Chapter 4 Comparisons of swing energy flow characteristics between the young
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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56 Table 4-2
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.
Energy flow analysis is a powerful tool to observe the energy transfer through
the segment compared to the traditional joint angle or joint moment analysis. In this
study, the representative energy flow pattern of the entire lower extremity clearly
visualize the difference of the energy transfer between the early phase and late phase of
the swing leg. During the early swing phase, the energy source to propel the lower
extremity could be composited of the negative pelvis distal flow (i.e. energy flowing
out of the distal pelvis) and the positive hip power (i.e. energy generation from the hip),
collectively transfer into the thigh and then the shank, with the trivial knee power
(Figure 4-1a). This downward energy was partially contributed by the thigh and shank
with positive thigh energy change rate and shank energy change rate (Figure 4-1e), and
the shank distal flow eventually become the energy source of the foot due to the
insignificant role of the ankle power (Figure 4-1i). During the late swing phase, which
is also known as the deceleration phase of the swing leg, substantial amount of the
stored energy in the whole swing leg required to be released by means of the negative
thigh, shank, and foot energy change rate and the released energy was primarily
absorbed by the knee joint, i.e. the negative knee power. Thus the energy flow
analysis could be used to reveal the transfer of the mechanical energy across multiple
segments and joints of a swing leg.
The energy flow model showed the merit to illustrate the changes of the
different sources of energy throughout the lower extremity based on the energy-time
plot. Nevertheless, it could only be noted that the elderly at the fast walking speed especially showed the great energy fluctuation and great individual variations upon the comparisons among the different conditions (e.g. the young adults and elderly at the
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self-selected or the fast walking speed) (Figure 4-1). In addition, there’s no clear definition of the time event in the swing phase of the gait for the dedicated comparisons among the conditions. Although researchers/clinicians usually acknowledge that the swing phase consists of the acceleration and deceleration stage, unlike the well-defined time events such as heel strike, heel off, and toe off during the stand phase, the definitions for the initial swing, mid-swing, and terminal swing stage are vague given that the swing limb is off the ground. The high-dimensional and temporal-dependent characteristics of the energy flow elements in different conditions still need a systematic method to be easily compared and comprehended.
The energy flow model utilized in previous studies mostly focused on analyzing
an instant gait event [50, 51]. The current study applied the factor analysis to reduce
the high-dimensional dataset and showed that the hip power and knee power typically
correspond to the acceleration and deceleration phase of the leg swing respectively.
As a representative pattern in the young subject at the self-selected walking speed, the
1st factor highly covaried with energy flow elements especially below the knee (i.e., the
knee power, the shank proximal flow, the shank energy change rate, the shank distal
flow, and the foot proximal flow) with mostly being negative which means the energy
was expelled from the segment/joint (Table 4-3). Moreover, this flow pattern was
dominated by the knee power absorption among those high-loading parameters. As
shown in Figure 4-2a, the knee-dominated flow pattern could be visualized as an
upward energy transfer, i.e. the energy flows from distal to proximal for absorbing the
segmental energy. Accordingly, the 1st factor could be the governing factor for swing
deceleration during the late swing. On the other hand, the 2nd factor mainly attributed
to the energy flow elements above the knee with positive values which means the
energy was gained in the segment/joint. This pattern was dominated by hip power
generation with highest loadings. Thus the 2nd factor was a hip-dominated flow
pattern with a downward energy transfer from proximal to distal for storing the
segmental energy and corresponds to the leg acceleration during the early swing. The
current results evidenced the previous conception that the hip power and knee power
play roles during the early and late swing phases [34]. The current study further
showed that the 1st factor explained more variance than the 2nd factor (Table 4-2), which
could imply that people put more efforts on the deceleration than acceleration.
The identified energy flow patterns based on the factor analysis also help to
reveal the difference in the control mechanism of the lower extremity between the
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young adults and elderly. In young adults at the self-selected and fast walking speeds,
the energy flow characteristic was functionally analogous, that is, the knee power
dominated the 1st factor to decelerate the swing leg, while the hip power dominated the
2nd factor for leg acceleration. The elderly showed similar characteristics to the young
adults at self-selected speed. But their pattern changed fundamentally at the fast
walking speed such that the 1st factor oppositely became the governing factor for the
leg acceleration since the high-loading energy flow elements were mostly positive and
above the knee, and the 2nd factor became the one corresponded to the swing
deceleration, i.e. the high-loading energy flow elements were mostly negative and
below the knee. Compared to the corresponding energy flow patterns of the young
adults, the 1st factor of the elderly during the fast walking showed the overwhelming
highest loading at the hip power, and the 2nd factor showed a centered high loading
pattern exclusively at the knee power (Table 4-3). In addition, the 1st factor for swing
acceleration in elderly at the fast walking explained even more variance than the 1st
factor for swing deceleration in other conditions (Table 4-2). In other words, during
the fast walking, the elderly especially put more efforts on the acceleration than the
deceleration. Judge et al. reported that the hip flexor power in elderly would increase
not only for assisting swing leg advancement but also for compensating the decreased
ankle plantarflexor power [36]. De-Vita and Hortobagyi also found that the hip
extensor moment and power would increase together with a reduction of ankle and knee
power in elderly at the fast walking speed [26]. The enhanced role of the hip to drive
the swing could increase the propelling speed of the leg at the cost of augmenting the
sway of the center of mass around the lumbar area. Moreover, the great reliance on
the knee to decelerate the swing leg and the reduced efforts on the deceleration may
increase the difficulty to precisely place the foot. Thus those compensative strategies
used by the elderly could be the reasons leading to the tripping or even fall when they
perform a challenged walking such as crossing the street, chasing the bus, or doing a
brisk walk exercise.
Several study limitations should be addressed. First, only the energy
characteristics during the swing phase were discussed. The swing phase is the focus
of this study because the unsuccessful advancement of the leg could be critical issues
on tripping in the elderly. Our study was the first to systematically reveal to
distinguishable difference of the energy flow characteristics of the swing leg in elderly.
Second, the energy flow analysis in this study focused on the energy changes of the
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segments rather than the energy magnitudes. The magnitudes of the energy vary
among subjects, but the pattern of the energy changes across the segments would be
analogous and could be appropriate for revealing the control strategy of human
movements. Finally, the mechanical energy discussed in this study was to highlight
the personal ability to drive the limb against the surrounding challenges. Future study
was warranted to incorporate with the electromyography or the cardiopulmonary
function measures to facilitate the understanding of the comprehensive energy transfer
both mechanically and biologically.
In summary, the young adults demonstrated similar energy flow characteristics
of the swing leg at both the fast and the self-selective walking speeds, in which they
put more efforts on the swing deceleration than on the swing acceleration.
Nevertheless, the elderly showed a distinct energy flow pattern at the fast walking that
they put significantly great hip and thigh efforts on the swing acceleration but
exclusively rely on the knee function to decelerate the swing leg, which might lead to
an unstable gait.
Chapter 5 Conclusions
We had developed an energy flow model for intuitively identifying movement
strategy by observing the energy flow characteristics in terms of flow pattern and
energy distribution. New symbolic convention in the developed energy flow 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. The beauty of the proposed model is to
graphically interpret the specific movement strategy in a systematic view rather than
focusing on a single joint/segment. Key terms of the energy flows within the model
such as joint power or segmental energy change rate are already widely used in clinical
research and therefore previous knowledge can directly fit into the proposed model.
Another feature of this model is that it is easy to implement from various commercial
motion analysis software.
Our results have demonstrated the proposed energy flow analysis can lay a
foundation of the energy utilization in human gait and from where the role of joint
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powers can be further clarified. This research also explicitly revealed the energy
change processes occurred during the leg advancement, and the factor analysis to be
able to compare the energy flow characteristics in different subject groups. We expect
that many unexplored movement strategies can be found under a systematic view
constructed by the proposed energy flow model in the future. Not only to human gait,
the energy flow diagram with the symbolic convention can also be employed to track
the energy source(s) of the movements performed by elite athletes in order to design
better training programs. Similarly, this energy flow diagram can be a useful tool that
assists research across disciplines in studying clinical intervention of rehabilitation and
innovations in exoskeletal robotics.
Future works of this research will be:
1. Corelate the physiological energy with the mechanical energy by taking
consideration of muscle co-contraction.
2. Reduce the high-dimensional dataset for factor analysis.
3. Automatic identification of energy flow characteristics in real-time.
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