Short communication Predicting timing of foot strike during running, independent of striking technique, using principal component analysis of joint angles Sean T. Osis a,n , Blayne A. Hettinga a , Jessica Leitch b , Reed Ferber a,c a Running Injury Clinic, Faculty of Kinesiology, University of Calgary, Calgary AB, Canada T2N 1N4 b Run3D Inc. Oxford, UK, OX4 1EQ and Oxford University, Oxford, OX1 2JD, UK c Faculty of Nursing, University of Calgary, Calgary AB Canada T2N 1N4 article info Article history: Accepted 6 June 2014 Keywords: Treadmill running Foot strike Kinematics Gait Biomechanics abstract As 3-dimensional (3D) motion-capture for clinical gait analysis continues to evolve, new methods must be developed to improve the detection of gait cycle events based on kinematic data. Recently, the application of principal component analysis (PCA) to gait data has shown promise in detecting important biomechanical features. Therefore, the purpose of this study was to define a new foot strike detection method for a continuum of striking techniques, by applying PCA to joint angle waveforms. In accordance with Newtonian mechanics, it was hypothesized that transient features in the sagittal-plane accelera- tions of the lower extremity would be linked with the impulsive application of force to the foot at foot strike. Kinematic and kinetic data from treadmill running were selected for 154 subjects, from a database of gait biomechanics. Ankle, knee and hip sagittal plane angular acceleration kinematic curves were chained together to form a row input to a PCA matrix. A linear polynomial was calculated based on PCA scores, and a 10-fold cross-validation was performed to evaluate prediction accuracy against gold- standard foot strike as determined by a 10 N rise in the vertical ground reaction force. Results show 89–94% of all predicted foot strikes were within 4 frames (20 ms) of the gold standard with the largest error being 28 ms. It is concluded that this new foot strike detection is an improvement on existing methods and can be applied regardless of whether the runner exhibits a rearfoot, midfoot, or forefoot strike pattern. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Running continues to be the number one participation sport in North America, however, approximately 50% of runners will sustain a musculoskeletal injury each year (Taunton et al., 2002; Ferber et al., 2009). As the cost of optical motion capture becomes more affordable, it has likewise become feasible to use 3- dimensional (3D) motion-capture for clinical gait analysis, and thus, injury assessment and prevention (Leigh et al., 2014). However, many clinical settings preclude the use of over-ground analysis due to the large space required and the cost associated with multiple cameras required to cover the analysis volume. Additionally, though 3D motion capture technology has become cheaper, kinetic measurement systems that can be easily integrated with motion capture are still costly and installation requirements can be challenging. Consequently, clinical analyses of running gait are often limited to treadmill-based motion capture without ground reaction force data. Many kinematic variables of interest during running rely on the detection of gait cycle events. Without ground reaction forces, gait events must be detected using kinematic data of the runner. Highly accurate methods of detecting the moment of toe-off have been identified (Fellin et al., 2010), however finding an accurate definition for the moment of contact between the foot and ground (foot strike) has proved more challenging. Kinematic methods have been found to have errors up to 100 ms, and some of these methods rely on specialized marker placement to facilitate detec- tion (Fellin et al., 2010; Leitch et al., 2011). Detection can be especially difficult when a runner uses midfoot or forefoot strike techniques, as current methods of event detection are less accu- rate when applied to these patterns (Leitch et al., 2011). Therefore, the purpose of this study was to define a new foot strike detection method for a continuum of strike techniques, and to test the accuracy of the method as compared to detection based on vertical ground reaction force. It was expected that the impulsive application of force to an unconstrained, multi-joint body at ground contact would result in correlated transient changes in the angular Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics http://dx.doi.org/10.1016/j.jbiomech.2014.06.009 0021-9290/& 2014 Elsevier Ltd. All rights reserved. n Correspondence to: Post: 2500 University Dr NW, Calgary AB, Canada T2N1N4. Tel.: þ1 403 220 7019; fax: þ1 403 220 0546. E-mail address: [email protected](S.T. Osis). Journal of Biomechanics 47 (2014) 2786–2789
Transcript
Short communication
Predicting timing of foot strike during running, independent of strikingtechnique, using principal component analysis of joint angles
Sean T. Osis a,n, Blayne A. Hettinga a, Jessica Leitch b, Reed Ferber a,c
a Running Injury Clinic, Faculty of Kinesiology, University of Calgary, Calgary AB, Canada T2N 1N4b Run3D Inc. Oxford, UK, OX4 1EQ and Oxford University, Oxford, OX1 2JD, UKc Faculty of Nursing, University of Calgary, Calgary AB Canada T2N 1N4
As 3-dimensional (3D) motion-capture for clinical gait analysis continues to evolve, new methods mustbe developed to improve the detection of gait cycle events based on kinematic data. Recently, theapplication of principal component analysis (PCA) to gait data has shown promise in detecting importantbiomechanical features. Therefore, the purpose of this study was to define a new foot strike detectionmethod for a continuum of striking techniques, by applying PCA to joint angle waveforms. In accordancewith Newtonian mechanics, it was hypothesized that transient features in the sagittal-plane accelera-tions of the lower extremity would be linked with the impulsive application of force to the foot at footstrike. Kinematic and kinetic data from treadmill running were selected for 154 subjects, from a databaseof gait biomechanics. Ankle, knee and hip sagittal plane angular acceleration kinematic curves werechained together to form a row input to a PCA matrix. A linear polynomial was calculated based on PCAscores, and a 10-fold cross-validation was performed to evaluate prediction accuracy against gold-standard foot strike as determined by a 10 N rise in the vertical ground reaction force. Results show89–94% of all predicted foot strikes were within 4 frames (20 ms) of the gold standard with the largesterror being 28 ms. It is concluded that this new foot strike detection is an improvement on existingmethods and can be applied regardless of whether the runner exhibits a rearfoot, midfoot, or forefootstrike pattern.
& 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Running continues to be the number one participation sport inNorth America, however, approximately 50% of runners willsustain a musculoskeletal injury each year (Taunton et al., 2002;Ferber et al., 2009). As the cost of optical motion capture becomesmore affordable, it has likewise become feasible to use 3-dimensional (3D) motion-capture for clinical gait analysis, andthus, injury assessment and prevention (Leigh et al., 2014).However, many clinical settings preclude the use of over-groundanalysis due to the large space required and the cost associatedwith multiple cameras required to cover the analysis volume.Additionally, though 3D motion capture technology has becomecheaper, kinetic measurement systems that can be easily integratedwith motion capture are still costly and installation requirementscan be challenging. Consequently, clinical analyses of running gait
are often limited to treadmill-based motion capture without groundreaction force data.
Many kinematic variables of interest during running rely on thedetection of gait cycle events. Without ground reaction forces, gaitevents must be detected using kinematic data of the runner.Highly accurate methods of detecting the moment of toe-off havebeen identified (Fellin et al., 2010), however finding an accuratedefinition for the moment of contact between the foot and ground(foot strike) has proved more challenging. Kinematic methodshave been found to have errors up to 100 ms, and some of thesemethods rely on specialized marker placement to facilitate detec-tion (Fellin et al., 2010; Leitch et al., 2011). Detection can beespecially difficult when a runner uses midfoot or forefoot striketechniques, as current methods of event detection are less accu-rate when applied to these patterns (Leitch et al., 2011).
Therefore, the purpose of this study was to define a new footstrike detection method for a continuum of strike techniques, and totest the accuracy of the method as compared to detection based onvertical ground reaction force. It was expected that the impulsiveapplication of force to an unconstrained, multi-joint body at groundcontact would result in correlated transient changes in the angular
accelerations of body segments. In addition, it has been previouslyshown that a pattern recognition method using principle componentanalysis (PCA) may be used to provide a means of detectingpreviously unknown, temporally correlated features from multiplesignals simultaneously (Federolf et al., 2012). Based on these pre-mises, it was hypothesized that transient features in sagittal-planeaccelerations of lower extremity joints, detected and described byPCA, would be temporally correlated with the application of theground reaction force to the foot at foot strike.
2. Methods
A query from the existing database (Osis et al., in press) provided complete setsof gait kinematics and kinetics for 154 subjects (mean7st dev, age: 38.7710.4 yrs,
height: 173.079.0 cm, mass: 70.3712.3 kg, gender: 81 female, 73 male) duringtreadmill running (mean7st dev, speed: 2.6570.22 m/s). Data in the database werecollected as follows: Kinematics were collected using 8 high-speed (Vicon Inc.,Oxford, UK: 200 Hz) infrared cameras and retroreflective markers. Clusters ofmarkers were strapped to the shanks, thighs and pelvis, and additional markerswere attached to define anatomical joint locations and axes, in the mannerdescribed by Pohl et al. (2010). Segment kinematics were calculated based oncluster movement, using a singular-value decomposition approach (Söderkvist andWedin, 1993) and a joint coordinate system (Cole et al., 1993).
Kinetics were collected at 1000 Hz while subjects ran on an instrumentedtreadmill (Bertec Inc., Columbus, OH). Kinetics and kinematic marker positionswere filtered using a zero-lag Butterworth filter with a 20 Hz cutoff. The instant offoot strike was determined from the filtered vertical ground reaction force usinga rising-threshold of 10 N.
After retrieval, data were further processed in MATLAB (The Mathworks, Natick,MA). Joint angles in the sagittal plane were double-differentiated to calculate sagittalplane angular accelerations at each joint. A random sub-sample of 10 subjects waschosen and sagittal plane angular acceleration curves for the foot, relative to the labcoordinate system, were visually inspected to examine any features correspondingwith foot strike, as defined by 10 N of vertical force. A concurrent peak was isolated(FApk), and subsequently found to exist for all subjects, regardless of their strikingtechnique: rearfoot, midfoot, or forefoot. Subsequently, a section of kinematic datafrom 35 frames (175 ms) prior, to 35 frames (175 ms) following FApk was extractedfor each foot strike event. These data included sagittal plane angular accelerations forthe foot, ankle, knee and hip. These curve segments were then chained together toform a row input to the matrix for principle component analysis (PCA). A PCA wasperformed on the resulting 154�284 matrix of data, generating a 284�284 matrixof loading factors, grouped column-wise into principle components (PCs). Eachsubject was scored on each PC by multiplying the original data matrix with thematrix of loading factors. The output was a 154�284 matrix of scores for eachsubject on each PC. Subject scores on the first column PC (PC1) were plotted againstthe time-delay between the gold-standard foot strike determined by kinetics, and thetime point of FApk, to examine the relationship between them.
A 10-fold cross-validation was performed to evaluate the performance of thelinear polynomial to predict foot strike detection from 350 ms snippets ofkinematic data centered about FApk. The total sample of 154 subjects was randomlydivided into 10 sub-samples, and the algorithm was run iteratively 10 times over.For each iteration, 9 of the sub-samples were used to calculate the linearpolynomial, and the remaining sub-sample was used for validation. Foot striketiming was predicted from the polynomial on a step-by-step basis and comparedwith the gold standard foot strike timing for each step, as determined by kinetics.The mean discrepancy between the two was then calculated across all steps.
3. Results
Results are only presented for left side data, as all results wereidentical for the right. Curves demonstrating the identified peak,
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Fig. 1. Foot sagittal-plane angular acceleration waveform data from all subjects(n¼154). Waveforms are means of 15 or more left side cycles, and are centeredabout the mean time of foot strike as determined by kinetics. The time delaybetween peak foot acceleration (FApk) and foot strike by kinetics is indicated forone subject.
Fig. 2. Sagittal-plane waveform row input to the PCA matrix from one subject (solid line), and resulting PC1 loadings on the waveform data (shaded area). Waveforms werecentered about the time point of peak foot acceleration (FApk) as shown in the leftmost panel. Data have been segmented into separate curves for clarity, but were analyzedas a contiguous block.
S.T. Osis et al. / Journal of Biomechanics 47 (2014) 2786–2789 2787
FApk, and associated time-delay, are shown in Fig. 1. This peak wasfound to exist for all subjects regardless of striking technique.A plot of one row-input to the PCA matrix along with correspond-ing loadings from PC1, accounting for 12.5% of the total variance, isshown in Fig. 2. PC1 was loaded on (correlated with) the originalfoot, ankle and knee accelerations prior to FApk. Fig. 3 shows ascatterplot of subject scores on PC1 against the time-delay of FApk
relative to gold standard foot strike detection by kinetics.A significant relationship between the two was described by alinear polynomial.
Results of the 10-fold cross validation are shown in Fig. 4. Forthose subjects who exhibited rearfoot striking technique (n¼133;foot angle 43 degrees, or toe up, at FApk), 94% of all predicted footstrikes were within 4 frames (20 ms) of the gold standard. Forthose subjects who exhibited midfoot/forefoot striking technique(n¼21; foot angle o3 degrees, or toe level/down, at FApk), 89% ofall predicted foot strikes were within 4 frames (20 ms) of the goldstandard. Overall, 94% of all predicted foot strikes were within4 frames (20 ms) of touchdown as defined by the gold standard,regardless of striking technique.
4. Discussion
The purpose of the present study was to define a new footstrike detection method for a continuum of striking techniques,and to test the accuracy of the method as compared to detectionbased on vertical ground reaction force. Prior methods based onthe use of marker trajectories have produced mixed results. Insome instances, these methods have exhibited mean errors of57 ms (Fellin et al., 2010). This problem becomes exacerbatedwhen a midfoot/forefoot striking technique is used, as mean errorscan range from 20 ms up to 100 ms (Leitch et al., 2011). Thecurrent study improves upon these results, demonstrating noerrors larger than 28 ms, and with 94% of errors less than 20 ms.This improvement over prior methods likely arises due to theincreased availability of kinematic information from joint angles asopposed to single marker trajectories. A single marker providespoint kinematics and may not effectively represent subtle changesin segment motion, while a joint angle provides 3D rigid-bodykinematics, including descriptions of segment interactions. Thesedata therefore constitute a more comprehensive description ofsegment motion. Additionally, the new method described herein istechnique-independent, providing substantial benefit in that it
may be applied without prior knowledge of foot strike techniqueemployed by the runner.
A novel and important finding of the current study is the effectof errors in detection of foot strike on the determination of jointangles at touchdown. The mean joint angle curves shown in Fig. 4indicate that poor detection would tend to affect knee sagittalplane angles the most (95% interval of 7 degrees), while hip anglewould be the least affected (95% interval of o1 degree). This islikely due to differences in the velocities at each joint at touch-down. Knee flexion velocities tend to be the largest during touch-down, hence making this variable more sensitive to errors in thetiming of foot strike. This result helps to place detection errors inthe context of biomechanical analysis, allowing the researcher and
−9 −8 −7 −6 −5 −4 −3 −2 −1 0
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Fig. 3. Correlation for all subjects (n¼154) between score on PC1 and the timedelay between FApk and foot strike determined by kinetics (as shown in Fig. 1).
0-20 -10-30-50
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Fig. 4. Cross-fold validation of the new method of event detection using allsubjects (n¼154) once for validation. The bottom panel indicates the distributionof errors relative to the gold standard foot strike by kinetics, while the top threepanels show mean sagittal plane joint angles across all subjects. The verticalshaded rectangle indicates the 95% interval of the distribution of errors indetermining foot strike time point, and the horizontal shaded rectangles demon-strate the resulting effect on determining joint angles from the mean waveform forall subjects.
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clinician to make informed decisions on the use of angle informa-tion at the time of foot strike. Based on these findings, even goodmethods of foot strike detection may pose a problem in theselection of knee sagittal angles at contact, and caution is thereforeadvised in the interpretation of this variable.
This work is another example of the successful application ofpattern recognition techniques to an existing biomechanical data-base (Osis et al., in press), and this approach continues to showpromise in advancing biomechanical analysis by addressing meth-odological issues. Moreover, recent research has shown thatpattern recognition methods have been applied to better under-stand running injury pathomechanics, and have achieved goodclassification performance with regard to several important clas-sification problems (Fukuchi et al., 2011; Maurer et al., 2012; Nigget al., 2012). Thus, the continued adoption of database and patternrecognition technologies may be an important means to advancethese new areas of biomechanical research.
It is concluded that the new foot strike detection method cansuccessfully detect striking events for a continuum of strikingtechniques with no observed errors larger than 28 ms, and with94% of errors less than 20 ms. The method presented herein istechnique-independent and can be applied regardless of whetherthe runner exhibits a rearfoot, midfoot, or forefoot strike patternand without prior knowledge of the striking technique employedby the runner.
Conflict of Interest Statement
None of the authors have any conflicts with respect tothis study.
Acknowledgments
Alberta Innovates: Health Solutions (AIHS) partially funded thisresearch along with a 2013 Canada-UK Collaboration DevelopmentAward through the UK’s Science & Innovation Network in Canada.
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