Pendular model of paraplegic swing-through crutch ambulation · studies, crutch ambulation has been...

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\i. y 4. \ r Veterans Administration Journal of Rehabilitation Research and Development Vol . 25 No . 4 Pages 1—16 Pendular model of paraplegic swing-through crutch ambulation JOSHUA S . ROVICK, MS, and DUDLEY S . CHILDRESS, PhD Rehabilitation Engineering Program, Northwestern University, Chicago, IL 60611 Abstract—Kinematics of swing-through crutch ambu- lation for an individual with complete Tll-T12 spinal cord injury was examined and quantitative aspects of the body-swing phase used to formulate and evaluate a 3-link pendular model . Model simulation parallels measured kinematics when shoulder motion is forced to follow the measured motion while hips and crutch tips are free pivots . Shoulder control contributes to increased ground clearance, influences timing and stride length, and gives flowing gait . Results indicate that mechanical work requirements during the body-swing phase are low. Metabolic energy demands exceed mechanical work re- quirements, due particularly to support of the body by the arms and shoulders . Exploiting low mechanical work requirements of the body-swing phase might be achieved through alternative mechanisms to assist ground clearance and to stabilize the wrists, arms, and shoulders while weight bearing. Key words : crutch, gait, paraplegic, kinematic, model. INTRODUCTION Crutches have been used as an ambulation aid for the past 5,000 years (4) . They remain a useful aid for disabled persons with a variety of disabilities. The energy cost and physical difficulty of using crutches is high for all individuals, although some- Address all correspondence and requests for reprints to J .S . Rovick, Rehabilitation Engineering Program, Northwestern University, 345 East Superior St ., Chicago, IL 60611 . what variable depending on the nature of the disability and the particular ambulation style adopted . Persons with paraplegia are sometimes effective crutch users . The purpose of this study is to examine some characteristics of paraplegic swing- through crutch ambulation. Persons with paraplegia are encouraged to use crutches, when possible . Nonetheless, many choose wheelchairs as their exclusive or preferred method of locomotion . The rejection of crutches occurs more frequently in individuals with higher level lesions and with more complete lesions (17) . The dislike of the orthoses which stabilize the joints of the lower limbs during stance is thought to be one reason for choosing wheelchairs over crutches . The knee-ankle- foot orthoses (KAFOs), needed by persons with upper lumbar and thoracic level lesions, are particu- larly cumbersome . Another deterrent to crutch use often cited is the physical difficulty of crutch ambulation . A greater understanding of crutch ambulation may stimulate ideas for reducing the difficulty of this ambulation style which may make crutch use an attractive alternative for some wheel- chair users . The problems associated with long-term wheelchair use are well-documented . Crutch-assisted gait has the advantage of positioning users upright, at the level of their peers . It permits a greater freedom from architectural barriers and the upright stance may be beneficial to general health . On the other hand, crutch ambulation is energy-demanding, may be wearing on the joint cartilage and joint capsules, and the users may be endangered by falls .

Transcript of Pendular model of paraplegic swing-through crutch ambulation · studies, crutch ambulation has been...

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\i.y4.\r VeteransAdministration

Journal of Rehabilitation Researchand Development Vol . 25 No . 4Pages 1—16

Pendular model of paraplegic swing-through crutch ambulationJOSHUA S . ROVICK, MS, and DUDLEY S . CHILDRESS, PhDRehabilitation Engineering Program, Northwestern University, Chicago, IL 60611

Abstract—Kinematics of swing-through crutch ambu-lation for an individual with complete Tll-T12 spinalcord injury was examined and quantitative aspects of thebody-swing phase used to formulate and evaluate a 3-linkpendular model. Model simulation parallels measuredkinematics when shoulder motion is forced to follow themeasured motion while hips and crutch tips are freepivots . Shoulder control contributes to increased groundclearance, influences timing and stride length, and givesflowing gait . Results indicate that mechanical workrequirements during the body-swing phase are low.Metabolic energy demands exceed mechanical work re-quirements, due particularly to support of the body bythe arms and shoulders . Exploiting low mechanical workrequirements of the body-swing phase might be achievedthrough alternative mechanisms to assist ground clearanceand to stabilize the wrists, arms, and shoulders whileweight bearing.

Key words : crutch, gait, paraplegic, kinematic, model.

INTRODUCTION

Crutches have been used as an ambulation aid forthe past 5,000 years (4) . They remain a useful aidfor disabled persons with a variety of disabilities.The energy cost and physical difficulty of usingcrutches is high for all individuals, although some-

Address all correspondence and requests for reprints to J .S . Rovick,Rehabilitation Engineering Program, Northwestern University, 345 EastSuperior St ., Chicago, IL 60611 .

what variable depending on the nature of thedisability and the particular ambulation styleadopted . Persons with paraplegia are sometimeseffective crutch users . The purpose of this study isto examine some characteristics of paraplegic swing-through crutch ambulation.

Persons with paraplegia are encouraged to usecrutches, when possible . Nonetheless, many choosewheelchairs as their exclusive or preferred method oflocomotion . The rejection of crutches occurs morefrequently in individuals with higher level lesionsand with more complete lesions (17) . The dislike ofthe orthoses which stabilize the joints of the lowerlimbs during stance is thought to be one reason forchoosing wheelchairs over crutches. The knee-ankle-foot orthoses (KAFOs), needed by persons withupper lumbar and thoracic level lesions, are particu-larly cumbersome. Another deterrent to crutch useoften cited is the physical difficulty of crutchambulation . A greater understanding of crutchambulation may stimulate ideas for reducing thedifficulty of this ambulation style which may makecrutch use an attractive alternative for some wheel-chair users . The problems associated with long-termwheelchair use are well-documented . Crutch-assistedgait has the advantage of positioning users upright,at the level of their peers . It permits a greaterfreedom from architectural barriers and the uprightstance may be beneficial to general health . On theother hand, crutch ambulation is energy-demanding,may be wearing on the joint cartilage and jointcapsules, and the users may be endangered by falls .

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A 1974 survey article (16) illustrated that relativelyfew scientific analyses of crutch ambulation havebeen made. The largest group of scientific investiga-tions have been metabolic energy studies . In thesestudies, crutch ambulation has been equated withmoderate to heavy work (8), and with jogging orrunning (7,14) . All investigators agree that crutchambulation is more energy-consumptive than nor-mal walking (5,10,11), although for some crutchusers, this difference becomes insignificant at highwalking speeds (6) . What is not clear, is whatnecessitates this excess metabolic input; whether it isprimarily related to the mechanical work require-ments of the activity, or perhaps to the poorphysiologic efficiency of the task . To answer thesequestions, one must analyze the mechanics ofcrutch-assisted gait, and the mechanics of theassociated musculature.

Shoup et al . (16) performed a kinematic analysisof crutch gait by measuring the angles and eleva-tions of body segments throughout the gait cycle.He concluded that one area of excessive energy useresulted from vertical height fluctuations of thebody mass center . This conclusion assumed thatthere is no interchange between kinetic and potentialenergies, which is an unfounded assumption . Othersources of energy loss identified were excessivelateral crutch excursions, and the shock of crutches-strike . Wells (18) performed a more extensive studyusing similar techniques. Body segment angles andkinetic and potential energies were examined forable-bodied subjects . The participants were able-bodied subjects in which disabling conditions werealso simulated by immobilization at either the kneejoint or both the hip and knee joints . Looking atmechanical energy inputs (i .e ., tally of kinetic andpotential energies, as opposed to the metabolicenergy cost), he concluded that the internal mechan-ical energy for crutch ambulation was similar tonormal walking. However, this may not be the casefor the spinal cord injured, where ground clearancebecomes a difficult and important consideration . Healso concluded that the use of the arms to supportand propel the body, and the discontinuous natureof crutch ambulation, accounted for the increaseddifficulty and energy demand relative to normalbiped walking.

A more recent study by McGill and Dainty (12)used the methods of Wells (18), in conjunction withforce plate data, to analyze crutch ambulation in

children . This study was directed toward the am-bulation styles common to persons using crutchesfor short periods during rehabilitation, rather thanthe ambulation styles of more permanent crutchusers, such as the spinal cord injured.

In this paper, we describe results from a kinematicanalysis of crutch ambulation performed by aparaplegic subject using the swing-throughambulation style. In addition, we present a mathe-matical model that simulates these kinematics duringthe period when the body swings. The 3-linkpendular model was a simplified 2-dimensionalrepresentation of the crutches, body, and legs . Themodel was solved as both a conservative system withfreely pivoting joints at the crutch tips, shouldersand hips, and also as a forced system where the timehistory of the shoulder kinematics was specified.The purpose of this study was not to provide auniversal model of crutch ambulation. Rather, wehave used a model to reveal some of the mechanicalaspects of paraplegic swing-through crutchambulation . This study used quantitative data takenfrom only 1 subject. We have observed thisambulation mode in other individuals . However, theprevalence of this form of ambulation among otherparaplegic ambulators would be the subject ofanother study. We hope this work may form thebasis for future studies, and that it may suggestdesign alternatives for the assistive aids currentlyused by persons who walk using crutches.

METHODS

The subject was a 40-year-old male diagnosed ashaving a complete spinal cord lesion between tho-racic vertebral levels 11 and 12. He used forearmcrutches in a swing-through gait style and had reliedprimarily on that method of locomotion for almost20 years . Knee-ankle-foot orthoses immobilized hisankles, knees, and feet, which permitted weightbearing during body stance . Flexion and extensionat the hip joints were passive phenomena, since hehad no voluntary control of his hip flexor andextensor muscles . The range of motion at the hipswas not obstructed and hyperextension of up to 20degrees was observed.

Knowledge of the masses and moments of inertiafor the various body segments was needed formathematical modeling of the body-swing phase of

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gait . Published data is available which allows esti-mation of these parameters based on body heightand weight . This anthropomorphic data was ad-justed for our subject, since it is not representativeof active paraplegics whose weight distribution maybe non-standard (e .g ., more developed in the upperbody and less developed in the lower limbs) . Totalbody height and weight were measured . The weightof the KAFOs were also measured . The weight ofthe subject's lower limbs was then measured, utiliz-ing a method proposed by Williams and Lissner(19) . A sling attached to a spring scale was loopedunder the heels, and the legs were suspended hori-zontally . Assuming a normal weight distribution inthe legs, the scale reading was a given proportion ofthe total weight based on a simple mechanical forceand moment balance . The weight of the orthoseswas included in this measurement . The weight of therest of the body was total weight minus leg weight.Using the data of Dempster (2) and Drillis andContini (3), 2 adjusted body weights were thencomputed . The first of these adjusted body weightsreflected the total weight of an average individualwhose legs would have had the same weight as thoseof our subject, while the second body weightsimilarly reflected an individual whose upper bodyweight would match that of our subject . Theseadjusted body weights were used to estimate sep-arately the segment masses and moments of inertiafor the legs and for the rest of the body (Table 1).

In this study, body length refers to total bodyheight, and the other lengths are functional segmentlengths. Leg length is the distance from the sole of

Table 1.Body segment parameters used in the solution of thependular models.

TotalBody* Legs* Trunk Crutches

Mass (kg) 94 .4 32 .5 51 .3 13 .8

Length (m) 1 .83 0 .84 0 .51 1 .51

Moment of inertia aboutmass center (kg m 2) 2 .4 3 .6 2 .0

Distance

from

proximalpivot to mass center (m) 0 .42 0 .17 0 .47

Initial angular velocity attoes-off (deg/sec) -4 .1 -13 .2 -35 .0

*Includes 5 .5 kg mass of KAFO .

the foot to the hip joint with the knee in extension.Trunk length is the distance from the hip joint to thegleno-humeral joint, and crutch length is the dis-tance from the gleno-humeral joint to the crutch tipwith the arm extended . The angular velocities followa sign convention where angles are measured withrespect to the vertical and defined positive in thecounterclockwise direction.

White circular targets 4 cm in diameter were usedto mark the rotational centers of the ankle, knee,hip, shoulder, elbow, wrist, and crutch tip . The hipmarker was fixed to the subject's shorts, the anklemarker to the boot, and all other markers wereapplied directly to the skin . The ear was used as anadditional landmark. Videographic gait analysistechniques were used. A JVC HR2200U videocassette recorder and RCA 000011 color televisioncamera with zoom lens were used to record thewalking trials . The camera was positioned 10 metersfrom the walkway and orthogonal to it . The focallength of the lens was adjusted to give an imagewidth of at least 2 stride lengths . With this camerasetup, errors in body segment angles due to visualperspective were estimated to be no greater than 1 .5degrees. A grid with lines every 10 cm was used as abackdrop and was positioned 1 meter behind thewalkway. The video cassette recorder had thecapacity for playback with variable speeds, includ-ing freeze frame display (Figure 1) with single frameadvance. The recording rate was 30 images persecond.

Ten ambulation trials were recorded as the subjecttraversed the walkway at his normal, comfortablespeed. Seven of the recordings had the subjectcrossing the walkway, entering the field of viewafter the second stride . Two recordings had thesubject starting from a standstill at the center of thefield of view. The final recording had the subjectapproaching the camera, perpendicular to the walk-way . A 2-dimensional sagittal plane analysis wasperformed.

The data were transcribed from videotape on aframe-by-frame basis . A sheet of transparent mylarplastic was placed on the face of the televisionmonitor and a small dot was marked on the plasticover each body segment landmark . The videotapewas then advanced 1 frame, and the new positionsof the landmarks were marked on the same plasticsheet . The resulting transparency contained a locusof points for each of the landmarks, from heels-

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Figure 1.Subject at toes-off : Photograph of television monitor during still-frame videotape playback.

strike of 1 stride to heels-strike of the followingstride (approximately 50 points) . To prevent paral-lax errors while transcribing the videotape, a simplejig was used to hold the head in a stable position,and an eye patch covered 1 eye . From the resultingassemblage of points (Figure 2), the angular orienta-tion of each body segment was determined as itprogressed through the gait cycle . The angulartranscription and measurement was estimated to beaccurate to within 0 .5 degrees based on the scatterof the angle data after curve smoothing . Thecombined transcription and projection error, there-fore, was within 2 degrees . Comparing the datafrom different experimental runs showed a consis-tency in the subject's gait pattern . In each successivestride, the pattern of motion was repeated both inthe magnitudes of angular motion as well as theassociated time histories of that motion .

MOTION CHARACTERISTICS

A visual examination of the subject's gait revealedthe following characteristics: the gait cycle is initi-ated from a stance posture by bringing the crutchesforward, shifting balance, and falling forward. Thecrutches are planted, and there is a short double-support phase before the body-swing phase begins.At crutches-strike, the elbows are slightly flexed . Tobegin body-swing, the toes are lifted off the groundby extension of the elbows and depression of theshoulder girdle . Therefore, body-swing phase doesnot flow directly from the preceding phase ; rather, itmust be initiated by an active lifting of the toes(through the trunk and legs) off the walking surface.

During the first half of the body-swing phase, thetrunk appears to maintain a nearly constant orienta-tion relative to the vertical, while the crutches pivotforward about the crutch tips, and the legs swing

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ROVICK and CHILDRESS: Paraplegic Swing-through Crutch Ambulation

Figure 2.Locus map used to determine body segment orientations . The map shows the time-varying position of each body landmark for 1complete gait cycle, beginning at heels-strike . Separation between points is 1/30 second . Every third point is darkened. The events ofcrutches-strike and toes-off are shown with diamonds rather than circles.

from the hips, past the crutch tips, in pendularfashion. The trunk swings through in the last half ofthe body-swing phase; the crutches continue to pivotand the body straightens, preparing for heels-strike.When the heels strike the ground, there is a secondshort double-support phase before the body-stancephase begins. During the body-stance phase, thecrutches are brought forward in preparation for thenext cycle . The orientation of the crutches is nearlyvertical as the weight is transferred to the crutches inpreparation for the body-swing phase . The compos-ite image of Figure 3 shows these body positions inrelation to the trajectories of the joint markers.

Averaging over all the experimental runs, thesubject ambulated at a speed of 0 .9 meters persecond, with a stride length of 1 .5 meters. Thisvelocity is faster than those reported by Huang (8) inhis metabolic energy studies using paraplegics (mean0.23 m/s, range 0.04-0.75 m/s), and slower than the

mean velocities reported by Wells (18) in hiskinematic studies using non-paraplegics (mean 1 .02m/s, range 0.27-1 .42 m/s). On average, the relativeproportion of time spent in each of the 4 phases ofswing-through gait were : body-stance phase, 30percent ; first double-support phase, 12 percent;body-swing phase, 48 percent ; second double-sup-port phase, 10 percent . The body-swing phasefollowed equally well from a stationary standingposture as it did from flowing gait (i .e ., steady stateseemed to be reached almost immediately afterbeginning ambulation).

MATHEMATICAL MODELS

Swing-through crutch gait has 2 major phasesseparated by 2 transition phases . They are : 1) thebody-swing phase, where the weight is supported on

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Journal of Rehabilitation Research and Development Vol . 25 No . 4 Fall 1988

Figure 3.Strobed photograph of the subject in swing-through crutch gait . Reflective markers are fixed along the shoe at the hip and on the earlobe . The strobe frequency is 10 Hz with an intensified image every fourth strobe (2 .5 Hz) to highlight the body position . Thisphotograph was taken for illustration purposes only, and it should be noted that the stroboscopic techniques were not used for datacollection.

the crutches and the feet are off the ground ; and, 2)the body-stance phase, where the body weight issupported entirely on the feet and the crutches areoff the ground. In the transition phases, both thefeet and the crutches are on the ground, and supportis being transferred from one to the other . For thecrutch ambulator with paraplegia, the body-stancephase was thought to be relatively unimportant froman energy and modeling standpoint . The hips remainextended throughout this phase and, with the excep-tion of bringing the crutches forward, the body actsmore or less as a rigid column pivoting over the feet.So long as there is sufficient kinetic energy to carrythe body past the vertical position and on tocrutches-strike, the body-stance phase will progressto the next phase. In contrast to the body-stancephase, the body-swing phase has more complexkinematics and greater metabolic energy require-ments . During the body-swing phase, there is signif-

icant angular motion at the hips and shoulders, inaddition to pivoting at the crutch tips . There is alsothe possibility of active involvement of the shouldermusculature, restraining or driving the motion ofthe shoulder . The body-swing phase is presumably aphase of large metabolic activity, since the elbowsmust be kept extended during weight bearing toprevent flexion under the force of body weight.Similar muscular activity is needed to maintain theneutral position of the wrist and the stability of thescapula and the gleno-humeral joint.

From a mechanical point of view, it has beensuggested that fluctuations in the potential energyare responsible, in part, for the high metabolicenergy cost (16) . Mathematically modeling the body-swing phase could facilitate the analysis and under-standing of this apparently complicated motion . Inparaplegic crutch gait, there are many subtletiesused for control of the swinging body : examples are,

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thrusting of the head, depression of the shoulders,and extension of the elbows (1) . As a first approachto the modeling effort, these subtleties were notconsidered, and a simplified representation wasadopted . A 3-link pendular model of the body-swingphase was chosen because, in the sagittal plane,there are 3 main points of rotation connected bymore or less rigid links. The points of rotation areprojections of 3 parallel axes which connect theapproximated centers of rotation of the 2 hips, the 2shoulders, and the 2 crutch tips . The 3 links wereassumed to be rigid for the purpose of the model.The 3 pendular links were defined as : link 1) a rigidbody composed of the arms and crutches with asingle pivot at the crutch tips and a single pivot atthe estimated center of rotation of the gleno-humeral joints ; link 2) a second rigid body com-posed of the head, neck, and trunk, sharing acommon pivot with link 1 at the shoulders andhaving a second pivot at the estimated center ofrotation of the hips ; link 3) a third rigid bodycomposed of the legs, feet, and orthoses, sharing acommon pivot with link 2 at the hips . The pendularmodel is depicted schematically in Figure 4.

The differential equations which govern the con-servative motion of these 3 links were derived usingthe methods of Lagrange, and are as follows:

-(Mc*L)*g*sin(0)

( *T + ML*B)*g*sin(0)

- (Mc*A + MT*C + M L*C)*g*sin(a)

Symbol meanings are given in the Appendix andsegment angles are measured counterclockwise fromthe vertical . The equations are similar in form tothose developed by Mochon and McMahon (13) fora pendular model of biped walking.

The solution of these equations was carried outwith a digital computer utilizing Gear's method forsolving ordinary differential equations . For ournumerical solution, a step size of 1/3000 second wasused. Initial angular velocities and accelerationswere determined by differentiation of angular posi-tion versus time curves after fitting our kinematicdata with least squares cubic splines in the vicinityof toes-off . Solution began at toes-off and pro-ceeded until heels-strike was expected (approxi-mately 0.8 seconds).

This first phase of modeling assumed a friction-less system operating entirely under the influence ofgravity with no torques applied at the joint pivots,and all links assumed rigid . The solution of thisfreely swinging model is shown in Figure 5, alongwith the corresponding measured data . The modelresponse in the form of stick figures is shown inFigure 9a for the first half of the body-swing phase.The model response does not correlate well with themeasured data ; trunk motion deviates markedly inphase, crutch motion deviates in magnitude, and leg

= (IL + mL*L2)*0

- (Mc*C*L)*o*cos(a-0)

+ (ML*C*L)*o-2*sin(o--8)

+ (ML*B*L)*0cos(O-0)

- (M L *B*L)*0 2 *sin(O-0)

= (IT + MT*T2 + mL*B 2 )*o+ (M L *B*L)*O*cos(O-0)

+ (M L*B*L)O 2 *sin(4-0)

- (M T*C*T + Mc*C*B)*a*cos(a-cb)

+ (M T*C*T + M L*C*B)*a 2 *sin(o-O)

= (1c + Mc A2 + M T*C2 + ML*C 2)*a

- (M T*C*T +M L*C*B)*O*cos(o-O)

- (M T*C*T + M L*C*B)>0 2 *sin(a-cp)

- (M L *C*L)*Cl*cos(a-0)

- (M L*C*L)*6 2 *sin(a-0)

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Link 1:Crutches& Arms

Open Circles = Joint Pivots

Closed Circles = Mass Canters

Link 3:Legs &Feet

Figure 4.Schematic diagram of the 3 pendular links used in themodel (crutches, trunk, and legs), and definition ofthe angles used in the model.

motion deviates in both magnitude and phase . Thepoor correspondence between the measured andmodeled data indicates that the fully conservativeassumption is not a good one . Nevertheless, thereare some interesting implications that come outfrom the presentation of this model.

For our subject, the legs were observed to swingto a particular angular orientation in the first 60percent of the body-swing phase, and then maintaina nearly constant orientation with respect to thevertical until the heels strike the ground . Initially,the solution of the conservative model correspondsclosely to the observed angular movement of thelegs, but rather than being restricted to the initial 60

percent of the body-swing phase, the modeled legmotion continues to progress throughout the entirephase . This results in a large angular deviationbetween the measured data and the modeled re-sponse by the time heels-strike should actuallyoccur. The trunk was observed to swing slightlybackward with respect to the vertical in the first 50percent of the body-swing phase and then swingthrough in the final half of this phase . In contrast,the response of the conservative model is for thetrunk to immediately begin swinging forward at theshoulders, and to continue with this progressionthroughout the simulation . For the arms-crutchessegment, the observed angular velocity was approxi-

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ROVICK and CHILDRESS : Paraplegic Swing-through Crutch Ambulation

10

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mately constant from the time of toes-off untilheels-strike . For the conservative model, however,the arms-crutches show only about one-fourth of theangular displacement as that measured from thesubject, and additionally includes a slight oscilla-tion. In spite of these differences between themeasured data and the simulated response of themodel, it is important to note that the fullyconservative system did progress from toes-off to anacceptable heels-strike position (heels forward of thecrutch tips and just above the ground) . This accept-able heels-strike position occurs prematurely, rela-tive to the normal body-swing time . Hence, thenormal distance traveled in the body-swing phase

Figure 5.

Solution of the pendular model when all pivots arefrictionless and unrestricted . Continuous curves are

10o the modeled solutions and points are measured data.Plots begin at toes-off and end at heels-strike.

would be reduced by approximately 25 percent, andthe amount of time spent in the body-swing phasewould be reduced by 33 percent.

In the next phase of the modeling, the assumptionof a 3-link pendular system was preserved, but therestriction to a fully conservative system was re-laxed. No torques can exist at the pivot of the crutchtips, and our subject was unable to produce muscu-lar torques at the hips . It therefore seemed reason-able to assume that the deviation of this conserva-tive model from the measured data might be dueprimarily to muscular torques acting at the shoulderpivot . The pendular model was modified by rework-ing the equations using the shoulder angle, S,

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Journal of Rehabilitation Research and Development Vol . 25 No. 4 Fail 1988

which was defined as the angle between the trunkand the crutches (6=0-a) . This modification ofModel 1 gives the following equations of motion:

L)*g*sin(0) = (IL+ML*L 2)*8

+ (ML*B*L)*(6 +a)*cos(6 +a-8)

(Mc*A + MT*C + M L*C)*g*sin(a)-

(M T *T + M L *B)*g*sin(8 + a)

(M L *B*L)* (a +Q) 2 *sin(b + a-8)

(I L + IT + Mc*A 2 -MT*C 2 + MT*T2-ML *C2 + M L *B 2)*a

+ (I T +MT*T2 +ML *B 2)*S

- (MT*C*T+ML*C*B+ML*C*L)*(b+ 2a)*cos(6)

+ (MT*C*T+ML*C*B+ML*C*L)*($2+ 2(6*6r))*sin(6)

+ (ML*B*L)*8 *cos(S + a-8)

+ (ML*B*L)*8 2*sin(6+a-8)

The solution of these equations not only requiresinitial conditions, but a function S(t) . This functionS(t) was determined by a least squares cubic splinecurve fit of the measured data, which was continu-ous through the second derivative . The smoothingallowed input data to be provided at the 1/3000second step interval used in the solution of themodel, and also allowed reasonable differentiationof the data . Continuity on the second derivative isrequired, since the equations of motion include boththe first and second derivative of the shoulder angle.Using this scheme, the torque at the shoulders neednot be computed directly. Rather, the effects ofthese torques are provided for by the time-varyingfunction of S and its derivatives . In Figure 6 thesolution to this forced pendular model is plottedalong with the measured data . The patterns ofmotion for this second model correspond to thepatterns of the measured motion . The magnitudes ofangular motion deviate from the measured values byan increasing amount as the cycle progresses, withthe legs angles having the best representation ofactual motion and the crutches angles having thepoorest.

In an effort to gain insight into the effects ofvarious measurement inaccuracies on the solution ofthe models, the link parameters and initial condi-tions were varied one at a time during repetitivesolutions of Model 2. This provided a form ofsensitivity analysis . The results of this analysis

relative to the unperturbed, forced pendular model,are listed in Table 2. The greatest effect on thesolution of the model occurred when the initialangular orientation of the links were varied . Whenthe initial angular positions were varied by 5 .5degrees, the following maximum change in the

Table 2.Effects of variations in the body segment parameters andinitial conditions on the solution of the pendular model.

MAGNITUDE OF MAXIMUM ANGULAR VARIATION ( 010)PERTURBATION*

Legs

Trunk

Crutches

AO = 5'h ° 10 .50 0 .75 0 .50

Aao, A 4 o = 5'h ° 4 .50 26 .50 24 .50

A9 0 = 10% 0.50 0 .25 0 .25

Aao, Acb 0 =10 010 0 .50 7 .00 7 .50

AA= 10% 2.75 1 .50 1 .50

AL = 10% 3 .50 2 .75 3 .00

AT =10% 2.75 1 .25 1 .25

AC =10% 2.75 0 .50 0 .75

AB = 10% 5 .50 3 .50 3 .50

AMc, AIc=10010 2 .75 1 .50 1 .50

AMT, AI T =10°10 2 .75 2 .00 2 .25

AML, AIL =10% 2.75 1 .50 1 .50

*Percentages are based on the initial values at toes-off.

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R0VICK and CHILDRESS : Paraplegic Swing-through Crutch Ambulation

0

25

50

75

loo

PERCENT of SWING PHASE

output curves resulted : 10 .5 percent when initial legorientation was shifted, and up to 26 .5 percent wheninitial crutch and trunk orientation was shifted.Varying each of the following link parameters by 10percent resulted in the corresponding maximumchange in the output curves : initial angular velocity,7.5 percent ; position of the mass center on the link,3 .5 percent ; length of the link, 5 .5 percent; andmass/moment of inertia of the link, 2 .75 percent . Ingeneral, the output response was more sensitive tothe initial angular positions of the links than to theother link parameters.

Inaccuracies in the measured kinematic data havecontributions from various sources : transcriptionand measurement error in recording the position ofthe individual joint markers, placement error in thepositioning of joint markers on the subject, anderror introduced when the actual physical system isreduced to a simplified system for modeling . Tran-

Figure 6.Solution of the pendular model when the shoulderangle is forced to conform to the measuredpattern of movement . Continuous curves are themodeled response and discrete points indicate themeasured data . Plots begin at toes-off and end atheels-strike.

scription and measurement was estimated to beaccurate to within 2 degrees . The other 2 sources ofinaccuracy, marker placement and model represen-tation, do not change the resolution of the measure-ments, but instead, result in baseline shifts of the 3measured angular quantities (i .e ., an angular offsetof all the measured angle values for a given link).

Segment angles as measured in this study wereangles, with respect to the vertical, of a lineconnecting the proximal and distal joint markers fora given segment (i .e., crutch tip and shouldermarker, shoulder and hip marker, hip and anklemarker). If a joint marker were malplaced, the angleof the wrong line would be measured. The angularchange between successive points in the data setwould be proper, but the measured angles would beoffset by a constant amount equal to the anglebetween the line that was measured, and the linethat should have been measured . Malplacement of a

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Journal of Rehabilitation Research and Development Vol . 25 No. 4 Fall 1988

Figure 7.Solution to the pendular model with controlledshoulder angle after small adjustments to theinitial positions of the 3 links of the model, andwith corresponding baseline shifts of the mea-sured data . Curves represent the modeled re-sponse and the points correspond to the mea-sured data . Plots begin at toes-off and end atheels-strike.

HZW

q

20

W

15

10

50q 0w N

Olt -5m -10

-15

- 20

-25

-30

- 35

0 25

I

50 75 100

xx

Xx

PERCENT of SWING PHASE

5

0

• -5

• -10

-15

• -20

-25

0

50

• -5

-10

- 15

- 20

xx

joint marker by a few centimeters can result inbaseline angle shifts of 2 to 5 degrees . For a longlink, like the crutch, up to 2 degrees offset canresult: for a short link, like the trunk, up to 5degrees offset can result . The polycentric nature ofthe joints (particularly the shoulder joint) couldexacerbate this problem, since accurate markerplacement is difficult. In the modeling of thephysical system, each segment mass center wasassumed to lay on a line connecting the proximaland distal joint pivots for that link. Deviations fromthis ideal could result in additional baseline shifts.This is noteworthy, in view of the fact that errors ininitial angular positions (i .e ., baseline values) havethe greatest effect on the solution of the model.

With this in mind, small baseline shifts were madeto the measured data and Model 2 was again solved

with the goal of bringing the modeled response intocloser correlation with the measured data . Outputsusing baseline shifts of – 3 degrees for the legs-angles ; 6 degrees for the trunk-angles; and – 6degrees for the crutches-angles are plotted in Figure7 . These small angle shifts bring the measured andmodeled data into close agreement . The curveshapes are quite similar and the magnitude differ-ences are within 5 degrees of measured values . Stickdiagrams representing the actual measured motionand the solution of this model are shown in Figures8a and 8b . While some variation between actual andmodeled motion is evident, the similarities arepronounced .

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ROVICK and CHILDRESS : Paraplegic Swing-through Crutch Ambulation

Diagram A.

Diagram B.

Figure 8.Diagram A . The measured data is presented as stick figures at successive points in the body-swing phase . Progression is from left toright, beginning at toes-off and ending at heels-strike . The time between images is 1/10 second . Diagram B is a similar representationof the output response, but from the final mathematical model . This sequence also begins at toes-off and runs for the same period oftime as in Diagram A.

DISCUSSION

We have performed a kinematic analysis ofparaplegic swing-through crutch gait and used thisanalysis in the development and evaluation of amathematical model of the body-swing phase . Com-parison between the modeled and observed kinemat-ics gives insight into the mechanisms of control usedin the body-swing phase, and provides quantitativeinsight into the mechanical energy demand of thebody-swing phase . Additionally, an examination ofthe overall gait style gives clues to possible reasonswhy swing-through crutch ambulation is such anexhausting activity.

Our first model was a simple, 3-link pendularmodel with freely swinging joints at the crutch tips,shoulders, and hips . When compared to the ob-served motion patterns, this model exhibited mini-mal forward rotation of the crutches, a reducedstride length and, if allowed to swing for the normalbody-swing time, a final body orientation that wasinappropriate for heels-strike . However, after 67percent of the normal body-swing time, the body isin a reasonable orientation for heels-strike to occur.This indicates that given the initial conditions at

toes-off, there is sufficient energy in the system tocarry it to a heels-strike position without the inputof any mechanical work . While the kinetic energy attoes-off is sufficient to get to heels-strike, a conflictexists between the modeled response and the physi-cal environment, since the toes pass below thesurface of the walkway, indicating that the bodymust be elevated slightly during the body-swingphase. Also, when the body is in a position to acceptheels-strike, the heels are slightly above the ground,indicating that the body must be lowered to theground for heels-strike . These 2 incompatibilitieswith the physical environment imply that if thispendular model is representative of the physicalsystem, some mechanical work must be appliedduring the body-swing phase.

In the second model, the 3-link pendular systemhad a forced input at the shoulder . The forcingfunction used in this model represented muscularcontrol of the shoulder angle and was applied insuch a way that the modeled shoulder angle corre-sponded to the observed shoulder angle at each timestep in the body-swing phase . The motion patternsof this model more closely matched the observedkinematics than when the shoulder was allowed to

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Journal of Rehabilitation Research and Development Vol . 25 No . 4 Fall 1988

Diagram A.

Diagram B.

Figure 9.The first half of the body-swing phase, beginning at toes-off, isrepresented using stick figures . Diagram A is the solution of thependular model with all pivots frictionless and unrestrained.Diagram B is another solution, using the same initial conditions,but with the shoulder angle kept fixed .

swing freely . There was a smooth progression fromtoes-off to heels-strike and the body maintained anormal orientation throughout that phase . In thefirst half of the body-swing phase, shoulder anglecontrol was essentially a restriction of shoulderrotation, which caused the trunk to pivot about thecrutch tips rather than about the shoulder . In such aconfiguration, the level of the hips are elevated asthe body pivots over the crutch tips and reach amaximum height when the hips are aligned verticallyabove the crutch tips . In addition, the restriction ofshoulder rotation causes swing-through of the legsalone. The resulting hip flexion after toes-off resultsin an effective shortening of the body length . Themaintenance of a fixed shoulder angle, therefore,provides a mechanism for increasing ground clear-ance after toes-off, as illustrated in Figure 9 . When,as in Model 1, the shoulder was allowed to pivotfreely, the body swings at both the hips andshoulders as soon as the toes lift off . As the trunkpivots about the shoulder, the height of the hips arelowered, while at the same time, the extending hipscause a lengthening of the body and a reduction inground clearance . The imposed control of shoulderangle in the system simulation was sufficient toeliminate the ground interference problem and alsoacts to increase the stride length.

The physiological effort required to control theshoulder angle during the body-swing phase isunlikely to account for the significant metabolicenergy expenditure during this same period . Aconsequence of operating a mechanical system byphysiological means is that metabolic "work" mustbe provided during activities where no mechanicalwork is required; the muscles are actively used tocontrol the position and compliance of the jointseven when there is no joint motion . The legs arenormally well-suited for weight bearing, havingstable joints and large muscles with large lever arms.By contrast, the arms and shoulders are poorly-suited for supporting the body . The crutches areweight bearing for about 48 percent of the gait cyclein swing-through crutch ambulation. Supporting thebody with the arms requires that stabilizing forcesbe provided to the wrists, elbows and shoulders.These joints have multiple, independent degrees-of-freedom and are served by relatively small muscleswhich are heavily taxed when weight bearing . Onestrategy for reducing the effort required whenambulating in the swing-through style would be to

FLOOR

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ROVICK and CHILDRESS : Paraplegic Swing-through Crutch Ambulation

support the body weight with a mechanical struc-ture, rather than through the arms and shoulders.The results of the pendular model simulation suggestthat any such device should not interfere with theindividual's ability to control the angle of theshoulder while in the body-swing phase . Of thecommonly prescribed crutch types, the axillarycrutch, when used properly (i .e ., no weight bearingthrough the underarm pad) provides no stability tothe arm. The forearm crutch may provide somestability to the wrist ; and the Canadian crutch,which bears on the brachial muscles, provides somestability to both the elbow and the wrist . Notsurprisingly, the metabolic energy consumption isreported to be lowest for the Canadian crutch,highest for the axillary crutch, and in-between forthe elbow crutch (15) . The saddle crutch, designedby Joll (9), eliminates the arms and shoulders fromweight bearing entirely . With this device, the indi-vidual sits on a saddle which is suspended by strapsfrom the tops of the crutches, like a playgroundswing . The weight is borne through the seat, and thearms are merely used for controlling the motion.

Another area of energy expenditure apparentfrom observation, happens during the transitionbetween the stance and swing phases . The period ofweight transfer occurs prior to toes-off and hencewas not included in the modeling effort . In thistransition phase, weight bearing is transferred fromthe legs to the arms, and hence there are some of thesame weight bearing issues that are present in thebody-swing phase . More importantly, the body-swing phase must be initiated by an active lifting ofthe toes off the ground . For many crutchambulators, the toes can be lifted by bending of theknees. However, for the paraplegic ambulator, adifferent strategy is used : the entire body is lifted byelbow extension and shoulder depression to initiatetoes-off . This lifting is continued after toes-off,presumably to gain additional ground clearance forthe toes . In essence, the paraplegic crutch ambulatormust perform 1 push-up with each stride . Thispush-up activity has a second drawback in that amore stabilizing crutch, like the Canadian crutch,cannot normally be used by the paraplegic, since therequired elbow extension would lift the arm out ofthe cuff and negate the benefits of that crutchdesign . Body elevation, using shoulder depression, isstill possible with the Canadian crutch, but theamount of elevation is reduced from when the

elbows can be extended as well . A device like thesaddle crutch would completely eliminate the possi-bilities for pushing-up the body, since either elbowextension or shoulder depression would result inlifting the individual off the seat of the crutch.

Some criteria for design are suggested, based onthis study : 1) Any crutch design should not interferewith the ability of the individual to control the angleof the shoulder in the swing phase. 2) The individualmust be able to initiate the body-swing phase bylifting the toes off the ground somehow. 3) Methodsof relieving the joints of the arms and shouldersfrom load bearing should reduce the metabolicenergy expenditure during the body-swing phase . 4)There must be sufficient clearance between the feetand the ground to prevent interference during thebody-swing phase.

The Canadian and saddle crutches are interestingdesigns which satisfy the design goal of arm stabili-zation, but at the same time, interfere with anotherone of the design goals that cannot be violated, i .e .,ground clearance . If a mechanism for toes lift-offand ground clearance could be provided for by amechanism in the orthoses (perhaps assisted byfunctional neuromuscular stimulation [FNS] of theankle or knee), then these stabilizing crutch designsmight have application for the paraplegic . The finaldesign solution, it would seem, may require a hybridsystem consisting of a specialized orthosis and astabilizing crutch ; or FNS and a stabilizing crutch,which when combined, can reduce the difficulty ofcrutch-aided gait, while providing for functionalambulation by paraplegic persons.

CONCLUSIONS

1. The body-swing phase of swing-through para-plegic crutch ambulation has been successfully mod-eled as a pendular system with muscular control ofthe shoulder angle . During the first half of thebody-swing phase, the muscular control is primarilyrestriction of shoulder joint rotation . This contrib-utes to increased ground clearance, as well ascontrolling body orientation and the timing of thebody-swing phase.

2. Areas of obvious energy demand are thestabilization of the joints of the arms and shouldersduring the body-swing phase, and the active liftingof the toes to initiate the body-swing phase. Those

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Journal of Rehabilitation Research and Development Vol . 25 No . 4 Fall 1988

interested in designing devices which may reduce theenergy demand of swing-through crutch ambulationfor paraplegics may want to consider hybrid mecha-nisms which address these two issues.

ACKNOWLEDGMENTThis work was funded by NIDRR Grant #6008200024.

APPENDIX

In this section, Legs refers to the pendular linkcomposed of both legs with KAFOs; Trunk refers to thependular link representing the head, neck and trunk ; andCrutches refers to the pendular link of both arms withcrutches .

SYMBOL MEANING

Mc Mass of the Legs, Trunk and Crutches.

I L , IT , Ic Moment of inertia of the Legs, Trunk andCrutches about their respective mass centers.

0, 0, a Angle of the Legs, Trunk and Crutches withrespect to vertical.

0, 0, a Angular

velocity

of the

Legs,

Trunk

andCrutches.

8 , 0, a Angular acceleration of the Legs, Trunk andCrutches.

6, h, S Shoulder angle (6 = O-a), angular velocity andacceleration.

L Distance from the hip to the Legs mass center.

T Distance from the shoulder to the Trunk masscenter.

B Length of Trunk (link 2).

C Length of Crutches (link 3).

A Distance from crutch tip to Crutches masscenter.

g Gravitational acceleration .

1. Childs TF : An analysis of the swing-through crutch gait.Phys Ther 44(9) :804-807, 1964.

2. Dempster WT : Space requirements of the seated operator.Wright Air Development Center, United States Air Force,Technical Report 55-159, 1955.

3. Drillis R, Contini R : Body segment parameters . TechnicalReport 1166-03, School of Engineering, New York Uni-versity, 1966.

4. Epstein S : Art history and the crutch . Ann Med Hist9 :304-313, 1937.

5. Fisher SV, Patterson RP : Energy cost of ambulation withcrutches . Arch Phys Med Rehabil 62:250-256, 1981.

6. Ghosh AK, Tibarewala DN, Dasgupta SR, Goswami A,Ganguli S : Metabolic cost of walking at different speedswith axillary crutches . Ergonomics 23(6) :571-577, 1980.

7. Gordon EE : Physiological approach to ambulation inparaplegia . JAMA 161(8) :686-688, 1956.

8. Huang CT, Kuhlemeier KV, Moore NB, Fine PR : Energycost of ambulation in paraplegic subjects using Craig-Scott braces . Arch Phys Med Rehabil 60 :595-600, 1969.

9. Joll CA: An improved crutch . Lancet 1 :538, 1917.10. Lunsford B, Mercer L, Hamilton S : Energy cost of

walking and wheelchair propulsion and upper extremityergonometry in patients with spinal cord injury . AnnualReports of Progress, REC Rancho Los Amigos Hospital,Feb . 1979-Jan . 1980.

11. McBeath AA, Bahrke M, Blake B : Oxygen consumptionmeasurement . J Bone Joint Surg 56A(5) :994-1000, 1971.

12. McGill SM, Dainty DA : Computer analysis of energytransfers in children walking with crutches . Arch PhysMed Rehabil 65 :115-120, 1984.

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14. Patterson R, Fisher SV : Cardiovascular stress of crutchwalking . Arch Phys Med Rehabil 62 :257-260, 1981.

15. Sankarankutty M, Stallard J, Rose GK: The relativeefficiency of "swing through" gait on axillary, elbow andCanadian crutches compared to normal walking . JBiomed Eng 1 :55-57, 1979.

16. Shoup TE, Fletcher LS, Merrill BR: Biomechanics ofcrutch locomotion . JBiomech 7 :11-19, 1974.

17. Stauffer ES, Hoffer MM, Nickel VL : Ambulation inthoracic paraplegia . J Bone Joint Surg 60A(6) :823-824,1978.

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