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Metabolic Energy Consumption in a Box-Lifting Task: A Parametric Study on the Assistive Torque Mohammad S. Shourijeh, Moonki Jung, and Michael Damsgaard Abstract— This study showcases effect of adding assistive torques to the hip, knee, and ankle joints in the sagittal plane on the total human body metabolic energy expenditure using the AnyBody musculoskeletal modeling system. To this goal, a box-lifting task was targeted and metabolic energy was computed for several cases including when each of the three joints was assisted at a time. Simulation results showed that the hip joint assistance affects the total metabolic energy consumption more than the knee and ankle joints. I. INTRODUCTION M energy consumption has been shown to be a serious criterion in human movements. Simulation studies have used this measure to provide information on optimality level of human motion [1]. Rate of VO2 consumption, which is deemed to be equivalent to overall rate of metabolic energy consumption, have been simulated in musculoskeletal dynamic simulations by means of simple [2] to complex [3] mathematical models. Additionally, metabolic energy has been used and speculated to be important in efficacy of exoskeletons. How an assistive device contributes to both the local joint-level and total human body has been a design objective for the neuro-rehabilitation engineers. Experimental measurement of VO2 consumption have been used for assessing performance of human body with and without wearing assistive devices. However, VO2 rate only reflects the total metabolic energy rate and is neither informative about effects at the local muscles or joints nor the contribution of the local elements to the total metabolic energy consumption. Therefore in design of assistive devices, if the question is to evaluate efficiency of the device at the joint level or in some applications, essentially which joint must be assisted most, computer simulations have the potential to play an important role. The goals of this study were 1) to exemplify use of musculoskeletal modeling for assistive wearables in a boxlifting task and 2) to determine which joint is the most crucial to be assisted within the desired movement. ETABOLIC This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 680754 (The MovAiD project, www.movaid.eu). M. S. Shourijeh is with the AnyBody Technology, Aalborg, Denmark (email: [email protected]). M. Jung is with the AnyBody Technology, Aalborg, Denmark ([email protected]). M. Damsgaard are with the AnyBody Technology, Aalborg, Denmark ([email protected]). II. METHODS AnyBody modeling software [4] has been used to simulate the box-lifting task. Metabolic energy rate model was a modified model of [3]. Ground reaction forces were predicted by the reaction force prediction tool in AnyBody to keep the model dynamic equilibrium; for more details, please see [5]. A. Musculoskeletal model (MSM) The full human body model in the AnyBody Managed Model Repository (AMMR v1.6.3) was used for this study; see Figure I. The model includes 63 segments, and 834 muscles. The model was 75.6 Kg and 1.80 m. Three-element Hill-type muscle model was chosen for the muscles, which consists of a contractile element (CE), a parallel elastic element (PE), and a serial elastic element (SE) [6]. B. Box-lifting movement The vertical kinematics of the box was prescribed by an assumed 6th order polynomial with zero velocity and acceleration for the initial and final points. Following that, the kinematics of the model was predicted using the center of mass driver in AnyBody while keeping the center of pressure within the model feet region in order to maintain model balance. C. Metabolic energy The model for the muscle metabolic power E was defined as E H W (1) which models the decrease rate in muscle internal energy. In equation (1), H is the heat rate generated by the muscle defined as the sum of basal, activation, maintenance, and shortening/lengthening heat rates. W is the external work done by the muscle and defined as (2) W fce (l ce , vce , a)vce where l ce and v ce are length and velocity of the contractile element (CE) in the muscle model, respectively; f ce is the CE force function and a is muscle activation. The total body metabolic energy Etot was defined as N tf i 1 t0 Etot Ei dt (2) where t 0 and t f are initial and final movement time, which were set to 0 s and 3 s, respectively; i refers to muscle index, and N is the total number of muscles in the model. D. Assistive torque The assistive torque was modeled as a rotational actuator, torque of which is proportional to the joint angle as Tassist K (3) where K (Nm/rad) is the pseudo-stiffness of the assistive device that can be negative, zero (no assist), or positive. In a parametric study, K was changed between [-300, 300] Nm/rad for each joint at a time that seemed to be a reasonably large range for this study. Fig. I. The musculoskeletal model in AnyBody applied for the boxlifting task. Ground reaction forces and moments are predicted by AnyBody. E. Box Interaction with the MSM A cube (0.4x0.4x0.4 m3) with a mass of 5 Kg, with Ixx=Iyy=Izz=0.768 Kgm2 was assumed for the box. The interaction between the hands and the two sides of the box was modeled as two weld joints. Box bottom was also assumed to move from 0.1 m to 0.6 m of the floor. III. RESULTS Total Metabolic Energy Rate (W) Figure II depicts the total metabolic power for the four cases in this study: unassisted, and optimally-assisted at hip (K=+100), knee (K=+50), and ankle (K=-100) joints. The total metabolic energy for these cases were 30.3, 25.6, 29.2, and 29.7 kJ, respectively. 400 Ankle -100 Knee +50 Hip +100 None 350 300 250 200 150 100 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 Time (s) Fig. II. Simulated total metabolic power of the box-lifting task for unassisted (black), optimally hip-assisted (green), knee-assisted (blue), and ankle-assisted (red) scenarios. IV. DISCUSSION All the three optimal assisted cases led to less metabolic energy required to perform the task. Out of the three joints, hip joint was found to be most influential on the design criterion (i.e. over 31% less metabolic energy). It must be noted that the hip flexion is negative in the model; therefore, a positive pseudo-stiffness for the hip joint will lead to a positive hip extensor torque, which is desired for assistance in the lifting phase. The optimal joint to assist can be dependent on the style of lifting (stooped versus squat). It must be pointed out that in the simulations of this study, the model used the hip more than the knee for the lifting task. The absolute angle variations for the hip and the knee joints were 1.58 rad and 0.524 rad, respectively, which showed that the lifting was more like a stooped style. It is speculated that if a human subject chooses to perform a squat style lifting, knee will be the optimal joint for assistance. The less is the metabolic energy required from the human, the more comfortable will be the human to perform the task; however, the required assisted torque from the external device might be constrained by the motor size, material properties, etc., which might lead to less assistive torque generation capability. Therefore, computer modeling of the assistive devices must be done with consideration of design and fabrication limitations in order to reach a realistic optimal design. V. CONCLUSIONS AND FUTURE WORK Effect of adding external assistive torques to the hip, knee, and ankle joints was studied using the AnyBody software. Total metabolic energy over the period of the box-lifting motion was computed and utilized as the design variable. As metabolic energy measure has been broadly used in studies for design optimization of the exoskeletons, musculoskeletal modeling environments such as AnyBody that can provide such information in detail at the joint and muscle levels can significantly contribute. Model kinematics was assumed to be the same between the four cases. However, as the lifting styles might be subjectively different, studying how a range of lifting styles from stooped to squat affects the metabolic energy consumption could be a future research study. REFERENCES [1] M. S. Shourijeh and J. McPhee, "Forward Dynamic Optimization of Human Gait Simulations: A Global Parameterization Approach," Journal of Computational and Nonlinear Dynamics, vol. 9, p. 031018, 2014. [2] M. Voigt, F. Bojsen-Møller, E. B. Simonsen, and P. Dyhre-Poulsen, "The influence of tendon Youngs modulus, dimensions and instantaneous moment arms on the efficiency of human movement," Journal of biomechanics, vol. 28, pp. 281-291, 1995. [3] B. R. Umberger, "Stance and swing phase costs in human walking," Journal of the Royal Society Interface, vol. 7, pp. 1329-1340, 2010. [4] M. Damsgaard, J. Rasmussen, S. T. Christensen, E. Surma, and M. De Zee, "Analysis of musculoskeletal systems in the AnyBody Modeling System," Simulation Modelling Practice and Theory, vol. 14, pp. 11001111, 2006. [5] R. Fluit, M. S. Andersen, S. Kolk, N. Verdonschot, and H. F. J. M. Koopman, "Prediction of ground reaction forces and moments during various activities of daily living," Journal of biomechanics, vol. 47, pp. 2321-2329, 2014. [6] F. E. Zajac, "Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control," Critical reviews in biomedical engineering, vol. 17, pp. 359-411, 1988.