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Foot velocity profiles during stance phase in gait
Abstracts / Gait & Posture 33S (2011) S1–S66
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Maximal Distance (MD) were quantified for ankle rotation angles calculated using cluster (i) and (ii). Results The lateral bar marker resulted to move with respect to the relevant shank reference in the order of the centimetre during walking, the motion was time-varying and particularly associate to the inertial phenomena at toe-off and heel contact. The RMSD(MD) between ankle rotation angles calculated with (cluster (i)) and without (cluster (ii)) the lateral bar was in the order of 1◦ (3◦ ) for Dorsi/Plantar-flexion and Prono/Supination and 9◦ (20◦ ) for Internal/External rotation (Fig. 1). The use of different anatomical references of the foot affected only ankle Internal/External rotation, with a maximal difference of 3◦ . Discussion The motion of the shank lateral bar resulted to significantly affect the ankle rotation angles quantified during motion. The effect of lateral bar motion particularly affects prono/supination, with errors up to the 20% of the range, and internal/external rotation, with errors up to 120% of the range. The preliminary results show that not only the alignment of the lateral bar is critical, but its inertial motion critically affects relevant joint kinematics. The acquisition of 20 + 20 subjects is currently being performed, aiming at the quantification of the propagation of lateral bar to relevant ankle kinematics and at the validation of a compensation method based on the proposed Davis integrated protocol [1].
References [1] Moretti, et al. Gait Posture 2009. [2] Stagni R, et al. Gait Posture 2005.
doi:10.1016/j.gaitpost.2010.10.029 O25 Foot velocity profiles during stance phase in gait A. Peruzzi 1 , A. Cereatti 1,2 , U. Della Croce 1 1
Department of Biomedical Sciences, University of Sassari, Sassari, Italy 2 Casa di Cura e Riabilitazione, Santa Maria Bambina, Oristano, Italy Introduction Space and time gait parameters can be estimated with wearable inertial units. Linear displacement information is typically obtained by double integrating accelerometer data over each gait cycle. However, usually a drift affects the resulting displacement signals and therefore its effects should be minimized. In the majority of studies using accelerometers, drift is corrected on the hypothesis that during the stance phase, the velocity of the sensor placed on the foot is zero [1]. This assumption allows to set to zero the estimated velocity at both the beginning and the end of the gait cycle. Despite the use of the latter hypothesis is crucial for the drift correction, to the authors’ knowledge, no quantitative validation of this hypothesis is available in the literature. This study aimed at determining the velocity profiles of various points of the foot during the stance phase of the gait cycle while walking at different speeds.
Materials and methods Twenty healthy subjects were enrolled in this study (mean height 168 ± 9 cm). Retro-reflective markers were placed on different positions of the right foot and tibia segments (Fig. 1). Subjects were asked to walk at three different self selected speeds (slow, normal and fast). For each speed, three trials were recorded. Markers trajectories were reconstructed using a stereo-photogrammetric system (six camera Vicon T20) whereas ground reaction forces
Fig. 1. Description of the marker locations.
were measured using a force platform (AMTI). Sampling frequency for position data was set at 120 frames per second. The beginning and the end of the stance phase were identified setting a threshold of 5 N for the vertical component of the ground reaction force. The 3-D position data were smoothed using cubic-splines [2]. Absolute marker velocities were computed by analytical differentiation of the splines. Mean gait speed was computed for each trial and normalized to the subject’s height. Based on the height-normalized gait speed, trials were reorganized in three subsets with a homogeneous number of trials (Slowh , Normh , Fasth ). Within each subset and for each marker location, the average of the absolute minimal velocities (v0 ) throughout the stance phase and its standard deviation, were computed. Results The foot point characterized by the lowest v0 value was the VM (Slowh : 4 ± 2 mm/s; Normh : 6 ± 10 mm/s; Fasth : 8 ± 9 mm/s). Among the various foot points, the highest v0 value was found at CUN2 (Slowh : 11 ± 6 mm/s; Normh : 16 ± 10 mm/s; Fasth : 27 ± 16 mm/s). As expected, the two tibia points had the highest v0 values. For all the analyzed foot points, the minimum velocity values increased with the height-normalised gait speed (Fig. 2). Discussion In the present study, the validity of the hypothesis that foot velocity can be assumed equal to zero sometimes during the stance phase has been tested. Results showed that none of the tested points on the foot had zero absolute velocity at any time during stance. Moreover, foot points absolute velocity values were highly variable, therefore an appropriate choice for the sensor position is crucial when a zero velocity technique is used for drift error reduction. Let vmin be the smallest velocity of a given foot point during stance phase and T, the duration of the gait cycle, if foot velocity anytime during stance is set to zero, the absolute error ed associ-
Fig. 2. Average values of the minimal velocity v0 for points described in Fig. 1.
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Abstracts / Gait & Posture 33S (2011) S1–S66
ated with the estimate of the total foot displacement throughout the gait cycle is ed = T · vmin . As an example, if the gait cycle duration is 1 s, the total foot displacement is 1.5 m and by setting vmin within one standard deviation of the mean v0 , ed would be about 1% of the total foot displacement if the accelerometer is located on VM, 3% if located on CUN2, and 7% if located on TIB.
Table 1 Activity classification. Individual training 5-Fold cross validation Leave-1-out validation
99.6% 99.7% 95.2%
References [1] Yun X, et al.IEEE international conference on robotics and automation. 2007. [2] Woltring HJ. Adv Eng Software 1986;8:104–13.
doi:10.1016/j.gaitpost.2010.10.030 O26 Automatic machine learning methods for analysis of signals from accelerometers: Classification of human activity and walking–running speed estimation A. Mannini, A.M. Sabatini Arts Lab, Scuola Superiore Sant’Anna, Pisa, Italy Introduction The development of wearable sensor systems based on inertial sensors, in combination with sophisticated computational methods (aimed at classification of human activity and estimation of gait parameters) is nowadays an important research topic in many labs. Their availability is expected to promote interesting applications in the field of functional assessment of daily living activities, and estimation of the energy expenditure incurred in their execution. Moreover, other applications can be envisaged for improving the human–robot interaction and in the development of pedestrian navigation systems [1]. In this work we present our approach for using data from a single tri-axis accelerometer in order to perform activity classification and estimation of walking (running) speed. Materials and methods For the purpose of this research, six healthy subjects (age: mean 27.3 ± std 2.0, in years) were recruited, after being informed about the nature and goals of the experimental procedures. One tri-axis accelerometer (Analog Devices ADXL325), with measuring range ± 5 g (g = 9.81 m/s2 ), was fixed on the thigh in a lateral position. Care was taken to orient one sensitivity axis in the vertical direction. Data were acquired at the sampling frequency fs = 250 Hz using the ActiNav system, currently under development in our lab [2]. The subjects performed 5 activities: sitting, standing, cycling (on an exercise bike), walking and running (on a treadmill). Walk and run trials lasted for 2 min each, with the speed varying in the interval between 1.2 and 9.6 km/h with 0.6 km/h steps. Each subject was asked to freely choose the speed for the transition from walking to running. The data from the first minute of activity were discarded from further analysis. The remaining data were windowed (250 points included within each window, with 50% overlap) and feature vectors were evaluated for each window. The selected features included the mean values and the Pearson’s correlation coefficients computed for each of the three measurement axis [3,4]. The activity type and the speed value were obtained by means of two SVM (Support Vector Machines) classifiers. The SVM classifiers were structured over two different classification levels. The first-level classifier was devised to perform the activity classification. When walking or running were detected, the second-level classifier assigned a specific speed class to the feature vectors under testing. A logistic regression classifier, cascaded to the second-level classifier, allowed us to obtain a point estimate of walking (running) speed by means of a Bayesian soft assignment rule. The validation procedure was conducted through three different approaches: a
Fig. 1. Speed estimation according to two different validation methods (mean ± std).
validation based on the training of classifiers for each single subject [3,4], N-fold cross validation and leave-1-out validation [5]. The ActiNav system was able to deliver the activity label and the point estimate of the walking (running) speed two times per second. Results and discussion The results in terms of activity classification accuracy are reported in Table 1. The classifiers tested on subjects never seen during training (leave-1-out method) are less accurate than classifiers trained and validated according to the other methods considered in this paper (Fig. 1). In the case of individual classifier calibration the root mean square of the error turns out to be ERMS = 0.4 km/h. The estimation accuracy of systems similar to ActiNav are comparable to ours. However, it must be pointed out that these systems are mostly limited to walking [1,3] or they may produce an indirect walking–running speed estimate by deriving it from an estimate of the walking–running distance [6]. Currently, our research activity concentrates on tricks to extend the range of measured speeds. In particular, we intend to deal with two problems: first, the critical transition from stand to walk (very low speed conditions); second, the problem of accelerometer saturation, which may arise at the highest tested speeds. References [1] Sabatini AM. Computational intelligence for movement sciences. IG Publishing; 2006. p. 70–100. [2] Bernini P, et al.Secondo Congresso Nazionale di Bioingegneria, Atti. Bologna: Patron Editore; 2010. [3] Aminian K, et al. IEEE Transactions on Instrumentation and Measurement 1995;44(3):743–6. [4] Mannini A, Sabatini AM. Sensors 2010;10:1154–75. [5] Altun K, et al. Pattern Recognition 2010;43(10);3605–20. [6] Song Y, et al. Proceedings of the IEEE EMBS 2007:3224–7.
doi:10.1016/j.gaitpost.2010.10.031
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Maximal Distance (MD) were quantified for ankle rotation angles calculated using cluster (i) and (ii). Results The lateral bar marker resulted to move with respect to the relevant shank reference in the order of the centimetre during walking, the motion was time-varying and particularly associate to the inertial phenomena at toe-off and heel contact. The RMSD(MD) between ankle rotation angles calculated with (cluster (i)) and without (cluster (ii)) the lateral bar was in the order of 1◦ (3◦ ) for Dorsi/Plantar-flexion and Prono/Supination and 9◦ (20◦ ) for Internal/External rotation (Fig. 1). The use of different anatomical references of the foot affected only ankle Internal/External rotation, with a maximal difference of 3◦ . Discussion The motion of the shank lateral bar resulted to significantly affect the ankle rotation angles quantified during motion. The effect of lateral bar motion particularly affects prono/supination, with errors up to the 20% of the range, and internal/external rotation, with errors up to 120% of the range. The preliminary results show that not only the alignment of the lateral bar is critical, but its inertial motion critically affects relevant joint kinematics. The acquisition of 20 + 20 subjects is currently being performed, aiming at the quantification of the propagation of lateral bar to relevant ankle kinematics and at the validation of a compensation method based on the proposed Davis integrated protocol [1].
References [1] Moretti, et al. Gait Posture 2009. [2] Stagni R, et al. Gait Posture 2005.
doi:10.1016/j.gaitpost.2010.10.029 O25 Foot velocity profiles during stance phase in gait A. Peruzzi 1 , A. Cereatti 1,2 , U. Della Croce 1 1
Department of Biomedical Sciences, University of Sassari, Sassari, Italy 2 Casa di Cura e Riabilitazione, Santa Maria Bambina, Oristano, Italy Introduction Space and time gait parameters can be estimated with wearable inertial units. Linear displacement information is typically obtained by double integrating accelerometer data over each gait cycle. However, usually a drift affects the resulting displacement signals and therefore its effects should be minimized. In the majority of studies using accelerometers, drift is corrected on the hypothesis that during the stance phase, the velocity of the sensor placed on the foot is zero [1]. This assumption allows to set to zero the estimated velocity at both the beginning and the end of the gait cycle. Despite the use of the latter hypothesis is crucial for the drift correction, to the authors’ knowledge, no quantitative validation of this hypothesis is available in the literature. This study aimed at determining the velocity profiles of various points of the foot during the stance phase of the gait cycle while walking at different speeds.
Materials and methods Twenty healthy subjects were enrolled in this study (mean height 168 ± 9 cm). Retro-reflective markers were placed on different positions of the right foot and tibia segments (Fig. 1). Subjects were asked to walk at three different self selected speeds (slow, normal and fast). For each speed, three trials were recorded. Markers trajectories were reconstructed using a stereo-photogrammetric system (six camera Vicon T20) whereas ground reaction forces
Fig. 1. Description of the marker locations.
were measured using a force platform (AMTI). Sampling frequency for position data was set at 120 frames per second. The beginning and the end of the stance phase were identified setting a threshold of 5 N for the vertical component of the ground reaction force. The 3-D position data were smoothed using cubic-splines [2]. Absolute marker velocities were computed by analytical differentiation of the splines. Mean gait speed was computed for each trial and normalized to the subject’s height. Based on the height-normalized gait speed, trials were reorganized in three subsets with a homogeneous number of trials (Slowh , Normh , Fasth ). Within each subset and for each marker location, the average of the absolute minimal velocities (v0 ) throughout the stance phase and its standard deviation, were computed. Results The foot point characterized by the lowest v0 value was the VM (Slowh : 4 ± 2 mm/s; Normh : 6 ± 10 mm/s; Fasth : 8 ± 9 mm/s). Among the various foot points, the highest v0 value was found at CUN2 (Slowh : 11 ± 6 mm/s; Normh : 16 ± 10 mm/s; Fasth : 27 ± 16 mm/s). As expected, the two tibia points had the highest v0 values. For all the analyzed foot points, the minimum velocity values increased with the height-normalised gait speed (Fig. 2). Discussion In the present study, the validity of the hypothesis that foot velocity can be assumed equal to zero sometimes during the stance phase has been tested. Results showed that none of the tested points on the foot had zero absolute velocity at any time during stance. Moreover, foot points absolute velocity values were highly variable, therefore an appropriate choice for the sensor position is crucial when a zero velocity technique is used for drift error reduction. Let vmin be the smallest velocity of a given foot point during stance phase and T, the duration of the gait cycle, if foot velocity anytime during stance is set to zero, the absolute error ed associ-
Fig. 2. Average values of the minimal velocity v0 for points described in Fig. 1.
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Abstracts / Gait & Posture 33S (2011) S1–S66
ated with the estimate of the total foot displacement throughout the gait cycle is ed = T · vmin . As an example, if the gait cycle duration is 1 s, the total foot displacement is 1.5 m and by setting vmin within one standard deviation of the mean v0 , ed would be about 1% of the total foot displacement if the accelerometer is located on VM, 3% if located on CUN2, and 7% if located on TIB.
Table 1 Activity classification. Individual training 5-Fold cross validation Leave-1-out validation
99.6% 99.7% 95.2%
References [1] Yun X, et al.IEEE international conference on robotics and automation. 2007. [2] Woltring HJ. Adv Eng Software 1986;8:104–13.
doi:10.1016/j.gaitpost.2010.10.030 O26 Automatic machine learning methods for analysis of signals from accelerometers: Classification of human activity and walking–running speed estimation A. Mannini, A.M. Sabatini Arts Lab, Scuola Superiore Sant’Anna, Pisa, Italy Introduction The development of wearable sensor systems based on inertial sensors, in combination with sophisticated computational methods (aimed at classification of human activity and estimation of gait parameters) is nowadays an important research topic in many labs. Their availability is expected to promote interesting applications in the field of functional assessment of daily living activities, and estimation of the energy expenditure incurred in their execution. Moreover, other applications can be envisaged for improving the human–robot interaction and in the development of pedestrian navigation systems [1]. In this work we present our approach for using data from a single tri-axis accelerometer in order to perform activity classification and estimation of walking (running) speed. Materials and methods For the purpose of this research, six healthy subjects (age: mean 27.3 ± std 2.0, in years) were recruited, after being informed about the nature and goals of the experimental procedures. One tri-axis accelerometer (Analog Devices ADXL325), with measuring range ± 5 g (g = 9.81 m/s2 ), was fixed on the thigh in a lateral position. Care was taken to orient one sensitivity axis in the vertical direction. Data were acquired at the sampling frequency fs = 250 Hz using the ActiNav system, currently under development in our lab [2]. The subjects performed 5 activities: sitting, standing, cycling (on an exercise bike), walking and running (on a treadmill). Walk and run trials lasted for 2 min each, with the speed varying in the interval between 1.2 and 9.6 km/h with 0.6 km/h steps. Each subject was asked to freely choose the speed for the transition from walking to running. The data from the first minute of activity were discarded from further analysis. The remaining data were windowed (250 points included within each window, with 50% overlap) and feature vectors were evaluated for each window. The selected features included the mean values and the Pearson’s correlation coefficients computed for each of the three measurement axis [3,4]. The activity type and the speed value were obtained by means of two SVM (Support Vector Machines) classifiers. The SVM classifiers were structured over two different classification levels. The first-level classifier was devised to perform the activity classification. When walking or running were detected, the second-level classifier assigned a specific speed class to the feature vectors under testing. A logistic regression classifier, cascaded to the second-level classifier, allowed us to obtain a point estimate of walking (running) speed by means of a Bayesian soft assignment rule. The validation procedure was conducted through three different approaches: a
Fig. 1. Speed estimation according to two different validation methods (mean ± std).
validation based on the training of classifiers for each single subject [3,4], N-fold cross validation and leave-1-out validation [5]. The ActiNav system was able to deliver the activity label and the point estimate of the walking (running) speed two times per second. Results and discussion The results in terms of activity classification accuracy are reported in Table 1. The classifiers tested on subjects never seen during training (leave-1-out method) are less accurate than classifiers trained and validated according to the other methods considered in this paper (Fig. 1). In the case of individual classifier calibration the root mean square of the error turns out to be ERMS = 0.4 km/h. The estimation accuracy of systems similar to ActiNav are comparable to ours. However, it must be pointed out that these systems are mostly limited to walking [1,3] or they may produce an indirect walking–running speed estimate by deriving it from an estimate of the walking–running distance [6]. Currently, our research activity concentrates on tricks to extend the range of measured speeds. In particular, we intend to deal with two problems: first, the critical transition from stand to walk (very low speed conditions); second, the problem of accelerometer saturation, which may arise at the highest tested speeds. References [1] Sabatini AM. Computational intelligence for movement sciences. IG Publishing; 2006. p. 70–100. [2] Bernini P, et al.Secondo Congresso Nazionale di Bioingegneria, Atti. Bologna: Patron Editore; 2010. [3] Aminian K, et al. IEEE Transactions on Instrumentation and Measurement 1995;44(3):743–6. [4] Mannini A, Sabatini AM. Sensors 2010;10:1154–75. [5] Altun K, et al. Pattern Recognition 2010;43(10);3605–20. [6] Song Y, et al. Proceedings of the IEEE EMBS 2007:3224–7.
doi:10.1016/j.gaitpost.2010.10.031