Identification of the contribution of the ankle and hip joints to multi-segmental balance control
Journal of NeuroEngineering and Rehabilitation
Identification of the contribution of the ankle and hip joints to multi-segmental balance control
Tjitske Anke Boonstra 0 1
Alfred C Schouten 0 1
Herman van der Kooij 0 1
0 Laboratory for Biomechanical Engineering, MIRA institute for biomechanical technology and technical medicine, University of Twente, Faculty of Engineering Technology , PO Box 217, 7500, AE Enschede , The Netherlands
1 Laboratory for Biomechanical Engineering, MIRA institute for biomechanical technology and technical medicine, University of Twente, Faculty of
Background: Human stance involves multiple segments, including the legs and trunk, and requires coordinated actions of both. A novel method was developed that reliably estimates the contribution of the left and right leg (i.e., the ankle and hip joints) to the balance control of individual subjects. Methods: The method was evaluated using simulations of a double-inverted pendulum model and the applicability was demonstrated with an experiment with seven healthy and one Parkinsonian participant. Model simulations indicated that two perturbations are required to reliably estimate the dynamics of a double-inverted pendulum balance control system. In the experiment, two multisine perturbation signals were applied simultaneously. The balance control system dynamic behaviour of the participants was estimated by Frequency Response Functions (FRFs), which relate ankle and hip joint angles to joint torques, using a multivariate closed-loop system identification technique. Results: In the model simulations, the FRFs were reliably estimated, also in the presence of realistic levels of noise. In the experiment, the participants responded consistently to the perturbations, indicated by low noise-to-signal ratios of the ankle angle (0.24), hip angle (0.28), ankle torque (0.07), and hip torque (0.33). The developed method could detect that the Parkinson patient controlled his balance asymmetrically, that is, the right ankle and hip joints produced more corrective torque. Conclusion: The method allows for a reliable estimate of the multisegmental feedback mechanism that stabilizes stance, of individual participants and of separate legs.
Balance control; Closed-loop system identification; Multivariate systems; Asymmetry
Maintaining an upright posture is a relatively easy task for
healthy humans [1,2]. However, bipedal upright stance is
inherently unstable, as small deviations from the upright
posture result in disturbing torques due to gravity, which
drives the system further away from upright posture .
To stay upright, the body generates corrective torques to
counteract the effects of internal (e.g., motor and sensory
noise) and external (e.g., uneven surfaces) perturbations.
When postural deviations are small, the body is often
simplified as an inverted pendulum pivoting at the ankles,
which describes the so-called ankle strategy [3-5].
However, several studies demonstrated that human movement
during stance is multi-segmental [6-8] and for example,
the hips substantially contribute to upright stance (i.e., the
hip strategy ). Human balance control is a closed-loop
multi-segmental process, i.e., sensory signals about the
movement of the body are fed back to the central nervous
system (CNS), and the CNS controls the muscles to
generate adequate responses [10,11]. In a noisy closed-loop
system, like human balance control, causality is difficult to
determine and the dynamics of the different components
(i.e., the body and the stabilizing mechanisms located in
the CNS) affect both the input (joint angles) and output
signals (joint torques). To open the loop and to separate
the dynamics of the different components, the balance
system need to be perturbed [11,12]. Furthermore, when
estimating the dynamics in a multivariate system,
multiple perturbations need to be applied [13,14].
Most studies investigating the multivariate nature of
balance control do not take the multivariate noisy closed-loop
nature into account, by either not using perturbations
[15-17], or by using only one perturbation [18-20]. Only
two studies investigated the multivariate nature of balance
control by applying two perturbations [2,21].
Fujisawa and colleagues  investigated the role of
the hip joint to upright stance by applying
pseudorandom perturbations (bandwidth 0 - 0.83 Hz) while
manipulating the support surface width. Subsequently, an
ARMAX model (with joint angles as input and joint
torques as outputs) was fitted to the data to obtain the
Frequency Response Functions (FRFs) of a two-segment
model of balance control. Results showed an increase of
balance contribution of the hip joint, when the support
surface became narrower.
Jeka and colleagues  identified neural feedback during
upright stance in 18 subjects, while applying two
mechanical perturbations (springs attached to a linear motor) and
one sensory perturbation (visual scene rotations). By
comparing the identified neural feedback (from joint angles to
weighted electromyograms (EMGs) of the leg and trunk
segments) with a large range of cost functions, it was
concluded that the CNS stabilizes stance with near minimum
Ageing and many neurological diseases are associated
with balance impairments and falls . Understanding
the (patho)physiology of upright stance could aid to
detect individuals with an increased risk of falls, help to
design and evaluate intervention programs or monitor
disease progression. Therefore, for clinical applications,
it is very important to obtain a reliable individual
estimate of balance control.
Of all neurological diseases, PD patients are at the
highest risk of falling [22-24], but the pathophysiology of
balance impairments in PD remains unclear [25,26].
Recently, it was suggested that one of the factors contributing
to decreased balance control in PD patients, is impaired
trunk control [27,28] or a decreased intersegmental
coordination [29,30]. Another factor could be asymmetrical
balance control, that is when one leg produces more force
than the other leg to maintain an upright posture.
Asymmetries in balance control have been rarely studied in PD,
although it is an asymmetrical disease . One study 
found balance control asymmetries in 24% of the PD
participants, indicating that balance asymmetries are
important in PD.
Currently, there is no method available that can
identify a multisegmental stabilizing mechanism of balance
control on an individual level, separating the
contribution of the joints of the left and right body side. We
developed and evaluated a non-parametric MIMO
(MultipleInput-Multiple-Output) identification method based on
the previously used non-parametric system SISO
(SingleInput-Single-Output) identification method . To obtain
a reliable individual response, periodic perturbations were
applied, which have the advantage of having power at
specific frequencies, decreasing the measurement time, and
increasing the participants response. In addition, the
stabilizing mechanisms were estimated based on left and
right joint torques (contrary to weighted EMGs; ), to be
able to investigate balance control asymmetries.
In sum, our goal was to develop a method that can
reliably estimate the stabilizing mechanisms of the
closedloop multivariate balance control system of individual
participants, making a distinction between the
contribution of the left and right leg. The (clinical) applicability
is demonstrated in an experiment that perturbed the
balance of seven healthy participants and a PD patient
with a novel device that can apply two independent
A two degree-of-freedom (DoF) balance control model
(described extensively in Appendix A) was implemented
in Matlab (The Mathworks, Natick, USA) and simulated
with Simulink (equations were solved with a fifth order
Dormand-Prince algorithm). The human balance model
consisted of a two-segment human body with two
actuators (ankle and hip), which were controlled using
feedback of the joint angles (ankle and hip). In the model,
no distinction between the left and right leg was made.
We perturbed the model with one and two perturbations.
Two possible perturbation configurations of the two
perturbations were evaluated: 1) external forces at the hip and
shoulder (see Figure 1), similar to push-pull rods and 2) a
combination of platform forward-backward platform
translations and a perturbation torque around the ankle (see
Figure 2). Also, simulations without and with pink sensor
noise  and white (measurement) noise were evaluated:
i. two perturbation forces with noise (2F-N),
ii. two perturbation forces without noise (2F-Nn),
iii. platform perturbation and ankle torque with noise
iv. platform perturbation and ankle torque without
v. one perturbation and one perturbation round with
vi. one perturbation and one perturbation round
The characteristics of the perturbation signals are
described in detail in the Disturbance signals section and
the amplitudes and power spectra are reported in
Table 1. The input and output signals of the model were
sampled at 120 Hz.
Figure 1 Multiple-Input-Multiple-Output closed-loop balance control system. The body mechanics represent the dynamics of a
doubleinverted pendulum with the corrective ankle and hip torques as inputs and the joint angles as outputs. The stabilizing mechanisms represent the
dynamics of the combination of active and passive feedback pathways of the concerned body(part) and generates a torque to correct for the
deviation of upright stance. The balance control model can be perturbed with support surface movements (Sx), perturbation forces at the hip
(Fp1) or at the shoulder (Fp2). Positive torques and positive angles are defined as counterclockwise.
Seven healthy participants (two female, mean age 65 yrs.
std 5.7) and a PD patient (male, 57 yrs) participated in
the study. The participants gave written informed
consent prior to participation. The protocol was approved
by the local medical ethics committee and was in
accordance with the Declaration of Helsinki.
Apparatus and recording
Two independent perturbations were administered with
a computer-controlled six DoF motion platform (Caren,
Motek, Amsterdam, The Netherlands) and a
custombuilt actuated device able to apply perturbing forces in
the anterior and posterior direction at the sacrum, called
the pusher (see Figure 2). The pusher was attached to
the platform and actuated using a series elastic actuator
 controlled with an electro motor (Maxon motor ag,
Sachseln, Switzerland). The pusher was force controlled
using a custom-built controller in xPC (The Mathworks,
Natick, USA) and had a bandwidth of 10 Hz and a
maximum torque of 50 Nm. The gravitational pull due to the
weight of the pusher was compensated for, such that the
participants did not experience additional forces other
than the perturbation force and a small force due to the
pushers inertia. The interaction force in between the
subject and the pusher was measured with a six DoF
force transducer (ATI-Mini45-SI-580-20).
Body kinematics and the platform movements were
measured using motion capture (Vicon Oxford Metrics,
Oxford, UK) at a sample frequency of 120 Hz. Reflective
spherical markers were attached to the following
anatomical landmarks: the first metatarsal, calcaneus,
medial malleolus, the sacrum, the manubrium and the last
vertebrae of the cervical spine (C7). In addition, a cluster
of three markers was attached to both anterior superior
iliac spines on the pelvis. Furthermore, one additional
marker was attached to the foot and two markers were
attached to the lower leg (one on the tibia) to improve the
estimation of the ankle joint rotational axis. Also, markers
were attached to the knee (just below the lateral
epicondyle) and shoulder joints (just in front of the acromion).
Three markers were attached to the platform. Reactive
forces from both feet were measured with a dual
forceplate (AMTI, Watertown, USA), embedded in the motion
platform. The signals from the dual forceplate, the 6 DoF
force transducer and the perturbation of the pusher were
sampled at 600 Hz and stored for further processing.
During the experiment, participants stood with their arms
folded in front of their chest on the dual forceplate and
strapped to the pusher, with a strap band that opened with
a click buckle, with their eyes open. They were instructed
to maintain their balance without moving their feet, while
multisine platform movements and multisine force
perturbations were applied simultaneously in the
forwardbackward direction; see Disturbance signals. Participants
wore a safety harness to prevent falling, but it did not
Figure 2 Experimental set-up. The participant stands on the dual
forceplate (A) embedded in the movement platform (B). Two
independent perturbations are applied with the movement platform
(B) and the pusher (C) in the forward-backward direction. Interaction
forces between the pusher (C) and the participant are measured
with a force sensor (D). Actual falls are prevented by the safety
harness (E). Reflective spherical markers (F) measure the movements
of the participant.
constrain movements, provide support or orientation
information in any way.
Before any data was recorded, the participants got
acquainted to the perturbations. The experimenter
determined the maximal amplitude the participant could
withstand while keeping the feet flat on the floor and assessed
whether the participant could withstand this amplitude for
the total of four trials. Four double perturbation trials of
180s were recorded: in the first two trials, the
perturbations had the same sign. In the other two trials, the
perturbations had opposite signs. If needed, the participants
were allowed rest in between trials.
For both the model simulations and the experiment we
used the same perturbation signal. During the model
simulations the perturbation signal was used to either produce
two perturbing forces, or a combination of a platform
translation and a torque around the ankle (see Model
simulations). In the experiment the perturbations were
applied with a movement platform and an actuated
backboard (see Apparatus and recording).
The perturbation signal was a multisine with a period
of 34.13 s (equal to 212 = 4096 samples at a sample rate
of 120 Hz) [4,35]. This signal contained power at 112
frequencies in the range of 0.064.25 Hz. To increase the
power at the excited frequencies the signal was divided
into five frequency bands: 0.06-2.37 Hz (80 frequencies),
2.63-2.84 Hz (8 frequencies), 3.11-3.31 Hz (8 frequencies),
3.57-3.78 Hz (8 frequencies), 4.04-4.25 Hz (8 frequencies).
The frequency points outside these frequency bands were
not excited. The signal is unpredictable for participants,
because the signal consists of many sinusoids. The power
of the signal was optimized by crest optimization .
The human body, i.e. the plant, is considered as a
doubleinverted pendulum, consisting of a leg and a
Head-ArmsTrunk (HAT) segment. Stabilizing mechanisms generate
ankle and hip torques based on sensory information of the
joint angles, (see Figure 1).
The stabilizing mechanisms have passive components
such as muscle stiffness, generated by passive muscle
properties and tonic activation. The active part
incorporates the controller within the CNS (e.g. reflexive muscle
activation), muscle activation dynamics, and time-delays,
representing the neural signal conduction times.
Movements from the upper body segment will
influence the movements of the lower body segment and vice
versa due to mechanical coupling [36,37]. The stabilizing
mechanisms have to deal with this mechanical coupling,
which is especially expressed in coupling terms between
ankles and hips (i.e., CATH and CH TA ). The direct
terms CATA and CH TH represent the corrective
actions of the ankle and hip joint, based on the ankle and
hip joint angle. In other words, this system is a multiple
input (two joint angles) multiple output (two joint
torques) system. When considering the corrective
actions of both legs separately, two stabilizing mechanisms
are defined; one for each leg [4,38].
For the model simulations, the perturbations, inputs
(joint angles) and outputs (joint torques) of the model
were determined for further processing. For the
experiment these signals were calculated as described below.
From the recorded movement trajectories of the markers,
the position of the center-of-mass (CoM) of the predefined
segments and of the whole body and the position of the
joints were estimated by custom written software [39,40].
In short, in each segment a local coordinate frame was
determined on the basis of the position of anatomical
landmarks, according to the method described by Koopman
et al., 1995 . The mass, CoM position and the inertia
tensor moment of the predefined segments (i.e., feet, legs
and HAT) and the joint positions were determined with
regression equations [41,42]. Subsequently, the CoMs
were determined as the weighted sum of the separate
segment CoM positions . From the static trial, the average
distance in the sagittal plane from the ankle to the total
body CoM (i.e., the length of the pendulum; lCoM) was
determined. The sway angle was calculated from lCoM and
the horizontal distance from the CoM to the mean
position of the ankles. Forces and torques of the force plate
and force sensor were filtered with a fourth-order
lowpass Butterworth filter with a cut-off frequency of 8 Hz
and subsequently resampled to 120 Hz. Forces and torques
of the force plate were corrected for the inertia and mass
of the top cover . On the basis of the corrected forces
and torques and recorded body kinematics, ankle and hip
joint torques were calculated with inverse dynamics .
In addition, the applied platform perturbation was
reconstructed from the platform markers.
Multiple-Input-Multiple-Output closed-loop system
To obtain a non-parametric spectral estimate of a two DoF
multivariate closed-loop system we adopted a method
described by Pintelon and colleagues stating that two
different combinations of a periodic excitation signal, D(k), in
two separate experiments should be applied . An
optimal choice of D( f ) (maximizing det (P(f )) using periodic
excitation is given by:
denotes the estimate of the cross spectral density (CSD) of
the disturbance and the outputs (joint angles and joint
Subsequently, the stabilizing mechanisms were
estimated using the joint input-output approach :
With G^ pTc f and G^ p1 f the estimated CSD from the
perturbations to the corrective torques and from the
perturbations to the joint angles. Note that C is a
two-bytwo matrix, see also Figure 1. p is a vector with the two
disturbances, ( f ) is a vector with ankle and hip joint
angles, and Tc( f ) is a vector with ankle and hip joint
torques for each frequency f; all expressed as Fourier
coefficients. The method assumes that the system does not
change between the two separate perturbation rounds,
with the two different combinations of the periodic
excitation signal (Eq. 1).
For both the model simulations and the experiment,
data was obtained for eight response cycles of the
perturbation signal for each perturbation round.
Subsequently, the data were Fourier transformed and only the
Fourier coefficients at the excited frequencies were used
for further processing. These were averaged over the
eight cycles, and the average Fourier coefficients were
used to calculate the power- and cross spectral density
(PSD and CSD, respectively). The PSDs and the CSDs
were smoothed by averaging over four adjacent
frequency points . The FRFs were calculated according
to Eq. 2 and 3 to obtain a non-parametric spectral
estimate of the total stabilizing mechanisms.
As the corrective torque which has to be delivered by
the participants is dependent on gravity, all FRFs were
normalized for the participants mass and length, i.e. the
gravitational stiffness (mgl), with m the total body mass, l
the length of the pendulum (from the ankles to the Center
of Mass; CoM), and g the gravitational constant. The
average FRF over all participants was obtained by taking the
mean over the individual normalized FRFs. Note that, as
we used a dual forceplate in the experiment, the
experimentally obtained Fourier coefficients of the left and right
FRFs were added to obtain the total FRFs.
Reliability of the estimated MIMO frequency response
To determine whether the above described MIMO
closedloop system identification technique gives reliable
estimates of the stabilizing mechanisms, several indicators
were calculated (described below).
Goodness of estimate
For the model simulations, the goodness of fit (GOF) was
determined by the object function . This function
With D( f ) the two perturbation signals. All calculations
were performed in the frequency domain with f the
frequency in Hz. This means that in the first round, both
inputs were excited with the same periodic excitation, while
in the second round the sign of the second perturbation
was changed. These perturbations excited the system and
the system responded with movements (joint angles) and
torques (corrective joint torques) at the frequencies of the
perturbation signal. Corrective torques are the torques that
restore the bodys equilibrium in response to motor and
sensor noise and the perturbation signal. The estimate
from the perturbation to inputs (joint angles) and outputs
(corrective joint torques) was first obtained from:
With Y( f ), a two-by-two matrix with on the first column
the responses of the first perturbation round (i.e., ankle
and hip joint angles or torques) and on the second column
the responses of the second perturbation round. G^ py f
compared the theoretical Transfer Function (TF) as
incorporated in the model (Appendix A) with the estimated
FRF as obtained in the model simulations:
Where a perfect estimation of the transfer function
will result in a GOF of zero, i.e., the lower the GOF the
better the estimation.
As a result of a periodic perturbation to the balance control
system, the systems response was periodic, while
timevariant behavior and/or noise resulted in a stochastic, i.e.
non-periodic response . The ratio of the non-periodic
(also called the remnant) and periodic response is expressed
by the noise-to-signal ratio (NSR):
Where Up( f ) represents the periodic response and 2u( f )
the variance of the remnant. The NSR was calculated in
the frequency domain with f frequency in Hz. When
multiple realizations are simulated or recorded, the periodic
response is obtained by calculating the average over the
realizations; the remnant can be estimated by calculating
the variance over the realizations.
A small NSR indicates low variability of the systems
response to the perturbation signal over the multiple periods.
This indicates time invariant behavior and a low presence
of noise . As such, it gives insight into whether linear,
time-invariant, system-identification methods can be used
and it gives an estimate of how well the system is
perturbed. More importantly, it quantifies how reliable the
estimate of the stabilizing mechanism is. For example, a
NSR of 1 indicates that the recorded data contains 50
percent response and 50 percent remnant. This means that
describing the system as a deterministic linear time
invariant (LTI) system (expressed by the estimated FRFs in this
study) explains 50 percent of the recorded data.
Single-Input-Single-Output frequency response functions
To assess whether the two perturbation rounds in the
experiment lead to a change in strategy of the participants
(i.e., time-variant behavior), we estimated
Single-InputSingle-Output (SISO) FRFs from sway angle to ankle
torque and from sway angle to hip torque with the
jointinput-output-method (Eq. 3; ).
For the SISO FRFs the (magnitude-squared) coherence
was calculated between the input signal (perturbations)
In which p represents the platform disturbance and y an
output signal. p,y, p,p and y,y are the CSDs and PSDs of
the perturbation and output signals. By definition, coherence
varies between 0 and 1, where coherence close to one
indicates a low noise level and time-invariant behaviour.
Balance contribution of the left and right body side
For the experiment we determined the relative
contribution of each ankle and hip joint to the total amount of
generated corrective torque to resist the perturbations
by calculating the contribution of the gain and phase of
each leg to the gain and phase of the total body :
With FRFl,r the left or right FRF and FRFt the total FRF.
The indicates the dot product of the FRFs. In this way
the contribution of the left or right leg to the total balance
control was expressed as a proportion. For example, a
proportion of 0.8 for the left leg means that the left leg
contributed for 80% to the total body stabilization. This was
done for each separate MIMO FRF (see Eq. 2 and 3).
Table 1 shows the GOF values and NSRs of the different
simulations. In case of no sensor and measurement noise,
a platform acceleration in combination with a perturbation
torque around the ankle (PLT-Nn) gave the same results as
two perturbation forces (2F-Nn). In these conditions, the
small GOF values indicated that the stabilizing
mechanisms were well estimated.
Adding sensor (pink) and measurement (white) noise to
the simulations resulted in slightly worse estimations; the
GOF values increased. However, the stabilizing
mechanisms were still correctly estimated (see Figure 3).
Platform acceleration and a perturbation torque around the
ankle (PLT-N) resulted in better estimations than two
perturbation forces (2F-N).
Figure 3 shows the model transfer function and the
estimated frequency response functions of the PLT-N and
PLN conditions. Clearly, applying two perturbations resulted
in very good estimations (see also Table 1). However,
applying only one perturbation to estimate the stabilizing
mechanisms of a MIMO system resulted in incorrect
Figure 3 Theoretical transfer function and estimated frequency response functions (CATA ;CATH ;CHTA and CHTH ). Results of the
model simulations in the presence of pink and white noise during the condition with a platform acceleration and perturbation torque around
the ankle are depicted (PLT-N; open dots) and during the condition with one perturbation (PL-N; solid grey dots). The bold solid line represents
the model transfer function of the stabilizing mechanisms. Applying two independent perturbations in combination with a multivariate
closedloop system identification method resulted in a correct estimation of the stabilizing mechanisms (FRF 2 perturbations, indicated with open dots),
whereas one perturbation resulted in an erroneous estimate (FRF 1 perturbation, indicated with solid grey dots).
estimates, although the responses were time-invariant as
shown by the NSRs values. In other words, applying one
perturbation resulted in biased estimates of the stabilizing
mechanisms. Note that the GOF values of the PL-Nn and
PL-N simulations were of the same magnitude.
Figure 4 shows the perturbations and the response of
one representative healthy participant to the applied
perturbations. For the healthy controls, the average peak-to
-peak amplitudes were 0.068 m (std: 0.005) for the
platform and 18.4Nm (std: 1.05) for the pusher. For the PD
patient the peak-to-peak amplitudes were 0.06 m and
20 Nm, see also Table 1. In general, the participant
responded in a consistent fashion as indicated by the
low standard deviation over the adjacent segments and
corresponding low NSRs (Table 1). The average median
NSRs (of both perturbation rounds) of all healthy
participants were: 0.24 (ankle angle); 0.28 (hip angle); 0.15
(sway angle); 0.56 (ankle torque) and 0.35 (hip torque).
Hence, on average, the healthy participants responded in
a consistent fashion (see Figure 4). Note, however, that
the response of the sway angle was even more consistent
than the joint angles. The PD patient was able to
complete the balance control experiment without any
problems. He could withstand the perturbations and the
duration of the trials. The patient also responded in a
Noise to Signal Ratio
Figure 4 Timeseries (left panels) and NSRs (right panels) of the first perturbation round of one representative participant. From top to
bottom: platform perturbation, pusher perturbation, ankle angle, hip angle, sway angle, ankle torque, and hip torque. The mean is depicted by
the solid line and the standard deviation over the eight cycles by the grey area. The black line in the right panels depicts NSR=1. Ideally, the
average NSR of the responses remains below one. The responses of the participant were consistent, as evidenced by small standard deviations
over the adjacent segments and low NSRs. This means that a large part of the data is captured by the time-invariant MIMO system
time-invariant fashion. He had even slightly lower NSRs
than the healthy controls.
Single-Input-Single-Ouput frequency response functions
Figure 5 shows the SISO FRFs from sway angle to ankle
torque and hip torque of each perturbation round of the
healthy controls. Gain and phase of the FRFs and
coherence of the joint torques were similar for both
perturbation rounds. There was a small discrepancy between
the gain of the FRFs at the lower and higher frequencies,
but this can be attributed to a less periodic response at
these frequencies (indicated by a decreased coherence),
and hence the reliability of the FRFs decreased. In
addition, the coherence of the sway angle was lower in
the second perturbation round, especially at frequencies
below 0.7 Hz. This resulted in a slightly worse estimate
of the FRFs, compared to the first perturbation round.
Similar results were found for the PD patient (data not
Multiple-Input-Multiple-Output frequency response
The MIMO FRFs of the stabilizing mechanisms of healthy
controls and the PD patient are shown in Figure 6. The
total of four FRFs are shown: from ankle angle to ankle
torque CH TA , from ankle angle to hip torque CATH ,
from hip angle to ankle torque CHTA and from hip
angle to hip torque CHTH representing the multivariate
stabilizing mechanisms of the participants.
In general, for the healthy controls, the relationship
between the ankle joint angle and the ankle joint torque
remained roughly constant over the whole frequency
1st perturbation round
2nd perturbation round
Figure 5 Single-Input-Single-Output frequency response functions and coherences of first and second perturbation round. The left
panel depicts the FRF from the sway angle to the ankle joint torque; the right panel the FRF from the sway angle to the hip joint torque. The
lower panels show the coherence between the perturbation, and the ankle joint torque, hip joint torque, and the sway angle. Similar gains and
phases of the frequency response functions of the first and second perturbation round indicate that participants did not change their balance
range, whereas the hip joint gain was high at the low
frequencies (<0.7 Hz), low at the mid frequencies (0.7-2 Hz)
and increased at higher frequencies (>2 Hz). The
coupling between the ankle joint angle to hip torque
increased with frequency, whereas the CH TA FRF
remained roughly constant over the frequency range.
The PD patient showed similar gain patterns for the
CATA and CH TA FRFs, but for the CATH and
CH TA FRFs the gains at the lower frequencies were
much higher than those of the healthy controls,
indicating an increased postural stiffness in the PD patient.
The phase of the CATA and CH TA FRFs of both the
HCs and the PD patient decreased with increasing
frequency (i.e. a phase lag), indicating a neural time delay.
The phase of the CATH showed a phase shift of about
+360 around 1.5 Hz. For the phase the largest difference
between the HCs and PD patient is found in the CATH
FRF. Both groups showed a negative phase shift around
2 Hz, but this shift was larger in the PD patient.
Balance contribution of the left and right body side
In healthy controls both legs contributed equally to the
body stabilization; the proportion for each FRF was 0.5.
However, for the patient, the right leg contributed more to
the balance control than the left leg, and this was the case
for both the ankle and the hip joint. Note that the patient
is clearly outside the 95% confidence interval (CI) of HCs
(see Figure 7). It can be seen that for the FRFs CATA and
CH TA the proportion between both legs was similar over
the whole frequency range, whereas for the FRFs CATH
and CH TH the asymmetry decreased with increasing
frequency and eventually disappeared above 1 Hz.
Bipedal upright stance is multisegmental and requires
the coordinated activity of multiple joints, including the
ankles and hips. We developed a system identification
method to investigate the balance control contribution
of the ankles and hips of the left and right leg separately
Figure 6 Multiple-Input-Multiple-Output frequency response functions of the stabilizing mechanisms. The solid line represents the
average of the healthy participants, with the shaded area indicating the 95% confidence interval and the dotted line the Parkinson patient.
of individual subjects. To investigate both DoF and their
interactions in a feedback loop, two perturbations are
required. Therefore, in our lab we developed an actuated
pusher placed on a motion platform to provide these
independent perturbations. Using model simulations, it was
demonstrated that these perturbations can identify the
system reliably. The (clinical) applicability of the method was
demonstrated in seven healthy controls and a PD patient.
Evaluation of the Multiple-Input-Multiple-Output
The model simulations indicated that two independent
perturbations are necessary to identify the stabilizing
mechanisms of a two DoF MIMO system. Applying only
one perturbation to the model resulted in biased
estimates of the stabilizing mechanisms. This bias was not
influenced by noise level. Two configurations with two
independent perturbations were evaluated, that is, a
combination of a platform acceleration and a disturbance
torque around the ankle and two perturbation forces in
the forward-backward direction. The stabilizing
mechanism were estimated very well with both configurations, and
the differences between the two approaches were small.
After adding sensor and measurement noise to the
simulation, the stabilizing mechanisms were still estimated well
with both configurations, with a slightly worse result when
perturbing with two forces. In short, the model simulations
showed that the implemented MIMO identification method
correctly identified the stabilizing mechanisms indicated by
Figure 7 The average contribution of the right leg of the healthy controls and of the PD patient to each
Multiple-Input-MultipleOutput frequency response function. The average contribution of the right leg for the healthy controls (HC) is shown by the solid line (mean)
and the grey area (95% confidence interval). The patient (dashed line) clearly controlled his balance asymmetrically, with the right leg producing
more corrective torque than the left leg to resist the perturbations.
small differences between the theoretical transfer function
of the model and the estimated frequency response
functions, even in the presence of realistic levels of noise.
In the experiment with human participants, the
perturbations were applied with a motion platform and a
custom-made actuated backboard (i.e., the first
configuration of the model simulations, which gave slightly
better results). The amplitudes of the applied perturbations
were easy to withstand, both for the healthy participant
as for the PD patient, making the method suitable for
use in a large range of participants.
To be clinically relevant, the MIMO identification
method should be able to reliably estimate the different
segmental contributions to the total balance control of a
single participant. First, the quality of our estimation was
expressed in the NSR. A low NSR indicates that a large
percentage of the data is captured by the estimated
stabilizing mechanisms. The NSR gives the ratio between the
(periodic) response to the perturbations and the remnant.
As the method assumes a LTI system, remnants can be
due to a) nonlinearities of the perturbed system, b)
timevariant system behavior, c) unmeasured system noise,
and d) measurement noise . Note that a low NSR
does not necessarily mean that the system is linear.
The average NSRs of the healthy controls of the ankle
and hip joint angle and of the ankle and hip torque were
0.24 and 0.28, 0.56 and 0.35, respectively. This results in
an average NSR of 0.36, meaning that about 74% (i.e., 1/
(1+0.36)) of the response is captured by the estimated
stabilizing feedback mechanisms. The PD patient had
lower NSRs than the average healthy subject, indicating
less variability over the repetitions of the perturbation
signal. Unfortunately, it is impossible to compare our
results with respect to reliability of the estimates with
other studies using two perturbations as these studies
did not report any parameters quantifying reliability and
only report averages over participants.
Secondly, the used MIMO identification scheme
consists of two perturbation rounds: in one round, the
perturbations have the same sign, while in the other round, the
perturbations have opposite signs. To determine whether
participants did not change their balance control
behaviour in both perturbation rounds, SISO FRFs for the ankle
and hip joints were determined. Gain, phase, and joint
torque coherence were comparable for both perturbation
rounds; hence the participants did not change their
balance control strategies. Note that the sway angle and ankle
and hip coherence was lower in the second perturbation
round at the lower frequencies (<0.7 Hz), indicating less
time invariant behavior (possibly due to fatigue) and/or a
higher noise level. This could be due to not randomizing
the perturbation rounds. However, this did not result into
quantitatively different behavior, as the SISO FRFs were
similar for both perturbation rounds.
The last requirement of the method is that it is able to
distinguish between the balance contributions of the
separate legs to investigate balance asymmetry. By using
a dual forceplate and calculating the FRFs for each leg
separately, balance control asymmetries were detected in
a PD patient.
Perturbing with a different set-up (for example two
push-pull rods), at different locations or by using
different signals could have elicited different responses. This
is not an artifact of the method, but reflects the
adaptability of the nervous system .
In sum, two unique features of the presented method
are the applicability on the individual level and
separation of balance contribution of each body side. The first
was accomplished by applying multisine perturbation
signals, which have the advantage of improving the
estimation of FRFs because they concentrate signal power
in a limited set of frequencies and are periodic. This
results in reliable individual results and shorter
measurement times [35,46]. Secondly, by measuring the reaction
forces of each foot with a dual forceplate balance
control, asymmetries can be detected.
Comparison with other multivariate methods
Most published studies investigating the multivariate
nature of balance control do not use perturbations, or use
only one perturbation [15,16,18-20]. However, the model
simulations indicated that two independent
perturbations are required to estimate the stabilizing mechanisms
of a multivariate balance control system. Using only one
perturbation in the model simulations gave biased and
The other two available methods [2,21] differ from the
presented method in this paper. Our method is
nonparametric, where Fujisawa  used a parametric method
(ARMAX model structure). A parametric method has the
advantage that it, theoretically, can better separate the
measurement noise from the actual signals. However,
knowledge about the structure of the system is required.
A non-parametric method has the advantage that no prior
knowledge of the system is needed . Despite the
differences between the applied methods in  and in this
manuscript the obtained FRFs are in the same range for
the low frequencies. That is the CATA FRF starts at unity
gain which slightly increases with frequency, whereas the
CATH , CH TA and CH TH have lower gains at the lower
frequencies (~0.05) but also increase with frequency. Note
that we can compare the FRFs only in the low frequency
range, as Fujisawa and colleagues  used a perturbation
signal with frequencies up to 0.83 Hz.
Recently, Jeka and colleagues [2,47] used an approach
to investigate task goals for upright stance, similar to
the one presented here. There are, however, a few
fundamental differences. First of all, Kiemel et al. 
used filtered white noise as a perturbation signal,
whereas we used multisines, which have the advantage
of improving the individual estimate of the stabilizing
mechanisms. Also, they define the input of the
stabilizing mechanisms as weighted EMG signals of the
anterior and posterior body sides, whereas we have used joint
torques. Therefore, the method presented by Jeka and
colleagues [2,47] focused on separating the reflexive
from the total contribution of the stabilizing
mechanisms by measuring EMG signals. This measurement
and analysis of EMG signals can easily be added to our
method. In order to detect balance control asymmetries,
joint torques (which we have used in this study) are
more suitable than EMG signals. Differences in EMG
amplitude can for example, be due to different electrode
placement on contralateral legs, different skin
conductivity or due to different background activity, making
these signals more prone to measurement artifacts. In
addition, joint torques are more suitable for
investigating joint stiffness.
Multisegmental balance control
With a MIMO method and by applying multiple
perturbations, multisegmental balance control strategies and
the interplay between the joints can be investigated.
This approach can be used to test hypotheses about the
role of the different joints, and also of sensory
It has been suggested that PD patients have a decreased
intersegmental coordination [29,30] or an increased hip
stiffness [25,28]. In this study, the most pronounced
difference between the healthy controls and the PD
patients was found in the CH TH FRF, that is, the PD
patient had a higher gain at the lower frequencies,
indicating an increased hip stiffness. With our method we
can now distinguish between coordination between the
upper and lower body and of coordination of the upper/
lower body separately. Further investigation of
intersegmental coordination could lead to a better
understanding of the pathophysiology of balance impairments in
PD and possibly improve intervention programs.
The PD patient asymmetrically controlled his balance
with both the ankle and the hip joint. This means that one
leg contributed more to body stability than the other leg.
Balance control asymmetries have been shown before in
PD patients, both during quiet stance [32,49] and with a
single DoF approach , but not taking into account the
contribution of the hip joint. The balance asymmetry was
also present in the intersegmental coordination, i.e. in the
FRFs from ankle angle to hip torque and from hip angle
to ankle torque. Hence, our new method has the
advantage of assessing balance control asymmetries during
perturbations, considering the role of the hip joint and
the interplay between joints. This creates the possibility
of assessing differences in balance control contribution
between distal and proximal joints, and it can be
investigated whether balance asymmetries influence
intersegmental coordination. Further necessary research in a
large group of PD patients and healthy matched
controls should demonstrate the (potential) clinical value of
the new method.
Furthermore, balance control can also be asymmetrical
in stroke patients [4,51]. During the recovering process,
restoration of the paretic body side and/or compensation
in the non-paretic body side may contribute to improved
balance maintenance. Investigating balance control
asymmetries provides the possibility of investigating different
recovery and compensation strategies during the
We presented a new method to identify the
multisegmental stabilizing mechanisms in human stance
control using non-parametric system identification techniques
and evaluated its performance. Model simulations showed
that the newly presented method correctly and reliably
estimated the balance control contribution of the ankle and
hip joints and interactions between the segments. A balance
control experiment showed the application in both healthy
and pathological participants. Furthermore, the method can
distinguish between the balance control contribution of
each ankle and hip joint separately. Taken together, this can
be used to create insights into the pathophysiology of
postural instability and asymmetry in patients and possibly
aid to develop and evaluate treatments.
shows the general model; the derivation of the subsystems
is described below.
Derivation of the equations of motion
Kanes method (TMT method) was used to derive the
equations of motions. In this method, the principles of
virtual power are used to rewrite the Newton-Euler
The first step is to define the degrees of freedom
(generalized coordinates, qt) of the model, which are in this case
the support surface (Sx) and segment angles: 1 and 2.
Secondly, a transformation matrix Tj, which describes
the Cartesian coordinates of the center of mass of the
segments (x,y coordinates) in the degrees of freedom of the
system (i.e., the generalized coordinates Sx, 1 and 2) is
2 Sx 3
6 Sx d1 cos1 7
With d1 and d2 the distance to the segments center of
gravity from the distal point, l1 denotes the length of the
leg segment. This matrix can be differentiated to the
generalized coordinates to obtain the first (Tj,t) and
second derivative (Tj,tl) of the transformation matrix.
The mass matrix is also defined:
M diag mf ; m1; m1; I1; m2; m2; I2
Human balance control model
To test the feasibility of the MIMO identification method,
model simulations were performed. A two-DoF mechanical
model with a stabilizing mechanism was derived, Figure 8
With mf, m1, m2, I1 and I2, the mass of the foot, the
segments masses and inertias respectively.
And we also define the external forces and moments
( f ): this is the sum of the gravitational forces Fgrav, i, the
external forces Fext, i , and the joint torques (joint,i):
Figure 8 Model of human balance control. The model consists of body mechanics and a controller with intrinsic stiffness and damping (Cpas),
an active proportional derivative controller (Cact), timedelays (), muscle activation dynamics (Hact), sensor and measurement noise. Tank and Thip
denote the respective joint torques, 1 and 2 the joint angles. Sx and Fpert are the force and platform perturbations, respectively. g is the
With g the gravitational acceleration (9.81m/s2),
p1 = Fp1 * p1 * sin(1), the perturbation torques due to
the external perturbation force. Note that joint moments
(ank and hip) are the inputs of the model (forward
simulation). Note, that the internal forces are not
incorporated in the force matrix; these are implicitly
incorporated in the Tj,t and Tj,tl matrices.
The movement equations with the TMT method lead
to the following expression:
With Mred1 T T MT and T = (Ti,t), is the first
derivative of the transformation matrix.
With f the external forces, M the mass matrix and g
Tj;tmq_ tq_ m ; this term corresponds to the centripetal term
of the movement equations. In the case of forward
simulation, we want to know the accelerations and the
torques that are the inputs of the model:
It can be deduced from Equation 11 and 12 that the
equations of motion can be rewritten as:
For which we have used the index notation.
In the case of a platform disturbance and a perturbation
force, one of the generalized coordinates is specified,
namely the platform movement (note that platform
accelerations generate the perturbation). Therefore, the
platform movement (Sx) can be considered as a known
degree of freedom, while the remaining degrees of
freedom are unknown:
This results in a split up of the Tj,t matrix in a part for the
known (Tj,k) and unknown degrees of freedom (Tj,u) and
differentiation of these matrices results in Tj;kpq_ k q_ p and
Tj;unq_ uq_ n, respectively. Note that the subscripts u and k
denote the unknown and known coordinates, respectively.
By substitution of these matrices in Equation 14, we get:
Mij Tj;k qk Tj;uqu Tj;unq_ uq_ n Tj;kpq_ k q_ p
MijTj;kpq_ k q_ p
MijTj;unq_ uq_ n
MijTj;kpq_ k q_ p
Linearization and state space notation
Subsequently, the equations of motion are linearized by
differentiating the equations of motion to the states of
velocity) and to the system inputs and external
bances ank ; hip; Sx; with a first order Taylor
Where a is the equilibrium point and x the deviation
from the operating point. In our case, the equilibrium
position is straight stance (segment angles are 90,
angular velocities, external perturbations, and joint torques
are zero). Note that the centripetal term of the
movement equations disappears with linearization.
Finally, the equations are rewritten in a state-space
Passive muscle stiffness and damping were added to
each joint; hence, only mono-arcticular muscles are
added. The built-up of muscle force is described by the
muscle activation dynamics and these were modeled as a
second-order dynamical system:
With s = j, the natural frequency (n) was set at 13.8
rad/s (2.2 Hz) and the relative damping () was 0.7. As
the sensory signals do not reach the CNS instantaneously
(because of neural conduction times) a time delay is also
modeled as a pure transport delay, see also Figure 8.
Parameter values were taken from the literature [47,52], see
Based on the A and B matrices of the state space
equations and intrinsic joint stiffness and damping, the
steadystate linear quadratic regulator (LQR), was used to
uniquely determine the components of the optimal state
feedback matrix Cact (see Figure 8). For the optimization,
activation dynamics and timedelays are not included in the
feedback pathway. The feedback parameters are obtained
by minimizing the cost function J of the form:
With x the systems states and u the systems input. Q
and R are diagonal matrices; the elements in Q are set
to 1 and in R set to 106.
As the sensory signals do not reach the CNS
instantaneously (because of neural conduction times) a time
delay is included as a pure transport delay, see Figure 8.
Parameter values were taken from the literature , see
Pink sensor noise was created off line, by scaling the
power spectrum of a random timeseries by 1.2 such that
at 1Hz, the power of the signal was 1.5*10-7.
Subsequently, this signal was added to the joint angles in the
model simulations; this lead to a spontaneous sway of
around 0.6 (peak-to-peak amplitude; comparable with
human quiet stance data). Measurement noise was
modeled as white noise (zero mean and 0.0001 variance) and
added to the joint angles and joint torques.
Table 2 Human balance control model parameters
Time delay ankle
Time delay hip
27.4 (Nm s/rad)
Anthropomorphic data is taken from . The controller properties values are
taken from .
CNS: Central nervous system; ARMAX: Auto regressive moving average
eXogenous; FRF: Frequency response function; EMG: ElectroMyoGram;
PD: Parkinsons disease; SISO: Single input single output; MIMO: Multiple
input multiple output; HAT: Head arms trunk; DoF: Degrees of freedom;
CoM: Center of mass; GOF: Goodness of fit; NSR: Noise-to-signal ratio;
LTI: Linear time invariant; USA: United States of America; m: Meter;
Nm: Newton/m; Hz: Hertz; std: Standard deviation; CLSIT:
Closed-loopsystem-identification-technique; yrs: Years.
The authors declare no competing interests.
TB performed the model simulations, participated in the conception and design
of the experiment, performed the data acquisition, analyzed the data, drafted
and revised the manuscript. AS has made a substantial contribution drafting and
critically revising the manuscript. HvdK conceived of the study and participated
in the design and the coordination of the study and critically revised the
manuscript. All authors have read and approved the final manuscript.
TB received the M.Sc. degree in human movement sciences of the Free
University (Amsterdam, The Netherlands) in 2006. She is currently working
towards her PhD degree at the laboratory of biomechanical engineering at
the University of Twente, in close collaboration with the Radboud University
medical Centre in Nijmegen. Her research focuses on developing new
techniques and methods based on system identification to investigate and
quantify human balance control. Concurrently, she is applying these new
and adopted methods for patients with Parkinsons disease in order to
create more insight into the pathophysiology of this disease.
AC received the M.Sc. and Ph.D. degrees in mechanical engineering from the
Delft University of Technology, The Netherlands, in 1999 and 2004,
respectively. He holds a position as an assistant professor at the Delft
University of Technology. He is co-founder of the Delft Laboratory for
Neuromuscular Control. His research interest is the field of neuromuscular
control and includes techniques to quantify the functional contribution of
afferent feedback, neuromuscular modeling, haptic manipulators, and system
identification. His research focuses on both able-bodied individuals and
individuals suffering from movement disorders.
HvdK (1970, Rotterdam, the Netherlands) received his Phd with honors (cum
laude) in 2000 and is professor in Biomechatronics and Rehabilitation
Technology at the Department of Biomechanical Engineering at the University
of Twente (0.8 fte), and Delft University of Technology (0.2 fte), the Netherlands.
His expertise and interests are in the field of human motor control, adaptation,
and learning, rehabilitation robots, diagnostic, and assistive robotics, virtual
reality, rehabilitation medicine, and neuro computational modeling. Dr.ir. H. van
der Kooij has published over 60 papers in the area of biomechatronics and
human motor control, and has directed approximately 6 million in research
funding over the past 10 years. He is associate editor of IEEE TBME, member of
IEEE EMBS technical committee of Biorobots and was member of several
scientific program committees in the field of rehabilitation robotics, bio
robotics, and assistive devices. At the UT he is founder and head of
Rehabilitation robotics laboratory that developed powered exoskeletons for the
rehabilitation of upper and lower extremities. He is founder and head of the
Virtual Reality Human performance lab that combines robotic devices, motion
capturing and virtual environments to asses and train human balance, walking,
and hand-eye coordination.
The authors gratefully acknowledge the support of the BrainGain Smart Mix
Programme of the Netherlands Ministry of Economic Affairs and the
Netherlands Ministry of Education, Culture and Science. We thank Jantsje Pasma
and Denise Engelhart for their assistance with the measurements. We also want
to acknowledge the constructive suggestions of the anonymous reviewers.
Engineering Technology, PO Box 217, 7500, AE Enschede, The Netherlands.
2Department of Biomechanical Engineering, Delft University of Technology,
Mekelweg 2, 2628, CD Delft, The Netherlands.
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