Continuous gait cycle index estimation for electrical stimulation assisted foot drop correction
Journal of NeuroEngineering and Rehabilitation
Continuous gait cycle index estimation for electrical stimulation assisted foot drop correction
Christine Azevedo Coste 2
Jovana Jovic 2
Roger Pissard-Gibollet 1
Jrme Froger 0
0 CHU Nimes , Nimes , France
1 INRIA , Montbonnot, 1 , France
2 DEMAR INRIA/LIRMM, UM2, CNRS , Montpellier , France
Background: Walking impairment after stroke can be addressed with the use of drop foot stimulators (DFS). Many studies have demonstrated that DFS improves walking speed, reduces spasticity and reduces the physiologic effort of walking. Current DFS, through activation of the common peroneal nerve, elicit ankle dorsiflexion during swing phase of gait. DFS are generally piloted by force sensing resistor placed in the shoe of the affected side with stimulation triggered ON by heel rise and triggered OFF by heel strike. A tilt sensor can also be used with stimulation triggered by the tilt of the shank of the affected leg. These triggering approaches are the standard for initiating stimulation. However, the real-time modulation of FES intensity to provide more optimized delivery of stimulation and also to regulate dorsiflexion in the presence of disturbances, such as fatigue and spasticity may increase the number of potential users of DFS. Concerning research domain, stimulators that would allow modulating the stimulation pattern in between heel rise and strike events would allow exploring new stimulation strategies. We propose to extract continuous information: the gait cycle index (GCI), from one inertial measurement unit (IMU) measuring shank tilt angle. In order to illustrate the use of this real-time information, we show the feasibility of piloting an electrical stimulator. Methods: 12 subjects with post-stroke hemiplegia participated. A wireless IMU was placed on the unaffected shank and was used to estimate GCI. Subjects performed 3 trials in each of the 3 conditions: C1 no stimulation aid, C2 electrical stimulation assistance triggered by heel switch, C3 electrical stimulation assistance triggered from GCI. Results: 1) the proposed algorithm was able to real-time estimate GCI, 2) events could be extracted from GCI information in order to trig a DFS. Conclusion: The estimation of the continuous GCI in individuals with stroke is possible. Events can be extracted from this information in order to trig a stimulator. These results are a first step towards the possibility to investigate new DFS paradigms based on real-time modulation of stimulation parameters.
Post-stroke; Foot drop; FES; Gait cycle index (GCI)
Walking impairment after stroke is a common and
universal problem [1,2] that is now being addressed successfully
with the use of drop foot stimulators (DFS) . Many
studies have demonstrated that a DFS improves walking
speed, reduces spasticity, makes walking safer and reduces
the physiologic effort of walking for stroke survivors
[4-13]. Current dropped foot stimulators, through
activation of the common peroneal nerve, elicit ankle
dorsiflexion on swing phase of gait. Reflex stimulation of the CPN
can also be used to improve hip and knee excursion where
1DEMAR INRIA/LIRMM, UM2, CNRS, Montpellier, France
Full list of author information is available at the end of the article
there is extensor spasticity necessitating compensatory gait
habits such as hip circumduction. Dropped foot stimulators
are generally piloted by a force sensing resistor heel switch
placed in the shoe of the affected side with stimulation
triggered ON by heel rise of the affected foot and triggered OFF
by heel strike [3,6,14-21]. A tilt sensor can also be used with
stimulation triggered by the tilt of the shank of the affected
leg . These triggering mechanisms, based on event
detection, have proved very reliable and are now the standard for
initiating stimulation during the gait cycle in most common
indoor and out door walking conditions [23-25].
However, real-time control of stimulation intensity is still
not available in existing devices . The modulation of FES
intensity to provide more optimized delivery of stimulation
and also to regulate dorsiflexion in the presence of
disturbances, such as fatigue and spasticity may increase the
number of potential users of the technology .
It would also be of great importance to be able to analyze
the orthotic and clinical outcome of other type of stimulation
strategies other than triggering ON and OFF a fixed pattern
based on gait events. Some research studies have suggested
that improvement in orthotic performance could be achieved
using stimulus intensity shapes matching more closely the
natural tibialis anterior biphasic activation pattern than the
trapezoidal shape classically used in the stimulators [27-31].
In this article we propose to extract continuous tilt angle
information from one inertial sensor fixed on patient
shank. As a first attempt to use this real-time information,
we show the feasibility of triggering an electrical
stimulator based this information. We embedded our gait
observation algorithm within a system involving a commonly
used Odstock stimulator. The goal was to show the
feasibility of processing the gait cycle index (GCI) from one
sensor, and to use it to pilot the stimulator.
In the present study, we: 1) explore the feasibility of
continuous tracking gait cycle in individuals with foot drop
using one sensor placed on the unaffected leg shank and
2) validate the feasibility of combining the observation
algorithm with a DFS controller.
Observation algorithm for gait phases estimation
The algorithm was first introduced and described by Heliot
and Espiau in , where more technical details can be
found. The method allows estimating the phase of the gait
cycle of a healthy person using a micro-sensor, which
associates 3 accelerometers and 3 magnetometers, placed on
persons thigh. The method was designed to allow
humanoid robot to mimic the walk of a human demonstrator .
Ahn et al., based on a similar framework, have proposed a
walking model, which can reproduce some behaviors of
human walking . But this approach is not intended to be
used online for human motion tracking and has not been
Our algorithm is based on defining OFFLINE a model
of a system, which in our case is human gait. In the field
of control of locomotion in humanoid robots, the
bipedal gait has been modeled as a non-linear oscillator
[32,34]. Two common oscillators can be used for this
purpose: the van der Pol oscillator and the Rayleigh
oscillator, which are very similar. The Van der Pol
oscillator was used in , and experimentally proved to be
robust and suitable for human gait modeling. Therefore,
the chosen model in this study is Van der Pol oscillator
which details are given in . Briefly, the Van der Pol
oscillator is a self-oscillating system that has a stable
periodic solution with a period of T0 and a frequency of
0. The equation of Van der Pol oscillator used in this
study is given by (1).
where , and 0 are positive constants. The choice of
, 0, and b constants is explained bellow.
Table 1 Sujects characteristics
Included patients characteristics
Time since stroke (months) Stroke diagnosis FAC
94 Left/isch/ST 5/5
With: Stroke diagnosis: ischemic (isch)/hemorrhagic (hemo)/infra-tentional (IT)/supra-tentorial (ST). FAC: Functional ambulation Categories (Collen et al., ).
BI: Barthel index assessment of daily activity impairment (autonomy evaluations). OS: orthopaedic shoes. - SC: simple cane- CC: Canadian crutch- TC: tripod cane.
In the phase plane (position versus velocity), periodic
stable solution of the oscillator is a trajectory called a
limit cycle (Figure 1). The phase is a coordinate along
this limit cycle:
The phase grows uniformly in the direction of
motion and gains 2 at each rotation. There is a
need to define the variable in such a way that it
rotates uniformly in the cycle of the oscillator. We
therefore define OFFLINE an isochron matrix that
allows us to associate a phase value to any point in the
vicinity of the limit cycle. Each point in the vicinity of
the limit cycle is associated with a point in the limit
cycle (Figure 1). This makes it possible to compute a
phase even in the vicinity of the limit cycle, for
example when the observed behavior differs from that of
Based on control theory framework, it is theoretically
possible to build an observer of this system that will be
able to estimate the internal state of the system, in our
case gait of a person with drop foot modeled as Van
der Pol oscillator, from the system output
measurement. In control theory, a state observer is defined as a
system that provides an estimate of the internal state
of a given real system, from measurements of the input
and output of the real system , and could be
represented using the following set of equations:
where: y is the output of the system, and x1, and x2
are the states of the system which should be estimated.
In our case, y corresponds to a measurement of shank
angle of the unaffected leg. The shank angle was chosen
because it is the easiest to be obtained by the sensor
technology used in this study. Knowing the value of y,
and solving the system of equations (3), we can obtain
state variables x1 and x2. From the observers state
variables we can compute the phase of the oscillator. We
defined the gait cycle index GCI from normalization
in order to get values ranging from 0 and 100% (the
cycle starts and stops at unaffected leg heel strike):
Figure 2 Principle of the observation algorithm. Inertial measurement unit (IMU) is used to estimate unaffected leg shank angle. The
measurement of the shank angle is set as an input to the state observer that estimates the variable . The gait cycle index (GCI) is calculated
from variable and used to trigger the electrical stimulator.
Figure 3 From shank angle observation to GCI estimation. Top: Measured shank angle (online). Middle left: Van der Pol model of the system
(offline). Middle right: Phase portrait of the measured angle evolution (online). Bottom: Estimation of the Gait Cycle Index.
mathematical details about the calculations are given in
. Prior to the experiments the participant was asked to
walk a couple of steps. The measurement of unaffected
shank angle was used to identify oscillator parameters.
We summarize the different steps of the method (see
Figures 2 and 3).
Oscillator design (OFFLINE)
1. The subject is asked to walk a few steps during
which the shank angle is measured.
2. The oscillator parameters , 0, and b are identified
through a dynamic optimization problem: the error
between the measured shank angle and the oscillator
output is minimized. The isochron matrix is computed.
3. The oscillator parameters are updated in the
observer of the system.
Gait Cycle Index estimation (ONLINE) - the observer
computes and GCI variables in real-time based on the
measured shank angle y.
The developed system is based on a wireless architecture of
sensors and actuators using WSN430 technology (https://
www.iot-lab.info/). A WSN430 node is an electronic system
which insures 3 functions: data acquisition using daughter
board sensor-specific, data processing based on a
microcontroller (Texas Instruments MSP430) and wireless
radiofrequency communication (based on Texas Instruments
CC1100). In our architecture, 3 types of WSN430 nodes
are used: one sink node connected to a laptop via a serial
port, one sensor node placed on the participants lower
limbs, and one control node which triggers the stimulator
as shown in Figure 4. This node allows communication
with the network of sensor node and actuator node.
ONLINE GCI computation
One inertial sensor node is placed on the patients
unaffected shank (Figure 4). It integrates one 3-axis
accelerometer (STMicroelectronics LIS3LV02DQ) and one
3-axes magnetometer (Honeywell HMC5843). The sensor
node sends data to the laptop via the sink node. The
sampling frequency was set at 100 Hz. The shank angle is then
computed based on accelerometer and magnetometer
signals as described in . This angle y is used by the
Observation algorithm for gait phases estimation, described
in section 1.2, to estimate the oscillator state variables and
then compute the gait cycle index GCI. The algorithm is
run on the laptop (Linux/Python). The sink node also
serves to send data to the actuator nodes.
A single-channel Odstock Dropped Foot Stimulator was
used. Two skin surface electrodes were placed, over the
common peroneal nerve and at the motor point of the
tibialis anterior. The stimulator parameters (current
Figure 4 System architecture. Description of the system architecture used in the study. A sensor node (inertial measurement unit (IMU)) is placed
on the unaffected side shank. Data is sent to the sink node of the laptop. Data is processed on the laptop and a gait cycle index is estimated.
Depending on the GCI value, the stimulator is switched ON through its trigger node. An extra sensor node also sends data to the sink node and the
data is saved for offline processing.
Figure 5 Illustration of the estimation/triggering algorithm. The shank inclination measured from the inertial sensor allows to estimate the
gait cycle index online and to modify the stimulator switch input depending on the GCI values (here stimulation is ON for GCI values between
0 and 40%).
intensity and pulse width) are triggered offline on the
patient in order to obtain efficient dorsiflexion/eversion
movement without discomfort or pain. The stimulator can
be used in normal mode using a footswitch placed under
the affected side heel in order to switch the stimulation
ON at heel off and OFF at heel strike. To test the
algorithm described in the Observation algorithm for gait
phases estimation, the actuator node was plugged onto
the switch connector of the stimulator in order to trigger
ON/OFF the stimulation depending on the information
received from the sink node (Figure 5).
In the protocol, each subject walked along the GAITRite
walkway. Each subject performed 3 successive trials for
each of the 3 conditions: C1) No stimulation, C2)
Stimulation triggered on the basis of heel switch information, C3)
stimulation triggered on the basis of the GCI information.
C2 and C3 were applied in a randomized order among the
patients (see Table 1).
Condition C2 was used as a control condition for
stimulation. In this preliminary validation work, the goal
was to reproduce the behavior of heel switch triggering
using our experimental observation algorithm. As the
swing phase in normal human walking lasts 40% of the
gait, the stimulation was triggered for 0 GCI 40% for
almost all the subjects in C3 condition. The exceptions
will be discussed here after.
The validation of the GCI estimation algorithm was
done on the C3 condition. To assess variability
between strides, we computed the mean value of the
cross-correlation between the GCI variable waveform
over the strides of each patient. Similarly, we applied
this to shank inclination waveform. To assess the
validity of the GCI information, we computed the
standard deviation of the GCI values corresponding to
heel OFF and heel ON (heel strike) events extracted
from GAITRite software.
A t-test was carried out to compare the average
walking speed in each condition (C1, C2, and C3).
Table 2 shows, for each subject, the number of trials
during which the stimulator was not triggered in
affected leg heel stride moment, as programmed by the
Number of analyzed strides
Figure 6 Example of the repeatability of shank inclination and GCI information for each placed on the unaffected side shank. It is
segmented using GAITRite data. One stride corresponds to the time between two heel offs of the (HOFF) events of the affected leg. Similarly,
the estimated GCI for each stride of one trial is plotted.
proposed GCI estimation algorithm. Table 2 also gives
the number of performed trials for each subject.
In Figure 6 correlation coefficients between each GCI
signal computed for each individual heel stride for each trial
in the C3 condition are shown. The average correlation
coefficient was 0.74 0.13. We also analyzed, for each trial,
the correlation coefficient between each unaffected leg
shank inclination signal estimated for each individual stride
in the C3 condition. The results are shown in Figure 6. The
average correlation coefficient obtained was 0.76 0.17
The GAITRite walkway was used as a gold standard to
verify heel on and heel off moments of affected leg for
each trial of each subject. The GCI values computed in
the C3 condition, corresponding to Heel OFF and Heel
Table 3 Variability of the GCI information
*Extracted from GAITRite.
ON were compared with events extracted from
GAITRite data for the affected leg. The comparison between
heel ON and heel OFF instants estimated using
GAITRite system and proposed Observation algorithm for
gait phases estimation is shown in Table 3 and an
example is given in Figure 7.
In Figure 8, we show the influence of the different
conditions on the walking speed. On average, the walking speed
was 12.8% higher in C3 (GCI estimation algorithm based
stimulation) than in C1 (no stimulation), this difference
was statistically significant (t-test, p < 0.05). No statistically
significant statistical difference between the walking speeds
in condition C2 (footswitch based stimulation) compared
with walking speeds in condition C3 was observed.
Ability of the observation algorithm to compute the gait
cycle index GCI
In this study we used the observation of the unaffected
leg shank angle to detect the heel strike moment
instead of commonly used heel-floor contact. Strong
positive correlation between unaffected leg shank
inclinations demonstrates that the shank angle is a
variable, which has similar repeatable shape during the
gait of a person with drop foot, and could be
potentially used to trigger the electrical stimulator.
In order to validate the relevance of the GCI
information, we compared the GCI values computed in the C3
condition, corresponding to Heel OFF and Heel ON
events extracted from GAITRite data for the affected leg
(Figure 7). The aim was to determine the extent to
which the GCI variable varies from one stride to the
next (Table 3) and if a given GCI value could reliably
represent a fixed gait event. Even though the oscillator
Figure 7 Comparison of the GCI estimated and the GAITRite information. We compare the values of the GCI corresponding to given events
of the gait cycle affected leg heel off and heel strike obtained from GAITRite. In light red, the intervals for which the GCI ranged from 0 to 40%.
parameters should ideally be identified on a reference
trajectory from a gait event after the patient is
stimulated and not on the C1 condition, as was done, the
results show that the GCI variable was stable over the
strides. The GCI information is more reliable when the
standard deviation (Std) is low. The mean Std for all
patients was 6.3% of the GCI for Heel OFF, which roughly
corresponds (assuming that the GCI evolution is linear)
to 0.13 s and 15% of GCI for Heel ON, which
corresponds (assuming that the GCI evolution is linear) to
0.3 s. The maximum standard deviation was 22%
(patient 11), which corresponds (assuming that the GCI
evolution is linear) to 0.44 sec (half a step). From a
mathematical point of view, the performances are good
(<15%). From a functional point of view the
corresponding error in seconds compared with the duration
of gait cycle of a person with drop foot would need to
be improved in order to allow for a fine triggering of the
stimulation. These averaged performances will have to
be improved in some patients in order to allow
triggering a stimulator at any instant of the gait cycle. This
should be possible by identifying the reference model
parameters after an adaptation period of the patient to
Figure 8 Comparison of walking speed in the 3 conditions. We compare the values of the walking speed in C1 (no stimulation), C2
(footswitch based stimulation) and C3 (GCI estimation algorithm based stimulation).
From the Table 3, we can observe low heel strike
coefficient of variations for subject 7 and subject 8. Those
subjects walk was more impaired compared to other subjects.
This makes general comments difficult on the
performance of GCI over all the subjects who have participated in
Among all 12 subjects, 282 strides were analyzed for the
trials in the C3 condition. In only 4% of the cases, the
stimulation was not triggered in affected leg heel strike
moment, as expected. That was due to problems with the
wireless communication such as loss of wireless signal
(Table 2). For patient 5 it was impossible to test the C2
condition. Indeed, we could not use a footswitch under
the affected side heel neither the unaffected side toes.
Indeed, the gait of this patient was too impaired and the foot
strikes too lateral to make a direct link between the
footswitch state and the stimulator ON/OFF status. However, it
was possible to test the C3 condition for this same patient.
In this case, stimulation was ON for GCI2 ranging from
30% to 70%. Patients 1 to 4 and 7 to 12 were stimulated
for GCI values ranging from 0% to 40%. Indeed, for these
patients the swing phase duration was similar to normal
gait. Patient 6 was stimulated for GCI values ranging from
0% to 50%.
The proposed approach allows selecting instants in
between heel OFF and heel ON in order to
appropriately trigger stimulation ON or OFF. This opens the
possibility of exploring new strategies for stimulation
like starting stimulation before heel OFF or applying
biphasic stimulation in between heel OFF and heel ON.
Compared to other approaches the optimization of
oscillator parameters to define the reference model for
each patient takes several minutes but can be an
automatized procedure, which would be done once by the
clinician. The use of this system by a patient is not more
constraining than existing ones.
This article experimentally validated, on post stroke
hemiplegic individuals, a new observation algorithm for gait
phase estimation. Gait cycle index is estimated online
from a single wireless sensor placed on the lower limbs.
GCI corresponds to a percentage of individual gait cycle
completion. Despite the heterogeneity in patient
characteristics, in of 95.7% the trials the algorithm was able to
compute GCI and trigger the electrical stimulator in
affected leg heel strike moment.
The main limitation of the study is an imprecise
detection of heel ON and OFF events when compared with
the detection of the same events using GaitRite system.
The algorithm performances will have to be improved in
order to decrease the standard deviation of events
extracted from GCI. This should be possible by
identifying the reference model parameters after some
adaptation period of the patient to stimulation.
The GCI is associated with the rhythmic nature of the
gait and allows us to track the gait cycle independently
of the motion amplitude or temporal aspects. The GCI
is related to the limit cycle of the oscillator used to
model the gait, associated with isochrone curves.
Intrinsically, due to the mathematical framework used, our
method is robust to gait changes, which is not the case
when using fixed events.
In this study, we showed the feasibility of triggering an
electrical stimulator based on the events extracted from
the GCI. We embedded the Observation algorithm for
gait phases estimation within a system involving a
commonly used Odstock stimulator. The goal was to show
the feasibility of processing the gait cycle index from one
sensor, and to use it to pilot the stimulator. In order to,
potentially, improve the FES assisted clinical performances
and incorporate the advantages of our approach, we plan
to use a programmable stimulator. Indeed, by online
tracking of the continuous evolution of the gait cycle
index, it could be possible to predict gait events and adapt
the stimulation parameters and stimulation time.
By using a programmable stimulator we could explore
the clinical interest of stimulating at different instants of
the gait cycle, which is not possible with other existing
methods. The method proposed here could also be used in
case of walking on uneven ground terrain, such as stairs.
The proposed method could also be used in the case of
strong foot inversion and eversion when heel-floor contact
cannot be detected using the footswitch technology.
The main contribution of this study in the field of
biomedical engineering is the potential to explore new
stimulation strategies that may have clinical validity. In the future
we plan to study the influence of the timing of stimulation
onset and adaptive biphasic stimulation and its effect on
orthotic performances/outcomes (walking speed,
propulsion force, etc.). We will also develop new controllers with
auto-adaptive properties in order to automatically modulate
stimulation parameters in order to assess walking in more
challenging conditions (stairs, slope).
CAC is the principle author and responsible for the study design,
experiments and data analysis. JJ was responsible for the different softwares
execution during the experiments. RPG developed the experimental setup.
JF was the medical doctor in charge of designing the protocol accepted by
the ethical committee, subject evaluation and inclusion. All the authors read
and approved the final manuscript.
This work was supported by INRIA (SENSAS ADT, MASEA Colors).
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