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Development of a Mechanistic Hypothesis Linking Compensatory Biomechanics and Stepping Asymmetry during Gait of Transfemoral Amputees

Development of a Mechanistic Hypothesis Linking Compensatory Biomechanics and Stepping Asymmetry... Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4769242, 15 pages https://doi.org/10.1155/2019/4769242 Research Article Development of a Mechanistic Hypothesis Linking Compensatory Biomechanics and Stepping Asymmetry during Gait of Transfemoral Amputees 1,2 1 3 1,4 Abeer Mohamed, Andrew Sexton, Kirsten Simonsen, and Chris A. McGibbon Institute of Biomedical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada Eastern Prosthetic Clinic, Moncton, New Brunswick, Canada Faculty of Kinesiology, University of New Brunswick, Fredericton, New Brunswick, Canada Correspondence should be addressed to Chris A. McGibbon; cmcgibb@unb.ca Received 12 August 2018; Accepted 24 October 2018; Published 3 February 2019 Academic Editor: Kiros Karamanidis Copyright © 2019 Abeer Mohamed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Objective. Gait asymmetry is a common adaptation observed in lower-extremity amputees, but the underlying mechanisms that explain this gait behavior remain unclear for amputees that use above-knee prostheses. Our objective was to develop a working hypothesis to explain chronic stepping asymmetry in otherwise healthy amputees that use above-knee prostheses. Methods. Two amputees (both through-knee; one with microprocessor knee, one with hydraulic knee) and fourteen control subjects participated. 3D kinematics and kinetics were acquired at normal, fast, and slow walking speeds. Data were analyzed for the push-off and collision limbs during a double support phase. We examined gait parameters to identify the stepping asymmetry then examined the external work rate (centre of mass) and internal (joint) power profiles to formulate a working hypothesis to mechanistically explain the observed stepping asymmetry. Results. Stepping asymmetry at all three gait speeds in amputees was characterized by increased stance phase duration of the intact limb versus relatively normal stance phase duration for the prosthesis limb. The prosthesis limb contributed very little to positive and negative work during the double support phase of gait. To compensate, the intact leg at heel strike first provided aid to the deficient prosthetic ankle/foot during its push-off by doing positive work with the intact knee, which caused a delayed stance phase pattern. The resulting delay in toe-off of the intact limb then facilitated the energy transfer from the more robust intact push-off limb to the weaker colliding prosthesis side. This strategy was observed for both amputees. Conclusions. There is a sound scientific rationale for a mechanistic hypothesis that stepping asymmetry in amputee participants is a result of a motor adaptation that is both facilitating the lower-leg trajectory enforced by the prosthesis while compensating for the lack of work done by the prosthesis, the cost of which is increased energy expenditure of the intact knee and both hips. 1. Introduction osteoarthritis of the intact knee and/or hips [11], and are more likely to become sedentary which contributes to declin- It is well documented that users of above-knee prostheses ing health and quality of life [12]. have persistent gait abnormalities [1–3], with increased gait How unilateral amputees biomechanically compensate asymmetry [4–6] and increased energy expenditure [7–9] for their prosthesis has been studied for decades [2, 3]. being two of the hallmark features of amputee gait. Transfe- Whether below- or above-knee, one of the most common moral amputees have more falls than their age-matched characteristics of amputee gait is the reduction of push-off peers [10], have a significantly higher risk of developing power of the artificial foot in terminal stance, requiring 2 Applied Bionics and Biomechanics complex wrapped distally and sutured to the biceps femoris. the hip of the amputee’s residual limb to compensate for this deficiency [7, 13–15]. Another common finding among Both amputee participants used their currently fitted pros- studies is the asymmetric stepping pattern, typically charac- thesis in the study and were recruited through the same local terized as a longer stance phase duration of the intact limb, clinic. One participant used a microprocessor-controlled compared to the prosthetic limb [1, 16–18]. knee (C-Leg® X2 microprocessor knee and Axiton foot from Presently, there is no consensus on why stance dura- Otto Bock Inc., Duderstadt, Germany), and the other used tion asymmetry is such a common chronic feature of a hydraulic passive-mechanical controlled knee (Mauch amputee gait. One possibility is that users preferentially Knee and XC foot from Ossür Inc., Reykjavik, Iceland). spend more time on their intact limb to minimize time Other than the type of prosthesis used, the two amputees’ on their prosthesis limb, due to lack of confidence in the residual limb, socket liners, and clinical management his- prosthesis [6, 18]. Another possibility is that the lack of tory were similar. propulsive power of the prosthesis requires greater impulse 2.2. Experimental Procedures from the intact limb [1, 17], which can be achieved by extending the duration of intact leg loading. Consistent 2.2.1. Gait Analysis. Motion analysis data was collected at with these findings is that stance duration asymmetry is the Andrew and Marjorie McCain Human Performance greater for transfemoral amputees compared to transtibial Laboratory (HPL) at the University of New Brunswick. amputees [6]. However, asymmetry has also been shown The HPL is equipped with a twelve-camera Vicon T160 to decrease with walking speed [1, 6], which suggests that (Oxford Metrics, UK) motion tracking system and six lack of confidence and/or ankle power cannot be the only Kistler force plates (Kistler Instruments, Winterthur, Swit- factors involved. It may also be that users develop locomo- zerland) arranged in a 2 × 3 matrix embedded in the floor. tor adaptations to optimally accommodate the actions of Thirty-nine markers were placed on limbs and torso as the prosthesis, as suggested by Maaref et al. [16], but there shown in Figure 1. All markers (14 mm) were attached to is presently no mechanistic hypothesis by which to explore participants’ skin (or prosthesis surface) using a double- this question. sided tape, with the exception of the sacral cluster that Given the high cost of using a transfemoral prosthesis in was a rigid plate with three markers. For amputee partici- terms of energy expenditure [7–9] and fall risk [10, 19], a bet- pants, markers on the socket, shank, and foot components ter understanding of the mechanisms underlying stepping were attached in similar “anatomical” locations as on the asymmetry is required. Such knowledge could inform intact limb as indicated in Figure 1 (see also Supplementary designers of above-knee prostheses as well as provide clini- Table S1 for marker details). cians with a framework for addressing gait asymmetry when The experimental protocol began with two sequential 2 s training clients to use above-knee prostheses. Our objective static calibration trials where the participant was asked to in this case study was to develop a mechanistic hypothesis stand perfectly still. Participants then completed three con- linking compensatory biomechanics and stepping asymme- strained chair rise trials [20]. The static standing and chair try in transfemoral amputees. rise trials were used to generate the body segment model, as described below. Participants were then asked to walk in a 2. Methods straight line through the viewing volume at three different speeds in the following order. 2.1. Human Subjects. The study was approved by the Univer- sity of New Brunswick (Fredericton), Research Ethics Board (1) Normal (preferred) speed: the subject was instructed (REB), and all participants gave their informed consent prior to walk at their preferred comfortable pace to participation in the study. Participants were included if (2) Fast speed: the subject was instructed to walk as fast they were in good physical health and between 19 and 55 as they can without breaking into a jog years of age. Amputee participants were included if they had a unilateral amputation above or through the knee (3) Slow gait: the subject was instructed to walk as (>1 yr ago) and normally use a transfemoral prosthesis for though they were in a slowly moving line daily activity. Participants were excluded for any medical or chronic condition effecting gait or contraindicating moderate Participants performed at least three repetitions of each physical activity, and any recent injuries requiring treatment gait speed. Trials were repeated (up to six trials) if poor foot (<6 mo) or surgeries (<1 yr) involving the lower extremities strikes were observed, such as neither foot cleanly striking a and back. force plate or two feet on the same plate at the same time. Participants were recruited through the local university Participants rested 30 s between similar speed conditions community and regional prosthetic clinic. Fifteen limbed and at least 60 s between different speed conditions. adults (7 male, 8 female) and two adult males with transfe- 2.2.2. Body Segment Model. As shown in Figure 1, triad clus- moral (through-knee) amputation volunteered to participate in the study. ters were used to track segments and anatomical markers Both amputee participants lost their lower leg from were used to reference joint axes of rotation, for a total of trauma (>5 years prior to enrolling in this study) that thirty-nine markers (see Table S1 for details). First, each resulted in surgical through-knee disarticulation whereby participant’s static trial was used to build a subject-specific 6-degree of freedom (6-dof) model of the participant, as the distal femur was preserved and the patella-quadriceps Applied Bionics and Biomechanics 3 Anterior view FHD RHD LHD Neck RAC LAC STR RSHD LSHD Trunk origin Back MSC LAS LSC RAS RSC RHIP LHIP Pelvis origin Hip RT3 LT1 RT1 LT3 RT2 LT2 RKNE LKNE RLE LLE Knee Thigh origin LME RME RS3 LS1 RS1 LS3 RS3 LS3 RS2 LS2 RLM RANK LLM RMM Shank origin LMM LANK Ankle Foot origin RVM LVM RMTP RFM LFM RCA LCA LMTP LPM RPM Posterior view Figure 1: Positioning of the thirty-nine markers used for tracking the musculoskeletal system during movement, which includes triad clusters on each segment plus anatomical markers required to define joint centres and the segment-embedded coordinate system (origins shown, right hand coordinate system), where x is anterior pointing, y is lateral pointing, and z is vertical pointing. described elsewhere [21]. The chair rise trials were used to The same inverse kinematic and dynamic model was compute the embedded knee joint flexion/extension axis of applied to the amputee’s prosthetic limb, except the inertial rotation, using the SARA algorithm [22]. Hip centres were properties of the socket, shank, and foot components were computed from anatomical scaling as previously described derived from CAD approximations of the user’s prosthesis [23]. Anatomical reference frames and inertial properties components and the known (measured) mass of each partic- were taken from Dumas et al. [24]. ipant’s prosthesis. The following adjustments were made to The resulting 6-dof subject-specific model was then the anatomical model. applied to each gait trial of the subject, producing 3D The mass of each amputee’s residual thigh was first esti- kinematics of left and right foot, shank, thigh, and pel- mated from Dumas’ scaling factors and adjusted for atrophy vis. Force plate data were then used with the kinematic of the residual thigh. Jaegers et al. [25] used MRI to quantify data and anatomical (and body segment inertial) data to atrophy in residual thigh and found that it could be reduced compute the 3D net joint moments at the ankle, knee, as much as 30%. Based on clinical judgment, a value of 20% and hip. was used. The socket and adjusted residual thigh centres of 4 Applied Bionics and Biomechanics stride velocity (m/s), calculated from the stride distance mass, masses, and inertia tensors were then combined to model the thigh-socket as a rigid link. Knee centres were divided by stride time. determined as for limbed participants, using chair rise trials Phase parameters consisted of stance phase duration, cal- culated as the time between iHS and iTO of the ipsilateral and SARA algorithm [22] for locating the segment- embedded axis of rotation. Although neither amputee’s pros- limb, divided by stride time and multiplied by 100, and dou- thesis had a sagittal plane rotational degree of freedom at the ble support duration was calculated from the time between “ankle,” natural deflection of their foot prosthesis allowed for contralateral limb cHS preceding ipsilateral limb iTO, the measurement of an angular displacement and moment of divided by stride time and multiplied by 100. Stride parameters were used to quantify if, and how, the their prosthetic “ankle” (coupling between shaft and foot components), as commonly done in prosthesis gait studies amputees modified their gait speed symmetry. Phase param- eters were used to quantify if, and how, the amputees modi- [26]. As such, the intact limb and prosthetic limb are treated by the model in the same way. fied the relative timing of stride events (heel strikes and toe off) of the intact and prosthesis side. Gait parameters for 2.2.3. Time Normalization. During processing of each sub- slow, normal, and fast speed walking were compared between ject’s trials, custom-written algorithms scanned the foot amputees and control subjects, using single-sample t-tests marker and force plate data to precisely register the stride (α =0 01). event frames (HS-TO-HS: heel strike–toe off–heel strike) for 2.3.2. External Work on the Body Centre of Mass. Using the the left and/or right side. Kinematic and kinetic data were approach described by Donelan et al. [28], external work on then cycled (using a cubic polynomial spline function, with increment of 1% cycle) between successive heel strikes of the CoM was first estimated using ground reaction forces and CoM velocity to estimate the work rate of each limb on the ipsilateral limb for each registered stride. Data for the contralateral limb was also cycled to the ipsilateral iHS-i- the CoM. However, rather than examine the total energy as others have done [14, 17, 29], we separated the interlimb TO-iHS events to enable analysis of the step-to-step transi- work rate into kinetic and potential components. This was tion (double support phase, cHS-iTO). By this designation, the ipsilateral limb contacts the floor first (leading limb), done by first computing the total external work rate (P ) Ext in the sagittal plane for each limb: followed by the contralateral limb (trailing limb), i.e., iHS- cHS-iTO-iHS-. R R R The 2 × 3 arrangement of force plates enabled us to cap- P = F ⋅ v + F ⋅ v , Ext x COMx y COMy ture HS-TO-HS events for successive strides of both limbs, 1 L L L and most gait trials for control subjects and amputees cap- P = F ⋅ v + F ⋅ v , Ext x COMx y COMy tured three strides. This produced three sequential (right- left-right or left-right-left) foot step/contacts on three sepa- where the R and L superscripts represent right and left limbs, rate plates, thus providing two sequential double support F is the vertical ground force and F is the anterior- y x phases: one for the intact side and one for the prosthesis side, posterior ground force, and CoM velocities are given by as the leading limb. v and v (from the biomechanical model). From COM COM y x 2.2.4. Data Reduction for Repeated Trials. Even though here on, we neglect the mediolateral terms in computing the external work, since the internal work methods (below) healthy control subjects can exhibit some gait asymmetry are limited to the sagittal plane. The kinetic “impulse” work [27], evidence suggests this is small relative to asymmetries rate of each limb on the CoM was then found from observed in users of prostheses [4]. Therefore, for controls, ipsilateral and contralateral cycled data were pooled for left Imp,R R R R∗ ∗ and/or right sides when averaging repeated trials, and then P = F ⋅ v + F − c m g ⋅ v , Ext x COMx y COMy means were taken across the subjects to arrive at sample Imp,L L L L∗ ∗ means and standard deviation boundaries, for each variable P = F ⋅ v + F − c m g ⋅ v , x COMx y COMy Ext in the analysis, and for each gait speed category. The same approach was used for amputee participants where m is the total body mass and g is the acceleration of except that left and right sides were not averaged, but rather 2 gravity (9.81 m/s ), and where c is the instantaneous propor- were assigned to an “intact” and “prosthesis” side. Because tion of body weight being supported by the limb, or this was a case study with N =2, the amputee participants’ data were not averaged across subjects. R L R c = , c =1 − c 3 R L 2.3. Biomechanical Analysis F + F y y 2.3.1. Gait Parameters. Gait parameters included stride Finally, the work rate of the limb to overcome gravity of parameters and phase parameters. Stride parameters con- the CoM is found from sisted of stride time, the time in seconds (s) elapsed between successive heel strikes of the limb; stride length, the distance Imp,R Grav,R R in metres (m) between the foot “centre” (defined here as the P = P − P Ext Ext Ext average of the heel and two metatarsal markers) during their Imp,L Grav,L L P = P − P respective (and sequential) mid-stance portion of gait; and Ext Ext Ext Applied Bionics and Biomechanics 5 33]. We used a similar approach except that the threshold Work done by each limb was then computed by integrat- ing the work rate (power) over a specified time interval. was the confidence interval (CI) on the mean of the refer- ence group modelled as a t-distribution (appropriate for 2.3.3. Internal Work of the Leg (and Prosthesis) Joints. Joint small samples) with α =0 01, using a custom algorithm writ- net power and mechanical energy flow were calculated as ten in Matlab (v.R2017b, The MathWorks, Natick, MA). As previously described [30] for the ankle, knee, and hip in the such, it is similar to conducting a single-sample t-test. sagittal plane, by expressing the net joint power as the sum Although this does not provide inferences to the population of the adjacent (distal d and proximal p) segmental powers of transfemoral amputees, it does provide a way to place con- at the joint j fidence on the case-wise identification of compensatory step- ping patterns and joint kinetics. P = P + P = τ ω − ω = τ ω , 5 j d,j p,j j p d j j 3. Results Participant characteristics are summarized in Table 1. Of the where the sign of the net power (positive = power genera- fifteen control subjects, all but one participant had a com- tion; negative = power dissipation) dictates whether the plete set of slow, normal, and fast speed trials. Therefore, joint’s muscle action is concentric (power generation) or the control subject data was generated from the fourteen par- eccentric (power dissipation). Joint powers were computed ticipants with complete sets of data. Both amputees also had a about all three axes, but only the sagittal plane data were complete set of slow, normal, and fast walking trials for both used in this study. The internal mechanical work of the their intact and prosthesis sides. joints was found from integrating the joint power curve over a specified time interval. 3.1. Gait Parameters 2.3.4. Analysis of the Double Support Phase. The gait cycle phase of interest for this study was the double support 3.1.1. Stride Parameters. Very little asymmetry was found for phase. During this phase, the step-to-step transfer of for- the stride parameters. As shown in Table 2, there were only ward momentum occurs [31]. This is obviously a critical minor differences between amputee participants and control phase of the gait cycle and is known to be asymmetric subjects for stride length. Stride time was significantly longer in amputees due to the deficiencies in the prosthesis, pri- (p < 01) for the Mauch user’s preferred and fast speed gait, marily the weak “push-off” of the ankle/foot component and as a result their gait speed was slower than controls [17]. Amputees’ trials were analyzed for two cases (for (p < 01). The C-Leg user’s preferred gait speed was slightly each gait speed). faster than control subjects. Importantly, however, the differ- ences relative to control subjects were consistent for both Case 1. Intact side is the “push-off” limb and prosthesis side is amputees’ intact and prosthesis sides, indicating that stride the “colliding” limb. parameters were well matched between intact and prostheses sides or were symmetric. Case 2. Prosthesis side is the “push-off” limb and intact side as the “colliding” limb. 3.1.2. Phase Parameters. The most striking asymmetry (intact versus prosthesis side) was observed for stance dura- Of primary interest was the positive and negative external tion, which was longer for the intact limb compared to the and internal work done by the push-off and colliding limbs prosthesis limb, for both amputees at all three gait speeds. during the double support phase. Double support time was slightly asymmetric, but not con- External work was computed by integrating positive and sistently so; the amputee with the C-Leg had a shorter dou- negative regions of the CoM work rate curves (impulse and ble support time for their prosthesis limb compared to their gravity). Internal joint work was computed for the positive intact limb, while the opposite was true for the amputee and negative regions of the joint power curves. External work with the Mauch prosthesis. on the CoM and internal work of joints for amputees was In comparison to controls, significant differences were compared to data for the control subjects for the Case 1 observed in stance duration and double support duration and Case 2 trials of slow, normal, and fast speed walking, for both amputees. For the amputee with the C-Leg using single-sample t-tests (α =0 01). prosthesis, only stance duration of their intact side was sig- nificantly longer compared to controls (p < 2.4. Statistical Analysis. For the purpose of this case analy- 01). This sub- sis for developing a hypothesis, we performed mostly ject’s prosthesis side had normal stance phase duration at descriptive statistics (means and standard deviations), but all three walking speeds. For the amputee with the Mauch we also performed quantitative single-subject comparisons prosthesis, the biggest differences were seen in the intact side, between amputees and control subjects for the gait param- but the prosthesis side also had slightly longer stance dura- eters, external CoM work, and internal joint work. A tion for slow and normal speed walking (both were signifi- common approach for single-subject comparisons is estab- cant at p < 01). Double support time was significantly lishing a threshold for a meaningful change, such as 2 longer (p < 01) for both amputees intact and prostheses sides standard deviations from the reference group mean [32, compared to control subjects. 6 Applied Bionics and Biomechanics Table 1: Participant characteristics (mean ± standard deviation) for controls (N =14) and two transfemoral amputees. Subjects Prosthesis Age (years) Height (cm) Body mass (kg) Sex Controls 27 ± 7.5 169 ± 9.2 68.6 ± 12.5 M =6; F =8 Amputee C-Leg 31 178 75 M Amputee Mauch 34 180 63 M Table 2: Gait parameters measured for controls (N =14) and two transfemoral amputees during slow, normal, and fast speed gait, and results of the single sample t-test between amputee and sample of control subjects. Control subjects Amputee: C-Leg/Mauch Mean/(SD) Intact side Prosthesis side Slow Norm Fast Slow Norm Fast Slow Norm Fast Stride params 1.43 1.02 0.91 1.43 1.02 0.93 Stride time (s) 1.40 (0.22) 1.07 (0.07) 0.86 (0.09) ‡ ‡ ‡ ‡ 1.48 1.25 1.03 1.48 1.23 1.04 1.11 1.29 1.49 1.07 1.32 1.46 Stride dist. (m) 1.16 (0.08) 1.26 (0.08) 1.40 (0.13) 1.16 1.32 1.46 1.13 1.27 1.45 ‡ ‡ 0.78 1.27 1.63 0.75 1.29 1.57 Stride vel. (m/s) 0.85 (0.14) 1.18 (0.11) 1.64 (0.16) † † † † 0.78 1.05 1.41 0.77 1.03 1.40 Phase params ‡ ‡ ‡ 70.6 65.0 63.9 62.8 59.0 57.0 Stance duration (% cycle) 61.5 (1.97) 59.2 (1.19) 57.7 (1.89) ‡ ‡ ‡ ‡ ‡ 70.2 65.6 63.9 64.1 62.6 57.9 ‡ ‡ ‡ ‡ ‡ ‡ 20.3 14.8 14.3 16.2 13.1 11.8 Double support (% cycle) 12.9 (1.86) 11.2 (0.96) 9.57 (1.44) ‡ ‡ ‡ ‡ ‡ ‡ 17.2 14.4 13.2 18.9 17.9 14.2 † ‡ Score is significantly lower at p < 01; score is significantly higher at p < 01. 3.2. External CoM and Internal Joint Work excluded for clarity. As above, the double support period of gait is bracketed by contralateral heel strike (cHS) and ipsilat- 3.2.1. Control Subjects. Figure 2 shows the external work eral toe-off (iTO). Joint power profiles behaved as expected rate on the CoM by the ipsilateral (solid line) and contra- for healthy control subjects, having a relatively invariant gait lateral (dashed line) limbs at slow, normal, and fast walking cycle pattern that scales proportionally to walking speed [34]. speed, for the control subjects. The double support period Plots showing joint angles, moments, and joint power for the of gait is bracketed by contralateral heel strike (cHS) and full 0-100% cycle, for slow, normal, and fast walking, are ipsilateral toe-off (iTO) shown by vertical dashed lines. shown in Supplementary Figure S2 . The horizontal axis is time normalized to the 0-100% cycle of the ipsilateral limb, and therefore, the corresponding 3.2.2. Amputees. Table 3 shows positive and negative exter- contralateral limb is also expressed in ipsilateral cycle time. nal work at slow, normal, and fast speed for control subjects Work rate profiles and magnitudes were similar to other and the two amputees’ intact limb and prosthesis limb. studies of healthy gait [8, 28]. Table 4 shows, in a similar arrangement, the positive and The work rate of each limb to overcome gravity negative internal joint work for the control subjects and (Figure 2(a)), when summed (Figure 2(d)), shows the smooth two amputees. Single-sample t-test results are shown using transition between limbs for body weight support. Of partic- symbols, where † = significantly lower than control subjects ular interest in this study was the impulse work rate of each and ‡ = significantly higher than control subjects with an limb (Figure 2(b)) during the double support phase of gait. alpha level of 0.01. Note that the timing of the ipsilateral and contralateral External work results in Table 3 illustrate that com- “impulse power” on the CoM (Figure 2(b), shown by the pared to controls, both amputees did significantly less pos- arrows) is such that the energy gain from the ipsilateral itive and negative work on the CoM with their prosthesis push-off event is balanced by the contralateral collision event, limb (p < 01) and in some cases with their intact limb, par- which result in a smooth transference of propulsive energy ticularly for the kinetic impulse work. Internal joint work in (Figure 2(e)). Table 4 shows that, with only minor exceptions, amputees Figure 3 shows ankle, knee, and hip joint power curves did less work than control subjects with their prosthetic for control subjects at slow, normal, and fast walking speeds. ankle and knee and more work with the hip of their pros- Magnitudes were similar to other studies of healthy adult gait thesis side (p < 01). For amputees’ intact limb, there was [34]. In these plots, the contralateral limb power curves are no difference at the ankle, but amputees did significantly Applied Bionics and Biomechanics 7 Interlimb gravity power Interlimb impulse power 6 6 IIpsi psilat lateral eral to toee of off f C Con onttrralat alateral eral lim limb 4 4 0 0 + = ‒2 ‒2 ‒4 IIpsilat psilateral eral lim limbb ‒4 C Coon nttrralat alateral eral he heeell st strriike ke ‒6 ‒6 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (a) (b) Interlimb total power Total limb gravity power ‒2 ‒2 ‒4 ‒4 ‒6 ‒6 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (c) (d) Total limb impulse power Total limb power 6 6 4 4 2 2 0 0 ‒2 ‒2 ‒4 ‒4 ‒6 ‒6 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (e) (f) Figure 2: External work on the body CoM during the gait cycle. Data are shown for the ipsilateral limb (solid line) and corresponding contralateral limb (dashed line), for slow (red), normal (green), and fast (blue) speed walking, of nonamputee control subjects. (a, b, c) Work rate of ipsilateral and contralateral limbs to overcome gravity (a) and inertia (b) and the total work rate of each limb (c). (d, e, f) The sum of ipsilateral and contralateral limbs, representing the total work rate of the legs to overcome gravity (d), inertia (e), and total work rate (f). Solid lines represent means across N =14 controls, and shaded boundaries represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb. Shaded boundaries represent ±1 standard deviation in event time. Power (W/kg) Power (W/kg) Power (W/kg) Power (W/kg) Power (W/kg) Power (W/kg) 8 Applied Bionics and Biomechanics Ankle power Knee power 7 2 IIpsilat psilateral eral ttooee oof ff f 4 0 ‒1 1 ‒2 C Coon nttralat ralateral eral ‒3 ‒1 he heeell st stri rike ke ‒2 ‒4 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (a) (b) Hip power 1.5 0.5 ‒0.5 ‒1 ‒1.5 ‒2 020 40 60 80 100 % gait cycle Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) (c) Figure 3: Internal work of the leg joints during the gait cycle. Data are shown for slow (red), normal (green), and fast (blue) speed walking, of nonamputee control subjects. (a, b, c) Work rate of ankle (a), knee (b), and hip (c). Solid lines represent means across N =14 controls, and shaded boundaries represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb. Shaded boundaries represent ±1 standard deviation in event time. contralateral heel strike (cHS) events are shown by vertical more work than did control subjects with knee and hip of their intact side (p < 01). dashed lines (and with s.d. boundaries for control subjects). Figure 4 shows the gravity and impulse work rate on the CoM for the two amputee subjects, against the means for control subjects’ ipsilateral and contralateral limbs with 4. Discussion standard deviation boundaries, at their fast walking speed. Joint (ankle, knee, and hip) power plots for amputees are Whether lack of confidence in the prosthesis causes users to similarly arranged in Figure 5. The time scale of plots in spend more time on their intact limb during stance phase Figures 4 and 5 were set to 30-80% cycle in order to more of gait, or users extend stance of the intact limb to increase clearly visualize the double support phase. Plots showing impulse generation [6], users of transfemoral prostheses external work rate and internal joint power for the full must adapt to both the actions and the deficiencies of the 0-100% cycle, for slow, normal, and fast walking, are prosthesis [16]. Although increased internal work [7, 13, shown in Supplementary Figure S3 . 35] is suspected as playing a role in compensating for lack Results for the amputee with the C-Leg prosthesis are of external work on the CoM by the prosthesis [8, 17], an shown in Figure 4(a) and Figure 5(a) (blue = intact, red = understanding of how this compensation relates to stance prosthesis), and results for the amputee with the Mauch duration asymmetry is lacking for transfemoral amputees. hydraulic knee prosthesis are shown in Figure 4(b) and The primary purpose of this study was to develop a mecha- Figure 5(b) (green = intact, orange = prosthesis). Ipsilateral nistic hypothesis linking compensatory biomechanics and toe-off (iTO) events are shown by vertical solid lines, and stepping asymmetry in TF amputees. Power (W/kg) Power (W/kg) Power (W/kg) Applied Bionics and Biomechanics 9 Table 3: Interlimb external work on CoM for controls and two transfemoral amputees during the 0-100% gait cycle of slow, normal, and fast speed walking, with results from the single sample t-test between amputee and sample of control subjects. Wp = positive work (J/kg); Wn = negative work (J/kg); Wt = total work (J/kg), where Wt = Wp + ∣Wn∣. Control subjects Amputee: C-Leg/Mauch Work (J/kg) Mean/(SD) Intact side Prosthesis side Slow Norm Fast Slow Norm Fast Slow Norm Fast Impulse ‡ † † † 0.254 0.423 0.658 0.108 0.126 0.234 Wp 0.295 (0.061) 0.367 (0.078) 0.500 (0.138) † † † † † 0.218 0.254 0.450 0.057 0.087 0.151 † † † † † † 0.105 0.268 0.369 0.168 0.251 0.294 Wn 0.307 (0.046) 0.372 (0.074) 0.525 (0.125) † † † † † 0.069 0.130 0.572 0.156 0.184 0.134 † † † † 0.359 0.691 1.027 0.276 0.377 0.528 Wt 0.602 (0.083) 0.739 (0.145) 1.024 (0.245) † † † † † 0.287 0.384 1.021 0.213 0.271 0.285 Gravity † † 0.249 0.320 0.402 0.238 0.297 0.348 Wp 0.320 (0.062) 0.354 (0.079) 0.442 (0.112) ‡ † † 0.297 0.315 0.664 0.264 0.378 0.303 † † 0.277 0.350 0.492 0.224 0.289 0.289 Wn 0.281 (0.055) 0.327 (0.084) 0.402 (0.107) ‡ ‡ 0.332 0.341 0.455 0.261 0.413 0.466 † † 0.526 0.670 0.894 0.462 0.585 0.637 Wt 0.601 (0.105) 0.681 (0.154) 0.844 (0.210) 0.629 0.656 1.119 0.525 0.791 0.769 † ‡ Significantly lower at p < 01; Significantly higher at p < 01. Table 4: Internal joint work for controls and two transfemoral amputees during the 0-100% gait cycle of slow, normal, and fast speed walking, with results from the single sample t-test between amputee and sample of control subjects. Wp = positive work (J/kg); Wn = negative work (J/kg); Wt = total work (J/kg), where Wt = Wp + ∣Wn∣. Control subjects Amputee: C-Leg/Mauch Work (J/kg) Mean/(SD) Intact side Prosthesis side Slow Norm Fast Slow Norm Fast Slow Norm Fast Ankle † † † 0.193 0.315 0.418 0.035 0.068 0.083 Wp 0.212 (0.061) 0.276 (0.083) 0.352 (0.119) † † † 0.211 0.256 0.286 0.080 0.095 0.194 0.177 0.154 0.135 0.135 0.146 0.164 Wn 0.179 (0.029) 0.154 (0.033) 0.119 (0.071) ‡ ‡ ‡ 0.186 0.171 0.199 0.192 0.205 0.225 † † † 0.371 0.469 0.554 0.170 0.214 0.247 Wt 0.391 (0.047) 0.430 (0.075) 0.471 (0.130) † † 0.397 0.428 0.485 0.272 0.299 0.420 Knee ‡ ‡ † † 0.088 0.182 0.191 0.020 0.016 0.015 Wp 0.049 (0.037) 0.089 (0.047) 0.158 (0.076) ‡ ‡ ‡ † † † 0.121 0.200 0.363 0.012 0.013 0.015 ‡ ‡ ‡ † † 0.327 0.587 0.714 0.093 0.180 0.192 Wn 0.139 (0.056) 0.249 (0.079) 0.442 (0.081) ‡ ‡ † † 0.360 0.371 0.469 0.115 0.132 0.203 ‡ ‡ ‡ † † † 0.415 0.769 0.905 0.114 0.196 0.208 Wt 0.188 (0.087) 0.338 (0.118) 0.600 (0.140) ‡ ‡ ‡ † † 0.481 0.572 0.832 0.127 0.145 0.219 Hip ‡ ‡ ‡ ‡ 0.201 0.340 0.466 0.106 0.215 0.245 Wp 0.103 (0.051) 0.144 (0.067) 0.278 (0.095) ‡ ‡ ‡ ‡ ‡ ‡ 0.336 0.345 0.445 0.196 0.230 0.392 ‡ ‡ ‡ 0.078 0.145 0.235 0.162 0.281 0.307 Wn 0.083 (0.032) 0.120 (0.054) 0.185 (0.064) † ‡ ‡ ‡ ‡ 0.048 0.143 0.300 0.218 0.343 0.497 ‡ ‡ ‡ ‡ ‡ ‡ 0.279 0.486 0.700 0.268 0.496 0.552 Wt 0.186 (0.052) 0.264 (0.065) 0.463 (0.076) ‡ ‡ ‡ ‡ ‡ ‡ 0.384 0.487 0.744 0.414 0.573 0.889 † ‡ Significantly lower at p < 01; significantly higher at p < 01. 10 Applied Bionics and Biomechanics Amputee with C-Leg prosthesis Case 1 Push-off + intact limb (blue) ; Collision = prosthesis (red) 5 5 cH cHSS 0 0 iT iTO O iT iTO O ‒5 ‒5 cHS cHS 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Case 2 Push-off + prosthesis limb (red) ; Collision = intact limb (blue) 5 5 iT iTO O cHS cHS cHS cHS iT iTO O ‒5 ‒5 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle (a) Amputee with C-Leg prosthesis Amputee with Mauch prosthesis Case 1 Push-off = intact limb (green) ; Collision = prosthesis limb (orange) 5 5 cHS cHS 0 0 iT iTO O iiT TO O ‒5 ‒5 cHS cHS 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Push-off = prosthesis (orange) ; Collision = intact limb (green) 5 5 cHS cHS iiT TO O 0 0 iiT TO O cHS cHS ‒5 ‒5 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle (b) Amputee with Mauch prosthesis Figure 4: External work on the body CoM during the double support phase of the gait cycle. Data are shown for amputee with C-Leg prosthesis (a) and amputee with Mauch prosthesis (b). The first column of plots shows gravity work rate (power) on centre of mass (CoM), and the 2nd column shows impulse work rate (power) on CoM. For each amputee, the first row shows Case 1 where the intact limb is the push-off limb (blue) and Case 2 where the push-off limb is the prosthesis (red line). The mean for control subjects (N =14)is shown by dark solid lines with shaded boundaries that represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb, and the shaded boundaries represent ±1 standard deviation in event time. The horizontal axis shows the 30-80% gait cycle. and for the other (C-Leg) it was located at the edge of the 4.1. Stepping Asymmetry. Clearly evident for both amputees’ Case 1 in both Figures 4 and 5 is the delayed iTO event for the shaded region. intact limb, occurring later in the gait cycle, by more than 5% For Case 2, the iTO event of the push-off prosthesis and well outside the shaded boundary region on the iTO limb for both amputees was slightly earlier compared to event of control subjects. Also notable was that the cHS event controls, but within the control iTO boundary. The cHS event of the amputees’ colliding intact limb, in prosthesis for the colliding prosthesis limb, in intact limb “cycle time,” was also delayed compared to controls. Although a smaller “cycle time,” occurred approximately 3-5% earlier in the departure, for one amputee (Mauch) the cHS event fell out- cycle, consistent with a faster swing phase to compensate side the shaded boundary on the cHS region for controls, for the longer stance duration. Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Impulse power (W/kg) Applied Bionics and Biomechanics 11 Amputee with C-Leg prosthesis Push-off = intact limb (blue) ; Collision = prosthesis limb (red) Case 1 8 4 iTO cHS cHS cHS 0 2 iTO ‒2 0 iTO ‒2 ‒2 ‒4 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Case 2 Push-off = prosthesis (red) ; Collision = intact limb (blue) 8 4 4 cHS iTO cHS iTO cHS iTO 4 0 2 ‒2 ‒2 0 ‒4 ‒2 ‒6 ‒4 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle % gait cycle (a) Amputee with C-Leg prosthesis Amputee with Mauch prosthesis Case 1 Push-off = intact limb (green) ; Collision = prosthesis limb (orange) 8 2 8 cHS cHS cHS iTO 6 6 4 0 4 iTO 2 2 ‒1 iTO 0 ‒2 0 ‒2 ‒3 ‒2 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Case 2 Push-off = prosthesis limb (orange) ; Collision = intact limb (green) 8 2 4 cHS iTO cHS iTO cHS iTO 6 1 4 0 ‒1 ‒2 0 ‒2 ‒2 ‒4 ‒3 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle % gait cycle (b) Amputee with Mauch prosthesis Figure 5: Internal joint work rate (power) during the double support phase of the gait cycle. Data are shown for amputee with C-Leg nd prosthesis (a) and amputee with Mauch prosthesis (b). The first column of plots shows ankle power, the 2 column shows knee power, rd and the 3 column shows hip power. For each amputee, the first row shows Case 1 where the intact limb is the push-off limb (blue) and Case 2 where the push-off limb is the prosthesis (red line). The mean for control subjects (N =14) is shown by dark solid lines with shaded boundaries that represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb, and the shaded boundaries represent ±1 standard deviation in event time. The horizontal axis shows the 30-80% gait cycle. These event departures reflect that the primary conse- to accommodate the asymmetry in stance duration. The quence of motor adaptations to the prosthesis have resulted first column of plots showing the interlimb work rate of in a stepping asymmetry characterized by increased stance gravity on the CoM reveals a relatively normal pattern duration (and reduced swing time) of the intact side of for both amputees when their prosthetic limb was the amputee participants, while maintaining (relative to con- push-off limb (Case 2). When the push-off limb was trols) normal phase parameters of the prosthesis side. the intact limb, however, the work rate of gravity was delayed for the intact side (Case 1). This effect was pres- ent for both amputees but more noticeable for the Mauch 4.2. Compensatory Biomechanics Knee user. 4.2.1. External Work on CoM. Plots for the C-Leg user Most revealing were the observed differences between (Figure 4(a)) and Mauch user (Figure 4(b)) identify how amputees and control subjects in the pattern of interlimb the energy transfer from the legs to and from the CoM is able impulse work rate on the CoM. These characteristics were Ankle power (W/kg) Ankle power (W/kg) Ankle power (W/kg) Ankle power (W/kg) Knee power (W/kg) Knee power (W/kg) Knee power (W/kg) Knee power (W/kg) Hip power (W/kg) Hip power (W/kg) Hip power (W/kg) Hip power (W/kg) 12 Applied Bionics and Biomechanics between the 40 and 45% cycle that preceded the intact limb’s consistent for both the C-Leg and Mauch user at all three gait speeds (see also Figure S3 ). heel strike (cHS). For Case 1, when the intact limb (blue line) was the push-off limb, the lengthened stance (delayed iTO) appeared 4.3. A Mechanistic Hypothesis for Stepping Asymmetry. Over- to accommodate the slow development of negative work on all, Figures 4 and 5 demonstrate the similarity in asymmet- the colliding prosthetic limb (red line). Indeed, the negative ric stepping patterns of the intact and prosthetic limbs of work rate of the prosthesis side following cHS was consider- the two amputees. Although the two amputees used very ably lower than for controls, but nevertheless the transfer of different prostheses (both knee and foot components), they energy from the intact to prosthesis side maintained its prin- both appeared to adapt to their prosthesis in the same way. ciple form. Waveforms for normal speed and slow speed walking For Case 2, when the prosthesis limb (red line) was the showed the same asymmetry patterns (also see Figure S3), push-off limb, the impulse power generated by the prosthesis indicating that the stepping asymmetry observed was not side at push-off was, as expected, significantly lower than for a function of speed. controls, although the iTO event for the prosthesis limb was These findings suggest that transfemoral amputees mod- the same as for control subjects. For the colliding intact limb ify both heel strike time (in prosthesis side cycle time) and (blue line), the earlier cHS event appeared to enable a brief toe-off time (in intact limb cycle time) to enable the stance positive power region that was not present for controls. In phase to be lengthened and the swing phase to be shortened. other words, the colliding intact limb was carrying out a pos- The shorter swing phase of the intact limb was timed to col- itive power task prior to taking on its role to accept energy lide earlier relative to the prosthesis limbs’ cycle to enable a from the transferring push-off limb. This appears to compen- transfer of positive power to the CoM prior to the prosthesis sate in part for the reduced positive work of the push-off side push-off, while extending intact limb stance duration to limb, by accelerating the CoM with the intact leg just after compensate for collision work deficiency of the prosthesis. heel strike, which is timed earlier to allow for the “normal” The data suggest that the intact knee joint plays a pivotal role transfer of weight support. in this process. For the two amputees we observed, their prosthetic limb While the hip of the intact limb was clearly compensating did little to contribute to impulse work during push-off and for power generation at push-off, the role of the hip earlier in collision. The weak collision of the prosthesis limb was com- the gait cycle was not as clear from the data. Of particular pensated by extending stance duration of the intact limb. interest though was the substantial negative work done by Then, during the weak push-off of the prosthesis limb, the the hip of the prosthesis limb in late stance. This characteris- intact side compensated by adding positive power prior to tic has been reported for amputees [13, 35, 36] and has also push-off of the prosthesis limb. We now examine the poten- been observed in seniors with disability [37] and may be a tial sources for these compensations. mechanism for transferring energy to the upper body [38], which for the amputee would otherwise be wasted by the 4.2.2. Internal Work of Joints. Joint power plots for the C-Leg prosthesis’ inability to return that energy. user (Figure 5(a)) and Mauch user (Figure 5(b)) identify the internal sources that explain the above compensations. For Case 1 (intact limb is push-off limb) of both amputees, the 4.4. Limitations. There are several notable limitations of the ankle plantar-flexion power burst at push-off (blue line) study. Most significant was having only two participants with was the same as for control subjects, just delayed in cycle limb amputation. Furthermore, the degree of stepping asym- time. Also delayed was the late stance negative power region metry was similar but not identical for the two amputees, of the intact knee (blue line) that followed a significant posi- which is probably related to individual differences and those tive power region in the earlier portion of stance phase, as related to their specific prosthesis. However, in the context of seen at the lower boundary (30% cycle) of the knee power the study’s objective, and with the very good agreement with plots for Case 1. Additionally, the peak positive and negative past literature, we feel our conclusions are well supported. powers for the hip of the intact limb (blue line) were delayed Larger studies examining these effects over time, from first and had greater peak magnitudes than in control subjects. fitting to long-term follow-up, will likely be more informative Power profiles of the colliding prosthesis limb show no effec- than studies with large N. Nevertheless, these studies will be tive response at the knee, and possibly higher hip power of required to definitively answer the question if neural reorga- the prosthesis limb following heel strike, although this was nization is responsible for these adaptations and to what end. not consistent for the two amputees. A more significant limitation may be in generalizability For Case 2 (prosthesis limb is push-off limb) of both of the results to the above-knee amputee population, given amputees, the timing of the artificial ankle/foot power burst that both participants had had through-knee disarticulation was similar to controls but the magnitude was significantly amputations, which results in a long residual limb and causes attenuated. The compensatory function of the intact knee the prosthesis knee axis to be more distal than the intact knee (blue line) of the colliding limb, however, is clearly evident, axis. Although this geometric asymmetry could play a role, in particular the spike in positive knee power just following studies examining residual limb length effects on amputee heel strike, when normally the knee would be dissipating gait generally show little, if any, difference in the biomechan- power at load acceptance. For the hips, the push-off prosthe- ics of gait for longer versus shorter residual limbs [11, 16]. sis limb (red line) had a significant negative power region However, we are not able to analyze this effect with our Applied Bionics and Biomechanics 13 above-knee prosthesis to do the required positive work dur- current data. Future studies should include individuals with different levels of amputation. ing push-off and negative work during collision. Another limitation is how we controlled gait speed. Our data are supported by most, if not all, of the prior Although there is an argument for using a treadmill to ensure studies that show increased concentric energy expenditure experimental control of gait speed, we opted for the more of the intact knee in stance phase [35], increased concentric ecologically realistic condition of over-ground walking. energy expenditure of both the intact and prosthesis side hips While pace control can still be implemented with over- [7, 13, 35], and increased negative work of the prosthetic side ground walking (e.g., using a metronome), we instead chose hip in late stance [13]. However, our analysis goes beyond to use a set of verbal instructions (i.e., “walk as if…”) that these studies by identifying the connection between these would be contextually understood for each of the three compensations and the adapted heel strike and toe-off events self-selected speeds. Given that we observed the same adapta- of the intact limb. tions and compensations in both amputees at all three self- The extended stance duration of the intact limb has been selected gait speeds, suggests that using self-selected speeds suggested as a strategy to increase the impulse of the intact may be more of a strength than a weakness. Had we con- limb on the CoM [16, 18], which indeed may be a conse- trolled speeds artificially, it could be argued that the compen- quence, but our data suggest that the motor program of the sations observed were specificto “non-self-selected” speeds intact leg is purposefully delayed to allow two key compensa- and thus less valuable clinically. tions to occur: (1) a brief period of positive work added by the Finally, our model was not complete. Firstly, we neglected intact limb following its collision, to supplement the weak push-off of the prosthesis limb, which allows (2) the more any external work due to the force couple on the CoM caused by a translating centre of pressure. Mathematically, this is robust push-off leg to time its delivery to minimize the influ- equivalent to a slipping contact, but its contribution to exter- ence of the deficient collision work of the prosthesis limb. nal work during walking has been traditionally neglected (c.f. Based on the data, we suspect that physical interventions [28, 31, 39–41]). Future studies might evaluate the validity of attempting to reestablish “normality” of the intact leg’s stance and swing duration, without improvements to the this assumption. We also used crude estimates of the mass of the amputee’s residual thigh; sensitivity analyses in future prosthesis, could result in less safe walking. Our data, though modelling efforts will be required. Also, we did not examine limited, suggests that the solution is to focus efforts on better the power flow to and from the upper body. The highly defi- push-off and collision control of the prosthesis. cient negative work of the prosthesis limb on the CoM sug- gests that internal work of the musculoskeletal system is Data Availability managing a more complex behavior at and above the hips The data used to support the findings of this study are avail- that warrants future attention. able from the corresponding author upon request. Conflicts of Interest 5. Conclusions The authors have no competing interests to declare. Our study supports the notion that stepping asymmetry in users of artificial limbs is an adaptation to increase function- Acknowledgments ality and safety of their gait, which has been observed both in gait re-education programs [42] and in model simulations The project was funded by the Canadian Institutes of Health [17]. Despite using very different prostheses, the two ampu- Research, Regional Partner Program, and New Brunswick tees demonstrated very symmetric stride characteristics Health Research Foundation. The authors acknowledge the (stride length and speed), and the stance/swing duration of support of staff and students of the Institute of Biomedical the prosthesis limb was more similar to control subjects than Engineering and the Andrew and Marjorie McCain Human the amputee’s intact side. This may reflect that they were > 5 Performance Laboratory. We also thank our participants years since starting to use their current prosthesis and thus for their contribution to this scholarly work. had “fined-tuned” their gait to maximize symmetry of speed (stride time and distance). Supplementary Materials The asymmetry in stance duration was characterized by significant alteration of intact limb heel strike and toe-off Supplementary 1. S1: motion analysis marker descriptions. events, all the while a near normal stance/swing phase for Table S1 contains detailed information about body marker the prosthesis limb was being achieved. This may be a con- locations used for control subjects and amputee participants. straint induced by the advanced control mechanisms of the two devices (the C-Leg and Mauch knees provide both stance Supplementary 2. S2: joint kinematics and kinetics. Graphs and swing phase control), which were intelligent enough to shown in the manuscript are limited to double-support phase enforce a relatively normal periodicity upon the prosthesis (30%-80% gait) of fast gait. For the reader to see the whole limb (i.e., ~60% stance and ~40% swing). gait cycle for all three gait speeds, we include the following Although a rationale design feature, the data from the supplements for walking trials at slow, preferred, and fast present study and past studies would suggest that this speed, from 0 to 100% gait cycle (heel strike to heel strike). enforcement does not overcome the deficiency of the Figure S2.1 contains joint angles and moments for healthy 14 Applied Bionics and Biomechanics controls with data for two amputees (C-Leg user and Mauch extremity amputees,” Archives of Physical Medicine and Reha- bilitation, vol. 82, no. 8, pp. 1031–1037, 2001. user) superimposed. Figure S2.2 contains joint and segment powers for healthy controls with data for two amputees [11] P. A. Struyf, C. M. van Heugten, M. W. Hitters, and R. J. 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Development of a Mechanistic Hypothesis Linking Compensatory Biomechanics and Stepping Asymmetry during Gait of Transfemoral Amputees

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Copyright © 2019 Abeer Mohamed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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10.1155/2019/4769242
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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4769242, 15 pages https://doi.org/10.1155/2019/4769242 Research Article Development of a Mechanistic Hypothesis Linking Compensatory Biomechanics and Stepping Asymmetry during Gait of Transfemoral Amputees 1,2 1 3 1,4 Abeer Mohamed, Andrew Sexton, Kirsten Simonsen, and Chris A. McGibbon Institute of Biomedical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada Eastern Prosthetic Clinic, Moncton, New Brunswick, Canada Faculty of Kinesiology, University of New Brunswick, Fredericton, New Brunswick, Canada Correspondence should be addressed to Chris A. McGibbon; cmcgibb@unb.ca Received 12 August 2018; Accepted 24 October 2018; Published 3 February 2019 Academic Editor: Kiros Karamanidis Copyright © 2019 Abeer Mohamed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Objective. Gait asymmetry is a common adaptation observed in lower-extremity amputees, but the underlying mechanisms that explain this gait behavior remain unclear for amputees that use above-knee prostheses. Our objective was to develop a working hypothesis to explain chronic stepping asymmetry in otherwise healthy amputees that use above-knee prostheses. Methods. Two amputees (both through-knee; one with microprocessor knee, one with hydraulic knee) and fourteen control subjects participated. 3D kinematics and kinetics were acquired at normal, fast, and slow walking speeds. Data were analyzed for the push-off and collision limbs during a double support phase. We examined gait parameters to identify the stepping asymmetry then examined the external work rate (centre of mass) and internal (joint) power profiles to formulate a working hypothesis to mechanistically explain the observed stepping asymmetry. Results. Stepping asymmetry at all three gait speeds in amputees was characterized by increased stance phase duration of the intact limb versus relatively normal stance phase duration for the prosthesis limb. The prosthesis limb contributed very little to positive and negative work during the double support phase of gait. To compensate, the intact leg at heel strike first provided aid to the deficient prosthetic ankle/foot during its push-off by doing positive work with the intact knee, which caused a delayed stance phase pattern. The resulting delay in toe-off of the intact limb then facilitated the energy transfer from the more robust intact push-off limb to the weaker colliding prosthesis side. This strategy was observed for both amputees. Conclusions. There is a sound scientific rationale for a mechanistic hypothesis that stepping asymmetry in amputee participants is a result of a motor adaptation that is both facilitating the lower-leg trajectory enforced by the prosthesis while compensating for the lack of work done by the prosthesis, the cost of which is increased energy expenditure of the intact knee and both hips. 1. Introduction osteoarthritis of the intact knee and/or hips [11], and are more likely to become sedentary which contributes to declin- It is well documented that users of above-knee prostheses ing health and quality of life [12]. have persistent gait abnormalities [1–3], with increased gait How unilateral amputees biomechanically compensate asymmetry [4–6] and increased energy expenditure [7–9] for their prosthesis has been studied for decades [2, 3]. being two of the hallmark features of amputee gait. Transfe- Whether below- or above-knee, one of the most common moral amputees have more falls than their age-matched characteristics of amputee gait is the reduction of push-off peers [10], have a significantly higher risk of developing power of the artificial foot in terminal stance, requiring 2 Applied Bionics and Biomechanics complex wrapped distally and sutured to the biceps femoris. the hip of the amputee’s residual limb to compensate for this deficiency [7, 13–15]. Another common finding among Both amputee participants used their currently fitted pros- studies is the asymmetric stepping pattern, typically charac- thesis in the study and were recruited through the same local terized as a longer stance phase duration of the intact limb, clinic. One participant used a microprocessor-controlled compared to the prosthetic limb [1, 16–18]. knee (C-Leg® X2 microprocessor knee and Axiton foot from Presently, there is no consensus on why stance dura- Otto Bock Inc., Duderstadt, Germany), and the other used tion asymmetry is such a common chronic feature of a hydraulic passive-mechanical controlled knee (Mauch amputee gait. One possibility is that users preferentially Knee and XC foot from Ossür Inc., Reykjavik, Iceland). spend more time on their intact limb to minimize time Other than the type of prosthesis used, the two amputees’ on their prosthesis limb, due to lack of confidence in the residual limb, socket liners, and clinical management his- prosthesis [6, 18]. Another possibility is that the lack of tory were similar. propulsive power of the prosthesis requires greater impulse 2.2. Experimental Procedures from the intact limb [1, 17], which can be achieved by extending the duration of intact leg loading. Consistent 2.2.1. Gait Analysis. Motion analysis data was collected at with these findings is that stance duration asymmetry is the Andrew and Marjorie McCain Human Performance greater for transfemoral amputees compared to transtibial Laboratory (HPL) at the University of New Brunswick. amputees [6]. However, asymmetry has also been shown The HPL is equipped with a twelve-camera Vicon T160 to decrease with walking speed [1, 6], which suggests that (Oxford Metrics, UK) motion tracking system and six lack of confidence and/or ankle power cannot be the only Kistler force plates (Kistler Instruments, Winterthur, Swit- factors involved. It may also be that users develop locomo- zerland) arranged in a 2 × 3 matrix embedded in the floor. tor adaptations to optimally accommodate the actions of Thirty-nine markers were placed on limbs and torso as the prosthesis, as suggested by Maaref et al. [16], but there shown in Figure 1. All markers (14 mm) were attached to is presently no mechanistic hypothesis by which to explore participants’ skin (or prosthesis surface) using a double- this question. sided tape, with the exception of the sacral cluster that Given the high cost of using a transfemoral prosthesis in was a rigid plate with three markers. For amputee partici- terms of energy expenditure [7–9] and fall risk [10, 19], a bet- pants, markers on the socket, shank, and foot components ter understanding of the mechanisms underlying stepping were attached in similar “anatomical” locations as on the asymmetry is required. Such knowledge could inform intact limb as indicated in Figure 1 (see also Supplementary designers of above-knee prostheses as well as provide clini- Table S1 for marker details). cians with a framework for addressing gait asymmetry when The experimental protocol began with two sequential 2 s training clients to use above-knee prostheses. Our objective static calibration trials where the participant was asked to in this case study was to develop a mechanistic hypothesis stand perfectly still. Participants then completed three con- linking compensatory biomechanics and stepping asymme- strained chair rise trials [20]. The static standing and chair try in transfemoral amputees. rise trials were used to generate the body segment model, as described below. Participants were then asked to walk in a 2. Methods straight line through the viewing volume at three different speeds in the following order. 2.1. Human Subjects. The study was approved by the Univer- sity of New Brunswick (Fredericton), Research Ethics Board (1) Normal (preferred) speed: the subject was instructed (REB), and all participants gave their informed consent prior to walk at their preferred comfortable pace to participation in the study. Participants were included if (2) Fast speed: the subject was instructed to walk as fast they were in good physical health and between 19 and 55 as they can without breaking into a jog years of age. Amputee participants were included if they had a unilateral amputation above or through the knee (3) Slow gait: the subject was instructed to walk as (>1 yr ago) and normally use a transfemoral prosthesis for though they were in a slowly moving line daily activity. Participants were excluded for any medical or chronic condition effecting gait or contraindicating moderate Participants performed at least three repetitions of each physical activity, and any recent injuries requiring treatment gait speed. Trials were repeated (up to six trials) if poor foot (<6 mo) or surgeries (<1 yr) involving the lower extremities strikes were observed, such as neither foot cleanly striking a and back. force plate or two feet on the same plate at the same time. Participants were recruited through the local university Participants rested 30 s between similar speed conditions community and regional prosthetic clinic. Fifteen limbed and at least 60 s between different speed conditions. adults (7 male, 8 female) and two adult males with transfe- 2.2.2. Body Segment Model. As shown in Figure 1, triad clus- moral (through-knee) amputation volunteered to participate in the study. ters were used to track segments and anatomical markers Both amputee participants lost their lower leg from were used to reference joint axes of rotation, for a total of trauma (>5 years prior to enrolling in this study) that thirty-nine markers (see Table S1 for details). First, each resulted in surgical through-knee disarticulation whereby participant’s static trial was used to build a subject-specific 6-degree of freedom (6-dof) model of the participant, as the distal femur was preserved and the patella-quadriceps Applied Bionics and Biomechanics 3 Anterior view FHD RHD LHD Neck RAC LAC STR RSHD LSHD Trunk origin Back MSC LAS LSC RAS RSC RHIP LHIP Pelvis origin Hip RT3 LT1 RT1 LT3 RT2 LT2 RKNE LKNE RLE LLE Knee Thigh origin LME RME RS3 LS1 RS1 LS3 RS3 LS3 RS2 LS2 RLM RANK LLM RMM Shank origin LMM LANK Ankle Foot origin RVM LVM RMTP RFM LFM RCA LCA LMTP LPM RPM Posterior view Figure 1: Positioning of the thirty-nine markers used for tracking the musculoskeletal system during movement, which includes triad clusters on each segment plus anatomical markers required to define joint centres and the segment-embedded coordinate system (origins shown, right hand coordinate system), where x is anterior pointing, y is lateral pointing, and z is vertical pointing. described elsewhere [21]. The chair rise trials were used to The same inverse kinematic and dynamic model was compute the embedded knee joint flexion/extension axis of applied to the amputee’s prosthetic limb, except the inertial rotation, using the SARA algorithm [22]. Hip centres were properties of the socket, shank, and foot components were computed from anatomical scaling as previously described derived from CAD approximations of the user’s prosthesis [23]. Anatomical reference frames and inertial properties components and the known (measured) mass of each partic- were taken from Dumas et al. [24]. ipant’s prosthesis. The following adjustments were made to The resulting 6-dof subject-specific model was then the anatomical model. applied to each gait trial of the subject, producing 3D The mass of each amputee’s residual thigh was first esti- kinematics of left and right foot, shank, thigh, and pel- mated from Dumas’ scaling factors and adjusted for atrophy vis. Force plate data were then used with the kinematic of the residual thigh. Jaegers et al. [25] used MRI to quantify data and anatomical (and body segment inertial) data to atrophy in residual thigh and found that it could be reduced compute the 3D net joint moments at the ankle, knee, as much as 30%. Based on clinical judgment, a value of 20% and hip. was used. The socket and adjusted residual thigh centres of 4 Applied Bionics and Biomechanics stride velocity (m/s), calculated from the stride distance mass, masses, and inertia tensors were then combined to model the thigh-socket as a rigid link. Knee centres were divided by stride time. determined as for limbed participants, using chair rise trials Phase parameters consisted of stance phase duration, cal- culated as the time between iHS and iTO of the ipsilateral and SARA algorithm [22] for locating the segment- embedded axis of rotation. Although neither amputee’s pros- limb, divided by stride time and multiplied by 100, and dou- thesis had a sagittal plane rotational degree of freedom at the ble support duration was calculated from the time between “ankle,” natural deflection of their foot prosthesis allowed for contralateral limb cHS preceding ipsilateral limb iTO, the measurement of an angular displacement and moment of divided by stride time and multiplied by 100. Stride parameters were used to quantify if, and how, the their prosthetic “ankle” (coupling between shaft and foot components), as commonly done in prosthesis gait studies amputees modified their gait speed symmetry. Phase param- eters were used to quantify if, and how, the amputees modi- [26]. As such, the intact limb and prosthetic limb are treated by the model in the same way. fied the relative timing of stride events (heel strikes and toe off) of the intact and prosthesis side. Gait parameters for 2.2.3. Time Normalization. During processing of each sub- slow, normal, and fast speed walking were compared between ject’s trials, custom-written algorithms scanned the foot amputees and control subjects, using single-sample t-tests marker and force plate data to precisely register the stride (α =0 01). event frames (HS-TO-HS: heel strike–toe off–heel strike) for 2.3.2. External Work on the Body Centre of Mass. Using the the left and/or right side. Kinematic and kinetic data were approach described by Donelan et al. [28], external work on then cycled (using a cubic polynomial spline function, with increment of 1% cycle) between successive heel strikes of the CoM was first estimated using ground reaction forces and CoM velocity to estimate the work rate of each limb on the ipsilateral limb for each registered stride. Data for the contralateral limb was also cycled to the ipsilateral iHS-i- the CoM. However, rather than examine the total energy as others have done [14, 17, 29], we separated the interlimb TO-iHS events to enable analysis of the step-to-step transi- work rate into kinetic and potential components. This was tion (double support phase, cHS-iTO). By this designation, the ipsilateral limb contacts the floor first (leading limb), done by first computing the total external work rate (P ) Ext in the sagittal plane for each limb: followed by the contralateral limb (trailing limb), i.e., iHS- cHS-iTO-iHS-. R R R The 2 × 3 arrangement of force plates enabled us to cap- P = F ⋅ v + F ⋅ v , Ext x COMx y COMy ture HS-TO-HS events for successive strides of both limbs, 1 L L L and most gait trials for control subjects and amputees cap- P = F ⋅ v + F ⋅ v , Ext x COMx y COMy tured three strides. This produced three sequential (right- left-right or left-right-left) foot step/contacts on three sepa- where the R and L superscripts represent right and left limbs, rate plates, thus providing two sequential double support F is the vertical ground force and F is the anterior- y x phases: one for the intact side and one for the prosthesis side, posterior ground force, and CoM velocities are given by as the leading limb. v and v (from the biomechanical model). From COM COM y x 2.2.4. Data Reduction for Repeated Trials. Even though here on, we neglect the mediolateral terms in computing the external work, since the internal work methods (below) healthy control subjects can exhibit some gait asymmetry are limited to the sagittal plane. The kinetic “impulse” work [27], evidence suggests this is small relative to asymmetries rate of each limb on the CoM was then found from observed in users of prostheses [4]. Therefore, for controls, ipsilateral and contralateral cycled data were pooled for left Imp,R R R R∗ ∗ and/or right sides when averaging repeated trials, and then P = F ⋅ v + F − c m g ⋅ v , Ext x COMx y COMy means were taken across the subjects to arrive at sample Imp,L L L L∗ ∗ means and standard deviation boundaries, for each variable P = F ⋅ v + F − c m g ⋅ v , x COMx y COMy Ext in the analysis, and for each gait speed category. The same approach was used for amputee participants where m is the total body mass and g is the acceleration of except that left and right sides were not averaged, but rather 2 gravity (9.81 m/s ), and where c is the instantaneous propor- were assigned to an “intact” and “prosthesis” side. Because tion of body weight being supported by the limb, or this was a case study with N =2, the amputee participants’ data were not averaged across subjects. R L R c = , c =1 − c 3 R L 2.3. Biomechanical Analysis F + F y y 2.3.1. Gait Parameters. Gait parameters included stride Finally, the work rate of the limb to overcome gravity of parameters and phase parameters. Stride parameters con- the CoM is found from sisted of stride time, the time in seconds (s) elapsed between successive heel strikes of the limb; stride length, the distance Imp,R Grav,R R in metres (m) between the foot “centre” (defined here as the P = P − P Ext Ext Ext average of the heel and two metatarsal markers) during their Imp,L Grav,L L P = P − P respective (and sequential) mid-stance portion of gait; and Ext Ext Ext Applied Bionics and Biomechanics 5 33]. We used a similar approach except that the threshold Work done by each limb was then computed by integrat- ing the work rate (power) over a specified time interval. was the confidence interval (CI) on the mean of the refer- ence group modelled as a t-distribution (appropriate for 2.3.3. Internal Work of the Leg (and Prosthesis) Joints. Joint small samples) with α =0 01, using a custom algorithm writ- net power and mechanical energy flow were calculated as ten in Matlab (v.R2017b, The MathWorks, Natick, MA). As previously described [30] for the ankle, knee, and hip in the such, it is similar to conducting a single-sample t-test. sagittal plane, by expressing the net joint power as the sum Although this does not provide inferences to the population of the adjacent (distal d and proximal p) segmental powers of transfemoral amputees, it does provide a way to place con- at the joint j fidence on the case-wise identification of compensatory step- ping patterns and joint kinetics. P = P + P = τ ω − ω = τ ω , 5 j d,j p,j j p d j j 3. Results Participant characteristics are summarized in Table 1. Of the where the sign of the net power (positive = power genera- fifteen control subjects, all but one participant had a com- tion; negative = power dissipation) dictates whether the plete set of slow, normal, and fast speed trials. Therefore, joint’s muscle action is concentric (power generation) or the control subject data was generated from the fourteen par- eccentric (power dissipation). Joint powers were computed ticipants with complete sets of data. Both amputees also had a about all three axes, but only the sagittal plane data were complete set of slow, normal, and fast walking trials for both used in this study. The internal mechanical work of the their intact and prosthesis sides. joints was found from integrating the joint power curve over a specified time interval. 3.1. Gait Parameters 2.3.4. Analysis of the Double Support Phase. The gait cycle phase of interest for this study was the double support 3.1.1. Stride Parameters. Very little asymmetry was found for phase. During this phase, the step-to-step transfer of for- the stride parameters. As shown in Table 2, there were only ward momentum occurs [31]. This is obviously a critical minor differences between amputee participants and control phase of the gait cycle and is known to be asymmetric subjects for stride length. Stride time was significantly longer in amputees due to the deficiencies in the prosthesis, pri- (p < 01) for the Mauch user’s preferred and fast speed gait, marily the weak “push-off” of the ankle/foot component and as a result their gait speed was slower than controls [17]. Amputees’ trials were analyzed for two cases (for (p < 01). The C-Leg user’s preferred gait speed was slightly each gait speed). faster than control subjects. Importantly, however, the differ- ences relative to control subjects were consistent for both Case 1. Intact side is the “push-off” limb and prosthesis side is amputees’ intact and prosthesis sides, indicating that stride the “colliding” limb. parameters were well matched between intact and prostheses sides or were symmetric. Case 2. Prosthesis side is the “push-off” limb and intact side as the “colliding” limb. 3.1.2. Phase Parameters. The most striking asymmetry (intact versus prosthesis side) was observed for stance dura- Of primary interest was the positive and negative external tion, which was longer for the intact limb compared to the and internal work done by the push-off and colliding limbs prosthesis limb, for both amputees at all three gait speeds. during the double support phase. Double support time was slightly asymmetric, but not con- External work was computed by integrating positive and sistently so; the amputee with the C-Leg had a shorter dou- negative regions of the CoM work rate curves (impulse and ble support time for their prosthesis limb compared to their gravity). Internal joint work was computed for the positive intact limb, while the opposite was true for the amputee and negative regions of the joint power curves. External work with the Mauch prosthesis. on the CoM and internal work of joints for amputees was In comparison to controls, significant differences were compared to data for the control subjects for the Case 1 observed in stance duration and double support duration and Case 2 trials of slow, normal, and fast speed walking, for both amputees. For the amputee with the C-Leg using single-sample t-tests (α =0 01). prosthesis, only stance duration of their intact side was sig- nificantly longer compared to controls (p < 2.4. Statistical Analysis. For the purpose of this case analy- 01). This sub- sis for developing a hypothesis, we performed mostly ject’s prosthesis side had normal stance phase duration at descriptive statistics (means and standard deviations), but all three walking speeds. For the amputee with the Mauch we also performed quantitative single-subject comparisons prosthesis, the biggest differences were seen in the intact side, between amputees and control subjects for the gait param- but the prosthesis side also had slightly longer stance dura- eters, external CoM work, and internal joint work. A tion for slow and normal speed walking (both were signifi- common approach for single-subject comparisons is estab- cant at p < 01). Double support time was significantly lishing a threshold for a meaningful change, such as 2 longer (p < 01) for both amputees intact and prostheses sides standard deviations from the reference group mean [32, compared to control subjects. 6 Applied Bionics and Biomechanics Table 1: Participant characteristics (mean ± standard deviation) for controls (N =14) and two transfemoral amputees. Subjects Prosthesis Age (years) Height (cm) Body mass (kg) Sex Controls 27 ± 7.5 169 ± 9.2 68.6 ± 12.5 M =6; F =8 Amputee C-Leg 31 178 75 M Amputee Mauch 34 180 63 M Table 2: Gait parameters measured for controls (N =14) and two transfemoral amputees during slow, normal, and fast speed gait, and results of the single sample t-test between amputee and sample of control subjects. Control subjects Amputee: C-Leg/Mauch Mean/(SD) Intact side Prosthesis side Slow Norm Fast Slow Norm Fast Slow Norm Fast Stride params 1.43 1.02 0.91 1.43 1.02 0.93 Stride time (s) 1.40 (0.22) 1.07 (0.07) 0.86 (0.09) ‡ ‡ ‡ ‡ 1.48 1.25 1.03 1.48 1.23 1.04 1.11 1.29 1.49 1.07 1.32 1.46 Stride dist. (m) 1.16 (0.08) 1.26 (0.08) 1.40 (0.13) 1.16 1.32 1.46 1.13 1.27 1.45 ‡ ‡ 0.78 1.27 1.63 0.75 1.29 1.57 Stride vel. (m/s) 0.85 (0.14) 1.18 (0.11) 1.64 (0.16) † † † † 0.78 1.05 1.41 0.77 1.03 1.40 Phase params ‡ ‡ ‡ 70.6 65.0 63.9 62.8 59.0 57.0 Stance duration (% cycle) 61.5 (1.97) 59.2 (1.19) 57.7 (1.89) ‡ ‡ ‡ ‡ ‡ 70.2 65.6 63.9 64.1 62.6 57.9 ‡ ‡ ‡ ‡ ‡ ‡ 20.3 14.8 14.3 16.2 13.1 11.8 Double support (% cycle) 12.9 (1.86) 11.2 (0.96) 9.57 (1.44) ‡ ‡ ‡ ‡ ‡ ‡ 17.2 14.4 13.2 18.9 17.9 14.2 † ‡ Score is significantly lower at p < 01; score is significantly higher at p < 01. 3.2. External CoM and Internal Joint Work excluded for clarity. As above, the double support period of gait is bracketed by contralateral heel strike (cHS) and ipsilat- 3.2.1. Control Subjects. Figure 2 shows the external work eral toe-off (iTO). Joint power profiles behaved as expected rate on the CoM by the ipsilateral (solid line) and contra- for healthy control subjects, having a relatively invariant gait lateral (dashed line) limbs at slow, normal, and fast walking cycle pattern that scales proportionally to walking speed [34]. speed, for the control subjects. The double support period Plots showing joint angles, moments, and joint power for the of gait is bracketed by contralateral heel strike (cHS) and full 0-100% cycle, for slow, normal, and fast walking, are ipsilateral toe-off (iTO) shown by vertical dashed lines. shown in Supplementary Figure S2 . The horizontal axis is time normalized to the 0-100% cycle of the ipsilateral limb, and therefore, the corresponding 3.2.2. Amputees. Table 3 shows positive and negative exter- contralateral limb is also expressed in ipsilateral cycle time. nal work at slow, normal, and fast speed for control subjects Work rate profiles and magnitudes were similar to other and the two amputees’ intact limb and prosthesis limb. studies of healthy gait [8, 28]. Table 4 shows, in a similar arrangement, the positive and The work rate of each limb to overcome gravity negative internal joint work for the control subjects and (Figure 2(a)), when summed (Figure 2(d)), shows the smooth two amputees. Single-sample t-test results are shown using transition between limbs for body weight support. Of partic- symbols, where † = significantly lower than control subjects ular interest in this study was the impulse work rate of each and ‡ = significantly higher than control subjects with an limb (Figure 2(b)) during the double support phase of gait. alpha level of 0.01. Note that the timing of the ipsilateral and contralateral External work results in Table 3 illustrate that com- “impulse power” on the CoM (Figure 2(b), shown by the pared to controls, both amputees did significantly less pos- arrows) is such that the energy gain from the ipsilateral itive and negative work on the CoM with their prosthesis push-off event is balanced by the contralateral collision event, limb (p < 01) and in some cases with their intact limb, par- which result in a smooth transference of propulsive energy ticularly for the kinetic impulse work. Internal joint work in (Figure 2(e)). Table 4 shows that, with only minor exceptions, amputees Figure 3 shows ankle, knee, and hip joint power curves did less work than control subjects with their prosthetic for control subjects at slow, normal, and fast walking speeds. ankle and knee and more work with the hip of their pros- Magnitudes were similar to other studies of healthy adult gait thesis side (p < 01). For amputees’ intact limb, there was [34]. In these plots, the contralateral limb power curves are no difference at the ankle, but amputees did significantly Applied Bionics and Biomechanics 7 Interlimb gravity power Interlimb impulse power 6 6 IIpsi psilat lateral eral to toee of off f C Con onttrralat alateral eral lim limb 4 4 0 0 + = ‒2 ‒2 ‒4 IIpsilat psilateral eral lim limbb ‒4 C Coon nttrralat alateral eral he heeell st strriike ke ‒6 ‒6 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (a) (b) Interlimb total power Total limb gravity power ‒2 ‒2 ‒4 ‒4 ‒6 ‒6 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (c) (d) Total limb impulse power Total limb power 6 6 4 4 2 2 0 0 ‒2 ‒2 ‒4 ‒4 ‒6 ‒6 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (e) (f) Figure 2: External work on the body CoM during the gait cycle. Data are shown for the ipsilateral limb (solid line) and corresponding contralateral limb (dashed line), for slow (red), normal (green), and fast (blue) speed walking, of nonamputee control subjects. (a, b, c) Work rate of ipsilateral and contralateral limbs to overcome gravity (a) and inertia (b) and the total work rate of each limb (c). (d, e, f) The sum of ipsilateral and contralateral limbs, representing the total work rate of the legs to overcome gravity (d), inertia (e), and total work rate (f). Solid lines represent means across N =14 controls, and shaded boundaries represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb. Shaded boundaries represent ±1 standard deviation in event time. Power (W/kg) Power (W/kg) Power (W/kg) Power (W/kg) Power (W/kg) Power (W/kg) 8 Applied Bionics and Biomechanics Ankle power Knee power 7 2 IIpsilat psilateral eral ttooee oof ff f 4 0 ‒1 1 ‒2 C Coon nttralat ralateral eral ‒3 ‒1 he heeell st stri rike ke ‒2 ‒4 020 40 60 80 100 020 40 60 80 100 % gait cycle % gait cycle Slow speed (0.85 ± 0.10 m/s) Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) Fast speed (1.64 ± 0.11 m/s) (a) (b) Hip power 1.5 0.5 ‒0.5 ‒1 ‒1.5 ‒2 020 40 60 80 100 % gait cycle Slow speed (0.85 ± 0.10 m/s) Normal speed (1.18 ± 0.08 m/s) Fast speed (1.64 ± 0.11 m/s) (c) Figure 3: Internal work of the leg joints during the gait cycle. Data are shown for slow (red), normal (green), and fast (blue) speed walking, of nonamputee control subjects. (a, b, c) Work rate of ankle (a), knee (b), and hip (c). Solid lines represent means across N =14 controls, and shaded boundaries represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb. Shaded boundaries represent ±1 standard deviation in event time. contralateral heel strike (cHS) events are shown by vertical more work than did control subjects with knee and hip of their intact side (p < 01). dashed lines (and with s.d. boundaries for control subjects). Figure 4 shows the gravity and impulse work rate on the CoM for the two amputee subjects, against the means for control subjects’ ipsilateral and contralateral limbs with 4. Discussion standard deviation boundaries, at their fast walking speed. Joint (ankle, knee, and hip) power plots for amputees are Whether lack of confidence in the prosthesis causes users to similarly arranged in Figure 5. The time scale of plots in spend more time on their intact limb during stance phase Figures 4 and 5 were set to 30-80% cycle in order to more of gait, or users extend stance of the intact limb to increase clearly visualize the double support phase. Plots showing impulse generation [6], users of transfemoral prostheses external work rate and internal joint power for the full must adapt to both the actions and the deficiencies of the 0-100% cycle, for slow, normal, and fast walking, are prosthesis [16]. Although increased internal work [7, 13, shown in Supplementary Figure S3 . 35] is suspected as playing a role in compensating for lack Results for the amputee with the C-Leg prosthesis are of external work on the CoM by the prosthesis [8, 17], an shown in Figure 4(a) and Figure 5(a) (blue = intact, red = understanding of how this compensation relates to stance prosthesis), and results for the amputee with the Mauch duration asymmetry is lacking for transfemoral amputees. hydraulic knee prosthesis are shown in Figure 4(b) and The primary purpose of this study was to develop a mecha- Figure 5(b) (green = intact, orange = prosthesis). Ipsilateral nistic hypothesis linking compensatory biomechanics and toe-off (iTO) events are shown by vertical solid lines, and stepping asymmetry in TF amputees. Power (W/kg) Power (W/kg) Power (W/kg) Applied Bionics and Biomechanics 9 Table 3: Interlimb external work on CoM for controls and two transfemoral amputees during the 0-100% gait cycle of slow, normal, and fast speed walking, with results from the single sample t-test between amputee and sample of control subjects. Wp = positive work (J/kg); Wn = negative work (J/kg); Wt = total work (J/kg), where Wt = Wp + ∣Wn∣. Control subjects Amputee: C-Leg/Mauch Work (J/kg) Mean/(SD) Intact side Prosthesis side Slow Norm Fast Slow Norm Fast Slow Norm Fast Impulse ‡ † † † 0.254 0.423 0.658 0.108 0.126 0.234 Wp 0.295 (0.061) 0.367 (0.078) 0.500 (0.138) † † † † † 0.218 0.254 0.450 0.057 0.087 0.151 † † † † † † 0.105 0.268 0.369 0.168 0.251 0.294 Wn 0.307 (0.046) 0.372 (0.074) 0.525 (0.125) † † † † † 0.069 0.130 0.572 0.156 0.184 0.134 † † † † 0.359 0.691 1.027 0.276 0.377 0.528 Wt 0.602 (0.083) 0.739 (0.145) 1.024 (0.245) † † † † † 0.287 0.384 1.021 0.213 0.271 0.285 Gravity † † 0.249 0.320 0.402 0.238 0.297 0.348 Wp 0.320 (0.062) 0.354 (0.079) 0.442 (0.112) ‡ † † 0.297 0.315 0.664 0.264 0.378 0.303 † † 0.277 0.350 0.492 0.224 0.289 0.289 Wn 0.281 (0.055) 0.327 (0.084) 0.402 (0.107) ‡ ‡ 0.332 0.341 0.455 0.261 0.413 0.466 † † 0.526 0.670 0.894 0.462 0.585 0.637 Wt 0.601 (0.105) 0.681 (0.154) 0.844 (0.210) 0.629 0.656 1.119 0.525 0.791 0.769 † ‡ Significantly lower at p < 01; Significantly higher at p < 01. Table 4: Internal joint work for controls and two transfemoral amputees during the 0-100% gait cycle of slow, normal, and fast speed walking, with results from the single sample t-test between amputee and sample of control subjects. Wp = positive work (J/kg); Wn = negative work (J/kg); Wt = total work (J/kg), where Wt = Wp + ∣Wn∣. Control subjects Amputee: C-Leg/Mauch Work (J/kg) Mean/(SD) Intact side Prosthesis side Slow Norm Fast Slow Norm Fast Slow Norm Fast Ankle † † † 0.193 0.315 0.418 0.035 0.068 0.083 Wp 0.212 (0.061) 0.276 (0.083) 0.352 (0.119) † † † 0.211 0.256 0.286 0.080 0.095 0.194 0.177 0.154 0.135 0.135 0.146 0.164 Wn 0.179 (0.029) 0.154 (0.033) 0.119 (0.071) ‡ ‡ ‡ 0.186 0.171 0.199 0.192 0.205 0.225 † † † 0.371 0.469 0.554 0.170 0.214 0.247 Wt 0.391 (0.047) 0.430 (0.075) 0.471 (0.130) † † 0.397 0.428 0.485 0.272 0.299 0.420 Knee ‡ ‡ † † 0.088 0.182 0.191 0.020 0.016 0.015 Wp 0.049 (0.037) 0.089 (0.047) 0.158 (0.076) ‡ ‡ ‡ † † † 0.121 0.200 0.363 0.012 0.013 0.015 ‡ ‡ ‡ † † 0.327 0.587 0.714 0.093 0.180 0.192 Wn 0.139 (0.056) 0.249 (0.079) 0.442 (0.081) ‡ ‡ † † 0.360 0.371 0.469 0.115 0.132 0.203 ‡ ‡ ‡ † † † 0.415 0.769 0.905 0.114 0.196 0.208 Wt 0.188 (0.087) 0.338 (0.118) 0.600 (0.140) ‡ ‡ ‡ † † 0.481 0.572 0.832 0.127 0.145 0.219 Hip ‡ ‡ ‡ ‡ 0.201 0.340 0.466 0.106 0.215 0.245 Wp 0.103 (0.051) 0.144 (0.067) 0.278 (0.095) ‡ ‡ ‡ ‡ ‡ ‡ 0.336 0.345 0.445 0.196 0.230 0.392 ‡ ‡ ‡ 0.078 0.145 0.235 0.162 0.281 0.307 Wn 0.083 (0.032) 0.120 (0.054) 0.185 (0.064) † ‡ ‡ ‡ ‡ 0.048 0.143 0.300 0.218 0.343 0.497 ‡ ‡ ‡ ‡ ‡ ‡ 0.279 0.486 0.700 0.268 0.496 0.552 Wt 0.186 (0.052) 0.264 (0.065) 0.463 (0.076) ‡ ‡ ‡ ‡ ‡ ‡ 0.384 0.487 0.744 0.414 0.573 0.889 † ‡ Significantly lower at p < 01; significantly higher at p < 01. 10 Applied Bionics and Biomechanics Amputee with C-Leg prosthesis Case 1 Push-off + intact limb (blue) ; Collision = prosthesis (red) 5 5 cH cHSS 0 0 iT iTO O iT iTO O ‒5 ‒5 cHS cHS 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Case 2 Push-off + prosthesis limb (red) ; Collision = intact limb (blue) 5 5 iT iTO O cHS cHS cHS cHS iT iTO O ‒5 ‒5 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle (a) Amputee with C-Leg prosthesis Amputee with Mauch prosthesis Case 1 Push-off = intact limb (green) ; Collision = prosthesis limb (orange) 5 5 cHS cHS 0 0 iT iTO O iiT TO O ‒5 ‒5 cHS cHS 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Push-off = prosthesis (orange) ; Collision = intact limb (green) 5 5 cHS cHS iiT TO O 0 0 iiT TO O cHS cHS ‒5 ‒5 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle (b) Amputee with Mauch prosthesis Figure 4: External work on the body CoM during the double support phase of the gait cycle. Data are shown for amputee with C-Leg prosthesis (a) and amputee with Mauch prosthesis (b). The first column of plots shows gravity work rate (power) on centre of mass (CoM), and the 2nd column shows impulse work rate (power) on CoM. For each amputee, the first row shows Case 1 where the intact limb is the push-off limb (blue) and Case 2 where the push-off limb is the prosthesis (red line). The mean for control subjects (N =14)is shown by dark solid lines with shaded boundaries that represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb, and the shaded boundaries represent ±1 standard deviation in event time. The horizontal axis shows the 30-80% gait cycle. and for the other (C-Leg) it was located at the edge of the 4.1. Stepping Asymmetry. Clearly evident for both amputees’ Case 1 in both Figures 4 and 5 is the delayed iTO event for the shaded region. intact limb, occurring later in the gait cycle, by more than 5% For Case 2, the iTO event of the push-off prosthesis and well outside the shaded boundary region on the iTO limb for both amputees was slightly earlier compared to event of control subjects. Also notable was that the cHS event controls, but within the control iTO boundary. The cHS event of the amputees’ colliding intact limb, in prosthesis for the colliding prosthesis limb, in intact limb “cycle time,” was also delayed compared to controls. Although a smaller “cycle time,” occurred approximately 3-5% earlier in the departure, for one amputee (Mauch) the cHS event fell out- cycle, consistent with a faster swing phase to compensate side the shaded boundary on the cHS region for controls, for the longer stance duration. Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Gravity power (W/kg) Impulse power (W/kg) Applied Bionics and Biomechanics 11 Amputee with C-Leg prosthesis Push-off = intact limb (blue) ; Collision = prosthesis limb (red) Case 1 8 4 iTO cHS cHS cHS 0 2 iTO ‒2 0 iTO ‒2 ‒2 ‒4 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Case 2 Push-off = prosthesis (red) ; Collision = intact limb (blue) 8 4 4 cHS iTO cHS iTO cHS iTO 4 0 2 ‒2 ‒2 0 ‒4 ‒2 ‒6 ‒4 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle % gait cycle (a) Amputee with C-Leg prosthesis Amputee with Mauch prosthesis Case 1 Push-off = intact limb (green) ; Collision = prosthesis limb (orange) 8 2 8 cHS cHS cHS iTO 6 6 4 0 4 iTO 2 2 ‒1 iTO 0 ‒2 0 ‒2 ‒3 ‒2 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 Case 2 Push-off = prosthesis limb (orange) ; Collision = intact limb (green) 8 2 4 cHS iTO cHS iTO cHS iTO 6 1 4 0 ‒1 ‒2 0 ‒2 ‒2 ‒4 ‒3 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 30 35 40 45 50 55 60 65 70 75 % gait cycle % gait cycle % gait cycle (b) Amputee with Mauch prosthesis Figure 5: Internal joint work rate (power) during the double support phase of the gait cycle. Data are shown for amputee with C-Leg nd prosthesis (a) and amputee with Mauch prosthesis (b). The first column of plots shows ankle power, the 2 column shows knee power, rd and the 3 column shows hip power. For each amputee, the first row shows Case 1 where the intact limb is the push-off limb (blue) and Case 2 where the push-off limb is the prosthesis (red line). The mean for control subjects (N =14) is shown by dark solid lines with shaded boundaries that represent ±1 standard deviation from the mean at each % cycle. Vertical solid lines represent toe-off time of the ipsilateral limb, and the dashed vertical lines represent heel strike of the contralateral limb, and the shaded boundaries represent ±1 standard deviation in event time. The horizontal axis shows the 30-80% gait cycle. These event departures reflect that the primary conse- to accommodate the asymmetry in stance duration. The quence of motor adaptations to the prosthesis have resulted first column of plots showing the interlimb work rate of in a stepping asymmetry characterized by increased stance gravity on the CoM reveals a relatively normal pattern duration (and reduced swing time) of the intact side of for both amputees when their prosthetic limb was the amputee participants, while maintaining (relative to con- push-off limb (Case 2). When the push-off limb was trols) normal phase parameters of the prosthesis side. the intact limb, however, the work rate of gravity was delayed for the intact side (Case 1). This effect was pres- ent for both amputees but more noticeable for the Mauch 4.2. Compensatory Biomechanics Knee user. 4.2.1. External Work on CoM. Plots for the C-Leg user Most revealing were the observed differences between (Figure 4(a)) and Mauch user (Figure 4(b)) identify how amputees and control subjects in the pattern of interlimb the energy transfer from the legs to and from the CoM is able impulse work rate on the CoM. These characteristics were Ankle power (W/kg) Ankle power (W/kg) Ankle power (W/kg) Ankle power (W/kg) Knee power (W/kg) Knee power (W/kg) Knee power (W/kg) Knee power (W/kg) Hip power (W/kg) Hip power (W/kg) Hip power (W/kg) Hip power (W/kg) 12 Applied Bionics and Biomechanics between the 40 and 45% cycle that preceded the intact limb’s consistent for both the C-Leg and Mauch user at all three gait speeds (see also Figure S3 ). heel strike (cHS). For Case 1, when the intact limb (blue line) was the push-off limb, the lengthened stance (delayed iTO) appeared 4.3. A Mechanistic Hypothesis for Stepping Asymmetry. Over- to accommodate the slow development of negative work on all, Figures 4 and 5 demonstrate the similarity in asymmet- the colliding prosthetic limb (red line). Indeed, the negative ric stepping patterns of the intact and prosthetic limbs of work rate of the prosthesis side following cHS was consider- the two amputees. Although the two amputees used very ably lower than for controls, but nevertheless the transfer of different prostheses (both knee and foot components), they energy from the intact to prosthesis side maintained its prin- both appeared to adapt to their prosthesis in the same way. ciple form. Waveforms for normal speed and slow speed walking For Case 2, when the prosthesis limb (red line) was the showed the same asymmetry patterns (also see Figure S3), push-off limb, the impulse power generated by the prosthesis indicating that the stepping asymmetry observed was not side at push-off was, as expected, significantly lower than for a function of speed. controls, although the iTO event for the prosthesis limb was These findings suggest that transfemoral amputees mod- the same as for control subjects. For the colliding intact limb ify both heel strike time (in prosthesis side cycle time) and (blue line), the earlier cHS event appeared to enable a brief toe-off time (in intact limb cycle time) to enable the stance positive power region that was not present for controls. In phase to be lengthened and the swing phase to be shortened. other words, the colliding intact limb was carrying out a pos- The shorter swing phase of the intact limb was timed to col- itive power task prior to taking on its role to accept energy lide earlier relative to the prosthesis limbs’ cycle to enable a from the transferring push-off limb. This appears to compen- transfer of positive power to the CoM prior to the prosthesis sate in part for the reduced positive work of the push-off side push-off, while extending intact limb stance duration to limb, by accelerating the CoM with the intact leg just after compensate for collision work deficiency of the prosthesis. heel strike, which is timed earlier to allow for the “normal” The data suggest that the intact knee joint plays a pivotal role transfer of weight support. in this process. For the two amputees we observed, their prosthetic limb While the hip of the intact limb was clearly compensating did little to contribute to impulse work during push-off and for power generation at push-off, the role of the hip earlier in collision. The weak collision of the prosthesis limb was com- the gait cycle was not as clear from the data. Of particular pensated by extending stance duration of the intact limb. interest though was the substantial negative work done by Then, during the weak push-off of the prosthesis limb, the the hip of the prosthesis limb in late stance. This characteris- intact side compensated by adding positive power prior to tic has been reported for amputees [13, 35, 36] and has also push-off of the prosthesis limb. We now examine the poten- been observed in seniors with disability [37] and may be a tial sources for these compensations. mechanism for transferring energy to the upper body [38], which for the amputee would otherwise be wasted by the 4.2.2. Internal Work of Joints. Joint power plots for the C-Leg prosthesis’ inability to return that energy. user (Figure 5(a)) and Mauch user (Figure 5(b)) identify the internal sources that explain the above compensations. For Case 1 (intact limb is push-off limb) of both amputees, the 4.4. Limitations. There are several notable limitations of the ankle plantar-flexion power burst at push-off (blue line) study. Most significant was having only two participants with was the same as for control subjects, just delayed in cycle limb amputation. Furthermore, the degree of stepping asym- time. Also delayed was the late stance negative power region metry was similar but not identical for the two amputees, of the intact knee (blue line) that followed a significant posi- which is probably related to individual differences and those tive power region in the earlier portion of stance phase, as related to their specific prosthesis. However, in the context of seen at the lower boundary (30% cycle) of the knee power the study’s objective, and with the very good agreement with plots for Case 1. Additionally, the peak positive and negative past literature, we feel our conclusions are well supported. powers for the hip of the intact limb (blue line) were delayed Larger studies examining these effects over time, from first and had greater peak magnitudes than in control subjects. fitting to long-term follow-up, will likely be more informative Power profiles of the colliding prosthesis limb show no effec- than studies with large N. Nevertheless, these studies will be tive response at the knee, and possibly higher hip power of required to definitively answer the question if neural reorga- the prosthesis limb following heel strike, although this was nization is responsible for these adaptations and to what end. not consistent for the two amputees. A more significant limitation may be in generalizability For Case 2 (prosthesis limb is push-off limb) of both of the results to the above-knee amputee population, given amputees, the timing of the artificial ankle/foot power burst that both participants had had through-knee disarticulation was similar to controls but the magnitude was significantly amputations, which results in a long residual limb and causes attenuated. The compensatory function of the intact knee the prosthesis knee axis to be more distal than the intact knee (blue line) of the colliding limb, however, is clearly evident, axis. Although this geometric asymmetry could play a role, in particular the spike in positive knee power just following studies examining residual limb length effects on amputee heel strike, when normally the knee would be dissipating gait generally show little, if any, difference in the biomechan- power at load acceptance. For the hips, the push-off prosthe- ics of gait for longer versus shorter residual limbs [11, 16]. sis limb (red line) had a significant negative power region However, we are not able to analyze this effect with our Applied Bionics and Biomechanics 13 above-knee prosthesis to do the required positive work dur- current data. Future studies should include individuals with different levels of amputation. ing push-off and negative work during collision. Another limitation is how we controlled gait speed. Our data are supported by most, if not all, of the prior Although there is an argument for using a treadmill to ensure studies that show increased concentric energy expenditure experimental control of gait speed, we opted for the more of the intact knee in stance phase [35], increased concentric ecologically realistic condition of over-ground walking. energy expenditure of both the intact and prosthesis side hips While pace control can still be implemented with over- [7, 13, 35], and increased negative work of the prosthetic side ground walking (e.g., using a metronome), we instead chose hip in late stance [13]. However, our analysis goes beyond to use a set of verbal instructions (i.e., “walk as if…”) that these studies by identifying the connection between these would be contextually understood for each of the three compensations and the adapted heel strike and toe-off events self-selected speeds. Given that we observed the same adapta- of the intact limb. tions and compensations in both amputees at all three self- The extended stance duration of the intact limb has been selected gait speeds, suggests that using self-selected speeds suggested as a strategy to increase the impulse of the intact may be more of a strength than a weakness. Had we con- limb on the CoM [16, 18], which indeed may be a conse- trolled speeds artificially, it could be argued that the compen- quence, but our data suggest that the motor program of the sations observed were specificto “non-self-selected” speeds intact leg is purposefully delayed to allow two key compensa- and thus less valuable clinically. tions to occur: (1) a brief period of positive work added by the Finally, our model was not complete. Firstly, we neglected intact limb following its collision, to supplement the weak push-off of the prosthesis limb, which allows (2) the more any external work due to the force couple on the CoM caused by a translating centre of pressure. Mathematically, this is robust push-off leg to time its delivery to minimize the influ- equivalent to a slipping contact, but its contribution to exter- ence of the deficient collision work of the prosthesis limb. nal work during walking has been traditionally neglected (c.f. Based on the data, we suspect that physical interventions [28, 31, 39–41]). Future studies might evaluate the validity of attempting to reestablish “normality” of the intact leg’s stance and swing duration, without improvements to the this assumption. We also used crude estimates of the mass of the amputee’s residual thigh; sensitivity analyses in future prosthesis, could result in less safe walking. Our data, though modelling efforts will be required. Also, we did not examine limited, suggests that the solution is to focus efforts on better the power flow to and from the upper body. The highly defi- push-off and collision control of the prosthesis. cient negative work of the prosthesis limb on the CoM sug- gests that internal work of the musculoskeletal system is Data Availability managing a more complex behavior at and above the hips The data used to support the findings of this study are avail- that warrants future attention. able from the corresponding author upon request. Conflicts of Interest 5. Conclusions The authors have no competing interests to declare. Our study supports the notion that stepping asymmetry in users of artificial limbs is an adaptation to increase function- Acknowledgments ality and safety of their gait, which has been observed both in gait re-education programs [42] and in model simulations The project was funded by the Canadian Institutes of Health [17]. Despite using very different prostheses, the two ampu- Research, Regional Partner Program, and New Brunswick tees demonstrated very symmetric stride characteristics Health Research Foundation. The authors acknowledge the (stride length and speed), and the stance/swing duration of support of staff and students of the Institute of Biomedical the prosthesis limb was more similar to control subjects than Engineering and the Andrew and Marjorie McCain Human the amputee’s intact side. This may reflect that they were > 5 Performance Laboratory. We also thank our participants years since starting to use their current prosthesis and thus for their contribution to this scholarly work. had “fined-tuned” their gait to maximize symmetry of speed (stride time and distance). Supplementary Materials The asymmetry in stance duration was characterized by significant alteration of intact limb heel strike and toe-off Supplementary 1. S1: motion analysis marker descriptions. events, all the while a near normal stance/swing phase for Table S1 contains detailed information about body marker the prosthesis limb was being achieved. This may be a con- locations used for control subjects and amputee participants. straint induced by the advanced control mechanisms of the two devices (the C-Leg and Mauch knees provide both stance Supplementary 2. S2: joint kinematics and kinetics. Graphs and swing phase control), which were intelligent enough to shown in the manuscript are limited to double-support phase enforce a relatively normal periodicity upon the prosthesis (30%-80% gait) of fast gait. For the reader to see the whole limb (i.e., ~60% stance and ~40% swing). gait cycle for all three gait speeds, we include the following Although a rationale design feature, the data from the supplements for walking trials at slow, preferred, and fast present study and past studies would suggest that this speed, from 0 to 100% gait cycle (heel strike to heel strike). enforcement does not overcome the deficiency of the Figure S2.1 contains joint angles and moments for healthy 14 Applied Bionics and Biomechanics controls with data for two amputees (C-Leg user and Mauch extremity amputees,” Archives of Physical Medicine and Reha- bilitation, vol. 82, no. 8, pp. 1031–1037, 2001. user) superimposed. Figure S2.2 contains joint and segment powers for healthy controls with data for two amputees [11] P. A. Struyf, C. M. van Heugten, M. W. Hitters, and R. J. Smeets, “The prevalence of osteoarthritis of the intact hip (C-Leg user and Mauch user) superimposed. and knee among traumatic leg amputees,” Archives of Phys- Supplementary 3. S3: external and internal work rate. ical Medicine and Rehabilitation, vol. 90, no. 3, pp. 440–446, These graphs show results for the 0-100% gait cycle for the intact limb and for the prosthetic limb, at each of [12] T. Schoppen, A. Boonstra, J. W. Groothoff, J. de Vries, L. N. the three speeds, for each of the two amputees. Figure Goeken, and W. H. Eisma, “Physical, mental, and social pre- S3.1 contains external work rate (gravity and impulse) dictors of functional outcome in unilateral lower-limb ampu- for healthy controls with data for two amputees (C-Leg tees,” Archives of Physical Medicine and Rehabilitation, user and Mauch user) superimposed. Figure S3.2 contains vol. 84, no. 6, pp. 803–811, 2003. internal work rate (ankle, knee, and hip) for healthy con- [13] R. E. Seroussi, A. Gitter, J. M. 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