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Simulative Analysis of Joint Loading During Leg Press Exercise for Control Applications
9th IFAC Symposium on Biological and Medical Systems 9th on Biological and Medical Systems 9th IFAC Symposium on Biological and Aug.IFAC 31 - Symposium Sept. 2, 2015. Germany 9th IFAC onBerlin, Biological and Medical Medical Systems Systems Aug. 31 -- Symposium Sept. 2, 2015. Berlin, Germany Available online at www.sciencedirect.com Aug. 31 Sept. 2, 2015. Berlin, Germany Aug. 31 - Sept. 2, 2015. Berlin, Germany
ScienceDirect IFAC-PapersOnLine 48-20 (2015) 435–440
Simulative Simulative Simulative Simulative During Leg During During Leg During Leg Leg
Analysis of Joint Loading Analysis of Joint Loading Analysis of Joint Loading Analysis of Joint Loading Press Exercise for Control Press Exercise for Control Press Exercise for Control Press Exercise for Control Applications Applications Applications Applications
Melanie Kolditz ∗∗ Thivaharan Albin ∗∗ Dirk Abel ∗∗ ∗ Thivaharan ∗ Dirk Abel Melanie Kolditz Albin ∗∗ ∗∗ ∗ ∗ Thivaharan ∗ Melanie Kolditz Albin Dirk Alessandro Fasse Br¨ u∗ggemann Melanie Kolditz Thivaharan Albin Dirk Abel Abel ∗∗ Gert-Peter ∗∗ ∗∗ Gert-Peter ∗∗ ∗∗ Alessandro Fasse Br¨ u ggemann ∗∗ ∗∗ Alessandro Fasse Gert-Peter Br¨ u ggemann Kirsten Albracht ∗∗ Alessandro Fasse Gert-Peter Br¨ u ggemann Kirsten Albracht ∗∗ Kirsten Kirsten Albracht Albracht ∗∗ ∗ ∗ Institute of Automatic Control, RWTH Aachen University, Germany ∗ Institute of Automatic Control, RWTH Aachen University, Germany ∗ Institute of Automatic Control, (e-mail: [email protected]) Institute of Automatic Control, RWTH RWTH Aachen Aachen University, University, Germany Germany (e-mail: [email protected]) ∗∗ (e-mail: [email protected]) Institute of Biomechanics and Orthopaedics, German Sport (e-mail: [email protected]) ∗∗ ∗∗ Institute of Biomechanics and Orthopaedics, German Sport ∗∗ InstituteCologne, of Orthopaedics, German University Germanyand (e-mail: [email protected]) InstituteCologne, of Biomechanics Biomechanics and Orthopaedics, German Sport Sport University Germany (e-mail: [email protected]) University Cologne, Germany (e-mail: [email protected]) University Cologne, Germany (e-mail: [email protected]) Abstract: Leg extension is a multi-articular movement allowing flexibility of muscular actiAbstract: Leg extension is a multi-articular movement allowing flexibility of muscular actiAbstract: Leg is movement allowing flexibility of activation and control. Therefore, joint loadings during leg press exercise can only be estimated Abstract: Leg extension extension is a a multi-articular multi-articular movement allowing flexibility of muscular muscular activation and control. Therefore, joint loadings during leg press exercise can only be estimated vation and control. Therefore, joint loadings during leg press exercise can only be estimated using the whole reaction force vector together with the leg posture. A dynamic model of the vation and control. Therefore, joint loadings during leg press exercise can only be estimated using the the whole whole reaction reaction force force vector together with the leg posture. A dynamic model of the using together with the leg posture. A dynamic of the musculoskeletal system asforce wellvector as experimental data from a diagonal leg pressmodel are used to using the whole reaction vector together with the leg posture. A dynamic model of the musculoskeletal system as well as experimental data from a diagonal leg press are used to musculoskeletal system well as experimental data from diagonal leg press are used to investigate external kneeas joint loadings and the influence of aadifferent orientations of the foot musculoskeletal system as well as experimental data from diagonal leg press are used to investigate external knee joint loadings and the influence of different orientations of the foot investigate external knee joint loadings and the influence of different orientations of the foot plate. Varying orientation in sagittal plane affects ankle, knee and hip loadings by changing the investigate external knee joint loadings and the influence of different orientations of the foot plate. Varying orientation in sagittal plane affects ankle, knee and hip loadings by changing the plate. Varying in plane and loadings the leg posture andorientation the direction of the resulting force ankle, vector.knee Different orientations in changing frontal plane plate. Varying in sagittal sagittal plane affects affects and hip hip loadings by by the leg posture posture andorientation the direction direction of the the resulting resulting force ankle, vector.knee Different orientations in changing frontal plane plane leg and the of force vector. Different orientations in frontal move the center of pressure ofofthe force vector across the Different foot and thus change in knee adduction leg posture and the direction the resulting force vector. orientations frontal plane move the center of pressure of the force vector across the foot and thus change knee adduction move the of the vector across the and thus change knee and abduction Theof in this paper indicate, that high forces, which areadduction required move the center centermoments. of pressure pressure ofresults the force force vector across the foot foot and thus change knee adduction and abduction moments. The results in this paper indicate, that high forces, which are required and abduction moments. The results in this paper indicate, that high forces, which are required for an effective training, can be controlled using the foot orientation as manipulated variable. and abduction moments. The results in this paper indicate, that high forces, which are required for an effective training, can be controlled using the foot orientation as manipulated variable. for an effective training, can be controlled using the foot orientation as manipulated variable. Thereby, unphysiological loadings and training-induced damage can be avoided. for an effective training, can be controlled using the foot orientation as manipulated variable. Thereby, unphysiological unphysiological loadings loadings and and training-induced training-induced damage damage can can be be avoided. avoided. Thereby, Thereby, unphysiological training-induced be avoided. © 2015, IFAC (International loadings Federationand of Automatic Control) damage Hosting bycan Elsevier Ltd. All rights reserved. Keywords: Dynamic model, Musculoskeletal model, Inverse dynamic problem, Manipulated Keywords: Dynamic Dynamic model, model, Musculoskeletal Musculoskeletal model, model, Inverse dynamic Keywords: dynamic problem, problem, Manipulated Manipulated variables, Robotics, Keywords: Dynamic Sensor model, system. Musculoskeletal model, Inverse Inverse dynamic problem, Manipulated variables, Robotics, Robotics, Sensor system. variables, Sensor system. variables, Robotics, Sensor system. 1. INTRODUCTION 1. INTRODUCTION INTRODUCTION 1. 1. INTRODUCTION Sarcopenia as well as loss of muscle strength and power are Sarcopenia as as well well as as loss loss of muscle muscle strength strength and and power power are are Sarcopenia important factors active independent aging Sarcopenia as well compromising as loss of of muscle strength and power are important factors factors compromising active independent aging important compromising active independent aging (Narici andfactors Maffulli (2010), Mian et al. (2007)). These important compromising active independent aging (Narici and and Maffulli Maffulli (2010), (2010), Mian Mian et et al. al. (2007)). (2007)). These These (Narici factors are only associated withet an impaired motor (Narici and not Maffulli (2010), Mian al. impaired (2007)). motor These factors are not only associated with an factors are not only associated with an impaired motor performance during daily activities but also with an infactors are not only associated with an impaired motor performance during during daily daily activities activities but but also also with with an an ininperformance creased risk for the development of chronic agewith and wealth performance during daily activities but also an increased risk risk for for the the development development of of chronic chronic age age and and wealth wealth creased related diseases. Participating in of regular physical activity, creased risk for the development chronic age and wealth related diseases. diseases. Participating Participating in in regular regular physical physical activity, activity, related both aerobic andParticipating strength exercises, canphysical slow down the related diseases. in regular activity, both aerobic and strength exercises, can slow down the both aerobic and strength exercises, can slow down the physiological deconditioning associated with aging, and both aerobic and strength exercises, can slow down the physiological deconditioning deconditioning associated associated with with aging, aging, and and physiological prevent or decelerate the development and progression of physiological deconditioning associated with aging, and prevent or or decelerate decelerate the the development development and and progression progression of of prevent chronic disease. Muscular-skeletal disorders (MSD) are one prevent or decelerate the development and progression of chronic disease. Muscular-skeletal disorders (MSD) are one chronic disease. Muscular-skeletal disorders (MSD) are one of the most common cause of severe long-term pain and chronic disease. Muscular-skeletal disorders (MSD) are one of the the most most common common cause cause of of severe severe long-term long-term pain pain and and of physical disability (Woolf Pfleger (2003)). pain In Gerof the most common cause and of severe long-term and physical disability (Woolf and Pfleger (2003)). In In GerGerphysical disability (Woolf and Pfleger (2003)). many, 36.2% of the (Woolf patientsand treated 2012(2003)). in inpatient rephysical disability Pfleger In Germany, 36.2% 36.2% of of the the patients patients treated treated 2012 2012 in in inpatient inpatient reremany, habilitation centres, i.e. a total of 596000 patients, suffered many, 36.2% of the patients treated 2012 in inpatient rehabilitation centres, i.e. a total of 596000 patients, suffered habilitation centres, i.e. aaand total of 596000 patients, suffered from MSD, such as knee hip arthrosis or osteoporosis habilitation centres, i.e. total of 596000 patients, suffered from MSD, MSD, such such as as knee knee and hip hip arthrosis arthrosis or osteoporosis osteoporosis from (Statistisches Bundesamt (2013)). from MSD, such as knee and and hip arthrosis or or osteoporosis (Statistisches Bundesamt (2013)). (Statistisches Bundesamt (2013)). Resistance training as a therapy traumatic sports in(Statistisches Bundesamt (2013)).for Resistance training training as aa therapy therapy for traumatic traumatic sports sports ininResistance for juries (e.g. training rupture as of athe anterior cruciate ligament) is Resistance as therapy for traumatic sports injuries (e.g. rupture of the anterior cruciate ligament) is juries (e.g. rupture of the anterior cruciate ligament) is already widely established. The use of training to increase juries rupture of the The anterior cruciate is already(e.g. widely established. use of of trainingligament) to increase increase already widely established. The use training to or reduce the loss of muscle The strength fortraining osteoarthritic and already widely established. use of to increase or reduce the loss of muscle strength for osteoarthritic and or reduce the of strength for and rheumatic patients is now also being seen as increasor the loss loss of muscle muscle strength for osteoarthritic osteoarthritic and or reduce rheumatic patients is now now also being being seen as as increasincreasor rheumatic patients is also seen ingly important, as muscle weakness due to atrophied and or rheumatic patients is now also being seen as increasingly important, important, as as muscle muscle weakness weakness due due to to atrophied atrophied and and ingly quickly fatiguing muscles can result in high joint loading ingly important, musclecan weakness to atrophied and quickly fatiguing as muscles result due in high high joint loading loading quickly fatiguing muscles can result in joint (Karamanidis andmuscles Arampatzis turnloading fosters quickly fatiguing can (2009)). result inThis highin joint (Karamanidis and Arampatzis (2009)). This in turn fosters (Karamanidis and (2009)). This fosters joint inflammation and pain, thus influencing progressive (Karamanidis and Arampatzis Arampatzis (2009)). This in in turn turn fosters joint inflammation inflammation and pain, pain, thus thus influencing progressive joint and influencing progressive degeneration. Even following endoprosthetic joint rejoint inflammation and pain, thus influencing progressive joint degeneration. degeneration. Even Even following following endoprosthetic endoprosthetic joint joint rerejoint joint degeneration. Even following endoprosthetic joint re-
placement, postoperative rehabilitation in a rehabilitation placement, postoperative postoperative rehabilitation rehabilitation in in aa rehabilitation rehabilitation placement, hospital or postoperative center as wellrehabilitation as the subsequent outpatient placement, in a rehabilitation hospital or center center as as well well as as the the subsequent subsequent outpatient hospital or outpatient phase involve consistent regular muscular resistance trainhospital or center as well as the subsequent outpatient phase involve involve consistent consistent regular regular muscular muscular resistance resistance traintrainphase ing. Thus, muscle strength training can be considered an phase involve consistent regular muscular resistance training. Thus, muscle strength training can be considered an ing. Thus, muscle strength training can be considered important intervention for aging people to recover from an or ing. Thus, muscle strength training can be considered an important intervention intervention for for aging aging people people to to recover recover from from or or important prevent theintervention development and progression of MSD. Howimportant for aging people to recover from or prevent the the development development and and progression progression of of MSD. MSD. HowHowprevent ever, there isdevelopment a trade-off between training effectiveness and prevent the and progression of MSD. However, there there is is a trade-off between between training training effectiveness effectiveness and and ever, training-induced damage. Effective muscle strengthening ever, there is aa trade-off trade-off between training effectiveness and training-induced damage. Effective muscle strengthening training-induced damage. Effective strengthening requires high muscle forces on onemuscle side. On the other training-induced damage. Effective muscle strengthening requires high high muscle muscle forces forces on on one one side. side. On On the the other other requires side, the high control of these highon forces necessary to avoid requires muscle forces one is On the other side, the the control control of these these high forces forces isside. necessary to avoid avoid side, of high is necessary to unphysiological loading onhigh the musculoskeletal system and side, the control of these forces is necessary to avoid unphysiological loading loading on on the the musculoskeletal musculoskeletal system system and and unphysiological to guarantee a safe training. unphysiological loading on the musculoskeletal system and to guarantee a safe training. to guarantee training. The leg pressaa safe is one of the most common examples of to guarantee safe training. The leg leg press press is is one of of the the most common common examples examples of of The training prescribed for neuromuscular training The leg equipment press is one one of the most most common examples of training equipment prescribed for neuromuscular neuromuscular training training equipment prescribed for training of the leg extensor prescribed muscles. Most often, the horizontal training equipment for neuromuscular training of the the leg leg extensor extensor muscles. muscles. Most Most often, often, the the horizontal horizontal of force, velocity and range motion used as of themovement leg extensor muscles. Most of often, the are horizontal force, movement velocity and range of motion are used as as force, movement velocity and range of motion are used the only indicators for joint loading and training stimulus. force, movement velocity and range and of motion arestimulus. used as the only only indicators for joint joint loading training the indicators for loading and training stimulus. However, leg extension is a loading multi-articular movement althe only indicators for joint and training stimulus. However, leg extension extension is aa multi-articular multi-articular movement alHowever, leg is allowing flexibility of muscular activation and movement control. MonHowever, leg extension is a multi-articular movement allowing flexibility of muscular activation and control. Monlowing flexibility of muscular activation control. Monfeld (2003) clearly demonstrated in hisand study analysing lowing flexibility of muscular activation and control. Monfeld (2003) (2003) clearly clearly demonstrated demonstrated in in his his study study analysing analysing feld knee extensor muscle strength in in patients afteranalysing cruciate feld clearly demonstrated his study knee (2003) extensor muscle strength in in patients patients after cruciate cruciate knee extensor muscle strength after ligament reconstruction, that ainsimilar horizontal force knee extensor muscle strength patients after cruciate ligament reconstruction, reconstruction, that that aa similar similar horizontal horizontal force ligament does not necessarily implythat similar muscular effort forforce the ligament reconstruction, a similar horizontal force does not not necessarily necessarily imply imply similar similar muscular muscular effort effort for for the does knee extensor muscles. Due similar to the different direction of the does not necessarily imply muscular effort for knee extensor extensor muscles. muscles. Due Due to to the different different direction direction of of the the knee force vector, the joint moments fordifferent the ankle, knee and hip knee extensor muscles. Due to the the direction of the force vector, the the joint moments moments for the the ankle, ankle, knee and and hip force vector, joint for knee hip and thus the the contribution of thefor legthe extensor muscles differ force vector, joint moments ankle, knee and hip and thus the contribution of the leg extensor muscles differ and thus the contribution the leg extensor differ considerably. In Fig. 1 theof knee joint momentmuscles in the lower and thus the contribution of the leg extensor muscles differ considerably. In In Fig. Fig. 11 the the knee knee joint joint moment moment in in the the lower considerably. example is small and1thus therejoint is hardly no muscle force considerably. In Fig. the knee moment in the lower lower example is small and thus there is hardly no muscle force example small and thus there is hardly no muscle force from the is knee extensor muscles. example is small and thus there is hardly no muscle force from the the knee knee extensor extensor muscles. muscles. from from the knee extensor muscles.
Copyright 435 Hosting by Elsevier Ltd. All rights reserved. 2405-8963©©2015 2015,IFAC IFAC (International Federation of Automatic Control) Copyright © 2015 IFAC 435 Copyright © 435 Peer review underIFAC responsibility of International Federation of Automatic Copyright © 2015 2015 IFAC 435Control. 10.1016/j.ifacol.2015.10.179
9th IFAC BMS 436 Aug. 31 - Sept. 2, 2015. Berlin, GermanyMelanie Kolditz et al. / IFAC-PapersOnLine 48-20 (2015) 435–440
The plate reaction force vector in frontal plane (Fig. 1, right) muscle models. The whole training scenario consists of a lower extremity sagittal plane frontal plane model and a leg press model. Together they build up a closed kinematic chain. As rigid bodies in OpenSim can only have one parent body, closed kinematic chains are coupled by constraints, here by a constraint between the foot and the leg press plate. 2.1 Musculoskeletal Lower Extremity Model
Fig. 1. Multi-articular movements allow for compensation mechanisms in sagittal plane (left). Inappropriate postures or varus and valgus deformities affect knee adduction and abduction moments in frontal plane (right). highlights a cause for a potential training-induced damage. High external knee adduction moments reflect high compressive forces acting on the medial knee compartment (Kutzner et al. (2013)) and are supposed to foster osteoarthritis (OA) development and progression, when occurring during locomotion (Reeves and Bowling (2011), Andriacchi et al. (2004), Trepczynski et al. (2014)). Thus, training in the leg press with OA patients and elderly people should focus to reduce knee adduction moments. The magnitude of the knee adduction moment mainly depends on the magnitude of the reaction force and the moment arm of the reaction force about the knee joint center. One strategy to reduce adduction moments during locomotion are lateral or medial wedged insoles of 5 to 15◦ to induce a mediolateral shift of the center of pressure beneath the foot (Reeves and Bowling (2011), Kerrigan et al. (2002), Lewinson et al. (2014)). Therefore, it is supposed that during resistance training at the leg press a medial or lateral wedge influences mainly external frontal plane knee moments while a wedged support for heel or toe offset changes the geometry of the leg and influences the ankle, knee and hip extensor moments mainly in the sagittal plane. These studies indicate, that effectiveness and safety of leg extension training can be improved by developing a novel robotic leg press device. The idea is to use mechanical models of the musculoskeletal system to estimate joint loadings and control these loads actively with the orientation and position of the foot plate as a manipulating variable. The evaluation of the orientation as a manipulating variable is presented in this paper. 2. DYNAMIC MODEL OF TRAINING SCENARIO The software system OpenSim was used for the simulation of the training scenario. OpenSim is a freely available software for dynamic simulations, especially of the musculoskeletal system (Delp et al. (2007)). Multibody systems are modeled as rigid bodies with mass and inertia properties connected by different types of joints with up to six degrees of freedom (dof). Movement coordinates are defined with respect to the joint coordinate system and can be actuated either directly by defining a corresponding force or torque or in case of the musculoskeletal system by 436
The Gait 2354 model from OpenSim was used as a basic musculoskeletal model of the lower extremity. It consists of twelve rigid bodies, 54 muscles and 23 dof, whereas each leg has seven dof as shown in Fig. 2. Detailed information of
mass centers
knee 1 dof (+ 1 add.)
toes 1 dof
ankle 2 dof
hip 3 dof Fig. 2. Musculoskeletal model with twelve bodies and seven dof for each leg. this model can be found in the OpenSim documentation 1 . 2.2 Model Extension The lower extremity model is needed to solve the inverse dynamics problem and determine the generalized torques from the equations of motion M (q)¨ q + C(q, q) ˙ + G(q) = τ , where q, q, ˙ q¨ are the generalized positions, velocities and accelerations of each dof, M (q) is the mass matrix and C(q, q) ˙ and G(q) are the vectors of the Coriolis and gravitational forces, respectively. In sagittal plane there is at least one dof per joint, and so the loadings for hip, knee and ankle joint for each dof result from the inverse dynamics calculation. For frontal plane moments, one possibility is the calculation of muscle forces from the generalized torques (Sritharan et al. (2012)). But as individual muscle forces are not explicitly needed in further calculations, the basic Gait 2354 model is extended by an additional dof for the knee adduction as shown in Fig. 3. This coordinate is fixed to zero degrees, so that no movement occurs, but by solving the inverse dynamic problem, the external adduction moment is delivered, directly. The second extension is the definition of a reference coordinate system for the contact constraint of the foot with the leg press plate. It is assumed that if the contact force between foot and plate is high enough, there is no motion of the foot on the plate. The contact plane has a fixed orientation with respect to the calcaneus as shown in Fig. 3. The origin of the coordinate system is positioned in 1 http://simtk-confluence.stanford.edu:8080/display/OpenSim/ Gait+2392+and+2354+Models, accessed: 02/2015
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large and small medial/lateral wedges knee adduction 11.52°
contact plate
8.37°
wooden wedge for heel and toe offset
calcaneus Fig. 3. Model extensions: additional reference frame for contact between foot and plate and coordinate for knee adduction. the origin of the coordinate system of the force plate with an offset only in normal direction. This allows both the application of external forces measured by a force plate directly with respect to this reference frame and an easy way of varying the orientation of the foot on the leg press plate. 2.3 Leg Press Model A standard leg press allows a linear motion along a horizontal, vertical, or – as chosen for this setup – 45◦ line. The leg press model is needed for constraining the motion of the force plate to a linear motion along this line. It has four dof: two dof for the position of this line with respect to the ground frame, one for the orientation around the normal axis of the ground frame and one for the translational movement of the plate. Both the real leg press and the corresponding OpenSim model are shown in Fig. 4. In the force plate model, the size of the experimental setup
Fig. 4. Leg press model with four degrees of freedom: three for the position in the world frame and one for the 45◦ translational movement of the plate. is represented and serves as the coupling body between the lower extremity model and the leg press model.
9.19° Fig. 5. Experimental setup: Diagonal (45◦ ) leg press with a force plate, markers for the tracking system and wooden wedges for different plate orientations. UK) with a video frame rate of 200 Hz. Markers were placed on the force plate and on the leg. To evaluate the influence of plate orientations on external joint moments, three wooden wedges are used: a small (8.37◦ ) and large (11.52◦ ) lateral/medial wedge and a wedge with 9.19◦ for a heel and toe offset (Fig. 5). Force and motion data were acquired from one healthy subject lifting and lowering the weight of about 100 kg in the diagonal leg press with and without the wedges under the foot. In total seven different conditions were recorded: foot flat, small and large lateral wedge, small and large medial wedge, heel and toe offset. 4. DATA ANALYSIS In order to analyze external joint moments, motion data needed to be appended to the models. Therefore, the optical markers were added to the lower extremity and the leg press model in OpenSim. For solving the inverse kinematic problem, i.e. calculating joint angle trajectories from marker trajectories, the marker configuration in Fig. 6 was used. Three marker positions are defined
metatarsophalangeal joint II medial / lateral malleolus
3. EXPERIMENTAL SETUP The experimental setup is shown in Fig. 5. It consists of a diagonal (45◦ ) leg press with a piezoelectric force plate (Kistler, Winterthur, Switzerland) with a weight of about 30 kg mounted at the foot plate. Together with the basic weight of the leg press, the overall weight that needed to be pushed was about 100 kg with one leg. Three dimensional sensors are placed in each corner of the plate. Measured forces are converted into forces and moments in six dof with respect to a coordinate system at the center of the plate, 54 mm beneath the surface. It delivers measurements with a frame rate of 2 kHz. Motion was captured using an optical tracking system (Vicon, Oxford, 437
medial / lateral femur condyle trochanter major
Fig. 6. Optical markers used for inverse kinematics. with respect to the coordinate system of the femur body, the one at trochanter major and the two markers at the medial and lateral femur condyle. Two markers are placed
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5. RESULTS In sagittal plane, three motions with different foot orientations on the plate were evaluated: foot flat, heel offset, toe offset. Fig. 7 shows the results for external sagittal hip, knee and ankle moments over knee angle. The movement starts from a flexed leg position and joint moments close to zero. In each joint, the moment rises with hardly any motion until the resulting force in moving direction is high enough to move the weight. The figure clearly shows that the three tested conditions affect the external joint moments in the sagittal plane. The condition ’toe offset’ resulted in the lowest maximum external knee flexion moment and highest dorsiflexion moment at the ankle. This indicates that the knee extensor muscles have to generate 438
heel offset
foot flat
external knee moment (Nm)
external hip moment (Nm)
100 0 −100 −200 −300
toe offset extension
−80
−60
−40
200
flexion −20 0 flexion
100 0
−100
external ankle moment (Nm)
at the medial and lateral malleolus, and one marker at the metatarsophalangeal joint II. The force plate was equipped with eight makers, from which at least three were used for inverse kinematic calculations, as some of the markers were covered during motion or from the wedge for toe or heel offset. First, the position and orientation of the leg press model was determined with a static measurement of the marker positions and the inverse kinematics tool. The lower extremity model represents a 1.8 m tall person with a mass of 75.16 kg and needs to be scaled to fit the subject in this experiments. The model was scaled and inverse kinematics was calculated iteratively using a static pose, until the marker position error was small enough. After scaling and positioning with respect to the world coordinate system, the motion of the leg press was constrained. Only one dof for the 45◦ movement of the foot plate was used for further calculations. The scaled lower extremity model was added to the leg press model and the constraint between contact plane and leg press plate restricting any motion between these to bodies, was appended to the model. The defined constraint can be adjusted easily for the motions with the wedges. Raw marker trajectory data was low-pass filtered with a cutoff frequency of 6 Hz within the inverse kinematics tool of OpenSim. The second input for the inverse dynamics tool is the reaction force and the corresponding center of pressure (COP) with respect to the applied body. Before transforming the forces and moments into the contact plane coordinate system, raw data was filtered with a moving average filter with a length of 10. The transformation consists of two steps: first, the COP was calculated from the force and moment vector F = (Fx , Fy , Fz , Mx , My , Mz ) in force plate coordinates (FP), with the z-axis as normal vector, and the distance d = 54 mm between the force plate origin and its surface. The coordinates are deterMy −dFx Mx −dFy and mined as xCOP,F P = F z3 , yCOP,F P = Fz zCOP,F P = 0. Second, the transformation between force plate and contact plane coordinates was done. From inverse dynamics, the generalized torques for each relevant dof, i.e. flexion/extension of the hip, knee and ankle joint in the sagittal plane and knee adduction/abduction in the frontal plane, are delivered. In frontal plane, the adduction moment has shown to reflect medial tibiofemoral contact forces (Kutzner et al. (2013)). Thus high external knee adduction moments should be minimized to avoid training-induced damage.
−80
−60
−40
extension −20 0
0
−100 −200
−80
−60 −40 knee angle (°)
dorsiflexion −20 0
Fig. 7. External hip, knee and ankle moment over knee angle for foot flat condition and with support for heel and toe offset. A knee angle of 0◦ represents full knee extension. lower muscle forces which are compensated by the higher muscle forces of the plantarflexor muscles to lift and lower the same weight. This effect is illustrated in Fig. 8 for a knee angle of 60◦ . In the knee joint, the loading with
heel offset
toe offset
Fig. 8. Force vector and moment arms in hip, knee and ankle joint for a knee angle of 60◦ for foot positions on the wooden wedge to support heel and toe offset. toe offset is smaller than for heel offset, because the force vector has a smaller moment arm to the knee joint center. The weight, that needed to be pushed was equal for both motions. Therefore, the other joints, i.e. hip and/or ankle joint, must generate a higher moment for the same force in leg press direction. In the evaluated measurements, the COP where the force is applied to the leg was hardly affected. Inefficient movements, e.g. where the knee joint is not loaded at all, can be detected by measuring the leg position and the resulting force vector, and influenced by changing the plate orientation of the leg press. The results of the inverse dynamics calculation in frontal plane were compared for five motions: foot flat condition, small and large medial wedge, small and large lateral wedge. In Fig. 9 both the knee abduction and adduction
9th IFAC BMS Aug. 31 - Sept. 2, 2015. Berlin, GermanyMelanie Kolditz et al. / IFAC-PapersOnLine 48-20 (2015) 435–440
y coordinate (m)
moments over the knee angle and the positions of the COP on the force plate are depicted. The foot flat condition
0.2 0.1 0 −0.1 −0.2
external frontal knee moment (Nm)
40
foot flat
large lateral wedge
wedges: large lateral small lateral foot flat small medial large medial
COP on force plate
0.2
small medial wedge
439
0.1 0 −0.1 z coordinate (m)
−0.2
abduction
20 0 −20 adduction −40 −80 −60
−40 knee angle (°)
−20
Fig. 10. Force vector for a knee angle of 30◦ for a small medial wedge and a large lateral wedge compared to a flat foot position directly on the plate.
0
Fig. 9. Knee abduction and adduction moment over knee angle and center of pressure (COP) on force plate for different medial and lateral wedges. (green) shows already an external adduction moment of about 18 Nm. The small medial wedge (orange) increased the adduction moment to 30 Nm. The movement with the large medial wedge (red) yielded to a smaller adduction moment. The different lateral wedge angles showed a more obvious effect on the knee joint loadings. A small lateral wedge of 8.37◦ (light blue) changed the loading from adduction to abduction of less than 10 Nm. A large lateral wedge (dark blue) increased the abduction moment to about 25 Nm. In opposite to the results in sagittal plane, a different plate orientation in frontal plane influences not only the moment arms to the knee joint, but also the COP on the force plate. The corresponding COP to the five investigated motions are depicted at the top of Fig. 9. For this specific subject, the COP postions during the foot flat conditions are in the middle of the force plate, a medial wedge (orange and red) moves the COP to the medial foot area, whereas a lateral wedge (light and dark blue) moves it to the lateral part of the foot. This effect is also illustrated in Fig. 10, where the force vectors for a knee angle of 30◦ are compared for small medial wedge, foot flat condition and large lateral wedge. The COP in the foot flat condition is at the third toe. A medial wedge moves the COP to the second toe and thereby increases the distance of the force vector from the knee joint center, which results in the higher adduction moment. The COP for the large lateral wedge is moved in the other direction to the fifth toe. The force vector here is on the other side of the knee joint and therefore an abduction moment is measured. The experiments at the leg press showed the same effect that was described in Reeves and Bowling (2011) and Lewinson et al. (2014). Medial and lateral wedges under the foot can manipulate knee adduction and abduction moments 439
as the COP of the force vector is moved and therefore the moment arm to the knee can be changed. The results of this experiments show, that the horizontal force alone is not sufficient to conclude to joint loadings during training. As leg extension is a multi-articular movement, the whole resulting force vector together with the corresponding leg joint configuration allows for determining joint moments and guarantee for a safe and efficient training. Furthermore, these first experiments highlight the potential of a person-specific plate orientation for an improvement of leg press exercise outcome. In sagittal plane, a desired knee joint moment and training stimulus can be adjusted by varying support for heel and toe offset of the foot, whereby the COP of the force vector is not affected. In frontal plane, knee abduction and adduction moments and thus tibiofemoral contact forces (Kutzner et al. (2013)) can be minimized by an appropriate individual lateral or medial foot lifting, where also the COP is moved across the foot. 6. CONCLUSION The results confirm the potential in improving effectiveness and safety of leg press exercise by influencing joint loadings with the orientation of the foot plate in sagittal and frontal plane. These loads can be estimated with a sensor system consisting of a force plate, an optical motion tracking system and inverse dynamic calculations as shown in this paper. A control loop with the joint loading as controlled and the foot orientation as manipulated variable is depicted in Fig. 11. The actuator of the training device should be able to control the resistive force, movement velocity and range of motion by applying individual training movements. As research on other manipulated variables, including an optimization of the training trajectory needs to be done, a realization of the hardware of this actuator should be adaptable easily to other scenarios. An indus-
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foot orientation
desired loading -
REFERENCES
current loading system
controller
sensor Fig. 11. Control loop with the joint loading as controlled and foot orientation as manipulated variable. An industrial robot is used as actuator and the human is within the controlled system. trial robot with six degrees of freedom, which can apply arbitrary six dimensional motions fulfills this requirement. As a well-trained sportsman can push up to 300 kg with one leg, a high payload robot is needed. The vision of such a robotic leg press with a KUKA KR 300 robot with a payload of 300 kg (see KUKA Roboter GmbH (2013) for specification) is shown in Fig. 12. The muscular system can
Fig. 12. Vision of a novel robotic leg press training device visualized in OpenSim. exert high loads only with low velocities and therefore this robot is certainly over-dimensioned. A detailed evaluation of the loads on the robot joints during leg press exercise is subject to further investigations. Future work in this project will be done in the development of a functional model of the presented robotic training device in order to investigate intra and inter individual variabilities and the dynamic behavior of the human in the control loop. For a translation of the results into a practical setup for rehabilitation centers, the requirements for a low-cost training device including the accuracies of motion tracking can be deduced from this high end setup. ACKNOWLEDGEMENTS This project is supported by KUKA Roboter GmbH, Augsburg, Germany. 440
Andriacchi, T.P., M¨ undermann, A., Smith, R.L., Alexander, E.J., Dyrby, C.O., and Koo, S. (2004). A framework for the in vivo pathomechanics of osteoarthritis at the knee. Annals of biomedical engineering, 32(3), 447–457. Delp, S., Anderson, F., Arnold, A., Loan, P., Habib, A., John, C., Guendelman, E., and Thelen, D. (2007). Opensim: Open-source software to create and analyze dynamic simulations of movement. Biomedical Engineering, IEEE Transactions on, 54(11), 1940–1950. Karamanidis, K. and Arampatzis, A. (2009). Evidence of mechanical load redistribution at the knee joint in the elderly when ascending stairs and ramps. Annals of biomedical engineering, 37(3), 467–476. Kerrigan, D.C., Lelas, J.L., Goggins, J., Merriman, G.J., Kaplan, R.J., and Felson, D.T. (2002). Effectiveness of a lateral-wedge insole on knee varus torque in patients with knee osteoarthritis. Archives of physical medicine and rehabilitation, 83(7), 889–893. KUKA Roboter GmbH (2013). KR QUANTEC ultra — Specification. KUKA Roboter GmbH. Kutzner, I., Trepczynski, A., Heller, M.O., and Bergmann, G. (2013). Knee adduction moment and medial contact force–facts about their correlation during gait. PloS one, 8(12), e81036. Lewinson, R.T., Collins, K.H., Vallerand, I.A., Wiley, J.P., Woodhouse, L.J., Reimer, R.A., Worobets, J.T., Herzog, W., and Stefanyshyn, D.J. (2014). Reduced knee joint loading with lateral and medial wedge insoles for management of knee osteoarthritis: a protocol for a randomized controlled trial. BMC musculoskeletal disorders, 15(1), 405. Mian, O.S., Baltzopoulos, V., Minetti, A.E., and Narici, M.V. (2007). The impact of physical training on locomotor function in older people. Sports medicine, 37(8), 683–701. Monfeld, C. (2003). Biomechanische Analyse von Trainings¨ ubungen an einer Funktionsstemme in der Rehabilitation nach Knieverletzungen. Ph.D. thesis, German Sports University Cologne. Narici, M.V. and Maffulli, N. (2010). Sarcopenia: characteristics, mechanisms and functional significance. British medical bulletin, 95(1), 139–159. Reeves, N.D. and Bowling, F.L. (2011). Conservative biomechanical strategies for knee osteoarthritis. Nature Reviews Rheumatology, 7(2), 113–122. Sritharan, P., Lin, Y.C., and Pandy, M.G. (2012). Muscles that do not cross the knee contribute to the knee adduction moment and tibiofemoral compartment loading during gait. Journal of Orthopaedic Research, 30(10), 1586–1595. Statistisches Bundesamt (2013). Diagnosedaten der Patienten und Patientinnen in Vorsorge- oder Rehabilitationseinrichtungen. Gesundheit, 12(6.2.2). Trepczynski, A., Kutzner, I., Bergmann, G., Taylor, W.R., and Heller, M.O. (2014). Modulation of the relationship between external knee adduction moments and medial joint contact forces across subjects and activities. Arthritis & Rheumatology, 66(5), 1218–1227. Woolf, A.D. and Pfleger, B. (2003). Burden of major musculoskeletal conditions. Bulletin of the World Health Organization, 81(9), 646–656.
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Simulative Simulative Simulative Simulative During Leg During During Leg During Leg Leg
Analysis of Joint Loading Analysis of Joint Loading Analysis of Joint Loading Analysis of Joint Loading Press Exercise for Control Press Exercise for Control Press Exercise for Control Press Exercise for Control Applications Applications Applications Applications
Melanie Kolditz ∗∗ Thivaharan Albin ∗∗ Dirk Abel ∗∗ ∗ Thivaharan ∗ Dirk Abel Melanie Kolditz Albin ∗∗ ∗∗ ∗ ∗ Thivaharan ∗ Melanie Kolditz Albin Dirk Alessandro Fasse Br¨ u∗ggemann Melanie Kolditz Thivaharan Albin Dirk Abel Abel ∗∗ Gert-Peter ∗∗ ∗∗ Gert-Peter ∗∗ ∗∗ Alessandro Fasse Br¨ u ggemann ∗∗ ∗∗ Alessandro Fasse Gert-Peter Br¨ u ggemann Kirsten Albracht ∗∗ Alessandro Fasse Gert-Peter Br¨ u ggemann Kirsten Albracht ∗∗ Kirsten Kirsten Albracht Albracht ∗∗ ∗ ∗ Institute of Automatic Control, RWTH Aachen University, Germany ∗ Institute of Automatic Control, RWTH Aachen University, Germany ∗ Institute of Automatic Control, (e-mail: [email protected]) Institute of Automatic Control, RWTH RWTH Aachen Aachen University, University, Germany Germany (e-mail: [email protected]) ∗∗ (e-mail: [email protected]) Institute of Biomechanics and Orthopaedics, German Sport (e-mail: [email protected]) ∗∗ ∗∗ Institute of Biomechanics and Orthopaedics, German Sport ∗∗ InstituteCologne, of Orthopaedics, German University Germanyand (e-mail: [email protected]) InstituteCologne, of Biomechanics Biomechanics and Orthopaedics, German Sport Sport University Germany (e-mail: [email protected]) University Cologne, Germany (e-mail: [email protected]) University Cologne, Germany (e-mail: [email protected]) Abstract: Leg extension is a multi-articular movement allowing flexibility of muscular actiAbstract: Leg extension is a multi-articular movement allowing flexibility of muscular actiAbstract: Leg is movement allowing flexibility of activation and control. Therefore, joint loadings during leg press exercise can only be estimated Abstract: Leg extension extension is a a multi-articular multi-articular movement allowing flexibility of muscular muscular activation and control. Therefore, joint loadings during leg press exercise can only be estimated vation and control. Therefore, joint loadings during leg press exercise can only be estimated using the whole reaction force vector together with the leg posture. A dynamic model of the vation and control. Therefore, joint loadings during leg press exercise can only be estimated using the the whole whole reaction reaction force force vector together with the leg posture. A dynamic model of the using together with the leg posture. A dynamic of the musculoskeletal system asforce wellvector as experimental data from a diagonal leg pressmodel are used to using the whole reaction vector together with the leg posture. A dynamic model of the musculoskeletal system as well as experimental data from a diagonal leg press are used to musculoskeletal system well as experimental data from diagonal leg press are used to investigate external kneeas joint loadings and the influence of aadifferent orientations of the foot musculoskeletal system as well as experimental data from diagonal leg press are used to investigate external knee joint loadings and the influence of different orientations of the foot investigate external knee joint loadings and the influence of different orientations of the foot plate. Varying orientation in sagittal plane affects ankle, knee and hip loadings by changing the investigate external knee joint loadings and the influence of different orientations of the foot plate. Varying orientation in sagittal plane affects ankle, knee and hip loadings by changing the plate. Varying in plane and loadings the leg posture andorientation the direction of the resulting force ankle, vector.knee Different orientations in changing frontal plane plate. Varying in sagittal sagittal plane affects affects and hip hip loadings by by the leg posture posture andorientation the direction direction of the the resulting resulting force ankle, vector.knee Different orientations in changing frontal plane plane leg and the of force vector. Different orientations in frontal move the center of pressure ofofthe force vector across the Different foot and thus change in knee adduction leg posture and the direction the resulting force vector. orientations frontal plane move the center of pressure of the force vector across the foot and thus change knee adduction move the of the vector across the and thus change knee and abduction Theof in this paper indicate, that high forces, which areadduction required move the center centermoments. of pressure pressure ofresults the force force vector across the foot foot and thus change knee adduction and abduction moments. The results in this paper indicate, that high forces, which are required and abduction moments. The results in this paper indicate, that high forces, which are required for an effective training, can be controlled using the foot orientation as manipulated variable. and abduction moments. The results in this paper indicate, that high forces, which are required for an effective training, can be controlled using the foot orientation as manipulated variable. for an effective training, can be controlled using the foot orientation as manipulated variable. Thereby, unphysiological loadings and training-induced damage can be avoided. for an effective training, can be controlled using the foot orientation as manipulated variable. Thereby, unphysiological unphysiological loadings loadings and and training-induced training-induced damage damage can can be be avoided. avoided. Thereby, Thereby, unphysiological training-induced be avoided. © 2015, IFAC (International loadings Federationand of Automatic Control) damage Hosting bycan Elsevier Ltd. All rights reserved. Keywords: Dynamic model, Musculoskeletal model, Inverse dynamic problem, Manipulated Keywords: Dynamic Dynamic model, model, Musculoskeletal Musculoskeletal model, model, Inverse dynamic Keywords: dynamic problem, problem, Manipulated Manipulated variables, Robotics, Keywords: Dynamic Sensor model, system. Musculoskeletal model, Inverse Inverse dynamic problem, Manipulated variables, Robotics, Robotics, Sensor system. variables, Sensor system. variables, Robotics, Sensor system. 1. INTRODUCTION 1. INTRODUCTION INTRODUCTION 1. 1. INTRODUCTION Sarcopenia as well as loss of muscle strength and power are Sarcopenia as as well well as as loss loss of muscle muscle strength strength and and power power are are Sarcopenia important factors active independent aging Sarcopenia as well compromising as loss of of muscle strength and power are important factors factors compromising active independent aging important compromising active independent aging (Narici andfactors Maffulli (2010), Mian et al. (2007)). These important compromising active independent aging (Narici and and Maffulli Maffulli (2010), (2010), Mian Mian et et al. al. (2007)). (2007)). These These (Narici factors are only associated withet an impaired motor (Narici and not Maffulli (2010), Mian al. impaired (2007)). motor These factors are not only associated with an factors are not only associated with an impaired motor performance during daily activities but also with an infactors are not only associated with an impaired motor performance during during daily daily activities activities but but also also with with an an ininperformance creased risk for the development of chronic agewith and wealth performance during daily activities but also an increased risk risk for for the the development development of of chronic chronic age age and and wealth wealth creased related diseases. Participating in of regular physical activity, creased risk for the development chronic age and wealth related diseases. diseases. Participating Participating in in regular regular physical physical activity, activity, related both aerobic andParticipating strength exercises, canphysical slow down the related diseases. in regular activity, both aerobic and strength exercises, can slow down the both aerobic and strength exercises, can slow down the physiological deconditioning associated with aging, and both aerobic and strength exercises, can slow down the physiological deconditioning deconditioning associated associated with with aging, aging, and and physiological prevent or decelerate the development and progression of physiological deconditioning associated with aging, and prevent or or decelerate decelerate the the development development and and progression progression of of prevent chronic disease. Muscular-skeletal disorders (MSD) are one prevent or decelerate the development and progression of chronic disease. Muscular-skeletal disorders (MSD) are one chronic disease. Muscular-skeletal disorders (MSD) are one of the most common cause of severe long-term pain and chronic disease. Muscular-skeletal disorders (MSD) are one of the the most most common common cause cause of of severe severe long-term long-term pain pain and and of physical disability (Woolf Pfleger (2003)). pain In Gerof the most common cause and of severe long-term and physical disability (Woolf and Pfleger (2003)). In In GerGerphysical disability (Woolf and Pfleger (2003)). many, 36.2% of the (Woolf patientsand treated 2012(2003)). in inpatient rephysical disability Pfleger In Germany, 36.2% 36.2% of of the the patients patients treated treated 2012 2012 in in inpatient inpatient reremany, habilitation centres, i.e. a total of 596000 patients, suffered many, 36.2% of the patients treated 2012 in inpatient rehabilitation centres, i.e. a total of 596000 patients, suffered habilitation centres, i.e. aaand total of 596000 patients, suffered from MSD, such as knee hip arthrosis or osteoporosis habilitation centres, i.e. total of 596000 patients, suffered from MSD, MSD, such such as as knee knee and hip hip arthrosis arthrosis or osteoporosis osteoporosis from (Statistisches Bundesamt (2013)). from MSD, such as knee and and hip arthrosis or or osteoporosis (Statistisches Bundesamt (2013)). (Statistisches Bundesamt (2013)). Resistance training as a therapy traumatic sports in(Statistisches Bundesamt (2013)).for Resistance training training as aa therapy therapy for traumatic traumatic sports sports ininResistance for juries (e.g. training rupture as of athe anterior cruciate ligament) is Resistance as therapy for traumatic sports injuries (e.g. rupture of the anterior cruciate ligament) is juries (e.g. rupture of the anterior cruciate ligament) is already widely established. The use of training to increase juries rupture of the The anterior cruciate is already(e.g. widely established. use of of trainingligament) to increase increase already widely established. The use training to or reduce the loss of muscle The strength fortraining osteoarthritic and already widely established. use of to increase or reduce the loss of muscle strength for osteoarthritic and or reduce the of strength for and rheumatic patients is now also being seen as increasor the loss loss of muscle muscle strength for osteoarthritic osteoarthritic and or reduce rheumatic patients is now now also being being seen as as increasincreasor rheumatic patients is also seen ingly important, as muscle weakness due to atrophied and or rheumatic patients is now also being seen as increasingly important, important, as as muscle muscle weakness weakness due due to to atrophied atrophied and and ingly quickly fatiguing muscles can result in high joint loading ingly important, musclecan weakness to atrophied and quickly fatiguing as muscles result due in high high joint loading loading quickly fatiguing muscles can result in joint (Karamanidis andmuscles Arampatzis turnloading fosters quickly fatiguing can (2009)). result inThis highin joint (Karamanidis and Arampatzis (2009)). This in turn fosters (Karamanidis and (2009)). This fosters joint inflammation and pain, thus influencing progressive (Karamanidis and Arampatzis Arampatzis (2009)). This in in turn turn fosters joint inflammation inflammation and pain, pain, thus thus influencing progressive joint and influencing progressive degeneration. Even following endoprosthetic joint rejoint inflammation and pain, thus influencing progressive joint degeneration. degeneration. Even Even following following endoprosthetic endoprosthetic joint joint rerejoint joint degeneration. Even following endoprosthetic joint re-
placement, postoperative rehabilitation in a rehabilitation placement, postoperative postoperative rehabilitation rehabilitation in in aa rehabilitation rehabilitation placement, hospital or postoperative center as wellrehabilitation as the subsequent outpatient placement, in a rehabilitation hospital or center center as as well well as as the the subsequent subsequent outpatient hospital or outpatient phase involve consistent regular muscular resistance trainhospital or center as well as the subsequent outpatient phase involve involve consistent consistent regular regular muscular muscular resistance resistance traintrainphase ing. Thus, muscle strength training can be considered an phase involve consistent regular muscular resistance training. Thus, muscle strength training can be considered an ing. Thus, muscle strength training can be considered important intervention for aging people to recover from an or ing. Thus, muscle strength training can be considered an important intervention intervention for for aging aging people people to to recover recover from from or or important prevent theintervention development and progression of MSD. Howimportant for aging people to recover from or prevent the the development development and and progression progression of of MSD. MSD. HowHowprevent ever, there isdevelopment a trade-off between training effectiveness and prevent the and progression of MSD. However, there there is is a trade-off between between training training effectiveness effectiveness and and ever, training-induced damage. Effective muscle strengthening ever, there is aa trade-off trade-off between training effectiveness and training-induced damage. Effective muscle strengthening training-induced damage. Effective strengthening requires high muscle forces on onemuscle side. On the other training-induced damage. Effective muscle strengthening requires high high muscle muscle forces forces on on one one side. side. On On the the other other requires side, the high control of these highon forces necessary to avoid requires muscle forces one is On the other side, the the control control of these these high forces forces isside. necessary to avoid avoid side, of high is necessary to unphysiological loading onhigh the musculoskeletal system and side, the control of these forces is necessary to avoid unphysiological loading loading on on the the musculoskeletal musculoskeletal system system and and unphysiological to guarantee a safe training. unphysiological loading on the musculoskeletal system and to guarantee a safe training. to guarantee training. The leg pressaa safe is one of the most common examples of to guarantee safe training. The leg leg press press is is one of of the the most common common examples examples of of The training prescribed for neuromuscular training The leg equipment press is one one of the most most common examples of training equipment prescribed for neuromuscular neuromuscular training training equipment prescribed for training of the leg extensor prescribed muscles. Most often, the horizontal training equipment for neuromuscular training of the the leg leg extensor extensor muscles. muscles. Most Most often, often, the the horizontal horizontal of force, velocity and range motion used as of themovement leg extensor muscles. Most of often, the are horizontal force, movement velocity and range of motion are used as as force, movement velocity and range of motion are used the only indicators for joint loading and training stimulus. force, movement velocity and range and of motion arestimulus. used as the only only indicators for joint joint loading training the indicators for loading and training stimulus. However, leg extension is a loading multi-articular movement althe only indicators for joint and training stimulus. However, leg extension extension is aa multi-articular multi-articular movement alHowever, leg is allowing flexibility of muscular activation and movement control. MonHowever, leg extension is a multi-articular movement allowing flexibility of muscular activation and control. Monlowing flexibility of muscular activation control. Monfeld (2003) clearly demonstrated in hisand study analysing lowing flexibility of muscular activation and control. Monfeld (2003) (2003) clearly clearly demonstrated demonstrated in in his his study study analysing analysing feld knee extensor muscle strength in in patients afteranalysing cruciate feld clearly demonstrated his study knee (2003) extensor muscle strength in in patients patients after cruciate cruciate knee extensor muscle strength after ligament reconstruction, that ainsimilar horizontal force knee extensor muscle strength patients after cruciate ligament reconstruction, reconstruction, that that aa similar similar horizontal horizontal force ligament does not necessarily implythat similar muscular effort forforce the ligament reconstruction, a similar horizontal force does not not necessarily necessarily imply imply similar similar muscular muscular effort effort for for the does knee extensor muscles. Due similar to the different direction of the does not necessarily imply muscular effort for knee extensor extensor muscles. muscles. Due Due to to the different different direction direction of of the the knee force vector, the joint moments fordifferent the ankle, knee and hip knee extensor muscles. Due to the the direction of the force vector, the the joint moments moments for the the ankle, ankle, knee and and hip force vector, joint for knee hip and thus the the contribution of thefor legthe extensor muscles differ force vector, joint moments ankle, knee and hip and thus the contribution of the leg extensor muscles differ and thus the contribution the leg extensor differ considerably. In Fig. 1 theof knee joint momentmuscles in the lower and thus the contribution of the leg extensor muscles differ considerably. In In Fig. Fig. 11 the the knee knee joint joint moment moment in in the the lower considerably. example is small and1thus therejoint is hardly no muscle force considerably. In Fig. the knee moment in the lower lower example is small and thus there is hardly no muscle force example small and thus there is hardly no muscle force from the is knee extensor muscles. example is small and thus there is hardly no muscle force from the the knee knee extensor extensor muscles. muscles. from from the knee extensor muscles.
Copyright 435 Hosting by Elsevier Ltd. All rights reserved. 2405-8963©©2015 2015,IFAC IFAC (International Federation of Automatic Control) Copyright © 2015 IFAC 435 Copyright © 435 Peer review underIFAC responsibility of International Federation of Automatic Copyright © 2015 2015 IFAC 435Control. 10.1016/j.ifacol.2015.10.179
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The plate reaction force vector in frontal plane (Fig. 1, right) muscle models. The whole training scenario consists of a lower extremity sagittal plane frontal plane model and a leg press model. Together they build up a closed kinematic chain. As rigid bodies in OpenSim can only have one parent body, closed kinematic chains are coupled by constraints, here by a constraint between the foot and the leg press plate. 2.1 Musculoskeletal Lower Extremity Model
Fig. 1. Multi-articular movements allow for compensation mechanisms in sagittal plane (left). Inappropriate postures or varus and valgus deformities affect knee adduction and abduction moments in frontal plane (right). highlights a cause for a potential training-induced damage. High external knee adduction moments reflect high compressive forces acting on the medial knee compartment (Kutzner et al. (2013)) and are supposed to foster osteoarthritis (OA) development and progression, when occurring during locomotion (Reeves and Bowling (2011), Andriacchi et al. (2004), Trepczynski et al. (2014)). Thus, training in the leg press with OA patients and elderly people should focus to reduce knee adduction moments. The magnitude of the knee adduction moment mainly depends on the magnitude of the reaction force and the moment arm of the reaction force about the knee joint center. One strategy to reduce adduction moments during locomotion are lateral or medial wedged insoles of 5 to 15◦ to induce a mediolateral shift of the center of pressure beneath the foot (Reeves and Bowling (2011), Kerrigan et al. (2002), Lewinson et al. (2014)). Therefore, it is supposed that during resistance training at the leg press a medial or lateral wedge influences mainly external frontal plane knee moments while a wedged support for heel or toe offset changes the geometry of the leg and influences the ankle, knee and hip extensor moments mainly in the sagittal plane. These studies indicate, that effectiveness and safety of leg extension training can be improved by developing a novel robotic leg press device. The idea is to use mechanical models of the musculoskeletal system to estimate joint loadings and control these loads actively with the orientation and position of the foot plate as a manipulating variable. The evaluation of the orientation as a manipulating variable is presented in this paper. 2. DYNAMIC MODEL OF TRAINING SCENARIO The software system OpenSim was used for the simulation of the training scenario. OpenSim is a freely available software for dynamic simulations, especially of the musculoskeletal system (Delp et al. (2007)). Multibody systems are modeled as rigid bodies with mass and inertia properties connected by different types of joints with up to six degrees of freedom (dof). Movement coordinates are defined with respect to the joint coordinate system and can be actuated either directly by defining a corresponding force or torque or in case of the musculoskeletal system by 436
The Gait 2354 model from OpenSim was used as a basic musculoskeletal model of the lower extremity. It consists of twelve rigid bodies, 54 muscles and 23 dof, whereas each leg has seven dof as shown in Fig. 2. Detailed information of
mass centers
knee 1 dof (+ 1 add.)
toes 1 dof
ankle 2 dof
hip 3 dof Fig. 2. Musculoskeletal model with twelve bodies and seven dof for each leg. this model can be found in the OpenSim documentation 1 . 2.2 Model Extension The lower extremity model is needed to solve the inverse dynamics problem and determine the generalized torques from the equations of motion M (q)¨ q + C(q, q) ˙ + G(q) = τ , where q, q, ˙ q¨ are the generalized positions, velocities and accelerations of each dof, M (q) is the mass matrix and C(q, q) ˙ and G(q) are the vectors of the Coriolis and gravitational forces, respectively. In sagittal plane there is at least one dof per joint, and so the loadings for hip, knee and ankle joint for each dof result from the inverse dynamics calculation. For frontal plane moments, one possibility is the calculation of muscle forces from the generalized torques (Sritharan et al. (2012)). But as individual muscle forces are not explicitly needed in further calculations, the basic Gait 2354 model is extended by an additional dof for the knee adduction as shown in Fig. 3. This coordinate is fixed to zero degrees, so that no movement occurs, but by solving the inverse dynamic problem, the external adduction moment is delivered, directly. The second extension is the definition of a reference coordinate system for the contact constraint of the foot with the leg press plate. It is assumed that if the contact force between foot and plate is high enough, there is no motion of the foot on the plate. The contact plane has a fixed orientation with respect to the calcaneus as shown in Fig. 3. The origin of the coordinate system is positioned in 1 http://simtk-confluence.stanford.edu:8080/display/OpenSim/ Gait+2392+and+2354+Models, accessed: 02/2015
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large and small medial/lateral wedges knee adduction 11.52°
contact plate
8.37°
wooden wedge for heel and toe offset
calcaneus Fig. 3. Model extensions: additional reference frame for contact between foot and plate and coordinate for knee adduction. the origin of the coordinate system of the force plate with an offset only in normal direction. This allows both the application of external forces measured by a force plate directly with respect to this reference frame and an easy way of varying the orientation of the foot on the leg press plate. 2.3 Leg Press Model A standard leg press allows a linear motion along a horizontal, vertical, or – as chosen for this setup – 45◦ line. The leg press model is needed for constraining the motion of the force plate to a linear motion along this line. It has four dof: two dof for the position of this line with respect to the ground frame, one for the orientation around the normal axis of the ground frame and one for the translational movement of the plate. Both the real leg press and the corresponding OpenSim model are shown in Fig. 4. In the force plate model, the size of the experimental setup
Fig. 4. Leg press model with four degrees of freedom: three for the position in the world frame and one for the 45◦ translational movement of the plate. is represented and serves as the coupling body between the lower extremity model and the leg press model.
9.19° Fig. 5. Experimental setup: Diagonal (45◦ ) leg press with a force plate, markers for the tracking system and wooden wedges for different plate orientations. UK) with a video frame rate of 200 Hz. Markers were placed on the force plate and on the leg. To evaluate the influence of plate orientations on external joint moments, three wooden wedges are used: a small (8.37◦ ) and large (11.52◦ ) lateral/medial wedge and a wedge with 9.19◦ for a heel and toe offset (Fig. 5). Force and motion data were acquired from one healthy subject lifting and lowering the weight of about 100 kg in the diagonal leg press with and without the wedges under the foot. In total seven different conditions were recorded: foot flat, small and large lateral wedge, small and large medial wedge, heel and toe offset. 4. DATA ANALYSIS In order to analyze external joint moments, motion data needed to be appended to the models. Therefore, the optical markers were added to the lower extremity and the leg press model in OpenSim. For solving the inverse kinematic problem, i.e. calculating joint angle trajectories from marker trajectories, the marker configuration in Fig. 6 was used. Three marker positions are defined
metatarsophalangeal joint II medial / lateral malleolus
3. EXPERIMENTAL SETUP The experimental setup is shown in Fig. 5. It consists of a diagonal (45◦ ) leg press with a piezoelectric force plate (Kistler, Winterthur, Switzerland) with a weight of about 30 kg mounted at the foot plate. Together with the basic weight of the leg press, the overall weight that needed to be pushed was about 100 kg with one leg. Three dimensional sensors are placed in each corner of the plate. Measured forces are converted into forces and moments in six dof with respect to a coordinate system at the center of the plate, 54 mm beneath the surface. It delivers measurements with a frame rate of 2 kHz. Motion was captured using an optical tracking system (Vicon, Oxford, 437
medial / lateral femur condyle trochanter major
Fig. 6. Optical markers used for inverse kinematics. with respect to the coordinate system of the femur body, the one at trochanter major and the two markers at the medial and lateral femur condyle. Two markers are placed
9th IFAC BMS 438 Aug. 31 - Sept. 2, 2015. Berlin, GermanyMelanie Kolditz et al. / IFAC-PapersOnLine 48-20 (2015) 435–440
5. RESULTS In sagittal plane, three motions with different foot orientations on the plate were evaluated: foot flat, heel offset, toe offset. Fig. 7 shows the results for external sagittal hip, knee and ankle moments over knee angle. The movement starts from a flexed leg position and joint moments close to zero. In each joint, the moment rises with hardly any motion until the resulting force in moving direction is high enough to move the weight. The figure clearly shows that the three tested conditions affect the external joint moments in the sagittal plane. The condition ’toe offset’ resulted in the lowest maximum external knee flexion moment and highest dorsiflexion moment at the ankle. This indicates that the knee extensor muscles have to generate 438
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at the medial and lateral malleolus, and one marker at the metatarsophalangeal joint II. The force plate was equipped with eight makers, from which at least three were used for inverse kinematic calculations, as some of the markers were covered during motion or from the wedge for toe or heel offset. First, the position and orientation of the leg press model was determined with a static measurement of the marker positions and the inverse kinematics tool. The lower extremity model represents a 1.8 m tall person with a mass of 75.16 kg and needs to be scaled to fit the subject in this experiments. The model was scaled and inverse kinematics was calculated iteratively using a static pose, until the marker position error was small enough. After scaling and positioning with respect to the world coordinate system, the motion of the leg press was constrained. Only one dof for the 45◦ movement of the foot plate was used for further calculations. The scaled lower extremity model was added to the leg press model and the constraint between contact plane and leg press plate restricting any motion between these to bodies, was appended to the model. The defined constraint can be adjusted easily for the motions with the wedges. Raw marker trajectory data was low-pass filtered with a cutoff frequency of 6 Hz within the inverse kinematics tool of OpenSim. The second input for the inverse dynamics tool is the reaction force and the corresponding center of pressure (COP) with respect to the applied body. Before transforming the forces and moments into the contact plane coordinate system, raw data was filtered with a moving average filter with a length of 10. The transformation consists of two steps: first, the COP was calculated from the force and moment vector F = (Fx , Fy , Fz , Mx , My , Mz ) in force plate coordinates (FP), with the z-axis as normal vector, and the distance d = 54 mm between the force plate origin and its surface. The coordinates are deterMy −dFx Mx −dFy and mined as xCOP,F P = F z3 , yCOP,F P = Fz zCOP,F P = 0. Second, the transformation between force plate and contact plane coordinates was done. From inverse dynamics, the generalized torques for each relevant dof, i.e. flexion/extension of the hip, knee and ankle joint in the sagittal plane and knee adduction/abduction in the frontal plane, are delivered. In frontal plane, the adduction moment has shown to reflect medial tibiofemoral contact forces (Kutzner et al. (2013)). Thus high external knee adduction moments should be minimized to avoid training-induced damage.
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Fig. 7. External hip, knee and ankle moment over knee angle for foot flat condition and with support for heel and toe offset. A knee angle of 0◦ represents full knee extension. lower muscle forces which are compensated by the higher muscle forces of the plantarflexor muscles to lift and lower the same weight. This effect is illustrated in Fig. 8 for a knee angle of 60◦ . In the knee joint, the loading with
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Fig. 8. Force vector and moment arms in hip, knee and ankle joint for a knee angle of 60◦ for foot positions on the wooden wedge to support heel and toe offset. toe offset is smaller than for heel offset, because the force vector has a smaller moment arm to the knee joint center. The weight, that needed to be pushed was equal for both motions. Therefore, the other joints, i.e. hip and/or ankle joint, must generate a higher moment for the same force in leg press direction. In the evaluated measurements, the COP where the force is applied to the leg was hardly affected. Inefficient movements, e.g. where the knee joint is not loaded at all, can be detected by measuring the leg position and the resulting force vector, and influenced by changing the plate orientation of the leg press. The results of the inverse dynamics calculation in frontal plane were compared for five motions: foot flat condition, small and large medial wedge, small and large lateral wedge. In Fig. 9 both the knee abduction and adduction
9th IFAC BMS Aug. 31 - Sept. 2, 2015. Berlin, GermanyMelanie Kolditz et al. / IFAC-PapersOnLine 48-20 (2015) 435–440
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Fig. 10. Force vector for a knee angle of 30◦ for a small medial wedge and a large lateral wedge compared to a flat foot position directly on the plate.
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Fig. 9. Knee abduction and adduction moment over knee angle and center of pressure (COP) on force plate for different medial and lateral wedges. (green) shows already an external adduction moment of about 18 Nm. The small medial wedge (orange) increased the adduction moment to 30 Nm. The movement with the large medial wedge (red) yielded to a smaller adduction moment. The different lateral wedge angles showed a more obvious effect on the knee joint loadings. A small lateral wedge of 8.37◦ (light blue) changed the loading from adduction to abduction of less than 10 Nm. A large lateral wedge (dark blue) increased the abduction moment to about 25 Nm. In opposite to the results in sagittal plane, a different plate orientation in frontal plane influences not only the moment arms to the knee joint, but also the COP on the force plate. The corresponding COP to the five investigated motions are depicted at the top of Fig. 9. For this specific subject, the COP postions during the foot flat conditions are in the middle of the force plate, a medial wedge (orange and red) moves the COP to the medial foot area, whereas a lateral wedge (light and dark blue) moves it to the lateral part of the foot. This effect is also illustrated in Fig. 10, where the force vectors for a knee angle of 30◦ are compared for small medial wedge, foot flat condition and large lateral wedge. The COP in the foot flat condition is at the third toe. A medial wedge moves the COP to the second toe and thereby increases the distance of the force vector from the knee joint center, which results in the higher adduction moment. The COP for the large lateral wedge is moved in the other direction to the fifth toe. The force vector here is on the other side of the knee joint and therefore an abduction moment is measured. The experiments at the leg press showed the same effect that was described in Reeves and Bowling (2011) and Lewinson et al. (2014). Medial and lateral wedges under the foot can manipulate knee adduction and abduction moments 439
as the COP of the force vector is moved and therefore the moment arm to the knee can be changed. The results of this experiments show, that the horizontal force alone is not sufficient to conclude to joint loadings during training. As leg extension is a multi-articular movement, the whole resulting force vector together with the corresponding leg joint configuration allows for determining joint moments and guarantee for a safe and efficient training. Furthermore, these first experiments highlight the potential of a person-specific plate orientation for an improvement of leg press exercise outcome. In sagittal plane, a desired knee joint moment and training stimulus can be adjusted by varying support for heel and toe offset of the foot, whereby the COP of the force vector is not affected. In frontal plane, knee abduction and adduction moments and thus tibiofemoral contact forces (Kutzner et al. (2013)) can be minimized by an appropriate individual lateral or medial foot lifting, where also the COP is moved across the foot. 6. CONCLUSION The results confirm the potential in improving effectiveness and safety of leg press exercise by influencing joint loadings with the orientation of the foot plate in sagittal and frontal plane. These loads can be estimated with a sensor system consisting of a force plate, an optical motion tracking system and inverse dynamic calculations as shown in this paper. A control loop with the joint loading as controlled and the foot orientation as manipulated variable is depicted in Fig. 11. The actuator of the training device should be able to control the resistive force, movement velocity and range of motion by applying individual training movements. As research on other manipulated variables, including an optimization of the training trajectory needs to be done, a realization of the hardware of this actuator should be adaptable easily to other scenarios. An indus-
9th IFAC BMS 440 Aug. 31 - Sept. 2, 2015. Berlin, GermanyMelanie Kolditz et al. / IFAC-PapersOnLine 48-20 (2015) 435–440
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REFERENCES
current loading system
controller
sensor Fig. 11. Control loop with the joint loading as controlled and foot orientation as manipulated variable. An industrial robot is used as actuator and the human is within the controlled system. trial robot with six degrees of freedom, which can apply arbitrary six dimensional motions fulfills this requirement. As a well-trained sportsman can push up to 300 kg with one leg, a high payload robot is needed. The vision of such a robotic leg press with a KUKA KR 300 robot with a payload of 300 kg (see KUKA Roboter GmbH (2013) for specification) is shown in Fig. 12. The muscular system can
Fig. 12. Vision of a novel robotic leg press training device visualized in OpenSim. exert high loads only with low velocities and therefore this robot is certainly over-dimensioned. A detailed evaluation of the loads on the robot joints during leg press exercise is subject to further investigations. Future work in this project will be done in the development of a functional model of the presented robotic training device in order to investigate intra and inter individual variabilities and the dynamic behavior of the human in the control loop. For a translation of the results into a practical setup for rehabilitation centers, the requirements for a low-cost training device including the accuracies of motion tracking can be deduced from this high end setup. ACKNOWLEDGEMENTS This project is supported by KUKA Roboter GmbH, Augsburg, Germany. 440
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