DynamicMuscleFatigueEvaluationinVirtual WorkingEnvironment 9 ∗ 0 LiangMAa, DamienCHABLATa FouadBENNISa WeiZHANGb 0 aInstitutde Recherche enCommunications etenCybern´etique de Nantes, UMR CNRS6597, 2 E´cole Centrale de Nantes n 1,rue de laNo¨e - BP92 101 - 44321 NantesCEDEX 03, France a bDepartment of Industrial Engineering,Tsinghua University J 100084, Beijing,P.R.China 2 ] O Abstract R Musculoskeletal disorder (MSD) is one of the major health problems in mechanical work especially in manual handling jobs. . sMusclefatigueisbelievedtobethemainreasonforMSD.PostureanalysistechniqueshavebeenusedtoexposeMSDrisksofthe c work,butmostoftheconventionalmethodsareonlysuitableforstaticpostureanalysis.Meanwhilethesubjectiveinfluencesfrom [ theinspectorscanresultdifferencesintheriskassessment.Anotherdisadvantageisthattheevaluationhastobetakenplaceinthe 1workshop,soitisimpossibletoavoidsomedesigndefectsbeforedatacollectioninthefieldenvironmentanditistimeconsuming. vIn order to enhance the efficiency of ergonomic MSD risk evaluation and avoid subjective influences, we develop a new muscle 2 fatigue modelandanewfatigue indextoevaluatethehumanmusclefatigue duringmanualhandlingjobsin thispaper.Ournew 2 fatiguemodeliscloselyrelatedtothemuscleloadduringworkingproceduresothatitcanbeusedtoevaluatethedynamicworking 2 process. This musclefatigue model is mathematically validated andit isto befurtherexperimentalvalidated and integrated into 0 avirtualworking environmenttoevaluate themusclefatigue andpredict theMSDrisks quicklyand objectively. . 1 0Relevancetoindustry 9 0 MusclefatigueisoneofthemainreasonscausingMSDsinindustry,especiallyformechanicalwork.Correctevaluationofmuscle : vfatigue is necessary to determinework-rest regimens andreducetherisksof MSD. i X rKeywords: Musclefatigue; musclefatigue index; musclefatigue model;virtual reality; virtualenvironment a 1. Introduction musclesandthe worstfunctionaldisabilityinmusclesand othertissuesofhumanbody.Hence,itbecomes animpor- Musculoskeletal disorder is defined as injuries and dis- tantmissionforergonomiststofindanefficientmethodto orders to muscles, nerves, tendons, ligaments, joints, evaluate the muscle fatigue and further more to decrease cartilage and spinal discs and it does not include in- MSDriskscausedby musclefatigue. juries resulting from slips, trips, falls or similar accidents Therearevarioustoolsavailableforergonomiststoeval- (MaierandRoss-Mota, 2000). From the report of HSE uatetheMSDrisks,mostofthemarelistedandcompared (HSE,2005)and1993WAStateFundcompensableclaims inpaper(Li andBuckle,1999).Forgeneralpostureanaly- (State ofWashingtonDepartmentofLabor, 2005), over sis, Posturegram,Ovako Working Posture Analyzing Sys- 50% of workers in industry have suffered from muscu- tem(OWAS),posturetargetingandQuickExposureCheck loskeletaldisorders.According to the analysis in the book (QEC) were developed. Further more, some special tools Occupational Biomechanics (ChaffinandAndrersson, aredesignedforspecified partsof humanbody.For exam- 1999), overexertion of muscle force or frequent high mus- ple,RapidUpperLimbAssessment(RULA)isdesignedfor cle load is the main reason to cause muscle fatigue, and assessingtheseverityofposturalloadingandisparticularly further more, it results in acute muscle fatigue, pain in applicable for sedentary jobs. The similar systems include HAMA, PLIBELandsoon(Stantonetal.,2004). ∗ Correspondingauthor:Tel:+33240376958;Fax:+332403769 In these methods, several “risk factors” of mechanical 30 jobs are taken into consideration, like physical work load Email address: [email protected] (Liang MA). Preprintsubmitted toElsevier 5 January 2009 factors, psychosocial stressors and individual factors. The clefatigueatatimeinstantandcannotevaluatetheoverall level of exposure to physical work load can be evaluated musclefatigueoftheworkingprocesses.Meanwhileinthis withrespecttointensity(ormagnitude),repetitivenessand pHmusclefatiguemodel,althoughtheforcegenerationca- duration (LiandBuckle, 1999). Using these tools, MSD pacitycanbemathematicallyanalyzed,theinfluencesfrom risks can be effectively reduced, but there are still several the muscle forces are not considered enough. Rodr´ıguez limitations.Atfirst,evenjustforliftingjob,fiveprevailing proposesahalf-jointfatiguemodel(Rodr´ıguezet al.,2002, tools (NIOSH lifting index, ACGIH TLV,3DSSPP,WA L 2003a,b), more exactly a fatigue index, based on mechan- &I,Snook)weredeveloped.Theevaluationresultsofthem ical properties of muscle groups. The fatigue is quantified forasametaskweredifferent,andsometimesevencontra- by accumulation of the proportion of actual holding time dictory (J.Russelletal., 2007). Second, most of the tradi- overthepredictedmaximumholdingtime.Withthishalf- tionalmethodshavetobecarriedoutinfieldenvironment, jointmodel,itcanadjusthumanpostureduringaworking thereisnoimmediateresultfromtheobservationanditis processdynamically,butitcannotpredictindividualmus- timeconsumingfortherepetition.Furthermore,thereare cle fatigue due to its half-joint principle. The maximum differentevaluationresultsfromdifferentsubjectsevenus- endurance equation of this model was from static posture ingasamemethod(Lamkulletal.,2007).Atlast,onlypos- analysisanditismainlysuitableforevaluatingstaticpos- ture information and limited working conditions are con- tures.In(Liuetal.,2002),adynamicmusclemodelispro- sidered in these methods, and thus they are not able to posed based on motor units principles, but there are just estimate the MSD risks into detailed analysis andcannot parameters available under maximum voluntary contrac- furtherenhancethesafetyofthework.Themostsignificant tionsituationwhichis rareinmanualhandling work. problem is that muscle fatigue prediction and assessment In this paper, we are going to propose a dynamic mus- toolisstill inblankinconventionalmethods. cle fatigue model and a fatigue index with consideration In order to evaluate the human work objectively and of muscle load history and personal factors. This fatigue quickly, virtual human techniques have been developed model is going to be verified with comparison of the pre- to facilitate the ergonomic evaluation. For example, Jack vious static endurance time models and several dynamic (Badleretal., 1993), ErgoMan (Schaubetal., 1997), musclefatiguemodels.Atlast,wearegoingtoproposethe 3DSSPP (Chaffin, 1969), Santos (VSRResearchGroup, experimentalvalidationprocedureinavirtualenvironment 2004;Vignes,2004)andsoon,thesehumanmodelingtools framework. are used in field of automotive, military, aerospace and industrial engineering. These human modeling tools are 2. DynamicMuscleFatigue Model mainlyusedforvisualizationtoprovideinformationabout body posture, reachability and field of view and so on. In paper (Jayarametal., 2006), a method to link virtual We believe that the fatigue of muscle is closely related environment (Jack) and quantitative ergonomic analysis to the external load of the muscle with the time and the tools (RULA) in real time for occupational ergonomics is strength of the muscle. These factors can represent the presented, and it allows that ergonomic evaluation can be physicalriskfactorsmentionedbefore:theexternalloadthe carried out in real time in their prototype system. But muscle with the time can include the intensity (or magni- untiltoday,theseisstillnofatigueindexavailableinthese tude),repetitivenessandduration;andthemusclestrength virtual human tools for dynamic working process. It is canbedeterminedindividually.Thus,themuscleforcehis- necessary to develop the muscle fatigue model and then toryandmaximumvoluntarycontraction(MVC)aretaken integrate it into the virtual human softwares to evaluate to construct our muscle fatigue model. MVC is defined the muscle fatigue and analyze the mechanical work into as“theforcegeneratedwithfeedbackandencouragement, details. whenthesubjectbelievesitisamaximaleffort”(Vollestad, For objectively predicting muscle fatigue, several mus- 1997).Theeffectofmaximumvoluntarycontractiononen- clefatiguemodelsandfatigueindexhavebeenproposedin durance time is often used in ergonomic applications to publications.Inaseriesofpublications(Wexler etal.,1997; definetheworkercapabilities(Gargetal.,2002).Here,we Ding etal.,2000a,b,2002b,a,2003),Wexlerandhiscolleges aregoingtouseMVCtodescribethemaximumforcegen- haveproposedanew musclefatiguemodelbasedonCa2+ erationcapacityofanindividualmuscle. cross-bridgemechanismandverifiedthemodelwithstimu- Ourfatigueindexistryingtodescribethehumanfeelings lationexperiments,butitismainlybasedonphysiological (subjectiveevaluation)aboutthefatigueanditisexpected mechanism and it is too complex for ergonomic applica- to have a close correlation between subjective evaluation tion.Furthermore,thereareonlyparametersavailablefor and objective evaluation about muscle fatigue during me- quadriceps.ThismodelwasintegratedintoVSRsystemfor chanicalwork. several muscle fatigue simulations with lots of limitations For ergonomic evaluation, there are several self-report (Vignes, 2004). Taku Komura et al. (Komuraetal., 1999, methods to assess the physical load, body discomfort or 2000)haveemployedamusclefatiguemodelbasedonforce- work stress. These subjective assessments of body strain pHrelationship(Giatetal.,1993)incomputergraphicsto and discomfort have been the most frequently used form visualizethemusclefatigue,butitjustevaluatedthemus- duetotheeaseofuseandapparentfacevalidity.Butsubjec- 2 tiveratingsarepronetomanyinfluences.Thiskindofap- t F (u) load proachhastoolowvalidityandreliability.Butergonomists F(t)= du (4) Z MVC haveto concentratethemselves onthe feeling of the work- 0 ers.Severalauthorseveninsistthat“Ifthepersontellsyou MVC isaconstantvalueforanindividualperson,sowe that he is loaded and effortful, then he is loaded and ef- canchangetheequation3intoequation5.IfF /MVCis fortfulwhateverthebehavioralandperformancesmeasures load constantand equals to C, then F(t) =Ct, equation 3 can may show” (LiandBuckle, 1999). Thus, to combine the be further simplified. This constant case can occur during subjective evaluation and objective evaluation can reduce staticposture andstatic load. thecontradictoryproblemsbetweenthemandcanratethe muscle fatiguecorrectly. F (t) The generalfeeling ofhumanbody about fatigue is:the cem =e−kF(t) =e−kCt (5) MVC larger the force is, the faster people can feel fatigue; the longer the force maintains, the more fatigue; the smaller The feeling of ourfatigue is a function below andwhich capacity of the muscle is, the more easily we can feel fa- isclosedrelatedtoMVCandFload(t).MVCcanrepresent tigue. Based on this description, the equation 1 is used to the personal factors (Chaffin andAndrersson, 1999), and describethesubjectiveevaluation.Theparametersusedin Fload(t) is the force exerted on the muscle along the time theequationsarelistedanddescribedintable1.Thisequa- andit reflectsthe influences ofexternalloadsequation6. tioncanbe explainedasfollows: 1 1 (i) Fcem describesthe capacityofthemuscleaftersome U(t)= e2kF(t)− e2kF(0) (6) contraction,the restforcegenerationability. 2k 2k (ii) F (t)/F (t) is relative load which describes the Inthismodel,personalfactorsandexternalloadhistory load cem muscleforcerelativetothecapacityofthemuscleat are considered to evaluate the muscle fatigue. It can be atime instantt. easilyusedandintegratedintosimulationsoftwareforreal (iii) MVC/F (t) describes the smaller capacity of the time evaluation especially for dynamic working processes. cem muscle,the fasterthe muscle getfatigued. Thismodelstillneedstobe mathematicallyvalidatedand ergonomic experimental validated, and meanwhile muscle Table 1 recovery procedure should also be included to make the Parameters inDynamicFatigue Model fatigueindex completed. Item Unit Description MVC N Maximum voluntary contraction, maximum ca- pacity of muscle 3. StaticValidation Fcem(t) N Currentexertablemaximumforce,currentcapac- ityof muscle 3.1. Validation result Fload(t) N Externalloadofmuscle,theforcewhichthemus- cleneeds to generate Our dynamic muscle fatigue model is simply based on k min−1Constant value, 1 thehypothesisonthereductionofthemaximumexertable U min Fatigue Index forceofmuscle.Itshouldbeabletodescribethemostspe- cialcase-staticsituations.Instaticpostureanalysis,there %MVC Percentageofthevoluntarymaximumcontraction isnomodeltodescribethereductionofthemusclecapacity fMVC %MVC/100 relatedtomuscleforce,butthereareseveralmodelsabout maximumendurancetime(MET)whichisameasurement relatedtostaticmuscularwork.METrepresentsthe max- dU(t) MVC F (t) load = (1) imum time during which a static load can be maintained dt F (t) F (t) cem cem (Elahracheetal.,2006).TheMETismostoftencalculated Meanwhile, the current maximum exertable force F cem in relation to the percentage of the voluntary maximum is changingwiththe time due tothe externalmuscleload. contraction (%MVC) or to the relative force (f = MVC Itmakessensethat:Thelargertheexternalload,thefaster %MVC/100)requiredbythetask.Thesemodelswhichare F decreases;the smaller F is, the more slowly F cem cem cem citedfrom(Elahracheet al.,2006)arelistedintable 2. decreases.ThedifferentialequationforF isequation2. cem Inourdynamicmodel,supposethatF (t)isconstant, load anditrepresentsthestaticsituation.METistheduration dF (t) F (t) cdemt =−k MceVmC Fload(t) (2) in which Fcem falls down until the current Fload. Thus, METcanbe figuredoutinequation7 and8. The integrationresultofequation2 isequation3. t F (u) t F (u) load load −k du −k du MVC MVC Fcem(t)=MVCeR0 (3) Fcem(t)=MVCeR0 =Fload(t) (7) Assume thatF(t) is: 3 F (t) ln load Intraclass Correlation between Dynamic model and General models t=MET =− MVC =−ln(fMVC) (8) 8 kFload(t) kfMVC 7 Rohmert In order to analyze theMreVlaCtionship between MET of els [min]6 MHSauotinjogoedns d our dynamic model and the other models, two correlation al mo5 MSjaongeanaircda coefficientsarecalculated.OneisPearson’scorrelationrin ner Rose Ge4 Dynamic equation9andtheotheroneisintraclasscorrelationICC n e i in equation10. r indicates the linear relationshipbetween Tim3 tworandomvariablesandICC canrepresentthesimilarity nce betweentworandomvariables.Thecloserristo1,themore ura2 d n the two models are linear related. The closer ICC is to 1, E1 the more similar the models are. MS is the mean between 0 square between different MET values in different fMVC 0 1 2 3 4 5 6 7 8 Endurance Time in Dynamic model [min] values,MS isthemeansquarewithinMETvaluesin within different models at the same f level. p is the number MVC Fig.2. ICC ofgeneral models of models in the comparison. In our case, we compare the othermodelswithourdynamicmodelonebyone,kequals Endurance Time in Shoulder Models to2.Thecalculationresultsareshownintable2andfigure 10 Sato 1 to8. 9 Rohmert Mathiassen (An−A¯)(Bn−B¯) 8 GDyanrgamic r = Pn (9) n] 7 (An−A¯)2 (Bn−B¯)2 me [mi 6 rPn Pn e Ti 5 ICC = MSbetween−MSwithin (10) duranc 4 MSbetween+(p−1)MSwithin En 3 2 Endurance Time in General Models 1 10 Rohmert 0 9 Monod 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Huijgens F /MVC 8 Sato load Manenica n] 7 SRiojosgeaard Fig. 3.Endurance timeinshoulder endurance models e [mi 6 Dynamic m nce Ti 5 8 Intraclass Correlation between Dynamic model and Shoulder models ura 4 End 3 min]7 RSaothomert 2 odels [6 MGaarthgiassen 1 er m5 Dynamic d ul 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sho4 Fload/MVC e in Tim3 e Fig.1. Endurance timeingeneral models nc a2 ur d n E 1 3.2. Discussion 0 0 1 2 3 4 5 6 7 8 Endurance Time in Dynamic model [min] Fromthecomparisonresultsofthestaticvalidation,itis obviousthatMETmodelderivedfromourdynamicmodel Fig.4. ICC of shoulder endurance models has a great linear correlationwith the other experimental staticendurancemodels,andalmostallthePearson’scor- hip/backmodel.Forelbowmodels,theaverageICC isap- relationr areabove0.97. proximate 0.9, but for the back/hip models, ICC varies From ICC column, the similarity betweenour dynamic from-0.057to 0.9447.The explanationis:in shoulderand model andthe othermodels indescend sequenceis: elbow back/hip of human body, the anatomical structure is in a models, hand model, general model, shoulder models and much more complex way than in the elbows and hands. 4 Table 2 Static validation results (Elahrache et al., 2006) Model Equation r ICC General models Rohmert MET =−1.5+ fM2.V1C − fM20.V6C + fM30.V1C 0.9937 0.8820 Monodand Scherrer MET =0.4167(fMVC−0.14)−2.4 0.8529 0.6474 Huijgens MET =0.865 1−fMVC −2.4 0.9964 0.8800 fMVC−0.15 Sato et al. MET =0.3802(cid:2)(fMVC−0.0(cid:3)4)−1.44 0.9992 0.8512 Manenica MET =14.88exp(−4.48fMVC) 0.9927 0.9796 Sjogaard MET =0.2991f−2.14 0.9935 0.9917 MVC Roseet al. MET =7.96exp(−4.16fMVC) 0.9897 0.7080 Upper limbsmodels Shoulder Sato et al. MET =0.398f−1.29 0.9997 0.7188 MVC Rohmertet al. MET =0.2955f−1.658 0.9987 0.5626 MVC Mathiassen andAhsberg MET =40.6092exp(−9.7fMVC 0.9783 0.7737 Garg MET =0.5618f−1.7551 0.9981 0.9029 MVC Elbow Hagberg MET =0.298f−2.14 0.9935 0.9921 MVC Manenica MET =20.6972exp(−4.5fMVC) 0.9929 0.9271 Sato et al. MET =0.295f−2.52 0.9838 0.9712 MVC Rohmertet al. MET =0.2285f−1.391 0.9997 0.7189 MVC Roseet al.2000 MET =20.6exp(−6.04fMVC) 0.9986 0.9594 Roseet al.1992 MET =10.23exp(−4.69fMVC) 0.9943 0.7843 Hand Manenica MET =20.6972exp(−4.5fMVC) 0.9929 0.9840 Back/hip models Manenica (body pull) MET =27.6604exp(−4.2fMVC) 0.9901 0.6585 Manenica (body torque) MET =12.4286exp(−4.3fMVC) 0.9911 0.9447 Manenica (back muscles)MET =32.7859exp(−4.9fMVC) 0.9957 0.7306 Rohmert(posture 3) MET =0.3001f−2.803 0.9745 0.5353 MVC Rohmert(posture 4) MET =1.2301f−1.308 0.9989 0.7041 MVC Rohmert(posture 5) MET =3.2613f−1.256 0.9984 -0.057 MVC In this case, during these experimental models, the mea- 4. DynamicValidation surementofMVC isanoverallperformanceofthe muscle group, but not an individual muscle. Meanwhile from fig- 4.1. Validation result ure7,the differencesbetweenthe experimentalmodelsfor hip/backaremuchgreaterthanintheothermodelslikein Static validation results have shown that our dynamic elbowmodels(figure5).Itcanbeexplainedas:indifferent model can be used to predict the MET for general static working conditions (for example, different postures), the loadandevenforsomespecificbodyparts.Butstaticproce- engagement of the muscles in the task in the hip/back of duresarestillquitedifferentfromdynamicsituations,thus humanbodyvariesduetothecomplexityofthestructure. ourdynamicmodelneedtobeunderexaminationwiththe Thus, the error between our model and the other models other dynamic models. For this objective, we are going to isclosedrelatedtothecomplexityofthestructureandour verify our dynamic model through comparison with some modelcanfitmostoftheexperimentalmodelswithahigh existing muscle fatigue models, quantitatively or qualita- similarity. tively. Overall,thestaticvalidationcanprovethatourdynamic In paper (FreundandTakala, 2002), a muscle fatigue modelcanbe usedtopredictMET instaticsituations. 5 Endurance Time in Elbow Models Intraclass Correlation between Dynamic model and Hip/back models 10 8 Hagberg 9 Manenica Sato n]7 8 Rohmert mi me [min] 67 RRDooynsseea09m02ic Back models [56 e Ti 5 Hip/4 Enduranc 234 ndurance Time in 23 MMMRRooaaahhnnnmmeeennneeiiirrcccttaaa8888866666−−−−−34ptbouarlcqlkue E1 Rohmert86−5 1 Dynamic 0 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 F /MVC Endurance Time in Dynamic model [min] load Fig.5. Endurance timeinelbow endurance models Fig. 8.ICC of hip/back models Intraclass Correlation between Dynamic model and elbow models 8 model,therecoveryanddecayratesdependonSl−S0and Hagberg muscle forceS (equation11). The constantsα andβ were 7 Manenica n] Sato obtainedby fitting the solutionusingexperimentalresults mi els [6 RRoohsem0e0rt fromstaticendurancetimetest.Inthismodel,muscleforce mod5 Rose92 is taken into consideration as a factor causing muscle fa- ow Dynamic tigue, and further more, muscle force production capacity b e in El4 S0 was proposed just like in our dynamic model Fcem to m describe the capacity of the muscle after performing cer- Ti3 nce taintask.Butinthismodel,theforceproductioncapacity a ur2 and the muscle force are decoupled with eachother which d n E isdifferentinour model. 1 00 1 2 3 4 5 6 7 8 dS0 Endurance Time in Dynamic model [min] =α(Sl−S0)−βS (11) dt Fig. 6. ICC of elbow endurance models Wexler’s dynamic muscle fatigue model based on Ca2+ cross-bridgemechanismcanalsoverifyourdynamicmodel Endurance Time in Hip/Back Models quantitatively.Thismodelcanbeusedtopredictthemus- 10 Manenica pull cle force fatigue under different stimulation frequencies. 9 Manenica torque Manenica muscle From figure 9, it is clear that the faster the stimulation 8 RRoohhmmeerrtt34 frequency is, the larger the force can be generated by the n] 7 RDoynhammeirct5 muscle.Ifeachcurveisnormalizedintofigure10,itisobvi- mi e [ 6 ousthat:thelargerthepeakforceis,thefasterthemuscle m e Ti 5 getsfatigue.Butthismodelcanonlybeusedtopredictthe nc muscleforceunderastimulationpatternanditcannotpre- ura 4 nd dictorevaluatethemuscleforcegenerationcapacityunder E 3 astimulationpatternwhenthe muscleis gettingfatigue. 2 In the paper (Liu etal., 2002), another dynamic model 1 of muscle activation, fatigue and recovery was presented. This model is based on biophysical mechanisms: a muscle 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 consists of many motor units which can generate force or F /MVC load movement.Thenumberofthemotorunitsdependsonthe Fig. 7.Endurance timeinhipand back models sizeandfunctionofthemuscle.Thegeneratedforceispro- portional to the activated motor units in the muscle. The model was proposedand integratedinto a dynamic model braineffortB,fatiguepropertyF andrecoverypropertyR of forearm. In this model, the muscle was treated like a ofmusclecandecide the number ofactivatedmotorunits. kindofreservoir,andforceproductioncapacityS0reduces The relationship is expressed by equation 12. The param- with the time that the muscle is contracted. S0 varies be- etersinthis equationis explainedintable 3. tween0andtheupperlimitsofthemuscleforceSl.Inthis 6 dM A = BM −FM +RM uc A F dt 2000 dM Frequency 100 [ms] F = FM −RM (12) A F 1800 Frequency 50 [ms] dt 1600 FFrreeqquueennccyy 120 [ m[ms]s] Muc = M0−MA−MF 1400 When t = 0 under the initial conditions of M = 0, A e [N]1200 MF =0,Muc =M0,wecanhaveequation13. e forc1000 Muscl 800 MA(t) = γ + β e−(1+γ)Ft M 1+γ (1+γ)(β−1−γ) 600 0 (13) β−γ 400 − e−βFt β−1−γ 200 00 0.5 1 1.5 2 Table3 Time [ms] x 104 Parameters inActive Motor Model ItemUnitDescription Fig. 9. Maximum exertable force and time relationship in Wexler’s F s−1 fatiguefactor, fatigue rateof motor units Model R s−1 recovery factor, recoveryrate of motor units B s−1 braineffort, brainactive rateof motor units 1 M0 total number of motor units inthe muscle Frequency 100 [ms] 0.9 Frequency 50 [ms] MA number of activated motor units inthe muscle Frequency 10 [ms] 0.8 Frequency 2 [ms] MF number of fatigued motor units inthe muscle orce0.7 Muc number of motor units stillinthe rest uscle f0.6 β B/F d M0.5 γ R/F e aliz0.4 Norm0.3 Inourfatiguemodel,weassumethatthereisnorecovery during mechanical work, and the workers are trying their 0.2 besttofinishtheworkwhichmeansthebraineffortisquite 0.1 large. In this assumption, we set γ=0 and β → ∞, then 0 the equation 14 represents the motor units which are not 0 0.5 1 1.5 2 Time [ms] x 104 fatiguedinthemuscleandMA(t)/M0representsthemuscle forcecapacity.Wecansimplifytheequation13toequation Fig.10.Normalizedmaximumexertableforceandtimerelationship 14 which does have the same form of our dynamic model inWexler’s Model equation5. M (t) A =e−Ft−e−βFt =e−Ft (14) M 0 This fatigue model has been experimentally verified (Liuetal., 2002). In the experiment, each subject per- formed an MVC of the right hand by gripping a handgrip devicefor3min.Andthefittingcurvefromtheexperiment result has almost the same curve of our model in MVC condition(figure 12).In this model,F andR areassumed to be constantfor anindividual under MVC working con- ditions. There is no experiment result for F and R under the other load situations, thus this muscle fatigue model canonly verifyourmodelinMVC condition. 4.2. Discussion Through dynamic validation, our dynamic model is Fig. 11. Illustrationof the active motor model (Liu etal.,2002) quantitatively and qualitatively verified with the other existing muscle fatigue models. The fatigue model used in 7 comparison result between active motor model and dynamic model stantduringtheworkshouldbecalculated.Itrequiresdy- 1 namic information like acceleration,velocity, position and 0.9 externalload.Theseinformationcanbefurtherinputinto 0.8 dynamicformulastocalculatethemuscleforce.Inorderto get these information, motion capture method should be 0.7 involved.Asmentioned,thetraditionalmethodshavesev- 0.6 eral drawbacks for ergonomic analysis, a virtual environ- max0.5 f/f mentneedstobeconstructedtodecreasethetimecostand 0.4 physicalprototypecost. Active Motor Experiment result,F=0.0206,β=254,γ=0.398 0.3 Dynamic Model, f /MVC = 1 load 0.2 5.2. System Structure 0.1 0 0 10 20 30 40 50 Theoverallobjectiveoftheframeworkistoevaluatehu- time unit [s] manworkandpredictpotentialhumanMSDrisksdynam- ically, especially for human muscle fatigue. The function Fig. 12. Comparison between the experimental result of the active structure of the framework is shown in figure 13 and dis- motor model and dynamic model inthemaximum effort cussedbelow. the forearm used the same conception like in our fatigue In order to avoid field-dependent work evaluation, vir- model:the muscle forcecapacityis relatedto muscleforce tual reality techniques and virtual human techniques are with time. Wexler’s model based on Ca2+ cross-bridge used. Immersive work simulation system should be first shows the reduction of the muscle force during the time constructed to provide the virtual working environment. under different stimulation frequencies, the reduction of Meanwhile, virtual human should be modeled and driven the musclecapacityshowsthe sametrendlikeinourmus- by the motion capture data to map the real working pro- cle fatigue model. With comparison of the active motor cedureinto the virtualenvironment.Haptic interfacescan model,themuscleforcecanbeexpressedinthesameform beusedtoenablethe interactionsbetweentheworkerand under extremity situation.Butinthe activemotormodel, virtualenvironment. only parameters are available for MVC contraction case. For any ergonomic analysis, data collection is the first The active motor does not supply further validation for important step. All the necessary information needs to be other loadsituations. But we believe that the muscle load collected for further processing.From section 2, necessary caninfluentthe fatigue factorinthe activemotormodel. information for dynamic manual handling jobs evaluation Overall, our dynamic model is simple and easy to use consistsofmotion,forcesandpersonalfactors.Motioncap- and it can evaluate the muscle fatigue during a dynamic turetechniquescanbeappliedtoachievethemotioninfor- workingprocess. mation.Ingeneral,thereareseveralkindsoftrackingtech- niquesavailable,likemechanicalmotiontracking,acoustic tracking, magnetic tracking, optical motion tracking and 5. ExperimentalValidation inertial motion tracking. Each tracking technique has its advantages and drawbacks for capturing the human mo- 5.1. Objective andmethodology tion. Hybrid motion tracking techniques can be taken to compensatethedisadvantagesandachievethebestmotion Aftermathematicalvalidationofourdynamicmodel,we data. aregoingtoconstructavirtualrealityframeworktoverify Force information can be recorded by haptic interfaces. thefatigueindexinexperimentalenvironment.Theobjec- Hapticinterfaceisthechannelviawhichtheusercancom- tiveoftheexperimentalvalidationistofindthecorrelation municatewithvirtualobjectsthroughhapticinteractions, betweensubjectivefatigueevaluationresultsandobjective and the interaction data between the worker and the vir- fatigueevaluationresults.Inourhypothesis,ifbothresults tual environment are also significant for evaluating other are highly linear related, that means the objective meth- ergonomic aspects. Individual factors can be achieved odscanrepresentthesubjectivefeelingoffatigueandthen from anthropometrical database and some biomechanical it canbe further integratedinto virtualhumansimulation database. software to evaluate human muscle fatigue during manual All the information, such as motion information, force handling work. historyandinteractionevents,isfurtherprocessedintoOb- Inordertorealizeourobjective,twoevaluationsystems jective Work Evaluation System (OWES). The output of shouldbeestablished:subjectiveevaluationsystemandob- theframeworkisevaluationresultsofthemechanicalwork. jective evaluation system. Subjective evaluation methods There are many ergonomic aspects of a mechanical work. have been mentioned in many papers, and here we are fo- For each aspect, corresponding criteria should be estab- cusingonobjectiveevaluationsystem.Forobjectiveevalu- lished to assess the dynamic work process. Further more, ation,accordingtoourmodel,muscleforceateachtimein- these criteria canalso be appliedjust into commercialhu- 8 mansimulationsoftwareto generatemuch morenaturally 6. Conclusionand Prospects andrealisticallyhumansimulation. Inthispaper,wepresentanewmusclefatiguemodeland anewfatigueindexbasedit.Themathematicalvalidation has provedthat the new model is very simple and easy to predicttheMETinstaticpostures.Thedynamicvalidation result proves that the new model can be further extended intodynamicworkingprocesstopredictthemusclefatigue. Forexperimentalvalidation,avirtualrealityframeworkis underconstructiontoverifythelinearrelationbetweenour fatigueindex andsubjectiveevaluationresult. The prototype system cannot only evaluate the fatigue, butalsotheotheraspectsofworkbyextendingtheevalua- tioncriteriaanddatacollectionmodules.Iftheframework can be verified in the future, it could be integrated with theotherCADsystemtooptimizetheproductdesignand workprocessdesign. Fig.13. The frameworkof the dynamic workevaluation system In future works, we will apply our results to enhance thesimulationsoftwaresuchthattheywillabletoproduce Three hardware systems are employed to construct a realisticsimulations. prototype system to realize this framework: virtual sim- ulation system, motion capture system and haptic inter- faces. Virtual Simulation system consists of graphic simu- lationmoduleanddisplaymodule.Simulationmoduleexe- cutesonacomputergraphicstation,anddisplaymoduleis Acknowlegement composed of projectionsystemand head mounted display This research was supported by the EADS and by the (HMD).Simulationmoduleisinchargeofgraphicprocess- R´egiondes PaysdelaLoire(France)inthecontextofcol- ing and display control. The projection system and HMD laborationbetweentheE´coleCentralede Nantes(Nantes, system can visualize the immersive environment. Motion France)andTsinghuaUniversity(Beijing, P.R.China). Capture system is taken to capture the movement of the workertocollecttherealworkingdata.TheOpticalMotion CaptureSystemdevelopedbyTsinghuaUniversityVRLIB (Wang etal.,2006)is used,andit canworkat25Hz data update rate.Eachkeyjoint of humanbody is attachedby References an active marker, and the overallskeletal structure of hu- Badler, N. I., Phillips, G. B., Webber, B. L., 1993. Simu- man body can be represented by 13 markers. Meanwhile, latingHumans.OxfordUniversityPress. data gloves are used to capture the movement of fingers. Chaffin,D.B.,1969.Acomputerizedbiomechanicalmodel- Haptic system is also going to be integrated into this pro- development of and use in studying gross body actions. totype,andnowwearestillunder preparation. JournalofBiomechanics,429–441. Chaffin, D. B., Andrersson, G. B., 1999. Occupational Biomechanics,3rdEdition.Willey-Interscience. Ding, J., S.Wexler, A., Binder-Macleod, S. A., 2000a. A predictive model of fatigue in human skeletal muscles. JournalofApplied Physiology,1322–1332. Ding, J., S.Wexler, A., Binder-Macleod, S. A., March 2002a.Apredictivefatiguemodeli:Predictingtheeffect of stimulation frequency and pattern on fatigue. IEEE TransactionsOnNeuralSystemsandRehabilitationEn- gineering10. Ding, J., S.Wexler, A., Binder-Macleod, S. A., March 2002b. A predictive fatigue model ii: Predicting the ef- fect of resting times on fatigue. IEEE Transactions On NeuralSystems andRehabilitationEngineering10. Ding,J.,Wexler,A.S.,Binder-Macleod,S.A.,2000b.De- velopment of a mathematical model that predicts op- Fig.14.SchemeofHardwaresystemfortheexperimentalvalidation timal muscle activation patterns by using brief trains. JournalofApplied Physiology,917–925. 9 Ding,J.,Wexler,A.S.,Binder-Macleod,S.A.,2003.Math- sualizinghumanfatigueatjointlevelwiththehalf-joint ematical models for fatigue minimization during func- pairconcept.In:VisualizationandDataAnalysis.Santa tional electrical stimulation. Electromyography Kinesi- Clara,CAUSA. ology,575–588. Schaub,K.,Landau,K.,Menges,R.,Grossmann,K.,1997. Elahrache,K.,Imbeau,D.,Farbos,B.,2006.Percentileval- A computer-aided tool for ergonomic workplace design uesfordeterminingmaximumendurancetimesforstatic and preventive health care. Human Factors and Er- muscularwork.IndustrialErgonomics,99–108. gonomicsinManufacturing,269–304. Freund, J., Takala, E.-P., 2002. A dynamic model of the Stanton,N.,Hedge,A.,Brookhuis,K.,Salas,E.,Hendrick, forearmincludingfatigue.JournalofBiomechanics,597– H., 2004.Handbook of Human Factors and Ergonomics 605. Methods.CRCPRESS. Garg, A., Hegmann, K., Schwoerer, B., Kapellusch, J., State of Washington Department of Labor, 2005. 2002. The effect of maximum voluntary contraction on Fitting the job to the worker: An ergonomics endurance times for the shoulder girdle. Industrial Er- program guideline. Tech. rep., ERGWEB, gonomics,103–113. http://www.ergoweb.com/resources/reference/guidelines/fit Giat, Y., Mizrahi, J., Levy, M., July 1993. A musculoten- Vignes, R. M., May 2004.Modeling muscle fatigue in dig- donmodelofthefatigueprofilesofparalyzedquadriceps ital humans. Master’s thesis, Graduate College of The muscle under fes. IEEE Transaction on Biomechanical UniversityofIowa. Engineering40,664–674. Vollestad, N. K., 1997.Measurement of human muscle fa- HSE, 2005. Self-reported work-related illness in tigue.JournalofNeuroscienceMethods,219–227. 2004/05. Tech. rep., Health, Safety and Executive, VSR Research Group, October 2004. Technical report for http://www.hse.gov.uk/statistics/swi/tables/0405/ulnpirnodje1c.thtvmir.tual soldier research. Tech. rep., Center for Jayaram, U., Jayaram, S., Shaikh, I., Kim, Y., Palmer, Computer-AidedDesign,The UniversityofIOWA. C.,2006.Introducingquantitativeanalysismethodsinto Wang, Y., Zhang, W., Bennis, F., Chablat, D., May virtual environments for real-time and continuous er- 2006.Anintegratedsimulationsystemforhumanfactors gonomicevaluations.ComputersInIndustry,283–296. study. In: The Institute of Industrial Engineers Annual J.Russell, S., Lori Winne, u., E.Camp, J., W.Johnson, P., Conference.Orlando,Florida. 2007.Comparingtheresultsoffiveliftinganalysistools. Wexler,A.S.,Ding,J.,Binder-Macleod,S.A.,May1997.A Applied Ergonomics,91–97. mathematicalmodel thatpredicts skeletalmuscle force. Komura,T.,Shinagawa,Y.,L.Kunii,T.,1999.Calculation IEEETransactionsOnBiomedicalEngineering. and visualization of the dynamic ability of the human body.VisualizationandComputer Animation,57–78. Komura, T., Shinagawa, Y., L.Kunii, T., 2000. Creating and retargetting motion by the musculoskeletalhuman. The VisualComputer,254–270. Lamkull, D., Hanson, L., Ortengren, R., 2007. The influ- ence of virtual human model appearance on visual er- gonomicspostureevaluation.AppliedErgonomics,713– 722. Li, G., Buckle, P., 1999. Current techniques for assessing physicalexposuretowork-relatedmusculoskeletalrisks, with emphasis on posture-based methods. Ergonomics 42,674–695. Liu, J. Z., Brown, R. W., Yue, G. H., 2002. A dynamical model of muscle activation, fatigue, and recovery. Bio- physicalJournal,2344–2359. Maier, M., Ross-Mota, J., 2000. Work- related musculoskeletal disorders. http://www.cbs.state.or.us/external/imd/rasums/resalert/msd.html. Rodr´ıguez, I., Boulic, R., D.Meziat, 2002. A joint-level model of fatigue for the postural control of virtual hu- mans. In: 5th Conference of Human and Computer. Tokyo. Rodr´ıguez, I., Boulic, R., Meziat, D., Jan.21-22 2003a. A model to assess fatigue at joint-level using the half- jointconcept.In:VisualizationandDataAnalysis.Santa Clara,CAUSA. Rodr´ıguez,I.,Boulic,R.,Meziat,D.,Jan.21-222003b.Vi- 10