Chapter 1 Introduction
1.3 Research objectives
The main purpose of this research is to propose a new convention of the energy
flow model for intuitively interpreting the movement strategy according to the observed
energy flow characteristics. The energy flow characteristics refer to the flow pattern
and energy distribution among joints and segments. Research procedure is shown in
Figure 1-2. The proposed model utilizes a new perspective for bridging the joint and
segmental energetics in order to make each term of energy flow within the new model
easy to comprehend. Consequently, interpreting movement strategy will become very
intuitive. Another feature of the new model will be easy to implement. The
advantages of the new model will be demonstrated via analyzing the gait trials of
healthy young adults and elders walking at different speeds. The proposed energy
flow model will have a significant impact on improving the design of assistive devices
for locomotion and suggesting clinical interventions on rehabilitation, orthopedics, and
sports medicine.
In order to demonstrate how to utilize the proposed model to interpret the
movement strategy, the first clinical application is to investigate the utilization of ankle
power generated during push-off by using a new symbolic convention of energy flow
diagram. We used energy flow analysis techniques developed by Winter and
Robertson [1]. In addition to improving the clarity of visual presentation of the energy
flow analysis, we proposed a new symbolic convention to provide a self-interpreting
energy flow diagram. This diagram, with the new convention, would manifest the flow
of mechanical energy and how joint power is utilized in the leg by combining the joint
and segmental energetics. It was hypothesized for the experiment that the ankle power
generated during push-off would primarily increase the energy of ipsilateral limb
segments rather than the pelvis. To test this hypothesis, an energy flow diagram was
constructed from the data collected at the instant of peak ankle power generation, and
the ankle power utilization was then analyzed.
The second clinical application is to identify the important factors that control the
swing leg and to compare the energy flow characteristics of the swing phase during
level walking in young adults and the elderly. Factor analysis would be utilized to
extract the characteristics of the energy flows from a high-dimensional dataset. Our
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research hypothesis was that the elderly presents distinct energy flow characteristics
that unveil the altered coordination among the segments of the lower extremity during
the swing phase. Our work would help to facilitate the understanding of the
neuromuscular adaptation due to aging, which can potentially contribute to the fall
prevention, orthopedic treatments and rehabilitation interventions for elderly.
Figure 1-2 Research procedure of this project. The movement strategy will be interpreted by observing energy flow characteristics in terms of flow pattern and
energy distribution
Chapter 2
Materials and Methods
2.1 Subjects
Healthy young adults and healthy elders were recruited in this research. Exclusion
criteria included the inability to follow instructions, cardiopulmonary dysfunctions,
joint replacements in the lower extremities, arthritis, diabetes, vestibular deficits, or any
type of neuromusculoskeletal problems that could interfere with the gait pattern. All
the participants were right foot dominant, defined as the preferred leg for kicking a ball.
The experimental protocol was approved by and performed in accordance with the
relevant guidelines and regulations of the Research Ethics Committee of National
Taiwan University Hospital (No. 201112121RIC). All subjects had provided their
signed informed consents before participating in the study. The blank informed
consent was shown in Appendix I.
2.2 Instrumentation
Two optoelectric position sensors (Optotrak Certus, Northern Digital Inc.,
Waterloo, Canada) were used to collect kinematic data during gait (Figure 2-1.a).
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Rigid bodies which contain three infrared-emitting diodes (IRED) in each set are
respectively attached on lower limb segments (Figure 2-1.b) and thus the segment-fixed
coordinate systems can then be established and tracked. By finishing the procedure
of digitizing segmental landmarks while the presence of the rigid bodies at static
standing posture (Figure 2-1.d), spatial coordinates of segmental landmarks can then
be tracked. Kinetic data were collected with two force platforms (Accugait, Advanced
Mechanical Technology Inc., Massachusetts, USA) (Figure 2-1.c). Both kinematic
and kinetic data were collected synchronously at the sampling rate of 50 Hz via a
program developed in LabVIEW 14.0 (National Instruments, Texas, USA) (Figure
2). An overview of the instrumentation setup in this research was shown in Figure
2-3.
Figure 2-1 (a) Optoelectric position sensor to track marker trajectory ; (b) rigid bodies
that contain three active markers in each set ; (c) force plates that are embedded in the
floor ; and (d) Apply rigid bodies on the subject.
Figure 2-2 LabVIEW program developed to collect gait trials for energy flow analysis
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Figure 2-3 An overview of the instrumentation setup in this research
2.3 Experimental Protocol
All subjects walked with shoes along a 10-meter walkway at the self-selected
speed and the fast speed respectively. The instruction for the fast speed was to ask the
subject simulating a functional task, i.e. crossing a street as fast as possible when the
green light is about to turn red in 10 seconds. Each subject was allowed to practice
and completed at least three successful gait trails. A trial was considered "successful"
when constant walking speed was obtained during gait.
Table 2-1 showed the 14 segmental landmarks that were digitized for capturing
body motions. Trajectories of all the landmarks were recorded and filtered with a
fourth-order, bidirectional Butterworth low-pass filter with a cutoff frequency of 10 Hz.
Origins and definitions of each segmental coordinate system determined by the
digitized segmental landmarks are listed in Table 2-2. The illustrations of each
segmental coordinate system together with the placements of the digitized landmarks
are also shown in Figure 2-4 and Figure 2-5.
The kinematic data were obtained by calculating the orientations of segmental
coordinate system. The mass and inertial properties were individually calculated with
reference to the coefficients from previous literature [39]. The kinetic data including
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joint force, moment, and power are analyzed by the methodology of inverse dynamics.
Table 2-1 Descriptions of the digitized segment landmarks for the right leg Segment Digitized Landmark Description
Pelvis
RASIS Right ASIS
LASIS Left ASIS
SAC Mid-point between the right and left PSISs
Right Thigh
RLFC Right lateral femoral epicondyle RMFC Right medial femoral epicondyle RGTO Right greater trochanter
Right Shank
RLMA Right lateral malleolus RMMA Right medial malleolus RFIH Right fibula head RTTR Right tibia tuberosity
Right Foot
RRCA* Right rear heel RLCA* Right lateral heel RMCA* Right medial heel
RTOE Right mid-point of 2nd and 3rd metatarsal heads
* Vertical coordinates of RRCA, RLCA, and RMCA at neutral position are equal
Table 2-2 Origins and definitions of segmental coordinate system for the right leg
Segment Origin Definition
Pelvis
Right hip joint center (RHJC) determined by the method proposed by Bell et al. [40]
The unit vector of the line passing from LASIS to RASIS The unit vector of the cross
product of the and The unit vector superiorly normal
to the plane containing RASIS, LASIS, and SAC passing from RMFC to RLFC The unit vector anteriorly normal
to the plane containing RGTO, RLFC, and RMFC
The unit vector of the cross product of the and
Right Shank
Right Ankle Joint Center (RAJC) determined by the mid-point of RLMA and RMMA
The unit vector of the cross product of the and the line passing from RAJC to RTTR The unit vector anteriorly normal
to the plane containing RFIH, product of the line passing from RRCA to RTOE and
The unit vector of the cross product of the and
The unit vector superiorly normal to the plane containing RRCA, RLCA, and RMCA
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Figure 2-4 Illustrations of segmental coordinate systems and the digitized landmarks for the (a) pelvis, (b) right thigh, and (c) right shank in A-P view
(a) Pelvis
(b) Thigh (c) Shank
Fig. 3.1 Illustrations of segmental ACSs and the digitized landmarks for (a)the pelvis, (b)right thigh, and (c)right shank in A-P view
Figure 2-5 Illustrations of segmental coordinate system and the digitized landmarks for the right foot in (a) top view, (b) posterior view, and (c) side view
(a) Top view
(b) Posterior view
(c) Side view
Fig. 3.2 Illustrations of segmental ACS and the digitized landmarks for right foot in (a)top view, (b)posterior view, and (c)side view
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2.4 Energy Flow Model
The energy flow diagram likens potential and kinetic energy to a fluid, while body
segments are likened to tanks that can store and release this fluid. The joints are
likened to flow sources and sinks, and the mechanical work that transmits energy
between body segments through joint forces and moments are like monoarticular pipes
that the fluid flows through between the tanks, hence the term energy flow. The
diagram can reveal the energy distribution over multiple segments, simultaneously.
2.4.1 Detailed energy flow diagram
A new symbolic convention of the detailed energy flow diagram which has four
core elements, namely translational energy flow (TF) mediated by joint forces,
rotational energy flow (RF) mediated by joint moments, segmental energy change
rate, and joint power was proposed in this research. TF was calculated by TF = 𝐹 ∙
𝑣( , whereas 𝑣( is the linear velocity of a joint center and F is the joint force. TF is
the power used to transmit the joint force while producing the translational movement
in the direction of energy flowing across a joint. In a detailed energy flow diagram
(Figure 2-6), the horizontal arrows that directly connect the body segments represent
translational energy flow.
RF was calculated by 𝑅𝐹 = 𝑀 ∙ 𝜔,, whereas ωs is the angular velocity of a
segment and M is the joint moment. In a detailed energy flow diagram (Figure 2-6),
the horizontal arrows connecting the segments through the joints represent the
rotational energy flow. For either translational or rotational energy flow, a positive
(negative) value represents an inflow (outflow) of energy to a segment. For either
translational energy flow or rotational energy flow, the direction of a horizontal arrow
is determined by the sign of the value obtained from energy flow analysis. For instance,
the arrow direction of a positive energy flow shall be toward a segment, which also
means the energy is flowing into the segment.
Figure 2-6 A new symbolic convention of the detailed energy flow diagram.
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The segmental energy change rate ( ) is for the change of the total mechanical
energy of a segment. Total mechanical energy refers to the sum of potential energy (PE),
translational kinetic energy (TKE), and rotational kinetic energy (RKE). PE was
calculated by 𝑃𝐸 = 𝑚𝑔ℎ, whereas m is the mass of a segment, g is the gravitational
acceleration, and h is the height of the center of mass of a segment. TKE was calculated
by 𝐸 =23𝑚𝑣,∙ 𝑣, , whereas 𝑣, is the linear velocity of a segment’s center of mass.
RKE was calculated by 𝐾𝐸 =23𝜔,∙ 𝐼𝜔, , whereas I is the moment of inertia of a
segment. In a detailed energy flow diagram (Figure 2-6), squares represent different
body segments where the direction of a vertical arrow within a square is determined by
the sign of the value of the corresponding segmental energy change rate. For example,
the arrow direction of positive segmental energy change rate is upward, which also
means that the segmental energy is increasing, i.e. energy storage.
Joint power (JP) was calculated by 𝐽𝑃 = 𝑀 ∙ 𝜔( whereas ωj is the angular
velocity of a joint. The role of joint power is to modulate rotational energy flow across
a joint. A positive (negative) joint power refers to power generation (absorption) by
muscles. In our energy flow model, the joint power also equals to the sum of proximal
RF of the distal segment and distal RF of the proximal segment, e.g., JPknee = RFshank,
E!s
proximal + RFthigh, distal. This equation can help to clarify the role of joint power on rotational energy flow. In a detailed energy flow diagram (Figure 2-6), circles
represent joints, and ‘+’ and ‘-’ symbols indicate whether the joints generate (symbol:
+) or absorb (symbol: -) energy.
By connecting ankle joint power with other energetic elements, the utilization of
ankle power can be intuitively tracked within the proposed detailed energy flow
diagram like a map, which further describes movement strategy of walking during ankle
push-off.
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2.4.2 Simplified energy flow diagram
In order to ease the observation of the energy flow characteristics, the detailed
energy flow diagram can be further simplified by merging translation energy flow and
rotational energy flow into either segmental proximal flow ( ) or segmental distal
flow ( ). The segmental proximal/distal flow was calculated by:
𝐸̇8(𝑜𝑟 𝐸̇=) = 𝐹 ∙ 𝑣( +𝑀 ∙ 𝜔,
The segmental proximal/distal flow indicates the energy entering or leaving a segment
at its proximal or distal part, which is easier to comprehend. Taking the thigh for
example, the positive thigh proximal flow ( ) represents there is an energy inflow
to the thigh at the hip joint, whereas the negative thigh distal flow ( ) represents
there is an energy outflow from the thigh to the knee joint (Figure 2-7).
Figure 2-7 Segmental proximal and distal flows in a simplified energy flow diagram
Ep
Ed
thigh
E!p,
thigh
E!d,
In a simplified energy flow diagram, the segmental energy change rate ( ) equals
to the summation of segmental proximal and distal flows of a segment, i.e.
. For example, 50 Watts of and -20 Watts of indicate that
increases 30 Watts (Figure 2-8). It allows us to look into the regulation of the
segmental energy. Through this observation, we can study how the energy flow
modulates the potential energy and kinetic energy of the segment.
Figure 2-8 An example of a simplified energy flow diagram including the thigh and the knee joint.
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In a simplified energy flow diagram, a positive joint power can result in two kinds
of flow pattern across the joint in terms of a pure energy source and increasing
transferring energy. In contrast, a negative joint power can result in two kinds of flow
pattern across in terms of a pure energy sink and decreasing transferring energy. The
amount of power leaving the joint equals that entering the joint, i.e., the joint power
equals to the summation of of the distal segment and of the proximal segment,
e.g. . For example, 50 Watts of and -20 Watts of
represent that the knee generates 30 Watts of power ( )(Figure 2-8).
Figure 2-9 showed another example of the energy flow characteristics presented
by the energy distribution and flow pattern in a simplified energy flow diagram. It is
effortless to conclude that the energy stored in the thigh and the shank is contributed by
the power generation of knee muscle. The example demonstrates that the proposed
energy flow model provides an intuitive way to observe joint power utilization.
Otherwise, either the role of joint power or the source of segmental energy change may
remain ambiguous if not bridging joint and segmental energetics together.
Another format of presenting the energy flow pattern of one leg was also adopted
in this research in order to intuitively link to the movement (Figure 2-10). Since there
Ep Ed
is no foot distal flow during the swing phase, i.e. foot does not contact the ground, foot
energy change rate is identical to the foot proximal flow. Accordingly, there are
eleven energy flow elements in the swing leg model, including the 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, and
foot proximal flow.
Figure 2-9 A simplified energy flow diagram to reveal the energy source of the thigh and the shank
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Figure 2-10 A complete simplified energy flow diagram of one leg. All energy flows are presented in the positive direction.
!
2.5 Data Analysis
2.5.1 Construction of a detailed energy flow diagram at the instant of push-off
The translational energy flow, rotational energy flow, joint power, and segmental
energy change rate were analyzed. Energy flow between the foot and ground were
calculated based on techniques in the literatures that account for energy dissipated in
foot deformation [41-43]. The detailed energy flow diagram was constructed at the
instant of peak ankle power generation since such instant is considered representative
of push-off phase [44-46]. Subsequently, the distribution of ankle power generated
during push-off was further investigated by analyzing the mechanical energy of each
segment. These analyses were performed to reveal how ankle power was utilized and
to test whether the ankle power generated during push-off delivered substantial
propulsive energy to the pelvis.
2.5.2 Factor analysis of the energy flow characteristics in swing phase
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
Chart and value of each energy flow within the proposed model can be conveniently