Dynamic Simulation of Human Movement Using Large-Scale Models of the Body

© 2000 S. Karger AG, Basel

Fax +41 61 306 12 34E-Mail [email protected] Accessible online at:www.karger.com www.karger.com/journals/pho

Biology of Communication and Motor Processes

Phonetica 2000;57:219–228

Marcus G. Pandy, PhDDepartment of Kinesiology and Health EducationBellmont Hall, Room 222, University of Texas at AustinAustin, TX 78712-D3700 (USA), Tel. +1 (512) 232-5404Fax +1 (512) 471-8914, E-Mail [email protected]

Dynamic Simulation of Human MovementUsing Large-Scale Models of the Body

Marcus G. Pandy Frank C. Anderson

Department of Kinesiology and Biomedical Engineering Program, University of Texasat Austin, Austin, Tex., USA

AbstractA three-dimensional model of the body was used to simulate two different motor

tasks: vertical jumping and normal walking on level ground. The pattern of muscleexcitations, body motions, and ground-reaction forces for each task were calculatedusing dynamic optimization theory. For jumping, the performance criterion was tomaximize the height reached by the center of mass of the body; for walking, the mea-sure of performance was metabolic energy consumed per meter walked. Quantitativecomparisons of the simulation results with experimental data obtained from peopleindicate that the model reproduces the salient features of maximum-height jumpingand normal walking on the level. Analyses of the model solutions will allow detailedexplanations to be given about the actions of specific muscles during each of thesetasks.

Copyright © 2000 S. Karger AG, Basel

Introduction

Many studies have used computer models to simulate the kinematic and kineticpatterns observed during human movement, but very few have included the actionsof the muscles in a three-dimensional model of the body. The reason is that detailedcomputer simulations involving dynamic models of the musculoskeletal system incurgreat computational expense [Anderson et al., 1995, 1996]. With the emergence ofhigh-speed, parallel supercomputers, it is now possible to use very detailed theoreticalmodels of the body to produce realistic simulations of movement.

An overall goal of our ongoing work is to develop a model of the body that couldbe used to simulate a wide range of locomotor tasks including walking and running atvarious speeds. A specific aim of this study was to use such a model, together withdynamic optimization theory, to simulate one full cycle of normal gait. Dynamic opti-mization was chosen because it presents a very powerful approach for simulatingmovement. Firstly, the dynamic optimization problem may be formulated independentof experimental data, which means that the motor patterns can be predicted rather thanassumed. Secondly, this theoretical approach allows a model of the system dynamics

Received: December 14, 1999Accepted: February 14, 2000

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(i.e. the body) and a model of the goal of the motor task to be included in the formula-tion of the simulation problem. Since the performance criterion for walking is some-what ambiguous, we first solved a dynamic optimization problem for vertical jumping.Jumping was chosen not only because it presents a well-defined goal (i.e. to jump ashigh as possible), but also because it involves the coordinated motion of all the bodysegments. This task therefore provides an excellent paradigm for evaluating thedynamic response of any model. Once the dynamic optimization problem for jumpingwas solved and the response of the model validated against experimental data, the samemodel could then be used with greater confidence to simulate normal walking overlevel ground.

Methods

Musculoskeletal Model of the BodyThe skeleton was represented as a ten-segment, 23-degree-of-freedom (dof) mechanical linkage.

The pelvis was modeled as a single rigid body with 6 dof; the remaining nine segments branched in anopen chain from the pelvis (fig. 1). The head, arms, and torso (HAT) were lumped into a single rigidbody, and this segment articulated with the pelvis via a 3-dof ball-and-socket joint located at the 3rdlumbar vertebra. Each hip was modeled as a 3-dof ball-and-socket joint, and each knee was modeled

Pandy/Anderson220 Phonetica 2000;57:219–228

Fig. 1. Frontal-plane view of the model skele-ton. The inertial reference frame is fixed to theground at the level of the floor. The axes of theinertial frame form a right-handed coordinatesystem: the X axis is directed forward, the Y axisis directed upward, and the Z axis is directed lat-erally. Twenty-three generalized coordinates areused to describe the position and orientation ofall the body segments in the model.

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Dynamic Simulation of Movement 221Phonetica 2000;57:219–228

as a 1-dof hinge. Two segments were used to model each foot: a hindfoot segment and a toes segment.The hindfoot articulated with the tibia via a 2-dof universal joint comprising two axes of rotation: onefor the ankle and the other for the subtalar joint. The toes articulated with the hindfoot via a 1-dofhinge joint. The positions and orientations of the axes of rotation of each joint were based on experi-mental data reported in the literature [e.g. Inman, 1976].

The interaction of the feet with the ground was simulated using a series of spring-damper unitsdistributed under the sole of each foot. Four ground springs were located at the corners of the hindfootsegment and one was positioned at the distal end of the toes. Each ground spring applied forces in thevertical, fore-aft, and transverse directions simultaneously. Details of the force-displacement-velocityrelations assumed for the ground springs are given by Anderson and Pandy [1999].

The model was actuated by 54 musculotendinous units. Each leg was actuated by 24 muscles,and relative movements of the pelvis and HAT were controlled by 6 abdominal and back muscles(fig. 2). The path of each actuator was based on geometric data (musculotendon origin and insertionsites) reported in the literature [e.g. Friederich and Brand, 1990]. Straight lines and combinations ofstraight lines and space curves were used to represent the three-dimensional path of each muscle in themodel. Each actuator was modeled as a three-element, Hill-type muscle in series with an elastic tendon

Fig. 2. Schematic diagramshowing some of the musclesincluded in the model. Fifty-four back, abdomen, and legmuscles were used to actuatethe model skeleton.

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[Zajac, 1989; Pandy et al., 1990]. Parameters defining the nominal properties of each actuator (i.e.peak isometric force and the corresponding fiber length and pennation angle of muscle plus tendonslack length) are reported by Anderson and Pandy [1999]. Muscle excitation-contraction dynamicswas modeled as a first-order process [Zajac, 1989]. Details of our neuromusculoskeletal model of thebody are given by Anderson and Pandy [1999] and Anderson [1999].

Optimization ProblemsThe model was used to simulate two tasks: vertical jumping and normal walking on the level.

Dynamic optimization theory was used to find the pattern of muscle excitations and the correspondingmuscle forces and limb motions subject to a performance criterion which models the goal of eachmotor task. For jumping, the problem was to find the pattern of muscle excitations needed to maximizejump height (i.e. the height reached by the center of mass of the whole body). No kinematic constraintswere imposed on the dynamic optimization solution for jumping; however, to reduce the size of theproblem, the muscle excitation histories for each side of the body were assumed to be identical.

For walking, the performance criterion was to minimize the total metabolic energy consumed bythe muscles over one cycle of gait. A large number of experimental studies have shown that walkingspeed is selected in order to minimize metabolic cost per unit distance traveled [Ralston, 1976]. Thus,the dynamic optimization problem for walking was to find the pattern of muscle excitations needed tominimize metabolic energy consumption per meter walked. Muscle energy production was calculatedby summing five terms: basal heat, activation heat, maintenance heat, shortening heat, and themechanical work done by all the muscles [Woledge et al., 1985].

Some heat is liberated by muscle merely as a consequence of being alive. This is called the rest-ing or basal heat. When muscle contracts, heat is liberated as a result of movement of calcium in andout of the sarcoplasmic reticulum. This is known as activation heat. Heat is also liberated as a result ofthe interaction between actin and myosin, as the myosin heads attach and detach from the actin fila-ments (cross-bridge cycling) during an isometric contraction. The heat produced during an isometriccontraction is called maintenance heat. When muscle contracts and shortens, extra heat is liberatedover and above that produced during an isometric contraction. This amount of heat is called shorteningheat or the Fenn effect. If during a contraction a muscle also changes its length, then mechanical workis done by the muscle as it moves the bones about the body joints. From the First Law of Thermo-dynamics, the total energy produced during a shortening or lengthening contraction is equal to the totalheat liberated plus the mechanical work done.

Two kinematic constraints were used to simplify the dynamic optimization problem for walking.First, the gait cycle was assumed to be bilaterally symmetric; that is, the left-side stance and swingphases were assumed to be identical with the right-side stance and swing phases, respectively. Intro-ducing this constraint simplifies the problem because it means that only one half of the gait cycle needsto be simulated. Second, the simulated gait pattern was made repeatable by constraining the states ofthe model to be equal at the beginning and end of the gait cycle.

Computational MethodThe dynamic optimization problems for jumping and walking were solved using parameter opti-

mization [Pandy et al., 1992]. In this method each muscle excitation history is discretized into a set ofindependent variables called control nodes. The problem then is to find the values of all the controlnodes which minimize the value of the performance criterion. Once the values of the control nodeshave been found, the excitation history for each muscle in the model is reconstructed by linearly inter-polating between the control nodes. Sixteen control nodes were used to represent the excitation historyfor each muscle in the model. For the 54 muscles included in the model the total number of unknownvariables was 864. Computational solutions to the dynamic optimization problems for jumping andwalking were found using two parallel supercomputers: an IBM SP-2 and a Cray T3E.

Human ExperimentsTo evaluate the model predictions, kinematic, kinetic, and muscle EMG data were recorded from

5 adult males. Each subject first performed a series of maximal vertical jumps. Each jump began froma static squatting position and was executed with the arms crossed over the chest. The subject thenwalked at his freely selected cadence and stride length on a level walkway in the laboratory. During


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each activity the three-dimensional positions of the body segments were recorded using a four-camera,passive-marker, video-based system. Vertical, fore-aft, and transverse components of the ground-reac-tion force were measured using a six-component, strain-gauge force plate. Muscle EMG data wererecorded using surface electrodes mounted over the following muscles on the right side of the body:tibialis anterior, soleus, lateral gastrocnemius, vastus lateralis, rectus femoris, hamstrings, adductormagnus, gluteus maximus, gluteus medius, erector spinae, and the external abdominal obliques.

Results

JumpingThere was quantitative agreement between the response of the model and the way

each of the subjects executed a maximal, vertical, squat jump. EMG data indicated astereotypic pattern of muscle coordination: the back, hip, and knee extensors were acti-vated at the beginning of the jump, followed by the more distal ankle plantar flexors.

Peak vertical forces measured for the subjects ranged from 1,500 to 2,100 N com-pared with a peak force for the model of 2000 N (fig. 3). Much smaller forces wereexerted on the ground in the fore-aft direction; peak fore-aft forces ranged from 120 to170 N for the subjects compared with 270 N for the model. The joint-angular displace-ments of the HAT, pelvis, hips, knees, and ankles were also similar for the model andthe subjects during the propulsion phase of the jump.

Fig. 3. Vertical ground-reaction force generated by the model (black line) and each of the 5 subjects(gray lines) during the ground-contact phase of a maximum-height, squat jump. For the model, theresultant force was found by summing the forces developed by the ground springs located under thesole of each foot. Time t = 0 s marks the instant that the model and the subjects leave the ground.

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The peak vertical acceleration of the center of mass of the model was 19 m/s2, wellwithin the range of values measured for the subjects. The model left the ground with avertical velocity of 2.3 m/s and jumped to a height of 36.9 cm. Subjects left the groundwith vertical velocities ranging from 2.0 to 2.5 m/s, and their mean jump height was37 cm.

WalkingGood agreement was also obtained between the simulation results and the experi-

mental data recorded for gait. The model and the subjects walked at an average speedof 81 m/min, which is very close to the optimal speed estimated by Ralston [1976].Compared with the muscles of the leg, the abdominal and back muscles were activatedat relatively low levels. The back muscles were quiet throughout the gait cycle, exceptin the neighborhood of opposite heel strike. The abductors were excited in a doubleburst: the first during double support and the second during the middle portion of sin-gle support. Consistent with experiment, vasti and biceps femoris short head in themodel were excited simultaneously between heel strike and opposite toe off. It is sig-nificant that the dynamic optimization solution predicts cocontraction of the uniarticu-lar quadriceps and hamstring muscles, for this result lends support to our minimum-metabolic-energy hypothesis for walking.

Translations of the model pelvis in the sagittal, frontal, and transverse planes wereconsistent with the prototypical patterns measured for the subjects. For example, in the


Fig. 4. Vertical ground-reaction force generated by the model (black line) and each of the 5 subjects(gray lines) during walking. For the model, the resultant force was found by summing the forces devel-oped by the ground springs located under the sole of each foot. OTO denotes opposite toe off, OHS isopposite heel strike, TO is toe off, and HS is heel strike. 0% and 100% indicate heel strike of the sameleg (one gait cycle) for the model and the subjects.

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transverse plane the pelvis traced a sinusoidal path as it moved forward and shifted lat-erally from over one foot to over the other. The amplitudes of lateral oscillation for themodel and the subjects were 2.6 and 4.0 cm, respectively. The joint-angle trajectoriesfor the back, hips, knees, and ankles in the model were also consistent with kinematicdata obtained from the gait experiments. For example, following heel strike the kneeflexed 20° until opposite toe-off, extended to near full extension prior to opposite heelstrike, flexed to 70° shortly after toe-off, and then extended once again to near fullextension at heel strike.

The vertical force exerted by the ground showed the familiar double-hump pat-tern, with the first hump occurring near opposite toe-off and the second occurring justprior to opposite heel strike (fig. 4). The fore-aft component was directed posteriorlyfrom heel strike to 30% of the gait cycle, and anteriorly thereafter. The variation in themediolateral component was more complicated, but the result predicted by the modelwas very similar to that measured for the subjects, at least until 40% of cycle time.

The model expended metabolic energy at a rate of 6.6 J/(kg·s), which is about50% higher than the value obtained from oxygen consumption measurements made inpeople [Burdett et al., 1983]. The model calculations also suggest that the mechanicalefficiency of muscles for walking at normal speeds is about 30%, which is a little lowerthan the value (approximately 40%) obtained from heat measurements made on iso-lated muscle [Hill, 1964].

Discussion

Several aspects of our work should be compared and contrasted with previousattempts to simulate whole-body movement. First, by changing only the performancecriterion and the initial conditions of the task, we have demonstrated that it is possibleto use the same model of the body to simulate two very different movements: verticaljumping and walking. Since the performance criterion for vertical jumping is clearlydefined, dynamic optimization solutions for jumping are ideally suited to evaluatingand refining a model of the system dynamics (i.e. the body). When the model is used tosimulate other tasks such as walking and running at various speeds, emphasis may thenbe placed on evaluating and refining a model of the performance criterion.

Second, the simulations of jumping and walking performed in this study are muchmore elaborate than what has been published previously. The model used in this studyhas 23 dof and is actuated by 54 muscles. The number of degrees of freedom is 2–3times greater and the number of muscles is 2–5 times greater than that included in pre-vious dynamic optimization models of movement [Hatze, 1976; Davy and Audu, 1987;Pandy et al., 1990; Yamaguchi and Zajac, 1990; Tashman et al., 1995].

Finally, our approach to simulating movement is predictive rather than descrip-tive; that is, the body-segmental motions, ground-reaction forces, and muscle excita-tion patterns are all calculated rather than assumed. Previous studies have simulatedmovement by forcing the model to track measurements of the time histories of body-segmental displacements and velocities [Davy and Audu, 1987; Yamaguchi and Zajac,1990]. In this study, the body-segmental motions, ground-reaction forces, and muscleexcitation patterns were all predicted given only the states of the model at the begin-ning and/or end of the simulated movement. This is an important aspect of ourapproach, because it guarantees that the muscle-force histories in the model are deter-


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mined almost entirely by the performance criterion used to model the goal of the motortask. For walking, in particular, the fact that the predicted kinematics, ground-reactionforces, and muscle coordination patterns all agree closely with those obtained fromexperiment supports the use of minimum metabolic energy as a measure of performance.

In summary, the feasibility of performing realistic simulations of movementdepends on a number of factors. First, a robust computational algorithm is needed tohandle nonlinear problems characterized by a large number of input controls [Pandy etal., 1992]. Second, high-performance, parallel supercomputers are needed to convergeto the optimal solution in a reasonable amount of time [Anderson et al., 1995]. Third, adetailed and computationally efficient model of the foot is needed to adequately simu-late repetitive contact of the feet with the ground. Lastly, very fast computer-graphicsworkstations (e.g. SGI Onyx) must be used, so that the simulation results may be visu-alized in real time while a good initial guess to the solution is being sought.

The work reported here lays the foundation for us to describe and explain the rela-tionships between mechanics and energetics of locomotion at a much deeper level thanhas been possible to date. A large number of experiments have described the variationin kinematics, kinetics, and metabolic cost with walking speed [Murray et al., 1966;Grieve, 1968; Margaria, 1976; Ralston, 1976; Chen et al., 1997]. The results of thesestudies can be used to evaluate the response of the model when it is used to simulatehumans walking on level ground at speeds in the range 3–9 km/h. Records of changesin kinematics, kinetics, and metabolic cost as humans walk up and down inclines [Mar-garia, 1976; Inman et al., 1981] can also be used to evaluate the response of the modelunder conditions of varying external load. Because the model gives detailed informa-tion about the forces developed by the leg muscles during movement, analyses of thesimulation results will allow (1) more detailed descriptions to be given for the relation-ships between metabolic energy consumption and muscle force [Taylor et al., 1980],and (2) rigorous testing of the hypothesis that metabolic cost of locomotion is deter-mined mainly by the cost of generating muscle force [Taylor, 1994].

Relevance of Modeling and Optimization to SpeechWhy is perhaps the most difficult question in biology to answer. Why do we move

our limbs in a characteristic manner during walking? And why do our vocal tractsmove in a certain way during speech? Experiments alone cannot produce unequivocalanswers to such questions. To answer the question for walking, the forces developed bythe leg muscles must be measured, and these data must then be correlated with inde-pendent measures of muscle energy consumption, joint-reaction forces, etc. Invasivemethods for quantifying muscle force such as instrumented buckle transducers cannotbe used on living people, and, unfortunately, noninvasive methods such as electromyo-graphy do not provide the quantitative accuracy needed nor do they permit access to allthe muscles of interest.

Computational modeling combined with optimization theory offers a powerfulalternative for determining muscle forces in the body, and there is every reason tobelieve that this approach can also be used to study the mechanics and energetics ofspeech. Physiological models of speech production have been developed and reportedin the literature [e.g. Laboissiere et al., 1995; Willhelms-Tricarico and Perkell, 1995],but, to our knowledge, these models have not yet been placed in the context of dynamicoptimization so that interactions between vocal tract movements and speech produc-tion may be explained.


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It is tempting to suggest that all cyclic body movements, including those forspeech, might be produced in the interests of minimizing metabolic energy consump-tion [Lindblom, 1999]. Although, as explained above, this hypothesis cannot be testedrigorously in the context of a physiological experiment, one may proceed for speech inthe same way as we have done for walking. A dynamic optimization problem may beformulated based on the hypothesis that muscle metabolic energy is minimized duringnormal, steady-state speech. Muscle metabolic energy may be estimated by summingthe heat produced and the work done by all the muscles that move the vocal tract.Should the optimization solution predict jaw movements at the same frequency as isobserved during normal, steady-state speech (roughly 5 Hz), then the minimum-energyhypothesis would be supported, but not proven. A more compelling case could be madeonly if the model predictions of energy cost compared favorably with oxygen con-sumption measurements made on people [Lindblom et al., 1999].

Increasing or decreasing the frequency at which we speak presumably scalesenergy cost in proportion, so frequency is a parameter that can be altered to test themodel further. Quantitative agreement between model and experiment over a widerange of speaking frequencies would demonstrate the model’s ability to simulate theenergetics of speech production for unconstrained movements of the vocal tract.Because the model simulations also provide information about muscle force, explana-tions could then be given for differences between hypo- and hyperspeech not only interms of energy cost, but also in terms of vocal tract mechanics.

Acknowledgments

Supported by the Whitaker Foundation, NASA Grant NAG5-2217, NASA-Ames Research Cen-ter, and the University of Texas Center for High Performance Computing.

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Dynamic Simulation of Human Movement Using Large-Scale Models of the Body