Transaction B: Mechanical EngineeringVol. 16, No. 5, pp. 451{462c Sharif University of Technology, October 2009

Estimation of Human LowerExtremity Musculoskeletal Conditions

During Backpack Load Carrying

A. Selk Ghafari1, A. Meghdari1;� and G.R. Vossughi1

Abstract. This paper focuses on the biomechanical aspects of the human lower extremity loadingcondition during backpack load carrying. A biomechanical framework was generated with the aim ofemploying a block-oriented structure of Simulink integrated with the Virtual Reality Toolbox of MATLABsoftware to provide a simulation study of the musculoskeletal system in a virtual environment. In this case,a ten-degrees-of-freedom musculoskeletal model actuated with sixteen muscles in each leg was utilized tosimulate movement in the sagittal plane. An inverse dynamics based optimization approach was employedto estimate the excitation level of the muscles. In addition, distributions of the mechanical power analysisfor lower extremity muscles were carried out to enhance the understanding of human leg morphologyand control mechanism to provide load support. Simulation results provide a biomechanical framework toidentify the muscles and joints, which are critically subjected to musculoskeletal injuries during the activityunder investigation. Analysis of the muscle activation patterns and their distribution of the mechanicalpowers revealed the important role of the plantar exors of the ankle and the extensors of the knee andhip joints in supporting the body during backpack load carrying.

Keywords: Lower extremity; Musculoskeletal; Backpack; Load carrying; Muscle activation.

INTRODUCTION

The action of muscles during normal activities producesbone loading and joint contact forces in surplus of bodyweight [1]. Musculoskeletal loading is in uenced by anumber of inter-individual factors, such as weight andgender [2] as well as the activity being undertaken [3,4].Determining in vivo loading conditions in human jointsis di�cult due to the combination of complex structuralanatomy, complicated movement and dynamics andoften indeterminate muscle function. As a result,mathematical models have been employed to estimatevarious activities, such as muscle and joint contactforces [5-7], contribution of the lower extremity musclesto body support and forward progression and swingleg kinematics during walking [8-10]. A model based

1. Center of Excellence in Design, Robotics and Automation,School of Mechanical Engineering, Sharif University of Tech-nology, Tehran, P.O. Box 11155-9567, Iran.

*. Corresponding author. E-mail: meghdari@sharif.edu

Received 7 July 2008; received in revised form 8 March 2009;accepted 18 April 2009

estimation of muscle force usually requires optimizationregardless of the inverse or forward dynamic strate-gies selected to solve the governing equations of themusculoskeletal system [11,12]. The redundancy ofmuscular load sharing can be addressed by minimiz-ing an objective function appropriately selected forthe movement under investigation. Both static anddynamic optimization approaches have been employedwith equivalent results for normal gait [13]. One of themost interesting problems in biomechanical studies isinvestigation of the main functional di�erences of lowerextremity muscles for various activities [14]. Thesestudies contain informative biomechanical aspects andreveal the contribution of individual muscles for loadsharing, body support and the provision of bodyforward progression during the movements under in-vestigation. Musculoskeletal systems were extensivelyutilized to study the relationship between impairedmuscle coordination and observed gait deviations inpeople with paretic muscles [15]. Carrying heavy loadsis one of the most common reasons behind the leadingcause of musculoskeletal injuries. Peoples employed

452 A. Selk Ghafari, A. Meghdari and G.R. Vossughi

in speci�c occupations, such as �re-�ghters in haulingheavy equipment upstairs, nurses and physiotherapistslifting patients on and o� beds or people who assistmedical personnel in carrying wounded people from dis-aster areas, often have to carry heavy loads. Further-more, foot soldiers often have to carry extremely heavybackpack loads and walk long distance in rough terrain.Much research has been carried out into the e�ects ofthe con�guration of load carriage on the kinematicsand kinetics of lower extremities [16], joint forces [17],the energy expenditure of locomotion [18,19], groundreactions [20] and the electromyographic activities ofback muscle groups [21]. To the authors' knowledge,there is no extensive study in the literature regardingthe musculoskeletal analysis of the lower extremityduring load carrying. Dynamic simulation of humanmovement under load carrying conditions not onlyo�ers a powerful methodology for characterization ofthe causal relationship between muscle excitation pat-terns and the movement under investigation, but alsoprovides a framework to perform appropriate rehabili-tation processes needed to improve gait abnormalities.This paper describes the contributions of the lowerextremity muscles under load carrying conditions withthe aim of developing a musculoskeletal model of thebody. Activation levels of the lower extremity muscleswere simulated employing an inverse dynamics basedoptimization approach. In addition, distribution ofa mechanical power analysis for individual muscleswas carried out to investigate the main functionaldi�erences between level walking and load carrying.Biomechanical analysis of the movement under in-vestigation enhances the understanding of human legmorphology and control mechanism in supporting loadsand provides a biomechanical framework to identifythe muscles and joints that are critically subjectedto musculoskeletal injury during load carrying. Inaddition, muscle energy highlights the design criterionof more e�cient, anthropometric and lightweight assis-tive device structures for load augmentation purposes.The appropriate actuation mechanism of such a systemshould provide an additional plantar exion torque inthe ankle joint and an extension torque in knee andhip joints. Besides, the results provide a useful toolto perform appropriate rehabilitation processes neededto improve gait performance after injuries sustained inthe musculoskeletal system during load carrying.

MUSCULOSKELETAL MODEL

A complete musculoskeletal model of the human lowerextremity was developed with the aim of employingMATLAB/Simulink and the Virtual Reality Toolbox.A three-dimensional model of lower extremity boneswas constructed, based on collected data from medicalimaging, mainly by a Computer Tomography (CT)

scan. Surfaces of the lower limb bones involvingthe left and right iliac bones, the femur, the patella,the tibia, the �bula and all bones of the foot werereconstructed. Then, a model of the Head, Arms andTorso (HAT) was generated as a single rigid body.The constraints of the motion were applied to themodel, based on the anatomical center of rotationof the joints. A total of 23 degrees-of-freedom wasconsidered to describe the motion of the musculoskele-ton in three-dimensional space. HAT was articulatedwith the pelvis via a three degrees-of-freedom jointlocated at the third lumbar vertebra. Each hip jointwas modeled as a three degrees-of-freedom ball andsocket joint. For the knee joint, a modi�ed planarmodel characterizing the knee extensor mechanism [22]was employed. The foot was modeled as a singlesegment which was articulated with the tibia via a threedegrees-of-freedom rotational joint. Also, six degrees-of-freedom were assigned to the HAT position andorientation relative to the ground. Twenty functionalmuscle groups, based on anatomical classi�cation, wereemployed to drive the model. The muscle groupsincluded in the model were GMAX (gluteus maximus,adductor magnus), IL (iliacus, psoas), HA (bicepsfemoris long head, medial hamistrings), VS (three-component vasti), RF (rectus femoris), BF (bicepsfemoris short head), TA (tibialis anterior), TP (tibialisposterior), GA (medial and lateral gastrocnemius) andSO (soleus). An orthogonal reference frame for eachsegment is assigned in the anatomical joint location,based on the data provided in the literature [23]. Thereference frames assigned in the proposed model arecharacterized by the pelvis (PEL) which is �xed atthe midpoint of the line connecting the two anteriorsuperior iliac spines, Femur (FEM) which is �xed atthe center of the femoral head, Tibia (TIB) which islocated at the mid point of the line between the medialand lateral femoral epicondyles, Talus (TAL) and Foot(F) which are located at the mid point of the linebetween the apices of the medial and lateral malleolus.The origin and direction of the segmental referenceframes in the skeletal model are illustrated in Figure 1a.The origin and insertion coordinates for each actuatorwere de�ned based on the assigned segmental referenceframes to describe the attachment sites of muscles onthe proposed skeletal model. Coordinates data for themuscles included in the proposed model are given inthe Appendix (Tables A1 and A2) [23]. In some cases,it is su�cient to describe the muscle path with a linesegment between the origin and the insertion points.In other cases, where the muscle wraps over bone oris constrained by retinacula, intermediate points, ore�ective origin and insertion points, were introduced torepresent the muscle path more accurately [23,24]. Theproposed musculoskeletal model and muscle groupsincluded in the model are illustrated in Figure 1b. The

Lower Extremity Muscle Functions During Load Carrying 453

Figure 1. (a) Segmental reference frames of the rightlower extremity. Origins and directions of the orthogonalreference frames are shown for the pelvis (PEL), femur(FEM), tibia (TIB), talus (TAL) and foot (F); (b) themusculoskeletal model of the lower extremity and musclegroups included in the model.

muscles within each group received the same excitationpattern. The force generating capacity of each actuatorwas considered based on a Hill-type model governedby muscle force-length-velocity characteristics [24]. Inthe proposed model, in addition to the active element,there is a passive viscoelastic element in parallel and anelastic tendon element in series. The muscle excitation-contraction dynamics were modeled using a �rst orderdi�erential equation to relate the rate of change inactivation to the muscle excitation signal, based on adescription from the literature [24]. In the proposedmodel, the activation level of the muscles can be variedcontinuously between zero and one; zero indicating noexcitation and one indicating full excitation. For agraphic representation of the musculoskeletal system,the constructed model was exported in a WRL formatwhich served as the input �le of the Virtual Realitytoolbox of MATLAB [25].

Since the exion-extension degrees of freedom atankle, knee and hip joints are subjected to the highestamount of power [26,27], the simulation analysis wasconstrained to the sagittal plane movement. Accord-ingly, a total of ten degrees-of-freedom was consideredto represent the motion of the musculoskeletal sys-tem. The governing equations of the musculoskeletalsystem were generated employing a vector bond-graphapproach [28]. The application of vector bond graphsto multi-body dynamic systems signi�cantly reducesthe amount of e�ort required to model such systems.

Each segment of the lower extremity is subjected tomuscle forces, thus the e�ects of the muscle forces canbe replaced by an external force and moment abouteach anatomical joint center. The segment's mass andinertia are indicated by mi and Ji, respectively, andthe body coordinate system is located at the center ofmass of the rigid body. The arm vectors from jointi � 1 and i to the center of mass of segment i arede�ned by Ri� and Ri+, respectively. A correspondingvector bond graph model for the rigid body segmentillustrated in Figure 2a is proposed as the systemdepicted in Figures 2b and 2c [29]. In the proposedbond graph model, the revolute joints connectingthe adjacent segments together are molded with 1-junctions. A detailed modeling procedure of the humanbody musculoskeletal system was presented in [28] andomitted here for the sake of brevity. The complete bondgraph model of the proposed musculoskeletal system isdepicted in Figure 3.

The governing equations of the musculoskeletalsystem in the compact form are derived according tothe bond graph model represented in Figure 3 andgeometrical parameters de�ned in Figure 2d given by:8>><>>:

~�ai = �~�i � ~Ri� � ~!i ��~!i � ~Ri�

�+ ~ai�1

~Fi = mi ~�ai +mig~j + ~Fi�1

Ji~�i = ~Mi � ~Mi�1 + ~Ri+ � ~Fi � ~Ri� � ~Fi�1(1)

where ai, �i, !i, Fi, and Mi represent the accelera-tion, angular acceleration, angular velocity, force andmoment of segment i, respectively. The dynamicalequations related to the right and left shank, thighand pelvis could be obtained iteratively employingEquation 1. The dynamic equations corresponding tothe right and left feet in the contact phase are givenby:8>><>>:

~�ai = �~�i � ~Copi � ~!i ��~!i � ~Copi

�~Fi = mi ~�ai +mig~j + ~GRFiJi~�i = ~Mi + ~Ri+ � ~Fi � ~Copi � ~GRFi

(2)

where GRF and Cop represent the ground reactionforce and center of pressure under each foot, respec-tively. Accordingly, the dynamic equations for HATare expressed by:8>><>>:

~�ai = �~�i � ~Ri� � ~!i ��~!i � ~Ri�

�+ ~ai�1

0 = mi~�ai +mig~j + ~Fi�1

Ji~�i = � ~Mi�1 � ~Ri� � ~Fi�1

(3)

Since the joint angles between skeletal limb segment, q,serve as the input for graphical representation of move-ment in a virtual environment, the governing equations

454 A. Selk Ghafari, A. Meghdari and G.R. Vossughi

Figure 2. (a) The equivalent force-couple system of ith rigid body; (b) An I �eld bond graph model representation for ithrigid body; (c) A detailed bond graph model representation for ith rigid body; (d) De�nition of the geometrical parametersfor a skeletal system.

Figure 3. The complete bond graph model representation of the musculoskeletal system.

Lower Extremity Muscle Functions During Load Carrying 455

of motion should be transferred and represented instandard form as:

A(q)�q + b(q; _q) + g(q) = Rm(q):Fm +RGRF:FGRF;(4)

where A(q), b(q: _q); g(q); Rm(q), Fm, RGRF and FGRFare system mass matrix, vector of centrifugal andCoriolis terms, vector of gravity terms, matrix ofmoment arms about the anatomical joints, vector ofmuscle forces, matrix of resultant ground reaction forcetransformation and generalized ground reaction forces,respectively. The muscle activation dynamics weredescribed with a �rst order di�erential equation withactivation and deactivation time constants of 22 and200 msec., respectively [24,28]. A computer model ofthe lower extremity musculoskeletal system was gener-ated employing a block oriented structure of Simulinkand integrated with the Virtual Reality toolbox ofMATLAB software for graphical representation. Theblock diagram representation of the complete system isillustrated in Figure 4.

OPTIMIZATION FRAMEWORK

Simulation of the time dependent behavior of humanmovement was carried out employing the solution ofa static or dynamic optimization problem for theredundant muscle groups involved. In this approach,

the muscular load sharing problem was solved by min-imizing an objective function subjected to a constraintequalizing the sum of individual muscular momentsaround a joint and the desired joint torques obtainedfrom inverse dynamics. Some additional constraints,such as the �nal time constraint and muscle forcebounds, should be considered in the optimization algo-rithm. The individual muscle moments around a jointwere calculated from the muscle force generated bythe optimization routine and the corresponding musclemoment arm which was derived from a musculoskeletalmodel employing experimental gait data. Performanceof the employed method for the estimation of lowerextremity muscle forces has been illustrated in the liter-ature extensively [30,31]. Speci�cally, the performancecriterion was considered as the weighted sum of squaredresiduals in the general form of:

J =mXj=1

nXi=1

wj(XSimij �XExp

ij )2; (5)

where XExpij , XSim

ij , wj , m and n are experimentallymeasured data, simulation data, weighting factor,number of tracking quantities and number of timesteps, respectively. Speci�c quantities evaluated in theobjective function include muscle force, muscle stress,joint kinetics, joint kinematics or a combination of

Figure 4. Neuro-musculoskeletal functional block diagram and three-dimensional interactive skeletal model developed inthe virtual environment.

456 A. Selk Ghafari, A. Meghdari and G.R. Vossughi

them which should be selected appropriately for themovement under investigation.

SIMULATION RESULTS ANDDISCUSSIONS

In this study, the inverse dynamics assisted datatracking approach was employed to estimate lowerextremity muscle activation during gait in both cases ofnormal gait and under load carrying conditions. Themodel anthropometry was set to the average data of�ve male subjects with an average age, height andweight of 26� 3 years, 177 � 3 cm and 70:1 � 7:8kg, respectively, which was reported in [32]. Param-eters de�ning the nominal properties of each actuator,containing peak isometric force, corresponding �berlength and pennation angle of muscle plus tendonslack length, were adapted based on data reportedin [23]. Kinetic and kinematical data of the lowerextremity related to walking with a 47 kg backpackload and under level walking conditions were extractedfrom the literature [33] and depicted in Figure 5.Kinematical data was fed into the developed virtual

Figure 5. Angular displacement of the ankle, knee andhip joints during normal gait and backpack load carryingbased on the data reported in [33].

model of the lower extremity and the moment armof the lower extremity muscles about the joint forboth cases were derived. The computer model of thesystem [28] was generated, employing a block orientedstructure of Simulink, and integrated with the virtualmodel to perform a dynamic simulation. The inversedynamics optimization problem for both cases wassolved employing a constrained minimization approach.The performance criterion for both cases was formu-lated to minimize the weighted sum of the muscleactivation squared when constrained to track the gaitkinetic quantities (i.e. the hip, knee, and ankle jointtorques), satisfying the �nal time constant and muscleactivation bound [12]. The excitation pattern for thelower extremity muscles were discretized to 26 pointsby 50 ms, which were allowed to vary continuouslybetween zero and one. The muscle excitation patternserved as a control parameter in the optimizationproblem. The algorithm �ne-tuned each muscle'sexcitation onset, duration and magnitude until thesum of the muscle activation squared and subjectedto the constraint of joint kinetics over the gait cyclewas minimized. An inverse dynamics assisted trackingapproach was able to track the experimental jointtorques accurately under normal walking and 47 kgbackpack load carrying conditions with only a smalldeviation from the experimental kinetics. Simulatedlower extremity joint torques and desired experimen-tal values were illustrated in Figure 6. Estimatedmuscle excitation patterns for eight of the musclesincluded in the model under normal walking and 47 kgbackpack load carrying conditions were illustrated inFigure 7. The muscle activation patterns are comparedwith mean (�1 S.D.) recti�ed electromyogram (EMG)activities of young adults during normal walking, asreported in the literature [34]. The excitation historyof the muscles illustrated that the ankle plantar exor(SO) and the knee extensor (RF) are the musclesthat exhibit a distinct excitation level between normalwalking and load carrying. This fact shows theimportant role of these muscles in the stance phase(� 0 � 60% of the gait cycle). Also, simulationresults illustrate that under the load carrying con-ditions, the primary contributions to body supportare provided by hip extensors (GMAX and HA) andthe knee extensor (RF) during the loading responsephase (� 0� 10% of the gait cycle). Furthermore,the forward acceleration and deceleration of the bodywere generated by the knee exor (BS) during theinitial swing phase (� 60� 70% of the gait cycle) andterminal swing phase (� 85 � 100% of the gait cycle),respectively.

Distribution of muscle mechanical powers underboth normal walking and load carrying conditions isillustrated in Figure 8. Power distribution analysisof the muscles reveals that the plantar exors of the

Lower Extremity Muscle Functions During Load Carrying 457

Figure 6. Simulated lower extremity joint torques closely tracked experimental values for normal walking and with 47 kgbackpack load carrying condition.

Figure 7. Estimated muscle activation patterns of normal walking and 47 kg backpack load carrying in comparison withthe corresponding EMG activities for normal walking reported in [34] for eight of the muscles included in the model.

458 A. Selk Ghafari, A. Meghdari and G.R. Vossughi

Figure 8. Distribution of the muscle power during normal walking and with 47 kg backpack load carrying conditions. Allunits are in Watts.

ankle, extensors of the knee and hip joints exhibitdistinct functional di�erences between normal walkingand under load carrying conditions. In other words,under the load carrying condition, plantar exors of theankle joint transfer the power to support the body dur-ing Contralateral Heel-Strike (CHS) to Toe-O� (TO),(� 50� 65% of gait the cycle). Furthermore, extensorsof the knee joint absorb power during Heel-Strike(HS) to Contralateral Toe-O� (CTO), (� 0� 15% ofthe gait cycle) and transfer the power to supportthe body during CTO to CHS (� 15 � 50% of thegait cycle). Additionally, the extensors of the hipjoint transfer the power to support the body duringHS to CHS (� 0 � 50% of the gait cycle) and the exors absorb the power and damp the impact energyduring the CHS to TO phase. Besides, the jointpower analysis which is depicted in Figure 9, points

to the fact that the backpack load did increase jointpower as compared to the no load condition. This isreasonable since the added load increases the downwardforce signi�cantly and translates into larger moments.The role of the ankle joint in transferring power andthe knee joint in absorbing power was dominatedduring CHS to TO. In other words, the ankle andknee joints provide additional e�ort in supporting theload during CHS to TO. Additionally, the hip jointplays an important role in balancing the transferringand absorbing powers in order to support the load,accelerating and decelerating the body during HS toCHS. In summary, the ankle and knee joints are majorcontributors in sharing load distribution under loadcarrying conditions. The moment arms of the musclesabout the anatomical joints are another biomechanicalaspect that is depicted in Figure 10. The major

Lower Extremity Muscle Functions During Load Carrying 459

Figure 9. Distribution of the joint powers during normalwalking and with 47 kg backpack load carrying conditions.

di�erences are shown in the moment arm of the musclesabout the ankle joint, in a comparison between bothcases. This aspect introduces the higher momentproduction capability of the ankle joint during loadcarrying.

The overall objective of this study was to gaina deeper understanding of the condition and func-tioning of the lower extremity muscles during loadcarrying. Determining in vivo loading conditions inhuman joints is di�cult, due to the combination ofcomplex structural anatomy, complicated movementdynamics and often indeterminate muscle functions.On the other hand, ethical considerations discouragethe use of invasive methods to determine muscle forcesin humans. Therefore, the only opportunity to estimatethe complex distribution of muscle activity is o�eredby computer simulations. The proposed model o�ers apowerful computational tool with the aim of employinga block oriented structure of Simulink integrated withthe Virtual Reality toolbox of MATLAB softwareto provide a biomechanical framework for simulatingvarious biomechanical aspects of movement in a vir-tual environment. In addition, employing a virtualframework analysis makes it possible to evaluate new

designed products before construction and is able toperform an optimal design to improve the quality ofproducts. The results of this study will help selectingthe proper actuation mechanism of the assistive devicesfor load carrying purposes. To conclude, the appro-priate actuation mechanisms of the assistive devicesmay include the actuators to provide additional exiontorque for the ankle joint, and an extension torquefor the knee and hip joints for the purpose of poweraugmentation.

CONCLUSIONS

To date, a non-invasive measurement of in vivo mus-cle forces is still impossible. Ethical considerationsdiscourage the use of invasive methods to determinemuscle forces in humans. Therefore, computer sim-ulations o�er the only opportunity to analyze thehuman biomechanical complex. A complete muscu-loskeletal model of the body, with sixteen muscu-lotendon actuators per leg, was generated with theaim of employing Simulink and the Virtual RealityToolbox of MATLAB software for this purpose. Aninverse dynamics optimization data tracking approachwas utilized to estimate the lower extremity muscleload sharing conditions during backpack load carrying.Furthermore, a muscle power consumption analysiswas carried out to identify the critical importanceand contribution of individual muscles in supportingload during movement. Simulation results illustratethe accuracy and performance of the proposed methodto solve muscular load sharing problems during levelwalking and load carrying. On the other hand, thecritical contribution of the plantar exors of the anklejoint and extensors of the knee and hip joints duringload carrying were revealed by the simulation analy-sis. Biomechanical analysis of the movement underinvestigation enhances our understanding of humanleg morphology and control mechanisms in supportingloads. In addition, by employing a simulation study,it was possible to identify the muscles and joints thatare critically subjected to musculoskeletal injury duringthe activity under investigation. In this case, duringload carrying, the dominant roles of the ankle joint intransferring power and the knee joint for its capabilityof power absorption were highlighted. Besides, muscleenergy provides a biomimetic design criterion for an-thropometric structures of load augmentation assistivedevices. In this case, an additional exion torque in theankle joint and an extension torque in the knee and hipjoints should be provided by an assistive mechanism.The proposed model can also be employed as a usefultool to provide an appropriate rehabilitation processwhich can be developed by therapists to improve thegait performance of individuals after musculoskeletalinjury.

460 A. Selk Ghafari, A. Meghdari and G.R. Vossughi

Figure 10. The comparison of the moment arm of the muscles about anatomical joints between normal walking and 47 kgbackpack load carrying; subscripts A, K and H stand for the ankle, knee and hip joints, respectively. All units are in mm.

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APPENDIX A

Included here are the origin and insertion coordinatesof the lower extremity muscles included in the proposedmusculoskeletal model in Tables A1 and A2.

462 A. Selk Ghafari, A. Meghdari and G.R. Vossughi

Table A1. Origin coordinates of the lower extremity muscles included in the proposed musculoskeletal model.

CoordinatesMusculotendon

ActuatorReference

Framex (m) y (m) z (m)

SO Talus -0.0292 0.2467 0.0006

TA Talus-0.01550.0259

0.21750.0257

0.0134-0.0093

TP Talus -0.0268 0.2419 0.0356

GA Tibia -0.0203 0.0071 -0.0073

BF Tibia -0.0007 0.1784 0.0144

VS Tibia 0.0106 0.2026 0.0205

RF Femur 0.0326 0.0323 0.0174

IL Femur 0.0075 0.1350 -0.0400

HA Femur -0.0409 -0.0455 -0.0140

GMAX Pelvis-0.1556-0.1529

-0.0314-0.1052

0.00580.0403

Table A2. Insertion coordinates of the lower extremity muscles included in the proposed musculoskeletal model.

CoordinatesMusculotendon

ActuatorReference

Framex (m) y (m) z (m)

SO Foot -0.0365 -0.0288 0.0056

TA Foot 0.1850 -0.0510 -0.0330

TP Foot 0.0715 -0.0420 -0.0260

GA Foot -0.0368 -0.0289 0.0028

BF Talus -0.0384 0.3323 0.0433

VS Talus -0.0005 0.4056 0.0005

RF Talus 0.0041 0.4084 -0.0006

IL Tibia -0.0180 0.3351 0.0116

HA Talus -0.0508 0.3321 0.0073

GMAX Femur-0.0299-0.0060

-0.1041-0.1419

0.01350.0411