Chapter 3 Mechanical energy utilization of ankle push-off in young adults
3.6 Discussion
At the instant of ankle peak power generation, our energy flow diagram showed
that the ankle power was an important source of power for the motion of the ipsilateral
leg. The ankle power supplied most of the energy required by the foot (0.13±0.04
W/kg) in the form of the rotational energy flow since another energy inflow from the
ground was relatively small (0.01±0.03 W/kg) (Figure 3-1). We also found that the
ankle power transformed into translational energy flow (6.72±0.96 W/kg) at the ankle
joint, and such translational energy flow was the sole energy inflow to supply the energy
required for the motion of the shank (Figure 3-1). As for the thigh, the hip-induced
rotational energy flow (1.29±0.24 W/kg) and the translational energy flow (0.27±0.51
W/kg) from the shank were both energy sources (Figure 3-1). Our study gives a
clinical application on how to use the energy flow diagram with the proposed
convention to link joint energetics to segment energetics so that the movement strategy
can be further explained. Since most of the ankle power supplies energy to ipsilateral
foot, shank, and thigh, it can be readily inferred that the ankle power generated during
push-off mainly propels the trailing leg forward as it transitions from stance to swing
phase.
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The purpose of examining pelvic energetics was to assess the role played by ankle
power on forward propulsion. Based on the kinematics, we calculated that the
mechanical energy of the pelvis decreased (0.42±0.24 W/kg) at the moment of peak
ankle power (Figure 3-1), and such decrease was largely determined by a decrease in
kinetic energy (Figure 3-3e), indicating that the upper body is decelerating during
push-off. Furthermore, we found that the trailing leg only performed positive work on the
pelvis for less than half of the push-off period (Figure 3-2) and the net work performed
by the trailing leg on the pelvis during the push off period was negative. The positive
power supplied by the trailing leg was not enough to prevent the mechanical energy of
the pelvis from decreasing during push-off (Figure 3-3a). The positive work
performed by the trailing leg may mitigate some of the energy lost during double-limb
support, but such does not contribute to a net increase in kinetic energy which is often
associated with forward propulsion. Based on the distribution of power throughout
the trailing leg and the relatively small amount of energy transferred to the pelvis, it
implies that the primary role of ankle during push-off is to propel the trailing leg
forward rather than deliver substantial propulsive energy to the pelvis.
Our study analyzed the utilization of ankle power generated during push-off by
illustrating energy flow diagram in a new symbolic convention that combines core
mechanical energetic elements together. Another schematic energy flow diagram was
used previously [1]; however, the choice of symbols and the close proximity of the
different symbols as well as numbers made identifying the different quantities and the
direction of rotational energy flow difficult. The regular structure of our diagram
eliminates such confusion; our symbolic convention clearly and readily shows where
energy is increasing, where it is transferred to, and where it is generated or absorbed.
Our symbolic convention in the diagram facilitates the conceptualization of mechanical
energy transfer between body segments as water flowing through a system of pipes,
storage tanks, and pumps. Such comparison allows readers use their understanding of
a more familiar system and fluid flow to intuit energy transfer within the body. In
addition, it eases the interpretation of energy flow analysis, especially when comparing
energy flow characteristics of different movements or subject groups. Comparing
energy flow patterns of various gait events between the able-bodied and patients with
neuromuscular disorders would require numerous energy flow diagrams lining up
together in order to discern the movement strategy. We expect that the symbolic
convention in the energy flow diagram can give a more succinct and standardized
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representation than the previous diagram.
Another benefit of the symbolic convention in the energy flow diagram compared
to alternative energy analysis techniques [18, 48] is the ability to show where and how
energy has been transmitted during a movement, especially for the energy flow across
adjacent segments. Thus, current techniques allow us to better explore the role of
ankle during push-off in relation to other segments to be analyzed. For example, the
ankle power generated during push-off can be tracked to demonstrate the power
utilization shown in the energy flow diagram, which provides evidences to support
previous studies that suggested the role of the ankle during push-off primarily
contributes to the initiation of swing [16–19]. A previous study also yielded similar
results in the push-off period which claimed that the power was generated at the hip
and the ankle, absorbed at the knee, and very little was transferred to the trunk [1].
However, the joint power magnitudes of the knee and the hip from the previous study
[1] were much smaller than those of this study partly since the previous study performed
the analysis at some point in late push off, while our analysis was carried out at peak
ankle power generation. Differences in equipment may also account for the
discrepancy, as the contemporary digital 3D motion capture used in this study is more
precise than the hand digitizing of markers from cine film, which was used in the
previous study [1]. Differences are also attributed to the fact that our research took
the energy dissipated in foot deformation into account. Our reported values of joint
power compare better with those from a more recent investigation [5] than those from
the previous study [1].
Several limitations of this research should be addressed in the future.
Calculations of joint center velocity differ slightly between proximal and distal
segments, which results in a discrepancy in the translational energy flow between those
segments. The only discrepancy with significant figures was a 0.27 W/kg difference
in the translational energy flow between the proximal shank and the distal thigh.
Nevertheless, this discrepancy does not affect our findings since the direction of the
translational energy flow from the shank to the thigh is consistent between the proximal
shank and distal thigh. Therefore, in order to simplify the diagram, we only show the
translational energy flow values calculated from the proximal end of the segments.
Regardless of the source of such energy flow discrepancy is from the physical
translation within the joint or the limitations of rigid body assumptions [49], a more
recent study has found that taking account of the energy flow discrepancy can better
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capture energy changes of the body [48].
Another limitation of this study is that only the energy flow of trailing leg was
presented. Nevertheless, ignoring the energy flow of the leading leg does not affect
our results on the pelvis energetics even if the leading leg transmits energy to the pelvis
during push-off due to the fact that we calculate the mechanical energy of the pelvis by
pelvis kinematics only. In addition, the validity of the energy flow analysis has to be
rigorously checked before applying to other areas such as sports or rehabilitation
medicine, given our analysis was performed on the basis of limited number of healthy
subjects. In order to give a more comprehensive example of applying our new
symbolic convention, a future work of the whole body energy flow diagram at different
gait phases is warranted.
Chapter 4
Comparisons of swing energy flow characteristics between the young adults and the elders
Ten healthy elderly (mean age: 68.1±6.4 years; 5 females and 5 males) who could
walk without any assistance or aids, and ten healthy young adults (mean age: 25.1±1.6
years; 2 females and 8 males) participated in this study. For both subject groups, the
fast walking speed (1.77±0.15 m/s for the young adults, and 1.56±0.20 m/s for the
elderly) was significantly faster (p<0.05) than the self-selected walking speed (1.15±
0.24 m/s for the young adults, and 1.11±0.18 m/s for the elderly). The young adults
walked significantly faster (p=0.012) than the elderly at the fast walking speed, while
not at the self-selected walking speed.
4.1 Mean profiles of the energy flow data in swing phase
Mean profiles of all subjects in terms of the energy flow data of the entire lower
extremity during the whole swing phase was shown in Figure 4-1, including the energy
flow profiles of the thigh in the four conditions as the young adults at the self-selected
walking speed (Figure 4-1a) and at the fast walking speed (Figure 4-2b) as well as the
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elderly at the self-selected walking speed (Figure 4-1c) and at the fast walking speed
(Figure 4-1d), the energy flow profiles of the shank (Figure 4-1e-1h), and those of the
foot (Figure 4-1i-1l). In general, the fluctuation trends of the eleven energy flow
elements along the swing phase were analogous in all the four conditions.
Nevertheless, it was noted that there were great energy fluctuation and great variations
among the subjects especially in the elderly at the fast walking speed.
As a representative pattern in the condition of the young adults at the self-selected
walking, the early stage of the swing phase showed a negative pelvis distal flow,
positive hip power, positive thigh proximal flow, and positive thigh energy change rate
(Figure 4-1a). In addition, there were negative thigh distal flow, insignificant knee
power, positive shank proximal flow, and positive shank energy change rate (Figure
4-1e). There were also negative shank distal flow and positive foot proximal flow
(Figure 4-1i). During the late stage of the swing phase, only the pelvis distal flow,
thigh distal flow, and shank distal flow were positive. The rest of the energy flow
elements were all negative. The magnitude of ankle power was especially close to
zero during the entire swing phase.
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Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Young, Fast
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Young, Fast
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Elder, Fast
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Elder, Fast
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Young, Self-selected
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Young, Self-selected
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Young, Self-selected
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Elder, Self-selected
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Elder, Self-selected
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Elder, Self-selected
Shank Distal Flow Ankle Power Foot Proximal Flow
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Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Young, Fast
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Young, Fast
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Elder, Fast
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Elder, Fast
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Elder, Fast
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Young, Self-selected
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Young, Self-selected
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Young, Self-selected
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Elder, Self-selected
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Elder, Self-selected
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Elder, Self-selected
Shank Distal Flow Ankle Power Foot Proximal Flow
(a)
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Young, Fast
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Young, Fast
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Elder, Fast
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Elder, Fast
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%)
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Young, Self-selected
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Young, Self-selected
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Young, Self-selected
Shank Distal Flow Ankle Power Foot Proximal Flow
W/kg
Swing phase (%) Elder, Self-selected
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy Change Rate
W/kg
Swing phase (%) Elder, Self-selected
Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy Change Rate
W/kg
Swing phase (%) Elder, Self-selected
Shank Distal Flow Ankle Power Foot Proximal Flow
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Figure 4-1 Mean energy flows throughout the whole swing phase in the young adults
and the elderly at the self-selected and fast walking speeds. Positive segmental
proximal/distal flow represents that the energy flows into the corresponding segment.
Positive joint power represents power generation.
4.2 Factor analysis on energy flow mean profiles in swing phase
The complete correlation matrix of the energy flow elements covaried with each
other was shown in Table 4-1. Notably, the correlation coefficients of ankle power
were mostly smaller than 0.1 that could hardly influence the energy flow of the adjacent
segments and joints. The ankle power was accordingly excluded in the subsequent
analysis. By applying the factor analysis technique, the 1st and 2nd factors were
extracted from the correlation matrix since they could explain totally over 90% variance
in all conditions (Table 4-2). Table 4-3 showed the loadings of all energy flow
elements in the extracted 1st and 2nd factors with the signs of the loadings determine the
direction of the energy flow (flowing in or flowing out). The significant loadings and
the signs of the loadings in the 1st/2nd factor were analogous under the conditions in the
young adults at the self-selected and fast walking speeds as well as the elderly at the
self-selected walking speeds. Thus the energy flow patterns for those three conditions
corresponding to the 1st and 2nd factors were summarized as the following two kinds of
representative energy flow characteristics. Notably, the significance and sign of the
energy flow elements of the elderly at the fast speed were totally opposite to the two
representative patterns.
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Explained variance of extracted 1st and 2nd factors of the energy flow data in the young adults and the elderly.
Young Adults Elderly
Factor Self-Selected Fast Self-Selected Fast
1st Factor 57% 60% 50% 62%
2nd Factor 36% 35% 46% 33%
Total 93% 95% 96% 95%
Table 4-1
Correlation coefficient matrix of the eleven energy flow elements.
Pelvis Distal Flow Hip Power Thigh Proximal Flow Thigh Energy
Change Rate Thigh Distal Flow Knee Power Shank Proximal Flow Shank Energy
Change Rate Shank Distal Flow Ankle Power Foot Proximal Flow
Pelvis Distal Flow - -0.764 -0.987 -0.699 0.970 -0.837 -0.983 -0.987 0.965 0.039 -0.952
-* Correlation coefficients with poor significance (< 0.1).
Table 4-3
Loadings of energy flow elements in extracted factors for the young adults and elderly during the swing phase at the self-selected and fast walking speeds.
Young Adults Elderly
Self-Selected Fast Self-Selected Fast
Energy Flow 1st
* Significant absolute loading (> 0.8); § Highest loading in each column.
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4.3 Swing energy flow characteristics shown in simplified energy flow diagram
The first representative energy flow characteristics could be patterned in terms of
the 1st factor, which was with highest loading at the knee power, with most significant
loadings below the knee joint, and insignificant hip power and thigh energy change rate
(Table 4-3). This characteristic accordingly showed a knee-dominated pattern. It
was noted that the signs of the energy flow elements in this pattern perfectly agreed
with the signs of the energy flow profiles during the late stage of the swing phase as
shown in Figure 4-1. Thus, the knee-dominated pattern represents the energy flow
characteristic of swing deceleration. It could be illustrated as an upward energy
transfer since there was a substantial amount of energy flowing from the foot all the
way up to the pelvis and the segmental energy change rates decreased together with the
knee power absorption. The second energy flow characteristic could be found in the
2nd factor with highest loading at the hip energy flow and most significant loadings
above the knee joint. Since the signs of the energy flow elements of this
hip-dominated pattern agreed with the signs of the energy flow profiles during the early
stage of the swing, this pattern shows the energy flow characteristic of swing
acceleration. It can also be depicted as a downward energy transfer for the segmental
energy change rates increased together with the hip power generation (Figure 4-2a-2c).
Following the same process to reveal the energy flow pattern of the elderly during the
fast walking, different patterns were observed that the 1st factor oppositely corresponds
to swing acceleration with the signs of the loadings agreed with those in the 2nd factor
of the representative energy flow, and that the 2nd factor of the elderly during the fast
walking corresponds to swing deceleration. In addition, the high-loading energy flow
elements in this condition were especially above the knee during the swing acceleration,
and there was a centered pattern exclusively at the knee power during the swing
deceleration (Figure 4-2d).
Condition Swing Acceleration Swing Deceleration
(a) Young adults,
Self-selected
Hip Power
Shank Distal Flow Shank Proximal Flow
Foot Proximal Flow
Knee Power
Shank Energy
(-)
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Figure 4-2 Energy flow patterns corresponding to the swing acceleration and swing deceleration in the young adults and the elderly at the self-selected and fast walking
speeds.
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4.4 Discussion
This study demonstrated a systematic approach to extract the energy flow
characteristics of the swing leg in the young adults and elderly. The major findings
were: 1) the energy flows of the swing leg showed different patterns between the early
swing and the late swing with negligible ankle power; 2) the young adults showed
similar energy flow characteristics of the swing leg for both fast and self-selected
walking speeds, while the elderly showed an especially opposite energy flow pattern at
the fast walking speed; and 3) the hip power and the knee power mainly correspond to
the swing acceleration and deceleration, respectively. Our work demonstrated a
valuable analytic scheme to explore the changes of the gait characteristics and
potentially the mechanisms of the tripping risk in elderly.
potentially the mechanisms of the tripping risk in elderly.