Chapter 2 Materials and Methods
2.5 Data analysis
2.5.2 Factor analysis of the energy flow characteristics in swing phase…29
The kinematic data that was used to calculate the energy flow were normalized to
the duration of the swing phase (yielding the relative time profiles between 0% and
100%) and were averaged over the three recorded trials. The energy flow data of all
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subjects were then normalized to the subject’s body mass, and averaged according to
the normalized time profiles at 1 percent interval along with the swing duration. A
correlation coefficient matrix derived from the normalized averaged data of all the 11
energy flow elements in the swing leg model would be produced to evaluate the
correlation between each of the energy flow element. The correlation coefficient
ranges from 0 to 1 and the higher coefficient indicates the greater correlation. The
correlation matrix would be used as inputs for the factor analysis. By rotating the
principal components, factor analysis is then utilized to extract the characteristics of a
high-dimensional dataset. The extracted 1st and 2nd factors indicate the first two most
prominent energy flow patterns of the entire swing phase. For each factor, energy
flow elements with significant absolute loadings (> 0.8) would further be depicted in
the energy flow model while the sign of the loading determined the flow direction of
the corresponding energy flow element. Consequently, the energy flow characteristics
of the swing leg can be intuitively observed corresponding to each of the extracted
factors. The independent t-test was used to compare the walking speeds between the
young adults and the elderly.
2.5.3 Verification of the proposed energy flow analysis
This research has developed a software program to perform the proposed energy
flow analysis (Figure 2-11). Nevertheless, it would be difficult to judge the robustness
of the data if the accuracy of our energy flow analysis technique was not verified. Our
energy analysis technique was verified by comparing the segmental energy change rates
calculated from kinematic data with the summation of the corresponding energy
inflow/outflow that are calculated via inverse dynamics. Since the segmental energy
change rate was analyzed via simple calculations, it was less prone to error. Thus, the
accuracy of developed technique can be assured if the results from both calculations
are similar. In previous literatures, the discrepancy between these two calculating
methods was called power imbalance. Theoretically, the power imbalance is zero
since either calculation follows the principles of rigid-body dynamics.
Figure 2-12 showed the segmental energy change rates of thigh, shank, and foot
from a gait trial of a young healthy adult, in which data is processed by our developed
software. The results showed that each segmental energy change rate was highly
matched with the summation of the corresponding energy inflow/outflow. Since
nearly zero power imbalance was achieved, the accuracy of developed technique was
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assured. Another comparison of segmental energy change rates cited from the other
research [47] was showed in Figure 2-12 for reference.
Figure 2-11 The user interface of the developed energy flow analysis software.
Chart and value of each energy flow within the proposed model can be conveniently
assessed via the software. In addition, 3D animation of gait is shown together with
ground-reaction-forces in order to distinguish which gait event is being analyzed.
(a)
(b)
(c)
Figure 2-12 Segmental energy change rate of (a) thigh, (b) shank, and (c) foot
calculated by inverse dynamics (dash-line) and kinematic data (dot-line). Charts from
both calculations were highly matched, i.e. nearly zero power imbalance.
-0.6 Energy change rate of the thigh
Inverse Dynamic
Energy change rate of the shank
Inverse Dynamic Energy change rate of the foot
Inverse Dynamic Kinematic
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Figure 2-13 Comparison of segmental energy change rates cited from the other research [47]. Considerable power imbalance existed in the stance phase for all
segments whereas nearly zero power imbalance in the swing phase.
Chapter 3
Mechanical energy utilization of ankle push-off in young adults
3.1 Detailed energy flow diagram during ankle push-off
The gait data for this clinical application of energy flow analysis were collected at
self-selected speeds (1.43±0.09 m/s) from 8 healthy young adults (Age: 23±2 years old,
Gender: male). The energetic data obtained from the developed energy flow model
(Appendix II) were used to construct the detailed energy flow diagram at the moment
of peak ankle power generation (Figure 3-1).
Figure 3-1 A detailed energy flow diagram at the peak of ankle power generation during push-off. All values are reported in power normalized by body weight (W/kg) either above or below their corresponding symbol. Reported values are the average
change rate Joint power Energy flow
+
change rate Joint power Energy flow
+
change rate Joint power Energy flow
+
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3.2 Energy flow between the shank and the foot
There was an energy flow loop between the shank and the foot where energy
moved from the shank to the foot through rotational energy flow as well as where
energy moved back to the shank from the foot through translational energy flow (Figure
3-1). Within the loop, the ankle power (2.78±0.22 W/kg) joined the rotational energy
outflow from the shank (4.11±0.80 W/kg) and produced an augmented energy inflow
to the foot of 6.89±1.06 W/kg. A small portion of this augmented energy flow
powered the motion of the foot (0.13±0.04 W/kg), and even less of that was transmitted
to the ground (0.05±0.22 W/kg). However, the majority of this augmented energy was
transmitted to the shank through translational energy flow (6.72±0.96 W/kg). In other
words, this translational energy flow was transformed from the rotational energy flow
induced by ankle muscles as shown in the energy flow loop. The energy flow loop
between the shank and the foot is the energetic representation of ankle plantarflexor
moment (producing rotational power) inducing the upward ankle reaction force
(producing translational power) on the shank through the lever action of the foot.
3.3 Utilization of ankle power
The detailed energy flow diagram (Figure 3-1) shows how energy moved from the
lower leg segments all the way up to the pelvis through translational energy flow, which
could be considered the “push-off” power. However, we found that the magnitude of
translational energy flow moving from the shank to the thigh (0.27±0.51 W/kg) was
only about 10% of the ankle power (2.78±0.22 W/kg). The majority of ankle power
either increased the mechanical energy of the shank (1.29±0.24 W/kg, about 46%) or
was absorbed by the knee (1.05±0.51 W/kg, about 38%). The remaining
ankle-induced power moved from the shank to the thigh through translational energy flow
(0.27±0.51 W/kg) and was combined with power generated from the hip (1.29±0.34
W/kg) to increase the mechanical energy of the thigh (1.00±0.19 W/kg). Although
the translational energy flow from the thigh to the pelvis (0.36±0.61 W/kg) transmitted
some of the ankle joint power to the pelvis, the detailed energy flow diagram (Figure
3-1) clearly illustrates how the majority of power generated by the ankle during
push-off flowed to the ipsilateral leg and how little of that was transmitted toward the trunk.
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3.4 Energy flow of the pelvis
The utility of the energy flow diagram is that it graphically reveals the flow of
energy through the entire leg, rather than focusing on a single joint or segment.
However, one energy flow diagram only represents one instant at a time. In order to
verify that our results are not unique to this single instant, we examined the translational
energy flow from the trailing thigh to the pelvis during the entirety of push-off (Figure
3-2). We found that the translational energy flow applied to the pelvis was small
compared to ankle power, and that energy only flowed into the pelvis for less than a
half of the duration of push-off. We also examined the rotational energy flow between
the pelvis and trailing thigh, and found that a small amount of energy was consistently
flowing from the pelvis to the hip during the entirety of push-off (Figure 3-2).
Figure 3-2 Ankle power and the energy transmitted to the pelvis. The light gray
area indicates the period of push-off and the dark gray area indicates the duration of the
translational energy inflow (positive value) to the pelvis. Standard deviations are
shown as vertical bars. It can be observed that how much power generated by the
ankle during push-off and how little power transmitted to the pelvis.
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3.5 Segmental energetics
To better understand the utilization of ankle power generated during push-off, we
assessed the energy compositions of each segment in terms of potential energy and
kinetic energy (Figure 3-3a-3d). The change in the total mechanical energy of the
pelvis (-0.0222 J/kg) before and after push-off (Figure 3-3a) were dominated by the
change in kinetic energy (-0.0225 J/kg). Furthermore, we found that such change in
kinetic energy was largely determined by the change of the translational kinetic energy
(-0.0225 J/kg), especially in the anterior-posterior direction (-0.0223 J/kg), while the
change in rotational kinetic energy was several orders of magnitude smaller (<0.0001
J/kg) (Figure 3-3e).
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Figure 3-3 Energy characteristics of human gait. (a)-(d) The mechanical energy
compositions of the pelvis, thigh, shank, and foot, respectively. (e) The composition of
translational kinetic energy of the pelvis in terms of the anterior-posterior (A-P),
medial-lateral (M-L), and vertical directions. The light gray area indicates the period
of push-off. Standard deviations are shown as vertical bars.
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
W/kg