Suitability of Sacrum Motion in Computing
Dynamic Gait Stability IndicesZiqi Liu, Tomohito Kuroda, Shogo Okamoto

Yasuhiro Akiyama

Department of Computer ScienceTokyo Metropolitan UniversityHino, Japan

Department of Mechanical Engineering and Robotics
Shinshu University
Ueda, Japan

Abstract—Gait stability indices are expected to preemptively
detect people at high risk of falling. Among these, the marginof stability (MoS) is known as a valid index. Usually, thecomputation of MoS requires the motion-related informationof multiple feature points of the body; however, we have been
pursuing the use of only one feature point. We estimated theanterior and mediolateral MoS values from the velocity timeseries of the sacrum, knee, or toe using principal motion analysis.
Based on open gait data for 60 people over 60 years of age, thesacrum was best suited for computing MoS in the anterior andmediolateral directions. The correlation coefﬁcients between theestimated and observed values were 0.77 and 0.73, respectively.
Our ﬁndings will help establish an easy-to-access and accurate
measurement of MoS values using an inertial measurement unit
attached to a body feature.
Index Terms—Gait stability, sacrum, knee, toe, margin ofstability
Fig. 1. Anterior and mediolateral margins of stability from the overhead
viewpoint. Adapted from [7].

I. I NTRODUCTION
Gait stability indices are expected to preemptively identify
people at a high risk of falling [1]. Among these, the margin ofstability (MoS) [2] evaluates dynamic balance stability during
walking with good construct validity. MoS can be used fornormal and perturbed walking and provides omnidirectional
fall risks [3], [4]. Hence, MoS has been used by many
researchers for various applications.
The computation of MoS values requires the time-series
position data of the center of mass (CoM) of the body aswell as those of the feet, implying that at least three featurepoints are needed. Hence, MoS has been largely measured inlaboratory settings and rarely used in daily living. As a newchallenge in computing MoS values, only the translational
and angular velocities of the pelvis or CoM were used in
our previous studies [5], [6]. If MoS values can be estimatedsolely from the time-series data of a single-body point, thensmartphones with an inertial measurement unit installed canbe utilized to provide a reliable gait stability index in an easyto-access manner. However, it remains unknown which bodyparts are suitable for accurate estimation. In this study, wecompared three body features—the sacrum, knee, and toe—to estimate anterior and mediolateral walking stability. Usingan open gait database of 60 people aged over 60 years, wedetermined which body part was best to estimate MoS values.

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II. M EDIOLATERAL M ARGIN OF S TABILITY (M O S)
As shown in Fig. 1, MoS [2] is the distance between thepredicted position of the CoM and the tip of the base of thesupport in the transverse plane at moment t. The predicted
CoM position xcom (t) is its prospective position in the near
future and is calculated as√lxcom (t) = com (t) + ċom (t),(1)
gwhere com (t) and ċcom (t) are the position and velocity
vectors of the CoM, respectively. Here, g is the gravitational
acceleration and l is the height of the CoM from the ﬂoor inan upright body posture.
The MoS is deﬁned asmos (t) = bos (t) − xcom (t)(2)

where bos (t) is the position vector of the tip of the base of
the support area. The y and x components of mos (t) are
the anterior and mediolateral MoS values, respectively. The
minimum values in each direction during the gait cycle wereused as the MoS values for the most critical condition. As
these values are large, it is unlikely that people would losebalance or fall during walking.

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TABLE I
CORRELATION COEFFICIENT BETWEEN THE OBSERVED AND ESTIMATEDM O S VALUES USING DIFFERENT BODY FEATURES

Body Features
SacrumKneeToe

Mediolateral
0.73
0.64
0.63

Anterior
0.77
0.76
0.79

III. M ETHODS
A. Gait motion data
The three-dimensional motion data of various body pointsof 60 people over 60 years of age were used for the analysis,
including 30 males and 30 females. They were adopted froman open gait motion database [8]. Thus far, this database hasbeen used by various researches, e.g., [9]. For each person, ﬁve
gait cycles were analyzed, and 300 gait samples were includedin the analysis.
B. Principal motion analysis
Principal motion analysis is a supervised multivariate timeseries analysis [5], [10], [11]. It determines the basis timeseries of multiple variables called principal motions so that
their linear combinations approximate any sample in a learning dataset. The principal motions are determined such that
their score, which indicates the degree to which a sample
includes that principal motion, exhibits the greatest correlation
coefﬁcients with the anterior or mediolateral MoS values. We
used the minimum MoS values along these two directions in agait sample comprising two successive steps as the objectivevalues. The time series of triaxial velocities of the sacrum,knee, and toe served as predictors of the minimum MoS
values, as described in Section III-C.
C. Body features used to compute MoS
We used the tri-axial velocities of three lower-bodyfeatures—the sacrum, right knee, and right toe—to computeMoS values. The sacrum and toe are close to the CoM and tipsof the base of the support, respectively; hence, these featurepoints can help estimate the MoS values. The knee is nearly
the central point between the sacrum and the toe. The knee andtoe are referred to as the lateral condyle of the femur and thecenter of the second and third metatarsals, respectively. Thesacrum was referred to as the median sacral crest. In addition
to this, the reason we chose these parts of body features isbecause it is easier to recognize skeletal features from thebody surface.

Fig. 2. Results. Left) Correlation coefﬁcients for each body feature point.
Right) Scatter plot of observed mediolateral MoS values and those estimatedby using the motion data of sacrum. The MoS values are standardized.

anterior MoS were 0.77, 0.76, and 0.79, respectively. Thesevalues are summarized in Table I. Fig. 2 shows a scatter plotof the observed and estimated mediolateral MoS values whenthe motion data of the sacrum were used for the prediction.
Among the three feature points, the sacrum was the best for themediolateral MoS values, whereas all three were comparable
for the anterior MoS values.
V. C ONCLUSIONMoS is a popular gait stability index that indicates fall risk.
We estimated the minimum mediolateral and anterior MoS
values during a gait cycle by using the triaxial translational
velocities of each of the three body feature points, considering
the potential use of an inertial measurement unit. In the
mediolateral direction, the sacrum was the best among thethree features for estimating MoS values. There were no
substantial differences in the accuracy of estimation in theanterior direction. The sacrum is a good position for estimating
MoS values.
In the future, we need to compare a variety of body featuresin addition to the three investigated in this study. Furthermore,
we experiment with inertial measurement units for estimating
the MoS values, whereas the motion data of this study wererecorded using an optical motion capture system.

IV. R ESULTS
We computed the three principal motions for each of thethree body features. We estimated the minimum mediolateraland anterior MoS values using regression analysis, with thescores of the three principal motions as explanatory variables.
The correlation coefﬁcients between the observed and estimated minimum mediolateral MoS were 0.73, 0.64, and 0.63
for the sacrum, knee, and toe, respectively, and those for the346

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