JRRDJRRD Volume 51, Number 3, 2014

Pages 481–496

Posture-dependent control of stimulation in standing neuroprosthesis: Simulation feasibility study

Musa L. Audu, PhD;* Steven J. Gartman, MS; Raviraj Nataraj, PhD; Ronald J. Triolo, PhDDepartments of Biomedical Engineering and Orthopedics, Case Western Reserve University, Cleveland, OH; Louis Stokes Cleveland Department of Veterans Affairs Medical Center, Cleveland, OH

Abstract—We used a three-dimensional biomechanical modelof human standing to test the feasibility of feed-forward controlsystems that vary stimulation to paralyzed muscles based on theuser’s posture and desire to effect a postural change. The con-trollers examined were (1) constant baseline stimulation, whichrepresented muscle activation required to maintain erect stand-ing, and (2) posture follower, which varied muscle activation asa function of the location of the projection of whole-body centerof mass on the base of support. Posture-dependent control ofstimulation demonstrated significant benefits over open-loopstimulation. Posture follower reduced upper-limb (UL) effort byan average of 50% compared with UL effort alone and by anaverage of 34% compared with baseline stimulation. On theother hand, reduction in UL effort was an average of 32% whenusing baseline stimulation. Compared with using UL effortalone, both controllers result in more than a 50% reduction ineffort. The results of this study indicate that control systems thatfacilitate user-driven, task-dependent postures can be moreeffective and efficient than conventional open-loop stimulation.Also, they obviate the need for complicated posture-settingdevices such as switches and joysticks. Functional implicationsinclude the potential to expand reachable workspace and betterpreparation for anticipated disturbances that could challengebalance over existing neuroprostheses for standing.

Key words: biomechanical model, FNS, functional neuromus-cular stimulation, human standing, musculoskeletal modeling,neuroprosthesis, posture shifting, reaching, spinal cord injury,standing balance.

INTRODUCTION

Motor system neuroprostheses utilizing functionalneuromuscular stimulation (FNS) can provide a means toimprove the overall health and functional independence ofindividuals with paralysis resulting from spinal cordinjury (SCI). Advanced FNS systems have been designedand deployed in several settings to aid individuals withSCI to stand erect from their wheelchairs [1] and to modu-late stimulation levels according to sensor-based feedbackto maintain balance against postural perturbations [2–3].The use of such systems can have both physiological andfunctional benefits ranging from increased blood flow andmuscle mass and reduced incidence of pressure sores [4–5] to the ability to access and interact with objects in theenvironment in ways that are difficult or impossible while

Abbreviations: 3D = three-dimensional, AMAG1 = adductormagnus, AP = anterior-posterior, BoS = base of support, CoM =center of mass, DOF = degree of freedom, ESPINAE = erectorspinae, FNS = functional neuromuscular stimulation, GMAX1 =gluteus maximus, GMED1 = gluteus medius, LL = lower limb,MEDGAS = medial gastrocnemiums, ML = medial-lateral, PD =proportional derivative, SCI = spinal cord injury, SEMIMEM =semimembranosus, UL = upper limb, VASLAT = vastus lateralis.*Address all correspondence to Musa L. Audu, PhD;Motion Study Laboratory C15, Cleveland VA Medical Cen-ter, Cleveland, OH 44106; 216-791-3800, ext 3821; fax: 216-707-6489. Email: mxa93@case.eduhttp://dx.doi.org/10.1682/JRRD.2013.06.0150

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sitting. Current neuroprostheses for standing after SCIprevent collapse by stiffening the lower limbs (LLs)through constant continuous stimulation of the knee, hip,and trunk extensors. One drawback of this implementa-tion is that it does not allow for modulation of the stimula-tion in order to enable the user to assume postures otherthan remaining rigidly erect at the nominal standing posi-tion. Any postural shifts required by the user to reachobjects within or outside the immediate workspace or toprepare for activities or expected disturbances must beachieved by using the arms to pull or push against anassistive device such as a walker. Since constant stimula-tion patterns are customized to support a specific standingposture (i.e., erect neutral stance), these patterns will besuboptimal and will not aid in changing posture awayfrom neutral. This is because leaning away from neutralstanding may require more muscle effort to support thebody against the constant pull of gravity. Assuming thewhole-body center of mass (CoM) was located 1 m aboveground, a 10 forward lean about the ankle joints wouldresult in an increase in ankle torque of more than 120 N-mfor a 75 kg individual. If additional muscle effort were notrecruited to absorb this torque, it would have to be pro-vided by the upper limbs (ULs).

The ability to alter standing posture has severalpotential advantages. By changing the posture from oneposition to another, muscles of one side of the body couldbe rested to mitigate fatigue and thus prolong overallstanding times. It would also be beneficial for users ofstanding neuroprostheses to shift their postures in prepa-ration for tasks such as lifting and moving objects to andfrom shelves. In all such maneuvers, the location of theprojection of the overall body CoM on the base of support(BoS) will have to be changed smoothly and continu-ously. Previous work has determined that the ability toexecute maneuvers such as shifting weight from side toside or front to back would be essential to enable users offuture FNS systems to adjust their postures in executing awide variety of everyday tasks [6].

Studies of bipedal standing with neuroprostheses aredifficult to realize experimentally in real-time because ofthe limitations of existing FNS systems, which include acti-vation of only a few paralyzed muscles at a time. Elapsedstanding times with conventional FNS systems are also rel-atively short, typically 10 min, because of the fatigueinduced by continuously activating postural muscles [7].For these reasons, the most effective means for achieving awide variety of postures and standing maneuvers are best

explored in computer simulations that capture as manycharacteristics of the physical system as possible. Severalmusculoskeletal models have been proposed and used forthe study of standing balance with FNS [8–10]. A majoradvantage of a model-based approach is the ability toexamine a large number of scenarios without having toresort to difficult and potentially impractical human experi-mentation. Recent simulation studies have shown that it ispossible to hold the body statically at different postures in abipedal stance using muscles that have been compromiseddue to paralysis [11–12].

Other investigators have utilized sophisticated biome-chanical models to examine the potential reduction indegrees of freedom (DOFs) that could be achieved by theclosed-kinematic chain that defines bipedal standing [13].From these studies, it is clear that it is not necessary toactivate all joints in a bipedal standing maneuver. Only aminimal number commensurate with the total DOFs ofthe system need to be actively controlled, thus potentiallyreducing the number of stimulus channels required in astanding neuroprosthesis. We have developed a compre-hensive and realistic three-dimensional (3D) musculo-skeletal model that takes these and other biomechanicalfactors into account [14].

We hypothesize that standing performance can beimproved in terms of reduced use of the ULs for support bydeveloping a control system that modulates stimulationbased on current user posture and the desire for a posturalshift. The goal of this study was to test, in simulation, thefeasibility of two feed-forward control systems that wouldenhance the ability of neuroprosthesis recipients to changetheir standing postures. In the current work, the UL forceswere envisaged as the major input to the system while theexcitation of the muscles were altered only to assist withthe intended movements generated by the user pulling orpushing on a walker with his or her arms. In this way,stimulation “follows” the new CoM locations acquired as aconsequence of applying the UL forces rather than resistingmovement of the CoM, as in the case of conventional con-tinuous stimulation for standing. Due to the complex natureof the task and limitations with working with live subjects,this initial study was performed using a 3D biomechanicalstanding human model [15]. To simulate physiologicallyuseful postural changes, the model pose was changed byspecifying the UL forces required to place the overall bodyCoM in various locations within the BoS, as defined by thetwo feet in a nominal standing posture.

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METHODS

Model DescriptionA closed-chain model of the human legs and trunk

developed in SIMM (Musculographics Inc; Santa Rosa,California) was used in this study. The model had 14 DOFsand was actuated by 16 muscles that were previously deter-mined to be an optimal set for standing after SCI [12]. Themuscles were Hill-type muscle models and had their maxi-mal forces scaled to reflect the actual forces expected to beavailable in subjects with SCI [16–17]. The 14 DOFs weretrunk pitch; trunk lateral bending (roll) angles; and bilateral(right and left) subtalar, ankle, knee, hip flexion and exten-sion, hip adduction and abduction, and hip internal andexternal rotation angles. The muscles actuating the modelwere right medial gastrocnemius (MEDGAS), tibialis ante-rior, vastus lateralis (VASLAT), semimembranosus (SEMI-MEM), adductor magnus (AMAG1), gluteus medius(GMED1), gluteus maximus (GMAX1), and erector spinae(ESPINAE). The left side muscle names were prependedwith the letter “L.” Point forces were applied to each of themodel’s shoulders to simulate interactions with an assistivedevice such as a walker. The magnitude and direction of theforces were set by a proportional-derivative (PD) controllerthat used changes in the shoulder positions as input. Themathematical description of the model (skeleton and mus-cles) takes the form of a set of ordinary differential equa-tions that were integrated to determine the joint trajectories.The inputs to the model were the muscle forces, UL forces,and gravity; the outputs were joint trajectories. The seg-mental mass and inertia properties of the model were calcu-lated according to anthropometric tables [18] based on anaverage healthy male (weight 85 kg, height 1.72 m). Thedetails of the model development and its application to pos-ture shifting maneuvers were given in Audu et al. [15].

Posture OptimizationA sequential quadratic programming optimization

routine (SNOPT) [19] was used to find a set of posturesthat would allow the body’s CoM to be located across arange of positions while maximizing the height of thevertical component of the CoM and minimizing the totalchange in joint angles. The objective function for thisoptimization was defined as (Equation (1))—

where = the vector of the generalized coordinates thatwere adjusted to change the location of the projection ofthe CoM on the BoS; qi = the change in joint angles fromthe neutral posture, which consisted of an erect standingposture with the feet placed shoulder-width apart; andCoMIS = the vertical (inferior-superior) component of theCoM. J( ) was to be minimized subject to two equalityconstraints (Equation (2)):

where CoMAP and CoMML = the anterior-posterior (AP)and medial-lateral (ML) components of the CoM, respec-tively, with the superscripts denoting the “desired” and“actual” values. The second term in Equation (1) wasadded to maintain the body as erect as possible whileensuring that the joint angles appropriately changed toachieve the desired CoM position.

Optimal postures were determined for CoM locationsranging 10 cm left and right of neutral and 22 cm forwardfrom neutral in 2 cm increments. The neutral posturelocated the CoM at 5.2 cm in the AP direction and 0.0 cmin the ML direction measured from the ground referenceframe located at the midpoint between the calcaneusbones of the two feet. Figure 1 shows the CoM locations

q

q

Figure 1.Grid defined within boundaries of base of support defined by

two feet of person in nominal standing posture. Center of mass

is located statically at each of 132 grid points. Movements

(shifts) are defined as those from one grid point to neighboring

point.

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defined in a grid on the estimated BoS that covered thearea between the two feet for a typical normal humanstanding with feet placed shoulder-width apart [20]. Theoptimization routine was repeated 40 times for each pre-scribed CoM location, each time from a different ran-domly generated set of initial joint angles. This was doneto find a global minimum in the highly nonlinear solutionspace. The best solutions (g1, g2 1.0e–4 in Equation (2)and CoMIS 1.3 m in Equation (1)) were selected foreach prescribed CoM location, and a second-order poly-nomial surface was fit to the results for each joint angle.An initial study with polynomials of different degreesresulted in the choice of the second-order polynomialbecause it was the lowest degree that provided the best fitwith mean square error less than 1 percent. This ensuredthat an optimal posture, defined by a set of joint angles,for any given CoM location could be calculated. Theequation for the polynomial was (Equation (3))—

where xG and yG = the AP and ML coordinates of theCoM on the grid, respectively, and a1 . . . a6 = parametersof the quadratic polynomial that best fit the polynomialdata. The elements of the vector (p) on the left-hand side ofthe equation were the 14 DOFs defining the joint angles inthe model. A nonlinear least squares method optimization(function “lsqcurvefit,” MATLAB, MathWorks; Natick,Massachusetts) was used to determine the six parametersfor each of the joint angles. With the parameters a1 . . . a6known, the values of the angles for every choice of CoMlocation in the plane could be estimated. The polynomialdefined in Equation (3) defined what was called the“CoM-joint angle map.” The main motivation for settingup the CoM-joint angle map was to identify the optimaljoint angles for any specified CoM location that couldserve as inputs to an inverse dynamics algorithm to deter-mine the joint moments required to maintain the posture atthat desired location.

In practice, the CoM-joint angle map could also beused to determine the CoM given the joint angles. How-ever, this would be difficult to implement because it mayrequire a large number of sensors to capture all the rele-vant values. In actual implementation, the CoM could bereadily determined using a small number of inertial sen-sors appropriately placed at strategic locations on thebody [12].

Posture Controller DesignThe goal of the posture controller was to set muscle

activations appropriately to allow for postural changes, thusmaintaining sufficient muscle activity to support the bodyagainst gravity. Two controller paradigms were explored: abaseline controller that maintained the same muscle activa-tions at the optimum values required to maintain an erectstatic standing posture and a posture follower that continu-ously adjusted muscle activations based on the instanta-neous location of the CoM. Both controllers utilized a feed-forward command signal from the neuroprosthesis user toset the desired CoM location by using the ULs to exertforces on a support device such as a walker or countertop.Figure 2 depicts the control setup.

The posture follower design employed a map betweenCoM position and muscle activation values to drive itsactions. Inverse dynamic simulations were performedwith the model CoM placed in each of the grid points inFigure 1 to determine the joint moments at each of the(j = 1 . . . 14) DOFs required to statically maintain the pos-ture at that grid point. The inputs to the inverse dynamicscalculator were the joint angles read from the CoM-jointangles map. Once the joint moments were determined, amuscle force-sharing optimization problem was set up todetermine the activations that would generate thosemoments. The objective function and constraints for that

djT

Figure 2.Posture follower elements influencing center of mass (CoM)

transitions from one location to another within base of support.

User changes CoM location by using upper limbs to exert

forces on support device. Muscle activations are changed to aid

desired shift. AP = anterior-posterior, LL = lower limb, ML =

medial-lateral.

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optimization take the following form typically used forsimilar optimization problems (Equations (4)–(5)) [21]:

where J = objective function, a = vector of muscle activa-tions, nm = number of muscles, Fi = force output frommuscle i, Ai = physiologic cross-sectional area of musclei, df = number of controlled DOFs, and Tj = instantaneoustorque produced at DOF j by the muscles crossing it.

The mapping for the posture follower was developedby fitting a third-order polynomial surface to the requiredmuscle activation values for each muscle against thelocation of the CoM within the BoS. The equation for thepolynomial was given by (Equation (6)):

where xG and yG = AP and ML locations of the CoM gridpoint, respectively, and a1 . . . a10 = coefficient parametersof the third-order polynomial that fit the values of the staticmuscle activations defined by the quantity ps on the left-hand side of the equation. A nonlinear least squaresmethod optimization was used to determine the 10 parame-ters for each of the static muscle activations. With this“static muscle activation map,” the instantaneous values ofthe muscle activations required to maintain the model inany given posture within the BoS could be determined andapplied continuously as the body moved from one CoMlocation to another.

Upper-Limb ContributionPrior to doing forward simulations to test the control-

lers, the effect of the ULs on the dynamics of the move-ments was considered. In several studies, force productionin the ULs was modeled as an impedance control phe-nomenon typically represented by an equation of form(Equation (7)) [22–24]:

where M, B, and K = generalized inertia, damping, andstiffness factors, respectively, of the arm; X(t) = changein hand position; and F(t) = change in applied force atthe hand. In supported standing, the maneuvers mayinvolve slow movements characterized by negligibleacceleration of the shoulders and, therefore, constantvelocities. At such steady-state conditions, Equation (7)reduces to (Equation (8)) [25]—

A fundamental assumption in our study was that since,in human standing, the hands were fixed in space (in contactwith a static support device), the same equation as Equation(8) would model the impedance of the arm in force produc-tion such that shoulder movements in space X(t) wereaccompanied by a force F(t) at the shoulders. As a firstapproximation, therefore, interactions of the user with a sup-port device were represented by the forces exerted at theshoulders as determined by a PD controller acting onchanges in the shoulder positions [26–27]. At every instantof time during the simulation, the UL effort applied at theshoulders was computed via (Equation (9))—

where the first term was the proportional term defined as(Equations (10)–(11))—

and the second term in Equation (9) was the derivativeterm defined as (Equations (12)–(13))—

where represents the UL forces applied at the right(m = R) or the left (m = L) shoulders along the fore-aft (i =1), ML (i = 2), and inferior-superior (i = 3) direc-tions; and are the proportional and derivative

miUE

mPiK m

DiK

, (5)

and (4)

, (7)

. (8)

, (9)

and (10)

, (11)

and (12)

, (13)

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gains (similar meanings apply for i and m as for ). and represent the instantaneous and com-

manded positions of the shoulders, respectively. The posi-tions of the left and right shoulders were computed fromthe model using the orientations of the body segments.The commanded positions of the shoulders were thosecomputed with the body in the erect nominal standingposition. Equation (12) represents a filtered derivativeterm using a first-order filter where N is a constantbetween 8 and 16 [28]; TD is the derivative time constant;and t is the controller update step size, set at 0.005 s forall simulations. Altogether, there were six proportionaland six derivative gains to be determined before the PDcontroller was applied in simulation. An optimizationalgorithm where the overall body CoM was required totrack a set of specified trajectories involving shifts in theAP, ML, and diagonal directions was used to determinethe gains. The trajectories of the CoM were chosen arbi-trarily to represent movements that would imitate actualshifts in body pose such as would be required to retrieveobjects in the space around a standing human. Theyinvolved shifts in projections of the CoM from the neutralposture to a forward, sideways, or diagonal locationwithin the BoS and return to neutral. The PD gains weredetermined so as to minimize an objective function givenby (Equation (14))—

where and = actual and com-manded positions of the body CoM along the AP, ML, ordiagonal directions. W is a weighting parameter thatweighs the tracking error relative to the UL effort duringa movement. W was determined such that at the nominalstanding posture with baseline stimulation, the two termsin square brackets in Equation (14) were about equal.That value was used throughout the rest of the optimiza-tion to scale the second term relative to the first.

In a forward simulation, the combined forces acting onthe system, in addition to gravity, were (1) the UL effortrepresenting the interaction with the walker and (2) muscleforces generated via constant baseline muscle activationsor via variable muscle activations applied to the muscles asfunction of the instantaneous location of the projectedwhole-body CoM onto the BoS.

The impedance parameters (PD gains) for the UL con-tribution were determined as part of a series of dynamicsimulations involving the five specific shifts in the CoM asdepicted in Figure 3 for each of the three conditions: ULeffort only, baseline activation, and posture follower. Inevery optimization step, the term in square brackets inEquation (14) was computed for each of the five move-ments, and the final objective was the sum of the five out-comes. After the gains for each of the three conditionswere determined, their mean values were computed andused in the same optimization but with the objective func-tion being the sum of the three objectives. To alleviate thecomputational burden, all optimization runs were done in asupercomputer cluster consisting of two 32-processornodes running the parallel optimization software APPS-PACK (Asynchronous Parallel Pattern Search Package)developed at the Sandia National Laboratories (Albuquer-que, New Mexico) [29]. Thereafter, the performance ofeach control paradigm was tested by doing similar forwarddynamic simulations of posture shifts that moved thewhole-body CoM from the nominal position to five differ-ent targets individually in the transverse plane alongstraight-line trajectories. The targets were located in a neu-tral position, 10 cm to the left and right of neutral, 10 cmforward from neutral, and 10 cm at the left-forward andright-forward diagonal locations (Figure 3). Each simula-tion was 30 s in duration and consisted of an initial stabili-zation period of 5 s, a movement from one target to anadjacent target (up ramp) with a duration of 6 s, a dwell at

miUE

miIPS m

iCPS

actualiCoM commanded

iCoM

Figure 3.Target locations for forward simulations with baseline stimula-

tion and with posture follower. All movements commence from

nominal posture.

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the target position for 8 s, and a return to the initial target(down ramp) in 6 s with another stabilization period of 5 s.For comparison purposes, the simulations were repeatedwith no muscles active. Only the UL forces were used toexecute the various movements, although reaching in thesecases would not be possible since both limbs would alwaysbe required for support and balance.

Testing Controller PerformanceThe simulation procedures for testing controller

performance were the same as those used to determinethe PD gains in the previous section. These simulationswere carried out to test the two stimulation conditions:(1) “open-loop control” in which constant, optimal (orbaseline) activations were applied and the ULs generatedthe movement and (2) “posture follower control” in whichstimulation was modulated based on the current locationof the CoM. The UL effort required to generate the move-ment was used as a metric of system performance. Thedifferences between the UL efforts used when the control-lers were active against the situation when the UL forcesacted alone with no muscles active were assessed using(Equation (15))—

where EUE = mean effort without stimulation and only theULs were active, and ECO = mean effort when one of thetwo controllers (baseline stimulation or posture follower)was active. A similar approach was used to determine theperformance of the posture follower relative to the conven-tional clinical case of standing with continuous constantstimulation. The mean efforts were computed as the areasunder the curve of the UL forces over the time interval0.25 s t 30 s. The period up to t = 0.25 s was taken asthe stabilization period when the body was adjusting andthus was ignored in the integration.

RESULTS

Posture OptimizationFigure 4 shows 3D plots of the profiles of each of the

14 joint angles versus the AP and ML locations of eachgrid point. The asterisks show the actual data points whilethe continuous colored mat shows the fitted map. Theresults of the optimization routine indicate that a combi-nation of ankle, hip, and trunk angle changes contributed

mainly to movement of the CoM in the sagittal (AP direc-tion) plane. The knees and rotation of the hips were fairlyconstant for all changes in CoM. There was no apparentcontribution from hip adduction and trunk bend when theCoM moved forward or backward. For postures with theCoM shifted in the coronal (ML direction) plane, a combi-nation of subtalar angle, hip abduction and adduction, andtrunk bend were required. Trunk movement contributedmost to the optimal maneuvers followed by subtalarmotion, implying that trunk bend or roll and subtalarangles are the preferred methods for achieving change ofCoM in the ML direction. Hip abduction and adductionwere the least important contributor, and the remainingjoint angles remained relatively constant as the CoM posi-tion was varied in the coronal plane.

Upper-Limb Impedance ParametersThe Table shows the values of the gains obtained

using Equation (14). These parameters are applicable asUL impedance values for all movement directions andfor all controller types. The mean UL proportional gainswere largest in the inferior-superior direction (mean5,020 N/m). These are followed by those in the fore-aftdirection (mean 3,170 N/m) and then those in the MLdirection (mean 1,330 N/m). All derivative gains assumea mean value of 109 N-s/m. The larger value of propor-tional gain in the inferior-superior direction may beattributable to the need to sustain the overall body weightin that direction, while the lower value in the ML direc-tions may be due to the higher stability in that directionassociated with the width of the BoS. Lower values forthe derivative gain were important to avoid overshoots inthe UL control forces despite utilizing filtered derivativesfor all velocity inputs. A constant value of 1.0e–3 wasfound adequate for the weighting parameter (W) inEquation (14) for all cases.

Posture Follower MapThe posture follower relied on a series of maps

between CoM locations in the transverse plane and themuscle activations required to (1) support the postureagainst gravity and (2) allow for generation of forward,backward, left, and right shifts in CoM location. Figure 5shows plots of the activations of each of the 16 musclesversus the AP and ML locations of each grid point. Thesemaps specifying the muscle activations required to sup-port the body against gravity confirm the findings of pre-vious reports that each of these muscles was important

, (15)

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Figure 4.Three-dimensional plots of 14 free degrees of freedom (joint angles) plotted against anterior-posterior (AP) and medial-lateral (ML)

directions on base of support. Two bottom plots represent trunk pitch and trunk roll to left and right, respectively. *Actual data points

(continuous colored mat shows fitted map). Add = adduction, CoM = center of mass, Flx = flexion, Rot = rotation, Trk = trunk.

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AUDU et al. Control of standing balance with FNS

for standing in various static postures [12]. The muscleswith the highest activations across all tested postureswere those that are traditionally associated with posturalsupport: ankle plantar flexors to stiffen the ankle, SEMI-MEM and ESPINAE to maintain hip and trunk exten-sion, and AMAG1 and GMED1 to stiffen the hips againstfurther adduction and abduction in sideways leaning pos-tures. The muscles with lower average activation are stillimportant to maintain specific nonerect postures; how-ever, activations of the GMAX1 and VASLAT were smalland relatively unchanged across all postures.

Controller PerformanceThe performance of the controllers was tested in a

series of simulated postural shifts with the task of movingthe CoM between various targets along a straight-line tra-jectory. Postural shifts between every adjacent targetwere tested while the mean UL effort required to gener-ate the movement, as well as the mean error between tar-get and actual CoM position in the transverse plane, wasoptimized. Figure 6 shows actual and commanded CoMpositions in the transverse plane to illustrate the shape ofthe trajectories and tracking errors for each system. Fig-ure 7 depicts temporal histories of the CoM trajectoriesfor the forward, leftward, and left diagonal shifts for theposture follower, while Figure 8 depicts the histories ofthe joint angles obtained by integrating the model differ-ential equations for the case of the forward leaningmaneuver for all three conditions (UL effort alone, base-

line stimulation, and posture follower) against the desiredangles as computed from the CoM-joint angle map. FromFigure 8, it appears that forward shift maneuvers wereaccomplished primarily by changes in ankle angle, withmost of the other joint angles remaining relatively con-stant. All controllers exhibited good tracking for the rele-vant CoM components with very small overshoot duringthe left diagonal movements when the UL effort wasused alone and with open-loop baseline stimulation.

Figure 9 shows the UL effort histories applied duringthe specified maneuvers. The mean UL effort required tomaintain a steady-state posture at the nominal erect pos-ture was between 90 and 100 N when the UL effort alonewas used, while it reduced to 40 to 50 N when any of themuscle controllers were activated. Stimulation greatlyreduced UL effort even in steady-state standing when theCoM was kept at a fixed position.

Figure 10 summarizes the percentage difference inmean UL force exerted during the time interval (2.5 s t 30 s) for each of the five maneuvers shown in Figure 9.Posture follower performed better than constant baselinestimulation (about 34% reduction in UL effort) mainlyduring the forward and diagonal movements. During theextreme right and left movements, the reduction wasabout 8 percent. On the other hand, constant (open-loop)stimulation performed only slightly better than UL effortalone for the forward and diagonal movements. Theapproximately 20 percent improvement over no stimula-tion for this controller was due to reduced UL effort dur-ing the steady-state periods. During the extreme left andright movements, both controllers performed much better(up to about 50%) than UL effort alone. The two control-lers performed equally well during these two maneuverswhen compared with no stimulation, probably becauseonly portions of the ESPINAE muscles were recruited formovements in the ML plane (Figure 5). The other mostactive muscles (MEDGAS and SEMIMEM) were mainlyactive in the AP plane alone.

DISCUSSION

The primary goal of this study was to determinewhether we could apply posture-specific stimulation toimprove the performance of neuroprostheses for standing.We defined performance using two metrics: (1) reducingthe effort required from the user to maintain a posture andswitch between postures and (2) improving the user’s

Table.Gains for upper-limb proportional-derivative controller.

Shoulder Gain TypeMovement Direction

Value

Right Proportional (N/m) x 3.17E+03

y 5.02E+03

z 1.33E+03

Derivative (N-s/m) x 1.09E+02

y 1.09E+02

z 1.09E+02

Left Proportional (N/m) x 3.17E+03

y 5.03E+03

z 1.33E+03

Derivative (N-s/m) x 1.09E+02

y 1.09E+02

z 1.09E+02Note: x = fore-aft, y = inferior-superior, z = medial-lateral.

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ability to maintain and track particular postures as definedby target CoM locations. Using a feed-forward controlstructure, the average UL effort was reduced by over 20 to50 percent during postural shifts over using UL effortalone. CoM target tracking was excellent using all con-troller types with only a little overshoot during one of themaneuvers when the UL effort was used alone and whenopen-loop stimulation was used.

We tested two control structures: baseline open-loopstimulation and the posture follower. The baseline stimu-lation control structure was the simpler of the two andrepresented the conventional application of constantstimulation to all muscles. The posture follower variedmuscle activation based on the location of the whole-body CoM in the transverse plane. This controller would

allow optimal stimulation to be applied as the user movedbetween postures using his or her arms to drive the move-ment, in essence using the body itself as a joystick-likecommand input. The average UL effort was reduced byover 50 percent during postural shifts with the posturefollower for all five maneuvers, over the 20 to 45 percentreduction with conventional open-loop continuous stimu-lation. The performance of continuous baseline stimula-tion was comparable with the posture follower only forthe extreme leftward and rightward shifts. For the otherthree movements, the posture follower outperformedbaseline stimulation by achieving up to 34 percent furtherreduction in UL effort. As illustrated in Figure 9, anyform of LL stimulation reduced the UL effort required tosupport the body in the nominal posture and move the

Figure 5.Three-dimensional plots of 16 muscle activations for posture follower fitted to values of center of mass (CoM) grid locations on base of sup-

port. *Actual data points (continuous colored mat shows fitted map). AMAG1 = right adductor magnus, AP = anterior-posterior, ESPINAE =

right erector spinae, GMAX1 = right gluteus maximus, GMED1 = right gluteus medius, LAMAG1 = left adductor magnus, LESPINAE = left

erector spinae, LGMAX1 = left gluteus maximus, LGMED1 = left gluteus medius, LMEDGAS = left medial gastrocnemius, LSEMIMEM =

left semimembranosus, LTIBANT = left tibialis anterior, LVASLAT = left vastus lateralis, MEDGAS = right medial gastrocnemius,

ML = medial-lateral, SEMIMEM = right semimembranosus, TIBANT = right tibialis anterior, VASLAT = right vastus lateralis.

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CoM to new targets by more than half that required byusing the ULs alone without stimulation. In reality, usersof standing neuroprostheses in particular and individualswith SCI in general rarely stand to reach objects by usingonly their ULs and instead rely on stimulation or externalorthoses, respectively.

The low UL effort required to shift between posturesand the high precision of CoM target tracking whileusing the posture follower means that any additional con-trol structure could only offer minor benefits at the costof system complexity and need for additional controlinputs. These findings indicate that it would be best tofocus on transitioning the posture follower into a real-world system instead of adding the unnecessary compli-cations that more sophisticated control structures such asjoystick control, etc., would bring.

Our previous studies investigated use of CoM forfeedback control based on 3D acceleration of CoM forthe express purpose of disturbance rejection about thenominal posture setpoint [2–3,26]. Stimulation levelswere modulated to respond to unanticipated, dynamicchanges occurring only while standing at that nominalposition. However, constant baseline stimulation was uti-lized for vertical support while volitional user effortalong with the actions of the controller maintained it atthe nominal steady state value. In the current study, weinvestigated a potential to improve the clinical utility andfunctionality of standing by exploring an advanced con-trol system that allows efficient shifts of the nominal pos-ture itself. Specifically, this study explored modulatingstimulation to more efficiently shift to other setpoint

positions in concert with user volition. As such, CoMposition was the process variable of interest. This vari-able can be estimated online from joint position mea-sured by any number of methods, including segmentaccelerations that would avoid implementing awkwardbody-worn sensors that cross the hips, knees, and ankles.The posture follower approach, therefore, is compatiblewith the purely dynamic feedback provided by acceler-ometers located on the trunk and pelvis to estimate CoMaccelerations for disturbance rejection.

Regardless of the control structure that is chosen, thetransition to laboratory demonstration and clinical imple-mentation will be a challenge. The primary limitation ofeither control system is the use of the whole-body CoMas a surrogate for body posture. Two inherent assump-tions were made in the development of these controllers:(1) we can enforce a desired set of postures so that thereis an optimal 1-to-1 mapping between CoM position andposture, and (2) we can determine CoM position withsufficient precision to accurately drive the controller. Thefirst assumption is important because the muscle activa-tions will be optimized for a specific set of postures, andif the user deviates too far from these postures, then theseactivations will not be optimal and could be detrimentalto stable standing. This issue will need to be investigatedfurther, but if stimulation alone is insufficient to generateunique, optimal postures, then the appropriate orthosescould be added at the problematic joints for a direct and

Figure 6.Actual and commanded center of mass (CoM) paths for case of

applying (a) upper-limb (UL) effort only and two controller condi-

tions of (b) baseline constant stimulation and (c) posture fol-

lower for five specified path trajectories depicted in Figure 3.

AP = anterior-posterior, ML = medial-lateral. Figure 7.Typical center of mass (CoM) trajectories (actual and com-

manded) for case of posture follower active. Top row: Changes

in anterior-posterior (AP) CoM. Bottom row: Changes in medial-

lateral (ML) CoM.

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Figure 8.Histories of joint angles obtained by integrating model differential equations for three types of loading conditions: upper-limb (UL)

effort alone (blue), UL effort and baseline stimulation (black), and UL effort and posture follower (magenta). Commanded joint angles

obtained from center of mass-joint angle map are shown in red. Add = adduction, Flx = flexion.

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effective solution. The second issue is related to the rela-tively small variations in CoM location as the posturecontinually adapts and accommodates. Any system thattracks changes in CoM would need to be sensitive androbust in the presence of measurement noise. In the labo-ratory, optical motion-capture systems offer ample sensi-tivity to track very small changes in body position. Suchsystems are currently available for the home and in thecommunity, although recent gaming technologies, suchas the Nintendo Wii and Microsoft Kinect, provide hopethat inexpensive, at-home motion-capture systems mayeventually be possible. Currently, the best option wouldmost likely be to use accelerometers or other orientationsensors placed at strategic locations on the trunk, pelvis,and limbs and to combine their signals in such a way asto give good estimates of whole-body CoM location and

joint positions [26]. The simulation study described inNataraj et al. determined that the typical noise and track-ing errors reported for such sensors were within accept-able boundaries to still resolve postural positions withsufficient accuracy for effective feedback control of neu-roprosthetic standing [30]. While the required precisionof the sensors was not assessed in this study, the previousutilization of such sensors with our customized implant-able stimulator for feedback control of neuroprostheticstanding suggests potential feasibility for live-subjectimplementation for setpoint control as well [2–3].

The model-based study presented here has someintrinsic limitations. First, the assumption that the ULcontributes to the control of movement via a PD-typeaction is an oversimplification of the yet unknown behav-ior of the UL effort of a user under live conditions. It is

Figure 9.Upper-limb (UL) effort (red line) exerted during different maneuvers shown in Figure 3 while applying two types of control elements:

baseline stimulation (blue line) and posture follower (black line).

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unclear how best to validate that the ULs behave in thesame manner as impedance control systems for handmanipulation. Further studies need to be carried out tovalidate the nature of UL contributions to movements inthe AP and ML directions, especially when LL muscleaction is compromised. Another limitation is that themaps were developed using static information only. Themaps could be developed using the actual dynamic tra-jectories of the activations computed by undertaking awide variety of dynamic maneuvers by changing the pro-jected CoM from one random location to another. How-ever, such maps would require more sophisticated andcomputationally expensive approaches, such as usingdynamic neural networks. The potential benefits of suchcomplex designs need to be further evaluated relative totheir efficiency for clinical deployment. From Figure 9,we observed that the results did not seem to display anexact symmetry between the left and right and betweenthe left diagonal and right diagonal UL forces. This alsoreflected in the percent difference in mean UL effortshown in Figure 10. The main reason for this lack ofsymmetry was because of the nature of the closed-chainconstraint associated with the requirement to have thetwo feet be firmly placed on the ground throughout thesimulations. In reality, only the right foot was fully con-strained to the ground. The requirement for having theleft foot also to be constrained fully to the ground couldonly be achieved via the satisfaction of an algebraic con-

straint at every time step of the simulation. Thus, anymodel involving bipedal standing must solve a combineddifferential and algebraic set of equations [13,15]. Smallerrors in satisfying these algebraic constraint equationscould cause the outputs between left and right sides todiffer. This problem could be avoided by completelyeliminating the closed-chain constraint equations fromthe model prior to any simulations. This approach wouldrequire enormous additional effort in the modeling of thesystem and is currently under study. Finally, the musculo-skeletal model assumed there was no twist movement ofthe trunk. For many useful activities of daily living, con-trol of trunk twist notably improves functionality. How-ever, excessive axial rotation should be avoided for aneuroprosthesis user because this could compromise thestability attained while holding on to the support device.

This study sought to determine the feasibility of aposture-dependent muscle activation controller for astanding FNS system. Our results show that such a sys-tem could benefit a neuroprosthesis user by reducing theeffort required to change postures while standing andallowing for finer control of posture. Both of these bene-fits would make reaching and performing activities whilestanding easier for a user of the standing system.

CONCLUSIONS

We have explored the potential of designing simplecontrol structures that could be implemented in neuro-prostheses to restore standing balance and allow individ-uals paralyzed by SCI to set task-specific and user-drivenstanding postures. By using smooth interpolating maps todetermine which instantaneous muscle activations toapply in order to achieve movement maneuvers in thesagittal and coronal planes, we obviate the need fordesigning and deploying otherwise complex controllersfor an inherently unstable and highly nonlinear biome-chanical system. The results showed that advanced feed-forward systems are feasible and can potentially outper-form conventional open-loop baseline stimulation interms of reduced UL effort. The application of such con-trol structures will expand the capabilities of current FNSsystems, which rely on constant baseline stimulation tomaintain standing balance.

Figure 10.Percent difference in mean upper-limb (UL) effort with baseline

continuous open-loop stimulation and posture follower relative

to UL effort alone and baseline continuous open-loop stimula-

tion relative to posture follower calculated during forward (FW),

left (LE), left diagonal (LD), right (RI), and right diagonal (RD)

shifts shown in Figure 3.

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ACKNOWLEDGMENTS

Author Contributions:Study concept and design: R. J. Triolo, M. L. Audu, S. J. Gartman, R. Nataraj.Computer simulations: M. L. Audu, S. J. Gartman.Analysis and interpretation of results: R. J. Triolo, M. L. Audu, S. J. Gartman, R. Nataraj.Preparing draft manuscript: S. J. Gartman, M. L. Audu.Critical revision of manuscript for important intellectual content: R. J. Triolo.Study supervision: R. J. Triolo, M. L. Audu.Financial Disclosures: The authors have declared that no competing interests exist.Funding/Support: This material was based on work supported by the National Institute of Neurological Disorders and Stroke (grant R01NS040547).Additional Contributions: Mr. Gartman is now with The Progressive Corporation, Mayfield Village, Ohio.

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Submitted for publication June 25, 2013. Accepted inrevised form November 15, 2013.

This article and any supplementary material should becited as follows:Audu ML, Gartman SJ, Nataraj N, Triolo RJ. Posture-dependent control of stimulation in standing neuropros-thesis: Simulation feasibility study. J Rehabil Res Dev.2014;51(3):481–96.http://dx.doi.org/10.1682/JRRD.2013.06.0150