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Walking symmetry and energy cost in persons with unilateral transtibial amputations: Matching prosthetic and intact limb inertial properties
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Walking Symmetry and Energy Cost in Persons With Unilateral Transtibial Amputations: Matching Prosthetic and Intact Limb Inertial Properties Sarah J. Mattes, MS, Philip E. Martin,
PhD, Todd D. Royer, MS
ABSTRACT. Mattes SJ, Martin PC, Royer TD. Walking symmetry and energy cost in persons with unilateral transtibial amputations: matching prosthetic and intact limb inertial properties. Arch Phys Med Rehabil2000;81:561-8. Objectives: To investigate the hypothesis that increasing the mass and moment of inertia of the prosthetic limb of people with unilateral, transtibial amputations to match the mass and moment of inertia of the intact limb improves walking symmetry without increasing energy cost. Design: Gait symmetry and metabolic energy cost of walking for six subjects with unilateral, transtibial amputations were evaluated under three prosthesis loading conditions. Setting: University research laboratory. Subjects: Six ambulatory individuals with unilateral, transtibia1amputations. Interventions: Subjects walked at 1.34m/sec under three prosthetic limb loading conditions: (1) no added load; (2) loading that produced a match of prosthetic shank and foot massand moment of inertia with those of the intact limb (100% load); and (3) a load that was half that of the 100% condition (50% load). Main Outcome Measures: Step length, swing time, stance time, and metabolic energy expenditure. Results: As mass and moment of inertia of the prosthetic limb became more closely matched to the intact limb, step length, swing time, and stance time became less symmetrical. Energy cost for the 100% load condition was significantly greater (6% to 7%) than the baseline and 50% conditions. Conclusions: The loading configuration required to produce a match in the moments of inertia of the prosthetic and intact lower legs resulted in greater gait asymmetry and higher energy cost. Key Words: Amputation; Prosthesisdesign; Walking; Biomechanics; Energy metabolism; Rehabilitation. 0 2000 by the Americun Congress of Rehabilitation Medicine and the American Acudemy of Physical Medicine and Rehabilitution
From the Exercise and Sport Research Institute. Arizona Srak University, Tempe. AZ. Submitted April 12. 1999. Accepted in revised form July 29, 1999. Supported by an Arizona Slale University Graduate Research Support Office Granl and the Douglas L. Conley Memorial Scholarship. Presented in pan at the 21~ Annual Meeting of the American Society of Biomechanics. September 26. 1997. Clemson. SC. and the 4th annual meeting of the Gail and Clinical Movement Analysis Society, March I I. 1999, Dallas, TX. No commercial party having a direct financial interest in the results of the research supporting this article has or will confer a benefit upon the authors or upon any organization with which the authors are associated. Reprint requests to Philip E. Martin, PhD. Department of Exercise Science & Physical Education. Arizona State University. Tempe, AZ 85287-0404. 6 2000 by the American Congress of Rehabilitation Medicine and the American Academy of Physical Medicine and Rehabilitation 0003-9993/00/8105-5564$3.00/O doi: 10.1053/nu.2000.385 I
EOPLE WITH UNILATERAL, transtibial amputations P often demonstrate significant asymmetrical gait pattems.le5 Specifically, the prosthetic limb has a smaller push-off force, longer swing time, longer step length, and a shorter stance time than the intact limb. In addition, persons with transtibial amputation expend 10% to 30% more energy during walking than persons with amputation when energy cost is compared for comparable walking speeds or is expressed per unit of distance traveled.6-10In general, clinicians and researchers have embraced the notion that prosthesesshould be as light as possible, presumably in part to minimize muscular effort and metabolic energy demand during locomotion and perhaps also to facilitate faster walking speeds.II-l3 This is based on the premise that an important component of metabolic demand during gait is associatedwith accelerating the legs with each stride. Thus, the demands on the musculature should be reduced as the mass and moment of inertia of the leg are reduced. Another consequence of the use of lightweight prostheses, however, is that people with unilateral, transtibial amputations often possess a substantial inertial asymmetry between their limbs. The mass of the residual limb plus a common prosthetic limb for an adult with a transtibial amputation may typically only be 30% to 40% of that of the intact shank and foot.14.15At present, the relation between lower extremity inertia asymmetries, gait asymmetries, and higher energy costs is not well understood. Previous modeling studies have suggested that gait symmetry should be improved if the mass and moment of inertia of the prosthetic and intact limbs are well matched.‘6-18 Mena and colleaguesI specifically stated that “a ‘lightweight’ prosthesis would be less desirable than a ‘heavy’ prosthesis, while a prosthesis that had the same inertial properties of the removed limb may be the most desirable.” Only recently have experimental efforts begun to assessthe effects of prosthetic limb inertia changes on the energy cost’5*19 and mechanics of walking of people with transtibial amputations.11,20Results of these studies have either been equivocal or lacking in sufficient information to draw definitive conclusions. For example, Lehmann and associatesI observed as much as an 8.6% increase in aerobic demand at self-selected and fast (120m/min) walking speeds as prosthetic limb mass was increased from a low of 42% of intact limb mass up to 70% of intact limb mass and prosthetic limb center of mass was manipulated proximally and distally by altering mass dishibution. In contrast, Gailey and coworkers19 concluded that up to 907g evenly distributed on the prosthetic limb did not alter the energy cost in persons with transtibial amputation when walking at 76m/min. The effects of inertial manipulations on gait mechanics are also not clear. Donn and associates” systematically manipulated shoe mass by as much as 200g in subjects with unilateral, transtibial amputation and found that optimum shoe mass, ie, that which resulted in the most symmetrical walking pattern, showed little correlation with the subjects’ own shoe mass but was highly correlated with preferred mass. Hillery and colleagues20reported minor alterations for a single
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subject with a unilateral amputation in both walking kinematics (eg, increased stride length) and ground reaction force profiles (eg, higher peak forces for vertical and anterior-posterior components in early stance) as prosthetic limb mass was increased from 1.08 to 2.54kg. Based on the limited available experimental research and inconsistency in empirical findings, there is a need for additional research focusing on the sensitivity of energy cost and kinematic and kinetic features of walking to prosthetic limb inertia changes, particularly in people with transtibial amputations. In addition, investigators typically have not considered the existing differences in inertial properties of prosthetic and intact limbs when manipulating the inertial properties of the prosthesis in experimental studies. Specifically, there appear to be no empirical data in the published literature testing the effects of matching mass and moment of inertia characteristics of prosthetic and intact limbs on gait symmetry and energy cost. Thus, our purpose was to determine the effect of decreasing lower extremity inertial asymmetry on walking symmetry and energy expenditure in people with unilateral, transtibial amputations. Based on early modeling results,*s we hypothesized that the gait patterns of persons with unilateral, transtibial amputation are more symmetrical when the mass and moment of inertia of the prosthetic limb are more closely matched to those of the intact limb. We also hypothesized that energy cost of walking is not adversely affected as the prosthetic limb inertia properties are increased to approach those of the intact limb. METHODS Subjects Six individuals with unilateral, transtibial amputations between 18 and 50 years of age served as subjects. All were interviewed regarding general health, activity level, and history of using a prosthetic limb (table 1). To control for metabolic confounds associated with cardiovascular abnormalities, individuals whose amputations were associated with peripheral vascular disease were excluded. Additionally, subject recruitment focused on individuals who were fully ambulatory, predominantly used an energy storing prosthetic limb in their vocational and recreational activities, and maintained some degree of physical activity in their daily activities. These restrictions helped to ensure that the subjects were able to complete all treadmill and overground exercise tests aerobically and without substantial fatigue and to control for prosthetic limb design effects on walking mechanics and energy cost. These same restrictions, however, resulted in a small sample size that limits the generalizability of our results to all individuals with unilateral, transtibial amputations. Data Collection Each subject completed an orientation session and an experimental session within a l-week period. During the orientation Table Age Subject
(Vd
1 2
29 50
3 4
37 18 45 29
5 6 Mean
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2 SD
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35 + 12
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1: Subject
Characteristics
Height km)
Body Mass kg)
186.4 170.1 184.2 175.7
90.5 75.2 84.0 60.5 86.4
178.3 177.0 176.6 t 5.9
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Years With Amputation 3 7 4 15 4
91.1
10
64.6 2 6.1
7.1 + 4.6
May
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Reason Trauma Blood clot Cancer Birth defect Trauma Trauma
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session. the project’s purpose and procedures were explained to the subject and written informed consent was obtained in accordance with university human subjects policies. Subjects then completed 30 minutes of treadmill walking to ensure they were well accommodated to the treadmill before data collection. To acclimate subjects to test conditions, practice included a minimum of 10 minutes of treadmill walking while breathing through a mouthpiece and 10 minutes of walking with a l-kg load aflixed to the distal aspect of the prosthetic shank. After treadmill practice, the subject’s relevant anthropometric data were obtained and the inertial properties of the prosthetic and intact limbs were measured or estimated. Prosthetic limb mass was measured directly using a standard laboratory scale.Center of mass position was quantified using a reaction board method, and moments of inertia of the prosthetic limb about transverse axes through its center of mass and the knee joint were estimated via an oscillation technique.*’ The residual limb (below-knee) was modeled as a frustum of a right circular cone,?* and its volume was subsequently estimated geometrically. Mass of the residual limb was estimated from its volume and by assuming a 1. log/cm3 uniform tissue density.Z3 The center of mass location of the residual limb was assumed to be coincident with the center of volume for this frustum. The center of mass of the total complex-residual limb, prosthetic socket, and prosthetic limb-was calculated using the measured or estimated masses and centers of mass of each of the component parts. For the purpose of estimating intact limb inertial properties, total body mass was adjusted to reflect symmetrical lower extremity structure, because prosthetic limb mass was less than that of the intact limb. Intact limb inertial properties were subsequently estimated using adjusted body mass and intact limb anthropometric measures according to methods outlined by deLeva.24q25 During the experimental session,subjectscompleted 8-minute treadmill walking bouts and multiple overground walking trials at 1.34m/sec under three load conditions: (1) a baseline conditions in which no load was added to the prosthetic limb; (2) a 100% added mass condition in which the prosthetic limb mass and moment of inertia about a transverse axis through the knee were matched to those of the intact lower leg; and (3) a 50% added mass condition in which the added load was 50% of the difference between the limb masses but positioned in the same location as that of the 100% added load condition. The order of load conditions was randomized to minimize any order effects. The nominal walking speed of 1.34rn/sec (3.0mph) was chosen because of our interest in presenting some challenge to the subjects without producing excessive fatigue. The targeted speed was modestly faster than typical preferred walking speeds reported for individuals with unilateral, transtibial amputation using an energy storing prosthesis.8*‘4,26 Mass was added to the prosthetic limb using two concentrated and equal-sized packets of lead shot affixed to the anterior and posterior aspect of the prosthetic limb. The packets were positioned such that the estimated prosthetic limb moment of inertia about a transverse axis through the knee under the 100% added mass condition was equal to that of the intact limb. The placement of the added mass was determined using the parallel axis theorem: d=
Let
d-
-
$3ms
m
where d is the distance below the knee that the masswas placed, and Ipros are the estimated moments of inertia for the intact and prosthetic limbs about a transverse axis through the knee
hact
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and m is the additional massrequired to match the massof the intact limb (100% mass condition). Because concentrated rather than distributed masseswere used to produce the inertial manipulations, it was not possible to ensure that center of mass locations of the prosthetic and intact limbs would also be matched under the 100% load condition. Nevertheless. adding load to the distal aspect of the prosthetic limb had the effect of shifting its center of mass more distally and, under the 100% load condition, resulted in a reasonably close approximation of the center of mass location for the intact limb (table 2). Aerobic demand was measured during treadmill walking using a standard, commercially available metabolic cart. Oxygen and carbon dioxide sensorswere calibrated before each test using gases of known concentrations. The pneumotach used to measure the volume of expired ,air was calibrated using a 3-L syringe. Mean oxygen uptake (VO:) over the last 2 minutes of each g-minute trial was used as an estimate of each subject’s steady-state aerobic demand. The rate of energy cost was estimated from aerobic demand according to Weir”:
joint,
Ii = (3.9) \jO? + (1.1) vco, where k is energy cost in kcal/min, and 90, and carbon dioxide uptake (VCO?) are in L/min. E was subsequently converted to units of J/set. Overground walking trials for a given load condition were collected immediately after the treadmill walking bout for the same load condition. After reflective markers were placed bilaterally over the medial and lateral aspectsof the heel and on the fifth metatarsal head, subjects traversed a 15meter walkway. Because of the absence of anatomical landmarks on the artificial limb, the locations of markers applied to the prosthetic foot were matched with those of the intact limb.?” Walking speed was monitored by a digital clock activated by the sequential interruption of photocells positioned approximately 3m apart. Acceptable trials were those in which average speed through the measurement zone was within 3% of the target speed. Five acceptable trials for both the prosthetic and intact sides were collected for each load condition. Sagittal plane motion was recorded at a rate of 60Hz with a video camera positioned approximately 5m from the walkway. A l-meter scaling object was imaged in a plane that approximated a sagittal plane passing through the foot on the side of the body closest to the camera so that video position data could be converted into object space coordinates. The camera lens focal length was adjusted to ensure that an entire stride cycle (heel
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strike of one foot to subsequent heel strike of the same foot) was recorded. Data Analysis Video data for one complete stride from all five acceptable trials for each load condition were digitized into twodimensional coordinate data using a video digitizing system. Coordinate data for a minimum of IO additional fields just prior to and following the stride were also digitized because of endpoint problems commonly associated with data smoothing techniques. The coordinate data were subsequently scaled to object space coordinates and digitally filtered at 6Hz using a fourth order, recursive Butterworth digital filter. Ipsilateral and contralateral heel strike and toe-off events were visually identified and marked during the digitizing process and were used to compute stance and swing times for both legs. Prosthetic limb step length was defined as the horizontal distance between the heel marker of the intact foot at heel strike and the heel marker of the prosthetic foot at the subsequent heel strike. Step length for the intact limb was calculated similarly as the distance between prosthetic and intact heel markers for consecutive foot contacts. Symmetry indices (SI) were computed to provide a descriptive marker for the degree of symmetry between the prosthetic (P) and intact (I) limbs for stance and swing times and step length using the following equationZ9:
SI=IP-1)1 0.5 (P + I)
100%
A SI of zero reflects perfect symmetry between the limbs, whereasincreasingly positive or negative values indicate increasing asymmetry for a variable in question. In addition, positive values indicate the value for the prosthetic limb was greater than that of the intact limb, while negative values denote that the intact limb value was greater. Statistical Analysis A single factor repeated measures analysis of variance (ANOVA) was used to test for differences in energy cost between the baseline (no load added), 50%, and 100% load conditions. A two-factor, repeated measures ANOVA was used to examine leg (ie, prosthetic and intact) and load (ie, no load, 50%, and 100%) main effects and their interaction for swing and stance times and step length. The alpha level was set at .05 for all statistical tests. RESULTS
Table
2: Mass and Center of Mass Properties of Intact Prosthetic Limbs and Added Masses
and
Mean + SD
Limb mass properties Intactshank + foot mass (kg) Prosthesismass (kg) Residuallimb mass (kg) Added mass properties 50% added mass (kg) 100% added mass (kg) Distanceadded masswas placed below
knee(m)
Centerof mass location below knee Intact shank + foot(m) Prostheticlimb, unloaded (m) Prostheticlimb, 50% load (m) Prostheticlimb, 100% load (ml
4.91 e .40 1.48 2 .32 1.74 -t .36 .85 z .31 1.70 2 .62 .41 + .06 .252 .162 .212 .244
t t -t I!
.014 .015 .009 .014
Range
4.30-5.36 1.25-2.12 1.23-2.23 .44-l .36 .87-2.73 .34-.49 ,235 .139 .201 .224
2 + + -c
.273 ,162 .225 ,264
Inertial Manipulations The goal of our inertia manipulation was to match the prosthetic and intact limb massesand moments of inertia about a transverseaxis through the knee (Ike) under the 100% added mass condition. Figure 1 displays the average effect of the added masseson Ih,, during the stride cycle and confirms the systematic effect of loading on the moment of inertia of the shank and foot about the knee. Although matching the moments of inertia of the two limbs about the hip (Ihip) was not the specific goal of the manipulation, figure 2 demonstrates that Ibp also became more closely matched for the two limbs with loading. Thus, the desired experimental manipulation of both mass and moment of inertia was produced successfully. Temporal and Kinematic Responses and Gait Symmetry Step length was significantly longer for the prosthetic limb than the intact limb (fig 3; limb main effect Fl.5 = 31.89, Arch
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1.05 + Pros +lntact
1 z z 0.95 E 5 g 0.9 z
; 0.30 al .-c s 0.20 E E 0.10 t
IL”..
0.85
0.00 -I
0.5 NL
50%
100%
load condition
NL
i
50% load condition
100%
Fig 1. Moment of inertia of the prosthetic (Pros) and intact shank and foot relative to a transverse axis through the knee joint flk.,). The mass was positioned on the distal aspect of the prosthetic limb such that Iu,,, for the two limbs was the same under the 100% load condition. NL, no load.
Fig 3. Although step length for the prosthetic limb cantly different for the three load conditions, there step length to increase as its mass and moment increased. There was no change in step length for intact leg. NL, no load.
p = .002), as has been reported previously.1.30-3’The addition of load to the prosthetic limb, however, produced no significant change in step length (load by limb interaction effect F2.10 = 2.48,~ = .13; load main effect F2.to = .86, p = .45). A close examination of figure 3, however, suggests a subtle tendency for step length of the prosthetic limb to increase as its mass and moment of inertia increased, whereas step length for the intact limb showed little change with prosthetic limb loading. As a result and in contrast to our hypothesis, the symmetry in step length between the prosthetic and intact legs did not improve as the mass and moment of inertia of the two limbs became more closely matched. Rather, the extent of the step length asymmetry tended to increase (no load SI = 2.1%. 50% load SI = 2.6%. and 100% load SI = 4.5%).
Swing time for the prosthetic limb swing time was significantly higher than that for the intact limb (fig 4; limb main effect Ft.5 = 118.11, p < ,001). In addition, prosthetic limb swing time increased as its mass and moment of inertia were increased, whereas that for the intact limb was relatively unaffected by inertial manipulation of the prosthetic limb (load by limb interaction FZJO= 7.306, p = .Oll). Stance times for the prosthetic and intact limbs showed divergent responses as load was added to the prosthetic limb (fig 5; load by limb interaction Fz,ta = 7.78, p = .009). Whereas stance times for the two limbs were quite similar for the baseline condition, prosthetic limb stance time decreased and intact limb stance time increased as the prosthetic limb inertia was increased. Thus, contrary to our hypothesis, matching the mass and moment of inertia characteristics of the prosthetic limb to those
3.0-
0.5
g
2.5 -
f .B E 2.0E i
/El
NL
50%
100%
load condition Fig 2. Moment of inertia of the entire prosthetic (Pros) and intact legs relative to a transverse axis through the hip joint (l,,u). A reasonably close agreement in I,,,,, for the two legs was produced by loading the distal aspect of the prosthetic limb. NL, no load.
Phys
bled
2
0.45 -
E ‘3 .-P 2
0.4 -
Pros Intact
T
T
e Proa I+lntact
1.5 !
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I
,
+ +
T
was not signifiwas a trend for of inertia were the unloaded,
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0.35 -I NL
50% load condition
Fig 4. Swing time for the prosthetic (Pros) mass and moment of inertia were increased, change in swing timeforthe unloaded, intact
limb increased as its whereas there was no leg. NL, no load.
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0.8
0.75
3
5 425 % 8
5 E = E s b
0.7
3 f 375 aa
0.65
NL
50%
cl
NL
100%
50% load condition
load condition Fig 5. Stance time decreased for the prosthetic (Pros) limb increased for the unloaded, intact leg as the mass and moment inertia of the prosthetic limb were increased. NL, no load.
and of
Fig 7. Energy cost of walking was not different and 50% load conditions, but was significantly the 100% load condition.
of the intact limb had the effect of increasing asymmetries for both swing and stance times (fig 6). Energy Cost of Walking The energy cost of walking increased significantly as the inertial properties of the prosthetic and intact limbs became more similar due to prosthetic limb loading (fig 7; load effect F 2.1,~ = 7.29, p = .043). A close inspection of figure 7 reflects a nonlinear energy cost response. The energy cost of ambulating under the 50% load condition was almost identical to that for the baseline condition, whereas the energy cost for the 100% condition was 6% to 7% higher than those for the baseline and 50% conditions.
h4
’ 1
50%
100%
1’ 1
100%
/
1
n Swing 0 Stance I load condition
Fig 6. Symmetry indices for swing and stance times indicate the increasing asymmetries that developed for both variables in response to increased mass and moment of inertia of the prosthetic leg. Positive symmetry indices for swing time indicate that the prosthetic limb values were greater than those of the intact limb. Negative symmetry indices for stance time reflect greater values for the intact limb. NL, no load.
for the unloaded (NL) higher (6.9%) under
DISCUSSION Gait Symmetry Modeling research’* suggeststhat the inertial characteristics of transtibial prosthesesshould match those of the intact limb to maximize gait symmetry and minimize energy expenditure during walking. The results of this project are inconsistent with these modeling predictions. Step length, swing time, and stance time symmetry either did not improve or worsened as mass and moment of inertia of the prosthetic limb were increased to match those of the intact limb. The swing phase of human walking has been modeled as a pendulum swinging about a transverse axis through the hip joint.33 While a simple pendular model may be an oversimplification of the dynamics of the swing phase, it offers a means of examining the interplay of limb inertial factors during leg swing. The half-period of oscillation of a simple pendulum (T) is computed from the following relationship:
where Iaxisis the pendulum moment of inertia about its axis of rotation, m is its mass, g is the acceleration due to gravity, and d the distance from the axis of rotation to its center of mass. Using this simple model, the relation between the inertial manipulations that were implemented in this project and the half-period of oscillation can be explored mathematically. The addition of mass to any pendulum will increase its mass and moment of inertia about the axis of rotation. The magnitude of the effect of the added mass on d and Imisdepends on where the added mass is positioned. Thus, the ultimate effect of the added mass on T depends on the relative changes in Iais and the product of m and d. If Imisincreasesmore than the product of m and d, then the half-period of oscillation increases, a change that would be consistent with an increase in swing time. Conversely, if the product of m and d increases to a greater extent than Iaxis,then T will decrease,a change consistent with a decrease in swing time, the desired effect in this investigation. Table 3 summarizes the effects of mass additions used in this
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Table 3: Average Inertial Properties of the Entire Prosthetic Leg Used as Inputs to a Simple Pendular Model That Predicted the Half-Period of Oscillation of the Pendulum Under the Three Experimental Load Conditions 50% Load No Load
Absolute [hip
kg
Mass
d b-4 Mass x d (kg m) Half-period of
Absolute
1.840
2.336
15.43 ,268 4.134
16.28 ,298 4.850
,670
,696
.427
.441
m2)
(kg)
oscillation (set) Measured swing time (set)
100% Load %
96
Increase*
Absolute
Increese*
27.0
2.900
57.6
17.3
17.12 .325 5.565
34.6
,724 .446
Average measured swing times are provided with half-period of oscillation. Abbreviations: lhip, moment of inertia relative mass location relative to the hip. l Percent increases in lhip and the product expressed relative to the unloaded condition.
for
trend
comparison
to the hip; d, center of
mass
and
of
d are
study on inertial characteristics of the entire leg and on the half-period of oscillation of a simple pendulum representing the leg. As load was added to the distal aspect of the prosthetic limb to match the inertial properties of the intact and prosthetic shank and foot, Ihip experienced a proportionally greater increase than the product of m and d. Thus, the predicted half-period of oscillation of the leg modeled as a pendulum swinging about the hip increased, which is consistent with the observed increase in the swing time for the prosthetic leg. Skinner and Barrack34 observed that asymmetrical application of mass to the leg of able-bodied individuals produced similar effects on temporal features of the loaded limb and led to temporal asymmetries between limbs. When 1.82kg of mass was added near the ankle joint of one leg, swing time increased (3.9%) and stance time decreased (2.5%) for the loaded leg relative to an unloaded baseline condition. In our investigation, adding mass to the distal aspect of the prosthetic limb produced a similar response (swing time increased 4.4% for an average load of 1.70kg). Unfortunately, previous research on persons with transtibial amputations provides little data for direct comparison with our results. Donn and colleagues” studied the effect of symmetrical manipulation of shoe mass in 10 subjects with transtibial amputation on gait symmetry as the subjects walked at selfselected speeds. In a search for a shoe mass that contributed to the greatest degree of symmetry, they manipulated the mass of a standardized lab shoe in 50-g increments up to 2OOg, and quantified the symmetry of several gait variables for each load condition. Subjects were also asked to subjectively identify the shoe mass condition that they most preferred. Donn and colleagues” concluded that “lightweight footwear does not necessarily provide the most symmetrical gait . . . or the most acceptable gait as preferred by the amputee.” In addition, the shoe mass that contributed to the most symmetrical walking pattern was correlated substantially more strongly with preferred shoe mass than with the subjects’ own shoe mass. Prior to any exposure to the load conditions explored in this study, it is worth noting that our subjects generally anticipated having a negative reaction to the addition of any mass to their prosthetic limbs. Based on anecdotal comments of the subjects, however, the 50% load condition produced little negative reaction from the subjects. The effect of the smaller added load either was not noticed or was easily tolerated by the subjects. Substantially more negative comments, however, were exArch
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pressed about the 100% load condition. Our subjects clearly did not like to walk with the heavier load on their prosthesis despite the fact that it created an inertial symmetry between the prosthetic and intact limbs. Hillery and associatesZostudied the response of a single individual with a transtibial amputation to massesof 530g and 1,460g added to the distal aspect of the prosthetic limb during walking at self-selected normal and fast speeds.They noted that the extent of asymmetries in the relative time spent in single limb support was affected by the mass condition. At the fast walking speed, the unloaded prosthesis resulted in the most symmetrical outcome, whereas the intermediate load produced the most symmetrical response at a normal preferred walking speed. Although the research of both HilleryZo and Dorm” and their colleagues offers some interesting observations about gait symmetry and demonstrates that both symmetrical and asymmetrical loading of the distal aspect of the legs affects gait kinematics, their data are difficult to interpret and generalize. The use of self-selected walking speeds makes it difficult to distinguish independent effects produced by inertial changes and walking speed changes. Hillery and associatesZoreported an increase in normal self-selected walking speed as load on the prosthetic limb increased, whereas Donn and colleagues” reported no walking speed data. Although the results of our investigation clearly indicate that matching the inertial properties of the prosthetic and intact lower legs did not improve walking symmetry and imposed a higher energy cost of walking on the amputees, there are a number of limitations of our experimental design that restrict the generalizability of these conclusions. We specifically chose to limit our investigation to relatively young, physically active individuals who used an energy storing prosthetic limb in their daily activities. Additionally, we chose to limit our investigation to subjects with transtibial amputation. Thus, our results may not be applicable to a broader group of persons with transtibial amputation who are older and less physically active than our subjects, and certainly cannot be generalized to persons with transfemoral amputations. We also chose to investigate a single walking speed. Because stride frequency is a function of walking speed, it is possible that the ideal inertial properties of a prosthetic limb may vary with the walking speed and stride frequency. Thus, the scope of future investigations should be expended to include a broader range of subjects and multiple speeds of locomotion. Considering the results from the present investigation and the implications of the pendular model, it appears that alternative inertial manipulations must also be considered if the goal is to enhance temporal and kinematic symmetry. Although our distal loading configuration produced a reasonable match in the inertial properties of the prosthetic and intact limbs, it also had the undesired effect of altering the swing and stance times of the prosthetic limb, such that the system became more asymmetrical. This suggests that a proximal loading configuration, most notably one that is more proximal to the center of mass of the limb, is more likely to produce the desired effect of decreasing prosthetic limb swing time such that it more closely matches that of the intact limb. From the perspective of the pendular model, proximal loading would have a smaller relative effect on the moment of inertia of the swinging system than on the limb center of mass position. Using a pendular model, Bachi suggested it is possible to identify a loading location that minimizes the period of oscillation of a simple pendulum and that both this loading location and the magnitude of the temporal effect produced are dependent on the magnitude of the load itself. Although subjects with transfemoral amputations
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have been shown to reduce the swing time of the prosthetic leg when the shank is loaded proximally,35~36it remains to be seen how patients with transtibial amputations respond to this type of inertial manipulation. The model of a simple pendulum provides a reasonable explanation why prosthetic leg swing time increased as mass and moment of inertia were increased, but it does not explain why the swing time of the prosthetic limb is longer than that of the intact side under unloaded conditions. Using inertial properties of the intact and prosthetic legs, the half-period of oscillation was calculated about a transverse axis through the hip for both limbs (table 4). Because of the differences in mass distribution properties between the limbs, the modeled halfperiod of oscillation of the prosthetic limb is shorter than that of the intact limb. Published literature indicates that intact limb stance time is greater than the prosthetic limb to minimize single support time on the prosthesis.‘-5Thus, the longer swing time for the prosthetic limb under normal conditions may be a simple result of the amputee intentionally increasing the stance time of the intact limb. Reasons for this are unclear but may include pain or discomfort in the residual limb, instability within the socket, lack of proprioceptive feedback regarding foot position, strength decrements on the prosthetic side, and/or reduced confidence in supporting body weight on the prosthetic leg. Energy
Cost of Walking
Research indicates that amputees consume more energy than able-bodied individuals when walking at the same speeds.6-i0 Lower extremity loading studies in able-bodied individuals suggest that the cost of carrying load on the legs increases systematically as load increases and that the cost of carrying load on the distal aspect of the lower extremities is significantly greater than that when load is carried more proximally on the limb or on the trunk.‘7-‘9 This may be part of the rationale underlying the use of prostheses that are as light as possible. It is less clear how amputees’ energy cost of walking is affected by limb inertial manipulations. Czemiecki and colleaguest4 found the addition of as much as 1.34kg near the center of mass of the shank on the prosthetic leg of subjects with transfemoral amputations produced no significant increase in the energy cost of walking for speeds ranging from 0.6 to I .5m/sec. It was this experimental outcome in subjects with transfemoral amputation that led to our prediction that load added to the prostheses of persons with transtibial amputation does not necessarily produce an increase in energy cost. Our results demonstrated that the energy cost of walking was essentially the same for the baseline and 50% load conditions, but was significantly higher (6% to 7%) under the 100% load condition. Although the absence of an energy cost difference between the baseline and 50% conditions might be interpreted as partial support for our hypothesis that energy cost is not adversely affected by prosthetic limb inertial increases, the robustnessof the observed nonlinear response of energy cost to
CONCLUSIONS
Based on our results, we concluded that manipulations of the inertial characteristics of the prosthetic limb to match those of the intact limb produce greater asymmetries between limbs in swing time, stance time, and step length in persons with transtibial amputation. Thus, these results did not support our hypothesis that matching inertial characteristics results in more symmetrical gait. Our results also failed to provide support for our hypothesis that energy cost of walking is not adversely affected when mass and moment of inertia of the prosthetic and intact limbs are matched. Energy cost was significantly higher under the 100% load condition relative to the baseline and 50% load conditions. Therefore, it is apparent that distal loading configurations tend to be detrimental in terms of both gait symmetry and energy cost. Proximal loading configurations, on the other hand, may hold promise for improving gait symmetry without imposing higher energy costs and await experimental assessment.Such configurations should be investigated in both able-bodied individuals and amputees at multiple walking speeds to determine the systematic effects produced by limb mass and mass distribution. Acknowledgment: The authors acknowledgethe assistanceof David J. Sanderson(Schoolof Human Kinetics,Universityof British Columbia, Vancouver,B.C.) for his helpful commentson-this manuscript.
References
I. Lehmann JF, PriceR, Boswell-BessetteS, Dralle A, QuestadK. Comprehensiveanalysisof dynamicresponsefeet: Seattleankle/ lite foot versusSACH foot. Arch Phys Med Rehabil 1993;74: 853-6
Prosthetic
Mass [hip
of leg (kg)
(kg
II-?)
Distance,hip to center of mass of Half-periodof oscillation(secl Observed
swing
time
(set)
leg (m)
Limb
17.12 2.71 .324 .70
,427
.396
1.
RobinsonJL, Smidt CL, Arora JS.Accelerographic,temporaland distanceeait: factorsin below-kneeamputees.PhvsTher 1977;57:
898-904.3. Sanderson
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15.42 1 .a4 .268 .67
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increasing prosthetic limb inertia awaits further testing. Additionally, our hypothesis clearly was not supported when the inertial properties of the prosthetic and intact limbs were matched. Gailey and associatest9 reported nonsignificant increasesof 2.3% and 4.7% in the aerobic demand of walking at 76m/min for distributed shank loads of 4.548 and 907g. respectively, in subjects with transtibial amputation. This amounts to an aerobic demand increase of approximately 5% per kilogram of added mass, which is quite comparable to the increase observed in the present study for the 100% load condition (6.9% per 1.70kg or 4% per kilogram). More interestingly, Lehmann and coworkerst5 examined the effects of both prosthetic limb mass and mass distribution on walking aerobic demand in subjects with transtibial amputation. Limb mass conditions were 42%, 60%, or 70% of the intact limb mass, whereas mass was distributed either proximally or distally, as reflected by the limb’s center of mass location below the knee (either 47% or 60% of shank length, respectively). Aerobic demand proved to be insensitive to mass per se, but highly sensitive to the distribution of the mass. Redistribution of the intermediate mass more distally resulted in a 6.1% increase in aerobic demand, while the same redistribution of the heavy mass produced a 4.4% increase.
2. Table 4: Pendular Model Estimations of the Period of Oscillation of the Entire Leg (Hip Joint Axis of Rotation) and the Observed Swing Time for the Prosthetic Limb and the Intact Limb
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DJ, Martin PE.Lower extremitykinematicand kinetic adantationsin unilateral below-knee amputees during walking. GaGPosture1997;6:126-36. SchneiderK. Hart T. Zemicke RF. SetoguchiY. OnnenheimW. Dynamics oi below-knee child amputee gait: SACK foot versus flex foot. J Biomech 1993;26:1191-1204. Seliktar R. Mizrahi J. Some gait characteristicsof below-knee amputeesand their reflectionon the ground reactionforces.Eng Med
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6. Fisher SV, Gullickson G. Energy cost of ambulation in health and disability: a literature review. Arch Phys Med Rehabil 197859: 124-33. 7. Gailev RS. Wenger MA. Raya M, Kirk N, Erbs K, Spyropoulos P, et al. Energy expenditure of trans-tibia1 amputees du&tg~ambulation at self-selected uace. Prosthet Orthot Int 1994: l8:84-9 I. 8. Torbum L, Perry J, Ayyappa E, Shanfield SL. Below-knee amputee gait with dynamic response prosthetic feet: a pilot study. J Rehabil Res Develop 1990;27:369-84. 9. Waters RL, Perry J, Antonelli D, Hislop H. Energy cost of walking amputees: the influence of level of amputation. J Bone Joint Surg Am 1976;58:42-6. IO. Waters RL, Yakura JS. The energy expenditure of normal and pathological gait. Crit Rev Phys Med Rehabil 1989; I: 183-209. II. Donn JM, Porter D. Roberts VC. The effect of footwear mass on the gait patterns of unilateral below-knee amputees. Prosthet Orthot Int 1989; I 3: 140-4. 12. Godfrey CM. Brett R, Jousse AT. Foot mass effect on gait on the prosthetic limb. Arch Phys Med Rehabil 1977;58:268-9. 13. Van De Veen PG. Van Der Tempel W. De Vreiss J. Bondgraph modeling and simulation of the dynamic behaviour of above-knee prosthe&. Prosthet Orthot Int 1987; I I :65-70. 14. Czemiecki JM. Gitter A. Weaver K. Effect of alterations in prosthetic shank mass on the metabolic costs of ambulation in above-knee amputees. Am J Phys Med Rehabil 1994;73:348-52. 15. Lehmann JF. Price R. Okumura R. Ouestad K. de Lateur BJ. NCgretot A. Mass and mass distribution-of below-knee prostheses: effect on gait efficacy and self-selected walking speed. Arch Phys Med Rehabil 1998;79: 162-8. 16. Tsai CS, Mansour JIM. Swing phase simulation and design of above knee prostheses. J Biomed‘Eng 1986: IO8:65-72. 17. Bach TM. Optimizing mass and mass distribution in lower limb prostheses. gosthet &hot Aust 1995;10:29-35. IS. Mena D. Mansour JM, Simon SR. Analysis and synthesis of human swing leg motion during gait and its clinical applications. J Biomech 1981;14:823-32. 19. Gailey RS, Nash MS, Atchley TA, Zilmer RM, Moline-Little GR, Morris-Cresswell N, et al. The effects of prosthesis mass on metabolic cost of ambulation in non-vascular trans-tibia1 amputees. Prosthet Orthot Int 1997;21:9-16. 20. Hillery SC, Wallace ES, McIlhagger R, Watson P The effect of changing the inertia of a trans-tibia1 dynamic elastic response prosthesis on the kinematics and ground reaction force patterns. Prosthet Orthot Int 1997;2 I : I 14-23. 21. Martin PE, Mungiole M, Marzke MW, Longhill JM. The use of magnetic resonance imaging for measuring segment inertial properties. J Biomech 1989;22:367-76. 22. Hanavan EP A mathematical model of the human body (AMRLTR-64-102). Dayton (OH): Wright-Patterson Air Force Base; 1964.
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23. Mungiole M. Martin PE. Estimating segment inertial properties: comparison of magnetic resonance imaging with existing methods. J Biomech I990;23: 1039-46. 24. deLeva I? Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J Biomech 1996:29: 1223-30. 25. deLeva P. Joint center longitudinal positions computed from a selected subset of Chandler’s data. J Biomech 199629: I23 I-3. 26. Gitter A. Czemiecki JM, Weaver K. A reassessment of center-ofmass dynamics as a determinate of the metabolic inefficiency of above-knee amputee ambulation. Am J Phys Med Rehabil 1995:74: 332-8. 27. Weir LBV. New methods for calculating metabolic rate with special reference to protein metabolism. J Appl Physiol 1949; 109: l-9. 28. Czemiecki JM, Gitter A, Munroe C. Joint moment and muscle power output characteristics of below knee amputees during running: the influence of energy storing prosthetic feet. J Biomech 1991;24:63-75. 29. Herzog W, Nigg BM. Read LJ, Olsson E. Asymmetries in ground reaction force patterns in normal human gait. Med Sci Sports Exert l989;2 I : I 10-4. 30. Isakov E, Burger H. Krajnik J, Gregoric M, Marincek C. Influence of speed on gait parameters and on symmetry in trans-tibia1 amputees. Prosthet Orthot Int 1996;20: 153-8. 31. MacFarlane PA, Neilsen DH, Shurr DG, Meier K. Gait comparisons for below-knee amputees using a flex-foot versus a conventional prosthetic foot. J Prosthet Orthot 199 I ;3: 150-61. 32. Gitter A, Czemiecki JM, DeGroot DM. Biomechanical analysis of the influence of prosthetic feet on below-knee amputee walking. Am J Phys Med Rehabil 199 I ;70: 142-8. 33. Mochon S, McMahon TA. Ballistic walking. J Biomech 1980; 13: 49-57. 34. Skinner HB. Barrack RL. Ankle weighting effect on gait in able-bodied adults. Arch Phys Med Rehabil 1990:7 I : I 12-5. 35. Skinner HB, Mote CD. Optimization of amputee prosthesis weight and weight distribution. Rehabil Res Dev Prog Rep 1989;26:32-3. 36. Tashman S, Hicks R, Jendrzejczyk DJ. Evaluation of a prosthetic shank with variable inertial properties. Chn Prosthet Orthot 1985;9:23-8. 37. Martin PE. Mechanical and physiological responses to lower extremity loading during running. Med Sci Sports Exert 1985; 17: 427-33. 38. Myers MJ, Steudel K. Effect of limb mass and its distribution on the energetic cost of running. J Exp Biol 1985;116:363-73. 39. Steudel K. The work and energetic cost of locomotion. I. The effects of limb mass distribution in quadripeds. J Exp Biol 1990:154:273-85.
Walking Symmetry and Energy Cost in Persons With Unilateral Transtibial Amputations: Matching Prosthetic and Intact Limb Inertial Properties Sarah J. Mattes, MS, Philip E. Martin,
PhD, Todd D. Royer, MS
ABSTRACT. Mattes SJ, Martin PC, Royer TD. Walking symmetry and energy cost in persons with unilateral transtibial amputations: matching prosthetic and intact limb inertial properties. Arch Phys Med Rehabil2000;81:561-8. Objectives: To investigate the hypothesis that increasing the mass and moment of inertia of the prosthetic limb of people with unilateral, transtibial amputations to match the mass and moment of inertia of the intact limb improves walking symmetry without increasing energy cost. Design: Gait symmetry and metabolic energy cost of walking for six subjects with unilateral, transtibial amputations were evaluated under three prosthesis loading conditions. Setting: University research laboratory. Subjects: Six ambulatory individuals with unilateral, transtibia1amputations. Interventions: Subjects walked at 1.34m/sec under three prosthetic limb loading conditions: (1) no added load; (2) loading that produced a match of prosthetic shank and foot massand moment of inertia with those of the intact limb (100% load); and (3) a load that was half that of the 100% condition (50% load). Main Outcome Measures: Step length, swing time, stance time, and metabolic energy expenditure. Results: As mass and moment of inertia of the prosthetic limb became more closely matched to the intact limb, step length, swing time, and stance time became less symmetrical. Energy cost for the 100% load condition was significantly greater (6% to 7%) than the baseline and 50% conditions. Conclusions: The loading configuration required to produce a match in the moments of inertia of the prosthetic and intact lower legs resulted in greater gait asymmetry and higher energy cost. Key Words: Amputation; Prosthesisdesign; Walking; Biomechanics; Energy metabolism; Rehabilitation. 0 2000 by the Americun Congress of Rehabilitation Medicine and the American Acudemy of Physical Medicine and Rehabilitution
From the Exercise and Sport Research Institute. Arizona Srak University, Tempe. AZ. Submitted April 12. 1999. Accepted in revised form July 29, 1999. Supported by an Arizona Slale University Graduate Research Support Office Granl and the Douglas L. Conley Memorial Scholarship. Presented in pan at the 21~ Annual Meeting of the American Society of Biomechanics. September 26. 1997. Clemson. SC. and the 4th annual meeting of the Gail and Clinical Movement Analysis Society, March I I. 1999, Dallas, TX. No commercial party having a direct financial interest in the results of the research supporting this article has or will confer a benefit upon the authors or upon any organization with which the authors are associated. Reprint requests to Philip E. Martin, PhD. Department of Exercise Science & Physical Education. Arizona State University. Tempe, AZ 85287-0404. 6 2000 by the American Congress of Rehabilitation Medicine and the American Academy of Physical Medicine and Rehabilitation 0003-9993/00/8105-5564$3.00/O doi: 10.1053/nu.2000.385 I
EOPLE WITH UNILATERAL, transtibial amputations P often demonstrate significant asymmetrical gait pattems.le5 Specifically, the prosthetic limb has a smaller push-off force, longer swing time, longer step length, and a shorter stance time than the intact limb. In addition, persons with transtibial amputation expend 10% to 30% more energy during walking than persons with amputation when energy cost is compared for comparable walking speeds or is expressed per unit of distance traveled.6-10In general, clinicians and researchers have embraced the notion that prosthesesshould be as light as possible, presumably in part to minimize muscular effort and metabolic energy demand during locomotion and perhaps also to facilitate faster walking speeds.II-l3 This is based on the premise that an important component of metabolic demand during gait is associatedwith accelerating the legs with each stride. Thus, the demands on the musculature should be reduced as the mass and moment of inertia of the leg are reduced. Another consequence of the use of lightweight prostheses, however, is that people with unilateral, transtibial amputations often possess a substantial inertial asymmetry between their limbs. The mass of the residual limb plus a common prosthetic limb for an adult with a transtibial amputation may typically only be 30% to 40% of that of the intact shank and foot.14.15At present, the relation between lower extremity inertia asymmetries, gait asymmetries, and higher energy costs is not well understood. Previous modeling studies have suggested that gait symmetry should be improved if the mass and moment of inertia of the prosthetic and intact limbs are well matched.‘6-18 Mena and colleaguesI specifically stated that “a ‘lightweight’ prosthesis would be less desirable than a ‘heavy’ prosthesis, while a prosthesis that had the same inertial properties of the removed limb may be the most desirable.” Only recently have experimental efforts begun to assessthe effects of prosthetic limb inertia changes on the energy cost’5*19 and mechanics of walking of people with transtibial amputations.11,20Results of these studies have either been equivocal or lacking in sufficient information to draw definitive conclusions. For example, Lehmann and associatesI observed as much as an 8.6% increase in aerobic demand at self-selected and fast (120m/min) walking speeds as prosthetic limb mass was increased from a low of 42% of intact limb mass up to 70% of intact limb mass and prosthetic limb center of mass was manipulated proximally and distally by altering mass dishibution. In contrast, Gailey and coworkers19 concluded that up to 907g evenly distributed on the prosthetic limb did not alter the energy cost in persons with transtibial amputation when walking at 76m/min. The effects of inertial manipulations on gait mechanics are also not clear. Donn and associates” systematically manipulated shoe mass by as much as 200g in subjects with unilateral, transtibial amputation and found that optimum shoe mass, ie, that which resulted in the most symmetrical walking pattern, showed little correlation with the subjects’ own shoe mass but was highly correlated with preferred mass. Hillery and colleagues20reported minor alterations for a single
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subject with a unilateral amputation in both walking kinematics (eg, increased stride length) and ground reaction force profiles (eg, higher peak forces for vertical and anterior-posterior components in early stance) as prosthetic limb mass was increased from 1.08 to 2.54kg. Based on the limited available experimental research and inconsistency in empirical findings, there is a need for additional research focusing on the sensitivity of energy cost and kinematic and kinetic features of walking to prosthetic limb inertia changes, particularly in people with transtibial amputations. In addition, investigators typically have not considered the existing differences in inertial properties of prosthetic and intact limbs when manipulating the inertial properties of the prosthesis in experimental studies. Specifically, there appear to be no empirical data in the published literature testing the effects of matching mass and moment of inertia characteristics of prosthetic and intact limbs on gait symmetry and energy cost. Thus, our purpose was to determine the effect of decreasing lower extremity inertial asymmetry on walking symmetry and energy expenditure in people with unilateral, transtibial amputations. Based on early modeling results,*s we hypothesized that the gait patterns of persons with unilateral, transtibial amputation are more symmetrical when the mass and moment of inertia of the prosthetic limb are more closely matched to those of the intact limb. We also hypothesized that energy cost of walking is not adversely affected as the prosthetic limb inertia properties are increased to approach those of the intact limb. METHODS Subjects Six individuals with unilateral, transtibial amputations between 18 and 50 years of age served as subjects. All were interviewed regarding general health, activity level, and history of using a prosthetic limb (table 1). To control for metabolic confounds associated with cardiovascular abnormalities, individuals whose amputations were associated with peripheral vascular disease were excluded. Additionally, subject recruitment focused on individuals who were fully ambulatory, predominantly used an energy storing prosthetic limb in their vocational and recreational activities, and maintained some degree of physical activity in their daily activities. These restrictions helped to ensure that the subjects were able to complete all treadmill and overground exercise tests aerobically and without substantial fatigue and to control for prosthetic limb design effects on walking mechanics and energy cost. These same restrictions, however, resulted in a small sample size that limits the generalizability of our results to all individuals with unilateral, transtibial amputations. Data Collection Each subject completed an orientation session and an experimental session within a l-week period. During the orientation Table Age Subject
(Vd
1 2
29 50
3 4
37 18 45 29
5 6 Mean
Arch
2 SD
Phys
35 + 12
Med
Rehabil
1: Subject
Characteristics
Height km)
Body Mass kg)
186.4 170.1 184.2 175.7
90.5 75.2 84.0 60.5 86.4
178.3 177.0 176.6 t 5.9
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91.1
10
64.6 2 6.1
7.1 + 4.6
May
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Reason Trauma Blood clot Cancer Birth defect Trauma Trauma
PROSTHESES,
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session. the project’s purpose and procedures were explained to the subject and written informed consent was obtained in accordance with university human subjects policies. Subjects then completed 30 minutes of treadmill walking to ensure they were well accommodated to the treadmill before data collection. To acclimate subjects to test conditions, practice included a minimum of 10 minutes of treadmill walking while breathing through a mouthpiece and 10 minutes of walking with a l-kg load aflixed to the distal aspect of the prosthetic shank. After treadmill practice, the subject’s relevant anthropometric data were obtained and the inertial properties of the prosthetic and intact limbs were measured or estimated. Prosthetic limb mass was measured directly using a standard laboratory scale.Center of mass position was quantified using a reaction board method, and moments of inertia of the prosthetic limb about transverse axes through its center of mass and the knee joint were estimated via an oscillation technique.*’ The residual limb (below-knee) was modeled as a frustum of a right circular cone,?* and its volume was subsequently estimated geometrically. Mass of the residual limb was estimated from its volume and by assuming a 1. log/cm3 uniform tissue density.Z3 The center of mass location of the residual limb was assumed to be coincident with the center of volume for this frustum. The center of mass of the total complex-residual limb, prosthetic socket, and prosthetic limb-was calculated using the measured or estimated masses and centers of mass of each of the component parts. For the purpose of estimating intact limb inertial properties, total body mass was adjusted to reflect symmetrical lower extremity structure, because prosthetic limb mass was less than that of the intact limb. Intact limb inertial properties were subsequently estimated using adjusted body mass and intact limb anthropometric measures according to methods outlined by deLeva.24q25 During the experimental session,subjectscompleted 8-minute treadmill walking bouts and multiple overground walking trials at 1.34m/sec under three load conditions: (1) a baseline conditions in which no load was added to the prosthetic limb; (2) a 100% added mass condition in which the prosthetic limb mass and moment of inertia about a transverse axis through the knee were matched to those of the intact lower leg; and (3) a 50% added mass condition in which the added load was 50% of the difference between the limb masses but positioned in the same location as that of the 100% added load condition. The order of load conditions was randomized to minimize any order effects. The nominal walking speed of 1.34rn/sec (3.0mph) was chosen because of our interest in presenting some challenge to the subjects without producing excessive fatigue. The targeted speed was modestly faster than typical preferred walking speeds reported for individuals with unilateral, transtibial amputation using an energy storing prosthesis.8*‘4,26 Mass was added to the prosthetic limb using two concentrated and equal-sized packets of lead shot affixed to the anterior and posterior aspect of the prosthetic limb. The packets were positioned such that the estimated prosthetic limb moment of inertia about a transverse axis through the knee under the 100% added mass condition was equal to that of the intact limb. The placement of the added mass was determined using the parallel axis theorem: d=
Let
d-
-
$3ms
m
where d is the distance below the knee that the masswas placed, and Ipros are the estimated moments of inertia for the intact and prosthetic limbs about a transverse axis through the knee
hact
INERTIAL
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OF TRANSTIBIAL
and m is the additional massrequired to match the massof the intact limb (100% mass condition). Because concentrated rather than distributed masseswere used to produce the inertial manipulations, it was not possible to ensure that center of mass locations of the prosthetic and intact limbs would also be matched under the 100% load condition. Nevertheless. adding load to the distal aspect of the prosthetic limb had the effect of shifting its center of mass more distally and, under the 100% load condition, resulted in a reasonably close approximation of the center of mass location for the intact limb (table 2). Aerobic demand was measured during treadmill walking using a standard, commercially available metabolic cart. Oxygen and carbon dioxide sensorswere calibrated before each test using gases of known concentrations. The pneumotach used to measure the volume of expired ,air was calibrated using a 3-L syringe. Mean oxygen uptake (VO:) over the last 2 minutes of each g-minute trial was used as an estimate of each subject’s steady-state aerobic demand. The rate of energy cost was estimated from aerobic demand according to Weir”:
joint,
Ii = (3.9) \jO? + (1.1) vco, where k is energy cost in kcal/min, and 90, and carbon dioxide uptake (VCO?) are in L/min. E was subsequently converted to units of J/set. Overground walking trials for a given load condition were collected immediately after the treadmill walking bout for the same load condition. After reflective markers were placed bilaterally over the medial and lateral aspectsof the heel and on the fifth metatarsal head, subjects traversed a 15meter walkway. Because of the absence of anatomical landmarks on the artificial limb, the locations of markers applied to the prosthetic foot were matched with those of the intact limb.?” Walking speed was monitored by a digital clock activated by the sequential interruption of photocells positioned approximately 3m apart. Acceptable trials were those in which average speed through the measurement zone was within 3% of the target speed. Five acceptable trials for both the prosthetic and intact sides were collected for each load condition. Sagittal plane motion was recorded at a rate of 60Hz with a video camera positioned approximately 5m from the walkway. A l-meter scaling object was imaged in a plane that approximated a sagittal plane passing through the foot on the side of the body closest to the camera so that video position data could be converted into object space coordinates. The camera lens focal length was adjusted to ensure that an entire stride cycle (heel
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strike of one foot to subsequent heel strike of the same foot) was recorded. Data Analysis Video data for one complete stride from all five acceptable trials for each load condition were digitized into twodimensional coordinate data using a video digitizing system. Coordinate data for a minimum of IO additional fields just prior to and following the stride were also digitized because of endpoint problems commonly associated with data smoothing techniques. The coordinate data were subsequently scaled to object space coordinates and digitally filtered at 6Hz using a fourth order, recursive Butterworth digital filter. Ipsilateral and contralateral heel strike and toe-off events were visually identified and marked during the digitizing process and were used to compute stance and swing times for both legs. Prosthetic limb step length was defined as the horizontal distance between the heel marker of the intact foot at heel strike and the heel marker of the prosthetic foot at the subsequent heel strike. Step length for the intact limb was calculated similarly as the distance between prosthetic and intact heel markers for consecutive foot contacts. Symmetry indices (SI) were computed to provide a descriptive marker for the degree of symmetry between the prosthetic (P) and intact (I) limbs for stance and swing times and step length using the following equationZ9:
SI=IP-1)1 0.5 (P + I)
100%
A SI of zero reflects perfect symmetry between the limbs, whereasincreasingly positive or negative values indicate increasing asymmetry for a variable in question. In addition, positive values indicate the value for the prosthetic limb was greater than that of the intact limb, while negative values denote that the intact limb value was greater. Statistical Analysis A single factor repeated measures analysis of variance (ANOVA) was used to test for differences in energy cost between the baseline (no load added), 50%, and 100% load conditions. A two-factor, repeated measures ANOVA was used to examine leg (ie, prosthetic and intact) and load (ie, no load, 50%, and 100%) main effects and their interaction for swing and stance times and step length. The alpha level was set at .05 for all statistical tests. RESULTS
Table
2: Mass and Center of Mass Properties of Intact Prosthetic Limbs and Added Masses
and
Mean + SD
Limb mass properties Intactshank + foot mass (kg) Prosthesismass (kg) Residuallimb mass (kg) Added mass properties 50% added mass (kg) 100% added mass (kg) Distanceadded masswas placed below
knee(m)
Centerof mass location below knee Intact shank + foot(m) Prostheticlimb, unloaded (m) Prostheticlimb, 50% load (m) Prostheticlimb, 100% load (ml
4.91 e .40 1.48 2 .32 1.74 -t .36 .85 z .31 1.70 2 .62 .41 + .06 .252 .162 .212 .244
t t -t I!
.014 .015 .009 .014
Range
4.30-5.36 1.25-2.12 1.23-2.23 .44-l .36 .87-2.73 .34-.49 ,235 .139 .201 .224
2 + + -c
.273 ,162 .225 ,264
Inertial Manipulations The goal of our inertia manipulation was to match the prosthetic and intact limb massesand moments of inertia about a transverseaxis through the knee (Ike) under the 100% added mass condition. Figure 1 displays the average effect of the added masseson Ih,, during the stride cycle and confirms the systematic effect of loading on the moment of inertia of the shank and foot about the knee. Although matching the moments of inertia of the two limbs about the hip (Ihip) was not the specific goal of the manipulation, figure 2 demonstrates that Ibp also became more closely matched for the two limbs with loading. Thus, the desired experimental manipulation of both mass and moment of inertia was produced successfully. Temporal and Kinematic Responses and Gait Symmetry Step length was significantly longer for the prosthetic limb than the intact limb (fig 3; limb main effect Fl.5 = 31.89, Arch
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1.05 + Pros +lntact
1 z z 0.95 E 5 g 0.9 z
; 0.30 al .-c s 0.20 E E 0.10 t
IL”..
0.85
0.00 -I
0.5 NL
50%
100%
load condition
NL
i
50% load condition
100%
Fig 1. Moment of inertia of the prosthetic (Pros) and intact shank and foot relative to a transverse axis through the knee joint flk.,). The mass was positioned on the distal aspect of the prosthetic limb such that Iu,,, for the two limbs was the same under the 100% load condition. NL, no load.
Fig 3. Although step length for the prosthetic limb cantly different for the three load conditions, there step length to increase as its mass and moment increased. There was no change in step length for intact leg. NL, no load.
p = .002), as has been reported previously.1.30-3’The addition of load to the prosthetic limb, however, produced no significant change in step length (load by limb interaction effect F2.10 = 2.48,~ = .13; load main effect F2.to = .86, p = .45). A close examination of figure 3, however, suggests a subtle tendency for step length of the prosthetic limb to increase as its mass and moment of inertia increased, whereas step length for the intact limb showed little change with prosthetic limb loading. As a result and in contrast to our hypothesis, the symmetry in step length between the prosthetic and intact legs did not improve as the mass and moment of inertia of the two limbs became more closely matched. Rather, the extent of the step length asymmetry tended to increase (no load SI = 2.1%. 50% load SI = 2.6%. and 100% load SI = 4.5%).
Swing time for the prosthetic limb swing time was significantly higher than that for the intact limb (fig 4; limb main effect Ft.5 = 118.11, p < ,001). In addition, prosthetic limb swing time increased as its mass and moment of inertia were increased, whereas that for the intact limb was relatively unaffected by inertial manipulation of the prosthetic limb (load by limb interaction FZJO= 7.306, p = .Oll). Stance times for the prosthetic and intact limbs showed divergent responses as load was added to the prosthetic limb (fig 5; load by limb interaction Fz,ta = 7.78, p = .009). Whereas stance times for the two limbs were quite similar for the baseline condition, prosthetic limb stance time decreased and intact limb stance time increased as the prosthetic limb inertia was increased. Thus, contrary to our hypothesis, matching the mass and moment of inertia characteristics of the prosthetic limb to those
3.0-
0.5
g
2.5 -
f .B E 2.0E i
/El
NL
50%
100%
load condition Fig 2. Moment of inertia of the entire prosthetic (Pros) and intact legs relative to a transverse axis through the hip joint (l,,u). A reasonably close agreement in I,,,,, for the two legs was produced by loading the distal aspect of the prosthetic limb. NL, no load.
Phys
bled
2
0.45 -
E ‘3 .-P 2
0.4 -
Pros Intact
T
T
e Proa I+lntact
1.5 !
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,
+ +
T
was not signifiwas a trend for of inertia were the unloaded,
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0.35 -I NL
50% load condition
Fig 4. Swing time for the prosthetic (Pros) mass and moment of inertia were increased, change in swing timeforthe unloaded, intact
limb increased as its whereas there was no leg. NL, no load.
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0.8
0.75
3
5 425 % 8
5 E = E s b
0.7
3 f 375 aa
0.65
NL
50%
cl
NL
100%
50% load condition
load condition Fig 5. Stance time decreased for the prosthetic (Pros) limb increased for the unloaded, intact leg as the mass and moment inertia of the prosthetic limb were increased. NL, no load.
and of
Fig 7. Energy cost of walking was not different and 50% load conditions, but was significantly the 100% load condition.
of the intact limb had the effect of increasing asymmetries for both swing and stance times (fig 6). Energy Cost of Walking The energy cost of walking increased significantly as the inertial properties of the prosthetic and intact limbs became more similar due to prosthetic limb loading (fig 7; load effect F 2.1,~ = 7.29, p = .043). A close inspection of figure 7 reflects a nonlinear energy cost response. The energy cost of ambulating under the 50% load condition was almost identical to that for the baseline condition, whereas the energy cost for the 100% condition was 6% to 7% higher than those for the baseline and 50% conditions.
h4
’ 1
50%
100%
1’ 1
100%
/
1
n Swing 0 Stance I load condition
Fig 6. Symmetry indices for swing and stance times indicate the increasing asymmetries that developed for both variables in response to increased mass and moment of inertia of the prosthetic leg. Positive symmetry indices for swing time indicate that the prosthetic limb values were greater than those of the intact limb. Negative symmetry indices for stance time reflect greater values for the intact limb. NL, no load.
for the unloaded (NL) higher (6.9%) under
DISCUSSION Gait Symmetry Modeling research’* suggeststhat the inertial characteristics of transtibial prosthesesshould match those of the intact limb to maximize gait symmetry and minimize energy expenditure during walking. The results of this project are inconsistent with these modeling predictions. Step length, swing time, and stance time symmetry either did not improve or worsened as mass and moment of inertia of the prosthetic limb were increased to match those of the intact limb. The swing phase of human walking has been modeled as a pendulum swinging about a transverse axis through the hip joint.33 While a simple pendular model may be an oversimplification of the dynamics of the swing phase, it offers a means of examining the interplay of limb inertial factors during leg swing. The half-period of oscillation of a simple pendulum (T) is computed from the following relationship:
where Iaxisis the pendulum moment of inertia about its axis of rotation, m is its mass, g is the acceleration due to gravity, and d the distance from the axis of rotation to its center of mass. Using this simple model, the relation between the inertial manipulations that were implemented in this project and the half-period of oscillation can be explored mathematically. The addition of mass to any pendulum will increase its mass and moment of inertia about the axis of rotation. The magnitude of the effect of the added mass on d and Imisdepends on where the added mass is positioned. Thus, the ultimate effect of the added mass on T depends on the relative changes in Iais and the product of m and d. If Imisincreasesmore than the product of m and d, then the half-period of oscillation increases, a change that would be consistent with an increase in swing time. Conversely, if the product of m and d increases to a greater extent than Iaxis,then T will decrease,a change consistent with a decrease in swing time, the desired effect in this investigation. Table 3 summarizes the effects of mass additions used in this
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Table 3: Average Inertial Properties of the Entire Prosthetic Leg Used as Inputs to a Simple Pendular Model That Predicted the Half-Period of Oscillation of the Pendulum Under the Three Experimental Load Conditions 50% Load No Load
Absolute [hip
kg
Mass
d b-4 Mass x d (kg m) Half-period of
Absolute
1.840
2.336
15.43 ,268 4.134
16.28 ,298 4.850
,670
,696
.427
.441
m2)
(kg)
oscillation (set) Measured swing time (set)
100% Load %
96
Increase*
Absolute
Increese*
27.0
2.900
57.6
17.3
17.12 .325 5.565
34.6
,724 .446
Average measured swing times are provided with half-period of oscillation. Abbreviations: lhip, moment of inertia relative mass location relative to the hip. l Percent increases in lhip and the product expressed relative to the unloaded condition.
for
trend
comparison
to the hip; d, center of
mass
and
of
d are
study on inertial characteristics of the entire leg and on the half-period of oscillation of a simple pendulum representing the leg. As load was added to the distal aspect of the prosthetic limb to match the inertial properties of the intact and prosthetic shank and foot, Ihip experienced a proportionally greater increase than the product of m and d. Thus, the predicted half-period of oscillation of the leg modeled as a pendulum swinging about the hip increased, which is consistent with the observed increase in the swing time for the prosthetic leg. Skinner and Barrack34 observed that asymmetrical application of mass to the leg of able-bodied individuals produced similar effects on temporal features of the loaded limb and led to temporal asymmetries between limbs. When 1.82kg of mass was added near the ankle joint of one leg, swing time increased (3.9%) and stance time decreased (2.5%) for the loaded leg relative to an unloaded baseline condition. In our investigation, adding mass to the distal aspect of the prosthetic limb produced a similar response (swing time increased 4.4% for an average load of 1.70kg). Unfortunately, previous research on persons with transtibial amputations provides little data for direct comparison with our results. Donn and colleagues” studied the effect of symmetrical manipulation of shoe mass in 10 subjects with transtibial amputation on gait symmetry as the subjects walked at selfselected speeds. In a search for a shoe mass that contributed to the greatest degree of symmetry, they manipulated the mass of a standardized lab shoe in 50-g increments up to 2OOg, and quantified the symmetry of several gait variables for each load condition. Subjects were also asked to subjectively identify the shoe mass condition that they most preferred. Donn and colleagues” concluded that “lightweight footwear does not necessarily provide the most symmetrical gait . . . or the most acceptable gait as preferred by the amputee.” In addition, the shoe mass that contributed to the most symmetrical walking pattern was correlated substantially more strongly with preferred shoe mass than with the subjects’ own shoe mass. Prior to any exposure to the load conditions explored in this study, it is worth noting that our subjects generally anticipated having a negative reaction to the addition of any mass to their prosthetic limbs. Based on anecdotal comments of the subjects, however, the 50% load condition produced little negative reaction from the subjects. The effect of the smaller added load either was not noticed or was easily tolerated by the subjects. Substantially more negative comments, however, were exArch
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pressed about the 100% load condition. Our subjects clearly did not like to walk with the heavier load on their prosthesis despite the fact that it created an inertial symmetry between the prosthetic and intact limbs. Hillery and associatesZostudied the response of a single individual with a transtibial amputation to massesof 530g and 1,460g added to the distal aspect of the prosthetic limb during walking at self-selected normal and fast speeds.They noted that the extent of asymmetries in the relative time spent in single limb support was affected by the mass condition. At the fast walking speed, the unloaded prosthesis resulted in the most symmetrical outcome, whereas the intermediate load produced the most symmetrical response at a normal preferred walking speed. Although the research of both HilleryZo and Dorm” and their colleagues offers some interesting observations about gait symmetry and demonstrates that both symmetrical and asymmetrical loading of the distal aspect of the legs affects gait kinematics, their data are difficult to interpret and generalize. The use of self-selected walking speeds makes it difficult to distinguish independent effects produced by inertial changes and walking speed changes. Hillery and associatesZoreported an increase in normal self-selected walking speed as load on the prosthetic limb increased, whereas Donn and colleagues” reported no walking speed data. Although the results of our investigation clearly indicate that matching the inertial properties of the prosthetic and intact lower legs did not improve walking symmetry and imposed a higher energy cost of walking on the amputees, there are a number of limitations of our experimental design that restrict the generalizability of these conclusions. We specifically chose to limit our investigation to relatively young, physically active individuals who used an energy storing prosthetic limb in their daily activities. Additionally, we chose to limit our investigation to subjects with transtibial amputation. Thus, our results may not be applicable to a broader group of persons with transtibial amputation who are older and less physically active than our subjects, and certainly cannot be generalized to persons with transfemoral amputations. We also chose to investigate a single walking speed. Because stride frequency is a function of walking speed, it is possible that the ideal inertial properties of a prosthetic limb may vary with the walking speed and stride frequency. Thus, the scope of future investigations should be expended to include a broader range of subjects and multiple speeds of locomotion. Considering the results from the present investigation and the implications of the pendular model, it appears that alternative inertial manipulations must also be considered if the goal is to enhance temporal and kinematic symmetry. Although our distal loading configuration produced a reasonable match in the inertial properties of the prosthetic and intact limbs, it also had the undesired effect of altering the swing and stance times of the prosthetic limb, such that the system became more asymmetrical. This suggests that a proximal loading configuration, most notably one that is more proximal to the center of mass of the limb, is more likely to produce the desired effect of decreasing prosthetic limb swing time such that it more closely matches that of the intact limb. From the perspective of the pendular model, proximal loading would have a smaller relative effect on the moment of inertia of the swinging system than on the limb center of mass position. Using a pendular model, Bachi suggested it is possible to identify a loading location that minimizes the period of oscillation of a simple pendulum and that both this loading location and the magnitude of the temporal effect produced are dependent on the magnitude of the load itself. Although subjects with transfemoral amputations
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have been shown to reduce the swing time of the prosthetic leg when the shank is loaded proximally,35~36it remains to be seen how patients with transtibial amputations respond to this type of inertial manipulation. The model of a simple pendulum provides a reasonable explanation why prosthetic leg swing time increased as mass and moment of inertia were increased, but it does not explain why the swing time of the prosthetic limb is longer than that of the intact side under unloaded conditions. Using inertial properties of the intact and prosthetic legs, the half-period of oscillation was calculated about a transverse axis through the hip for both limbs (table 4). Because of the differences in mass distribution properties between the limbs, the modeled halfperiod of oscillation of the prosthetic limb is shorter than that of the intact limb. Published literature indicates that intact limb stance time is greater than the prosthetic limb to minimize single support time on the prosthesis.‘-5Thus, the longer swing time for the prosthetic limb under normal conditions may be a simple result of the amputee intentionally increasing the stance time of the intact limb. Reasons for this are unclear but may include pain or discomfort in the residual limb, instability within the socket, lack of proprioceptive feedback regarding foot position, strength decrements on the prosthetic side, and/or reduced confidence in supporting body weight on the prosthetic leg. Energy
Cost of Walking
Research indicates that amputees consume more energy than able-bodied individuals when walking at the same speeds.6-i0 Lower extremity loading studies in able-bodied individuals suggest that the cost of carrying load on the legs increases systematically as load increases and that the cost of carrying load on the distal aspect of the lower extremities is significantly greater than that when load is carried more proximally on the limb or on the trunk.‘7-‘9 This may be part of the rationale underlying the use of prostheses that are as light as possible. It is less clear how amputees’ energy cost of walking is affected by limb inertial manipulations. Czemiecki and colleaguest4 found the addition of as much as 1.34kg near the center of mass of the shank on the prosthetic leg of subjects with transfemoral amputations produced no significant increase in the energy cost of walking for speeds ranging from 0.6 to I .5m/sec. It was this experimental outcome in subjects with transfemoral amputation that led to our prediction that load added to the prostheses of persons with transtibial amputation does not necessarily produce an increase in energy cost. Our results demonstrated that the energy cost of walking was essentially the same for the baseline and 50% load conditions, but was significantly higher (6% to 7%) under the 100% load condition. Although the absence of an energy cost difference between the baseline and 50% conditions might be interpreted as partial support for our hypothesis that energy cost is not adversely affected by prosthetic limb inertial increases, the robustnessof the observed nonlinear response of energy cost to
CONCLUSIONS
Based on our results, we concluded that manipulations of the inertial characteristics of the prosthetic limb to match those of the intact limb produce greater asymmetries between limbs in swing time, stance time, and step length in persons with transtibial amputation. Thus, these results did not support our hypothesis that matching inertial characteristics results in more symmetrical gait. Our results also failed to provide support for our hypothesis that energy cost of walking is not adversely affected when mass and moment of inertia of the prosthetic and intact limbs are matched. Energy cost was significantly higher under the 100% load condition relative to the baseline and 50% load conditions. Therefore, it is apparent that distal loading configurations tend to be detrimental in terms of both gait symmetry and energy cost. Proximal loading configurations, on the other hand, may hold promise for improving gait symmetry without imposing higher energy costs and await experimental assessment.Such configurations should be investigated in both able-bodied individuals and amputees at multiple walking speeds to determine the systematic effects produced by limb mass and mass distribution. Acknowledgment: The authors acknowledgethe assistanceof David J. Sanderson(Schoolof Human Kinetics,Universityof British Columbia, Vancouver,B.C.) for his helpful commentson-this manuscript.
References
I. Lehmann JF, PriceR, Boswell-BessetteS, Dralle A, QuestadK. Comprehensiveanalysisof dynamicresponsefeet: Seattleankle/ lite foot versusSACH foot. Arch Phys Med Rehabil 1993;74: 853-6
Prosthetic
Mass [hip
of leg (kg)
(kg
II-?)
Distance,hip to center of mass of Half-periodof oscillation(secl Observed
swing
time
(set)
leg (m)
Limb
17.12 2.71 .324 .70
,427
.396
1.
RobinsonJL, Smidt CL, Arora JS.Accelerographic,temporaland distanceeait: factorsin below-kneeamputees.PhvsTher 1977;57:
898-904.3. Sanderson
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15.42 1 .a4 .268 .67
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increasing prosthetic limb inertia awaits further testing. Additionally, our hypothesis clearly was not supported when the inertial properties of the prosthetic and intact limbs were matched. Gailey and associatest9 reported nonsignificant increasesof 2.3% and 4.7% in the aerobic demand of walking at 76m/min for distributed shank loads of 4.548 and 907g. respectively, in subjects with transtibial amputation. This amounts to an aerobic demand increase of approximately 5% per kilogram of added mass, which is quite comparable to the increase observed in the present study for the 100% load condition (6.9% per 1.70kg or 4% per kilogram). More interestingly, Lehmann and coworkerst5 examined the effects of both prosthetic limb mass and mass distribution on walking aerobic demand in subjects with transtibial amputation. Limb mass conditions were 42%, 60%, or 70% of the intact limb mass, whereas mass was distributed either proximally or distally, as reflected by the limb’s center of mass location below the knee (either 47% or 60% of shank length, respectively). Aerobic demand proved to be insensitive to mass per se, but highly sensitive to the distribution of the mass. Redistribution of the intermediate mass more distally resulted in a 6.1% increase in aerobic demand, while the same redistribution of the heavy mass produced a 4.4% increase.
2. Table 4: Pendular Model Estimations of the Period of Oscillation of the Entire Leg (Hip Joint Axis of Rotation) and the Observed Swing Time for the Prosthetic Limb and the Intact Limb
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