Step-to-step transitions
First we will consider the transition where the NPL was leading which is the second transition (T2) in Figures
1,
2,
3 and
4(B, D) and can be compared to the second transition (T2) in Figures
1,
2,
3 and
4(A, C). Our first hypothesis was that the PL would produce less push-off
\( {\overline{P}}^{+} \) than an unimpaired control limb in these transitions. This was assessed by comparing the
\( {\overline{P}}^{+} \) provided by each limb during transitions when it was the trailing limb (e.g. Figure
1C - T2, positive white bar for the PL). Our results did not support the hypothesis as the PL did not provide significantly less
\( {\overline{P}}^{+} \) than control limbs when trailing in a transition (Figure
1 - T2). This was despite peak instantaneous power during those transitions being less for the PL (PL = 0.46 W⋅kg
−1, NPL = 1.01 W⋅kg
−1, C = 1.19 W⋅kg
−1,
F(2,23) = 4.5,
p <0.001) and indicated a more prolonged, lower magnitude period of push-off by the PL as can be observed in Figure
1. Given that our first hypothesis was not supported, it is unsurprising that our second hypothesis was also not supported by our data. We predicted that the anticipated reduction in PL push-off
\( {\overline{P}}^{+} \) would lead to increased negative collision
\( {\overline{P}}^{-} \) by the NPL in the same transition. The
\( {\overline{P}}^{-} \) of the NPL in transitions when it was leading was not significantly different from
\( {\overline{P}}^{-} \) done by control limbs when leading (Figure
1C and D - T2, negative dark bars).
Despite the magnitudes of push-off and collision average power not being significantly different between H and C during T2, the ILM power curves were markedly different from those of the unimpaired controls (Figure
1A-B). For C, the trailing left limb did positive push-off work at the same time as the leading right limb did negative collision work and this occurred over the majority of the transition (Figure
1A -T2). This serves to redirect the centre of mass so it can begin the next inverted pendulum phase, as has been described for healthy gait previously [
6]. For H transitions when the NPL was leading, there was only a brief period (≈5% of a stride) when the two limbs were producing opposing powers (Figure
1B - T2). At the beginning of this transition, both limbs were generating negative COM power before the brief period when the PL provides positive power and the NPL provides negative power. The latter half of this transition involved both PL and NPL generating positive COM power (Figure
1B -T2). It was during this latter part of the transition where significant differences from controls were observed in terms of average powers. The leading NPL for H provided significantly (
F(2,23) = 4.7,
p = 0.009) more
\( {\overline{P}}^{+} \) during these transitions than the leading limb for C, that was predominantly providing negative collision work (Figure
1). Interestingly, this corresponded with greater
\( {\overline{P}}^{+} \) at the leading non-paretic hip (
F(2,23) = 3.51,
p = 0.003) and knee (
F(2,23) = 3.11,
p = 0.05) for H than at the leading hip and knee for C (Figures
3 and
4). Therefore it seems that H used a different temporal sequencing of limb and joint power production than C.
To interpret the effects of the altered temporal sequencing, we may gain some insight from a simple model of walking. Kuo [
22] presented a passive dynamic walking model [
3] with the ability to apply a trailing limb toe-off impulse just prior to heel strike or a leading limb hip torque after collision. Either could be used to redirect the centre of mass velocity in the transition between steps. Kuo [
22] observed that the overall mechanical work required per step was four times greater when the pre-emptive push-off impulse was not used and hip torque following collision was relied upon to redirect the COM. In this simple model the collision occurs instantaneously and the only source of work after the collision was a hip torque. Neither of these assumptions has to be true for human gait but the model does illustrate that if push-off work is not initiated prior to or at heel strike, the positive work required to maintain walking speed must be done later in the step and is larger in magnitude. Similarly, Soo and Donelan [
5] showed experimentally that deviating from preferred coordination in transitions can increase the mechanical work requirements of movement. This is relevant to the transition described above for H (where NPL is leading -T2) and might explain the need for additional
\( {\overline{P}}^{+} \) at the non-paretic hip and knee in these transitions. Figure
1B shows that, for a transition with the NPL leading, the push-off work from the PL was not initiated until 7 ± 2.0% of a stride after the NPL heel strike. This was significantly (
F(2,23) = 3.4,
p = 0.02) later after heel strike than for the control limb that initiated push-off almost at heel strike (1 ± 2.7%, Figure
1A). Also, the H group incurred a greater overall average positive power demand in the step starting with this transition than the C group did during a step (H = 0.17 W⋅kg
−1, C = 0.135 W⋅kg
−1,
F(2,23) = 3.2,
P = 0.04). This additional work came from significantly greater (compared to control) average powers generated at the knee and hip in the NPL and the hip in the PL in the transition (Figures
3 and
4 -T2). Additional
\( {\overline{P}}^{+} \) was also generated at the non-paretic knee after the transition was completed (Figure
3B,D). Our third hypothesis was that the non-paretic hip would provide additional
\( {\overline{P}}^{+} \) to meet the added work demands of this step (beginning with T2). This was supported but the non-paretic knee and the paretic hip also contributed to the additional work requirement in this step for H (Figures
3 and
4).
No hypotheses were made regarding the transition in which the PL was leading (the first transition, T1, in Figures
1,
2,
3 and
4) because it was expected that the NPL would be capable of providing push-off power comparable to healthy limbs. Indeed, the non-paretic trailing limb was capable and actually provided significantly greater
\( {\overline{P}}^{+} \) than control trailing limbs during the transition (Figure
1 - T1). This
\( {\overline{P}}^{+} \) increase was mostly owing to increases in hip average positive power in the NPL at this time (Figure
4). The reason for this additional positive work seems to have been to counteract a larger amount of collision
\( {\overline{P}}^{-} \) that was simultaneously being provided by the hip and ankle joints of the paretic leading limb, compared to control leading limbs (Figures
2 and
4). Based on the current data we were unable to provide an explanation for increased simultaneous positive and negative average power during this transition compared to C. Step length was not different and the timing of push-off was near optimal for the NPL (2.0 ± 4.9% after heel-strike). Stroke survivors commonly display impaired motor control [
23] in addition to muscle weakness [
8] and so perhaps the explanation is related to poor control of the movement. Thus the greater collision work might represent a limited ability to stabilize the leading PL against gravity during weight acceptance and the additional NPL positive work was a pre-emptive compensation, but this is speculation. Regardless of the reasoning, this large collision contributes to the overall increase in positive mechanical work required by H.
Distribution of positive work
As was expected from previous reports [
10,
14] of the external work requirements of hemiparetic gait, total
\( {\overline{P}}^{+} \) was greater for H than C. This increased demand was met by greater
\( {\overline{P}}^{+} \) from the NPL compared to the CL (Table
2). The PL provided similar
\( {\overline{P}}^{+} \) to the CL (Table
2). These findings were independent of what method (ILM or JPM) was used to quantify total
\( {\overline{P}}^{+} \). Summing joint average powers will show large discrepancies in absolute total
\( {\overline{P}}^{+} \) values compared to the ILM. This is to be expected as cancellations of work occur internally within the limb when two joints do simultaneous opposing work, leading to the ILM underestimating total
\( {\overline{P}}^{+} \) [
16]. This section will focus on the values determined via the JPM.
Our third and fourth hypotheses both predicted that the increased total positive work demand for H would be met by an increase in non-paretic hip work compared to C. As one might anticipate from the prior description of transition work, hip
\( {\overline{P}}^{+} \) was greater for the NPL than both the PL and CL (Table
2). This led to the non-paretic hip being responsible for 49% of the
\( {\overline{P}}^{+} \) provided by the NPL compared to 39% for C hips (Figure
5). The PL also relied on the hip joint
\( {\overline{P}}^{+} \) generation more than CL (47% vs. 39%, Figure
5). Therefore, in addition to H having to generate greater overall
\( {\overline{P}}^{+} \), they also redistributed
\( {\overline{P}}^{+} \) among joints to rely more on the hip than C. This agrees well with previous inverse dynamics-based studies of imposed ankle immobility during walking in healthy controls [
5,
24] and hemiparetic post-stroke gait [
8]. This supported the rationale for our final hypothesis regarding efficiency of positive mechanical work.
Efficiency of positive work
Metabolic power was 52% greater for hemiparetic individuals than it was for the unimpaired controls. This was to be expected given that total
\( \left({\overline{P}}^{+}\right) \) was significantly greater (Table
1). In our fourth hypothesis we proposed that the metabolic power increase for H would be greater than that expected from the increased mechanical work alone. This was rationalised by the theory that the shift to greater reliance on the hip for mechanical power would make locomotion less efficient [
13]. This prediction was not supported by the efficiency data that showed no significant difference in efficiency of positive work between H and C. On a cautionary note, the efficiency data had low statistical power and therefore we cannot with complete certainty reject the hypothesis. If the present result does hold true for a larger population, one plausible explanation for this is that slow walking is not very efficient for the C group. Walking at 0.75 ms
−1 is less efficient than walking at faster, more optimal speeds for unimpaired humans (0.26 vs. 0.34 [
11]). In this study the hypothesised decrease in efficiency was proposed to be due to reliance on less efficient hip musculature more than on efficient ankle plantar-flexors. However, since the efficiency of control walking at 0.75 ms
−1 seems to be similar to what one would expect from hip muscle anyway [
13], the rationale based on distribution of work no longer holds for this speed. The matched-speed study design employed allowed this finding to be highlighted and showed that mechanics associated with post-stroke gait can increase the metabolic cost of locomotion without necessarily making individuals less efficient than unimpaired controls walking at the same speed.
Limitations
There were some limitations to our study design. First, the controls were not matched for age with the stroke survivors. Therefore we cannot conclusively reject the possibility that some differences between the two groups were related to effects of ageing. As has been observed by Franz and Kram [
25], older individuals exhibit reduced trailing limb push off work during level walking compared to younger controls and this is compensated for in single support later in the step. However, these authors also showed that total work over a gait cycle was not significantly different during level walking between old and young individuals and the older individuals utilised similar timing and trajectories for COM mechanics even though some magnitudes were different. In contrast, our key findings for the hemiparetic group were that they exhibited altered timing of push off and collision work; asymmetrical mechanics and a resulting increased overall rate of mechanical work in comparison to younger healthy controls. Furthermore, the older adults in Franz and Kram [
25] were notably older than the majority of our hemiparetic individuals (72 ± 5 vs. 58 ± 11 years) although there was one notable exception at 80 years of age (participant 6, Table
1) whose data may have been more affected by age than others. Therefore, although there is some potentially confounding effect of age, we maintain that our comparison highlights altered walking mechanics that result from hemiparesis that have not been observed as a result of aging. Furthermore, our findings related to efficiency and mechanical work done on the COM were consistent with previous comparisons of matched unimpaired post-stroke cycling and walking [
9,
26].
Another limitation was that we did not control the level of impairment of the stroke survivors included in the study beyond them needing to be able to walk unassisted on the treadmill at 0.75 m⋅s
−1. This may explain some of the large standard deviations observed for H. The study employed matched walking speed for the control group with the aim of examining the effects of altered mechanics, independent of speed. However, as noted previously, this forces the control group away from their most efficient and preferred walking speeds. Therefore, care should be taken not to extrapolate the findings to comparisons of walking mechanics and energetics for self-selected speeds between post-stroke and unimpaired walking. A final limitation was that sample sizes were small, especially for H. Results of a post-hoc statistical power analysis performed with G*Power software v3.1 [
27] are shown in Table
3. Overall, statistical power values were greater than 0.97 for most mechanical variables and metabolic power. However, for efficiency data power was low (0.54). Thus we cannot have complete confidence in rejecting the possibility that the hemiparetic group walked less efficiently than the controls in this study.
Table 3
Results of statistical power analysis from exemplar statistical tests
Metabolic Power | t-test | 5.26 | 1.00 |
Total \( \left({\overline{P}}^{+}\right) \) from JPM | t-test | 1.94 | 0.98 |
Efficiency from JPM | t-test | 0.87 | 0.54 |
Total \( \left({\overline{P}}^{+}\right) \) from ILM | t-test | 0.78 | 0.48 |
Efficiency from ILM | t-test | 0.89 | 0.56 |
Limb \( \left({\overline{P}}^{+}\right) \) from ILM | ANOVA | 0.87 | 0.97 |
Limb \( \left({\overline{P}}^{+}\right) \) from JPM | ANOVA | 1.1 | 0.99 |
Ankle \( \left({\overline{P}}^{+}\right) \)
| ANOVA | 2.02 | 1.00 |