) or by contact connection occurring betweentransport disks the acetabulum and condyloid process heads

The assessment of causal relations taking place betweenthe occlusion force and muscle forces is a difficult issue fromthe point of view of biomechanics These difficulties arecaused by the fact that spatial structure of the placement ofmuscle fibres is able to generate various ranges of staticallyequivalent forces of combinations ensuring biostatic balanceof the mandible However the advantage of this diver-sity replacing the solutions is the possibility to counteractunwanted biomechanical reactions Restrictions and difficul-ties related to identification of forces generated by muscleswere the reason to undertake activities to formulate a bio-cybernetic mastication organ model In the biocyberneticperspective muscles are considered ldquoblack boxesrdquo whoseproperties adapt automatically to the nature of the load on thedental arch of the mandible The model approach proposedin this paper is an alternative to the so-far appliedmethods ofmuscles force identificationThe formal basis for the solutiondefined in such a way as a research problem is the methodsthat can be used in mechanics and control theory

2 Methods and Material The Formulation ofthe Numerical Model

During numeric model formulation used to identify themuscle forces of the mastication organ in the biocyberneticperspective the following assumptions were adopted Amathematical model was derived for the case of symmetricaldental arch load of the mandible with occlusion forces Thecondyloid process heads assume a stable location in the artic-ular space The mandible was treated as a nondeformablerigid form Adoption of the mandible as a rigid element is

justified from the point of view of model tests as its rigid-ity in comparison to muscle stiffness is much greater Inaddition during conducting numeric experiments there isa possibility of angular movement of the mandible in rela-tion to the axis running through the centres of condyloidprocess heads The assumption is also justified because inthe initial phase of abduction mandibular movement maybe described with great accuracy as ldquoclearrdquo rotation the so-called pivoting movement Additionally limitations resultingfrom maximum force that particular muscles are able togenerate during dental arches load have been taken intoaccountThe force on the dental arch of themandible changesfrom zero to the agreed value Additionally the direction ofits operation is perpendicular to the horizontal axis of thecoordinate system in respect of which numeric calculationswere performed Bearing in mind what the work of Ideand Nakazawa [13] stated and referring to the activity ofparticular muscles when generating occlusion forces in theset zones of dental arches of the mandible additional modelassumptions were made According to the aforementionedauthors temporal muscles are inactive when occlusion forcesare generated in the zone of incisors In order to demonstratethe relevance of the information stated by the abovemen-tioned researchers measurements of masticatorrsquos functionpotentials and temporal muscles during closing dental archesin the surroundings of incisors on dynamometer covers wereconducted These preliminary tests clearly proved change infunction potentials of temporal muscles Additionally theiractivity reaches the level of ca 10 of masticators activityIn order to make a precise mapping of the biomechanicalphenomena occurring at the time of incisors loading cross-sectional area of the temporal muscle was taken at the levelof 10 of the cross-sectional area masseter muscle Such anassumption is justified from the physiological point of viewsince growth in value of the recorded activity potential of themuscle is directly proportional to the force generated by themuscle The schematic diagram constituting a formal basisfor bringing necessary analytical dependencies which at thesame time reflects the occurring relations between the skele-tal system and the muscle system is presented in Figure 1

Bearing in mind the model assessment of the value offorces generated by adduction muscles of the masticationorgan in various zones of the dental arch the possibility ofocclusion force displacement was considered 119865119874 The param-eter defining the place of the occlusion force in the formulatedmodel is dimension 119886

119885119874 Points marked with symbols 119864

119894

(Figure 1) represent immobile muscles insertions to the cra-nial bonesThe location of muscles insertion to the mandibleis defined by polar coordinates which are defined with theposition vectors 119874119860 119874119861 119874119862 and 119874119863 and angles 120593

119872 120593119875 120593119871

and 120593119879 Lengths of particular muscles included in computer

simulations are marked with symbols 119871119894 The differential

equation of the mandible movement constituting a formalbasis for muscles forces identification takes the form of

119869 +119865119872

119877119872

119871119872(ℎ119872cos (120593

119872+ 120593) + 119886

119872sin (120593

119872+ 120593))

+119865119875

119877119875

119871119875

(ℎ119875 cos (120593119875 + 120593) + 119886119875 sin (120593119875 + 120593))


X

Y

O

A

B

CD

S

J

hT

hZL

hZPhZM

hL

hZT

hP hM

aZL

aT

LT

ET

FT

FLLL

ELEP

EMaL

aZP

aZM

aM

LP

LM

FP

FM

aP

aZT

aZO

120572T

120572L

120572P

120572M

120593L

120593T

120593

120593O

120593P

120593M

FO


+119865119879

119877119879

119871119879


minus119865119871119877119871

119871119871

(ℎ119871cos (120593

minus 120593) + 119886

119871sin (120593

119871minus 120593)) = 119865

119874119886119885119874

(1)






intinfin

0

120576 (119905) 119889119905 = 0 997904rArr intinfin

0

(119908119885

minus Δ119897) 119889119905 = 0 (2)






RegulatorPI

Variable of wZ +

minus

+

minus

120576 120576FS FM

Δl

Δl

Δl

Δl





120576119871

(119904) = 119904119871

119885(119904) minus Δ119897

119871(119904)

119865119871

119878(119904) = 119870

119871

1120576119871

(119904) +1198791198711119868

120576119871 (119904)

119904+ 119904119879119871

119863120576119871

(119904)

120576119871

1(119904) = 119865

119871

119878(119904) minus V119871

Δ119897(119904)

119865119871 (119904) = 119870

119871

2sdot 120576119871

1(119904) +

1198791198712119868

1205761198711

(119904)

119904

120576119875

(119904) = 119904119875

119885(119904) minus Δ119897

119875(119904)

119865119875

119878(119904) = 119870

119875

1120576119875

(119904) +1198791198751119868

120576119875 (119904)

119904+ 119904119879119875

119863120576119875

(119904)

120576119875

1(119904) = 119865

119875

119878(119904) minus V119875

Δ119897(119904)

119865119875 (119904) = 119870

119875

2120576119875

1(119904) +

1198791198752119868

1205761198751

(119904)

119904

120576119879

(119904) = 119904119879

119885(119904) minus Δ119897

119879(119904)

119865119879

119878(119904) = 119870

119879

1120576119879

(119904) +1198791198791119868

120576119879 (119904)

119904+ 119904119879119879

119863120576119879

(119904)

120576119879

1(119904) = 119865

119879

119878(119904) minus V119879

Δ119897(119904)

119865119879 (119904) = 119870119879

2120576119879

1(119904) +

1198791198792119868

1205761198791

(119904)

119904

120576119872

(119904) = 119904119872

119885(119904) minus Δ119897

119872(119904)

119865119872

119878(119904) = 119870

119872

1120576119872

(119904) +1198791198721119868

120576119872 (119904)

119904+ 119904119879119872

119863120576119872

(119904)

120576119872

1(119904) = 119865

119872

119878(119904) minus V119872

Δ119897(119904)

119865119872 (119904) = 119870

119872

2120576119872

1(119904) +

1198791198722119868

1205761198721

(119904)

119904

(3)





119885119874 The





The nervous system


sMZ

sPZ

sTZ

sLZ

++ +

+

+

+

+

+

+

+

+

+minus

+

minus

+

minus

+

minus

++

+

+

+

+

+

+

+

+

minus

+

minus

+

minus

+

minus

120576M

120576P

120576T

120576L

FM

FP

FT

FL

ΔlM

ΔlP

ΔlT

ΔlL

KM1

FMS

FPS

FTS

FLS

PΔl

MΔl

TΔl

LΔl

120576M1

120576P1

120576T1

120576L1

KM2

KP2

KT2

KL2

sminus1TM1I

sminus1TM2I

sminus1TP2I

sminus1TT2I

sminus1TL2I

sminus1TP1I

sminus1TT1I

sminus1TL1I

sTMD

sTPD

sTTD

sTLD

KP1

KT1

KL1


GoMe

Ar

Co

FMFP

FO

FL

FT

Ri

A

120572P

120572L

120572T

120572M

aZO

C

O

D

F (N)

t (s)

FO

t1

t2

X (cm)

Y (cm)





120593119894

Area 119865MAX 120572119894


Short face



Temporalis 353 4 602 2107 27

Normal face



Temporalis 364 2 507 1774 27

Long face






119860 In this




=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119879

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119875

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

(4)












40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)


06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)


10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)



LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















X

Y

O

A

B

CD

S

J

hT

hZL

hZPhZM

hL

hZT

hP hM

aZL

aT

LT

ET

FT

FLLL

ELEP

EMaL

aZP

aZM

aM

LP

LM

FP

FM

aP

aZT

aZO

120572T

120572L

120572P

120572M

120593L

120593T

120593

120593O

120593P

120593M

FO


+119865119879

119877119879

119871119879


minus119865119871119877119871

119871119871

(ℎ119871cos (120593

minus 120593) + 119886

119871sin (120593

119871minus 120593)) = 119865

119874119886119885119874

(1)






intinfin

0

120576 (119905) 119889119905 = 0 997904rArr intinfin

0

(119908119885

minus Δ119897) 119889119905 = 0 (2)






RegulatorPI

Variable of wZ +

minus

+

minus

120576 120576FS FM

Δl

Δl

Δl

Δl





120576119871

(119904) = 119904119871

119885(119904) minus Δ119897

119871(119904)

119865119871

119878(119904) = 119870

119871

1120576119871

(119904) +1198791198711119868

120576119871 (119904)

119904+ 119904119879119871

119863120576119871

(119904)

120576119871

1(119904) = 119865

119871

119878(119904) minus V119871

Δ119897(119904)

119865119871 (119904) = 119870

119871

2sdot 120576119871

1(119904) +

1198791198712119868

1205761198711

(119904)

119904

120576119875

(119904) = 119904119875

119885(119904) minus Δ119897

119875(119904)

119865119875

119878(119904) = 119870

119875

1120576119875

(119904) +1198791198751119868

120576119875 (119904)

119904+ 119904119879119875

119863120576119875

(119904)

120576119875

1(119904) = 119865

119875

119878(119904) minus V119875

Δ119897(119904)

119865119875 (119904) = 119870

119875

2120576119875

1(119904) +

1198791198752119868

1205761198751

(119904)

119904

120576119879

(119904) = 119904119879

119885(119904) minus Δ119897

119879(119904)

119865119879

119878(119904) = 119870

119879

1120576119879

(119904) +1198791198791119868

120576119879 (119904)

119904+ 119904119879119879

119863120576119879

(119904)

120576119879

1(119904) = 119865

119879

119878(119904) minus V119879

Δ119897(119904)

119865119879 (119904) = 119870119879

2120576119879

1(119904) +

1198791198792119868

1205761198791

(119904)

119904

120576119872

(119904) = 119904119872

119885(119904) minus Δ119897

119872(119904)

119865119872

119878(119904) = 119870

119872

1120576119872

(119904) +1198791198721119868

120576119872 (119904)

119904+ 119904119879119872

119863120576119872

(119904)

120576119872

1(119904) = 119865

119872

119878(119904) minus V119872

Δ119897(119904)

119865119872 (119904) = 119870

119872

2120576119872

1(119904) +

1198791198722119868

1205761198721

(119904)

119904

(3)





119885119874 The





The nervous system


sMZ

sPZ

sTZ

sLZ

++ +

+

+

+

+

+

+

+

+

+minus

+

minus

+

minus

+

minus

++

+

+

+

+

+

+

+

+

minus

+

minus

+

minus

+

minus

120576M

120576P

120576T

120576L

FM

FP

FT

FL

ΔlM

ΔlP

ΔlT

ΔlL

KM1

FMS

FPS

FTS

FLS

PΔl

MΔl

TΔl

LΔl

120576M1

120576P1

120576T1

120576L1

KM2

KP2

KT2

KL2

sminus1TM1I

sminus1TM2I

sminus1TP2I

sminus1TT2I

sminus1TL2I

sminus1TP1I

sminus1TT1I

sminus1TL1I

sTMD

sTPD

sTTD

sTLD

KP1

KT1

KL1


GoMe

Ar

Co

FMFP

FO

FL

FT

Ri

A

120572P

120572L

120572T

120572M

aZO

C

O

D

F (N)

t (s)

FO

t1

t2

X (cm)

Y (cm)





120593119894

Area 119865MAX 120572119894


Short face



Temporalis 353 4 602 2107 27

Normal face



Temporalis 364 2 507 1774 27

Long face






119860 In this




=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119879

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119875

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

(4)












40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)


06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)


10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)



LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















RegulatorPI

Variable of wZ +

minus

+

minus

120576 120576FS FM

Δl

Δl

Δl

Δl





120576119871

(119904) = 119904119871

119885(119904) minus Δ119897

119871(119904)

119865119871

119878(119904) = 119870

119871

1120576119871

(119904) +1198791198711119868

120576119871 (119904)

119904+ 119904119879119871

119863120576119871

(119904)

120576119871

1(119904) = 119865

119871

119878(119904) minus V119871

Δ119897(119904)

119865119871 (119904) = 119870

119871

2sdot 120576119871

1(119904) +

1198791198712119868

1205761198711

(119904)

119904

120576119875

(119904) = 119904119875

119885(119904) minus Δ119897

119875(119904)

119865119875

119878(119904) = 119870

119875

1120576119875

(119904) +1198791198751119868

120576119875 (119904)

119904+ 119904119879119875

119863120576119875

(119904)

120576119875

1(119904) = 119865

119875

119878(119904) minus V119875

Δ119897(119904)

119865119875 (119904) = 119870

119875

2120576119875

1(119904) +

1198791198752119868

1205761198751

(119904)

119904

120576119879

(119904) = 119904119879

119885(119904) minus Δ119897

119879(119904)

119865119879

119878(119904) = 119870

119879

1120576119879

(119904) +1198791198791119868

120576119879 (119904)

119904+ 119904119879119879

119863120576119879

(119904)

120576119879

1(119904) = 119865

119879

119878(119904) minus V119879

Δ119897(119904)

119865119879 (119904) = 119870119879

2120576119879

1(119904) +

1198791198792119868

1205761198791

(119904)

119904

120576119872

(119904) = 119904119872

119885(119904) minus Δ119897

119872(119904)

119865119872

119878(119904) = 119870

119872

1120576119872

(119904) +1198791198721119868

120576119872 (119904)

119904+ 119904119879119872

119863120576119872

(119904)

120576119872

1(119904) = 119865

119872

119878(119904) minus V119872

Δ119897(119904)

119865119872 (119904) = 119870

119872

2120576119872

1(119904) +

1198791198722119868

1205761198721

(119904)

119904

(3)





119885119874 The





The nervous system


sMZ

sPZ

sTZ

sLZ

++ +

+

+

+

+

+

+

+

+

+minus

+

minus

+

minus

+

minus

++

+

+

+

+

+

+

+

+

minus

+

minus

+

minus

+

minus

120576M

120576P

120576T

120576L

FM

FP

FT

FL

ΔlM

ΔlP

ΔlT

ΔlL

KM1

FMS

FPS

FTS

FLS

PΔl

MΔl

TΔl

LΔl

120576M1

120576P1

120576T1

120576L1

KM2

KP2

KT2

KL2

sminus1TM1I

sminus1TM2I

sminus1TP2I

sminus1TT2I

sminus1TL2I

sminus1TP1I

sminus1TT1I

sminus1TL1I

sTMD

sTPD

sTTD

sTLD

KP1

KT1

KL1


GoMe

Ar

Co

FMFP

FO

FL

FT

Ri

A

120572P

120572L

120572T

120572M

aZO

C

O

D

F (N)

t (s)

FO

t1

t2

X (cm)

Y (cm)





120593119894

Area 119865MAX 120572119894


Short face



Temporalis 353 4 602 2107 27

Normal face



Temporalis 364 2 507 1774 27

Long face






119860 In this




=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119879

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119875

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

(4)












40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)


06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)


10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)



LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















The nervous system


sMZ

sPZ

sTZ

sLZ

++ +

+

+

+

+

+

+

+

+

+minus

+

minus

+

minus

+

minus

++

+

+

+

+

+

+

+

+

minus

+

minus

+

minus

+

minus

120576M

120576P

120576T

120576L

FM

FP

FT

FL

ΔlM

ΔlP

ΔlT

ΔlL

KM1

FMS

FPS

FTS

FLS

PΔl

MΔl

TΔl

LΔl

120576M1

120576P1

120576T1

120576L1

KM2

KP2

KT2

KL2

sminus1TM1I

sminus1TM2I

sminus1TP2I

sminus1TT2I

sminus1TL2I

sminus1TP1I

sminus1TT1I

sminus1TL1I

sTMD

sTPD

sTTD

sTLD

KP1

KT1

KL1


GoMe

Ar

Co

FMFP

FO

FL

FT

Ri

A

120572P

120572L

120572T

120572M

aZO

C

O

D

F (N)

t (s)

FO

t1

t2

X (cm)

Y (cm)





120593119894

Area 119865MAX 120572119894


Short face



Temporalis 353 4 602 2107 27

Normal face



Temporalis 364 2 507 1774 27

Long face






119860 In this




=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119879

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119875

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

(4)












40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)


06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)


10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)



LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















120593119894

Area 119865MAX 120572119894


Short face



Temporalis 353 4 602 2107 27

Normal face



Temporalis 364 2 507 1774 27

Long face






119860 In this




=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119879

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119875

119865119879

+ 119865119872

+ 119865119875

+ 119865119871


=119865119872

119865119879

+ 119865119872

+ 119865119875

+ 119865119871

(4)












40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)


06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)


10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)



LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















40 70 100 130 160 190 220

06

05

04

03

02

01

0

FO (N)

wA

(a)

440 465 490 515 540 565 590 615 640

048

04

032

024

016

008

0

wA

FO (N)



(b)


06

05

04

03

02

01

030 60 90 120 150 180 210



FO (N)

wA

(a)

400 425 450 475 500 525 550 575

048

04

032

024

016

008

0



FO (N)

wA

(b)


10 30 50 70 90 110 130

06

05

04

03

02

01

0



FO (N)

wA

(a)

360 385 410 435 460

05

04

03

02

01

0



FO (N)

wA

(b)



LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















LongNormal

Short

250

200

150

100

50

0


F(N

)

(a)

700

600

500

400

300

200

100

0

minus100

LongNormal

Short

M PM LP T FOMAX

F(N

)

(b)




4 Discussion

















5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

























5 Conclusions







References

















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















research article identification of mastication organ...

Documents