Zach Dezman, B.S., James Carollo, Ph.D., P.E.

1
Gait Events can be Detected using the Trajectory
of the Whole-Body Center of Mass
Zach Dezman, B.S., James Carollo, Ph.D., P.E.
Colorado School of Mines Golden, Colorado
Center for Gait and Movement Analysis (CGMA) The
Childrens Hospital

• In multiple-frequency trials, the first
  fundamental frequency did not correlate with
  cadence (r20.01, pgt0.05), but the second
  fundamental frequency correlated strongly
  (r20.51, plt0.005).

Introduction
Methodology Functional Gait Task

• Inman first described the movement of the center
  of mass (COM) during normal walking while
  discussing the six determinants of gait (Inman,
  1980).
• The COM moves several centimeters in persons free
  of pathology during normal gait (Eames 1999), as
  shown in Figure 1, and is located just in front
  of S1.

• Steady-state gait subjects walked down a 30 ft
  walkway at a comfortable self-selected pace.
• Three trials were selected for 3-D kinematic COM
  calculation and further analysis.

Discussion
Methodology 3-D Kinematic COM Calculation

• These data showed that the number of fundamental
  frequencies of the vertical component of the
  whole body center of mass in patients with CP is
  significantly greater than age matched normal
  subjects.  
• One frequency, which matched the measured
  cadence, described the vertical displacement of
  the COM in normal subjects. This confirms Inmans
  theorized smooth, sinusoidal movement of the COM
  in the sagittal plane.
• The legs of normal subjects are comparable, both
  anatomically and functionally. This allows them
  to control the movement of their COM in a similar
  fashion every step, as evidenced in the smooth
  COM trajectory.
• In CP patients, the movement of the COM was
  constructed of two fundamental frequencies. The
  first was found to be less than the stride
  frequency (or one-half the step frequency). The
  second was equal to the step frequency. Both were
  of lower signal strength than the normal
  subjects single frequencies.
• The drop in signal strength implies that normal
  subjects move in a single, consistent pattern,
  while CP patients have a more variable one.
• Given that the first fundamental frequency is
  close to the stride frequency, it could be the
  result of one leg, probably the affected side. In
  addition, since it is less than one-half of the
  second frequency, this also shows a difference in
  the timing of the gait cycle of each leg.

Figure 1 Normal COM Trajectory Frontal plane
(a) figure-eight with a transverse plane
frequency equal to the stride frequency
(1Hz) Sagittal plane (b) smooth sinusoid with a
frequency equal to the step frequency (2 x stride
frequency)
Figure 3 The information presented in Figure 2
after applying a FFT (Subject RC0517).

• A 13-segment whole body kinematic model was
  processed.
• The whole body COM was then calculated using the
  Johan model (Eames 1999) and the Vicon PlugIn
  model.

• A Pearsons correlation was used to compare
  cadence (steps/sec), as measured by the Vicon
  system, with fundamental frequency in both single
  and multiple-frequency trials.

• These characteristics lend themselves to
  frequency domain signal analysis, particularly
  Fast Fourier Transforms (FFT).
• Applying FFT to COM trajectories of subjects with
  normal and asymmetric gait (hemiplegic cerebral
  palsy) will establish the utility of signal
  analysis for gait asymmetry detection.

Results
An example of the raw data is shown below in
Table 1.
Methodology Analysis of the COM Trajectory
Table 1 Fundamental frequency data for a patient
with CP (RC0522) and their age-matched normal
(RC0500)

Subject Trial 1st Freq. (Hz) 2nd Freq. (Hz) Subject Trial 1st Freq. (Hz) 2nd Freq. (Hz)
RC0522 7 0.7772 1.9366 RC0500 5 2.3445  
  9 0.8352 2.0228   13 1.2288 2.5418
  20 0.8631 2.0252   15 2.5908  
Average of Freq. Std Dev. Average of Freq. Std Dev. Average of Freq. Std Dev. 2.00 Average of Freq. Std Dev. Average of Freq. Std Dev. Average of Freq. Std Dev. 1.30.6

• Problem Subjects often do not walk directly
  across motion capture volume, making it difficult
  to separate deviations in the COM trajectory as a
  result of walking from the subjects changes in
  direction.
• Solution Vertical displacement (sagittal-plane
  movement) of the COM should contain symmetry
  information while being robust against
  medial-lateral deflections.

Hypotheses

• There is a significant difference in the number
  of fundamental frequencies of the vertical COM in
  children with CP compared to age-matched normal
  subjects.
• A strong correlation exists between cadence and
  the fundamental frequency of vertical COM

Frequency count results are shown in Tables 2 3.
Table 2 CP patient Table 3
Age-matched frequencies
normal subject frequencies
Clinical Significance
Subject Ave. of Freq. Std. Dev. Subject Ave. of Freq. Std. Dev.
RC0515 1.00 RC0516 1.00
RC0517 2.00 RC0511 1.00
RC0519 1.30.6 RC0543 1.30.6
RC0520 1.70.6 RC0524 1.00
RC0521 2.00 RC0536 1.00
RC0522 2.00 RC0500 1.30.6
RC0523 1.70.6 RC0538 1.70.6
RC0525 1.30.6 RC0555 1.00
RC0526 1.70.6 RC0545 1.00
RC0527 1.70.6 RC0541 1.00
RC0528 2.00 RC0534 1.30.6
RC0529 2.00 RC0542 1.00
RC0530 1.70.6 RC0512 1.00
RC0531 2.00 RC0518 1.00
RC0532 2.00 RC0544 1.30.6
CP Average 1.73 Normal Average 1.13
Std. Dev. 0.31 Std. Dev. 0.21
Conclusions

• This new method
• Quantifies the frequency content of walking,
  which may be a useful index of overall gait
  performance and help evaluate treatment efficacy.
• Is adaptable to wearable sensors that permit
  long-term ambulatory recording outside the
  laboratory
• Provides insight into biomechanical patterns of
  movement in children with and without
  neuromuscular disorders

• Applying signal analysis techniques to the
  vertical displacement of the COM can
  differentiate the gait of children with CP from
  that of normal subjects.
• Analysis of freq. content and number of
  fundamental freqs. in the COM displacement can
  provide important insight into a subjects
  overall gait performance.

Figure 2 Vertical displacement of COM during
gait for a cerebral palsy patient (Subject
RC0517).
Future Work

• By placing a tri-axial accelerometer on the
  pelvis at S1, long-term COM trajectory data could
  be recorded in the patients home and community.
  Processed in a manner shown here, these data
  could be used to describe gait symmetry outside a
  clinical setting.

• Autosignalby Systat Software Inc. was used to
  mathematically change the vertical displacement
  of the COM (time-domain) into signal strength as
  a function of freq. (frequency-domain) using a
  FFT (Figure 3).
• A freq. was considered fundamental if it was
  99.9 significant (plt0.01), as calculated by
  Autosignal.
• The fundamental freqs. describing the vertical
  displacement of COM were tabulated for all
  subjects.
• An average and standard deviation of the number
  of fundamental freqs. was calculated for every
  subject.
• The average number of frequencies for each
  subject in the CP population was compared to the
  same in the age-matched normals using a paired
  t-test.

Methodology Data Capture

• Data from 10 children with hemiplegic cerebral
  palsy, and 10 age-matched normal subjects were
  selected.
• The subjects height, weight, and distance
  between bony landmarks were measured.
• 35 retro-reflective skin markers were placed on
  areas of the subjects head, chest, arms, and
  legs bilaterally.
• A 6-camera Vicon 512 kinematic measurement system
  recorded the 3-dimensional displacements of the
  markers.

Acknowledgements
The authors graciously acknowledge the technical
contributions of Timothy Nicklas, M.S., and the
financial support of The Childrens Hospital
Research Institute and the J. T. Tai and Company
Foundation.

• The average number of fundamental frequencies in
  children with CP was found to be significantly
  larger than that of age matched normal subjects
  (plt0.005).
• Fundamental frequency correlated strongly with
  cadence (steps/sec) in single-frequency trials
  (r20.68, plt0.005).

References
Inman, et al, Human Walking, 1980, Williams
Wilkins Press Eames, et al, Human Movement
Science, 1999 18(5) 637-646