Manipulations of Leg Mass and Moment of Inertia: Effects on Energy Cost of Walking


Medicine & Science in Sports & Exercise: April 2005 - Volume 37 - Issue 4 - pp 649-656
Applied Sciences: Biodynamics

Purpose: To investigate effects that independent alterations in limb mass and moment of inertia about a transverse axis through the hip have on metabolic and mechanical power of walking and peak electromyography (EMG) amplitude. It was hypothesized that increases in metabolic cost would parallel increases in mechanical power, and that EMG amplitude would increase with greater limb mass or limb moment of inertia.

Methods: Metabolic and mechanical power and lower-extremity EMG were measured on 14 healthy adults walking at 1.5 m·s−1. Four leg-loading conditions were employed: 1) no load (NL) on the legs; 2) a baseline load (BSLN) condition, with a mean of 2.0 kg per leg distributed on the proximal and distal shank; 3) a load condition with a mean of 2.0 kg per leg distributed on the proximal and distal shank, such that lower-extremity moment of inertia was increased 5% about the hip (MOI5) from the BSLN, but having the same lower-extremity mass as BSLN; and 4) a load condition with a mean of 2.8 kg per leg, concentrated proximally on the shank to increase total lower-extremity mass by 5% (Mass5) from BSLN, but having the same moment of inertia as BSLN. Total subject mass was constant between conditions, as unused leg loads were carried in a waist belt.

Results: Changes in mechanical power paralleled changes in metabolic cost as hypothesized. Energy cost increased significantly (4.2%) from NL to BSLN, and from BSLN to MOI5 and Mass5 (3.4 and 4.0%, respectively). EMG did not effectively explain changes in metabolic cost.

Conclusion: Independent alterations in limb mass and moment of inertia about the hip joint influence energy cost similarly.

1Department of Health, Nutrition and Exercise Sciences, University of Delaware, Newark, DE; and 2Department of Kinesiology, Pennsylvania State University, University Park, PA

Address for correspondence: Todd D. Royer, Department of Health, Nutrition and Exercise Sciences, University of Delaware, Newark, DE 19716; E-mail:

Submitted for publication April 2004.

Accepted for publication December 2004.

The authors acknowledge support from the Arizona State University Conley Memorial Scholarship and the American Society of Biomechanics Graduate Student Grant-In-Aid.

Article Outline

People with a unilateral, lower-extremity amputation have approximately a 20% higher metabolic cost of walking than nonamputees (8,24). Because of this higher aerobic demand, factors affecting energy cost are of concern to patients, prosthetists, and clinicians. Modern prosthetic limbs are constructed with lightweight materials, resulting in an artificial limb that typically has lower mass and moment of inertia characteristics than the limb it replaced. Reducing the inertia of the prosthetic limb may minimize the muscle effort needed to accelerate the limb through the swing phase, and thus minimize the metabolic demand of locomotion. However, the inertial asymmetry may also contribute to their commonly observed asymmetrical gait pattern (14) and higher energy cost (8).

Asymmetrical limb inertia has led some investigators to examine more closely the relationship between the inertial properties of the prosthetic limb, metabolic cost, and symmetry of walking in people with a unilateral, lower-extremity amputation. Mattes and colleagues (14) matched the prosthetic limb inertia (mean added mass of 1.70 kg to the distal prosthesis shank) to the intact limb, which resulted in a significant increase (6.8%) in metabolic cost. However, when smaller load magnitudes (mean added mass = 0.85 kg) were added to the prosthetic limb, there was no significant change in energy cost. Czerniecki and associates (4) reported no differences in metabolic cost when 0.68- and 1.34-kg loads were added near the shank center of mass of above-knee prostheses. Lehmann and coworkers (11) reported no differences in metabolic demand when loads were added proximally to the below-knee prosthetic limb to increase total mass (residual limb, prosthetic limb, and added load) to 60 and 70% of the intact limb; however, metabolic demand was significantly greater (4–6%) when these loads were positioned distally on the prosthetic limb. Collectively, these studies suggest that energy cost is insensitive to small-and moderate-load magnitudes and proximal loading schemes.

Although the issues of lower-extremity mass and mass distribution have direct impact on people with a lower-extremity amputation, this special population has other confounding factors such as muscular deficits and instabilities that may influence experimental outcomes. Therefore, an alternative approach for considering the relationship between energy cost and limb inertia is to artificially manipulate limb inertia of nonamputees.

When loads are added to the leg of nonamputees or to the prosthetic limb of people with a lower-extremity amputation, both limb mass and moment of inertia about the hip joint increase simultaneously. Thus, it is unclear whether energy cost increases as a result of the limb’s increased mass, the limb’s increased moment of inertia, or both. The simultaneous increase in limb mass and moment of inertia associated with the addition of load to an unloaded limb prevents the complete understanding of each inertial parameter’s relative impact on metabolic cost. Clearly, there is a need to study the independent effects of mass and mass distribution on metabolic cost. Hence, the purpose of this study was to investigate effects of independent alterations in limb mass and moment of inertia about a transverse axis through the hip (Ihip) on metabolic cost of walking. Adding load to a limb increases its mass and moment of inertia, and may shift the location of the center of mass, while simultaneously affecting potential (PE), translational kinetic (TKE), and rotational kinetic (RKE) energies. Lower-extremity mechanical work has been shown to help explain differences in metabolic cost associated with the addition of limb loads during running (12). Therefore, we hypothesized that increases in mechanical power would parallel increases in metabolic cost associated with increased limb mass or limb moment of inertia. Furthermore, electromyographic (EMG) activity of lower-extremity musculature was measured to assist with interpreting how loading affects muscular demand; we hypothesized that EMG amplitude would increase with greater limb mass or limb moment of inertia.

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Fourteen healthy adults (seven males, seven females) served as subjects (mean age 27.8 ± 4.2 yr, mean height 170.2 ± 6.9 cm, mean mass 69.4 ± 11.7 kg). All subjects were free of orthopedic and neurological disorders that might affect their ability to complete the testing protocol. Subjects completed three test sessions: one for orientation purposes, and the remaining two for experimental data collection.

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Orientation/accommodation session.

During the orientation session, subjects provided written informed consent in accordance with university human subjects policies. Subjects then practiced treadmill walking with and without loads affixed to their shank, while also breathing through a metabolic mouthpiece/tubing apparatus in an attempt to lessen any discomfort or anxiety associated with this procedure. All subjects walked at 1.5 m·s−1, which is within the range of freely chosen walking speeds reported for healthy adults (1). Total walking accommodation was 30 min.

The loads used during the accommodation session were only approximations of the actual loads to be carried during subsequent experimental testing sessions, because the exact load magnitudes were dependent on limb-modeling calculations completed after the accommodation session. The approximate load conditions included affixing symmetrical loads to the limbs using two load configurations: 1) a total load of 3.0 kg on the medial and lateral aspects of the proximal shank (directly below the knee joint), and 2) a 2.0-kg load on the proximal shank and a 1.0-kg load on the distal aspect of the shank (directly above the ankle joint). To load the shank, pouches of lead shot were secured to the limb with elastic compression bandages.

The transverse axis of the hip joint serves as the lower extremity’s primary axis of rotation for the swing phase. During a typical stride cycle, the angular displacement of the knee and ankle joint cause the lower-extremity (i.e., composite thigh, shank, and foot) moment of inertia about a transverse axis through the hip, and the distance from the lower-extremity center of mass to the hip joint, to vary. The average inertial characteristics of the lower extremity for the entire stride cycle served as the basis for inertial manipulations. This procedure required a kinematic analysis of the leg without additional load to enable an accurate calculation of the experimental loads for each subject.

Reflective markers were affixed to the left leg to identify thigh-, shank-, and foot-segment endpoints. Two additional markers were used to represent the locations of added mass: one marker was positioned on the shank approximately 8 cm distal to the knee joint (representing the position of a proximal shank load), and the other marker was positioned 5 cm proximal to the ankle joint (representing the position of a distal shank load). These loading sites were chosen for three reasons: 1) the loads could be stabilized effectively in these two locations; 2) it was assumed that mass added to these sites prevented restriction of muscular contraction, that is, loads were not affixed directly over the bulk of the muscle belly; and 3) pilot testing modeling work indicated these sites allowed for manipulation of the inertial characteristics of the lower extremity (i.e., thigh, shank, and foot) needed to achieve the desired changes in limb mass and moment of inertia about a transverse axis through the hip joint. Subsequent to treadmill accommodation, sagittal plane video data (60 Hz) from the left side of the body was recorded for 30 s during steady-state treadmill walking (1.5 m·s−1 belt speed) with no load attached to the limbs. Before testing, a calibration object of known length was positioned in the plane of marker motion for video capture.

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Limb modeling and load calculation.

Video records of marker position for five complete stride cycles of unloaded walking were digitized using the Peak Performance Technologies (Englewood, CO) Motus Motion Measuring System, and scaled to object space. Ten additional fields immediately preceding the first stride and, following the fifth stride, were also digitized to eliminate endpoint problems commonly associated with data-smoothing procedures. Coordinate data were smoothed using a fourth-order, zero-lag Butterworth digital filter with 4- to 6-Hz cutoff frequencies.

Body-segment parameter equations from de Leva (5) were used to estimate thigh-, shank-, and foot-segment masses, segment centers of mass, and segment moments of inertia about a transverse axis through the segment’s center of mass. Lower-extremity center of mass and moment of inertia about a transverse axis through the hip were subsequently calculated for each video field, and then averaged over five stride cycles.

Because the addition of load to an otherwise unloaded limb results in a simultaneous increase in both limb mass and moment of inertia, an unloaded limb does not provide a suitable baseline condition from which to independently manipulate mass and moment of inertia. Therefore, a baseline condition having a distributed load on the legs was established. The total load carried on the body was held constant for all experimental loading conditions. Three load conditions customized for each subject were modeled (Fig. 1 and Table 1) by altering load distribution between three attachment sites: proximal and distal shank of both legs, and the torso. Torso loads were carried in a fanny pack worn around the waist. The following summarizes the three experimental conditions: 1) a baseline condition (BSLN) having smaller magnitudes of both total lower-extremity mass (lower-extremity mass plus added load) and moment of inertia about a transverse axis through the hip (Ihip) with respect to the other two conditions; 2) a large moment of inertia condition (MOI5) in which Ihip was increased 5% above BSLN while maintaining the BSLN lower-extremity mass (redistributing the BSLN loads distally achieved this goal); and 3) a large mass condition (Mass5) in which the total lower-extremity mass was increased 5% above BSLN while maintaining the BSLN Ihip (concentrating all carried load on the proximal shank achieved this goal).

It was desirable to utilize large load magnitudes to elicit the greatest energetic response to loading. It was determined through pilot testing that the maximum load attached to the shank should not exceed 20% of the lower extremity’s mass (i.e., sum of thigh, shank, and foot masses), because larger loads could not be securely and comfortably affixed to the subject’s proximal shank. Therefore, the load used in the Mass5 condition was calculated first for each subject. This established the total load carried on the body for all conditions. Once this load was determined, it was simply redistributed among the torso, proximal shank, and distal shank locations to achieve the desired lower-extremity mass and moment of inertia manipulations. For the Mass5 condition, the total load was concentrated on the proximal shank to minimize the effect of the load on Ihip. The mean proximal shank load of 2.8 kg used in this study was slightly more than the 1.5- to 2.0-kg loads applied to the distal shank or feet in previous research on persons with transtibial amputation (11,14) and on able-bodied subjects (13,23).

The BSLN condition was subsequently established by removing a portion of the proximal shank load for the Mass5, and repositioning that load on the torso. In addition, a portion of the remaining proximal shank load was redistributed distally to match Ihip for the BSLN and Mass5 conditions (Fig. 1 and Table 2). The MOI5 condition was achieved by redistributing most of the proximal shank load of the BSLN condition distally on the shank. This increased Ihip without altering total lower-extremity mass. Table 1 summarizes the average loads applied to the three loading sites to achieve the three experimental conditions, whereas Table 2 summarizes the average values for the lower-extremity mass, center of mass location, and Ihip that resulted from the load manipulations.

A condition in which all load was carried on the torso and no load was affixed to the legs (NL) served as a fourth testing condition (Table 1). The NL condition was included to determine whether adding load to an unloaded leg elicited a change in metabolic cost that was comparable to values associated with limb loading reported in the literature. Moreover, the NL condition also was used for EMG amplitude normalization.

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Experimental data collection sessions.

Due to the inability to simultaneously collect metabolic, EMG, and video data, subjects returned for two additional testing visits. The order of the four conditions was randomized within each subject, but balanced across all subjects, similar to a Latin square procedure. For all data collection, subjects performed 6-min walking bouts for each condition at a treadmill speed of 1.5 m·s−1. Subjects were instructed to walk as comfortably as possible.

Aerobic demand was quantified using a TrueMax 2400 Metabolic Measurement System (ParvoMedics Inc., Salt Lake City, UT). The gas analyzers were calibrated using gases of known concentrations of O2 and CO2 before each test. The pneumotach was calibrated using a 3-L reference volume calibration syringe. To measure expired air for metabolic analysis, subjects wore a nose clip and breathed through a metabolic breathing valve attached to the metabolic cart via a hose. Subjects stood quietly for 4 min as resting V̇O2 was collected. The first 4 min of each 6-min trial permitted subjects to reach an aerobic steady state, and served as a load accommodation period. Average aerobic demand (V̇O2) was computed from the last 2 min of the resting trial and each walking trial.

On a separate day, subjects completed their final experimental session, during which EMG and video data were recorded. The order of loading conditions was the same as the order used for metabolic collection. These data were recorded from the left leg only, because of the physical laboratory setup. Testing the same leg for each subject was deemed satisfactory because it has been shown that, on average, gait is symmetrical (9). To synchronize the electromyography data with gait cycle events, footswitch sensors were affixed to the heel and toe of the shoe sole, and simultaneously sampled with EMG data at 1000 Hz.

EMG was used to investigate the relative amplitude of leg muscular activity in an effort to determine potential explanations for the hypothesized metabolic cost outcomes. The rectus femoris (RF), vastus lateralis (VL), biceps femoris (BF), tibialis anterior (TA), soleus (SO), gastrocnemius (GA), and gluteus maximus (GM) were selected for EMG recording because of their predominant role in gait and their accessibility to surface EMG data collection.

Ag-AgCl surface electrodes, integrated with a differential preamplifier circuit (Therapeutics Unlimited Inc., Iowa City, IA; preamplification gain = 35; interelectrode distance = 22 mm; electrode diameter = 8 mm), were placed over the distal half of the muscle belly, such that the contact surfaces were aligned in parallel with the muscle fibers. In an effort to reduce impedance at the skin–electrode interface, the skin of each electrode site was shaved, abraded, and cleaned with isopropyl alcohol. A single reference electrode was placed on the skin proximal to the lateral malleolus.

EMG data were conditioned with an EMG-544 amplifier/processor module (Therapeutics Unlimited Inc.) before sampling. Amplification gains were selectable from 1,000 to 100,000 within a bandwidth of 20–4,000 Hz. Input impedance was greater than 15 MΩ at 100 Hz. Common-mode rejection ratio was 87 dB at 60 Hz. EMG data and footswitch outputs were sampled simultaneously at 1000 Hz with Labview software (National Instruments, Austin, TX). Four data recordings of 5 s, each capturing a minimum of four consecutive stride cycles, were collected during the final minute of each walking bout.

The same marker set that was used to identify segment endpoints and added loads during the orientation visit was used again during the EMG data collection session. Identical video data recording procedures were conducted during all conditions. Added load magnitudes and video records of lower-extremity position were used to confirm that the experimental loading configurations produced the desired moment of inertia (Ihip) changes predicted by the limb inertial model (Table 2).

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Data reduction.

Mean oxygen consumption values over the last 2 min of the 6-min trial were used as an estimate of each subject’s walking economy. V̇O2 (mL·kg−1·min−1) was converted to watts per kilogram with the conversion factor of 21.1 J·mL−1 O2 (7) and dividing by 60 s. Resting metabolic power was subtracted from each load condition to yield net metabolic power (W·kg−1).

A three-segment (foot, shank, and thigh) sagittal plane model was used to calculate mechanical work, estimated from changes in segmental energies allowing energy transfers within and between segments (17):

where i represents the thigh, shank, or foot segment at time j. Segment masses, centers of mass, and moments of inertia were estimated from de Leva (5). Segment linear and angular velocities were calculated from coordinate data using finite difference equations. The lowest vertical position of the toe marker during stance served as the reference height for calculating potential energy. Mechanical work was computed with the following equation:

Average mechanical power (W·kg−1) for the swing phase was computed by dividing the work by swing time, and normalizing to total subject mass (body mass plus added load).

Temporal gait characteristics were calculated to assess commonly observed differences in the duration of stride cycle components associated with altered limb inertia. Heel strike and toe-off events were identified using voltage data obtained from footswitches and subsequently used to calculate stance, swing, and stride times (ms). Stride frequency was calculated as the inverse of stride time, and converted to units of strides per minute.

A simple pendulum model was used to calculate the period of oscillation (T):

where Iaxis is the pendulum moment of inertia about its axis of rotation (i.e., Ihip), m is its mass (i.e., total lower-extremity mass plus added load), d is its center of mass relative to the axis of rotation (i.e., total lower-extremity mass plus added-load center of mass relative to the hip joint), and g is the acceleration due to gravity. Period of oscillation does not directly correspond to temporal characteristics of gait; however, it is an effective tool in examining relative changes in swing time when lower-extremity inertia is altered (16,22).

Heel strike and toe-off events were also used to normalize EMG data to each stride cycle. Raw EMG data from 12 strides per condition were converted to microvolts, corrected for dc bias, band-pass filtered (20–400 Hz), full-wave rectified, and filtered using a fourth-order, zero-lag, low-pass Butterworth filter with a cutoff frequency of 15 Hz to create a linear envelope. EMG amplitude for each condition was normalized to the peak EMG amplitude of the NL condition, that is, each data point was expressed as a percent (25).

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Statistical analyses.

A two-factor, repeated measures ANOVA was used to test for a significant measure (metabolic, mechanical) by load condition (NL, BSLN, MOI5, Mass5) interaction in power. A one-factor (load) repeated measures ANOVA was used to test for significant differences in temporal characteristics. A two-factor (muscle by load condition) ANOVA with repeated measures on both factors was used to test for a significant interaction in EMG. Statistical significance was determined at P < 0.05 for all tests. Tukey’s HSD test was used for all post hoc statistical analyses. Effect sizes (ES) were calculated when differences existed.

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The measure by load condition interaction for power was not significant [F(3,39) = 1.31, P = 0.29], indicating that mechanical and metabolic power responded similarly to loading condition (Fig. 2) as hypothesized. The condition main effect was significant [F(3,39) = 61.2, P < 0.001], as power increased with increases in limb mass and/or moment of inertia. The addition of a nominal load to the unloaded leg (NL) to create the BSLN condition resulted in a significant increase in power (P < 0.001; ES = 0.64). There was a significant increase in power from BSLN to MOI5 (P < 0.01; ES = 0.27) and a significant increase from BSLN to Mass5 (P < 0.01; ES = 0.29); however, power for MOI5 and Mass5 was not different (P = 0.99).

It was hypothesized that changes in peak EMG amplitude would reflect changes in energy cost between load conditions; however, changes in EMG were small (Fig. 3). Despite the trend for most muscles to have increased activation for both MOI5 and Mass5, the only significant differences in peak EMG were for VL (Mass5 greater than both BSLN, P = 0.001; ES = 0.59 and MOI5, P = 0.001; ES = 0.46) and for SO (MOI5 greater than Mass5, P < 0.05; ES = 0.74).

There were small but statistically significant differences in swing time [F(3,39) = 3.44, P < 0.05] and stride time [F(3,39) = 3.52, P < 0.05] among the loading conditions (Table 3). Specifically, swing time was 2.2% greater (P < 0.05; ES = 0.42) and stride time was 1.1% greater (P < 0.05; ES = 0.26) for MOI5 compared with NL. However, there were no differences in temporal gait characteristics among the three experimental conditions (BSLN, MOI5, Mass5). There were no differences in stance time among conditions [F(3,39) = 0.91, P = 0.44]. There was a significant difference in pendulum period of oscillation [F(3,39) = 171.36, P < 0.001] among the loading conditions (Table 3). Post hoc analyses indicated that pendulum periods of oscillation for all conditions were different from each other; most notably, MOI5 was 1.7% greater than BSLN (P < 0.001; ES = 1.00), whereas Mass5 was 2.1% smaller than BSLN (P < 0.001; ES = 1.27).

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Results of published studies examining the relationship between lower-extremity inertia and metabolic cost of walking in unilateral, transtibial amputees (14) and nonpathological subjects (2,13,23) suggest that metabolic cost of walking increases as lower-extremity inertia increases. However, these experimental manipulations did not reveal whether the higher metabolic demands were associated with increases in lower-extremity mass or moment of inertia about the hip joint (Ihip), because both inertial parameters were altered with the addition of load to a limb. The primary focus of our project was to extend our understanding of the effect of systematic manipulations of limb inertial characteristics on metabolic energy cost of walking, with potential implications for design considerations of lower-extremity prostheses. Our results indicated metabolic cost increased similarly (3.4% for MOI5; 4.0% for Mass5) when Ihip and lower-extremity mass were independently increased by 5% from a baseline load condition.

Martin (12) reported that lower-extremity mechanical work increased with increases in the metabolic cost of running with lower-extremity loading. Furthermore, mass applied only to the foot elicited a greater mechanical and metabolic response than when the same mass was applied only to the thigh. Likewise, mechanical power of the lower extremity during the swing phase in our study increased in parallel with metabolic power, suggesting the increased metabolic demand was associated with higher mechanical demands under increased inertia conditions. Interestingly, two recent investigations of walking by lower-extremity amputees observed little or no relationship between metabolic cost and mechanical work demands when prosthesis inertia was manipulated. Scherer and colleagues (20) compared the effect of a lighter titanium prosthesis versus a heavier stainless steel prosthesis on the mechanical work and metabolic cost of walking in transtibial and transfemoral amputees. Although the mechanical work demands of walking were lower for the titanium prosthesis than for the steel prosthesis, there was no difference in metabolic cost between these conditions. Similarly, Foerster et al. (6) reported a poor correlation between lower-extremity mechanical work and metabolic cost when mass was added to the prosthetic limb.

Contrasts of proximal and distal lower-extremity loading effects during walking have not been investigated in able-bodied individuals. Lehmann and colleagues (11), however, systematically investigated the effects of load magnitude and position on walking energy demand of transtibial amputees. Metabolic cost increased 4.2 and 7.9%, respectively, when mean loads of 1.0 and 1.5 kg were shifted from a location near the prosthetic limb’s center of mass to a distal location near the ankle. We observed a comparable effect. Metabolic cost was 3.4% higher for the MOI5 condition relative to the BSLN condition. This increase in energy cost was directly associated with an average shift of 0.52 kg distally on the leg. Collectively, these results have important implications for prosthesis mass distribution. For example, when the pylon of a prosthetic limb is enhanced with shock absorbing mechanisms, prosthesis designers should always consider proximal placement of these components, because a more distal distribution of mass will contribute to increased energy cost of walking.

We are aware of no published studies of walking or running that have attempted to independently manipulate total limb mass while maintaining a limb’s moment of inertia. Lehmann and colleagues (11) reported metabolic cost was not affected by the addition of 1.0 and 1.5 kg near the prosthetic limb center of mass. Similarly, Czerniecki and colleagues (4) reported no change in walking metabolic cost when 0.68- and 1.34-kg loads were applied near the prosthesis center of mass for persons with transfemoral amputation. Mattes and colleagues (14) reported no change in the cost of walking when 0.85 kg was added to the distal aspect of the prosthetic limb shank of unilateral transtibial amputees, but a 6% increase in cost when 1.70 kg were added. Collectively, results from these three studies suggest that metabolic demand of walking for lower-extremity amputees is less sensitive to mass increases if the load is positioned more proximally on a limb. In contrast, we observed a 4.0% higher energy cost for our Mass5 condition relative to the BSLN condition. The Mass5 condition was created by adding an average load of 0.81 kg bilaterally to the proximal aspect of the shank while also shifting an average of 0.68 kg from the distal to the proximal load site. To be consistent with trends observed by Lehman et al. and Czerniecki et al., we should have seen little or no effect of adding mass proximally to the shank.

Our results using able-bodied individuals clearly suggest that metabolic demand is equally sensitive to similar relative increases in limb mass and moment of inertia. Extrapolating our results to lower-extremity amputees suggests that prosthetic designers should be equally sensitive to any increases in limb mass and mass distribution when considering different design configurations. Mechanical advances in prosthetic ankle joint design may improve gait mechanics (3,18); however, these components may also have a greater mass than standard components, resulting in an increase in Ihip and, most likely, energy cost. Ankle-joint components are located distal to the loading positions examined in this study; therefore, Ihip would mostly likely increase a greater magnitude than investigated here, which would concomitantly affect energy cost. Lightweight components and proximal positioning of these components obviously should be considered when feasible for prosthetic limb design. However, because our results conflict with outcomes observed by others in their investigations of the effects of prosthetic limb mass and mass distribution changes on walking energy demand in lower-extremity amputees, the independent effects of mass and moment of inertia manipulations needs to be assessed directly for both transtibial and transfemoral amputees.

It was hypothesized that peak EMG amplitude for several prominent lower-extremity muscles would increase as both mass and moment of inertia increased. Despite increases in energy cost of approximately 4.0% from BSLN to both MOI5 and Mass5, and a trend for muscle excitation to be greater with increased mass and moment of inertia (Fig. 3), there were few statistically significant differences in EMG between load conditions. Thus, we have no objective evidence from our EMG assessment from which to conclude that an increase in the local demand on leg musculature explains the increased demand of walking under increased mass and moment of inertia conditions produced by our loading schemes. Nevertheless, it is worth noting that EMG levels were approximately 10% higher for BSLN, Mass5, and MOI5 conditions relative to the NL condition in which all load was carried on the torso (Fig. 3). Clearly, though, our EMG assessment was not sufficiently sensitive to distinguish our Mass5 and MOI5 conditions from the BSLN condition.

It has been suggested that the swing phase of gait involves minimal activation of muscles that cross the hip and knee (15,16), and the dynamics of the swinging limb are often compared with that of a simple pendulum (21). There is a consistent relationship between walking swing time and the period of oscillation of a simple pendulum; however, the values of each parameter are not equal. Changing the inertial characteristics of the limb would alter the period of oscillation described by a simple pendulum model, which has been shown to reflect increases or decreases in walking swing time (14,19). Our data show that swing time increased from BSLN for the MOI5 condition, and decreased from BSLN for the Mass5 condition, which is consistent with the passive pendulum model’s period of oscillation (Table 3). The trend for swing time to change in parallel with the pendulum period of oscillation suggests that the limb was swinging at a resonant frequency, which results in a minimization of metabolic cost (10). If the changes in swing time did not correspond to the changes in period predicted by the pendulum model, metabolic cost would have increased to a greater extent, reflecting the increased muscle activation required to alter the natural period of the swing limb.

In conclusion, our results showed similar increases in metabolic cost when both lower-extremity mass and moment of inertia about the hip joint were each increased independently from a nominal baseline condition. Mechanical power paralleled the changes in metabolic cost. Thus, independent alterations in each inertial characteristic influenced metabolic and mechanical power similarly. In addition, there were few differences in EMG amplitude across load conditions that support the observed changes in energy cost. Improving the comfort, stability, and performance of a prosthesis typically requires the addition of materials to the limb, thus increasing the limb’s mass and moment of inertia. Therefore, multiple combinations of mass magnitude and mass distribution should be investigated to more accurately identify the interplay between segment inertial characteristics and lower-extremity mechanical work that affect energy cost.

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