lv

en

xe

gif

Gait & Posture 40 (2014) 420428

Contents lists available at ScienceDirect

Gait & P

journa l homepage: www.e l sReceived in revised form 16 May 2014Accepted 23 May 2014

Keywords:Mobile deviceKinematicsDynamicsFootJoint

temporal, spatial, and pedobarographic parameters. The goal of this study was to design and evaluate aportable system for kinematic and dynamic analysis of the foot during gait. This device consisted of aforce plate synchronized with four cameras and integrated into a walkway. The complete system can bepackaged for transportation. First, the measurement system was assessed using reference objects toevaluate accuracy and precision. Second, nine healthy participants were assessed during gait trials usingboth the portable and Vicon systems (coupled with a force plate). The ankle and metatarsophalangeal(MP) joint angles and moments were computed, as well as the ground reaction force (GRF). The intra- andinter-subject variability was analyzed for both systems, as well as the inter-system variation. Theaccuracy and precision were, respectively 0.4 mm and 0.4 mm for linear values and 0.5 and 0.6 forangular values. The variability of the portable and Vicon systems were similar (i.e., the inter-systemvariability never exceeded 2.1, 0.081 N m kg1 and 0.267 N kg1 for the angles, moments and GRF,respectively). The inter-system differences were less than the inter-subject variability and similar to theintra-subject variability. Consequently, the portable system was considered satisfactory for biomechani-cal analysis of the foot, outside of a motion analysis laboratory.

2014 Elsevier B.V. All rights reserved.

1. Introduction

Currently, 3D biomechanical analysis of the foot is commonlyused for clinical evaluation. This tends to include description ofmotion of various anatomical segments of the foot. Approximatelyfteen models have been developed and proposed in the literature[1], including the Milwaukee foot model [2,3], the Oxford footmodel for adults [4,5] and children [6,7] and the Heidelberg footmeasurement method [8]. Spatial coordinates of anatomicallandmarks are used to calculate the kinematic and dynamicparameters. Several methods have been used for these purposes,based either on skin markers [18] or intracortical bone pins withmarkers [911]. Irrespective of the foot model or the method, amotion capture system and a force plate are required to performthe kinematic and dynamic analysis.

To analyze the temporal, spatial, or pedobarographic param-eters, some portable systems (e.g., GAITRite1, Footscan1) with

pressure-activated sensors have been devised. To the best of ourknowledge, a portable system to analyze foot kinematics anddynamics during gait has not yet been presented. This systemcould help measure foot biomechanics in patients, bringing themeasurement system to the patient rather than forcing the patientto come to a purpose-built laboratory. The goal of this study was todesign and evaluate a portable system for the kinematic anddynamic analysis of the foot during gait.

2. Methods

2.1. Description of the portable system

The system consisted of four blocks (dimensions of 80 cm,60 cm and 6 cm for the length, width and height, respectively)that were assembled to create a 3.2 m walkway (Fig. 1a). A forceplate (1000 Hz, Kistler, Kistler Instruments, Winterthur,Switzerland) was integrated into one of the walkway blocks torecord the ground reaction force and moment exerted by the footduring gait. The force plate was independent of the walkway (i.e.,a 2 mm space was between the force plate borders and the

* Corresponding author. Tel.: +352 26 37 60 24; fax: +352 26 17 68 21.E-mail address: william.samson.59@gmail.com (W. Samson).

http://dx.doi.org/10.1016/j.gaitpost.2014.05.0100966-6362/ 2014 Elsevier B.V. All rights reserved.A portable system for foot biomechanica

William Samson a,*, Stphane Sanchez b, Patrick SalVronique Feipel a

a Laboratory of Functional Anatomy (CP 619), Universit Libre de Bruxelles (ULB), route de Lb Lion Systems S.A., ecostart 2, rue du commerce, L-3895 Foetz, Luxembourgc Laboratory of Anatomy, Biomechanics and Organogenesis (CP 619), Universit Libre de Bru

A R T I C L E I N F O

Article history:Received 22 January 2013

A B S T R A C T

Modeling the foot is challenanalyze the biomechanics o analysis during gait

ia a,c, Serge Van Sint Jan c,

nik 808, 1070 Brussels, Belgium

lles (ULB), route de Lennik, 808, 1070 Brussels, Belgium

ng due to its complex structure compared to most other body segments. Tothe foot, portable devices have been designed to allow measurement of

osture

evier .com/ loca te /gai tpost

tion. 6, Lht di

W. Samson et al. / Gait & Posture 40 (2014) 420428 421walkway frame) and was only xed to the walkway block byfootplates. Four metallic arms were xed on each corner of thewalkway block containing the force plate. A lamp (9 LEDs) and a

Fig. 1. (a) Assembly of the portable system from the storage box to complete installablock with an integrated force plate; 3, walkway block; 4, support arm; 5, camera;checkerboard; 8, red laser; 9, laser ray; 10, reference points to set camera in the rigPictures from the MSC software to illustrate color marker detection.camera (140 Hz, 656 490 pixels) were xed to each of thesearms with a ball joint to enable camera orientation. Themeasurements described below (Sections 2.2 and 2.3) wererecorded at 100 Hz. The complete camera system (i.e., arm, lampand camera) can be stored inside the walkway block. The ethernetconnection and power supply of the camera system wereintegrated in the walkway block containing the force plate. Thecomplete system is transportable in a storage box (84 cm, 28 cmand 70 cm, for the length, width and height, respectively).Additional technical information is given in Appendix 1.

Software for sensor synchronization (MSC, Multi SensorControl, Lion Systems S.A., Foetz, Luxembourg) was used to record

Fig. 2. (a) Phantom feet (from left to right: feet 13); (b) Simulation of a foosimultaneously data from the cameras and force plate. A systemcalibration was performed by placing a checkerboard on the top ofthe force plate (Fig. 1b). The cameras were positioned using a laser

The camera system was stored in a walkway block (1, storage box; 2, main walkwayED lamp); (b) Checkerboard for camera calibration and laser for camera setting (7,rection; 11, reference point to position the checkerboard in the right direction); (c)placed on top of each camera and a reference point on thecheckerboard. The system recorded the 3D coordinates of coloredmarkers located on the foot and leg (Fig. 1c) (Appendix 2).

2.2. Accuracy and precision of the measurement system

To evaluate accuracy and precision, measurements were rstperformed on dened reference objects. Three phantoms ofdifferent lengths representing three different foot sizes (13, 18and 26 cm corresponding approximately to the feet of a one-year-old child, a 6-year-old child and an adult woman, respectively)were constructed from Lego1 bricks (Fig. 2a). Proportions of the

t rollover; (c) Color and reective markers with the same base location.

422 W. Samson et al. / Gait & Posture 40 (2014) 420428phantoms were dened carefully based on previously publishedfoot morphology studies [12]. Such models, rather than real feet,were used in order to test the marker conguration to avoidartifacts caused by soft tissue. On each foot phantom, markerswere similarly located to real test conditions. Three of the markers(lateral malleolus, lateral calcaneus, and fth metatarsal head)were used to evaluate the system accuracy and precision. Thelateral malleolus marker was positioned such that the threemarkers, lateral malleolus, lateral calcaneus and fth metatarsalhead, dened a right-angle triangle (Appendix 3). The sides andangle of this right-angle triangle were controlled, respectively by acaliper gauge and a setsquare to assess the reconstructionaccuracy. A footstep was simulated by manually moving the footphantom to simulate foot rollover (Fig. 2b). One static trial and vesimulated gait trials were recorded for each foot phantom tocalculate the measurement accuracy and precision.

2.3. Comparison to a standard system

To assess the results of the portable system, a gold standardsystem was used [18]. This system was composed of a motioncapture system (Vicon Motion Systems Ltd., Oxford, UK) that usedpassive reective skin markers and included eight cameras(model: MXT40s, data collection frequency: 100 Hz) coupled witha force platform (1000 Hz, AMTI, Watertown, USA). Nine healthyparticipants were included in the study (35.2 10.2 years,1.76 0.07 m, 69.3 7.6 kg), and these participants walked onthe portable system and the standard system in a random order(determined by rolling a dice). A medical examination waspreviously completed to exclude any foot deviations. The protocolwas approved by the local ethics committee (P2011/249). Nineplastic bases were xed to the anatomical landmarks (ALs) of theright foot using adhesive: the midpoint of the line joining thetibial tuberosity and the midpoint of the bimalleolar line, themedial and lateral malleoli, the top and the bottom of theposterior surface of the calcaneus, the lateral surface of thecalcaneus, the rst and fth metatarsal heads, and the proximalepiphysis of the distal phalanx of the hallux [13]. Different markertypes were set on these bases according to the motion capturesystem in use: reective markers and colored markers for thestandard system and the portable system, respectively. Themarker bases were left in place for all of the tests in order toreduce the intra-examiner variability (Fig. 2c). Five gait trials at aself-selected speed (with full contact of the foot on the forceplate) were completed by each subject with both of the systems.Within the portable system, marker tracking occurred automati-cally based on a marker color detection algorithm.

2.4. Data processing

To evaluate the measurement accuracy and precision of the rawdata, the accuracy (1) and the precision (2) were computed withthe following equations:

Accuracy 1t

Xti1

1f

Xf

j1jx0 xijj (1)

Precision 1t

Xti1

1f

Xf

j1xi xij2

vuut (2)

where x0 is the reference value (distance or angle), xij is the systemvalue at frame j during the trial i, and xi is the average system valueduring the trial i, and t and f are, respectively the number of trialsand frames. The linear accuracy and precision were respectivelydened by the mean value of the accuracy and precision valuesfrom the three sides of the right-angle triangle (previouslydescribed in the Section 2.2) followed by the mean value of thetrials. Angular accuracy and precision were respectively dened bythe mean value of the accuracy and precision values of the trialsfrom the right-angle of the right-angle triangle.

For inter-systemcomparisons, thesamedataprocessingwasusedfor both the portable and Vicon systems. After signal processing ofthe marker trajectories (fourth-order Butterworth lter, 6 Hz cut-offfrequency), the segment coordinate systems (SCS) of the shank,rearfoot and forefoot were dened (Appendix 4). The shank segmentwas used as the anatomical reference frame during a static trial. Thejoint angles were computed according to ISB recommendations [14].The ankle and metatarsophalangeal (MP) net joint moments werecomputed using the ground reaction vector technique [15,16],where the moment is transformed from the force plate to the MPjoint center using classical rigid body mechanics. The net jointmoments were expressed in the proximal SCS. The computation ofthe MP net joint moment was performed as soon as the antero-posterior component of the ground reaction force (GRF) was onlyanterior (i.e., approximately when the forefoot is solely in contactwith the force plate). Finally, the GRF and joint moments werenormalizedto bodymass,andallof thedatawerere-sampledto 100%of the stance phase. The stance phase was dened by a vertical GRFgreater than 5 N. First, the intra-subject variability was dened as thestandard deviation (SD1) at each time point of the stance phase curvebetween the ve gait trials of the same subject for one system. Themean, standard deviation and maximum variability were respec-tivelydenedby themean, thestandard deviationand the maximumvalues of SD1 over the nine subjects followed by an averaging of thenine subject values.

Second, the inter-subject variability was dened as follows: foreach subject, a mean curve was computed using the ve gait trialsof the same subject for one system. Then, the standard deviation(SD2) was computed at each time point of the subject mean curvebetween the nine subjects for one system. From these values, themean, standard deviation and maximum variability were respec-tively dened by the mean, the standard deviation and themaximum values of SD2 over the two systems.

Third, the inter-system variation was evaluated by consideringfour parameters: (i) The RMSE dened between the subject meancurves (see above) of the two systems followed by an averaging ofthe nine subject values; (ii) standard deviation and (iii) maximumvariability, respectively dened by the standard deviation and themaximum differences between the subject mean curves of the twosystems followed by an averaging of the nine subject values; (iv)CMCs inspired by Kadaba et al. [17]:

CMC

X2a1

X9

b1

X5c1

X100

d0Yabcd Yd2=101 2 9 5 1

X2a1

X9

b1

X5c1

X100

d0Yabcd Y 2=

101 2 9 5 1 (3)where is the ath system (1, 2) of the bth subject (19) of the cth gaittrial (15) on the dth time point (0100); where Yd is the average attime point d over the 2 9 5 gait trials; and Y is the grand meanover time.

3. Results

The results revealed that the accuracy and precision did notexceed, respectively 0.5 mm and 0.5 mm for the linear values and0.9 and 0.9 for the angular values (Table 1). No clear relationshipwas observed between the measurement accuracy, precision andfoot size.

Fig. 3 shows the mean curves of all of the subjects for the anklejoint, MP joint and GRF, obtained from both the portable and Viconsystems. The intra-subject, inter-subject and inter-system vari-ability are presented in Table 2.

The intra-subject variability was very small with a meanvariability that did not exceed, respectively 1.4, 0.068 N m kg1

and 0.325 N kg1 for angles, moments and GRF. The mean, standarddeviation and maximum variability were slightly higher with theportable system than with the Vicon system, notably concerningthe MP angles.

Concerning the inter-subject variability, the highest values

4. Discussion

This study proposed a portable system for foot kinematic anddynamic analysis. The main goal of this approach was to bring themeasurement system to the patient, rather than the other wayaround.

Using foot phantoms that did not include any soft tissueartifacts, the current system revealed average linear and angularaccuracies of 0.4 mm and 0.5, respectively. Even though the Viconsystem was found to be more accurate [18], the current results forthe system accuracy and precision of the portable system weresatisfactory for most of the common applications of foot analysesoutside of a motion analysis laboratory (e.g., physiotherapist'spractice, patient's home). These analyses often revealed inter-group angular differences (e.g., healthy vs. pathological subjects,pre-operative vs. post-operative) higher than 5.0, such asCharcotMarieTooth [19], hallux valgus [20], total ankle replace-ment [21], diabetic neuropathy [22], equinovarus foot [23], footdrop [24], and cavovarus foot [25]. Regarding biomechanicalevaluation, the results revealed similar curve patterns from boththe systems. These patterns were similar to the results found in theliterature for the dorsal/plantar exion motion, but presentedslight differences for the other planes, most likely due todifferences related to the foot model and/or biomechanicalprocessing [528]. The inter-system variation was systematicallyless than the inter-subject variability and similar to the intra-

Table 1The linear and angular accuracies and precisions of the system for the linear andangular measurements.

Foot 1 Foot 2 Foot 3 Mean

Static trailsDistance (mm) Accuracy 0.4 0.4 0.4 0.4

Precision 0.2 0.3 0.2 0.2Angle () Accuracy 0.3 0.3 0.5 0.4

Precision 0.4 0.6 0.3 0.4Dynamic trialsDistance (mm) Accuracy 0.5 0.4 0.4 0.4

Precision 0.5 0.5 0.3 0.4Angle () Accuracy 0.2 0.3 0.9 0.5

Precision 0.5 0.9 0.5 0.6

W. Samson et al. / Gait & Posture 40 (2014) 420428 423were noted for the maximum variability around the dorsal/plantar exion axes. Even if the inter-subject variability washigher than the intra-subject variability, the maximum differ-ences of the mean variability between both systems were,respectively 0.8, 0.021 N m kg1 and 0.04 N kg1 for angles,moments and GRF.

On the one hand, the inter-system variation was less than theinter-subject variability, and on the other hand, this value was veryclose to the intra-subject variability, with RMSE values that did notexceed, respectively 2.1, 0.081 N m kg1 and 0.267 N kg1 forangles, moments and GRF. CMCs were higher than 0.64 exceptfor the MP adduction/abduction moment (0.38).Fig. 3. Ankle, MP and GRF biomechanical parameters with both portable asubject variability, which was very low, as is generally observed[5,8,27,28]. The highest variability was noted around the rotationaxes with a high range of motion (i.e., dorsal/plantar exion), andthe lowest CMCs were observed for curves close to zero (i.e., MPinversion/eversion angle, MP adduction/abduction moment),similar to previous studies [8,26,28]. Several aspects could explainthe slight differences between the portable system and the Viconsystem, particularly for the MP joint. The compactness (e.g., smallwalkway length, cameras closed to the capture volume) as well asthe accuracy and the precision of the portable system (lower thanthe Vicon system) could explain the higher intra-subject variabilitythan the Vicon system. The inter-system variability could also bereduced if the stance phase of both the systems were recorded

nd Vicon systems (mean and standard deviation of the nine subjects).

am c

M

2

0

0

0

0

0

2

1

1

424 W. Samson et al. / Gait & Posture 40 (2014) 420428during the same gait trial. Unfortunately, such simultaneoussampling was not possible due to the specic markers used witheach system (i.e., reective markers and colored markers). Walkingvelocity was not controlled and could have contributed to thevariability between both systems. Nevertheless, the GRF curveswere very similar for both systems. Schwartz et al. showed that theGRF depends on the walking velocity [29] indicating that the meanwalking velocities for both systems were reasonably similar.

The portable system and the corresponding evaluation ofaccuracy and precision is a rst step, and thus some limitationsappear in the current study. The comparison was only performedwith one standard system (Vicon), assuming the accuracy of thissystem as a gold standard. The results of the present study couldalso be compared to other systems to verify this assumption. Thejoint moments were only computed with the ground reactionforce technique [15], and not using an inverse dynamic model.

Table 2The intra-subject, inter-subject and inter-system variabilities for the kinematic and dynMean: mean variability; RMSE: root mean square error; CMC: coefcient of multiple

Intra-subject

Portable Vicon

Mean S.D. Max Mean S.D.

Ankle Angles () Dorsal / plantarexion

0.1 0.3 2.2 0.9 0.2

Inversion/eversion

0.1 0.3 2.3 0.5 0.1

Adduction /abduction

0.9 0.2 2.3 0.6 0.1

Moments(N m kg1)

Dorsal / plantarexio

0.068 0.031 0.116 0.059 0.021

Inversion/eversion

0.026 0.007 0.035 0.022 0.005

Adduction /abduction

0.022 0.010 0.044 0.022 0.004

MP Angles () Dorsal / plantarexion

1.4 0.8 6.7 1.2 0.4

Inversion/eversion

1.3 0.7 8.1 0.9 0.1

Adduction /abduction

1.1 0.9 8.2 0.6 0.1 Although this approach has been criticized [30], this methoddemonstrates appropriate results when segment inertialparameters are negligible [31]. Moreover, no anthropometricregressions (required for inverse dynamic processing) areavailable for different foot segments. Due to the specic needsof the project, including the development of this portable system,a foot model developed internally was used in the rst instancefor software integration. The use of this model could explain somedifferences between our results and some studies in theliterature. Nonetheless, the aim of the current paper was toevaluate a new device rather than to propose a new foot model.Investigations are currently in progress to take into accountclassical 3D multi-segment foot models described in the review ofDeschamps et al. [1] (e.g., the Milwaukee foot model [2,3], Oxfordfoot model [6,7], and Heidelberg foot measurement method [8]).Finally, in the future additional blocks to extend the walkwaylength (in order to facilitate recording of natural walking) andthe size of the camera arms to include knee joint assessmentshould be considered.

5. Conclusion

The current study presented a portable system for kinematicand dynamic analyses of the foot. An evaluation of this novelsystem revealed average linear and angular accuracies of 0.5 mmand 0.4, respectively. Compared to a Vicon system, the currentdevice revealed similar patterns (the mean inter-system RMSE forthe angles, moments and GRF were 1.2, 0.040 N m kg1 and0.167 N kg1, respectively). These results suggest that the newlydeveloped portable system has satisfactory performance forevaluating most common foot deformities, where the inter-groupsvariability (e.g., healthy vs. pathological subjects) has beenreported to be higher than the current system accuracy. Althoughthe current version is limited to one foot model, futureinvestigations will consider other foot models presented in theliterature for software integration.

Acknowledgements

The development of the portable system was led by INESCOPand the German Sport University Cologne. The research leading to

ic parameters with both the portable and Vicon systems (Max: maximal variability;orrelation).

Inter-subject Inter-system

Portable Vicon

ax Mean S.D. Max Mean S.D. Max RMSE S.D. Max CMC

.2 3.5 1.0 5.7 2.9 0.7 4.3 1.7 0.4 3.0 0.95

.9 1.5 0.3 2.7 1.0 0.3 1.6 0.7 0.2 1.8 0.77

.8 1.4 0.2 2.2 1.0 0.2 1.4 0.4 0.2 1.5 0.72

.111 0.238 0.132 0.477 0.223 0.107 0.445 0.056 0.088 0.159 0.98

.033 0.075 0.024 0.133 0.058 0.018 0.097 0.081 0.074 0.171 0.65

.043 0.072 0.042 0.149 0.078 0.045 0.162 0.037 0.034 0.082 0.94

.1 5.3 2.7 11.8 4.5 2.4 9.5 2.1 0.9 5.7 0.94

.6 2.5 0.7 4.8 2.2 0.6 3.5 1.3 0.3 3.3 0.64

.2 1.9 1.5 6.9 1.3 0.7 4.0 0.9 0.3 4.4 0.88these results, has received funding from the European Commu-nity's Seventh Framework Programme (FP7/20072013) underSSHOES Project, grant agreement no. NMP2-SE-2009-229261. Thepresent study is supported by the National Research Fund,Luxembourg, under the form of the post-doctoral AFR grantto the rst author, WS (n 1215659). The authors would like toacknowledge Laurence Chze for his review of the manuscript.

Appendix 1. Portable system description

Fig. 4 and Table 3 provide additional information on theequipment characteristics integrated in the portable system.

Appendix 2. Denition of 3D location of color markers

This section describes the implementation of the multi-viewcolor marker-based optical motion capture (OMC) procedure usedin the above-described data collection. The OMC requires solvingmany non-trivial problems in computer vision. The main taskswere camera calibration, marker detection, marker matching andmarker assignment [32]. The calibration procedure consisted ofnding the intrinsic and extrinsic camera parameters [33] using areference object (checkerboard, Fig. 1b). The position andorientation relative to a chosen camera as a reference and theinternal characteristic (principal point, focal length, skew

Table 3Equipment characteristics integrated in the portable system.

Camera Description Gigabit ethernet progressive scan CCD camera(digital monochrome)

Dimensions 36 mm 36 mm 48 mmWeight 90 gResolution 656 490 pixelsExposure 1500 msGain 3 dbScan area 7.15 mm x 5.44 mm

Lamp Description 9 LED coupled and integrated in a metallic box(internal development)

Dimensions 60 mm 50 mm 40 mmWeight 200 gPower 15 wColor Cold whiteLuminosity intensity 1600 LmLight distibution 18

Force plate Description Multi-component force plate kistlerDimensions 600 mm 500 mm 50 mmWeight 8.6 kgMeasuring range Fx, Fy 2.52.5 kN; Fz 05 kNOverload Fx, Fy 3/3 kN; Fz: 0/8 kNLinearity < 0.5%FSOHysteresis

c-o-e-f--c-i-e-n-tsand distortion) were calculated. The cameras used RGB (red, green,and blue) color space, however, each component of this colormodel was very sensitive to lighting conditions. Therefore, the RGBimage was converted to HSV (hue, saturation, value) so that thechange in lighting only affected the value component of the image[34]. The HSV color space followed the human perception of color.The thresholds to separate the color markers were easier toidentify in the HSV color space than the RCG color space becauseidentication can be reduced to the selection of one colorcomponent (the hue in this study). Thanks to the availability ofthe H value that corresponded to each marker color used duringthe data collection, the signal processing procedure couldautomatically extract the location of each marker for each camera.Each marker was dened in the 2D local frame of each camera.Then, given a set of 2D marker positions in the various cameraframes, triangulation was used to compute the 3D position of the

Appendix 3. Foot phantoms measurements

On each foot phantom, markers were located similarly to thereal test conditions. Lateral malleolus (A), lateral calcaneus (B) andfth metatarsal head (C) were chosen to evaluate the accuracy andprecision of the portable system. The distances between themarkers were controlled by a caliper gauge with an accuracymeasurement of 0.1 mm and a maximal measurement error of0.03 mm (manufacturer data [36]). The measurements wereperformed using four contact points between the caliper gaugeand the foot phantom to minimize the measurement variability(Fig. 6a). A right angle (a) between the lines connecting A and B(AB), and B and C (BC) was dened by adjusting the A location(Fig. 6b). The right angle denition was rstly dened using a setsquare. Secondly, AB, BC and AC were measured (still using thecaliper gauge) to numerically control the value of a using the

Table3 (Continued)

Channels 16Resolution 16 bitsSample rate 250 kS s1

Throughput (all channels) 250 kS s1

Max voltage 10 VMaximum voltage range 10 V , 10 VMaximum voltage range accuracy 2.2 mVMinimum voltage range 0.2 V , 0.2 VMinimum voltage range accuracy 69 mV

odule allowing manual HSV setting.

426 W. Samson et al. / Gait & Posture 40 (2014) 420428markers in the scene [35]. HSV parameters can be adjustedmanually (Fig. 5), as well as the minimum number of pixels toconsider for marker detection. The maximum number of usablecolors was ve (red, green, blue, yellow, and magenta), even if thesystem conguration of the current study only worked with threecolors. With the current camera resolution and the current eld ofview, the accuracy of the 3D reconstruction of the marker positionin space was between 0.3 and 0.5 mm, depending on the number ofcameras viewing the marker. Interpolated signal (lost signal)represented an average of 1.6 1.1% of the stance phase on thecurrent measurements. The worst tracking performance wasobserved for the medial malleolus marker (interpolated signal:3.4 4.3% of the stance phase).

Fig. 5. Illustration of the software mCosine Law (i.e., a = cos1((AC2 AB2 BC2)/( 2 AB BC)))).With the current maximal measurement error of the calipergauge, the measurement accuracy of a was higher than 0.1 for allof the foot phantoms.

Appendix 4. Segment coordinates systems

The segment denition concerned the right foot:The shank coordinate system was dened as follows:

O, (origin) the midpoint of the bimalleolar line; Z, the line connecting the medial and lateral malleoli andpointing to the right;

W. Samson et al. / Gait & Posture 40 (2014) 420428 427 X, the line perpendicular to the plane dened by the Z-axis andthe midpoint of the line joining the tibial tuberosity and O, andpointing forward;

Y, the common perpendicular to the Z- and X- axis, pointing

Fig. 6. (a, b) distance and angle manual measurements of the foot phantoms,respectively (1, foot phantom; 2, contact point; 3, caliper gauge; 4, set square; ACcorrespond, respectively to the lateral malleolus, lateral calcaneus and fthmetatarsal head markers; a, the angle between BA and BC).upward.

The rearfoot coordinate system was dened as follows:

O, (origin) the inferior marker of the posterior surface of thecalcaneus;

Y, the line connecting the top and the bottom markers of theposterior surface of the calcaneus;

X, the line perpendicular to the plane dened by the Y-axis andthe line connecting O and the lateral surface of the calcaneus, andpointing forward;

Z, the common perpendicular to the X- and Y-axis, pointingupward.

The forefoot coordinate system was dened as follows:

O, (origin) the midpoint of the line joining the rst and fthmetatarsal heads;

Z, the line connecting the rst and fth metatarsal heads andpointing to the right;

Y, the line perpendicular to the plane dened by the Z-axis andthe proximal epiphysis of the distal phalanx of the hallux, andpointing upward;

X, the common line perpendicular to the Z- and Y-axis, pointingforward.

Conict of interest

The authors have nothing to disclose. One of the authors,Stphane Sanchez, is employed by Lion Systems S.A.. He hasdeveloped the algorithm of markers tracking and integrated it inthe Lion Systems platform.

References

[1] Deschamps K, Staes F, Roosen P, Nobels F, Desloovere K, Bruyninckx H, et al.Body of evidence supporting the clinical use of 3D multisegment foot models:a systematic review. Gait Posture 2011;33:33849.

[2] Myers KA, Wang M, Marks RM, Harris GF. Validation of a multisegment footand ankle kinematic model for pediatric gait. IEEE Trans Neural Syst RehabilEng 2004;12:12230.

[3] Kidder SM, Abuzzahab FS, Harris GF, Johnson JE. A system for the analysis offoot and ankle kinematics during gait. IEEE Trans Rehabil Eng 1996;4:2532.

[4] Theologis TN, Harrington ME, Thompson N, Benson MKD. Dynamic footmovement in children treated for congenital talipes equinovarus. J Bone JointSurg 2003;85:5727.

[5] Carson MC, Harrington ME, Thompson N, O'Conner JJ, Theologis TN. Kinematicanalysis of a multi-segment foot model for research and clinical applications: arepeatability analysis. J Biomech 2001;34:1299307.

[6] Curtis DJ, Bencke J, Stebbins JA, Stanseld B. Intra-rater repeatability of theOxford foot model in healthy children in different stages of the foot roll overprocess during gait. Gait Posture 2009;30:11821.

[7] Stebbins J, Harrington M, Thompson N, Zavatsky A, Theologis T. Repeatabilityof a model for measuring multi-segment foot kinematics in children. GaitPosture 2006;23:40110.

[8] Simon J, Doederlein L, McIntosh AS, Metaxiotis D, Bock HG, Wolf SI. TheHeidelberg foot measurement method: development, description andassessment. Gait Posture 2006;23:41124.

[9] Lundgren P, Nester C, Liu A, Arndt A, Jones R, Stacoff A, et al. Invasive in vivomeasurement of rear-, mid- and forefoot motion during walking. Gait Posture2008;28:93100.

[10] Arndt A, Wolf P, Lui A, Nester C, Stacoff A, Jones R, et al. Intrinsic footkinematics measured in vivo during the stance phase of slow running. JBiomech 2007;40:26728.

[11] Nester N, Jones RK, Lui A, Howard D, Lundberg A, Arndt A, et al. Foot kinematicsduring walking measured using bone and surface mounted markers. J Biomech2007;40:341223.

[12] Yu CY, Tu HH. Foot surface area database and estimation formula. Appl Ergon2009;40:76774.

[13] Van Sint Jan S. Color atlas of skeletal landmark denitions: guidelines forreproducible manual and virtual palpations. Edinburg: Churchill LivingstoneElsevier; 2007.

[14] Wu G, Cavanagh PR. ISB recommendations for standardization in the reportingof kinematic data. J Biomech 1995;28:125761.

[15] Wells RP. The projection of the ground reaction force as a predictor of internaljoint moments. Bull Prosthet Res 1981;10-35:159.

[16] Stefanyshyn DJ, Nigg BM. Mechanical energy contribution of the metatarso-phalangeal joint to running and sprinting. J Biomech 1997;30:10815.

[17] Kadaba MP, Ramakrishnan HK, Wootten ME, Gainey J, Gorton G, Cochran GVB.Repeatability of kinematic, kinetic and electromyographic data in normaladult gait. J Orthop Res 1989;7:84960.

[18] Windolf M, Gtzen N, Morlock M. Systematic accuracy and precision analysisof video motion capturing systems exemplied on the Vicon-460 system. JBiomech 2008;41:277680.

[19] Don R, Serrao M, Vinci P, Ranavolo A, Cacchio A, Ioppolo F, et al. Foot drop andplantar exion failure determine different gait strategies in CharcotMarieTooth patients. Clin Biomech (Bristol, Avon) 2007;22:90516.

[20] Deschamps K, Birch I, Desloovere K, Matricali GA. The impact of hallux valguson foot kinematics: a cross-sectional, comparative study. Gait Posture2010;32:1026.

[21] Cenni F, Leardini A, Pieri M, Berti L, Belvedere C, Romagnoli M, et al.Functional performance of a total ankle replacement: thorough assessmentby combining gait and uoroscopic analyses. Clin Biomech (Bristol, Avon)2013;28:7987.

[22] Sawacha Z, Guarneri G, Cristoferi G, Guiotto A, Avogaro A, Cobelli C. Integratedkinematics-kinetics-plantar pressure data analysis: a useful tool for charac-terizing diabetic foot biomechanics. Gait Posture 2012;36:206.

[23] Benedetti MG, Manca M, Ferraresi G, Boschi M, Leardini A. A new protocol for3D assessment of foot during gait: application on patients with equinovarusfoot. Clin Biomech (Bristol, Avon) 2011;26:10338.

[24] Hastings MK, Sinacore DR, Woodburn J, Paxton ES, Klein SE, McCormick JJ, et al.Kinetics and kinematics after the Bridle procedure for treatment of traumaticfoot drop. Clin Biomech (Bristol, Avon) 2013;28:55561.

[25] Charles YP, Louahem D, Dimglio A. Cavovarus foot deformity with multipletarsal coalitions: functional and three-dimensional preoperative assessment. JFoot Ankle Surg 2006;45:11826.

[26] Jenkyn TR, Nicol AC. A multi-segment kinematic model of the foot with a noveldenition of forefoot motion for use in clinical gait analysis during walking. JBiomech 2007;40:32718.

[27] Leardini A, Sawacha Z, Paolini G, Ingrosso S, Nativo R, Benedetti MG. A newanatomically based protocol for gait analysis in children. Gait Posture2007;26:56071.

[28] MacWilliams BA, Cowley M, Nicholson DE. Foot kinematics and kinetics duringadolescent gait. Gait Posture 2003;17:21424.

[29] Schwartz MH, Rozumalski A, Trost JP. The effect of walking speed on the gait oftypically developing children. J Biomech 2008;41:163950.

[30] Winter DA, Wells RP. Kinetic assessments of human gait. J Bone Joint Surg1981;63:1350.

[31] Dumas R, Chze L, Frossard L. Loading applied on prosthetic knee oftransfemoral amputee: comparison of inverse dynamics and direct measure-ments. Gait Posture 2009;30:5602.

[32] Guerra-Filhol G. Optical motion capture: theory and implementation. RITA2005;12:2.

[33] Bouguet JY. Camera calibration toolbox for Matlab. Computational vision at theCalifornia institute of technology. http://www.vision.caltech.edu/bouguetj/calib_doc/.

[34] Russ JC. The image processing handbook. 4th ed. CRC Press; 2002 [eBook].[35] Hartley RI, Zisserman A. Multiple view geometry computer vision. 2nd ed.

Cambridge University Press; 2004.[36] http://www.messschieber.org/messschieber-din-862.html.

428 W. Samson et al. / Gait & Posture 40 (2014) 420428

A portable system for foot biomechanical analysis during gait1 Introduction2 Methods2.1 Description of the portable system2.2 Accuracy and precision of the measurement system2.3 Comparison to a standard system2.4 Data processing

3 Results4 Discussion5 ConclusionAcknowledgementsAppendix 1 Portable system descriptionAppendix 2 Definition of 3D location of color markersAppendix 3 Foot phantoms measurementsAppendix 4 Segment coordinates systemsConflict of interestReferences