Advance Publication by J-STAGE
Journal of Biomechanical Science andEngineering

DOI: 10.1299/jbse.23-00183

Received date : 16 April, 2023
Accepted date : 7 July, 2023
J-STAGE Advance Publication date : 16 July, 2023

© 2023 The Japan Society of Mechanical Engineers. This article is licensed
under a Creative Commons Attribution 4.0 International license.
(https://creativecommons.org/licenses/by/4.0/).

Anterior and mediolateral dynamic gait stabilities attributed
to different gait parameters in different age groups
Tomohito KURODA∗ , Shogo OKAMOTO∗ and Yasuhiro AKIYAMA∗∗∗ Department of Computer Science, Tokyo Metropolitan University

6-6 Asahigaoka, Hino-shi, Tokyo, 191-0065, Japan
E-mail: okamotos@tmu.ac.jp∗∗ Department of Mechanics and Robotics, Shinshu University

3-15-1 Tokida, Ueda-shi, Nagano, 386-8567, Japan

Abstract
The margin of stability (MoS) is a gait stability index with good validity. MoS is computed in the anterior andmediolateral directions. However, their relationship has not been well investigated. Furthermore, previous studies
have little investigated the diﬀerences in MoS between distinct age groups. Inter-age comparisons reveal agespeciﬁc walking characteristics and their eﬀects on stability. In this study, we used multiple indicators and multiplecauses model, which is a type of structural equation modeling, to investigate the statistical relationships between
various types of gait parameters and MoSs for each of the healthy participant groups over 60 and in their 20s.
For the analysis, data from 120 individuals were obtained from a gait database. The model for the younger group
showed that the MoSs in the anterior and mediolateral directions were mostly separated. The stability in theanterior direction was independent of the stability in the mediolateral direction. In contrast, some gait parameterssimultaneously aﬀected the two MoSs in the elderly group. The stability in the anterior and mediolateral directions
was interdependent. For example, forward walking speed inﬂuenced the anterior and mediolateral MoSs in theelderly group, whereas it inﬂuenced only the anterior MoS in the younger group. These ﬁndings suggest that theage of people must be considered when discussing gait characteristics that contribute to stability.
Keywords : Margin of stability, Multiple indicators and multiple causes model, Age

1. Introduction
Gait stability indices, which quantify the risk of falling, are expected to reduce the number of falls by providing an
early warning. Among the many stability indices (Bruijin et al., 2013; Balance Project, 2014), the margin of stability(MoS) (Hof et al., 2005) is one of the most widely used gait stability indices. The MoS is based on the biomechanicalprinciple of an inverted pendulum and has excellent construct validity (Bruijin et al., 2013). Furthermore, MoSs arecomputed in the mediolateral and anterior directions, thus enabling an analysis of stability in diﬀerent directions (Akiyama
et al. 2023). The relationships between MoSs and gait parameters, including walking speed, stride length, step width,and cadence, have been investigated to understand the determinants of gait stability. However, these relationships havebeen found to be inconsistent (Hak et al., 2012; Hak et al., 2013; Hallesmans et al., 2018; Alamoudi et al., 2020; Iwasaki
et al., 2021, 2022). For example, several studies have suggested that anterior walking speed is a predictor of MoSs in
the mediolateral and anterior directions and that anterior walking speed impairs stability in the mediolateral direction(Alamoudi et al., 2020; Gill et al., 2019; Ohtsu et al., 2019; Iwasaki et al., 2022). However, according to Hak et al. (2013)and Hallesman et al. (2018), the correlation between mediolateral MoS and walking speed is weak. Furthermore, themediolateral MoS does not change at diﬀerent walking speeds according to Caterby et al. (2014). They suggested that anincrease in walking speed does not lead to a decrease in gait stability because, as walking speed increases, the mediolateralwidth between steps increases and stability is maintained. These inconsistencies in the eﬀects of gait parameters on MoSs
may be attributed to diﬀerences in the experimental conditions and participants. Furthermore, research on the relationship© The Japan Society of Mechanical Engineersbetween mediolateral and anterior MoSs is rare. For example, Hak et al. (2013) and Alamoudi et al. (2020) investigated
the relationships between gait parameters and mediolateral and anterior gait stabilities. However, they separately discussed
the MoSs in two directions. Therefore, the MoSs in diﬀerent directions must be analyzed using a single statistical model.
The risk of falling in the anterior direction diﬀers from that of falling in the mediolateral direction. Modeling the anterior
and mediolateral MoSs and various gait parameters in a single statistical model will enable an analysis of gaits that arestable in both directions.
Furthermore, earlier studies have rarely studied the diﬀerences in MoSs during steady walking between diﬀerent
age groups, despite young and elderly groups being investigated separately. One exceptional study was conducted by
Yamaguchi and Masani (2022). They performed an inter-age comparison of gait parameters and gait stability indicesincluding MoS. They showed that the step width and mediolateral MoS increased with age and found other age-related
diﬀerences in gait characteristics. Hallesmans et al. (2018) and Hak et al. (2013) studied MoSs in children and young
people, respectively. Brodie et al. (2018) measured MoSs during disrupted walking in healthy adults aged approximately
30 years. Ohtsu et al. (2019) investigated the balance strategies of healthy young people using MoSs. Iwasaki et al.
(2022) analyzed mediolateral MoSs during normal walking in the elderly. These earlier studies did not compare MoSs
and their relationships with gait parameters between diﬀerent age groups. Furthermore, other researchers focused onage-related diﬀerences in MoSs for gait conditions with disturbances. For example, Roeles et al. (2018) investigated theanterior and mediolateral MoSs of perturbed gait in young and elderly individuals and reported no signiﬁcant diﬀerences
between the two age groups. Martelli et al. (2017) suggested that the backward MoSs of elders were lower than thoseof young adults during and at the end of an early compensatory reaction under slip conditions. Other studies have also
compared MoSs during compensatory steps after perturbation in young and old adults (Bierbaum et al., 2010; Carty et al.,2011). Age-related diﬀerences in gait stability have also been studied using another representative index, the Lyapunov
exponent (Buzzi et al., 2003; Kang et al., 2009; Terrier et al., 2015). However, MoSs and Lyapunov exponents are largely
independent (Inagaki et al., 2023). Furthermore, Cromwell et al. (2004) compared the gait stability ratios calculated
from the walking velocity and cadence between young and elderly adults. Similarly, Rogers et al. (2008) compared thebalance abilities during walking on compliant grounds between young and elderly individuals. Moreover, Dean et al.
(2007) and Schrager et al. (2008) concluded that older people adopt greater step widths to maintain lateral stability inchallenging walking conditions; however, these researchers did not discuss stability indices. Thus far, the comparison of
MoSs between the young and elderly during normal gait has been rarely conducted.
Therefore, this study investigated the relationship between MoSs along the anterior and mediolateral directions andtypical gait parameters during steady walking in young adults (20–30 years old) and older adults (60–78 years old) using
the multiple indicators and multiple causes (MIMIC) model and structural equation modeling technique. We used an open
database as our source of gait motion data (Kobayashi et al., 2019). Unlike the aforementioned studies that separately
discussed the two types of MoSs, the MIMIC model explains the two types of MoSs using latent and common variables
called constructs, which are formed by the linear combination of several gait parameters. The results will enable us todiscuss the eﬀects of age on gait strategies in terms of gait parameters and dynamic stability. This study is based on ourearlier work (Kuroda et al., 2022), in which only the elderly were analyzed, and focuses on the comparison between theelderly and young.

2. Methods
2.1. Margin of stability (MoS)MoS is the margin against falling at any instant during walking. As shown in Fig. 1, MoS is deﬁned as the distance
between the prospective position of the center of mass (CoM) of the human body in the near future and the endpointsof the base of support (BoS). Despite the MoS being computable for all-round directions (Akiyama et al., 2023), theanterior and mediolateral directions are primarily discussed for straight walking. The prospective position of the CoM
was estimated using velocity of CoM in the mediolateral and anterior directions. MoS is deﬁned as
mos = bos − xcom
ucom
xcom = com +
ω
√
g
ω=
l

(1)
(2)
(3)

© The Japan Society of Mechanical Engineersx(mediolateral)Σo(groundfixed)y(anterior)

Com
vcom
ω
bos

xୡ୭୫
Fig. 1࢓௢௦Computation of margin of stability along the anterior and mediolateral direction.

XCoM

BoS
Anterior direction

XCoM and BoS (m)Mediolateral direction
0.2

1.0
Minimum
MoS

0.1

Minimum
MoS

Minimum
MoS
0.5

0

0
0

Fig. 250
Gait cycle (%)

100

0

50
Gait cycle (%)

100

Example of the time evolution of XCoM and BoS. Adapted from (Kuroda et al., 2022).

where bos and com are the position vectors of the BoS endpoint and CoM, respectively, on the x-y plane, as shown in
Fig. 1. ucom denotes the velocity vector of CoM. xcom is the position vector of the prospective CoM. l is the height of the
CoM from the ﬂoor, and g is the gravitational acceleration.
Figure 2 shows examples of temporal changes in the prospective CoM (XCoM) and BoS along the mediolateraland anterior directions. The horizontal axis represents the gait cycle, and the vertical axis represents the positions of the
XCoM and BoS. The gait cycle presents the normalization of two successive steps. At 0% of the gait cycle, the right heelcontacts the ground, and the double-support phase begins. Subsequently, left toe is oﬀ the ground and left heel contacts at
approximately 50%. Successively, the next right heel contact occurs at 100% of the gait cycle.
Greater mediolateral and anterior MoSs indicate more stable walking in each direction. MoS is always computed
during gait, and the minimum value during a gait cycle corresponds to the most unstable moment. The minimum values
were considered in this study.
The value of the mediolateral MoS is deﬁned by
(x)
(x)
m(x)
os = |bos − xcom |(4)

and its minimum value is typically observed at approximately 10 or 60% of the gait cycle. This is the most criticalcondition for balance loss in the mediolateral direction. The XCoM is usually located inside the BoS, and mediolateral
MoS is positive. A larger MoS indicates more stable walking in the mediolateral direction.
The value of the anterior MoS is deﬁned by
(y)
(y)
m(y)
os = bos − xcom

(5)
© The Japan Society of Mechanical Engineers

Table 1

Mean ± standard deviation of the MoSs for the elder and young adults.
Mediolateral MoS (m)Anterior MoS (m)Table 2Elder adults
0.033 ± 0.011−0.033 ± 0.031

Young adults
0.022 ± 0.011−0.032 ± 0.035

Means and standard deviations of the gait parameters, height, and weight for the elder and young adults.
Maximal mediolateral CoM speed (m/s)
Maximal anterior CoM speed (m/s)
Step width (m)Stride length (m)Swing duration (%)
Mediolateral MoS min Timing (%)
Anterior MoS min Timing (%)
Height (m)Weight (kg)

Mean value for elders
0.12 ± 0.025
1.44 ± 0.16
0.15 ± 0.027
1.26 ± 0.089
85.0 ± 6.7
9.04 ± 5.10
0.34 ± 0.89
159.62 ± 7.58
60.57 ± 9.33

Mean value for young adults
0.11 ± 0.030
1.50 ± 0.18
0.12 ± 0.033
1.36 ± 0.10
86.0 ± 3.3
7.81 ± 5.51
0.34 ± 0.85
164.88 ± 7.94
58.55 ± 9.79

and its minimum absolute value is observed at approximately 0 or 50% of the gait cycle, that is, immediately after the heelcontact. This corresponds to the most critical condition in the anterior direction. During a large part of the gait cycle orits entirety, the position of the XCoM is in front of the BoS, which is the toe of the leading foot. Thus, the anterior MoS
is generally negative. The smaller value of the anterior MoS indicates a riskier condition in the anterior direction.
2.2. Gait parameters
In this study, seven gait parameters were used. These gait parameters include the maximum velocity of the CoM in
mediolateral and anterior directions, step width, stride length, swing duration, and timing at which the mediolateral andanterior MoSs are minimized in the gait cycle.
Step width is the distance between the left and right feet in the mediolateral direction during walking. Stride length
is the distance between two successive steps of the same foot. Swing duration is the proportion of the swing phase in the
gait cycle. These gait parameters potentially relate to the MoSs according to earlier studies (Alamoudi et al., 2020; Hak
et al., 2012; Hak et al., 2013; Hallesmans et al., 2018; Iwasaki et al., 2022; Yamaguchi and Masani, 2022). Step widths
and stride lengths were normalized to the body height of each participant.
In addition to the aforementioned gait parameters, we considered the timing of the minimum mediolateral and anterior MoS values to be observed. This value indicates the timing at which the MoS reached its minimum in a gait cycle
and is expressed as a cycle percentage from 0 to 100%. One gait cycle includes two steps, and the minimum MoS value
during a gait cycle is observed either at the ﬁrst or second step. When this timing was above 50%, 50% was subtracted
from the value to cancel laterality. Such timing has rarely been considered in earlier gait stability analyses. The timingof the MoS value to become minimum largely depends on the prospective position of the center of mass, which is the
XCoM calculated from the CoM position and velocity. Individual diﬀerences in the kinematics of CoM produce those in
the timing at which the MoS value is critical. Thus, the timing at which the MoS reaches its minimum may pertain to the
MoSs. Despite no previous studies exploring the relationship between the timing at which the MoS reaches a minimum
and the gait stability indices, we adopted these timings as gait parameters.
2.3. Gait database
We used a gait database from AIST (Kobayashi et al., 2019) for the three-dimensional time-series coordinates of the
body features during walking. In each sample, a participant walked 10 m straight barefoot at a comfortable speed, and one
gait cycle in the middle of the walk was recorded. An optical motion capture system was used to measure the positions ofbody segments. We refer to the center of the second and third metatarsal bone as the toe.
In this study, we used samples from 30 healthy men and 30 healthy women aged 60–78 years as the elderly groupand 30 healthy men and 30 healthy women aged 20–30 years as the young adult group. Five gait cycles were analyzed
for each individual, starting from heel contact with the right foot. A total of 600 samples were used for the study: 300
samples each from elderly and young adults. Tables 1 and 2 show the mean values of the MoSs and gait parameters for
elderly and young adults, respectively. Typical reduction in the stride length and anterior speed and increase in the step
width for elders (Dean et al., 2007; Schrager et al., 2008; Ko et al., 2010) are seen in the samples used in this study.

© The Japan Society of Mechanical Engineers

Mediolateral MoS timing
Swing duration
Stride length

.56
.32

Construct1.87

Anterior
MoS

.26
Error
variance

.19

0.91

(

)

Anterior velocity of CoM.18

Mediolateral velocity of CoM
Step width

.56

.08

Construct
2.86

Mediolateral
MoS
(

.28
Error
variance)

Anterior MoS timing
Fig. 3

MIMIC model for the young (20–30s) adult group. Square nodes are observed variables. Circular nodes
are latent variables. They are normalized such that their means and standard deviations are 0 and 1,
respectively. GFI = 1.0. CFI = 0.99. p = 0.04. Error variances are the variances of the prediction errors.
Mediolateral MoS timing is not linked with the others. The correlation coeﬃcients among the formative
variables are not shown.

2.4. Multiple indicators and multiple causes (MIMIC) model
The MIMIC model is a type of model used in structural equation modeling (SEM). SEM analyzes the statistical
validity of a hypothetical linear relationship between several variables. In MIMIC models, latent variables are deﬁned
by linear combinations of several observed variables, and they inﬂuence another set of observed variables. The latentvariables are referred to as constructs. The observed variables that deﬁne the constructs are called formative indicators,
and those that are aﬀected by the constructs are called reﬂective indicators. Multiple formative and reﬂective indicators
are organized into a small number of constructs.
In this study, formative variables comprised the gait parameters and reﬂective variables comprised the minimum
MoS values along the anterior and mediolateral directions. SEM facilitates the discussion of the signiﬁcance of the overall
hypothetical structure and each branch. Incorporating the two types of MoSs into a single model provides a statisticallyvalid model of the relationship between them. lavaan in R was used for analysis. We used statistically signiﬁcant links
between variables with p-values less than 0.05. The models for young and elderly adults were computed separately. Allvariables were normalized to z-scores with means and standard deviations of 0 and 1, respectively.

3. Results
3.1. MIMIC model of young adults
The MIMIC model for the younger group is shown in Fig. 3. The numbers attached to the links represent the strengthof the inﬂuence of one node on another. The mean and standard deviation of the constructs are 0 and 1, respectively. The
major goodness-of-ﬁt indices were as follows: comparative ﬁt index (CFI) = 0.99, goodness-of-ﬁt index (GFI) = 1.00,
Akaike information criterion (AIC) = 932.4, RMSE = 0.08, and χ2 was 8.50 with a p-value of 0.04. These values largely
satisfy the general standards of a valid model (McDonald & Ho, 2002).
Only the anterior velocity of the CoM aﬀected both constructs 1 and 2, and the other gait parameters aﬀected only
one of the two latent constructs. However, the eﬀect of anterior velocity on construct 2 was less substantial as one-ﬁfth ofthat on construct 1. Constructs 1 and 2 mainly inﬂuenced the anterior and mediolateral MoSs, respectively. Conversely,
the mediolateral and anterior MoSs were mostly separate from each other.
The major determinants of anterior MoS were the anterior velocity of the CoM and swing duration, followed by stride
length. The decrease in the anterior velocity of the CoM and swing duration reduced the value of construct 1. A decreasein construct 1 led to an increase in the anterior MoS because the coeﬃcient of their linkage was negative. Collectively,
the model indicates that a slower walking speed, longer stride length, and shorter swing duration led to greater stability inthe anterior direction.
The gait parameters that substantially aﬀected the mediolateral MoS were the mediolateral velocity of the CoM
and the step width. The large step width and slow mediolateral velocity improved latent construct 2 and stability in the
mediolateral direction. Furthermore, the anterior velocity of the CoM slightly decreased construct 2, which resulted ininstability along the mediolateral direction.
© The Japan Society of Mechanical Engineers

Mediolateral MoS timing
Swing duration
Stride length
Anterior velocity of CoM

.22
.53

Construct1.71

Anterior
MoS

.59

(

.49
Error
variance

1.27
.33

)

.85

Mediolateral velocity of CoM
Step width.46

Construct
2

Mediolateral
MoS
(

.13
Error
variance)

Anterior MoS timing
Fig. 4

MIMIC model for the elder adults aged over 60 years old. GFI = 0.99. CFI = 0.98. p = 0.003. Anterior
and mediolateral MoS timings were not linked with the others. The correlation coeﬃcients among theformative variables are not shown.

Mediolateral MoS timing
Swing duration

Construct1

Anterior
MoS

Construct
2

Mediolateral
MoS

Stride length
Anterior velocity of CoM
Mediolateral velocity of CoM
Step width
Anterior MoS timing

Fig. 5More prominent in the elder adults
More prominent in the younger adults

The diﬀerences in the MIMIC models between the two age groups. Solid lines are connections that exist
only in the elder group or whose magnitudes of the coeﬃcients are signiﬁcantly greater for the elderly thanfor the young adults with p < 0.05 by t-test. Dotted lines are those that exist only in the model of young
adults.

3.2. MIMIC model of the elderly
Figure 4 illustrates the MIMIC model for adults aged 60 years and older. The goodness-of-ﬁt indices of this model
were as follows: CFI = 0.98, GFI = 0.99, AIC = 1087.82, RMSEA = 0.13, χ2 = 11.92, for which p-value was 0.003.
The model for older adults was more complex than that for young adults. In the model of the elderly, several gaitparameters aﬀected both constructs in the model. Construct 1 had nearly equal inﬂuences on the mediolateral and anterior
MoSs regarding magnitude. However, the signs of their coeﬃcients were opposite. Construct 1 decreased the anterior
MoS but increased the mediolateral MoS. Construct 2 positively aﬀected only mediolateral MoS.
Changes in single gait parameters led to changes in both types of MoSs. For example, a decrease in the anterior
velocity of the CoM increased the anterior MoS and decreased the mediolateral MoS by way of construct 1. Furthermore,
the decrease in the anterior velocity of the CoM improved the mediolateral MoS using construct 2. However, the MIMIC
model for the elderly shares similar characteristics with that for young people. For example, a slow walking speed, which
is an anterior velocity, a large step length, and a small swing duration, led to greater stability in the walking direction.
Furthermore, the large step width and slow mediolateral velocity of the CoM led to mediolateral stability.

4. Discussion
Figure 5 shows the diﬀerences between the two MIMIC models. The solid lines indicate connections that exist only
© The Japan Society of Mechanical Engineers

in the model of the elderly or whose inﬂuences are signiﬁcantly greater than those in the model of young adults withp < 0.05. Dotted lines represent connections that exist only in the young adult model. The diﬀerences between the two
age groups are complex. Particularly, the variables that form construct 1 and their impact on the anterior MoS diﬀer
substantially. However, no diﬀerences in the inﬂuence of construct 2 on the mediolateral MoS were observed between the
two age groups.
For easy access to the diﬀerences between the two MIMIC models, we computed multiple linear regression analyses
with MoSs and gait parameters as objective and explanatory variables, respectively. For these analyses, we used the
stepwise functions of MATLAB (2023a, Mathworks, Inc.), in which signiﬁcant explanatory variables with p < 0.05
were selected using the stepwise method. All variables were standardized to ensure that the regression coeﬃcients werecomparable to those of the MIMIC models.
The regression equation for mediolateral MoS in the young group was as follows:(young)

MoS ml= −0.47Vml + 1.11Width + 0.09S wing + 0.08T ant(6)with an adjusted coeﬃcient of determination R̂2 = 0.72. That for the elderly group was as follows:(elderly)

MoS ml= −0.50Vml + 1.06Width + 0.13S wing − 0.26Vant(7)

with an adjusted coeﬃcient of determination R̂2 = 0.74, where MoS ml , Width , S wing , and T ant are the mediolateral MoS,
step width, swing duration, and timing when the anterior MoS is minimized, respectively. Vml and Vant are the maximum
speeds of the CoM in the mediolateral and anterior directions, respectively.
As shown in Figs. 3 and 4 and in the regression models, the mediolateral MoSs are largely determined by the
mediolateral speed of the CoM and the step width. This is consistent with the deﬁnition of mediolateral MoS describedin Section 2. According to earlier studies, step width increases mediolateral MoSs (Iwasaki et al., 2022; Young andDingwell, 2012; Yamaguchi and Masani, 2022). In contrast, the eﬀect of anterior walking speed on mediolateral MoS
was signiﬁcant only in the regression model for the elderly. This result agrees with the MIMIC model for the elderly, as
shown in Fig. 4. As shown in Fig. 5, the inﬂuence of the anterior velocity of CoM on construct 2 was stronger for theelderly than for the young adults. Construct 2 largely determined the mediolateral MoS. Further, despite elderly people
with fast walking speeds tending to be unstable in the mediolateral direction, the mediolateral MoS of young adults
is not aﬀected by anterior walking speed. This ﬁnding helps comprehend the inconsistencies among previous studies.
Some studies have claimed that fast walking degrades the mediolateral MoS values (Gill et al., 2019; Ohtsu et al., 2019;
Alamoudi et al., 2020), whereas Hak et al. (2013) and Sivakumaran et al. (2018) reported no such relationship at the timeof heel contact. Our ﬁndings suggest that these incongruent reports may be because of the diﬀerent participant groups
involved in their studies. The eﬀects of walking velocity on the mediolateral MoS depend on the age at which the gait
strategy diﬀers. For example, elderly fallers tend to adopt conservative gait strategies with slow speeds and small strides(Lugade et al., 2011; Monaco et al., 2009).
Regarding the diﬀerence in the mediolateral MoS between young and older people, Yamaguchi and Masani (2022)
reported an intriguing aspect. They found that the angular momentum around the center of body mass in the frontal plane
was greater for older than for younger adults and that the older people appeared less stable and likely to lose balance;
however, the wide step width of the older adults dominantly determined the mediolateral MoS. Hence, the older adults are
more stable than the young during normal gait. Such aspects agree with the results of our study. As in Eqs. (4) and (5),the step widths were the most important predictor of the mediolateral MoS, and the velocity in the mediolateral direction,
which largely determines the momentum of the body, was a secondary parameter in determining the MoS.
As shown in Fig. 5, the eﬀects on the anterior MoSs from construct 1 are signiﬁcantly diﬀerent between young andelderly adults. The regression equation for the young adults was as follows:(young)

MoS ant= −0.74Vant + 0.26Length − 0.50S wing ,(8)

where R̂2 = 0.73. The equation for the elderly population was as follows:© The Japan Society of Mechanical Engineers(elderly)

MoS ant= −0.88Vant + 0.35Length − 0.14S wing + 0.18Vml − 0.14Width ,(9)where R̂2 = 0.52. MoS ant and Length are the anterior MoS and stride lengths, respectively. These regression equations
indicate that, for both age groups, the slower the walking speed and the larger the stride length, the more stable theanterior direction. These eﬀects are reasonable, considering the deﬁnition of the anterior MoS. In addition, the shorter theswing duration, the more stable the walking for all age groups. These characteristics were consistent between the two age
groups. In contrast, for the elderly group, the maximum mediolateral velocity Vml and step width Width were signiﬁcantdeterminants of the anterior MoS. These gait parameters are calculated in the frontal plane and apparently do not pertain
to the computation of the anterior MoSs. The MIMIC model shown in Fig. 4 also indicates that the parameters Vml andWidth inﬂuence the anterior MoSs for the elder group. These two parameters signiﬁcantly inﬂuenced the mediolateral
MoSs. Collectively, for the elderly, the anterior and mediolateral MoSs are not fully independent because the same gaitparameters, that is, Vml , Vant , and Width , simultaneously inﬂuence them.
This study introduced the timing at which MoS values were minimized in the gait cycle. As shown in Fig. 3, thetiming of the anterior MoS inﬂuenced construct 2 in the young adults. However, its eﬀect was smaller than that of theother gait parameters. Hence, we did not ﬁnd any meaningful relationship between these timings and MoSs.
Despite this study ﬁnding structural diﬀerences in the relationships between the MoSs and gait parameters between
young and elderly adults, the root causes are unknown. Gait strategies (Lugade et al., 2011; Monaco et al., 2009) andsensory and motor abilities (Osoba et al., 2019) diﬀer between these age groups. However, this study lacks basic data
to discuss how they relate to our ﬁndings. Furthermore, we used gait data of Japanese participants. Therefore, thegeneralizability of this study to other ethnicities remains unclear. These aspects should be studied further in the future.

5. Conclusion
No previous study has investigated the relationship between the MoSs in two directions and gait parameters during
steady walking or compared them between young and older adults. Therefore, MIMIC models were used to discuss the
single statistical model involving the MoSs and gait parameters. In the young adult group, the mediolateral and anterior
MoSs were mostly separated. By contrast, for the elderly group, the MoSs in the two directions interfered with each other.
The gait parameters deﬁned in the frontal plane, such as mediolateral speed and step width, aﬀected the anterior MoSs.
Furthermore, the anterior speed, which is deﬁned in the sagittal plane, correlated with the mediolateral MoSs. Despite theelderly with fast walking tending to be unstable in the mediolateral direction, the mediolateral MoS of young adults is not
aﬀected by anterior walking speed. These ﬁndings show diﬀerences in the structure of gait stability and gait parameters
between the elderly and young adults. Participant age must be considered when discussing gait stability. Nonetheless, thisstudy did not indicate the root causes of the diﬀerent variable structures between elderly and young adults, which will be
studied in the future.

Acknowledgment
This study was in part supported by the institutional research fund of Tokyo Metropolitan University.

References
Akiyama, Y., Kuboki, Y., Okamoto, S., Yamada, Y., Novel approach to analyze all-round kinematic stability during
curving steps. IEEE Access, Vol. 11 (2023), pp. 10326-10335.
Alamoudi, R., Alamoudi, M., Development of linear regression models to estimate the margin of stability based on
spatiotemporal gait parameters, IEEE Access, Vol. 8 (2020), pp. 19853-19859.
Bierbaum, S., Peper, A., Karamanidis, K., and Arampatzis, A., Adaptational responses in dynamic stability during disturbed walking in the elderly, Journal of Biomechanics, Vol. 43, Issue 12 (2010), pp. 2362-2368.
Brodie, M. A., Okubo, Y., Sturnieks, D. L, and Load, S. R., Optimizing successful balance recovery from unexpected trips
and slips (2018), Journal of Biomechanical Sience and Engineering, Vol. 13, No. 4, p. 17-00558, Advance online
Publication March 30, 2018.

© The Japan Society of Mechanical EngineersBruijin, S. M., Meijer, O. G., Beek, P. J., and van Die, J. H., Assessing of the stability of human locomotion: A review ofcurrent measures, Journal of the Royal Society Interface, Vol. 10, No. 83 (2013), p. 20120999.
Buzzi, U. H., Stergiou, M., Kurz, M. J., Hageman, P. A., Heidel, J., Nonlinear dynamics indicates aging aﬀects variability
during gait, Clinical Biomechanics, Vol. 18, Issue 5 (2003), pp. 435-443.
Balance Project, Balance augmentation in locomotion through anticipative, natural, and Cooperative control of exoskeletons: Report of BALANCE-Deliverable 3.1-Stability index (2013). Fundacion Tecnalia Research Innovation, Derio,
Spain, 2014.
Caderby, T., Yiou, E., Peyrot, N., Begon, M., Dalleau, G., Inﬂuence of gait speed on the control of mediolateral dynamic
stability during gait initiation, Journal of Biomechanics, Vol. 95, No. 2 (2014), pp. 417-423.
Carty, C. P., Mills, P., Barrett, R., Recovery from forward loss of balance in young and older adults using the stepping
strategy, Gait & Posture, Vol. 33 (2011), pp. 261-267.
Cromwell, R. L., and Newton, R. A., Relationship between balance and gait stability in healthy older adults, Journal of
Aging and Physical Activity, Vol. 12, Issue 1 (2004), pp.90-100.
Dean, J. C., Alexander, N. B., and Kuo, A. D., The eﬀect of lateral stabilization on walking in young and old adults, IEEE
Transactions on Biomedical Engineering, Vol. 54, No. 11 (2007), pp. 1919-1926.
Gill, L., Huntley, A. H., Mansﬁeld, A., Does the margin of stability measure predict medio-lateral stability of gait with aconstrained-width base of support?. Journal of Biomechanics, Vol. 95 (2019), p. 109317.
Hof, A., Gazendam, M., and Sinke, W., The condition for dynamic stability, Journal of Biomechanics, Vol. 38, No. 1(2005), pp. 1-8.
Hak, L., Houdijk, H., Steenbrink, F.,Mert, A., van der Wurﬀ, P., Beek, P. J., van Dieën, J. H., Speeding up or slowing
down?: Gait adaptations to preserve gait stability in response to balance perturbations, Gait & Posture, Vol. 36, No.
2 (2013), pp. 260-264.
Hak, L., Houdijk, H., Beek, P. J., van Dieën, J. H., Steps to take to enhance gait stability: the eﬀect of stride frequency,
stride length, and walking speed on local dynamic stability and margins of stability, Plos One, Vol. 8, No. 12 (2013),
p. e82842.
Hallemans, A., Verbecque, E., Dumas, R., Cheze, L., Van Hamme, A., Robert, T., Developmental changes in spatial
margin of stability in typically developing children relate to the mechanics of gait, Gait & Posture, Vol. 63 (2018),
pp. 22-28.
Inagaki, T., Akiyama, Y., Okamoto, S., Mayumi, T., and Yamada, Y., Relationship between gait stability indices and gaitparameters comprising joint angles using walking data of 288 people, Nagoya Journal of Medical Science, Vol. 85,
No. 2 (2023), pp. 211-222.
Iwasaki, T., Okamoto, S., Akiyama, Y., Inagaki, T., Yamada, Y., Kinematic Gait Stability Index Highly Correlated with
the Margin of Stability: Concept and Interim Report, Proceedings of the IEEE/SICE International Symposium on
System Integration (2021), pp. 347-350.
Iwasaki, T., Okamoto, S., Akiyama, Y., Yamada, Y., Gait stability index built by kinematic information consistent withthe margin of stability along the mediolateral direction, IEEE Access Vol. 10 (2022), pp. 52832-52839.
Kang, H. G., Dingwell, J. B., Dynamic stability of superior vs. inferior segments during walking in young and older
adults, Gait & Posture, Vol. 30, Issue 2 (2009), pp. 260-263.
Ko, S., Hausdorﬀ, J. M., Ferrucci, L., Age-associated diﬀerences in the gait pattern changes of older adults during fastspeed and fatigue conditions: results from the Baltimore longitudinal study of ageing, Age and Ageing, Vol. 39,
Issue 6 (2010), pp. 688-694.
Kobayashi, Y., Hida, N., Nakajima, K., Fujimoto, M., Mochimaru, M., AIST Gait Database 2019 (2019), available at[https://unit.aist.go.jp/harc/ExPART/GDB2019.html] (accessed on 1 Apr., 2021).
Kuroda, T., Okamoto, S., Akiyama, Y., Verifying the independence of anterior and mediolateral margin of gait stability
indices (2022), Proceedings of the IEEE Global Conference on Consumer Electronics 2022, pp. 590-592.
Lugade, V., Lin, V., Chou, Li-Shin., Center of Mass and Base of Support Interaction during Gait, Gait & Posture, Vol. 33,
Issue 3 (2011), pp. 406-411.
Martelli, D., Aprigliano, F., Tropea, P., Pasquini, G., Micera, S., Monaco, V., Stability against backward balance loss:
Age-related modiﬁcations following slip-like perturbations of multiple amplitudes, Gait & Posture, Vol. 53 (2017),
pp. 207-214.
McDonald, R. P., Ho, M. H., Principles and practice in reporting structural equation analysis. Psychological Methods,
Vol. 7, No. 1 (2002), pp. 64-82.
© The Japan Society of Mechanical Engineers

Monaco, V., Rinaldi, L. A., Macrı̀, G., Micera, S., During walking elders increase eﬀorts at proximal joints and keep low
kinetics at the ankle, Clinical Biomechanics, Vol. 24, Issue 6 (2009), pp. 493-498.
Ohtsu, H., Yoshida, S., Minamisawa, T., Takahashi, T., Yomogida, S., Kanzaki, H., Investigation of balance strategy overgait cycle based on margin of stability, Journal of Biomechanics, Vol. 95 (2019), p. 109319.
Osoba, M. Y., Rao, A. K., Agrawal, S. K., Lalwani, A. K., Balance and gait in the elderly: a contemporary review,
Laryngoscope investigative Otolaryngology, Vol. 4 (2019), pp. 143-153.
Roeles, S., Rowe, P. J., Bruijn, S. M., Childs, C. R., Tarfali, G. D., Steenbrink, F, Pijnappels, M., Gait stability inresponse to platform, belt, and sensory perturbations in young and older adults, Medical & Biological Engineering& Computing, Vol. 56 (2018), pp. 2325-2335.
Rogers, H. L., Cromwell, R. L., Grady, J. L., Adaptive changes in gait of older and younger adults as responses tochallenges to dynamic balance, Journal of Aging and Physical Activity, Vol. 16, Issue 1 (2008), pp. 85-96.
Schrager, M. A., Kelly, V. E., Price, R., Ferrucci, L., Shumway-Cook, A., The eﬀects of age on medio-lateral stability
during normal and narrow base walking, Gait & Posture Vol. 28, Issue 3 (2008), pp. 466-471.
Sivakumaran, S., Schinkel-Ivy, A., Masani, K., Mansﬁeld, A., Relationship between margin of stability and deviations inspatiotemporal gait features in healthy young adults Human Movement Science, Vol. 57 (2018), pp. 366-373.
Terrier, P., Reynard, F., Eﬀect of age on the variability and stability of gait: A cross-sectional treadmill study in healthy
individuals between 20 and 69 years of age, Gait & Posture, Vol. 41 (2015), Issue 1, pp. 170-174.
Yamaguchi, T., Masani, K., Eﬀects of age on dynamic balance measures and their correlation during walking across theadult lifespan. Scientiﬁc Reports, Vol. 12 (2022), p. 14301.
Young, P. M. M., Dingwell, J. B., Voluntary changes in step width and step length during human walking aﬀect the
dynamic margins of stability, Gait & Posture, Vol. 36, Issue 2 (2012), pp. 219-224.

© The Japan Society of Mechanical Engineers