Exp Brain Res (2003) 151:387–404
DOI 10.1007/s00221-003-1481-x
RESEARCH ARTICLE
S. B. Bortolami · P. DiZio · E. Rabin · J. R. Lackner
Analysis of human postural responses to recoverable falls
Received: 7 August 2002 / Accepted: 11 March 2003 / Published online: 13 June 2003
! Springer-Verlag 2003
Abstract We studied the kinematics and kinetics of
human postural responses to “recoverable falls.” To
induce brief falling we used a Hold and Release (H&R)
paradigm. Standing subjects actively resisted a force
applied to their sternum. When this force was quickly
released they were suddenly off balance. For a brief
period, !125 ms, until restoring forces were generated to
shift the center of foot pressure in front of the center of
mass, the body was in a forward fall acted on by gravity
and ground support forces. We were able to describe the
whole-body postural behavior following release using a
multilink inverted pendulum model in a regime of “small
oscillations.” A three-segment model incorporating upper
body, upper leg, and lower leg, with active stiffness and
damping at the joints was fully adequate to fit the
kinematic data from all conditions. The significance of
our findings is that in situations involving recoverable
falls or loss of balance the earliest responses are likely
dependent on actively-tuned, reflexive mechanisms yielding stiffness and damping modulation of the joints. We
demonstrate that haptic cues from index fingertip contact
with a stationary surface lead to a significantly smaller
angular displacement of the torso and a more rapid
recovery of balance. Our H&R paradigm and associated
model provide a quantifiable approach to studying
recovery from potential falling in normal and clinical
subjects.
Keywords Motor control · Posture · Modeling · Balance ·
Falling
S. B. Bortolami ()) · P. DiZio · E. Rabin · J. R. Lackner
Ashton Graybiel Spatial Orientation Laboratory,
Brandeis University,
Waltham, MA 2454-9110, USA
e-mail: simborto@brandeis.edu
Tel.: +1-781-7362033
Introduction
Our goal was to study postural control performance
during sudden exposure to off-balance conditions. Quantitative study of sudden off-balance conditions is relevant
for understanding the events preceding falling and the
functioning of short-latency postural restabilization mechanisms. We present a paradigm and a model, which have
general implications regarding the structure and functions
of the posture controller. Research on posture has
employed a variety of techniques to evaluate postural
control and many of these have relevance for understanding falling and short latency postural response mechanisms. We describe the advantages and limitations of
some of the key techniques before describing our
approach and its potential. Most approaches fall within
several broad categories: moving platform posturography,
pushes or pulls of the body, self-generated perturbations,
vertical drops, and releases from a leaning posture.
Considerable insight into postural control mechanisms
and their derangement due to various pathologies has
been gained with these methods.
Moving platform posturography
Platforms that can displace and tilt allow the evaluation of
postural responses to linear or angular displacement of the
support surface (Nashner 1971, 1987; Nashner and
Forssberg 1986). Platform perturbations are extensive in
magnitude and time, for example, 8 cm over 450 ms (see
Horak and MacPherson 1996). Electromyographic (EMG)
responses in the leg muscles occur within 70–90 ms
(Horak and MacPherson 1996; Horak and Nashner 1986).
With platform perturbations, normal subjects use three
general “strategies” depending on perturbation magnitude
and direction and the area of the support surface under the
feet. The ankle strategy is used when the platform moves
backward under the feet or rotates downward under the
toes. Subjects extend their feet to move the center of
pressure (cp) forward and to drive the center of mass
388
backwards under the feet; there is little rotation at other
joints (Horak and Nashner 1986; Nashner 1977). A hip
strategy is employed when the base of support is so
narrow that little force can be exerted with the toes and
when large platform perturbations occur (Horak and
Nashner 1986; Nashner and McCollum 1985). Stepping is
a third strategy that may be used with very large
perturbations and is a way to avoid falling (Horak and
MacPherson 1996). The response to platform perturbations differs depending on “central set,” for example,
whether the perturbation is predictable, and whether
vision is permitted (Horak and Nashner 1986).
Pushes and pulls on the body
Perturbations applied to the torso at force levels below
those toppling the body or forcing a step constitute a way
of studying integrative coordination of upper and lower
limbs (Cordo and Nashner 1982; McIllroy and Maki
1995; Schieppati et al. 1995a, 1995b; Holt et al. 2000).
EMG latencies in muscles counteracting predictable and
unpredictable lateral or forward forces applied at the
waist are approximately 75 ms (Elger et al. 1999; Gilles et
al. 1998). EMG latencies in arm and hip muscles are
similar, but close analysis suggests that they are under
parallel, centrally generated control rather than a single
general control pattern (Wing et al. 1997). Short latency,
compensatory EMG activity (approximately 50–70 ms)
appears also when perturbations are delivered by a
backpack apparatus that perturbs the trunk during quiet
stance or locomotion (Dietz 1992, 1996). When the
perturbations applied to the body are increased in
magnitude, subjects fall unless they make corrective
movements. For example, if subjects standing on one leg
are subjected to a progressively increasing or suddenly
destabilizing force on their torso, they exhibit a protective
hop (Roberts 1975). If they are standing on both legs, they
take a compensatory step (or steps) to restore balance
(Luchies et al. 1994, 1999; Pai and Patton 1997, Pai et al.
1998; Patton et al. 1999; Pidcoe and Rogers 1998).
Exposed to sudden backward pulls, young subjects (mean
age 22 years) take a single protective step whereas elderly
(mean age 73) subjects take multiple short, low steps
(Luchies et al. 1994). Thus, restoring strategies either
relate to maintaining upright posture with ankle or hip
movements or involve stepping.
Studies involving exposing the body to multiple
medial-lateral pushes at the trunk or pelvis at random,
but at relatively low force levels (below those initiating a
protective step) raise the possibility that muscle stiffness
rather than reflexive compensation may be the key
component of restabilization (Rietdyk et al. 1999).
Predictive models (static and dynamic) have been developed to characterize, based on an inverted pendulum
model, the boundaries for center of mass position and
velocity limits, before a protective step must be initiated
(Pai and Patton 1997; Patton et al. 1999).
The relative contribution of stiffness control to quiet
standing is a matter of some debate. Winter and
colleagues (1996, 1998, 2001) have proposed an inverted
pendulum model with the muscles serving as tunable
springs to drive the center of pressure in phase with the
center of mass. Morasso and Schieppati (1999) have
challenged this approach arguing that the relationship
between the center of mass and center of pressure is a fact
of physics and not the result of control patterns, and that
ankle stiffness per se is insufficient to stabilize the body.
They propose active control by the CNS and point to the
potential role of ankle proprioception and foot somatosensation in allowing for anticipatory control.
Self-generated perturbations
Movements of the arms and other parts of the body can
potentially destabilize posture. However, a variety of
anticipatory postural compensations occurs when subjects
make voluntary movements that have consequences for
their postural stability, for example, pulling on a handle or
raising an arm (Cordo and Nashner 1982; Marsden et al.
1981). These anticipatory compensations have the consequence of counteracting the impending torques on the
body and the shifts in center of mass. These studies are
insightful in illuminating the wide range of compensations that must be accompanying virtually all aspects of
voluntary movement and locomotion (Bouisset and
Zattara 1981, 1988; Cordo and Nashner 1982; Crenna
and Frigo 1991; Gelfand et al. 1971; Gurfinkel and Latash
1979; Gurfinkel and Osovets 1972; Gurfinkel et al. 1971,
1988; Marsden et al. 1978, 1981; Massion 1984; Massion
and Dufosse 1988; Nardone and Schieppati 1988; Nashner and Forssberg 1986; Sanes and Jennings 1984).
Recently it has been suggested that even during quiet
stance, a feed forward ankle joint stiffness strategy is
employed, based on predicting the loading pattern, to
control sagittal plane sway (Gatev et al. 1999). Anticipatory postural compensations are also present for ball
catching (Lacquaniti and Maoli 1989; Massion 1992;
Paulignan et al. 1989) and for self-induced perturbations
such as releasing a load (Aruin and Latash 1995, 1996;
Aruin et al. 2001; Beek and Santvoord 1996).
Vertical drops
Studies of actual falling have been carried out in which
subjects are suspended a short distance above the ground
by a handle that they grasp (Greenwood and Hopkins
1976, 1980; Melvill Jones and Watt 1971; Wicke and
Oman 1982). When the handle is suddenly released by an
electromagnet the subject falls under the action of gravity.
A pulley and weight system has also been used to drop
subjects at fractional g-levels (Greenwood and Hopkins
1976, 1980). EMG activity occurs within 60–80 ms
following release in the leg muscles involved in decelerating the body on landing as well as in other,
389
nonpostural muscles. This generalized response likely
represents an otolith related activation because labyrinthine-defective subjects do not show those early EMG
responses. By contrast, labyrinthine-defective subjects
show normal postural responses if the support surface on
which they are standing is displaced (Diener and Dichgans 1988; Dietz 1996).
Release from a leaning posture
A series of studies has evaluated the ability to take a step
to regain balance following release from various degrees
of forward tilt. Subjects lean forward while their body is
supported by a harness that takes up a controlled fraction
of their weight, thus allowing them to assume various
extents of body tilt. At a random time, the harness is
released. The body then gathers momentum as it is
accelerated downward by gravity and the subjects try to
take a forward step to regain balance. A safety harness
prevents impact with the floor if they are unable to step.
These studies have shown important age differences in
recovery as well as gender differences (Thelen et al. 1997;
Wojcik et al. 1999). EMG latencies in the muscles
involved in postural recovery range from 73–114 ms and
do not show any age-related dependency of functional
significance (Thelen et al. 2000).
Common drawbacks of current perturbation techniques
Most perturbation paradigms for studying posture apply
the perturbation to a specific part of the body. For
example, moving platforms initiate a perturbation at the
feet that is conveyed upward through successive segments
of the body. Perturbations at the torso, either externally
applied or self-generated by arm movements, affect the
head and the hips first and then upper legs and lower legs
and feet. Hip perturbations affect body segments successively both downwards and upwards. These types of
perturbations have many advantages in terms of allowing
successive segmental contributions to be identified. They
do, however, complicate the physical modeling and
characterization of the postural compensations. The
technique of dropping the test subject has the advantage
that all segments of the body are simultaneously accelerated downward together during the brief period of free
fall preceding the landing. However, the recovery of
balance after landing is difficult to characterize and
quantify. Another issue is the suddenness of the perturbation. Most techniques, other than releasing from an offvertical posture or vertical drops, must displace or deform
the body posture. This requires time and force, which for
practical reasons cannot be extremely large. Consequently
most perturbations induce a slow postural response. The
celerity of the stimulation is a key factor because it
reflects on the kind and order of the pathways responding
to the perturbation. Most posture studies also lack the use
of analytical and numerical models specific to their
paradigms.
The hold & release paradigm
Our goal was to employ a technique for creating a
simultaneous and sudden acceleration of all body segments about the feet using an approach amenable to
mathematical characterization so that we could model the
pattern of postural recovery. We wanted our paradigm to
share key characteristics with falling onset since posture
control, by its nature, functions to avoid falling. This
would allow us to determine whether stiffening is a
mechanism employed in recovering from falling. In
addition, we wanted to be able to quantify the magnitude
of the perturbation and to be able to scale its magnitude
across trials and different subjects to give the paradigm
flexibility and ease of implementation. The experimental
paradigm we adopted (Hold & Release, or H&R; Rabin et
al. 2000) is illustrated in Fig. 1. It is a variant of a
procedure developed in the clinical setting by Barin and
Stockwell (1983; see also Stockwell 1983; Krebs et al.
2001). In our situation a subject stands upright and
actively resists a horizontal force applied to the sternum.
The force is suddenly withdrawn (within 30–40 ms) and
the subject is projected forward pivoting at the ankles,
knees and hips because the center of foot pressure was
displaced toward the heels by the holding force on the
sternum.
An important characteristic of the H&R is that it
mimics, in a functionally relevant and repeatable manner,
what happens during unexpected loss of balance such as
tripping or loss of footing. A large number of falls, some
investigators suggest the majority, occur because of
stumbling or tripping on obstacles during walking (Blake
et al. 1988; Campbell et al. 1990; Overstall et al. 1977;
Ruberstein et al. 1988). In both tripping and H&R the
body is initially nearly upright and has forward momentum, but the center of foot pressure is misaligned with the
center of mass. Figure 2 schematizes the onset of falling
after tripping and the associated residual momentum of
the body. During walking all body segments move with
an average speed equal to the gait velocity, including the
feet. Just after the moment of tripping or loss of footing, if
the fall is physically recoverable, one or both feet
reacquire the footing (zero velocity at the foot/feet).
However, the rest of the body not only is still moving
forward with a residual velocity but also has the center of
mass and center of foot pressure misaligned and momentarily “out of control.” Thus the body pitches forward or
sideways pivoting about the ankles acted on by the
acceleration of gravity, the ground reaction forces, and
the acquired momentum. In H&R when the hold force on
the sternum is released, the body rapidly acquires angular
momentum about the ankles. It is this angular momentum
(not the holding force) and the sudden misalignment of
the center of mass and center of foot pressure which
390
Fig. 1 Illustration of the Hold & Release paradigm. Hold: the
experimenter applies a steady force, H, to the standing subject’s
sternum. The ankle, knee, and hip muscles produce torques (t)
moving the center of foot pressure toward the heels in order to
oppose the force applied at the sternum. Release: the force is
suddenly withdrawn and the offset between the center of foot
pressure and the center of mass propels the body forward. This is
the state illustrated in Fig. 2 for natural tripping or loss of balance.
Recoil: the fall is arrested after a latency by motor control and
skeletomuscluar systems moving the center of foot pressure
Fig. 2 During walking all body parts move with an average
velocity (V). After tripping on an unexpected obstacle, the rest of
the body is still moving forward with a residual velocity and the
center of mass and center of foot pressure are misaligned and
momentarily “out of control.” In our schematization, we can think
of walking as a pendulum on a moving trolley, and the standing
posture as a fixed upright pendulum. Tripping and subsequent
reacquisition of footing can be thought of as transforming the first
system (a pendulum on a moving platform) to the second system (a
pendulum on a nonmoving platform) quasi-instantaneously. Succinctly, the mechanism of tripping is to instantaneously switch the
mechanical nature of posture and introduce in it both a misalignment of the center of mass and center of pressure and a horizontal
velocity pulse that postural control must dissipate
constitute the perturbation that needs to be accommodated
to maintain balance.
We also wanted to determine whether a linear
multisegment inverted pendulum model would be adequate to describe the recovery of balance after H&R. Such
a model would have the advantages of linearity, which
permits a relatively simple mathematical characterization,
and of scalability of the response parameters across
differently sized perturbations. The model would also
forward. Settled: posture finally settles with a transient response.
The internal forces at the joints are only represented partially for
clarity. Specifically, we represented only the joint torques of the
multibody linkage applied from the feet to the shanks, from the
shanks to the thighs, and so forth. Internal forces per se do not
affect the motion of the center of mass directly but only the
configuration of the body. Internal forces are used to deform the
body in relationship to the ground to generate shear forces and
changes in center of foot pressure to make gravity and ground
support move the center of mass in a desired manner
allow us to determine whether reflexive mechanisms
producing stiffness and energy dissipation at the body’s
joints is a viable CNS scheme for recovering from falling
onset.
Many studies (see Fregly 1979) have demonstrated the
attenuating influence of vision on postural sway during
quiet stance. Therefore we included conditions with and
without sight of the surroundings to see how this would
affect the performance of the posture controller during
sudden off-balance conditions. We also included a
condition involving light touch of the hand at mechanically nonsupportive force levels. Such light contact with
a stable surface greatly attenuates body sway during
passive stance (Clapp and Wing 1999; Holden et al. 1987,
1994; Jeka and Lackner 1994, 1995; Jeka et al. 1998;
Rabin et al. 1999). Force levels of about 0.4 N are
spontaneously adopted by subjects (Holden et al. 1994;
Jeka and Lackner 1994, 1995), a value corresponding to
the maximum dynamic sensitivity range of the somatosensory receptors in the fingertip (Westling and Johansson 1987) and force levels as low as 0.05 N have some
stabilizing effect (Lackner et al. 2001). Labyrinthinedefective subjects cannot balance heel-to-toe for more
than a few seconds if their eyes are closed. However, they
can stand as stably as normal subjects when light touch of
their finger with a stable surface is allowed. In fact, they
are more stable than normal subjects (Lackner et al.
1999). Consequently we thought light touch might also
enhance recovery of equilibrium during dynamic tasks.
391
Materials and methods
Subjects
Ten subjects, nine men and one woman, ranging in age from 19 to
56 years participated after giving informed consent to a protocol
approved by the Brandeis University Committee for the Protection
of Human Subjects. All were healthy, physically active, and
without musculoskeletal or neurological problems that could
compromise their balance.
Apparatus
A Kistler force plate (model 9261A) was used to record the
standing subject’s anterior-posterior center of foot pressure (cpx),
with a relative uncertainty less than 1% (see Figliola and Beasley
1995). An Optotrak" system (Northern Digital) was used to
monitor the positions of infrared emitting diodes attached to the
subject’s shoulder, hip, knee, and ankle with an uncertainty voxel
(volume element) less than 0.5#0.5#0.5 mm. An instrumented,
hand-held dynamometric probe with a flat contact surface was used
to apply a holding force to the subject’s chest and to provide the
time of release. A second Kistler force plate (model 9286, relative
uncertainty less than 1% and noise less than 0.02 N rms) was
positioned at waist height in front of the subject to measure the
force applied by the right index fingertip in conditions involving
finger contact. All recording instruments received a signal allowing
data synchronization within 2 ms. EMG signals were recorded in
two subjects from the tibialis anterior, gastrocnemius, biceps
femoris, and rectus femoris muscles by means of a MT8 EMG
device (MIE Medical Research, UK). The EMG signals were bandpass filtered at 10–500 Hz and sampled at 1300 Hz.
zeroed prior to the start of a trial and its signals were not further
treated for bias. Data were averaged across repetitions separately
for each condition (EONT, ECNT, ECFT) and subject. The
resulting data (30 sets) were then analyzed and compared using
the algorithms described in the numerical model section.
Results and analysis
The postural response to H&R for an ECNT trial from one
subject is shown in Fig. 3. Figure 3 displays traces of
shoulder, hip, and knee displacements in the format ready
for numerical analysis. (The traces are extracted from the
measured data starting from the release point; see also
Fig. 4). Each trace initially reaches some peak value
before rebounding and finally settling within about 5–10 s.
Table 1 presents the means and standard deviations of the
values of peak deflections (pinnacles of the humps in
Fig. 3) of the shoulder, hip, and knee across all subjects
for the three different conditions. These displacement
values all correspond to body segment rotations of a few
degrees. The force plate data shown in Fig. 4A–4C for an
ECFT trial show how center of pressure varies during the
H&R perturbation. The center of foot pressure is by
definition zero when the posture is settled after recovery,
as it is elucidated in the modeling sections. The steplike
shape of the center of foot pressure response (see Fig. 4A)
is the signature of the H&R paradigm.
Procedure
Subjects stood barefoot in the standard Romberg posture, feet side
by side but not touching, attempting to stand as straight and still as
possible. The experimenter pushed against the subject’s sternum
with the dynamometer with a steady force level. The force level
was adjusted according to the size and the strength of the subject in
order to produce a roughly comparable sway response in all
subjects; it ranged from 10–40 N. The subject actively resisted this
force attempting to maintain a straight upright posture. Within the
next 10 s the force was suddenly and without warning withdrawn,
and the subject attempted to regain equilibrium as rapidly as
possible without shifting or lifting his or her feet. Each subject
participated in three types of conditions: eyes open, no touch
(EONT); eyes closed, no touch (ECNT); eyes closed, forward touch
(ECFT). In the touch condition the subject touched lightly ("1 N)
the force plate with his or her right index finger. This level of force
is insufficient for significant mechanical stabilization of sway but
provides a sensory spatial cue that reduces sway relative to no touch
conditions (Holden et al. 1994; Jeka and Lackner 1994). In the
conditions not involving touch the subject held his or her finger
above the force plate. Subjects were given two practice trials for
each condition prior to the start of the experiment proper. There
were four repetitions per condition and the trial order was
randomized for each subject. The duration of the trials was 25 s.
All data channels aside from the EMGs were sampled at 120 Hz.
Data reduction
Raw data from the stance force plate, the Optotrak", and the finger
force plate were synchronized and then box-car filtered with zero
phase shift at 30 Hz bandwidth. The instant of probe release was
used to synchronize data across trials, conditions, and subjects. The
stance force and postural position recordings at rest after release
(see “settled” in Fig. 1) were used as zero baselines for the force
plate and Optotrak" marker recordings. The finger touch plate was
Fig. 3 Horizontal displacements of the knee, hip, and shoulder for
a typical eyes closed, no touch (ECNT) trial. The ankle is used as
the origin. The stick figure on the right hand side shows the
Optotrak" marker locations relative to the measurement traces.
Time zero corresponds to the moment of release illustrated in Fig. 1.
The traces are in a format ready for numerical analysis. (The traces
are extracted from the measured data by cutting before the release
point). Each trace rises initially to some peak value (humps) before
rebounding and finally settling within about 5–10 s. Table 1
presents the means and standard deviations of the values of peak
deflections (pinnacles of the humps) across all subjects for the three
different experimental conditions
392
Fig. 4 Raw data sample from an H&R eyes closed forward touch
(ECFT) trial. A The panel shows the holding force and the center of
foot pressure. The center of foot pressure shift cpx (the difference
between the cpx values at equilibrium prior to release and at
equilibrium after release) is used as a normalization factor across
trials and subjects. The holding action is considered completely
withdrawn when the measured force crosses the zero value. The
panel shows head, shoulder, hip and knee displacements complemented by the respective traces of velocities and accelerations. The
body displacement traces demonstrate that the upright posture starts
to accelerate forward, “fall,” instantaneously after the onset of the
release as is dictated by Newton’s second law. Touch forces from
the fingertip are small and not of significantly supportive values. B
The variables of the previous panel are complemented here with the
recording of the ground shear force. Its good constancy for 125 ms
after release onset confirms that for a brief time interval after
release the subject “falls” forward unstopped and without the
possibility of sensing the fall from the foot soles. EMG recordings
are presented from the tibialis anterior, gastrocnemius, biceps
femoris, and rectus femoris muscles. C The variables in B have
been dilated in time to allow for better identification of the course
of action after release
393
Table 1 The upper three lines indicate the mean peak marker
displacements and standard deviations in cm of knee, hip, and
shoulder sway in the three experimental conditions (see Fig. 3 for
visualization): eyes open no touch (EONT), eyes closed no touch
(ECNT), eyes closed forward touch (ECFT). The variation cpx (cm)
indicates the displacement of cpx between the hold and settled
positions for each condition. The bottom three lines show the knee,
hip, and shoulder displacements for the experimental conditions
normalized in relation to thecpx displacement (cpx ) for each
condition. See also Fig. 6. The entries (cm/cm) represent marker
displacement in relation to cpx displacement (n=10)
Knee sway (cm)
Hip sway (cm)
Shoulder sway (cm)
cpx (cm)
Norm. knee sway (cm/cm)
Norm. hip sway (cm/cm)
Norm. shoulder sway
(cm/cm)
EONT
ECNT
ECFT
0.6€0.9
1.8€1.5
3.5€1.6
4.8€0.9
0.12€0.19
0.38€0.32
0.73€0.34
0.5€0.8
1.6€1.2
3.5€1.4
5.2€1.1
0.10€0.16
0.30€0.24
0.67€0.27
0.6€0.7
1.7€0.8
2.3€0.8
4.1€1.0
0.14€0.16
0.41€0.20
0.56€0.19
Conceptual model
Before entering a more complex level of analysis of the
H&R paradigm we recapitulate the paradigm as follows.
– Hold (see Figs. 1, 5): The experimenter applies a force
to the subject’s sternum. As a consequence the center
of foot pressure (cpx) is offset (backwards relative to
the subject) by an amount that is a function of the
holding force and the height of the point of application.
– Release (see Figs. 1, 5): After release the body
accelerates forward because the center of foot pressure, whose action had been opposing the force applied
by the experimenter, is still offset with respect to the
center of mass. Thus, the body is momentarily in a
state of falling.
– Recoil (see Fig. 1): After a delay new joint torques
shift the cpx in the direction opposite to its offset
during the hold period to arrest the fall and ultimately
bring about the recovery shown in Fig. 3.
– Settled (see Fig. 1) is the reestablished normal upright
posture.
The size (cpx ) of the cpx shift from the holding phase
plateau (see Fig. 4A) to the settled phase plateau is
directly proportional to the magnitude of the H&R
perturbation and can be used with sufficient approximation to normalize the body displacement and force data
because, as is shown below, the system is in a regime of
linearity.
The center of foot pressure normalization factors (cpx )
and resulting normalized peak marker displacements are
shown in the bottom four lines of Table 1. Figure 6 shows
stick figures drawn with the normalized marker displacements of Table 1 to allow visualization of the multisegment behavior at the peak of the body deflection
across conditions. It can be seen that the ECFT condition
is characterized by a greater degree of out-of-line sway of
Fig. 5 Layout of the variables involved in the analytical model of
the H&R paradigm and definitions for the conceptual analysis of
the H&R paradigm. O is the point of equilibrium of the center of
mass and center of foot pressure during the settled phase after
n
P
release (see Fig. 1); it was chosen as center of momenta. m ¼
mi
i¼1
is the total mass of the body and mi is the mass of each single body
segment where n is the number of body segments. N is the vertical
component of the ground support forces, which is considered
applied at the center of foot pressure cpx. S is the shear component
of the ground support forces; g equal to %9.81 m/s2 is the
acceleration of gravity; G equal to mg is the total weight of the
body. H is the holding force and d the holding height.
n
n
P
P
x ¼ 1=m mi xi and y ¼ 1=m mi yi ffi l are the coordinates of the
1
1
center of mass of the system. J is the angular coordinate of the
motion of the center of mass
the three body segments than the no touch conditions,
EONT and ECNT. This is attributable to the smaller
displacement of the torso when forward touch of the hand
is allowed, and represents a significant difference from
the other two conditions. (See comparison of different
conditions: normalized maximum sway amplitude, below.)
Analytical model
We analyze the four phases of the H&R paradigm
individually here. Figure 5 shows the layout of the system
and variables for this analysis.
394
Release
When the body is released, Fig. 4A–C shows that between
the total decay of the holding force and the initial
variation in the cpx a minimum of 90 ms elapses. For this
period of time the system’s dynamics is described by the
following equations obtained from Eq. 1 by removing the
holding force H. Also introducing Eq. 2 we obtain:
!
€
Gx % Gcpx ¼ Io J
ð3Þ
S
¼ m€x
Fig. 6 Peak marker values normalized using of the factor cpx to
allow for comparison across trials, subjects, and conditions. The
normalization factor cpx is the variation in the center of pressure
from hold to settled as shown in Fig. 4A. Abscissa Centimeters of
produced deflection per centimeter of displacement of the center of
pressure. Plotted values are also reported in Table 1
Hold
For the holding phase we can write the equilibrium
equations of the system taking advantage of Newton’s
laws of mechanics as follows:
8
€ ffi 0
< %Hd þ Gx þ Ncpx ¼ I0 ðtÞJ
ð1Þ
N þ mg
¼
m€y ffi 0
:
SþH
¼
m€x ffi 0
Where: O is the point of equilibrium of the center of mass
and center of foot pressure during the settled phase after
release (see Fig. 1), which was chosen as center of
momenta; m is the total mass of the body; N is the vertical
component of the ground support forces, which is
considered applied on the center of foot pressure cpx; S
is the shear component of the ground support forces; g is
the acceleration of gravity (%9.81 m/s2); G equal to mg is
the total weight of the body; H is the holding force and d
the holding height; I0 is the instantaneous moment of
inertia with respect to O; x and y are the coordinates of the
center of mass of the body; and J is the angular
coordinate of the center of mass motion with respect to
the center of momenta O. We can make the following
determinations because the angular movements are of the
order of magnitude J!€10& or less as indicated by the
displacement values in Table 1:
€y ¼ oð€xÞ y_ ¼ oð_xÞ
y ¼ oðxÞ l ffi constant:
ð2Þ
The term o(f) means infinitesimal of higher order and l is
the constant value approximation of the vertical coordinate of the center of mass y.
In order to simplify the treatment further we can assume
that the inertia of the upright body could be approximated
with I0!ml2 where l is height of the center of mass (we
lumped the whole body mass at the center of mass). In
addition, we can take advantage of the small displacement
relationship x ffi %lJ because segment movements are
small ("10&):
!
€ þ g J ¼ %Gcpx ¼ %mkgk ) kcpx k
J
l
ð4Þ
€
S¼
%ml2 J
Equation 4 is the equation of an inverted pendulum
(unstable) and is always applicable regardless of the
multi-degree of freedom nature of the system if the
motion of the system is analyzed as motion of the center
of mass (see Goldstein et al. 2002). Equation 4 is also
applicable to all remaining phases of the paradigm. In the
general case the moment of inertia of the system becomes
time varying, and eventually it must be differentiated
together with the angular velocity during the calculation
of the inertia forces. (This component is neglected here
because the differential of the moment of inertia is an
infinitesimal of higher order during H&R).
During the release phase, the forcing component on
the right hand side of upper Eq. 4 is a constant pushingover torque since the misalignment of the center of foot
pressure with respect to the center of mass remains
unchanged for at least 90 ms due to the slower reaction
time of the CNS (see Fig. 4C). Such a constant
pushover torque is a function only of the offset cpx of
the center of mass with respect to the center of pressure,
which in turn is determined by the magnitude of the
holding force H. The quantity cpx can be reliably
measured by means of the force plate the subject stands
on since it is the difference between the values of the
center of foot pressure during the hold phase and the
settled phase.
During the 90 ms after release before the cpx
changes position the system accelerates under gravity
(mkgk ) kcpx k is constant) and builds up speed even
though it is moving very little. Figure 4C shows that the
shear force S remains approximately constant as well, as
predicted by Eq. 4. This means that when released, the
center of mass is accelerating forward freely, i.e.,
“falling,” with an acceleration equivalent to the removed
holding force H until much later when the center of
pressure starts to react. Figure 4C shows that within 50–
60 ms from the onset of release the EMG activity in the
395
leg muscles changes with the gastrocnemius (gastrocnemius is the first to react) and the biceps femoris increasing
and the tibialis anterior and the rectus femoris decreasing
in activation (see also Figure 8). Due to the muscle
activation dynamics, at least another 50–70 ms elapses
before the ankles and knees start to extend and the center
of foot pressure begins to move (see Figure 4C). This
synergy moves the center of foot pressure forward. To
break the fall, the cpx needs to go ahead of the center of
mass. A mirror symmetric synergy later moves the center
of foot pressure in the opposite direction. Succinctly, we
can say that after release the body’s joint torques are
reversed from the ones of the holding phase and begins to
shift the cpx forward, a process taking approximately
90 ms. In the interim the body is falling forward under the
pull of gravity and the action of ground reaction forces.
This reaction time is comparable across subjects, so
we can estimate the
" peak velocity prior to the recoil as
_J0 ! mkgk ) kcpx k ml2 (from the impulse theorem of
"
mechanics), which yields J_ 0 / cpx l2
Recoil
The calculated velocity J_ 0 dictates the amount of energy
that is acquired during the off-balance interim, “fall,”
generated by the release. During the recoil phase, postural
control must not only realign the center of mass with the
center of foot pressure, but in the process it must dissipate
this acquired velocity J_ 0 . This energy can only be
dissipated by controlling the center of foot pressure and
the center of mass misalignment in phase contrast to the
sway velocity J_ to perform negative work. The CNS skill
in doing this is revealed by the shape of the transient (see
Figure 3) rather than by the magnitude of the sway
response, i.e., fast vs. slowly decaying transient.
The perturbation introduced by the H&R depends on
the magnitude of center of mass%center of foot pressure
misalignment and the J_ 0 acquired after the release. Both
are determined by the holding force, H, and are quantified
by the measure cpx . Therefore the data across trials and
subjects can be normalized by using the parameter cpx
(the linearity of the H&R dynamics is demonstrated
below) and importantly the holding force need not be
measured or controlled. The only requirement is that the
maximum sway produced by the release is not so
excessive as to elicit a step. In summary, the normalized
peaks of the sway (see Fig. 6) and the rapidity of
restoration of the upright posture (damping, see Fig. 3) are
two of the parameters yielded by the H&R that provide
quantification of CNS performance during sudden offbalance exposure.
Settled
After about 5–10 s from release, the subject’s posture
reaches a position of equilibrium. We adopt this as a
measurable experimental zero. This phase is regular
standing posture. In order not to overload the reader with
technical details, further features of analysis are discussed
in Appendices A and B
Neuromuscular mechanisms of the H&R
The H&R paradigm introduces a velocity and an offbalance disturbance to posture in a quantifiable manner.
This allows for addressing the neuromuscular mechanisms engaged in posture restabilization following H&R.
Table 1 and Fig. 6 show that with the H&R paradigm
movements are small so that from a geometrical standpoint the body is in a regime of “small oscillation.” This
means that the biomechanics of the upright posture is
linearizable. However, the control of posture can still be a
convoluted nonlinear problem if the neurophysiology of
the posture control is greatly nonlinear. In the introduction we advanced the hypothesis that H&R posture
control is a reflexive control mechanism performing as
a spring and damper (otherwise called PD controller) of
which the damping component is set up differently across
conditions. Moreover, characteristics of the controller
may be tuned during the falling phase. If our intuition is
correct, we expect the upright posture to perform during
the H&R as a multi-degree of freedom oscillator
subjected to an impulsive perturbation.
Numerical model: identification of the neuromuscular
control mechanisms
To determine whether the body exposed to H&R actually
behaves as we hypothesize we attempted to fit the
measured multidegree of freedom sway traces of Fig. 3
with a linear multidegree of freedom oscillator model.
Appendix B presents the mathematical basis for modeling
our data in terms of the equations of the following multidegree of freedom oscillator:
M€x þ C x_ þ Kx ¼ 0
ð5Þ
Appendix B shows that the measured properties of the
biomechanics combined with the properties of the
hypothesized joint control scheme yield a multidegree
of freedom system with stiffness and damping at the
joints, which is mathematically describable by Eq. 5. The
joint stiffness and damping are produced both by the
mechanical properties of the body and by the modulatable
and tunable reflexive pathways of postural control, which
are here identified. From linear ordinary differential
equation theory we know that the general solution of such
equations is a combination of simple components Fj,
j=1,..,3:
396
8
9
< a11 =
F1 ¼ a21 ea1 t sinðb1 t þ g1 Þ;
:
;
a31
8
9
< a12 =
F2 ¼ a22 ea2 t sinðb2 t þ g2 Þ;
:
;
a32
8
9
< a13 =
F3 ¼ a23 ea3 t sinðb3 t þ g3 Þ
:
;
a33
ð6Þ
Each component of the response, or modal component, j,
is in turn identified by the set of two parameters aj and bj,
which represent, respectively, the rate of decay and
pulsation of the component. For each modal component
the parameters aij, i, j=1,..,3, (unscaled eigenvectors)
define the shapes of the components (e.g., en bloc
movement or zig-zag movement). We searched for a set
of the parameters aij, ai, bi, and gi, i, j=1,..,3, to be
entered into Eq. 6, that would fit the experimental
recordings xi, i=1,..3 (i.e., knee, hip, and shoulder sway).
The fit of the postural responses (knee, hip, and shoulder)
of the ten subjects for the three different test conditions
yielded 30 sets of parameters. The search was conducted
in trial and error manner via nonlinear minimization using
a zero order searching method (Neddler and Mead 1965)
and the following cost function:
#
T#
#
3 Z #
3
X
X
#
#
aj t
G¼
aij e sinðbj t þ gj Þ# dt
#x i %
#
#
i¼1
j¼1
o
2
Data fit was achieved with only two terms of Eq. 6.
Including the third term in the numerical minimization
did not contribute a closer fit of the data. Examples of
data fitting in one subject are shown in Fig. 7A–C. The
average of the rms values of the residuals after model
fitting over the 30 sets of data was approximately 1.1 mm
with a standard deviation of 0.4 mm. These rms residual
values are a small fraction (5%) of the size of the grand
average of the peak sway over different markers, conditions and subjects, which was approximately 20 mm (see
Table 1). The rms values of the residuals were small in
each condition: 1.1 mm for EONT, 1.4 mm for ECNT,
and 0.8 mm for ECFT. The good fit of the model to our
experimental data confirms the hypothesis that posture
behaves linearly during the H&R paradigm and that the
model equations of a multiple degrees of freedom
oscillator as laid out in Appendix B are applicable. This
Fig. 7 Fit of the linear model with one subject’s measured, knee,
hip, and shoulder sway for each of the three experimental
conditions averaged across the four repetitions per condition
(EONT eyes open no touch; ECNT eyes closed no touch; ECFT
eyes closed forward touch). A, B and C the measured whole body
H&R responses are fully overlapped by the predictions of the
multilink model of Fig. 10. The dynamics model simulates the three
traces simultaneously as calculated displacements of the body
markers following release. The grand average, across the different
subjects and conditions, of the rms values of the residuals of the
model fit is 5% of the peak deflection of approximately 20 mm (see
also Table 1). This indicates that the model fits the experimental
data very well and in turn that postural control behaves as a linear
control mechanism providing reflexive stiffness and damping to the
body’s joints
397
Table 2 Frequency (w) and damping (x) characteristics of the two
modes that were sufficient to describe the experimental data of the
three conditions. The parameters w represent the frequencies of
oscillation of the harmonic components of the recovery transient of
the Hold and Release (see also Fig. 3) and the parameters x indicate
the rates of energy dissipation of the components. The H&R
approach to posture can be compared to plucking the strings of a
guitar. In such a case the parameters w would identify the strings
(notes), which were plucked and the parameters x the damping
characteristics causing them to fade out at different rates (n=10)
w1 (Hz)
x1
w2 (Hz)
x2
EONT
ECNT
ECFT
0.24€0.12
0.89€0.16
0.50€0.27
0.66€0.24
0.23€0.10
0.68€0.27
0.50€0.22
0.47€0.30
0.22€0.22
0.92€0.13
0.60€0.33
0.74€0.25
Table 3 Eigenvalues of the two modes for the three experimental
conditions derived using Kung’s eigenvalue realization algorithm
(n=10) Kung’s algorithm is applicable to virtually ideal mathematical systems. The good agreement of the algorithm’s calculations
and the results shown in Table 2 corroborates that the H&R is
amenable to close form mathematical modeling and that the
analytical and numerical treatments presented here are sound
w1 (Hz)
w2 (Hz)
EONT
ECNT
ECFT
0.16€0.05
0.42€0.17
0.16€0.05
0.42€0.17
0.15€0.06
0.52€0.25
means that the posture controller during H&R supplies
appropriate stiffness and damping joint characteristics by
means of somatosensory afferent feedback. The identified
model parameters were converted into the form of central
frequencies wj, i=1,..,3,
characteristics xj,
ffiffiffiffiffiffiffiffiffidamping
ffi
qffiffiffiffiffiand
i=1,..,3, where wi ¼ a2i þ b2i and xi ¼ jai =wi j: wj and xj
were averaged over subjects and are presented in Table 2.
The parameters wj represent the frequencies of oscillation
of the harmonic components of the recovery transient of
Fig. 3 while xj is proportional to the rates of energy
dissipation of the components. The H&R approach to
posture can be compared to plucking the strings of a
guitar. In such a case the wj would identify the strings
(notes), which were plucked, and xj the effect of each
one’s friction causing them to fade out at different rates.
Numerical model verification
To confirm the calculations of our minimization algorithm we performed additional system identifications on
the sway data using the eigenvalue realization algorithm
developed by (Kung 1979). Kung’s algorithm allows for
identification of the system eigenvalues when only the
impulsive response of the system is available and the
forcing input is zero. Table 3 shows that the averaged
eigenvalues produced by the eigenvalue realization algorithm calculations over the different subjects and conditions are in overall agreement with the results of Table 2.
Considering that Kung’s algorithm is applicable to almost
ideal mathematical systems, the good agreement of the
algorithm’s calculations and our results corroborates that
the H&R paradigm is amenable to close form mathematical modeling and that our analytical and numerical
treatments are sound.
Comparisons of different conditions:
normalized maximum sway amplitude
The linearity of the H&R dynamics that we have
demonstrated allows normalization of the marker displacement values of each condition’s data set in relation
to the cpx shift between the hold and settled phases (see
Table 1). Normalized deflections permit valid comparisons to be made across trials and conditions with
different perturbation magnitudes. An analysis of variance
was conducted and post hoc analyses with Bonferroni
corrections were carried out to identify the source of
significant differences. These analyses indicated that with
forward touch (ECFT) there was significantly less angular
displacement of the trunk, i.e., the trunk was kept
significantly closer to the vertical relative to the two no
touch conditions (ECNT, EONT), p<0.05 all comparisons. There were no significant differences between the
ECNT and EONT conditions for ankle, knee, hip, or
shoulder displacements. In addition, the peak postural
displacements in ECNT and EONT could be characterized within a good approximation by a single link
inverted pendulum pivoting at the ankle.
Comparisons of different conditions:
central frequency and damping
The identified central frequencies and damping factors
were compared with an analysis of variance to test for
effects of the experimental conditions on sway. We also
ran post-hoc pairwise comparisons. The two modal
frequencies were indistinguishable across conditions but
the power was low. This suggests that joint stiffness
properties may not be affected by the presence of visual
or tactile cues. Such a result was expected, since stiffness
is mostly determined by muscle properties and activation
levels. Kolmogorov-Smirnov tests of normality revealed
that damping factors do not meet the requirements for
parametric analysis. Therefore we compared damping
factors with the Wilcoxon test, which indicated that the
damping of both modes is increased by the presence of
touch or vision, each p<0.05. Therefore the presence of
tactile cues at the fingertip or of vision aids the dissipation
of the energy introduced by the perturbation. The peak
vertical touch force, averaged across subjects and repetitions, was 1.1€0.6 N and the fore-aft finger shear force
was 0.7€0.3 N. These forces at the finger are much too
low to provide significant mechanical stabilization of the
torso (see Holden et al. 1994). Figure 4A shows the
fingertip touch forces for a typical trial.
398
physiological terms this means that during exposure of the
body to sudden off balance conditions reflexive mechanisms provide specific stiffness and damping characteristics to the joints of the body that are not simply the
result of passive muscles mechanics. Figure 4 panels B
and C show rectified EMG recordings for one subject in a
forward touch condition, in which clear bursts are present,
which indicates reflexive control of posture. Figure 8
shows the EMG recordings taken in an eyes closed
without touch trial from another subject. The recordings
from the leg muscles are aligned to show the strong
pattern of muscle synergies that is responsible for the
viscoelastic (stiffness and damping) response predicted by
our modeling and numerical analysis. First principles
dictate that postural control can only resort to synchronization of muscle contractions in phase contrast with
muscle stretching in order to dissipate energy. The results
of this investigation indicate that with the aid of haptic
cues the postural controller is more effective in dissipating the energy of the perturbation. These two facts
combined mandate that the muscle synergies (patterned
muscle contractions) shown in Fig. 8 are finely timed with
respect to each other in a context specific manner.
Discussion
Fig. 8 Example of muscle activation (EMG) in the leg muscles of a
subject during Hold & Release from an EONT trial (arrow: time of
release). Differential recordings of surface EMG were made from
two pairs of muscles: (a) tibialis anterior and gastrocnemius
lateralis and (b) biceps femoris (long head) and rectus femoris. The
first pair flexes and extends the ankle, and the second pair act on
both knee and hip. The data were band-pass filtered at 10–500 Hz
and sampled at 1300 Hz. The envelope of the rectified signals is
presented with the signals offset to zero in the hold period. This
allows for easier visualization of the resulting activity changes.
After release, there is bursting of all four muscles with peaks at
different latencies. These bursts are the initial responses that arrest
the body’s forward motion. When the body is settled, the
gastrocnemius and biceps femoris are more active than during the
hold period while the tibialis and biceps femoris are less active. In
the transient period between bursting and settling, there are
multiple cycles of oscillation in the EMG patterns of all the
muscles. This pattern indicates that the harmonic nature of the
multilink postural model is correct
Muscle synergies and touch
The very close agreement between the postural sway data
and the fit of the presented model corroborate the thesis
that posture control behaves as a linear controller. In
Great interest lies in understanding the nature of postural
restabilization following sudden loss of balance. Our
approach was to study postural responses to recoverable
falls created experimentally to mimic key features of
tripping or loss of footing and at the same time to allow
easy mathematical treatment. We wanted to assess
whether recovery from being suddenly off-balance was
handled by a posture controller regulating stiffness and
damping properties of the body’s joints. In addition, we
wanted to gauge whether haptic and visual cues affected
the performance of such a controller. Finally, the
conjunction of a technique for inducing recoverable falls
and a model for analyzing them provides the potential for
easy and portable clinical use.
We demonstrated experimentally and analytically that
by using a H&R paradigm we are able to induce sudden
loss of balance and a brief period of forward falling. The
peak angular displacements at the shoulders, hips, and
knees were small following release. This allowed us to
model the resulting biomechanical behavior of the body
as a multilink, inverted pendulum in a regime of overall
small oscillations. We found that a three-link, invertedpendulum model described the experimental data very
well under all of our experimental conditions. Importantly, a compound linear inverted-pendulum model adequately described the behavior of all our subjects. This
means that the postural response to H&R could be
characterized using manageable linear systems theory.
The linearity of the paradigm dynamics is very
convenient for data scaling, data modeling, and system
analysis. However, the real significance lies in the
implications for the nature of the neuromuscular mech-
399
anisms responsible for balance recovery following release. Posture dynamics consists of biomechanics and
control. Because the biomechanics is linearizable, the
demonstrated linearity of the whole H&R response
indicates that stiffness and damping (the linear PD
controller we hypothesized above) is an excellent approximation of the neurophysiological characteristics of
the posture controller at the joint level. In addition, we
demonstrated that the stiffness and damping values are
produced by reflexive mechanisms and not by passive
muscle properties alone. Moreover, stiffness, and damping are with good approximation constant across the
recoil. This implies that starting with the sudden release
some mechanism determines the gains, set points, and
phases of the sensory-motor feedback to be used across
the whole recovery.
The question is what mechanism produces this behavior. Figure 4 panels A–C show a representative case of
H&R with touch cues from the fingertip. Note that the
center of foot pressure and the ground shear remain
unchanged for 125 ms after the onset of release. EMG
activity increases 55 ms after onset of release in the
gastrocnemius and biceps femoris muscles (see Fig. 4C).
Before the EMG activations only acceleration, velocity,
and position of the body segments (head included) show
variations. A vestibular elicited response with 60–80 ms
latencies is a possible basis for the EMG activity
(Greenwood and Hopkins 1976, 1980); however, muscle
spindle information is available sooner. Considering that
muscle spindles have a low threshold and large afferent
fibers, it is likely that within a few milliseconds after
release spindle feedback signals could drive corrective
responses. Another possibility is a predictive response.
However, in such a case it would be difficult to explain
why the response would take 55 ms to develop instead of
occurring sooner after release in order to avoid exposing
the body to falling. (In Appendix A, we discuss what
happens to the center of foot pressure variation if the
release is anticipated and how this can be used in the
H&R paradigm to discard predicted and therefore unsuccessful trials.)
Figure 9 presents a simplified schema of the neuromuscular mechanism underlying joint control. It shows
how spinal circuitry and supraspinal modulation can
perform postural joint control and how this could account
for our findings. Descending supraspinal commands, a
and b, drive a spinal servos. The common mode of the
supraspinal drives (a+b) sets or modulates the stiffness
and damping of the muscle pair around the joint. The
differential drive (a%b) is proportional to the net joint
torque, and it can provide additional set gain feedback or
modulated feedback proportional to velocity offsets
(damping) or position (stiffness) or force (impedance,
omitted here) through the mediation of higher centers
(supraspinal mechanisms). Spindle afferents and other
sensory signals are mediated and integrated at a supraspinal level and relayed to the spinal servos by means of
the a and b drives. This schema provides desired
Fig. 9 A simplified schema of the neuromuscular mechanism of
joint actuation. The a s represent the combined action of the spinal
motor-neurons of the agonist-antagonist muscle pair around a joint.
Afferent fibers II and Ia encode respectively joint position J and
displacement rate J_ errors. Their activity modulates the spinal a
motor servo and also projects to supraspinal centers where it is
integrated with other sensory afferents. The kinematics variables J
and J_ not only feed back on the spinal a motor servo through the
muscle spindles but also modulate the muscle mechanics of the
joint. J is the input to the force-length combined characteristic of
the agonist-antagonist joint pair; and, J_ determines the combined
viscous characteristic (Hill) of the agonist-antagonist joint pair. gs
represents the descending static drives which encode the desired set
point or motion reference of the joint. The a and b drives are the
descending supraspinal commands to the a spinal servos. Golgi
tendon organs, interneurons, and many other components of the
spinal circuitry are omitted because they are beyond the scope of
the figure. The common mode of the supraspinal drive (a+b) sets or
modulates the stiffness and damping of the muscle around the joint
in an open-loop, feedforward manner. Stiffness and damping are
also produced by spindle feedback (under the drive of the
descending gs, static, discharges: reference), which inhibits or
excites the a spinal servos proportional to position and velocity
(mostly) errors. The differential drive (a%b) determines the net joint
torque and can provide additional set gain feedback or modulated
feedback proportional to velocity, position, or force through
mediation of supraspinal mechanisms. Spindle afferent and other
sensory signals projecting centrally are integrated and interpreted
by supraspinal mechanisms, which adjust the a and b drives to
provide desired modulation of mechanical properties not achievable
solely by the a spinal circuitry
modulation of mechanical properties otherwise not
achievable solely by the a spinal circuitry.
Our findings suggest (1) that the common (a+b) drive
and reflexive spindle pathways are probably set to provide
constant stiffness since we find nop
significant
frequency
ffiffiffiffiffiffiffiffiffi
changes across conditions (w ¼ K=m, where K is
stiffness and m is mass), and (2) that the g drives and/or
the differential (a%b) drive are modulated by higher
centers to provide joint velocity feedback (torque)
appropriately timed to produce effective damping of
body sway during sudden off-balance conditions. This
sensory-motor integration scheme possibly could be tuned
before release; however, its precise configuration and
parametrical settings might also be adjusted within a few
tens of milliseconds following release.
In summary, we have demonstrated that postural
recovery following H&R has a reflexive viscoelastic
400
behavior. Figure 8 shows the muscle synergies responsible for this finding. Patterned activation of the gastronemius-biceps femoris pair vs. the tibialis anterior-rectus
femoris pair (and other muscles) allows for the control of
the fore-aft motion of the center of foot pressure. If
reflexive and descending control mechanisms were not
involved, the motion of the perturbed posture would
resemble that of a rocking chair and would extinguish
very slowly. The stiffening and relaxing of the muscles
must actually be timed in phase contrast to their stretching
and shortening to produce dissipation of sway (kinetic
energy). From an external point of view, this means that
the center of foot pressure is adjusted in phase contrast to
the sway velocity so that external forces create negative
work on the body. The light touch force on the finger in
touch trials is not responsible for the triggering of the
EMG responses because it shows variations at the same
time as the earlier EMG responses. However, light touch
makes a difference in how rapidly the muscle synergies
succeed in restoring balance. This suggests that there ae
two separate mechanisms, one ruling the early part of the
response and another the later phase (see also Denier and
Dichgans 1986). Alternatively, there might be only one
mechanism which utilizes all available information in a
sensory fusion manner. Further analysis and experimentation are needed to clarify this issue. The touch cues also
enabled the subjects to have smaller peak deflections of
the torso than in the absence of touch.
As discussed above, linear behavior carries the convenience that the magnitude of the postural response is
proportional to the magnitude of the initiating perturbation. Consequently, the shift, cpx , of the center of foot
pressure position between the hold phase and the settled
posture (see Fig. 4A) can be used as a scaling factor to
normalize the postural data across trials. This simplifies
the H&R paradigm by not requiring identical perturbations in every trial and it makes the comparison and
statistical treatment of data across conditions much
simpler. An additional advantage is that the H&R
paradigm can be used in patient populations using low
hold force levels or in strong and healthy subjects using
high force levels without affecting the validity of the later
analyses.
The H&R paradigm gives insights into what happens
during unintended falls and potential clues with regard to
possible prevention strategies. Even more importantly
H&R allows for quantification of recovery performance
from falling onset. Existing perturbation paradigms in
which the support surface is tilted and/or translated yield
important insights into postural control but are not
specific models of natural off-balance events and falling
onset. Posture platforms translate or rotate to induce a
misalignment between the center of foot pressure and the
center of mass, however, trials start with the two aligned.
Friction between the platform and the subject’s feet
during platform translation provides the force that constitutes the perturbation. The soles of the feet are therefore
stimulated in the process and contribute somatosensory
cues during the course of the perturbation that are not
specific to an off-balance condition, but only to the
posture platform. Moreover, a relatively long period of
time is commonly used to carry out the perturbation,
about 450 ms (see Horak and McPherson 1996). Such a
period is long enough to stimulate and engage feedback
loops from short to long, as well as volitional responses
(see Brooks 1986). With stance surface perturbations the
disturbance is also transmitted from the bottom up, linkby-link, through the entire chain of the body making the
analysis of the overall process difficult. The H&R
paradigm bypasses this first phase of joint flexion/
extension and starts with the center of foot pressure and
center of mass already misaligned.
Paradigms involving push and release from a hold
force applied laterally or frontally at the waist (see Wing
et al. 1993, 1995) by means of electromechanical devices
involve much longer time courses (200 ms) for force
removal than the simple manual releases in the H&R (35–
40 ms). A perturbation applied to the hip yields generally
greater angular displacement at the hip than at the
shoulder (Wing et al. 1995), which is the consequence of
nonuniform and nonsimultaneous stimulation of the
whole mechanical body chain. Wing et al. (1995) have
implemented a releasing from push paradigm in which a
mechanical apparatus applies a force laterally or frontally
to the subject’s waist which can then be diminished to
zero over an ffi200 ms period. This procedure is not
analogous to H&R because the body is partially mechanically constrained during the 200 ms in which the push
force is eliminated. In H&R, the release takes approximately 35 ms and the EMG synergies are activated within
approximately 55 ms of the onset of the release (see
Fig. 4A–C). By the time 200 ms has elapsed, the primary
activity to restore balance has already been completed.
In summary, we have introduced a H&R paradigm and
conceptual and mathematical model for studying restoration of balance from recoverable falls. These tools allow
quantitative measurements of postural performance to be
interrelated with underlying physiological mechanisms.
Acknowledgements We thank Dr. Joel Ventura and Dr. Stefano
Castallani for their valuable assistance and advice and Dr. Todd
Hudson for his review of our statistics. This research was supported
by National Aeronautics and Space Administration grant, NASA
NAG9-1263.
Appendix A
In our treatment, release has been addressed as instantaneous.
Figure 4A shows that the force withdrawal requires about 35 ms. To
reconcile this apparent contradiction we can compare the rise time
of the posture response with the time of force withdrawal. From the
H&R data presented above we can see that the fastest mode
affecting the body’s displacements, xi, has a central frequency of
approximately 0.55 Hz. Taking advantage of the Parseval theorem
we can calculate an approximate rise time of 0.73 s for the sway
response (quasi-analytical relationship tr ! 0.4/B; see also Kuo
1991, pp. 335–337, 571). Thus, instantaneous means that the rise
time of the system is much larger than the duration of the
perturbation. A withdrawal on the order of magnitude of 100 ms
would still be fast enough to be considered instantaneous.
401
The Hold force is applied manually therefore it varies a few
percent about its average value during the Hold period (Fig. 4C).
Even if it varied as much as 10–20% the force fluctuation still
would not be critical because the physical perturbation to postural
control in H&R is not the holding force but the angular momentum
acquired during the brief fall after release. Manual application of
the force features high compliance, which guarantees that the
means of application of the force would not “drive” the body as in
pushing paradigms where stiff actuators are rigidly attached to the
body. The only requirement of the paradigm is to produce a center
of foot pressure transient comparable with the one of Fig. 4A. A
steplike variation in the center of foot pressure and of the ground
shear force guarantees that there was not cueing on the part of the
experimenter. If the experimenter fails to catch the subject by
surprise, the trace of the center of foot pressure differs from steplike
and turns into oscillations or a hump. The steplike center of
pressure transition indicates brief falling which in turn indicates
surprise and the absence of this feature can be used as a criterion to
discard unsuccessful trials.
The dynamics and control of the H&R paradigm is linear in
nature allowing for scalability of the results. However, the question
is what is the scaling factor. Our analysis indicates that the center of
foot pressure shift cpx is a good choice because it can be easily
measured and it is proportional to the perturbation magnitude. Even
though the H&R mathematical treatment is not compromised,
differences between the settled posture and the initial hold posture
affect the validity of cpx as scaling factor. Our experience with the
H&R paradigm indicated that subjects, with good approximation,
assume the same initial and final postures, which is very desirable.
However, in cases where a great variability in final vs. initial
posture has occurred the experimenter would probably need to
integrate the cpx measure with other parameters in order carefully
to describe the center of foot pressure and center of mass
misalignment and the forward momentum, which constitute the
H&R perturbation.
Appendix B
”Small oscillations” of a triple inverted pendulum (or other stable
mechanical system) occur when the system moves in a contained
fashion about an equilibrium position with small angular displacements of its links (e.g., "10&). This allows sin (J) to be equated to
J, and cos (J) to be equated to 1. These conditions were met by the
kinematic data for all three links measured in our experiment. This
allowed us to approximate the kinetic (T) and potential (V) energies
as follows:
1
1
T ¼ q_ T H q_ ! ðq_ % q_ o ÞT ðHo þ H 0 ðq % qo ÞÞðq_ % q_ o Þ
2
2
1
! ðq_ % q_ o ÞT Ho ðq_ % q_ o Þ þ oðq % qo Þ3
2
V ¼ Vo þ
1 @2V
ðq % qo Þ2 þ oðq % qo Þ3
2 @q2
where @V=@qjq¼qo ¼ 0 because q0 is the position of equilibrium,
q=(J1, J2, J3). A layout of the system and of the geometrical
variables treated in this section is presented in Fig. 10. The
Lagrange function of the system results in:
1
1
L ¼ T % V ffi q~_ T H0 ~q_ þ g~qT P0 ~q
2
2
where ~q is equal to (q–q0) and the matrices H0 and P0 are as
follows:
Fig. 10 The triple inverted pendulum model. The xi, i=1,..3,
indicate the measured set of variables (also represented in Fig. 3).
From the measured variables xi, i=1,..3, the model implicitly relates
the angular variables Ji, i=1,..,3, utilized for determining the
multilink postural dynamics
H0 ¼
2
m1 a21 þ m2 ð‘1 þ a2 Þ2 þ m3 ð‘1 þ ‘2 þ a3 Þ2 þ I1 þ I2 þ I3
4 %m2 a2 ð‘1 þ a2 Þ % m3 ð‘2 þ a3 Þð‘1 þ ‘2 þ a3 Þ % I2 % I3
m3 a3 ð‘1 þ ‘2 þ a3 Þ þ I3
%m2 a2 ð‘1 þ a2 Þ % m3 ð‘2 þ a3 Þð‘1 þ ‘2 þ a3 Þ % I2 % I3
m2 a22 þ m3 ð‘2 þ a3 Þ2 þ I2 þ I3
%m3 a3 ð‘2 þ a3 Þ % I3
3
%m3 a3 ð‘1 þ ‘2 þ a3 Þ þ I3
%m3 a3 ð‘2 þ a3 Þ % I3 5
m3 a23 þ I3
2
Po ¼ 4
%m1 a1 þ m2 ð‘1 þ a2 Þ % m3 ð‘1 þ ‘2 þ a3 Þ
m2 a2 þ m3 ð‘2 þ a3 Þ
%m3 a3
3
m2 a2 þ m3 ð‘2 þ a3 Þ %m3 a3
%m2 a2 % m3 ð‘2 þ a3 Þ m3 a3 5;
m3 a3
%m3 a3
where m1–3 are the masses of the lower leg, upper leg and upper
body, respectively, a1–3 are the distances from ankle, knee and hip
to each segment’s center of mass, and ‘1%3 are the lengths of the
segments. Thus, applying the Lagrange equations we obtain:
~
q % gP~
q ¼ %KD ~
q_ % KP ~
H€
q
ð7Þ
where the terms in KD and KP are the zero and first order
approximations of the torques at the joints provided by the postural
control mechanism.
Our experimental observations provide measures of the displacements of the segments in the sagittal plane. To convert the
Lagrangean coordinates qi into our experimental coordinates xi, we
used the following transformation (for small oscillations):
402
2
dx
¼J¼4
dq
‘1
‘1 þ ‘2
‘1 þ ‘2 þ ‘3
3
0
0
%‘2
05
%ð‘2 þ ‘3 Þ ‘3
ð8Þ
The coordinates xi, i=1,..,3, depicted in Figs. 3 and 10, are the
horizontal displacements (sways) of respectively knee, hip, and
shoulder in the sagittal plane; the ankle is assumed as origin.
Substituting Eq. 8 within Eq. 7 we obtain the following:
ðJ %1 ÞT HJ %1€x þ ðJ %1 ÞT KD J %1 x_
þðJ %1 ÞT ½KP % gP+J %1 x ¼ 0
In conclusion, the system dynamics assume the following form:
M€x þ Cx_ þ Kx ¼ 0
ð9Þ
Equation 9 is the equation of a multidegree of freedom oscillator.
Since the upright posture is stable, it means that the matrices KP and
KD are constrained to yield a stable triplet M, C, K.
The general solution of Eq. 9 is a combination of simple
components Fj, j=1,..,3. (These equations have been anticipated in
the main text as Eq. 6.)
8
9
< a11 =
F1 ¼ a21 ea1 t sinðb1 t þ g1 Þ;
:
;
a31
8
9
< a12 =
F2 ¼ a22 ea2 t sinðb2 t þ g2 Þ;
:
;
a32
8
9
< a13 =
F3 ¼ a23 ea3 t sinðb3 t þ g3 Þ
:
;
a33
ð10Þ
Each component or modal response, j, is identified by the set of two
parameters aj and bj, which represent respectively the rate of decay
and pulsation of the component. For each modal response the
parameters aij, i, j=1,..3, (unscaled eigenvectors) embed the shapes
of the component contribution (e.g., en bloc movement or zig-zag
movement) of the links and the extent of the component’s
contribution (scaling factor).
The case-by-case solution depends on the initial conditions (x0,
ẋ0), which affect the phase parameters gij, i=1,..3, and the scaling of
the parameters aij, i, j=1,..3j. The intrinsic nature of the system
determines the parameters aj and bj, and the shapes of the modal
responses (mutual ratios of the aij within the same component). The
rate of decay a is an important parameter because the greater its
magnitude the quicker is the fading over time of the related
contribution to the overall response. Low values of the a parameter
relate to slowly recovering behavior. For easing the comparison of
experimental conditions the parameters aj and b were converted
into the frequency and damping representation (wj, xj) treated in the
results section, which carry overall the same physical meaning.
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