IEEE GCCE 2022 1570818858

1	  2	  3	  4	  5	  6	  7	  8	  9	  10	  11	  12	  13	  14	  15	  16	  17	  18	  19	  20	  21	  22	  23	  24	  25	  26	  27	  28	  29	  30	  31	  32	  33	  34	  35	  36	  37	  38	  39	  40	  41	  42	  43	  44	  45	  46	  47	  48	  49	  50	  51	  52	  53	  54	  55	  56	  57	  60	  61	  62	  63	  64	  65	  Verifying the Independence of Anterior andMediolateral Margin of Gait Stability Indices
Tomohito KurodaShogo Okamoto

Yasuhiro Akiyama

Department of Computer Science
Tokyo Metropolitan University
Hino, Japan

Department of Computer Science
Tokyo Metropolitan UniversityHino, Japan

Department of Mechanical Engineeringand Robotics
Shinshu University
Ueda, Japan

Abstract—Gait stability indices are used for the quantitative
assessment of individual fall risk. The margin of stability (MoS)
is a popular gait stability index. This index computes the fallrisks in the anterior and mediolateral directions; however, therelationships between the anterior and mediolateral MoSs havenot been studied. We analyzed the MoS values in these twodirections and several gait parameters using canonical correlation
analysis, and obtained the linear relationships between these twogroups. The gait kinematic data of 300 strides of 60 elderlies
from an open database were used for this analysis. Our analysis
verified that the MoS values in the anterior and mediolateral
directions exhibited a weak relationship. The anterior posture
became stable as the anterior gait speed decreased or thecadence increased. Furthermore, gait motions with greater step
widths exhibited higher mediolateral MoS values, indicatinggreater stability. These findings indicate that the anterior andmediolateral postural stabilities are independently related todifferent gait parameters, which can aid in understanding stable
walking strategies.
Index Terms—margin of stability, canonical correlation analysis, gait parameter

I. I NTRODUCTION
Gait stability indices allow the quantitative assessment ofindividual fall risk. The evaluation of gait stability and its applications, such as warnings of falling, have become accessible
owing to inexpensive inertial measurement units. Gait stability
assessment during daily life is an important field in consumer
electronics. The margin of stability (MoS) [1] is a popularindex to predict falling. The MoS can be computed along theanterior and mediolateral directions, and indicates the marginof falling in each direction. However, the relationships between
the MoSs along the two directions and popular gait parameters,such as the gait speed, step width, and stride length, havebeen inconsistent in previous studies [2]–[8]. Moreover, therelationship between the anterior and mediolateral MoSs has
not yet been clearly understood. For example, Hak et al.
[3] researched how gait parameters pertained to the anterior
and mediolateral MoSs; however, they did not target therelationship between the two directional MoSs.
We conducted canonical correlation analysis in order to clarify the relationship between the MoSs in the two directions andgait parameters. Understanding the stability against falling in
the anterior and mediolateral directions helps us comprehend
how stable walking is achieved. In particular, we verified if/22/$31.00 ©2022 IEEEFig. 1. Margin of stability values in the mediolateral (x) and anterior (y)directions

the anterior and mediolateral MoSs are mutually independentor positively or negatively correlated.
II. M ETHODS
A. Margin of stability (MoS)MoS indicates the margin against a critical condition to fall
during walking. The MoS is defined as the distance between
the prospective location of the center of mass (CoM) and theendpoint of the base of support (BoS) of the human body [1].
The prospective location of the CoM is estimated using thevelocity in the anterior and mediolateral directions. MoS isdefined as
mos = bos − xcomvcom
xcom = com +ωrg
ω=l(1)(2)(3)where bos and com are the position vectors of the BoS endpoint
and the CoM, respectively, on the x–y plane, as in Fig. 1.
vcom is the velocity vector of the CoM. xcom is the position
vector of the prospective CoM. l is the height of the CoM fromthe floor, and g is the gravitational acceleration. Note that thegreater mediolateral MoS value indicates a more stable posturein the mediolateral direction whereas the smaller absolutevalue of anterior MoS indicates a more stable posture in theanterior direction.

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The minimum value of mediolateral MoS and the minimum
absolute value of anterior MoS during the gait cycle are used
as an indicator of stability. If the mediolateral MoS is negative,
it is extremely likely to fall in the mediolateral direction.
Anterior MoS is generally negative. The larger the absolutevalue of anterior MoS, the more likely it is to fall anterior
direction.
B. Gait parameters
We analyzed five popular gait parameters: the maximal
mediolateral and anterior gait speeds of the CoM, step width,
stride length, and cadence. The step width is the distance between the right and left toes in the mediolateral direction. The
stride length is the anterior distance between two successive
steps of the left foot. The cadence is the number of strides
per minute. These gait parameters have been used in previous
studies [2]–[4].

Fig. 2. The first canonical coefficients (-) for mediolateral and anterior MoSs
and gait parameters. Values in parentheses are the canonical loadings.

C. Gait database
We used the AIST Gait Database [9] for the time-series
coordinates of each body part during walking for 30 womenand 30 men aged 60 years and older. Five strides of theindividual participants, starting from the right heel contact,were analyzed. Hence, a total of 300 strides were analyzed.
D. Canonical correlation analysis
Canonical correlation analysis, which determines the linear
relationship between two groups of variables through latent(canonical) variables, was used to analyze the MoSs and gaitparameters simultaneously. For each group, the canonical variable was determined as a linear combination of the variablesin that group, such that the two obtained canonical variables
exhibited a high correlation coefficient. In this study, one setof variables contained the anterior and mediolateral MoSs, andthe other set contained the five gait parameters.
III. R ESULTS
We computed two pairs of canonical variables. Figs. 2 and3 show the canonical coefficients for all variables for the firstand second canonical variable pairs, respectively. The values
nearby the arrows from the variables to the canonical variables
indicate the canonical coefficients. The canonical variables
are latent variables that represent each group of variables
and are determined as linear combinations of the variables
in individual groups.
As shown in Fig. 2 the first canonical correlation (correlation between the first canonical variables) was 0.88. The
first canonical variable exhibited strong positive linear relationship with the mediolateral MoS and step width. A higher
mediolateral MoS value indicates a more stable posture in the
mediolateral direction. Thus, the higher first canonical value
indicates greater stability in posture along the mediolateraldirection.
The second canonical correlation was 0.80. The second
canonical variable exhibited a strong negative linear relationship with the anterior MoS, and strong negative linear

Fig. 3. The second canonical coefficients (-) for mediolateral and anterior
MoSs and gait parameters. Values in parentheses are the canonical loadings.

relationship with the maximal anterior gait speed and strong
positive linear relationship with cadence. A lower anterior
MoS value indicates a more stable posture in the anterior
direction. Thus, the higher second canonical value indicateshigher stability in posture along the anterior direction.
IV. D ISCUSSION
The first and second canonical variables exhibited substantial loadings with the mediolateral and anterior MoSs, respectively, indicating that the MoS values for the two directions arelargely independent. Furthermore, no gait parameters prominently related to both types of MoS values. Hence, we suggestthat the mediolateral and anterior MoSs are independent ofeach other. To the best of our knowledge, this is the first report
to demonstrate the independence of two directional MoSs.
The results of this study are not completely consistent withthose of previous works. According to Hak et al. [3], cadence
was positively correlated with the mediolateral MoS, whereas
our analyses indicate that cadence is positively correlatedwith the anterior MoS, and only weakly correlated withthe mediolateral MoS. Moreover, in [3], the anterior MoS
increased as the stride length decreased or the walking speed
increased; however, in this study, the stride length exhibited
weak correlations with the anterior and mediolateral MoSs.

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A possible reason behind these differences is that the gaitparameters are correlated and hence their effects on the MoSs
are not independent of each other.
V. C ONCLUSION
In this study, we verified the independence of the anterior
and mediolateral MoSs. Furthermore, we observed that thestep width is strongly related to the mediolateral MoS, andthe anterior gait speed and cadence are strongly related tothe anterior MoS. Similar and extended analyses should be
conducted for different cohorts in the future for generalized
results.
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