Using Positional Heel-marker Data to More Accurately Calculate Stride Length for Treadmill Walking: A Step Length Approach
UUsing Positional Heel-marker Data to More Accurately Calculate Stride Length forTreadmill Walking: A Step Length Approach
Kevin Supakkul
Department of Mechanical EngineeringStanford UniversityStanford, California, [email protected]
Abstract —Treadmill walking is a convenient tool for studyingthe human gait; however, a common gait parameter, stridelength, can be difficult to calculate directly because relevantreference points continually move backwards. Although there isno direct calculation of stride length itself, we can use positionalheel-marker data to directly determine a similar parameter,step length, and we can sum two step lengths to result in onestride length. This proposed method of calculation is simplebut seems to be unexplored in other literature, so this paperdisplays the details of the calculation. Our experimental resultsdiffered from the expected values by 2.2% and had a verylow standard deviation, suggesting that this method is viablefor practical use. The ability to calculate stride length fortreadmill walking using heel-marker data may allow for quickand accurate gait calculations that further contribute to theversatility of heel data as a tool for gait analysis.
Keywords -Gait analysis, Stride length, Step length, Treadmillwalking, Vicon, heel marker
I. I
NTRODUCTION
Treadmills are useful for gait analysis because they arecontinuous and controllable. Treadmill walking has manybenefits, including but not limited to longer trial durations,consistent walking speeds and inclines, and more convenientenvironments to place sensors and cameras; such a mediumfor gait analysis has shown to be useful for multiple fieldssuch as rehabilitation [1] and robotic orthoses [2].Since the treadmill is a tool for gait analysis, we must beable to obtain accurate and consistent gait parameters fromit. One useful tool for finding gait parameters, especiallyspatial parameters, is a positional heel marker manufacturedby Vicon which measures the X,Y, and Z coordinates of theheels. However, even with positional heel markers, spatialparameters - namely stride length - can be difficult tocalculate in an accurate manner due to the mechanics oftreadmill walking. Stride length is defined as the distancefrom heel-strike to heel-strike of one foot [3]. This is difficultto directly track on a treadmill: if we subtract the location ofthe heel at the previous heel strike from the location of thecurrent heel strike, the result is close to zero because the footreturns to its original position after each stride (see Figure3 for a graphical representation of heel marker data). Thus,at the moment of a heel strike, there is no data point we can reference as the positional location of the previous heel strikerelative to the current heel strike, making a direct calculationof stride length difficult to obtain. The closest indication wehave of the previous heel strike location is the foot’s path oftravel during the stride, which is recorded in the Vicon data(Figure 3). However, although it may seem intuitively sound,taking a total-distance-traveled measurement of the heel doesnot result in an accurate stride length, as discussed later inthe paper. Therefore this issue of moving reference points isthe main challenge in the calculation of stride length fromtreadmill walking.Other researchers have calculated stride length valuesfrom treadmill walking. In general, many prior methodsthat we found are usable but contain key concerns that canbe improved. One previously used method involves videoanalysis of the treadmill walk [4] [5] [6]. Murray et al.analyzed video recordings by tracing reference points onpaper to determine spatial gait parameters [4]. This methodis very sound and is perhaps the most accurate way to mea-sure spatial parameters for treadmill walking; however, onedrawback is that this method requires manual calculationsof each stride. This manual video-based method is slowerand less convenient than digital algorithm-based methods,especially if a researcher’s desired analysis requires stridelength calculations from tens or hundreds of strides.Padulo et al., in addition to mentioning video analysis,also provided an alternative method for stride length calcu-lation [6]. After calibrating treadmill speed, one can obtainstride length after finding stride frequency. However, thisrequires an additional manual step in calibrating treadmillspeed, and there may be differences in walking speed fromstride to stride [7] that cannot be determined from a pre-walkcalibration, thus affecting stride length results. Qi et al. alsoemployed a digital stride length calculation [8]; however,their main focus was on the accuracy of sensor hardwareand not the stride length algorithm, so they did not test theirstride length calculations with a control specific to stridelength. Their algorithm for stride length estimation is similarto one we discuss in Section IV, which we demonstrate isnot the most accurate.Some sources that mentioned stride length in regards to a r X i v : . [ q - b i o . Q M ] O c t readmill walking did not explicitly state their algorithm forcalculating this parameter [9] [10]. Riley et al. also usedVicon Plug-in Gait data to calculate stride length. Althoughtheir stride length values looked consistent with the otherparameters, they mentioned that their data was pre-processedand thus did not provide specific stride length algorithmsin the paper [10]. Alton et al. used ankle and toe positionmarkers [9], similar to Vicon heel markers, but they did notshare a detailed algorithm and their results had a slight in-consistency. They studied the relationship between groundedwalking and treadmill walking by first having subjects walkon the ground then on a treadmill set to the average speed oftheir grounded walking (to the nearest .2 m/s). Therefore thewalking speed calculated from the treadmill data should beclose or equal to the walking speed obtained from groundedwalking. We calculated walking speed from their all-subjectsdata table using their stride lengths and swing/stance times,and we found that the average treadmill walking speed was1.40 m/s while the average grounded walking speed was1.28 m/s (a difference of over .4 km/hr), meaning that theirtreadmill walking speed has a not-insignificant 9.1 percenterror. Based on our reverse engineering from their reporteddata and descriptions, we speculate it is possible that thestride length calculation they used is one that is discussedlater in this paper (Section IV): calculating stride length asthe total distance traveled by the heel/foot during one stride.As later discussed in Section IV, although this method seemsthe most definition-based and the most intuitive, it is faultyfor treadmill walking, resulting in stride lengths and walkingspeeds that are too large due to how double stance timeaffects positional data during treadmill walking.This paper addresses some of the aforementioned con-cerns; our proposed method is digital so it can be performedon large or even real-time sets of data, our results show a2.2% error which is small enough to suggest that this methodis practical, and this paper contains specific details aboutthe stride length calculation. Our method of calculationis to sum two consecutive step lengths, with such steplengths to be calculated from horizontal heel-marker data.Since both feet are planted during a heel-strike moment,there exist reference points to perform a direct step lengthcalculation, and the sum of two consecutive step lengthsis geometrically equal to one stride length. This proposedcalculation is uncomplicated and rather basic, but we didnot see it in other literature and thus decided to explore thetheory and experimental numbers behind this method as wellas highlight a possible misinterpretation of heel-marker data.This paper is organized as follows: Section II presents ourapproach to determining stride length for treadmill walking,Section III elaborates on our experimental methods and data,Section IV discusses limitations of the study and investigatesa possible misinterpretation of heel-marker data, and SectionV concludes the paper. II. S OLUTION : A S
TEP L ENGTH A PPROACH
Our proposed method of stride length calculation fortreadmill walking is to sum two step lengths. Since bothfeet are on the ground at the same time during a heel strike,the feet are stationary relative to one other, so we can have adirect calculation of step length by subtracting the locationof one heel from the other (see Figure 2 for visual repre-sentation). Summing two step lengths to result in a stridelength might be seen as an unconventional way to calculatethis parameter, since the accepted definition of stride lengthis heel-to-heel distance of the same foot. However, the sumof two adjacent step lengths is geometrically identical to astride length [3][11] (see Figure 1), so the calculated valuesshould be equivalent.For our calculations, we focused on the horizontal (y-axis)heel-marker data, which graphically appears as displayedin Figure 3. As aforementioned, we calculate step lengthat the point of heel strike, and for filtered horizontal heel-marker data the heel strike moments can be found at thelocal maxima [12] [13]. Thus we calculate step length asthe distance between the right and left heels at the momentof a local maximum (see Figure 3). We then add this steplength to the adjacent step length from the opposite foot tocalculate the stride length:
Stride Length = RSL + LSLRSL = RH ( tRHS ) − LH ( tRHS ) LSL = LH ( tLHS ) − RH ( tLHS ) (1)where RSL is right step length, LSL is left step length, tRHSis the time of right-foot heel strike, tLHS is the time of left-foot heel strike, RH(t) is the horizontal location of the rightheel at time t, and LH(t) is the horizontal location of theleft heel at time t. Therefore, RH(tRHS) is the horizontallocation of the right heel at the time of right-foot heel strike,and so forth. Figure 1. Image from [11] illustrating the geometry of a stride length.Two consecutive step lengths are equivalent to one stride length.igure 2. At the moment of heel strike the two feet are on the ground andare stationary relative to each other. We can subtract the horizontal heel-marker distances to get a close measurement of step length. In this image,the calculated value will be the left foot step length. We can add this to thenext right foot step length to get the stride length for this particular stride.
III. E
XPERIMENT
The data we used are of 9 able-bodied subjects walkingfor 60 seconds on a treadmill set at 1 m/s with no incline.The data was captured with Vicon sensors and camerasat the University of Texas Southwestern and was filteredbefore we received it at our lab at the University of Texas atDallas. We used MATLAB (The MathWorks, Inc., Natick,Massachusetts, United States) to calculate stride lengths andcycle times (cycle time is the duration of a stride: wecalculated this as the time between consecutive same-footheel strikes) for every stride in each data set, and the averagevalues of the parameters are presented in Figure 4.Additionally, we calculated walking speed for each stride.This was calculated as (stride length)/(cycle time) [3], and isincluded in Figure 4. We use this parameter to compare theaccuracy and consistency of different stride length methods.The reason we use this parameter for comparison is thatit is the variable that most resembles a control; we didnot have a chance to manually measure each stride lengthto get an accurate value, so we chose to compare ourresults to the most consistent variable available. It is worthnoting that walking speed does have potential error: thisparticular treadmill has a tolerance of about 1 percent, andothers have discussed that walking speed can vary from theset treadmill speed [7]. However, since the potential erroris minimal, walking speed is a good variable to use forchecking whether our stride length calculation algorithm isclose and realistically reliable.Our calculated walk speeds had a mean of 0.9779 m/sand a standard deviation of 0.0081 m/s. The low standarddeviation suggests that this method works consistently fordifferent subjects, and the error of 2.2% is acceptable inregards to gait analysis [8], suggesting that this method issufficiently accurate.
Figure 3. This plot displays a visual representation of horizontal heel-marker data for treadmill walking. The data for both feet are graphed to-gether in different colors. The local maxima represent heel-strikes [12][13],and at these heel-strike moments we calculate step length as the horizontaldistance between the two heels. See Figure 2 for photo representation.
IV. D
ISCUSSIONS
There is a possible threat to validation that is worthdiscussing. Due to the mechanics of walking and themethodology of our step length calculation, there exists apotential for errors; depending on the subject, at the momentof heel-strike the heel of the hind foot may be lifted at alarge enough angle to cause a small offset in the horizontalposition of the heel. There also exists a limitation in ourexperiment; since we only tested our method with datafrom able-bodied subjects walking on 0 incline at 1 m/s,we cannot be sure that the same method of calculationwill provide a similar accuracy for all situations of humanlocomotion.Additionally, we discovered a potential misinterpretationof heel marker data that could lead to faulty stride lengthcalculations. We did not find many papers that made thisexact mistake (as aforementioned, Qi et al. [8] used a similarcalculation to the one discussed below), but we think it isworth addressing since it seems intuitive and might be aneasy mistake to make.
A. Possible errors and limitations
First, the calculated stride lengths are all less than theexpected value of 1 m/s. The percent of error is not large, soit is possible that this observation is insignificant and causedby minor errors in data or treadmill performance. However,there may be a legitimate theoretical explanation for thecalculated values being less than the expected value. Thiserror most likely occurs during the step length calculation:at the moment of heel strike, the heel of the opposite footis usually slightly off the ground. The horizontal distancelost in this lift is not much compared to the overall steplength and might be generally negligible, but if a subjecttends to lift their opposite heel high during heel strike, then igure 4. Calculated stride length values using our method. Included is the average walk speed (stride length divided by cycle time) which we use totest the consistency and accuracy of different methods. The treadmill was set to run at 1 m/s and has a margin of error of about 1 percent. The mean ofour calculated walk speeds is 0.9779 m/s, which is a 2.2 percent error. there may be a not-insignificant shift in horizontal positionthat could lead to a decrease in measured step length.Further research should be done to determine whether thiserror is a legitimate problem that potentially interferes withthe practical applications of stride length. Additionally, theproposed method has only been tested for 0 incline walking,so other situations such as running or inclined walking mayyield different results.Furthermore, the number of subjects in this study is low,and we did not have a control group that used an establishedaccurate method of stride length calculation such as thevideo-analysis method discussed in [4]. The reason for thelack of ideal experimental data is that this data was notoriginally collected to test different methods of stride lengthcalculations; our lab builds and studies robotic legs, so gaitcalculation is an intermediate step as opposed to the mainobjective for data collection. However, while working ongait calculations we deduced this new approach that is moreaccurate and may be worth sharing, so we used the dataavailable to demonstrate the merits of this method.
B. Total distance heel travels does not equal stride length
The most intuitive approach is a faulty one: stride length isdefined as the distance a foot travels from one heel strike tothe next, so intuitively it seems that the total distance the heeltravels during a stride is the stride length. This is accuratefor grounded walking; however, this is not the case fortreadmill walking. As others have mentioned, methods thatwork accurately for grounded walking may not necessarilytranslate to treadmill walking [14].To elaborate, the heel marker data collected from treadmillwalking can potentially be misinterpreted. When the heel-marker position is increasing, this is a swing, since the foot ismoving forward. When the horizontal position is decreasing,this is a stance, since the treadmill is bringing the plantedfoot backwards. The forward swing is legitimate distancethat the foot covers. However, the backwards movement isnot indicative of anything for that specific foot. Regardlessof how the moving platform affects the data, the planted footis not walking any distance while in stance. One may argue that while one foot is in stance time on the treadmill, theother foot is in swing, so the displacement of the stationaryfoot during that time should average out to equal the distancecovered by the other foot’s swing. There are two problemswith this idea: one is that swing distance is not equivalent tostep length, so summing two swing distances is not equal toa stride length. Another problem is that a fraction of a foot’sstance time is actually double stance time, when neither footis making any forward progress. This is the main issue.The reason the backwards displacement of the heel doesnot indicate anything important is that during double stancetime, the positional heel data shows distance traveled but thefoot is not actually doing anything (see Figure 5). Thus ifwe use total distance traveled as our measurement, we areincluding the heel’s backwards displacement during doublestance time which does not contribute any distance to thestride length.One may argue that the distance lost during double stancetime must be made up eventually, otherwise the personwould keep drifting backwards off the treadmill. Although itis true that the foot makes up the lost distance, we only needto measure that distance during the forward swing; we do notneed to measure it twice by including the backwards drift of
Figure 5. Here, double stance time (DST) is highlighted. During DST, bothheels are moving backwards since the feet are planted while the treadmillkeeps moving. This backwards drift is recorded in the data, but it does notcontribute any forward progress since both feet are stationary relative tothe platform.igure 6. The faulty total-distance-traveled method of stride length calculation resulted in average errors of over 12% (compared to the expected walkingspeed of 1 m/s) and had standard deviations that were larger than that of our method. double stance time. Consider the following metaphor: if wemeasure distance driven by a car, we measure the distancethe car moves forward. Suppose the car drives 10 meters,then a person manually pushes the car back 5 meters, andthe car drives 5 more meters: we conclude that the car drove15 meters. The distance we measure is the forward motionof the car: the car was not driving any distance when theperson pushed the car back, so we cannot say the car drove20 meters of distance. The car does make up the 5 meters itlost; this made up distance contributes to the total distancedriven. However, we do not need to include this 5 meterstwice. Similarly, during double stance time the treadmillpushes the person backwards, and the person has to makeup this distance. However, we only need to measure thisdistance once, meaning that the heel data measured duringdouble stance time is extraneous when considering stridelength. Therefore a total-distance-traveled calculation of theheel marker data would theoretically yield a larger stridelength than in actuality.To illustrate its noticeable error, we calculated stridelength and walking speed using the total-distance method.To calculate total-distance traveled by the heel betweenheel strikes, we subtracted the local minimum heel positionfrom the previous local maximum, then subtracted the localminimum from the next local maximum, then summed thetwo values. We repeated this process for each stride andaveraged the values, and we also calculated walking speedfor comparison. For some subjects, the results obtained fromthe left and right data were slightly different, so in Figure6 we included separate calculations for the two sides. Aspredicted, the calculated walking speeds from the total-distance method are much larger than the expected value(treadmill speed) of 1 m/s; furthermore, the percent error andinconsistency (evidenced by the standard deviation of thewalking speeds) of the total-distance method are noticeablyworse than those of our approach. The average error ofover 12% is also much too large to be explainable bythe treadmill’s aforementioned tolerance. These all suggestthat the total-distance method is not a viable method forcomputing stride length for treadmill walking. V. C
ONCLUSION
In this paper we presented a new approach to calculatingstride length from positional heel-marker data for treadmillwalking. Stride length is geometrically equivalent to thesum of two consecutive step lengths, and step length canbe directly calculated from heel-marker data. Thus we com-puted stride length in this manner: finding direct calculationsof step lengths at the times of heel strike, then summingconsecutive step lengths together. Overall, our method ofcalculating stride length is more accurate than other digitalmethods we found in literature. Our digital method is alsoan improvement in practicality over previously establishedvideo-based methods because digital methods do not requiremanual calculations for each stride. Additionally, this paperprovides an in-depth discussion and analysis of the stridelength calculation process, since such an explanation forstride length can be difficult to find in other literature.Additionally, the ability to accurately calculate stridelength from horizontal heel data further increases the ver-satility of this particular type of kinematic data. Horizontalheel data can already lead to the detection of heel strike andtoe-off events [13], which are very important for findinguseful gait parameters such as stance and swing times [15].The ability to use kinematic data such as horizontal heeldisplacement to determine so many spatial-temporal gaitparameters can be useful, especially if sufficient kinetic datais difficult to obtain [16]. Thus the method of stride lengthcalculation presented in this study adds a new tool to thealready important toolbox of heel marker data, allowing formore practical applications in gait analysis.However, our method still has potential for improvement.Further research can be done to investigate the limitations ofthis study. A study can be conducted to apply the method ofcalculation to multiple types of gait data, such as abnormalgait, inclined walking, or running. A study can also beconducted to test the accuracy of the method compared to anaccurate and established method such as the video-analysisstride length calculation; such a study would allow for aclearer conclusion of whether the potential horizontal offsetat heel strike affects the accuracy of the step length approach.I. A
CKNOWLEDGEMENTS
The author would like to thank Robert Gregg, Ph.D. andhis Locomotor Control Systems Laboratory at the Universityof Texas at Dallas for giving him an opportunity to workwith the lab as an undergraduate research intern. The authorwould especially like to thank David Quintero for takinghim in as a personal intern and mentoring him through theprocess of research. R
EFERENCES [1] R. Abel, M. Schablowski, R. Rupp, and H. Gerner, “Gaitanalysis on the treadmill-monitoring exercise in the treatmentof paraplegia,”
Spinal Cord , vol. 40, no. 1, p. 17, 2002.[2] G. Colombo, M. Joerg, R. Schreier, and V. Dietz, “Treadmilltraining of paraplegic patients using a robotic orthosis,”
Journal of rehabilitation research and development , vol. 37,no. 6, p. 693, 2000.[3] M. W. Whittle,
Gait Analysis: An Introduction . Butterworth-Heineman, 2014.[4] M. P. Murray, G. B. Spurr, S. B. Sepic, G. M. Gardner, andL. A. Mollinger, “Treadmill vs. floor walking: kinematics,electromyogram, and heart rate,”
Journal of Applied Physiol-ogy , vol. 59, no. 1, pp. 87–91, 1985.[5] J. C. Wall and J. Charteris, “A kinematic study of long-termhabituation to treadmill walking,”
Ergonomics , vol. 24, no. 7,pp. 531–542, 1981.[6] J. Padulo, K. Chamari, and L. P. Ardig`o, “Walking andrunning on treadmill: the standard criteria for kinematicsstudies,”
Muscles, ligaments and tendons journal , vol. 4,no. 2, p. 159, 2014.[7] G. Souza, F. Rodrigues, A. Andrade, and M. Vieira, “A simplemethod to determine gait speed from heel markers positionin single-belt treadmills,” 10 2016.[8] Y. Qi, C. B. Soh, E. Gunawan, K.-S. Low, and R. Thomas,“Estimation of spatial-temporal gait parameters using a low-cost ultrasonic motion analysis system,”
Sensors , vol. 14,no. 8, pp. 15 434–15 457, 2014.[9] F. Alton, L. Baldey, S. Caplan, and M. Morrissey, “Akinematic comparison of overground and treadmill walking,”
Clinical Biomechanics
Gait & Posture , vol. 42, no. 1, pp. 101 – 103,2015. [13] E. Desailly, Y. Daniel, P. Sardain, and P. Lacouture, “Footcontact event detection using kinematic data in cerebral palsychildren and normal adults gait,”
Gait & Posture , vol. 29,no. 1, pp. 76 – 80, 2009.[14] J. K. D. Witt, “Determination of toe-off event time dur-ing treadmill locomotion using kinematic data,”
Journal ofBiomechanics , vol. 43, no. 15, pp. 3067 – 3069, 2010.[15] D. A. Bruening and S. T. Ridge, “Automated event detectionalgorithms in pathological gait,”
Gait & Posture , vol. 39,no. 1, pp. 472 – 477, 2014.[16] B. D. Hendershot, C. E. Mahon, and A. L. Pruziner, “A com-parison of kinematic-based gait event detection methods ina self-paced treadmill application,”