Comparison of mechanical energy profiles of passive and active below-knee prostheses: A case study

Background

In the last half-century, prosthetic lower limbs have continuously evolved with the goal of restoring the natural ankle–foot function. Modern prostheses contain a wide range of structural components that can act as sources of mechanical energy during gait. These include passive structures that utilize material properties (e.g. carbon fiber foot, “shock-absorbing” pylons, elastic keels) ¹ or active components involving motors and/or actuators.^2,3 These various structures are often integrated to form a single prosthesis, and there is currently a great desire to evaluate the influence of these respective components to overall gait performance.

Existing biomechanical analyses quantify the amount of energy added or removed to the body via structures comprising a joint (i.e. joint power method)^4,5 and/or the rate of energy flowing into or out of a segment (i.e. segmental power method). ⁶ These techniques, however, require prosthetic-specific biomechanical models to capture the mechanics of an isolated region. Furthermore, the traditional approaches obtain estimates of kinetics, kinematics, and inertial parameters (i.e. center of mass location, moment of inertia) based on rigid segment models,^7,8 limiting its capacity to quantify energy of deforming structures (e.g. elastic components). These factors ultimately hinder the ability to directly compare prostheses with disparate structural components.

A viable solution, then, may be to model the entire prostheses as a unified deformable (UD) segment. ⁹ Contrary to traditional techniques, the UD segment power quantifies the summation effect of all structures distal to a fixed reference frame. The UD method was previously validated in anatomical limbs, in which forces and velocities within a shank-based reference frame were used to quantify the combined energy contributions of the biological ankle and deforming foot structures during barefoot walking. ⁹ Notably, the UD method does not require the defining of joints and/or segments distal to a chosen reference frame or estimates of inertial parameters. The UD analysis, therefore, may serve as a generalized method to accommodate limbs of varying structural components (e.g. elastic foot, motorized ankle) and distinct physical characteristics (e.g. articulating and non-articulating structures). Using this novel analysis, the purpose of this case study was to compare the mechanical energy profiles during stance in gait among anatomical and two disparate prostheses: a purely passive prosthesis and an integrated active prosthesis.

Case description and methods

This research was conducted under an institutional review board (IRB)–approved protocol at the University of Delaware, USA. A subject with a unilateral transtibial amputation (S1) participated in a fully instrumented gait analysis (subject characteristics are listed in Table 1). For daily activities, S1 routinely wears two types of prostheses: a passive prosthesis (Elation, Össur, Foothill Ranch, CA, USA) and an active prosthesis (BiOM, iWalk, Inc., Bedford, MA, USA). He has owned the Elation and BiOM prostheses for approximately 22 months and 5 months, respectively. The Elation prosthesis contains carbon fiber foot materials for elastic energy storage and an adjustable heel height with a single-axis ankle. The BiOM ankle unit (also a single-axis joint) comprises an actuator (direct current (DC) brushless motor and ball-screw transmission), an in-series carbon fiber leaf spring, and a parallel unidirectional leaf spring, and the ankle unit is attached to a carbon composite heel and forefoot components. ³ The BiOM actuation settings were guided by a certified prosthetist and the user’s subjective feedback. The settings from his daily use were maintained for this study.

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Table 1.

Subject characteristics.

Subject	Gender	Age (years)	Height (m)	Body mass (kg)	Years since amputation	Cause of amputation	Passive prosthesis	Active prosthesis
S1	Male	36	1.73	80.7	3	Traumatic accident	Elation, Össur	BiOM, iWalk, Inc.
Healthy controls	5 males; 6 females	24.2 ± 2.9	1.72 ± 0.08	75.3 ± 21.8

S1: subject with unilateral transtibial amputation.

Within a single gait analysis session, S1 walked with both prostheses (BiOM first and Elation second) while wearing the same shoes, socket, and suspension in both conditions. Each foot had a different foot build height, requiring separate pylons to preserve the same height that matched the intact limb. A certified prosthetist evaluated the prosthetic fit, alignment, and height. When switching between prostheses, S1 was given time to acclimate to the new condition until the subject felt stable and comfortable. For comparison, 11 healthy control subjects walking barefoot also participated in the protocol.

The gait analysis involved a six-camera motion capturing system (Motion Analysis Corp., Santa Rosa, CA, USA) for kinematic data (sampled at 120 Hz) and four strain gauge force platforms embedded in series along a straight-line walkway (AMTI, Watertown, MA, USA) for kinetic data (sampled at 360 Hz). Four retro-reflective markers were placed on the external prosthetic socket frame or on the anatomical shank (intact limbs in S1 and healthy controls) to capture kinematics required for the power estimates (Figure 1).

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Figure 1.

Four markers placed on the external socket were used to define the proximal rigid component of the unified deformable (UD) segment.

As measures of kinetics and mechanical power are sensitive to walking speeds, ¹⁰ all subjects were instructed to walk straight at a targeted speed of 0.79 statures/s (approximately 1.38 m/s for S1 and healthy controls), verified by two photocell beams located approximately 3.0 m apart. Trials were accepted for analysis if the subject’s entire foot was observed to contact a single force platform. All data were processed and analyzed using Visual3D software (C-Motion Inc., Germantown, MD, USA). A second-order dual-pass lower pass Butterworth filter (6 Hz for kinematic data and 25 Hz for kinetic data) was applied to the raw data. Ground reaction force (F_GRF) data and mechanical power were analyzed during stance phase, defined by a period in which the vertical F_GRF exceeded 20 N.

The UD segment power method is described in detail elsewhere. ⁹ Briefly, the UD segment model contains a proximal rigid component (defined by the prosthetic socket or the anatomical shank in intact limbs) with a distal deformable component. The distal deformation velocity (v_d) is quantified through the center-of-pressure (COP) velocity in the reference frame of the proximal rigid component, as shown in equation (1)—v_cm and ω are the translational velocity of the center of mass and angular velocity of the proximal rigid component, respectively, and r_COP is the vector from the center of mass to the COP

v d = v cm + ( ω × r COP )

(1)

It is noteworthy that v_d is mathematically insensitive to the presumed location of the segment center of mass, in which the summation of v_cm and ω × r_COP terms converge to the same v_d estimate regardless of where the center of mass is defined (analytical derivations shown elsewhere). ⁹ Total distal power of the UD segment (P_UD) is quantified by equation (2)—M_free is the free moment, which is normal to the force plate surface

P UD = F GRF ⋅ v d + M free ⋅ ω

(2)

Altogether, P_UD signifies the total power generated by all prosthetic structures attached distally to the socket, or the intact ankle–foot system.

Analyses were performed using custom-written scripts in Visual3D software (C-Motion Inc.). Magnitudes of F_GRF (scaled by body weight (BW)), magnitudes of peak power (scaled by body mass in kilogram) during late stance, and total positive and negative work during stance (found by integrating the P_UD as a function of time) were compared among the two types of prostheses and anatomical limbs (intact limb of S1 and healthy controls). For the healthy controls, individual trials of each subject were averaged (n ≥ 3 trials) prior to obtaining an average dataset.

Finally, P_UD estimates in S1 were compared with more traditional joint power techniques, where shank and foot segments were linked at the ankle, and segment kinematics were estimated using the targets placed on the prosthetic socket (or intact shank) and shoes, respectively. Specifically, ankle joint power using a 3-degree-of-freedom (DOF) model (P_ank3, that is, rotational power) and a 6-DOF model (P_ank6, that is, summed rotational and translational power)^5,11 was compared to P_UD. Notably, P_UD is equivalent to the summation of P_ank6 and the “distal foot power” (P_ftd), ⁹ in which P_ftd includes contributions of deforming foot structures (e.g. elastic foot, cosmetic materials, shoes).

Findings and outcomes

The average magnitudes of net anterior–posterior F_GRF impulse (in BW × s) during the gait cycle were as follows: −0.002 for S1’s passive prosthetic condition, −0.006 for active prosthetic condition, and 0.001 for healthy controls. These net impulse values equated to less than 5% change in the forward velocity relative to the subjects’ average walking speeds, suggesting all subjects walked at near steady-state conditions.

F_GRF data

The graphs of anterior–posterior and vertical F_GRF from the prosthetic and intact limb of S1 and from the healthy controls are shown in Figure 2. On the prosthetic side, the average peak anterior F_GRF during late stance was approximately 56% higher in the active prosthesis than the passive system (means ± 1 standard deviations of 0.266 ± 0.005 vs 0.171 ± 0.007 BW). Relative to the healthy controls, the active prosthesis had a 21% higher peak anterior F_GRF (difference greater than 2 standard deviations of healthy controls), while the passive prosthesis had a 22% lower peak anterior F_GRF (difference greater than 2 standard deviations of healthy controls). The average peak vertical F_GRF during late stance was approximately 5% greater with the active system than the passive (1.072 ± 0.024 vs 1.020 ± 0.015 BW).

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Figure 2.

Average ground reaction force (GRF) data during stance for S1 and 11 healthy controls: (a) Prosthetic limb (S1)—anterior/posterior GRF; (b) prosthetic limb (S1)—vertical GRF; (c) intact limb (S1)—anterior/posterior GRF; (d) intact limb (S1)—vertical GRF.

On the intact limb, the average peak posterior F_GRF during early stance was approximately 26% higher with the active prosthesis than the passive system (−0.243 ± 0.037 vs −0.196 ± 0.012 BW). Relative to the healthy controls, the intact limb of the active prosthesis was 24% higher (difference greater than 1 standard deviation of healthy controls). The average peak vertical F_GRF during early stance was approximately 7% lower in the active system compared to the passive (1.087 ± 0.056 vs 1.164 ± 0.016 BW).

P_UD data

For all limbs, P_UD was predominantly negative from early to mid-stance, followed by a phase of positive power during late stance (Figure 3). Compared to the passive prosthesis, the active system had 182% greater peak positive power during late stance (3.621 ± 0.432 vs 1.285 ± 0.061 W/kg) and 251% greater total positive work (0.337 ± 0.017 vs 0.096 ± 0.002 J/kg). Furthermore, these magnitudes of peak power and positive work produced by the active prosthesis were 17% and 50% greater than those of the intact limb (3.088 ± 0.224 W/kg of peak power and 0.266 ± 0.016 J/kg of positive work). Relative to the average of healthy controls, the active prosthesis showed 46% greater peak power and 94% greater positive work (both differences greater than 2 standard deviations of healthy controls), while the passive prosthesis showed 48% decreased peak power and 45% decreased positive work (both differences greater than 2 standard deviations of healthy controls).

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Figure 3.

Average data of UD segment power and work during stance for S1 and 11 healthy controls: (a) prosthetic limb (S1)—UD segment power; (b) intact limb (S1)—UD segment power; (c) S1—UD segment work.

In addition to the decreased magnitude of power, the passive prosthesis exhibited a delayed timing of positive power generation during late stance, where the transition from negative to positive power occurred at approximately 86% of stance, while the transition in the active system and healthy controls occurred at 79% and 80% of stance, respectively.

The increased energy generation during late stance in the active prosthesis was accompanied by an increased energy absorption/dissipation during early stance on the intact limb (Figure 3). The intact limb while wearing the active prosthesis performed total negative work of −0.316 ± 0.021 J/kg, which was 32% higher than that of the intact limb while wearing the passive dynamic system (−0.240 ± 0.012 J/kg) and 52% higher than that of the healthy control (difference greater than 2 standard deviations of healthy controls).

Comparison of P_UD and joint power analyses

Power profiles of P_UD and ankle joint power methods (P_ank3 and P_ank6) show notable differences, especially during early stance and late stance (Figure 4). During early stance, P_UD showed increased magnitude of negative power during early stance (relative to P_ank3 and P_ank6) in both prostheses and intact limb (both conditions). During late stance, P_UD showed decreased magnitudes of peak positive power (relative to P_ank3 and P_ank6) in active prosthesis and intact limb (both conditions), but increased magnitudes of peak positive power in passive prosthesis. The difference between P_UD and P_ank6 can be attributed to the deforming foot contributions (P_ftd). The magnitudes of positive and negative work for P_UD, P_ank3, and P_ank6 are shown in Table 2.

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Figure 4.

Comparison of power estimates obtained from the 3-degree-of-freedom (DOF) ankle joint model (P_ank3), 6-DOF ankle joint model (P_ank6), and UD segment model (P_UD): (a) prosthetic limb (S1)—passive; (b) prosthetic limb (S1)—active; (c) intact limb (S1)—passive; (d) intact limb (S1)—active.

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Table 2.

Positive and negative work values (in J/kg) derived from the methods of P_ank3, P_ank6, and P_UD.

Method	Work (J/kg)
	Passive		Active
	Positive work	Negative work	Positive work	Negative work
Prosthetic limb
Pank3	0.095	−0.116	0.441	−0.129
Pank6	0.075	−0.115	0.396	−0.115
PUD	0.096	−0.195	0.337	−0.151
Intact limb
Pank3	0.346	−0.221	0.354	−0.278
Pank6	0.320	−0.167	0.334	−0.230
PUD	0.244	−0.240	0.266	−0.316

UD: unified deformable.

Discussion

To the authors’ knowledge, this study is the first to evaluate prosthetic limbs using the UD analysis. While previous studies have compared ankle joint power profiles in active and passive prostheses and yielded similar findings (e.g. increased positive power during late stance in active prostheses compared to passive),^3,12,13 it is noteworthy that P_UD captured additional components of power—specifically estimates of P_ftd that includes contributions from the deforming foot structures (e.g. elastic foot and shoes). In both prostheses, P_UD captured additional energy absorption/dissipation during early stance and late stance and greater energy return prior to ground clearance (~last 5% of stance; Figure 4). Therefore, the UD method offers a more complete evaluation of the prostheses during stance in gait.

Interestingly, P_UD estimates during barefoot walking in healthy controls revealed slightly greater negative work (−207 J/kg) than positive work (0.174 J/kg). A large portion of this negative work can be attributed to plantar soft tissue and foot muscles, which collectively remove energy from the body.^14,15 This finding would suggest that in theory, purely passive prostheses with optimal physical properties (e.g. stiffness and damping) can preserve the total energy profiles of the normal ankle–foot system. This idea, however, was not supported from this case evaluation of S1’s Elation prosthesis. In addition to the decreased magnitude, there was a delayed timing of energy return by the passive prosthesis. A future design challenge for passive prostheses, then, may be optimizing both the magnitude and timing of energy return to maximize gait outcomes.

In contrast to S1’s passive prosthesis, his active prosthesis demonstrated the ability to generate net positive work during stance (i.e. magnitude of positive work exceeding that of negative work). While no prior adjustments were made to the actuation settings in attempt to capture his habitual gait mechanics, he subjectively mentioned following data collection that he prefers the power settings to be high enough to assist in other activities (e.g. stair ascent). Thus, it is likely that the prosthetic power assistance exceeded the functional requirement for steady-state level ground walking—leading to compensations in the intact limb, characterized by increased magnitudes of negative work and braking forces compared to his passive prosthetic condition.

A delimitation of the study is that S1 walked with shoes while healthy controls walked barefoot. The extent to which shoes contribute to P_UD estimates is currently unknown and should be investigated in future studies.

Conclusion

The UD analysis offers a more complete evaluation of prostheses compared to traditional joint power analyses and revealed notable differences in energy profiles between passive and active prostheses. The UD method, therefore, may be valuable for facilitating clinical prescription of prostheses based on mechanical power and work profiles and to objectively guide fine adjustments of prosthetic componentry (e.g. material properties of passive components or motor/actuator output settings) to optimize the performance of the prostheses.