BJMB
Brazilian Journal of Motor Behavior
Special issue:
Effects of aging on locomotor patterns
!
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
326 of 351
!
Mechanisms that stabilize human walking
A. M. VAN LEEUWEN
1,2
| SJOERD M. BRUIJN
1,2
| JAAP H. VAN DIEËN
1
1
Department of Human Movement Sciences, Faculty of Behavioural and Movement Sciences, Vrije Universiteit Amsterdam, Amsterdam Movement Sciences, Amsterdam,
The Netherlands.
2
Institute of Brain and Behavior Amsterdam.
Correspondence to: Sjoerd M. Bruijn!
Email: s.m.bruijn@gmail.com
https://doi.org/10.20338/bjmb.v16i5.321
ABBREVIATIONS
α
i
Angular acceleration of the i
th
Segment
CoM Center of mass
CöM Acceleration of the COM
CoM′ Position vector of the vertical
projection of the COM on the
ground
CoP Center of pressure (position vector
of the point of application of the
ground reaction force F
g
)
com
i
Position vector of the center of
mass of the i
th
segment
com
"
i
Linear acceleration of the i
th
segment
Fg
y
Vertical component of the ground
reaction force
𝐻
$
Change of angular momentum
around the body center of mass
l
i
Moment of inertia of the i
th
segment
m Body mass
m
i
Mass of the i
th
segment
n Number of segments
r
e
Position vector of the point of the
application of an external force F
e
PUBLICATION DATA
Received 04 11 2022
Accepted 14 12 2022
Published 15 12 2022
ABSTRACT
In this paper, we review what mechanisms are used to stabilize human bipedal walking. Based on mechanical
reasoning, potential mechanisms to control the body center of mass trajectory are modulation of foot placement,
stance leg control by modulation of ankle moments and push-off forces, and modulations of the body’s angular
momentum. The first two mechanisms and especially the first are dominant in controlling center of mass
accelerations during gait, while angular momentum control plays a lesser role, but may be important to control
body alignment and orientation. The same control mechanisms stabilize both steady-state and perturbed gait in
both the mediolateral and antero-posterior directions. Control is at least in part active and is affected by
proprioceptive, visual and vestibular information. Results support that this reflects a feedback process in which
sensory information is used to obtain an estimate of the center of mass state based on which foot placement and
ankle moments are modulated. These active feedback mechanisms suggest training approaches for populations
at risk of falling, through perturbations, augmented feedback, or constraining one mechanism to train the other
mechanisms.
KEYWORDS: Gait stability | Foot placement | Stance leg control | Angular momentum | Falls
1.INTRODUCTION
Stabilizing bipedal walking to avoid falls is challenging. This is readily apparent in
toddlers who learn to walk and usually master this only after many falls have occurred. At
the other end of the age spectrum, age-related but also disease-related impairments often
also cause problems in stabilizing gait. However, then the resulting falls are much more
problematic, as they often have serious adverse consequences, such as injury, fear of
falling, loss of independence, and social isolation
1,2,3
. Training interventions have been
successful at reducing fall rates in older adults
4
and in patients at high risk of falling
5
.
However, in our opinion, new training approaches to improve gait stability and methods to
assess and understand changes in gait stability can be derived from a better understanding
BJMB
Brazilian Journal of Motor Behavior
Special issue:
Effects of aging on locomotor patterns
!
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
327 of 351
!
of the mechanisms that are used to stabilize gait. In an earlier review, we covered foot
placement as the most dominant mechanism used to stabilize gait
6
. In this review, we
expand on this and provide an overview of gait stability control mechanisms and an outlook
on how insight into these mechanisms could be used to identify potential training
approaches.
For the purpose of this review, we will pragmatically define ‘stable’ gait as gait that
does not lead to falls. This requires control of the position of the body center of mass relative
to the base of support. In gait, the base of support is formed by those parts of the feet that
are in contact with the floor at any point in time. In humans, a large part of the total body
mass is located high above a small base of support, particularly in single stance.
Consequently, small deviations in body orientation result in substantial gravitational
moments that can easily move the center of mass away from the base of support. Therefore,
even the small variations in the center of mass position that occur in unperturbed gait need
to be corrected, to avoid cumulative effects over time. Thus ongoing (intermittent or
continuous) stabilization is needed. When a perturbation occurs, which can here be defined
as any external mechanical event that disturbs the relation between the center of mass and
base of support beyond the variance observed in unperturbed gait, it is evident that
stabilizing control is required. However, it is not evident that the same stabilizing
mechanisms are used for the small deviations during unperturbed gait and for the larger
deviations after perturbations.
Stabilization of gait can be achieved by passive and active mechanisms. Passive
stabilization relies on the passive mechanical properties (stiffness, damping and inertia of
the human body), whereas active mechanisms involve modulation of neural drive and
muscle activity in response to sensory information. Passive mechanisms may thus be
efficient, as in requiring low control effort and energy costs, but may not be amenable to
change for example by training. Active mechanisms are presumably more adaptive to task
requirements in the short term and may be more amenable to improvement by training in the
long term. Note that active and passive mechanisms may be used in parallel.
As mentioned above, stabilization of bipedal walking is challenging. Nevertheless,
a simple two-dimensional (sagittal plane) model of a bipedal walker can be stable without
any form of active control. In such a model, the forward fall of the center of mass is controlled
on a step-by-step basis through adequate foot placement resulting from the model’s passive
dynamics
7
. The ground contact force after foot placement creates a backward moment,
which catches the forward fall. However, these passive models cannot deal with
perturbations of realistic magnitude and also three-dimensional versions are unstable in the
mediolateral direction
8
. This indicates that additional active control must be exerted to
horizontally accelerate the center of mass in the desired direction, when the center of mass
deviates from its planned trajectory due to errors in control or external perturbations.
Modelling the human body as a system of linked rigid segments, we can write the
acceleration of the center of mass as
!"#$
%
&
!the sum of three mechanisms
9
:
(
"
!
#$%&'
)
×*
!
+,
(
$%-#$%&'
)
×*
"
#.
/
0($%& #$%& ')
' "#$
%
(1)
BJMB! ! ! ! ! ! ! !
Brazilian(Journal(of(Motor(Behavior(
(
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
328 of 351
!
Special issue:
Effects of aging on locomotor patterns
in which r
e
is the position vector of the point of application of an external force F
e
,!
"#$
′ is the position vector of the vertical projection of the center of mass (CoM) on the
ground, center of pressure (CoP) is the position vector of the point of application of the
ground reaction force F
g
,
(
)
!
(
)
is the change of angular momentum around the body center
of mass, and m is the body mass. The coordinate system is according to the ISB
recommendations: X-axis forward, Y-axis vertically upward, Z-axis to the right. Note this has
effects on the sign of the contribution of each of the three terms in the numerator on the right.
The denominator of the left-hand term consists of the product of body mass and the
height of the center of mass above the ground, which we will assume to be constant for now.
This leaves us three terms to consider:
(
𝑟
#
−𝐶𝑜𝑀
$
)
×𝐹
#
*
(
𝐶𝑜𝑃−𝐶𝑜𝑀
$
)
×𝐹
%
*
𝐻
-
*
Each of these terms reflects a mechanism to horizontally accelerate the center of
mass and hence a potential mechanism to stabilize gait. We will first consider the unipedal
stance phase of steady-state gait for each of these terms and then consider what is different
in bipedal stance.
Regarding the first term, external forces can be applied by grabbing hold of for
example a handrail, but also by foot placement or stepping. We will exclude mechanisms
like grabbing a handrail and focus on the only ‘external force generation’ that is considered
part of normal walking, i.e., stepping or foot placement. R
e
can be controlled by placing the
swing leg’s foot at the desired location and F
e
can be controlled by adjusting the swing leg’s
stiffness when reaching that location. Foot placement can also be seen as changing the
base of support and center of pressure and hence part of the second mechanism, in which
case the current term does not need to be considered. From this perspective, it is obvious
that foot placement has the advantage that it allows a shift of the center of pressure beyond
the original base of support. Given that clearly different responses at the joint level underly
these two mechanisms, we prefer to keep them separate and treat foot placement as the
generation of an external force. In double support, choosing a new foot placement location
is not an option.
Considering the second term, changes in the position of the CoP and the ground
reaction force are largely determined by actions of the stance leg. We will therefore refer to
the mechanism described by this term as stance leg control, to differentiate it from the first
mechanism foot placement. The center of pressure is always underneath the stance foot,
but it can be shifted within the foot contact area by means of ankle moments. Since CoP and
CoM’ are both on the ground, the horizontal accelerations of the center of mass due to this
term are further only dependent on the vertical component of the ground reaction force (Fg
y
in equation 2).
(
𝐶𝑜𝑃−𝐶𝑜𝑀
$
)
×𝐹
%
=
/
𝑥
&'(
−𝑥
&')
0
𝑧
&'(
−𝑧
&')
3
×
4
𝐹𝑔
*
𝐹𝑔
+
𝐹𝑔
,
6
=
4
−(𝑧
&'(
−𝑧
&')
)𝐹𝑔
+
(𝑧
&'(
−𝑧
&')
)𝐹𝑔
*
−(𝑥
&'(
−𝑥
&')
)𝐹𝑔
,
(𝑥
&'(
−𝑥
&')
)𝐹𝑔
+
6
(2)
BJMB! ! ! ! ! ! ! !
Brazilian(Journal(of(Motor(Behavior(
(
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
329 of 351
!
Special issue:
Effects of aging on locomotor patterns
The vertical ground reaction force can be modified to induce horizontal accelerations
as well, but this would be at the ‘cost’ of a vertical acceleration of the center of mass and
would not allow independent control of the mediolateral and anteroposterior acceleration of
the center of mass. In double support, the center of pressure can be shifted over a larger
area than in single support by modulating the ground reaction forces on both legs, e.g.,
pushing off more or less with either leg.
The third mechanism is creating a change in angular momentum of the body, which
equates to changing the moment of the ground reaction force relative to the center of mass.
The rate of change of angular momentum of a system of linked rigid segments equals:
𝐻
-
=
∑
(
𝑐𝑜𝑚
-
−𝐶𝑜𝑀
)
×𝑚
-
:
𝑐𝑜𝑚
;
-
−𝐶𝑜𝑀
;
<
+𝐼
-
𝛼
-
- ./
- .0
(3)
in which com
i
*
is the position vector of the center of mass of the i
th
segment, m
i
is the
mass of the i
th
segment, cöm
i
is the linear acceleration of the i
th
segment, I
i
is the moment of
inertia of the i
th
segment, α
i
is the angular acceleration of the i
th
segment, and n is the number
of segments to be considered.
As this equation shows, the horizontal acceleration of the center of mass can be
controlled by accelerating body segments with respect to the center of mass. Examples of
the use of this mechanism are the ‘hip strategy’
10
, involving trunk flexion for anteroposterior
stabilization after large perturbations of standing, and the arm movements used when
balancing on a slackline
11
. The use of this mechanism is in principle not different between
single and double support, except that leg segments (of the swing leg) can only be used in
single support.
In summary, horizontal acceleration of the body’s center of mass can be achieved
through three mechanisms: 1) generating an external force on the body by making contact
with the environment, 2) shifting the center of pressure of the ground reaction force within
the current base of support, 3) changing the angular momentum of body segments around
the center of mass
9
. The mechanisms described can be separated analytically, but in reality,
they will often interact. For example, changing the center of pressure without simultaneously
changing the direction of the ground reaction force will change the moment of the ground
reaction force relative to the center of mass and hence the angular momentum.
Observations from unperturbed gait can be used to assess the usage of the three
stabilizing mechanisms. In addition, perturbations of gait and changes in stabilization
demands (e.g., walking on a narrow beam versus a normal surface) have been employed to
probe their usage and the relevance of the observations for stabilization. This can provide a
first indication of whether training each mechanism could be useful. However, not only the
extent to which each mechanism plays a role, but also the extent to which this is the result
of passive dynamics or of active control is an important consideration, as only actively
controlled mechanisms would form a feasible target for training. Based on the model studies
mentioned above, this is likely to be different for control in the anteroposterior and
mediolateral directions.
In the subsequent sections of this review, we will summarize and discuss the
literature on the three mechanisms to stabilize gait identified above. For each mechanism,
we will first describe the evidence that it is actually used in the control of steady-state human
gait. We will then assess whether and how the usage of these mechanisms changes in
response to external perturbations. Next, we will discuss the sensory information and the
BJMB! ! ! ! ! ! ! !
Brazilian(Journal(of(Motor(Behavior(
(
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
330 of 351
!
Special issue:
Effects of aging on locomotor patterns
actuation underlying each of the mechanisms. For each of these topics, we will compare
control in the mediolateral and anteroposterior directions. Finally, we propose and discuss
some training approaches based on these mechanisms. We will start with foot placement as
this has received more attention in the literature and is considered the dominant mechanism
to stabilize gait.
2. THE THREE MECHANISMS DURING UNPERTURBED WALKING
2.1 Foot placement
Foot placement has extensively been discussed in our previous review
6
. We will
therefore only briefly summarize the main findings here.
To stabilize gait in the mediolateral direction, foot placement should be lateral to the
extrapolated center of mass position, that is a weighted sum of the center of mass position
and its velocity
12
. By placing the foot with a lateral offset relative to the extrapolated center
of mass, the sideward movement of the body center of mass towards the lateral edge of the
base of support will be reversed. This can of course be achieved by: (1) taking such wide
steps that the feet are always placed lateral to the extrapolated center of mass position, or
(2) by regulating foot placement, so that it’s just lateral to the extrapolated center of mass
position. For the latter, both an adequate estimate of the state of the center of mass with
respect to the feet, as well as sufficient ability to control the swing leg to place it at the
appropriate position are needed.
Supporting regulation of foot placement on a step-by-step basis, Wang and
Srinivasan
13
showed that as much as 80% of the variance in deviations from average
mediolateral foot placement could be explained by deviations from average in mediolateral
pelvis position and speed at midstance, and this was much more than could be explained
from swing leg state at midstance. The pelvis state used here can be considered a
reasonable proxy for center of mass state in unperturbed walking, with an offset difference
between sacrum marker and center of mass position
14
that does not affect the model used.
Positive coefficients in the model for both state variables indicate that when the pelvis is
displaced too far lateral or moves in this direction too fast, a more lateral placed step will
follow, and vice versa. These results thus suggest a stabilizing feedback mechanism. In
terms of equation 1, r
e
is determined by foot placement and the resulting change of (r
e
-
CoM) will correct deviations in center of mass velocity or position towards the average value.
The predictive value of the model increased for center of mass states from early swing
onwards and plateaued around mid-swing
13
, suggesting that foot placement location is
selected based on information obtained until this phase of the gait cycle. For anteroposterior
foot placement, predictors of foot placement were pelvis anteroposterior velocity plus
mediolateral pelvis position and velocity. Similar to mediolateral foot placement, increased
velocity of the pelvis predicts more forward foot placement. The coefficients for mediolateral
pelvis state in this model indicate that for example rightward pelvis perturbations at right leg
mid-swing imply shorter right steps. The variance explained by this model at mid-swing was
much lower than for mediolateral foot placement, at about 40%, and increased rapidly right
after foot placement, suggesting that pelvis state is adjusted to foot placement in the early
stance phase. This indicates that in this phase other stabilizing mechanisms may be used
for anteroposterior control of the center of mass.
The models proposed by Wang & Srinivasan
13
were successfully applied to data
BJMB! ! ! ! ! ! ! !
Brazilian(Journal(of(Motor(Behavior(
(
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
331 of 351
!
Special issue:
Effects of aging on locomotor patterns
from several other studies on mediolateral control
15,16,17,18,19,20,21,22,23
and to data from one
other study on anteroposterior control
13,24
. Jin et al.
24
showed that, as for mediolateral foot
placement, the anteroposterior center of mass position and velocity in the corresponding
direction only provide a good prediction of anteroposterior foot placement, supporting a more
parsimonious model for the control of foot placement than the original model
13
. In these
studies, the relative variance explained by the model and the RMS of the residual error were
used as measures for the quality of foot placement coordination and these measures were
shown to be sensitive to perturbations, ageing, pathology, fall risk and effects of enhanced
feedback
16,18,25
.
It is important to note, that foot placement also subserves other goals than
stabilization of gait, such as achieving intentional changes in velocity (speed and direction
12
) and avoiding obstacles or selecting suitable foot holds
26
. Some of these goals may
coincide. For instance, control of gait speed may well coincide with control of gait stability
27
and may in fact be inseparable from it.
2.2 Stance leg control
Stance leg control can shift the center of pressure in the mediolateral and
anteroposterior directions, respectively through ankle inversion/eversion and
plantar/dorsiflexion. Moreover, push-off can modulate the ground reaction force. In equation
1, stance leg control thus determines the following term: (CoP-CoM')×F
g
. The term (CoP-
CoM') then reflects ankle moment control to shift the center of pressure, whereas, F
g
can be
modulated through push-off.
In section 2.1, we already alluded to the use of other stabilizing mechanisms to
compensate for errors in foot placement. During steady-state walking, stance leg control is
indeed used to (partially) correct for foot placement errors, through shifting the center of
pressure and through push-off
24,28
. As the foot extends further in the anteroposterior as
compared to the mediolateral direction, more (effective) center of pressure modulation can
be achieved in the anteroposterior direction. However, despite the limited width of the foot,
mediolateral center of pressure modulation during single stance also functions as a
stabilizing mechanism during steady-state walking
28,29,30
.
During steady-state walking, ankle moment control is used in the mediolateral
direction, since the foot placement error, i.e. the residual of the foot placement model
described in section 2.1, predicts the mediolateral center of pressure shift during single
stance
28
. That these center of pressure shifts act as a stabilizing mechanism, is likely, as
they disappear when walking with external lateral stabilization
30
. So mediolateral ankle
moments correct for foot placement errors to stabilize gait during the new stance phase. In
addition, ankle moments in the previous stance phase can stabilize gait preceding placement
of the new stance leg
31
. This allows for an early correction, before foot placement can take
effect
32,33
, but might also be used to steer foot placement. Suggesting a steering role of
ankle moments, targeted stepping is preceded by an early center of pressure shift during
single stance
34
. A similar mechanism may be used during steady-state walking to steer foot
placement to comply with stability demands.
Motorized push-off, perturbations and modelling results suggest that push-off
modulation can contribute to mediolateral gait stability
35,36
. External lateral stabilization
seems to diminish active push-off modulation
37
, as the vestibulomotor coherence of the
medial gastrocnemius decreased during stabilized walking
37
. But, whether push-off
BJMB! ! ! ! ! ! ! !
Brazilian(Journal(of(Motor(Behavior(
(
!
van Leeuwen,
Bruijn, van Dieën
2022
VOL.16
N.5
332 of 351
!
Special issue:
Effects of aging on locomotor patterns
modulation is indeed implemented to stabilize gait in the mediolateral direction remains to
be investigated.
For the anteroposterior direction, it has been shown that foot placement errors are
corrected during double stance, achieved mainly through force generated by the trailing leg,
which is in turn mainly determined by the sagittal plane ankle moment
24
. This push-off
mechanism also contributes to the trailing leg’s trajectory and hence to reaching a targeted
location
26
. It thus seems likely that during steady-state walking, push-off is used as a
corrective mechanism for anteroposterior foot placement of the leading leg as well as to
control the trajectory of the trailing leg.
Although the above-mentioned evidence shows that stance leg control contributes
to stable steady-state walking, the lower relative explained variance of steady-state ankle
moment control models, as compared to foot placement models
24,28
, reflects its lesser
importance compared to the foot placement mechanism.
2.3 Angular momentum changes
Formula 1 indicates that next to foot placement (section 2.1) and stance leg control
(section 2.2), changes in angular momentum can be used to stabilize gait. Early work on
angular momentum during unperturbed human walking has shown that it is tightly regulated,
and some authors have even suggested that the goal is to keep a near zero angular
momentum
38,39
. Indeed, angular momentum has been shown to be increased in patient
populations, and the increase in angular momentum was correlated with worse scores on
clinical balance measures
40,41
. However, as walking inherently requires movement of the
limbs which will bring about a (change in) angular momentum, it is hard to tease apart
changes in angular momentum, which are explicitly aimed at stabilizing the center of mass
trajectory, from those that happen simply due to movements necessary for progression.
One way to tease these effects apart may be to make other stabilizing mechanisms
less available, such that subjects must rely more on angular momentum control. Indeed,
angular momentum control was largely responsible for maintaining standing balance on a
beam of only 4mm width
42
. On the other hand, when standing on balance boards which
could rotate in the mediolateral
43
, or antero-posterior direction
44
, the CoP mechanism was
dominant, with contributions of angular momentum changes often in the opposite direction
of the CoP mechanism. In a recent experiment, we tested whether subjects use angular
momentum control in walking, when their other possibilities to stabilize gait are diminished
45
. Subjects walked on a treadmill in a control condition, a condition wearing shoes which
restrict the use of the ankle mechanism, and in a condition in which they both wore these
shoes and were instructed to walk with narrow steps. The idea was that these conditions
would increasingly limit use of the other stabilizing mechanisms. Results showed that indeed
changes in angular momentum contributed more to center of mass accelerations during the
harder conditions, but the effect of foot placement also remained substantial. From this, we
concluded that the use of angular momentum changes may be limited, probably because
angular accelerations ultimately need to be reversed in view of anatomical constraints and
because of interference with other task constraints, e.g., interference with the gait pattern.
Using changes in angular momentum to affect (linear) center of mass acceleration will
inevitably lead to changes in body orientation, which may also lead to altered visual and
vestibular inputs, which in and of itself may be perturbing. All in all, it seems that humans
can use angular momentum changes to stabilize steady-state gait, but that they do so to a