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Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors
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GAIPOS-4467; No. of Pages 5 Gait & Posture xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors Tsolmonbaatar Khurelbaatar a,1, Kyungsoo Kim b,1, SuKyoung Lee c, Yoon Hyuk Kim a,* a
Department of Mechanical Engineering, Kyung Hee University, Yongin, Republic of Korea Department of Applied Mathematics, Kyung Hee University, Yongin, Republic of Korea c Department of Computer Science, Yonsei University, Seoul, Republic of Korea b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 17 September 2014 Received in revised form 21 January 2015 Accepted 16 April 2015
To analyze human motion such as daily activities or sports outside of the laboratory, wearable motion analysis systems have been recently developed. In this study, the joint forces and moments in wholebody joints during gait were evaluated using a wearable motion analysis system consisting of an inertial motion measurement system and an in-shoe pressure sensor system. The magnitudes of the joint forces and the moments in nine joints (cervical, thoracic, lumbar, right shoulder, right elbow, right wrist, right hip, right knee, and right ankle) during gait were calculated using the wearable system and the conventional system, respectively, based on a standard inverse dynamics analysis. The averaged magnitudes of the joint forces and moments of five subjects were compared between the wearable and conventional systems in terms of the Pearson’s correlation coefficient and the normalized root mean squared error to the maximum value from the conventional system. The results indicated that both the joint forces and joint moments in human whole body joints using wearable inertial motion sensors and in-shoe pressure sensors were feasible for normal motions with a low speed such as walking, although the lower extremity joints showed the strongest correlation and overall the joint moments were associated with relatively smaller correlation coefficients and larger normalized root mean squared errors in comparison with the joint forces. The portability and mobility of this wearable system can provide wide applicability in both clinical and sports motion analyses. ß 2015 Elsevier B.V. All rights reserved.
Keywords: Inertial motion sensor In-shoe pressure sensor Joint kinetics Gait Biomechanics
1. Introduction Human motion analyses, including joint kinematics and kinetics, have been conventionally performed using integrated systems of optical cameras to capture motion data, and force plates to measure ground reaction forces (GRFs). Although this conventional system has been utilized successfully in many research fields, such as sports and clinics, it is limited to the laboratory work space required by the camera and force plate system [1,2]. To analyze the human motion of daily activities or sports outside of the laboratory, wearable systems consisting of inertial motion sensors and in-shoe pressure sensors have been recently developed [1,3,4]. Their reliabilities were guaranteed by comparing these new systems with the conventional system in terms of the joint moments in three lower limb joints during walking [1], and
* Corresponding author. Tel.: +82 31 201 2028; fax: +82 31 202 8106. E-mail address: [email protected] (Y.H. Kim). 1 Both the authors contributed equally as first authors.
the joint angles, angular velocities, and moments of body parts during manual material handling tasks [3]. However, there was no study that included a kinetic analysis of a human whole body using the wearable systems. In this study, the joint forces and moments in whole-body joints during gait were evaluated using a wearable motion analysis system consisting of an inertial motion measurement system and an in-shoe pressure sensor system. These results were compared to those measured by the conventional motions capture system with force plates. 2. Methods Five healthy male subjects (age, 27 1 years; height, 171.4 3.9 cm; weight, 73.3 12.1 kg) participated in this study. This work was approved by our Institutional Review Board and the subjects gave informed consent to the work. The wearable motion capture system (wearable system) consisted of the MVN1 motion capture system (Xsens Technologies, Enschede, the Netherlands) with 17 inertial sensors and the Pedar-X1 (Novel GmbH, Munich, Germany) in-shoe pressure measurement system. The Pedar-X1 in-shoe pressure system
http://dx.doi.org/10.1016/j.gaitpost.2015.04.007 0966-6362/ß 2015 Elsevier B.V. All rights reserved.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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consisted of 85–99 sensors and its measurable pressure range was 15– 600 kPa with a resolution of 2.5 kPa. The conventional motion capture system (conventional system) was composed of the Hawk1 system (Motion Analysis, Santa Rosa, CA, USA) with 10 cameras and four MP40601 force plates (Bertec Corporation, Columbus, OH, USA). Seventeen inertial sensors, two in-shoe pressure sensors, and 37 passive photo-reflective markers were attached to the subject’s body (Fig. 1a and b). The inertial sensors were fixed to the subject’s head, trunk, pelvis, and upper and lower extremities, and the pressure sensors were secured to the subject’s bare feet. The passive photo-reflective markers were attached to anatomical landmarks that were pre-determined based on the existing literature [5,6]. To estimate the accuracy of the inertial sensor system, the orientation angle of a rigid body in a three-dimensional (3D) global X Y Z coordinate system was compared between the inertial sensor system and the optical motion capture system. Three optical markers and three inertial sensors were attached to the plastic rigid frame (Fig. 1c). Optical markers were attached to create a right angle between two vectors between three optical markers, and a local x y z coordinate system could then be defined. The inertial sensors were placed on the frame where the x0 and y0 axes of the local x0 y0 z0 coordinate system in the inertial sensor were parallel to the x and y axes of the local x y z coordinate system of optical markers, respectively. Then, the initial orientation angles of the x, y, and z axes of the optical markers were same as those of the x0 , y0 , and z0 axes of each inertial sensor with respect to the global coordinate system. The differences in the orientation angles of the x, y, and z axes of the optical markers and those of the x0 , y0 , and z0 axes of each inertial sensor were analyzed in terms of the root mean squared error (RMSE) when the frame moved as a single Zaxis rotation and as a free 3-axis rotation in the 3D space. Walking motion data were captured during a full gait cycle from a right heel strike to the next right heel strike with subjectpreferred speed using the wearable and conventional systems simultaneously. In the conventional system, the positions of 37 anatomical landmarks were recorded directly using photoreflective markers. Complete GRFs were also measured. In the wearable system, the orientation angles of each body segment, the
vertical component of GRF calculated by integrating pressure values, and the center of pressure (CoP) data were recorded. The positions of the anatomical landmarks were then calculated from the orientation angles of the body segments using the implemented software in the MVN1. The 3D GRF was then artificially restored based on a previous study [7] as the 3D GRF was directed from the CoP point to the center of gravity of each subject’s whole body as follows: ! GRFz ! GRF ¼ v
vz
!
where GRF is the GRF vector, GRFz is the vertical component of GRF, ! v represents an unit directional vector of the 3D GRF, and vz is the vertical component of the directional vector of GRF. A dynamic model of the human whole body, consisting of 16 segments (head, thorax, lumbar, pelvis, upper arms, forearms, hands, thighs, shanks, and feet) and 45 degrees of freedom linkages for 15 joints (cervical, thoracic, lumbar, shoulders, elbows, wrists, hips, knees, and ankles), was used as in our previous study [8]. Joint centers were defined based on the previous studies [9,10]. The reference frames of each segment were commonly set [5,6]. The joint angles were calculated as the Euler angles of the distal segment reference frame relative to the proximal segment reference frame. The magnitudes of the joint forces and moments were then calculated based on a standard inverse dynamics analysis using the motion data and GRF with MATLAB1 (MathWorksTM, Natick, MA, USA) [8,11]. Joint kinematic values, such as the angular velocity and acceleration of the ith segment, were calculated from motion capture data by the finite difference technique. The joint force and moment acting on the ith body segment were then calculated starting from the distal segment with the GRF and moment [8,11] using the following equilibrium equations: e e ~ ai ~ gÞ ~ F i1 F i ¼ mi ð~ e e ~ e ¼ Ii ~ ~ i ðIi v ~i Þ ~ M ai þ v li ~ F ~ li1 ~ F i
i
i1
e
~ M i1
where mi is the ith segmental mass, ~ ai is the translational acceleration vector of the ith segment’s center of gravity, ~ g is the
Fig. 1. (a) A subject equipped with inertial measurement system, in-shoe pressure system, and 37 photo-reflective markers, (b) the optical motion capture camera system and force plates, (c) a plastic rigid frame equipped with three optical markers and three inertial sensors.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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Fig. 2. Comparisons of predicted and measured GRFs.
gravitational vector, Ii is the moment of inertia around the center of ~ i and ~ gravity of the ith segment, v ai are the angular velocity and acceleration vector of the ith segment, ~ li is the distance from the segmental center of gravity of the ith segment to the distal joint
e ~ e are the jet joint force and moment acting center, and ~ F i1 and M i1 on the distal segment, called the (i 1)-th segment. Nine joints (cervical, thoracic, lumbar, right shoulder, right elbow, right wrist, right hip, right knee, and right ankle) were
Fig. 3. Comparisons of joint force magnitude between wearable and conventional systems.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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Fig. 4. Comparisons of joint moment magnitude between wearable and conventional systems.
investigated due to bilateral symmetry. One gait cycle was divided into 100 steps. The GRF as well as the averaged magnitudes of the joint forces and moments of five subjects at each step were compared between the wearable and conventional systems in terms of the Pearson’s correlation coefficient (r) and the normalized root mean squared error (NRMSE) to the maximum value from the conventional system using SPSS1 Statistics 21 (SPSS Inc., Chicago, IL, USA) and MATLAB1.
3. Results The orientation angles of the axes measured by the inertial sensor system were consistent with those measured by the optical system for both the single axis rotation and free rotation in the 3D space. For the single Z-axis rotation, the averaged RMSE standard deviation (SD) of three inertial sensors was 0.9 0.78. For the free 3-axis rotation in the 3D space, the averaged RMSE SD of three inertial sensors were 0.8 0.68 in the X-axis, 1.1 0.58 in the Y-axis, and 0.8 0.58 in the Zaxis, respectively. The predicted GRF from the wearable system showed a good agreement with the NRMSE of less than 9.1% and strong correlations of r 0.96 as compared to the conventional system, except for the anterior/posterior component of the GRF (NRMSE = 19.0% and r = 0.96) (Fig. 2). The angles between the predicted and measured GRFs from the wearable and conventional systems were under below 58 from 10% to 96% of the stance phase. The highest angle differences occurred in the starting (14.98) and ending (7.38) steps of the stance phase, while the magnitudes of the GRFs at those steps were only 4% of body weight (BW) in the starting step and 6% of BW in the ending step of the stance phase. The joint forces were strongly correlated between the wearable system and the conventional system with small NRMSEs in all joints (r = 0.71–0.99; NRMSE = 5.5– 6.2%) (Fig. 3). The lower extremity showed significantly higher correlation (r = 0.99) than the trunk (r = 0.80–0.81) and the upper extremity (r = 0.71–0.79). The joint
moments showed good agreement with strong correlations (r = 0.70–0.98) in all joints except the shoulder (r = 0.49) (Fig. 4). The NRMSEs of the joint moments were acceptable (8.0–16.9%) in all joints except the shoulder (24.1%) and elbow (35.2%). The lower extremity revealed the highest correlation values with an average correlation coefficient of 0.97 and an average NRMSE of 10.2%, while the upper extremity had the lowest values with an average correlation coefficient of 0.64 and an average NRMSE of 24.1%.
4. Discussion To evaluate the accuracy of the inertial sensor, the differences in orientation angles of the local coordinate systems between the optical sensor system and the inertial sensor system were investigated. The RMSEs for all axes were less than 1.18, both in the single axis rotation and the free 3-axis rotation. These results showed indirectly that the inertial sensor was reliable in measuring the inter-segmental angle, which was fundamental information required to calculate the kinematics. The overall comparison of the 3D GRFs between the predictions from the in-shoe pressure system and the measurements from the force plate showed good agreement with mean r = 0.97 and NRMSE = 10.3%. Forner-Cordero et al. [12] predicted the 3D GRF from the in-shoe pressure system with NRMSEs of 3.3% in the anterior/posterior, 13.3% in the medial/lateral, and 3.9% in the vertical components of GRF, while the corresponding NRMSEs in this study were 19.0%, 9.1% and 2.7%. These results indicated that the medial/lateral and vertical components of the GRF were consistent, although the anterior/posterior component of the GRF was relatively different. This difference might be caused by
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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relatively high differences at the starting and ending steps of the stance phase, where the direction angle difference was also the highest. This result could be derived from the assumption that a double stance phase was not considered in the starting and ending steps of the stance phase. However, the influence of this difference might be small, because these high differences occurred for a short duration with small magnitudes of GRFs (4% of BW in the starting step and 6% of BW in the ending step). The lower extremity joints (hip, knee, and ankle) showed the strongest correlations between the wearable and the conventional systems with average correlation coefficients and NRMSEs of 0.99 and 5.7% in joint force and 0.97 and 10.2% in joint moment, respectively. The trunk joints (cervical, thoracic, and lumbar) and the upper extremity joints (shoulder, elbow, and wrist) had strong or acceptable correlations. The correlation coefficients and NRMSEs in the lower extremity joint moments were consistent with a previous study [1] at 0.95–0.99 and 3.5–7.1% in the ankle, 0.96–0.98 and 4.1–13.4% in the knee, and 0.81–0.91 and 15.3– 21.0% in the hip, respectively. These superior results in the lower extremity could be from the relatively simple and wide-ranged motion. In contrast, the highest differences were derived in the upper extremity, where the average correlation coefficients and NRMSEs were 0.75 and 6.0% in joint force and 0.64 and 24.1% in joint moment, respectively, although they were still acceptable. This finding might have been caused by the combined and small range of motions in the upper extremity during gait. In addition, the overall joint moments resulted in relatively smaller correlation coefficients and larger NRMSEs in comparison with the joint forces. Since each joint moment was calculated from the applied force and its moment arm, the differences in forces and moment arms might have accumulated to cause the differences in the joint moments. Since the wearable system can be applicable in various environments, the output of the wearable system can be altered by magnetic disturbance from the environment. Thus, the wearable system is restricted in spaces with strong magnetic disturbances such as electric motors, magnetic resonance image (MRI) scans, and strong electric circuits. If inertial sensors need to be used in an environment with a magnetic disturbance, a specialized calibration procedure known as a hard and soft iron calibration should be performed. In addition, there was a lack of variety in activities. Since this study tested only walking motion with five subjects, it is necessary to examine various high-speed and weight-bearing activities in a future study. In conclusion, the measurements of both the joint forces and joint moments in human whole body joints using wearable inertial motion sensors
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and in-shoe pressure sensors were feasible for normal motions with a low speed such as walking, especially in the lower extremity joints. The portability and mobility of this wearable system can provide wide applicability in both clinical and sports motion analyses. Acknowledgement This research was supported by Sports Scientification of Convergent R&D Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT & Future Planning (NRF-2014M3C1B1033320).
Conflict of interest The authors declare that there are no conflicts of interest.
References [1] Liu T, Inoue Y, Shibata K, Shiojima K, Han MM. Triaxial joint moment estimation using a wearable three-dimensional gait analysis system. Measurement 2014;47:125–9. [2] Karaulova IA, Hall PM, Marshall AD. Tracking people in three dimensions using a hierarchical model of dynamics. Image Vision Comput 2002;20:691–700. [3] Kim S, Nussbaum MA. An evaluation of classification algorithms for manual material handling tasks based on data obtained using wearable technologies. Ergonomics 2014;57:1040–51. [4] Rouhani H, Favre J, Crevoisier X, Aminian K. A wearable system for multisegment foot kinetics measurement. J Biomech 2014;47:1704–11. [5] Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D, et al. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion-part I: ankle, hip, and spine. J Biomech 2002;35:543–8. [6] Wu G, van der Helm FC, Veeger HE, Makhsous M, Van Roy P, Anglin C, et al. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion – part II: shoulder, elbow, wrist and hand. J Biomech 2005;38:981–92. [7] Vukobratovic´ M, Borovac B. Zero-moment point – thirty five years of its life. Int J Humanoid Robot 2004;1:157–73. [8] Nha KW, Dorj A, Feng J, Shin JH, Kim JI, Kwon JH, et al. Application of computational lower extremity model to investigate different muscle activities and joint force patterns in knee osteoarthritis patients during walking. Comput Math Methods Med 2013;2013:314280. [9] Bell AL, Pederson DR, Brand RA. Prediction of hip joint center location from external landmarks. Hum Mov Sci 1989;8:3–16. [10] de Leva P. Joint center longitudinal positions computed from a selected subset of Chandler’s data. J Biomech 1996;29:1231–3. [11] Ren L, Jones RK, Howard D. Whole body inverse dynamics over a complete gait cycle based only on measured kinematics. J Biomech 2008;41:2750–9. [12] Forner Cordero A, Koopman HJ, van der Helm FC. Use of pressure insoles to calculate the complete ground reaction forces. J Biomech 2004;37:1427–32.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
GAIPOS-4467; No. of Pages 5 Gait & Posture xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors Tsolmonbaatar Khurelbaatar a,1, Kyungsoo Kim b,1, SuKyoung Lee c, Yoon Hyuk Kim a,* a
Department of Mechanical Engineering, Kyung Hee University, Yongin, Republic of Korea Department of Applied Mathematics, Kyung Hee University, Yongin, Republic of Korea c Department of Computer Science, Yonsei University, Seoul, Republic of Korea b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 17 September 2014 Received in revised form 21 January 2015 Accepted 16 April 2015
To analyze human motion such as daily activities or sports outside of the laboratory, wearable motion analysis systems have been recently developed. In this study, the joint forces and moments in wholebody joints during gait were evaluated using a wearable motion analysis system consisting of an inertial motion measurement system and an in-shoe pressure sensor system. The magnitudes of the joint forces and the moments in nine joints (cervical, thoracic, lumbar, right shoulder, right elbow, right wrist, right hip, right knee, and right ankle) during gait were calculated using the wearable system and the conventional system, respectively, based on a standard inverse dynamics analysis. The averaged magnitudes of the joint forces and moments of five subjects were compared between the wearable and conventional systems in terms of the Pearson’s correlation coefficient and the normalized root mean squared error to the maximum value from the conventional system. The results indicated that both the joint forces and joint moments in human whole body joints using wearable inertial motion sensors and in-shoe pressure sensors were feasible for normal motions with a low speed such as walking, although the lower extremity joints showed the strongest correlation and overall the joint moments were associated with relatively smaller correlation coefficients and larger normalized root mean squared errors in comparison with the joint forces. The portability and mobility of this wearable system can provide wide applicability in both clinical and sports motion analyses. ß 2015 Elsevier B.V. All rights reserved.
Keywords: Inertial motion sensor In-shoe pressure sensor Joint kinetics Gait Biomechanics
1. Introduction Human motion analyses, including joint kinematics and kinetics, have been conventionally performed using integrated systems of optical cameras to capture motion data, and force plates to measure ground reaction forces (GRFs). Although this conventional system has been utilized successfully in many research fields, such as sports and clinics, it is limited to the laboratory work space required by the camera and force plate system [1,2]. To analyze the human motion of daily activities or sports outside of the laboratory, wearable systems consisting of inertial motion sensors and in-shoe pressure sensors have been recently developed [1,3,4]. Their reliabilities were guaranteed by comparing these new systems with the conventional system in terms of the joint moments in three lower limb joints during walking [1], and
* Corresponding author. Tel.: +82 31 201 2028; fax: +82 31 202 8106. E-mail address: [email protected] (Y.H. Kim). 1 Both the authors contributed equally as first authors.
the joint angles, angular velocities, and moments of body parts during manual material handling tasks [3]. However, there was no study that included a kinetic analysis of a human whole body using the wearable systems. In this study, the joint forces and moments in whole-body joints during gait were evaluated using a wearable motion analysis system consisting of an inertial motion measurement system and an in-shoe pressure sensor system. These results were compared to those measured by the conventional motions capture system with force plates. 2. Methods Five healthy male subjects (age, 27 1 years; height, 171.4 3.9 cm; weight, 73.3 12.1 kg) participated in this study. This work was approved by our Institutional Review Board and the subjects gave informed consent to the work. The wearable motion capture system (wearable system) consisted of the MVN1 motion capture system (Xsens Technologies, Enschede, the Netherlands) with 17 inertial sensors and the Pedar-X1 (Novel GmbH, Munich, Germany) in-shoe pressure measurement system. The Pedar-X1 in-shoe pressure system
http://dx.doi.org/10.1016/j.gaitpost.2015.04.007 0966-6362/ß 2015 Elsevier B.V. All rights reserved.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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consisted of 85–99 sensors and its measurable pressure range was 15– 600 kPa with a resolution of 2.5 kPa. The conventional motion capture system (conventional system) was composed of the Hawk1 system (Motion Analysis, Santa Rosa, CA, USA) with 10 cameras and four MP40601 force plates (Bertec Corporation, Columbus, OH, USA). Seventeen inertial sensors, two in-shoe pressure sensors, and 37 passive photo-reflective markers were attached to the subject’s body (Fig. 1a and b). The inertial sensors were fixed to the subject’s head, trunk, pelvis, and upper and lower extremities, and the pressure sensors were secured to the subject’s bare feet. The passive photo-reflective markers were attached to anatomical landmarks that were pre-determined based on the existing literature [5,6]. To estimate the accuracy of the inertial sensor system, the orientation angle of a rigid body in a three-dimensional (3D) global X Y Z coordinate system was compared between the inertial sensor system and the optical motion capture system. Three optical markers and three inertial sensors were attached to the plastic rigid frame (Fig. 1c). Optical markers were attached to create a right angle between two vectors between three optical markers, and a local x y z coordinate system could then be defined. The inertial sensors were placed on the frame where the x0 and y0 axes of the local x0 y0 z0 coordinate system in the inertial sensor were parallel to the x and y axes of the local x y z coordinate system of optical markers, respectively. Then, the initial orientation angles of the x, y, and z axes of the optical markers were same as those of the x0 , y0 , and z0 axes of each inertial sensor with respect to the global coordinate system. The differences in the orientation angles of the x, y, and z axes of the optical markers and those of the x0 , y0 , and z0 axes of each inertial sensor were analyzed in terms of the root mean squared error (RMSE) when the frame moved as a single Zaxis rotation and as a free 3-axis rotation in the 3D space. Walking motion data were captured during a full gait cycle from a right heel strike to the next right heel strike with subjectpreferred speed using the wearable and conventional systems simultaneously. In the conventional system, the positions of 37 anatomical landmarks were recorded directly using photoreflective markers. Complete GRFs were also measured. In the wearable system, the orientation angles of each body segment, the
vertical component of GRF calculated by integrating pressure values, and the center of pressure (CoP) data were recorded. The positions of the anatomical landmarks were then calculated from the orientation angles of the body segments using the implemented software in the MVN1. The 3D GRF was then artificially restored based on a previous study [7] as the 3D GRF was directed from the CoP point to the center of gravity of each subject’s whole body as follows: ! GRFz ! GRF ¼ v
vz
!
where GRF is the GRF vector, GRFz is the vertical component of GRF, ! v represents an unit directional vector of the 3D GRF, and vz is the vertical component of the directional vector of GRF. A dynamic model of the human whole body, consisting of 16 segments (head, thorax, lumbar, pelvis, upper arms, forearms, hands, thighs, shanks, and feet) and 45 degrees of freedom linkages for 15 joints (cervical, thoracic, lumbar, shoulders, elbows, wrists, hips, knees, and ankles), was used as in our previous study [8]. Joint centers were defined based on the previous studies [9,10]. The reference frames of each segment were commonly set [5,6]. The joint angles were calculated as the Euler angles of the distal segment reference frame relative to the proximal segment reference frame. The magnitudes of the joint forces and moments were then calculated based on a standard inverse dynamics analysis using the motion data and GRF with MATLAB1 (MathWorksTM, Natick, MA, USA) [8,11]. Joint kinematic values, such as the angular velocity and acceleration of the ith segment, were calculated from motion capture data by the finite difference technique. The joint force and moment acting on the ith body segment were then calculated starting from the distal segment with the GRF and moment [8,11] using the following equilibrium equations: e e ~ ai ~ gÞ ~ F i1 F i ¼ mi ð~ e e ~ e ¼ Ii ~ ~ i ðIi v ~i Þ ~ M ai þ v li ~ F ~ li1 ~ F i
i
i1
e
~ M i1
where mi is the ith segmental mass, ~ ai is the translational acceleration vector of the ith segment’s center of gravity, ~ g is the
Fig. 1. (a) A subject equipped with inertial measurement system, in-shoe pressure system, and 37 photo-reflective markers, (b) the optical motion capture camera system and force plates, (c) a plastic rigid frame equipped with three optical markers and three inertial sensors.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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Fig. 2. Comparisons of predicted and measured GRFs.
gravitational vector, Ii is the moment of inertia around the center of ~ i and ~ gravity of the ith segment, v ai are the angular velocity and acceleration vector of the ith segment, ~ li is the distance from the segmental center of gravity of the ith segment to the distal joint
e ~ e are the jet joint force and moment acting center, and ~ F i1 and M i1 on the distal segment, called the (i 1)-th segment. Nine joints (cervical, thoracic, lumbar, right shoulder, right elbow, right wrist, right hip, right knee, and right ankle) were
Fig. 3. Comparisons of joint force magnitude between wearable and conventional systems.
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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Fig. 4. Comparisons of joint moment magnitude between wearable and conventional systems.
investigated due to bilateral symmetry. One gait cycle was divided into 100 steps. The GRF as well as the averaged magnitudes of the joint forces and moments of five subjects at each step were compared between the wearable and conventional systems in terms of the Pearson’s correlation coefficient (r) and the normalized root mean squared error (NRMSE) to the maximum value from the conventional system using SPSS1 Statistics 21 (SPSS Inc., Chicago, IL, USA) and MATLAB1.
3. Results The orientation angles of the axes measured by the inertial sensor system were consistent with those measured by the optical system for both the single axis rotation and free rotation in the 3D space. For the single Z-axis rotation, the averaged RMSE standard deviation (SD) of three inertial sensors was 0.9 0.78. For the free 3-axis rotation in the 3D space, the averaged RMSE SD of three inertial sensors were 0.8 0.68 in the X-axis, 1.1 0.58 in the Y-axis, and 0.8 0.58 in the Zaxis, respectively. The predicted GRF from the wearable system showed a good agreement with the NRMSE of less than 9.1% and strong correlations of r 0.96 as compared to the conventional system, except for the anterior/posterior component of the GRF (NRMSE = 19.0% and r = 0.96) (Fig. 2). The angles between the predicted and measured GRFs from the wearable and conventional systems were under below 58 from 10% to 96% of the stance phase. The highest angle differences occurred in the starting (14.98) and ending (7.38) steps of the stance phase, while the magnitudes of the GRFs at those steps were only 4% of body weight (BW) in the starting step and 6% of BW in the ending step of the stance phase. The joint forces were strongly correlated between the wearable system and the conventional system with small NRMSEs in all joints (r = 0.71–0.99; NRMSE = 5.5– 6.2%) (Fig. 3). The lower extremity showed significantly higher correlation (r = 0.99) than the trunk (r = 0.80–0.81) and the upper extremity (r = 0.71–0.79). The joint
moments showed good agreement with strong correlations (r = 0.70–0.98) in all joints except the shoulder (r = 0.49) (Fig. 4). The NRMSEs of the joint moments were acceptable (8.0–16.9%) in all joints except the shoulder (24.1%) and elbow (35.2%). The lower extremity revealed the highest correlation values with an average correlation coefficient of 0.97 and an average NRMSE of 10.2%, while the upper extremity had the lowest values with an average correlation coefficient of 0.64 and an average NRMSE of 24.1%.
4. Discussion To evaluate the accuracy of the inertial sensor, the differences in orientation angles of the local coordinate systems between the optical sensor system and the inertial sensor system were investigated. The RMSEs for all axes were less than 1.18, both in the single axis rotation and the free 3-axis rotation. These results showed indirectly that the inertial sensor was reliable in measuring the inter-segmental angle, which was fundamental information required to calculate the kinematics. The overall comparison of the 3D GRFs between the predictions from the in-shoe pressure system and the measurements from the force plate showed good agreement with mean r = 0.97 and NRMSE = 10.3%. Forner-Cordero et al. [12] predicted the 3D GRF from the in-shoe pressure system with NRMSEs of 3.3% in the anterior/posterior, 13.3% in the medial/lateral, and 3.9% in the vertical components of GRF, while the corresponding NRMSEs in this study were 19.0%, 9.1% and 2.7%. These results indicated that the medial/lateral and vertical components of the GRF were consistent, although the anterior/posterior component of the GRF was relatively different. This difference might be caused by
Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007
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relatively high differences at the starting and ending steps of the stance phase, where the direction angle difference was also the highest. This result could be derived from the assumption that a double stance phase was not considered in the starting and ending steps of the stance phase. However, the influence of this difference might be small, because these high differences occurred for a short duration with small magnitudes of GRFs (4% of BW in the starting step and 6% of BW in the ending step). The lower extremity joints (hip, knee, and ankle) showed the strongest correlations between the wearable and the conventional systems with average correlation coefficients and NRMSEs of 0.99 and 5.7% in joint force and 0.97 and 10.2% in joint moment, respectively. The trunk joints (cervical, thoracic, and lumbar) and the upper extremity joints (shoulder, elbow, and wrist) had strong or acceptable correlations. The correlation coefficients and NRMSEs in the lower extremity joint moments were consistent with a previous study [1] at 0.95–0.99 and 3.5–7.1% in the ankle, 0.96–0.98 and 4.1–13.4% in the knee, and 0.81–0.91 and 15.3– 21.0% in the hip, respectively. These superior results in the lower extremity could be from the relatively simple and wide-ranged motion. In contrast, the highest differences were derived in the upper extremity, where the average correlation coefficients and NRMSEs were 0.75 and 6.0% in joint force and 0.64 and 24.1% in joint moment, respectively, although they were still acceptable. This finding might have been caused by the combined and small range of motions in the upper extremity during gait. In addition, the overall joint moments resulted in relatively smaller correlation coefficients and larger NRMSEs in comparison with the joint forces. Since each joint moment was calculated from the applied force and its moment arm, the differences in forces and moment arms might have accumulated to cause the differences in the joint moments. Since the wearable system can be applicable in various environments, the output of the wearable system can be altered by magnetic disturbance from the environment. Thus, the wearable system is restricted in spaces with strong magnetic disturbances such as electric motors, magnetic resonance image (MRI) scans, and strong electric circuits. If inertial sensors need to be used in an environment with a magnetic disturbance, a specialized calibration procedure known as a hard and soft iron calibration should be performed. In addition, there was a lack of variety in activities. Since this study tested only walking motion with five subjects, it is necessary to examine various high-speed and weight-bearing activities in a future study. In conclusion, the measurements of both the joint forces and joint moments in human whole body joints using wearable inertial motion sensors
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and in-shoe pressure sensors were feasible for normal motions with a low speed such as walking, especially in the lower extremity joints. The portability and mobility of this wearable system can provide wide applicability in both clinical and sports motion analyses. Acknowledgement This research was supported by Sports Scientification of Convergent R&D Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT & Future Planning (NRF-2014M3C1B1033320).
Conflict of interest The authors declare that there are no conflicts of interest.
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Please cite this article in press as: Khurelbaatar T, et al. Consistent accuracy in whole-body joint kinetics during gait using wearable inertial motion sensors and in-shoe pressure sensors. Gait Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.007