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Jouricsml of ErgononaRazavi et al., J Ergonomics 2017, 7:1DOI: 10.4172/2165-7556.1000186Journal of ErgonomicsISSN: 2165-7556ResearchArticleResearchArticleOpen AccessA Comparison between Static and Dynamic Stability in Postural Sway andFall RisksHamideh Razavi*Department of Industrial Engineering, Ferdowsi University of Mashhad, Azadi Square, IranAbstractThe purpose of this study is to investigate the static stability of postural sway and compare it with dynamicstability by practical experiments. It can help the selection of appropriate personnel for highly exposed tasks andreduce fall risks and injuries. For static stability, index of COG% is defined regarding anthropometric specificationsincluding height, BOS width and length and sway angles. Therefore, tabular guidelines can be developed so thatbalance status for each operator can be anticipated. In terms of dynamic stability, maximum Lyapanov exponentsare calculated for time series data collected from gait analyzer tests and a written code in Matlab. The results revealacceptable correlation between index of static and dynamic stability and hence can provide useful information forergonomic concerns.Keywords: Postural sway; Static stability; Dynamic stability; BalanceIntroductionStability is one of the important factors in preventing falls whiledoing daily activities [1,2]. It has been the subject of many studies bothin standing upright or sway postures [3,4]. It has also been studied fordifferent groups of people in terms of age, gender and occupations [58]. For building construction operators who work on high structures,the balance becomes more critical because it may lead to severe injuriesor even death [9,10].Epidemiologic evidence indicates that injuries related to loss ofstability and falls are prevalent in many countries [11]. In the UnitedStates, up to 20% of all compensable industrial accidents reportedlyresult from falls [12]. In the construction industry that workers muststand or walk on high narrow structures, fall is considered as the maincause of mortality and the second reason of nonfatal injuries [12].According to the ILO, in construction industry, at least 60,000 fatalaccidents occur annually that its major cause is fall from height due toloss of balance [13]. The main reason in 17% of occupational accidentsper year recorded by Swedish information system is related to falls [14].Both physiological and neurological factors affect stability [15,16].In this study, physiological factors and their relation to anthropometricfactors of human is investigated through a practical experiment onthe participants. In previous studies, two types of stability, static anddynamic, have been investigated separately and the correspondingindices have been used [17-20]. In this study, both are considered inrelation to each other in postural sway.Postural sway is one of the most routine positions of the bodyeither in industrial tasks like assembling different parts or in nonindustrial tasks like balance exercises [1]. It can be described throughthe main rule of static stability: keeping the COG within the base ofsupport boundaries. Most of the studies in static stability follow thisrule [5,21,22]. For example Holbein et al. used the index COG% toaccess the static postural stability [23].Computational modelling is used for testing postural stability [2426]. However, most of the balance machines use dynamic stabilityindices. One of the well-known dynamic stability indices is maximumLyapunov exponent introduced by Aleksandr Lyapunov in 1892[27]. This is an index for local stability and its magnitude shows thedivergence rate of two points in state space which were closed to eachother at the beginning [28].J Ergonomics, an open access journalISSN: 2165-7556In this paper, static stability is studied in relation to anthropometricrange for COG, BOS and other parameters. For dynamic stability,a Matlab code is written and run in order to calculate Lyapunovexponent. Finally, the results of the two indices are compared anddiscussed in detail.Static StabilityMethodsIn this research, COG% (Center of gravity %) is used as the indexof static stability. It shows the percentage of the base of support coveredby the body’s center of gravity projection on the horizontal plane [23].So higher COG% means the person can better control his/her stabilityand sway angle can rise. Figure 1 and Equation 1 illustrate how COG%is calculated in anterior sway.COG% x/(W BOS 2)(1)Where WBOS width of the BOS is, WBOS is length of the BOS andis the distance between COG Projection in vertically erect position(point 1) and swayed position (point 2) in Figure 1. Hence this index isdirectly correlated with the BOS dimensions.Using the above method, we can develop a range of parameters anddetermine the state of balance for each setting in order to reach twomain objectives: 1) The upper limit for COG% in work positions withhigh risk like working on pylons or Scaffolds is determined (where theselection of a person with appropriate anthropometric characteristicsis desired); 2) A comparison between the calculated COG% of a personwith specific anthropometric characteristics and its limits in specificwork condition is done (where the risk of the task is determined and*Corresponding author: Hamideh Razavi, Associate Professor, Department ofIndustrial Engineering, Ferdowsi University of Mashhad, Azadi Square, Iran, Tel:00985138805126; E-mail: h-razavi@um.ac.irReceived December 30, 2016; Accepted January 20, 2017; Published January27, 2017Citation: Razavi H (2017) A Comparison between Static and Dynamic Stabilityin Postural Sway and Fall Risks. J Ergonomics 7: 186. doi: 10.4182/21657556.1000186Copyright: 2017 Razavi H, et al. This is an open-access article distributed underthe terms of the Creative Commons Attribution License, which permits unrestricteduse, distribution, and reproduction in any medium, provided the original author andsource are credited.Volume 7 Issue 1 1000186

Citation: Razavi H (2017) A Comparison between Static and Dynamic Stability in Postural Sway and Fall Risks. J Ergonomics 7: 186. doi: 10.4182/21657556.1000186Page 2 of 7Figure 1: Parameters of the sway of the body.appropriate solutions on changing the work condition or changing theBOS or wearing shoes can be recommended).Parameters settingIn order to arrange the settings, parameters’ range must be defined.So, based on the average of various studies, the ranges in Table 1 areconsidered for height, sway angle and COG% [23,29].In addition, in order to obtain the BOS dimensions, we use biometricrelationships between body height and other body part dimensions[30]. The BOS relationships, used in this study, are presented in Table2. In these statements, H represents height of the person.Also, as the height of COG in normal human is 57% of his height,Equation 2 calculates the variable in Equation 1.X (HCOG) tan(Angles)(2)Where HCOG and Angles are the COG height and Sway angle,respectively.Static stability resultsA sample of the tabular results, based on parameters range andrelations, is presented in Table 3. It is populated for the height of 170cm and anterior sway.It’s shown in Table 3 that if a person with 170 cm height and 29cm BOS width sway 4 in anterior direction, his COG% will be 46.73%;while the same person will obtain 70.24% if he can sway 6 in samedirection. When the sway angle increases, balance control becomesharder and if someone can keep his balance in higher sway angles, hisCOG% will increase which shows his ability to keep the balance. It isalso shown that for a person with specific height in a fixed sway angle,the smaller the BOS width, the higher the COG% which again meanshis ability to maintain his balance.Another way of result comparison can be as Table 4. It is developedfor COG% 60%. It can be inferred from this table that a particularperson having a certain COG% in higher sway angles, needs larger BOSdimensions.Dynamic StabilityMethodsOne of the well-known indices in dynamic stability is maximumlyapunov exponent (λmax) which was presented by Aleksandr LyapunovJ Ergonomics, an open access journalISSN: 2165-7556ParameterRangeStepHeight165-185 cm1 cmAnterior sway angle2.5-6.0 0.5 Posterior sway angle3.5-7.0 0.5 Medio-lateral sway angle6.0-9.5 0.5 COG% index50-70%50%Table 1: Parameters range.BOS dimensionsRelationshipBOS Width0.152 HBOS Length(0.055 0.191) HTable 2: BOS calculations.in 1892 [27]. The concept of stability in Lyapunov theory is that ifall the paths which start around an equilibrium point remain in aneighbourhood of that point for all time intervals, that point is stable inLyapunov concept [31]. In mathematics, the Lyapunov exponent of adynamical system is a quantity that characterizes the rate of separationof infinitesimally close trajectories. Quantitatively, two trajectoriesin phase space with initial separation δZ 0 diverge at a rate given byEquation 3. δZ(t) eλt δZ0 (3)The rate of separation can be different for different orientationsof initial separation vector. Thus, there is a spectrum of Lyapunovexponents, equal in number to the dimensionality of the phase space.It is common to refer to the largest one as the maximal Lyapunovexponent (MLE) which is defined by Equation 4.λmax lim(t ) lim (δZ 0 0) (1/t ln δZ((t)) /δZ0 (4)The maximum Lyapunov exponent is a measure of local stability.Large exponents indicate rapid divergence of two points that areinitially close in state space. By calculating the maximum Lyapunovexponent from data that is averaged over the entire time series, theglobal stability of the system is estimated [28].A positive MLE is usually taken as an indication that the systemis chaotic. This index is selected for the experimental tests of this study.In order to calculate this index, a program is written in Matlab R2010bwith the Algorithm 1.Volume 7 Issue 1 1000186

Citation: Razavi H (2017) A Comparison between Static and Dynamic Stability in Postural Sway and Fall Risks. J Ergonomics 7: 186. doi: 10.4182/21657556.1000186Page 3 of 7Sway angle ( )BOS 6.4464.5372.6380.7488.8697.00Table 3: COG% for different settings.Medio-LateralPosteriorAnteriorSway angle ( )Height 624.5814.5BOS 35.74835.94636.54536.94540.0495.5BOS 45.77746.2778.0BOS .27856.91457.23258.18658.822Table 4: BOS dimensions for COG% 60%.J Ergonomics, an open access journalISSN: 2165-7556Volume 7 Issue 1 1000186

Citation: Razavi H (2017) A Comparison between Static and Dynamic Stability in Postural Sway and Fall Risks. J Ergonomics 7: 186. doi: 10.4182/21657556.1000186Page 4 of 7A xlsread(‘file name.xls’)B matrix of the time series data (selected cells of A)Neighbor i [] % n 2 matrix of distances between point i and all other pointsDistances [] % n n matrix of distances between each 2 pointsNearestNeighbors [] % 3n 3 matrix of 3 nearest neighbors of each pointFor i 1:nFor j 1:nCalculates the distances between each point i and all other pointsFinds the first nearest neighbor (non-zero distance) of point i in Neighbor i.EndFor j 1:nFinds the second nearest neighbor (non-zero distance) of point i in Neighbor iEndFor j 1:nFinds the third nearest neighbor (non-zero distance) of point i in Neighbor iEndDistances matrix is prepared from Neighbor i matrixesNearest Neighbors matrix is prepared from first 3 nearest neighbors of each point iEndFor t 1:3*(n-1)For each row of the Nearest Neighbors matrix as a reference point, calculatesthe distance between this point and each nearest neighbor as both points evolveover timeThe expansion is defined as the relative increase in distance between the twopoints for some Δt.EndThe mean expansion is determined by averaging the expansion over all referencepoints and all nearest neighbors. Lyapunov Exponent is calculated from the meanexpansionAlgorithm 1: Calculating maximum lyapunov exponent.ParticipantsTwelve healthy volunteers, 6 males and 6 females, participated inthe tests. The age, height and weight ranges of the subjects are presentedin Table 5.ApparatusThe gait analyzer treadmill from the German company SCHEINwith the analysis system of Zebris FDM-T is used in the tests. This devicemeasures the dynamic pressure and force and analyses the pressuredistribution in standing, walking and running. In addition, this devicelets us adjust the angle instead of measuring it by goniometer so we cando the test while increasing or decreasing the angle.The data obtained from the treadmill are complete time series ofthe pressure, force, area and location of COP for each feet. In addition,the time series data on each cell of the treadmill surface can be obtainedby programming the original data. Therefore, we can use the time seriesof force and the COP location of both feet in order to calculate themaximum Lyapunov exponent.ProtocolSubjects were asked to stand on the treadmill surface and keep thefeet fully in contact with the surface throughout the tests. They wereinstructed to stand with their feet in a comfortable position, which wasapproximately separated equal to hip width and their hands at bodysides without any loads. They could rotate only about the ankles. Thedifference between tests was in the directions and magnitude of thesway angles. In addition, as people usually have safety shoes whileworking in industrial sites, in these tests, the effect of shoes on stabilitySubjectsAge range(years)Height range (cm) Weight range (kg)6 female28 3160.50 10.5059.10 11.906 male28 3179.75 7.2580.50 13.4028 3168.50 18.5070.55 23.35Average for allTable 5: Participants’ specifications.J Ergonomics, an open access journalISSN: 2165-7556is investigated. The shoes affect the BOS dimensions. Hence all the testson each subject were done twice; once without shoes and once wearingsafety shoes. Each subject performed 16 tests as per Figure 2.In “0-8 Sway” test, the angle of the treadmill surface is increasedfrom 0-8 in 35 s while the subject is standing anteriorly on it and tryingto keep his balance. The “Without Sway” test is the test of standing stillon the horizontal surface for 5 s and the “Fixed Sway” tests are the testsof standing on the inclined surface in corresponding direction for 5 s.The frequency of treadmill motion was adjusted on 50 Hz.Experimental resultsThe software of the treadmill divides the surface to 128 lines and56 columns (each cell 8.5*8.5 mm2) and the force and pressure of eachcell is recorded in each time interval. The total BOS area can also becalculated in each time interval so that the BOS length and width canbe achieved.After each test, the max Lyapunov exponent was calculated for COPlocation and force time series. Results of tests on 6 male participantswithout shoes are as listed in Table 6.According to the comparison between the result tables of the twotypes of tests (without shoes and wearing shoes), λmax for COP and totalforce has decreased in 53 and 54% of the tests, respectively. Also if weconsider the fixed sway tests, the λmax for COP has decreased in 7 out of12 subjects of anterior tests, 6 out of 12 subjects of posterior tests and6 out of 12 subjects of medio-lateral tests. This analysis for the λmax forforce shows 8, 3 and 6 out of 12 subjects, respectively.Based on the above analysis, we can conclude that wearing safetyshoes, in about 50% of times will improve stability of the person.Comparison of Static and Dynamic StabilityIn order to compare the results of dynamic stability with staticstability in previous sections, Table 7 is presented for four participants.It must be noticed that wearing shoes slightly change the height andweight of the person.In Table 7, it is shown that by increasing the sway angle in everydirection, the COG% increases which show the person had betterpostural stability. Meanwhile, the results of dynamic stability in samesituation show that by increasing the sway angle in every direction, λmaxrelated to COP shows a chaos in the COP path which needs more effortof the person to maintain stability. This means he has better ability ofstability maintenance. In fact, the comparison of results reveals that inspite of the fact that there is no specific mathematical relation betweenCOG% and λmax, these two indices have direct relation to each other.ConclusionFor many occupational tasks like working on pylons or Scaffolds,postural stability is highly important. In this study, static and dynamicstability were studied in relation to COG and other anthropometriccharacteristics. In static stability, the effect of anthropometric factorson COG% between 50-70%, height range of 165-185 cm, posturalsways of 2.5-6.0 anterior, 3.5-7.0 posterior and 6.0-9.5 medio-lateralwere investigated. It showed that a person with certain height and BOSdimensions can sway higher angles and have better ability to maintainstability. For a certain height, in a fixed angle, smaller BOS dimensionscause higher COG% which shows better stability maintenance. Also,a person who maintains a certain COG% in higher sway angles, musthave larger BOS dimensions.Volume 7 Issue 1 1000186

Citation: Razavi H (2017) A Comparison between Static and Dynamic Stability in Postural Sway and Fall Risks. J Ergonomics 7: 186. doi: 10.4182/21657556.1000186Page 5 of 70-8 SwayWithout SwaySway angle 3.5 Anterior Fixed SwaySway angle 5.0 With ShoesSway angle 4.5 Posterior Fixed SwaySway angle 6.0 Sway angle 7.0 Medio-Lateral Fixed SwayTestsSway angle 8.5 0-8 SwayWithout SwaySway angle 3.5 Anterior Fixed SwaySway angle 5.

The maximum Lyapunov exponent is a measure of local stability. Large exponents indicate rapid divergence of two points that are initially close in state space. By calculating the maximum Lyapunov exponent from data that is averaged over the entire time series, the global stability of the system is estimated [28].

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