Control of thumb force using surface functional electrical stimulation and muscle load sharing
Journal of NeuroEngineering and Rehabilitation
Control of thumb force using surface functional electrical stimulation and muscle load sharing
Ard J Westerveld 1
Alfred C Schouten 0 1
Peter H Veltink 1
Herman van der Kooij 0 1
0 Department of Biomechanical Engineering, Delft University of Technology , 2628 CD Delft , The Netherlands
1 Laboratory of Biomechanical Engineering, MIRA Institute for Biomedical Technology and Technical Medicine, University of Twente , 7500 AE Enschede , The Netherlands
Background: Stroke survivors often have difficulties in manipulating objects with their affected hand. Thumb control plays an important role in object manipulation. Surface functional electrical stimulation (FES) can assist movement. We aim to control the 2D thumb force by predicting the sum of individual muscle forces, described by a sigmoidal muscle recruitment curve and a single force direction. Methods: Five able bodied subjects and five stroke subjects were strapped in a custom built setup. The forces perpendicular to the thumb in response to FES applied to three thumb muscles were measured. We evaluated the feasibility of using recruitment curve based force vector maps in predicting output forces. In addition, we developed a closed loop force controller. Load sharing between the three muscles was used to solve the redundancy problem having three actuators to control forces in two dimensions. The thumb force was controlled towards target forces of 0.5 N and 1.0 N in multiple directions within the individual's thumb work space. Hereby, the possibilities to use these force vector maps and the load sharing approach in feed forward and feedback force control were explored. Results: The force vector prediction of the obtained model had small RMS errors with respect to the actual measured force vectors (0.22 0.17 N for the healthy subjects; 0.17 0.13 N for the stroke subjects). The stroke subjects showed a limited work range due to limited force production of the individual muscles. Performance of feed forward control without feedback, was better in healthy subjects than in stroke subjects. However, when feedback control was added performances were similar between the two groups. Feedback force control lead, especially for the stroke subjects, to a reduction in stationary errors, which improved performance. Conclusions: Thumb muscle responses to FES can be described by a single force direction and a sigmoidal recruitment curve. Force in desired direction can be generated through load sharing among redundant muscles. The force vector maps are subject specific and also suitable in feedforward and feedback control taking the individual's available workspace into account. With feedback, more accurate control of muscle force can be achieved.
FES; Load sharing; Muscle recruitment; Stroke; Rehabilitation; Force control; Thumb
Stroke has become a major cause of morbidity and
mortality in the western world. Incidence of stroke also increases
in less developed countries as a result of changing
lifestyles . Graying of society and improved health-care
are likely to result in an increase of stroke survivors.
Functional independence of stroke survivors is highly
influenced by their ability to perform a successful grasp. In
many activities of daily living, like drinking or opening a
door, grasp and release is an essential part of the required
Functional electrical stimulation (FES) of hand
muscles can be helpful to train grasp and release in stroke
subjects [2-4]. Depending on the ability of the
individual patient, the assistance may be (selectively) increased
or decreased in order to maximize the voluntary activity
which is important in relearning movements [5,6].
Grasping comprises coordinated finger and thumb
motion and controlled force exertion on the object to
be held. As muscles initiate human movement, accurate
control of muscle force is a prerequisite for movement
control. For grasping tasks the fingers can be regarded
as single degree of freedom (DoF) joints, since
movement of the individual phalanges is coupled because of the
under actuation of the finger. Furthermore, rotation along
the flexion-extension axis of the finger is by far the most
important movement for grasping and releasing objects.
The thumb, however, requires a different approach as it
moves along multiple axes. Controlling force and
movement of the thumb will be most challenging and may
serve as a model, which may be generalized/reduced to the
single DoF case for the other fingers.
A healthy thumb is actuated in several directions by nine
muscles in total [7,8]. However, not all nine muscles can
be targeted properly with surface FES. Mainly, because
of overlying muscles and nearby sensory nerves making
stimulation uncomfortable. Therefore, only a small
subset of thumb muscles is available for FES with surface
electrodes. This limits the movements which can be
controlled with FES. However, thumb movements relevant
for grasping (mainly opposition) are feasible with surface
Force distribution over multiple muscles is commonly
applied in biomechanical modelling, solving actuator
redundancy problems for a given task [9,10]. This load
sharing approach might also be useful for activating a
redundant muskuloskeletal system. In addition, by
sharing the load over all available muscles we maximize the
available range of force. However, to our knowledge, load
sharing has not been applied to external activation of
muscles with surface electrical stimulation. We will
evaluate this possibility and expect this approach to result in
accurate force control with a force distribution over the
individual muscles optimized by minimizing the sum of
squared recruitment over all muscles.
Recently, Lujan et al.  measured thumb forces
evoked by three thumb muscles in healthy subjects and
one spinal cord injured patient. Using the measured forces
they trained an artificial neural network (ANN) for feed
forward force control. They showed good control of the
isometric thumb force in 2D. With the current study we
aim at a more transparent approach: using linear
combinations of estimated muscle force vectors instead of
using a black-box ANN. This approach gives us the benefit
of learning more of the underlying physiological system,
by comparing combined muscle responses with
individual muscle responses. In addition, it might allow for a
more generally applicable approach, without the need of
training an ANN.
The goal of the current study is twofold: 1) Is it possible
to describe thumb muscle responses to FES by a sigmoidal
muscle recruitment curve and a single direction of force?
And if so, are these so called muscle force maps subject
specific, suitable for stroke subjects and time-invariant?
And 2) Are muscle force maps suitable for use in 2D
thumb force control with FES applying load sharing? And
if so, is feed forward control only sufficient and is the
approach also suitable for stroke subjects?
We will introduce the proposed generalized muscle force
model for thumb force control and muscle load sharing
first. Thereafter we will describe the experimental
evaluation of this model in both healthy subjects and stroke
Generalized muscle force model
We aimed at predicting muscle force resulting from FES
by a relatively simple model. At a specific thumb posture
we assumed that the force direction of each muscle, i,
is constant and that a nonlinear sigmoidal relation exists
between the stimulation amplitude and the generated
In Eq. 1, |Fi(Ai)| is the force magnitude of muscle i at
stimulus amplitude Ai; pi1 is related to the force
saturation level, i.e. the maximal output force of that muscle, pi2
is related to the inflection point of the sigmoidal
recruitment curve and pi3 is related to the horizontal scaling of
the recruitment curve, i.e. the amplitude range. The latter
term in Eq. 1 is an offset term, ensuring zero force if the
amplitude is zero. The muscle force directions, together
with the maximal force amplitudes for each muscle
represents the force vector map for a system of multiple
muscles, see Figure 1 for an example.
Feedforward thumb force model
We assumed a linear vector summation of the muscle
forces acting around the same joint.
In Eq. 2, the predicted thumb force vector F, is the
vector sum of the individual muscle forces (n = 3), modelled
as a recruitment fraction, xi, of the maximal muscle force
The model of Eq. 2 was used to obtain the muscle
stimulation levels given a desired thumb force. This inverse
problem is redundant: three muscles can be stimulated to
obtain a thumb force in two directions. In our (real-time)
controller implementation, we addressed this redundancy
problem by minimizing the squared muscle recruitment.
The combination of obtained stimulation amplitudes,
Ai, is the combination which theoretically would produce
a force equal to the reference force, Fr, or at least the force
which is minimizing Eq. 3 when the system has reached
its boundaries of operation. The constant C represents the
offset term as introduced in Eq. 1.
Five able bodied subjects (age 32 13 years, 3 men)
and five stroke subjects (age 55 18, 4 men) were
included for this study. Table 1 summarizes the
characteristics for the individual stroke subjects. The study
was in accordance with the declaration of Helsinki
and was approved by the local medical ethics
committee. All subjects gave written informed consent.
During the experiments, the subjects were asked to
relax their muscles, in order to avoid voluntary muscle
Table 1 Characteristics of included stroke subjects
The maximal obtainable Action Research Arm test (ARAT) score is 57 points
Stimulation amplitude [mA]
Figure 1 Force vector map. An example of the force vector map (direction (left) and magnitude (right)). The colored lines in the left pane show the
measurement x- and y-forces for the abductor pollicis longus (AbPL), opponens pollicis (OpP) and the flexor pollicis brevis (FPB) muscles. The
determined muscle force directions are indicated by the grey lines. The small variations indicate that the angles are relatively constant throughout
the operating range. The force vector map in the left pane is shown on top of an overview of a custom built setup for restraining wrist movements
and measurement of thumb forces with two pre loaded single axis force sensors. The fitted sigmoidal recruitment curves for the three thumb
muscles and the individual measurement points (steady state of step responses at different amplitudes) are shown on the right.
Minimal summed force is a typical criterion also used in
musculoskeletal modelling and load sharing studies [9,10].
The recruitment was modeled as a fraction of the maximal
force, thus we obtained a bounded problem which can be
formulated as minimizing the vector norm shown:
Fmaxx Fr 2
In which Fr is the [2x1] column vector equal to the
reference force and Fmax is the [2x3] matrix containing the
maximal x and y forces of each of the three muscles. x is
the [3x1] column vector with individual muscle
recruitment fractions. To take the bounds on x into account we
reformulated the vector norm shown in 3 as the equation
shown in Eq. 4.
Since the latter term is independent of x, the
optimal recruitment, x, minimizing Eq. 4 can be written as
a quadratic problem of the form as shown in Eq. 5, with
Q = FmTaxFmax and c = FmTaxFr.
Finally the calculated reference forces for each
muscle, xi|Fmax,i|, are converted to stimulation amplitudes by
using the inverse of the sigmoidal recruitment (Eq. 1)
curve shown in Eq. 6.
xi|Fmax,i| + C
Ai = p3i ln
Either the dominant arm (healthy subjects) or the affected
arm (stroke subjects) was strapped in a custom built
device. This setup was used to fixate the wrist and the
hand in neutral pronosupination, and to measure the
isometric thumb force in two directions perpendicular to
the axis of the thumb. Forces were measured by two 45.3
N load cells (Futek, Irvine) preloaded with springs. See
A special built 3 channel asynchronous biphasic
electrical stimulator (TIC Medizin, Dorsten, Germany) was
used to apply the electrical stimulation pattern.
Stimulation was applied at a constant frequency (30 Hz) and
pulse width (150 s). The amplitude could be controlled
via custom built controllers within the stimulators range
[ 0 30mA] in steps of 0.125mA. A single 50 50 mm
anode was used together with 16 19 mm cathodes for
each channel. Electrodes with similar size showed good
results on both selectivity and comfort in a simulation
An EtherCAT I/O system (Beckhoff Automation
GmbH, Verl, Germany) using Matlab/xPC (The
Mathworks, Nattick, USA) as EtherCAT master device was
used to control the stimulator parameters and to capture
analog data from the force sensors.
Preparation The Abductor pollicis longus (AbPL),
Opponens pollicis (OpP) and Flexor pollicis brevis (FPB)
muscles were selected for stimulation. We expected to
move the thumb sufficiently in directions needed for
grasp and release with these muscles. OpP opposes the
thumb (pre-grasp), FPB moves the thumb inward (grasp)
and AbPL moves the thumb up (release). Electrical
stimulation was applied (30 Hz; 150 s) when electrodes were
placed initially. The amplitude was increased to evaluate
responses and subject comfort. Electrodes were located
at the motor points based on exploration of the responses
to electrical stimulation. See Figure 2 for an example of
Force vector map determination The subject specific
force map (see Figure 1 for an example) was determined
in the isometric setup, with the thumb visually positioned
at 30 degrees of abduction and 30 degrees of
extension. The threshold and maximal stimulation amplitude
for each muscle were determined first: we stimulated
(30 Hz; 150 s) each muscle individually for 1 second,
followed by 0.5 second without stimulation. Every 1.5
second the amplitude was increased by 1mA. When either
a saturation in the force response was observed or the
subject reported unpleasant discomfort, the stimulation
Figure 2 Electrode placement. Example of placement of electrode
on (top) AbPL and placement of anode at the dorsum of the wrist and
(bottom) above FPB muscle and OpP muscle. The AbPL electrodes
was placed just medial of the radial bone, approximately 5 cm
proximal to the wrist joint, the OpP electrode was placed laterally on
the thenar, about 1/3 of the length of the first metacarpal bone,
measured from the proximal side. The FPB electrode was placed at
about half the length of the first metacarpal bone on the medial side
of the thenar. Exact electrode locations were determined
experimentally based on observed responses and subject comfort.
The range between the threshold minus 1mA and the
maximal amplitude was divided in ten equidistant
stimulation levels for each muscle. We applied these 30
stimulations (10 amplitudes per muscle) randomly and measured
the exerted thumb forces.
From this initialization measurement, we determined
the force direction of each individual muscle and the
recruitment curve relating muscle stimulation to exerted
force. The recruitment curves were described with a
sigmoidal function having three parameters, using Eq. 1.
Parameter values were obtained with a least-squares
fit, using the Levenberg-Marquardt algorithm . See
Figure 1 for an example of muscle recruitment curves and
force directions. This force vector map indicates the
ability to control the thumb force in different directions for a
Individual muscle controllers After determination of
the force vector maps, the feedback controller gains were
determined. Initial gains were obtained from an open loop
Ziegler-Nichols step response procedure . The step
response reference pattern had the following sequence:
[0.5 0.8 0.5 0.2 0.5] |Fmax|. The reference was held constant
for three seconds at each specific level. Thus,
excluding the steps at begin and end, this resulted in four step
responses in total (two positive and two negative steps
of step size 0.3|Fmax|). The signs of the negative step
responses were inverted and then the average of all four
step responses was used to determine the open loop
In Eq. 7 the open loop gain, Ko, is calculated from the
normalized input magnitude, X0, the measured steady
state output magnitude, Mu, the time until the output
responds, dead and the time between the first response
and the output reaching the steady state, . As suggested
in , the proportional gain, Kc, for each muscle was
calculated as 90% of the open loop gain and the
integration time for the PI-controller, Ti, was set as 3.3 times
For every muscle and subject the inverse of the
recruitment curve compensates the non-linear and subject and
muscle specific recruitment. In this way the non-linear
elements and maximal force levels are compensated
within the control loop leading to a linear feedback
controller between observed force error and reference force.
Furthermore it is expected that range of control gains
between the different muscles and different subjects is
relatively small, since the muscle and subject specific
recruitment curve transforms the outputs of the PI controllers
(forces) into the required stimulation amplitudes.
After determining the initial gains for each muscle, in
total four single muscle tests were done for each muscle
to be able to analyze performances of the individual
muscle controllers: 1) step response reference pattern with
feedback control, 2) 0.5 Hz sinusoidal reference pattern
with feedback controller, 3) step response reference
pattern with a combination of feedforward and feedback
control, and 4) 0.5 Hz sinusoidal reference pattern with a
combination of feedforward and feedback control.
When oscillatory behaviour was observed during the
first test, the proportional gain was lowered systematically
and the test was repeated until good tracking of the
reference was observed without severe oscillations. In some
cases the integration time Ti was increased slightly for
further fine tuning.
2D thumb force targets For evaluation of the 2D
controllers, 5 second constant reference force targets were
used. The targets were set at 0.5 N and 1.0 N in different
directions within the workspace of the subject. Initially,
directions were chosen at 90, 60, 30, 0, 30 and 60.
Angles outside the theoretical workspace of the subject
were not measured. When less than four target directions
were theoretically feasible, intermediate angles (15 step
size) were also evaluated.
Feedforward thumb force control The applicability of
the thumb force model was evaluated first in an
experiment based on feed forward control of the three muscles.
In this experiment control was based on the measured
muscle parameters and the thumb model described in
Eq. 2. Based on the previously determined force map,
target angles greater than the angle of the long abductor
muscle or smaller. The experiment was repeated three
times to explore the reproducibility of the methods. The
target sequence was the same in each repetition. The
sharing of the load was calculated by implementing Eq. 5 in
a real-time quadratic programming (QP) problem solver
using the online active set strategy .
Feedforward and Feedback thumb force control
Control performance might be improved by adding error
feedback. This was evaluated in a second set of control
trials in which the feed forward control was extended with
feedback error compensation. Force targets were the same
as in the feed forward control experiments. The error
vector between the reference force vector and the actual
force vector was used as reference input for a second QP
optimizer, which distributed the force error over the
individual muscles. Note that due to feed forward muscle
activation, forces can also be feedback controlled in the
negative direction of the individual muscle axis. The
calculated individual muscle force errors were fed back with
the individual muscle controllers. A schematic overview
of feedforward and feedback control paths is shown in
RMS errors were calculated from the magnitude of the
error vector between measured muscle force during the
initialisation procedure and muscle force estimate based
on the obtained parameters. In addition, the area of the
theoretical work range resulting from the muscle force
vectors obtained during the first initialization procedure
was calculated and compared between subjects.
An important factor for the controllability is the rate of
force change relative to the change of stimulation
amplitude for a given muscle. This factor can be expressed by
the maximal slope of the recruitment curve, calculated
from the derivative of Eq. 1, for a give muscle, i:
At the end of the session, we repeated the initialization
procedure to check for possible changes in recruitment
properties. In each repetition the sequence of applied
amplitudes and selected muscles was kept the same. Time
Figure 3 Controller scheme. Block diagram of feedforward and feedback thumb force controller. Stimulation for three individual muscles is
calculated based on a reference force. Force distribution over the muscles is calculated by solving a QP problem as shown in 5 indicated by the QP
blocks. These QP solvers take the previously determined force map and also boundaries on the recruitment into account. For clarity this is left out in
the schematic. The bounds for the feedforward QP problem are [0,1]. The bounds for the feedback QP problem depend on the current activation of
the muscle (from both feedforward and feedback path) and indicate the remainder of the operating range ([0,1]) and can thus also be negative
when the specific muscle is already active. In the feedback path a PI controller was used for each individual muscle force. When using a combination
of feedforward and feedback control, the feedforward path was reduced by a factor K = 0.8 to prevent overshoot and let the feedback path
compensate for the remainder. When evaluating the feedforward control performance without feedback, K was set to 1.
between subsequent initialization procedures was
approximately 45 minutes. We estimated the correlation
coefficients (Spearmans ) between the measured forces and
the forces predicted by the initially obtained model for
each subjects. This gives an indication of both the
prediction ability of the model and the repeatability of the
method. To estimate effects of muscle fatigue we
compared the force magnitudes in both initialization
procedures and calculated the least squares slope, m, for each
In which Fpre and Fpost, are the observed forces during
the procedures at the beginning and the end of the
session, respectively. The forces are summed over all applied
input amplitudes during the initialization procedure. The
slope, m, is an estimate of the ratio between initial force
generation and final force generation for a given muscle.
Single muscle control performances were evaluated
based on the sine tracking tasks. RMS errors between
the actual and reference forces were calculated. The 2D
controller performances were evaluated based on the
stationary error of the responses. This stationary error was
defined as the average magnitude of the force error vector
during the last 10 percent of the in total 5 seconds lasting
Due to the relatively small sample size, non-parametric
statistics was applied. We used Mann Whitney U tests
to statistically evaluate improvement with feedback
control over feedforward control only and also to evaluate
performance in stroke subjects with respect to healthy
Force vector maps
Results of the initialization procedures for all subjects and
all repetitions are summarized in Figure 4. Figure 5 shows
the distribution of theoretical workspace area based on
the determined muscle force maps for healthy subjects
and stroke subjects. The workspace area was larger in
healthy subjects, compared to stroke subjects: p=0.06
and p=0.02 for first and second initialization procedure
respectively. RMS errors for the predicted force vectors
were 0.10 0.02 N , 0.17 0.09 N and 0.19 0.11 N on
Figure 4 Force vector map determination. Force map data in subsequent force map measurements (Start and End of experiment) for all
(H)ealthy subjects and all (S)troke subjects. Grey arrows indicate maximal force for each muscle, obtained from the initialization procedure and the
average movement direction. Axes were omitted for clarity, however the axes scaling was the same in all sub figures.
Figure 5 Workspace areas. Boxplots of theoretical workspace area
for healthy subjects and stroke subjects. Workspaces calculated based
on determined maximal muscle forces and muscle directions during
the first initialization (Start) and the second initialization procedure
average for the healthy subjects for AbPL, OpP and FPB,
respectively. For the stroke subjects, the RMS errors were
0.66 0.12 N and 0.79 0.26 N for OpP and FPB,
respectively. The AbPL muscle was only activated in S4 and S5,
RMS errors were 0.14 N and 0.26 N for these subjects
respectively. Maximal slopes of the recruitment curves in
healthy subjects were 0.18 0.06 N /A, 0.17 0.06 N /A
and 0.70 0.52 N /A for AbPL, OpP and FPB
respectively. For the stroke subjects the maximal slopes were
0.09 0.06 N /A and 0.69 0.43 N /A for OpP and FPB
respectively. The maximal slopes for the AbPL in subjects
S4 and S5 were 0.07 N /A and 0.06 N /A respectively.
Correlations coefficients between predicted and
measured forces are shown in Table 2 for both
initialization procedures. The estimated force generation ratios
between first and second initialization procedure in
healthy subjects were 0.87 0.25, 0.93 0.10 and 0.97
0.06 for AbPL, OpP and FPB respectively. For the stroke
subjects the ratios were estimated at 0.14 0.09 and
0.31 0.14 for OpP and FPB, respectively. For the AbPL
Table 2 Force prediction
muscle, the ratios were 0.35 and 0.29 for subjects S4 and
Force controller evaluation
Single muscle controllers
The averaged proportional gain over all healthy subjects
was 0.22 0.28. For the stroke subjects the average
proportional gain was 1.04 1.16, note that these values are
dimensionless as the feedback controller has a force both
as input and as output, since the inverse recruitment is
placed after the controller. The average integral times were
0.56 0.12s and 0.62 0.45s for healthy subjects and
stroke subjects respectively.
During the single muscle control experiments, some
saturation effects (stimulation reaching predetermined
maximal amplitude) were observed, leading to a
nonlinear feedback system. Disregarding the cases were this
saturation occurred, the estimated controller gains were
0.17 0.12 and 0.57 0.12s on average for all subjects for
proportional gain and integral time respectively.
Results of the sine tracking experiments for the
individual muscle feedback controllers are shown in Figure 6.
Results for healthy subjects and stroke subjects are shown
separately. RMS tracking errors for the healthy subjects
were 0.30 0.07 N, 0.29 0.06 N and 0.50 0.25 N
for AbPL, OpP and FPB respectively. For the stroke
subjects, RMS errors were similar: 0.31 0.03 N, 0.37 0.10
N and 0.52 0.22 N for AbPL, OpP and FPB
respectively. For subjects S1, S2 and S3 the AbPL muscle could
not be targeted properly, therefore the AbPL tracking
measurements were skipped for these subjects.
Combined muscle controllers
2D step responses for the best (H5) and worst (H1) healthy
subject and best (S4) and worst (S2) stroke subject are
shown in Figure 7. Time series of stepresponses to a
single 0.5 N target and a single 1.0 N target for H5 and
S4 are shown in Figure 8. Responses over all subject are
summarized in bar plots of stationary errors, shown in
Figure 9. The stationary errors were averaged over all
targets within a group. Results were grouped by control
Correlations between predicted forces and measured forces during initialization procedures at start (initial) and end (final) of session.
Figure 6 Individual muscle control. Sine (0.5 Hz) tracking results averaged over all healthy subjects (left) and over all stroke subjects (right). Results
shown for the three selected muscles: Abductor Pollicis Longus (AbPL), Opponens Pollicis (OpP) and Flexor Pollicis Brevis (FPB) and for feedback
control only. The mean over all subjects is shown by the solid line, shaded areas indicate the standard deviation. For AbPL only data for S4 and S5 is
shown in (b), as in the other stroke subjects this muscle could not be activated.
type, target magnitude and subject type. With feedback
enabled, reduction in stationary errors was observed for
the stroke subjects for the 0.5 N targets (p<0.1).
Feedforward performance was less in stroke subjects,
compared to the healthy subjects (p=0.05 and p<0.01 for
the 0.5 N and 1.0 N targets respectively). The
stationary errors were larger for the 0.5 N targets compared
to the 1.0 N targets when normalized to the target
forces (p<0.01) with feedforward control in healthy
subjects. No significant differences in stationary errors were
observed between the two target levels for the stroke
We showed the possibility to describe responses to
electrical stimulation of individual thumb muscles as a force
vector map with a single activation direction and a sigmoidal
recruitment curve. As expected the variability between
subjects is relatively large (Figure 4) due to anatomical
differences. As a result, force maps always need to be
determined for each individual subject. Within subject
the results are repeatable, demonstrating the feasibility of
our approach (Figure 4 and Table 2). Note that for
subsequent sessions it is required to redo the initialization,
since the response is highly dependent on exact electrode
position . However, in stroke subjects the AbPL
muscle was difficult to target. In the subjects in which we were
able to target the muscle initially, the responses during the
second initialization procedure differed greatly from the
initial procedure as indicated by the low correlation
coefficients in Table 2 and in Figure 4. Therefore the AbPL
muscle seems less reliable for use in 2D force control tasks
compared to the other muscles.
The load sharing approach resulted in the muscle being
pulled nicely towards the target force by the feedback
controller. Since the error vector was used as input
for the feedback load sharing, the appropriate ratio of
muscle activations was calculated to generate force in
the right direction. To our knowledge this load sharing
approach is a novel application in electrically
stimulated muscle. In our opinion this could be an
appropriate solution to solve redundancy problems in activation
of multi-dimensional muskuloskeletal systems with FES
and simultaneously take the boundaries of the
individual force sources into account. The variation of
controller gains over different muscles and different subjects
was low, which gives the possibility to use fixed
values for these parameters when applying the methodology
presented here. Either as a true fixed value of as a
starting point for further fine tuning instead of the
ZieglerNichols methods  which were currently used. Thereby
further reducing the tunable parameters and setup
Performance of the 2D feedforward force controller was
worse for the stroke subjects compared to the healthy
subjects. For the stroke subjects, adding feedback terms
reduced stationary errors. For the healthy subjects the
differences between feedforward control only and combined
with feedback control were small, see Figure 9. However,
depending on the model accuracy of the individual
muscles input-output relation, the feedback controller also
reduced the control performance in certain cases. An
example of this can be observed from Figure 7 where the
feedback controller negatively influences the force
direction for the 0.5 N targets. This is likely a result of a
mismatch in the FPB model, causing the thumb being
Figure 7 2D force control. Example of responses to the target set points for the best (H5; top-left) and the worst (H1; bottom-left) healthy subject
and for the best (S4; top-right) and worst (S2; bottom-right) stroke subject. Top panes of each figure show results of solely feedforward control;
bottom panes show results for feedforward and feedback control. 0.5 N targets (left) and 1.0 N targets (right) are shown separately for readability.
The colored dotted lines show the measured force response to a target set point shown by the same colored circle in the plane perpendicular to
the thumb. For every 100ms in the response a dot was plotted to give an indication of the speed of the force response.
Best healthy subject
Best stroke subject
0.5 N FFonly
0.5 N FF+FB
1.0 N FFonly
1.0 N FF+FB
Figure 8 Step responses of 2D force control. Time series of responses to a step in target set point for healthy subject H5 (left) and stroke subject
S4 (right). Top panes of each figure show forces in X direction; bottom panes show forces in Y direction.
Figure 9 Stationary errors in 2D force control. Box plots of stationary errors in 2D force control trials. 0.5 N and 1.0 N targets are shown separately
for feedforward control only and the combination feedforward and feedback control and for healthy subjects and stroke subjects. Numbers above
the individual box plots indicate the total number of evaluated targets in that group, which was influenced by the workspace area of the individual
subjects. Significant differences between groups were calculated by the non-parametric Mann-Whitney U test and indicated by asterisks.
pulled in a more negative direction than needed.
Therefore we recommend estimating model accuracy before
starting the control trials, and redo the initialization if
We measured forces in two directions in a plane
perpendicular to the thumb. Therefore we neglected the forces
perpendicular to this plane. Due to this fact we might have
made some errors in absolute force recordings. However,
since we are using the same setup in both model
identification and control, we expect that the influence of these
non-measured forces on our performance observations
Forces in unmeasured direction could have led to the
relatively low observed forces compared to other studies
. However, we expect that these unmeasured forces
were small. The stimulated muscles are responsible for
thumb movement Therefore the force component in line
width the thumb will be small compared to the
perpendicular force components. A more likely cause is the fact
that we aimed at selective activation with small electrodes
leading to relatively low current densities and low
muscle activation. Even though the observed forces and the
evaluated targets of 0.5 N and 1.0 N are relatively low,
they are sufficient for positioning the thumb for functional
grasping of objects compared to the evaluated force levels
during grasping in [16,17]. Recently, we have shown
applicability of a similar approach during grasp and release of
In all subjects, the FPB muscle showed a steep
recruitment curve: when the stimulation came above threshold
force increase was high for an increase in stimulation
amplitude. This will have resulted in a bigger influence
of FPB modelling errors on the output force errors. The
steeper recruitment compared to other muscles is likely
a result from differences in neural innervation. The FPB
muscle is innervated from the recurrent branch of the
median nerve which is very superficial before entering the
FPB muscle. The OpP muscle is innervated by the same
nerve branch, but laterally the branch runs less
superficial . The AbPL muscle is innervated by the posterior
interosseus nerve which is also less superficial.
We reduced the experiment length by only testing
specific points along the recruitment curve during the
initialization phase. We did not specifically optimize this
method of recruitment curve sampling. However, the
results in pilot measurements where we compared our
current approach with more dense sampling of the muscle
recruitment resulted in only minor differences between
the obtained recruitment curves. Recently, Schearer and
colleagues  compared different methods of
recruitment curve sampling extensively. Application of methods
described there might further improve the accuracy of the
obtained recruitment curves of individual muscles, which
then could also improve the accuracy of the controllers.
The stroke subjects showed smaller workspaces
compared to the healthy subjects (Figure 5). This is likely
a result of non-use after stroke, which could have been
overcome partially by additional muscle training prior to
the experiment. However, since we only analyzed
performance from the trials where the target force vector was
within the theoretical workspace, this has not affected our
The ARAT scores of the stroke subjects had a broad
range. Therefore the subjects cannot be considered as
a homogeneous group. However, the emphasizes of
the current approach lies on modelling subject specific
recruitment relations. Therefore we did not observe lower
stimulation responses related to lower ARAT scores.
Furthermore, this is supported by the fact that the
subjects with the best ARAT scores showed the smallest
theoretical work range for the selected muscles.
We expect the remainder of the variation to have a
physiological cause. The most likely one is a non-linear additive
relation between the individual muscle directions and
recruitments. We expect that the linear addition of two
individual force magnitudes to produce the desired
combined force magnitude had the largest contribution to the
remainder of the observed variability.
Lujan and Crago  were able to control the thumb
forces in two directions by using an artificial neural
network. They also observed differences between the
measured force of combined muscle activation and the sum
of the individual components, which suggested a non
linear additive relation. Lujan and Crago stimulated different
muscles (Extensor Pollicis Longus, Abductor Pollicis
Brevis and Adductor Pollicis). The evoked forces in that study
are about five times higher than the forces which we
found, possibly caused by higher stimulation frequencies
(50 Hz compared to 30 Hz in our study) and the different
set of stimulated muscles. This makes a good comparison
between results difficult. Lujan and Crago only report 2D
control RMS errors of one healthy subject and one spinal
cord injured (SCI) patient, having implanted electrodes.
The RMS error of the SCI patient was 0.89 N , which is
very low compared to our results in stroke subjects when
relating to the achieved force range. However implanted
electrodes are known to produce higher muscle
selectivity and more direct muscle activation, which makes this
comparison unfair. The healthy subject they presented
showed an RMS error of 2.65 N , which is (taking the
factor 5 into account) within the same range as the
stationary RMS errors we observed. However, we were able
to obtain that similar performance without training and
optimizing an artificial neural network but with a more
transparent model consisting of only four parameters per
Schearer and colleges  recently published a single
case study on controlling multiple degrees of freedom
(in the shoulder) in a SCI subject with implanted
electrodes using a feedforward controller. They also solved
for redundancy by using a quadratic program and showed
initial RMS errors of 5.29 N . As shoulder muscles are
much stronger than thumb muscles, this value is again
difficult to compare with our results. Given the range of
their target forces (18 N to 4.5 N in the x direction,
18 N to 22.5 N in the y direction and 9 N to 0 N
in the z direction) one could say that the performance
of their controller was slightly better than ours, which
seems logical given the fact that the electrodes used by
Schearer and colleagues were implanted. Therefore their
stimulation was likely to result in more selective and
accurate activation of individual muscles. In addition, Schearer
et al suggest to improve the performance by adding a
feedback controller, which is exactly what we did in the
current study. We showed that adding the feedback path
can indeed improve performance when the feedforward
model is not accurate enough.
This study is a framework for evaluating
multidimensional control of joints with electrical stimulation.
To be clinically applicable in post-stroke rehabilitation,
the method needs several extensions. First of all, we
currently addressed only thumb muscles. For functional
grasp and release training the finger muscles are of
course equally important. However, compared to the
thumb, those joints do not have the redundancy in
actuation: mainly one extensor muscle and one superficial
flexor muscle. Therefore the current method could
easily be extended to the fingers, which we also evaluated
When using additional electrodes for (selective)
finger flexion and extension, the number of electrodes will
increase quickly. Since, electrode placement is subject
dependent and can be time consuming, the time required
for setup will also increase rapidly. From a practical point
of view, time can be gained with the application of
electrode arrays and an approach to automatically search for
proper electrode locations .
Finally, the relations between stimulation and
movement and control of movement for grasp and release are
also important. However proper force control is a
fundamental prerequisite for proper control of movement.
Therefore the current study can be seen as an
intermediate step towards an approach for assisting grasp and
release movements and next steps in our research will
focus on directly mapping muscle activation to evoked
Stroke subjects showed a limited workspace in our
study. Since they did not have severe spasticity, it is likely
that their muscle force have decreased dramatically due to
long time non-use after their stroke. Therefore, we expect
that results in more acute stroke subjects lie closer to
those of the healthy subjects in the current experiment.
However, this needs further evaluation and likely a subject
specific approach will lead to the best results.
The aim of this study was to evaluate the possibility to
predict thumb muscle force responses to FES and to control
thumb muscle force in 2D in both healthy and stroke
subjects. For a single muscle, the static relation between
muscle force and activation was described by a sigmoidal
muscle recruitment curve and a single direction of force.
Subsequently, load sharing was used to combine the
activation of individual muscles to actively control thumb
force in 2D.
From our results we can conclude that it is possible to
describe the thumb muscle responses to FES by a single
force direction and a sigmoidal recruitment curve. The
large variations between subjects indicate that these force
maps are highly subject specific, likely due to anatomical
differences, requiring an individual approach. The
relatively small variation within subjects demonstrates the
feasibility and time-invariance of our approach. Effects
of muscle fatigue were observed, especially in stroke
patients, so the approach presented here is applicable
mainly for short sessions (up to 30 minutes).
To our knowledge this is the first study applying a
load sharing paradigm in controlling multiple muscles
with surface FES in a multidimensional
biomechanical system. The load sharing approach controlled the
thumb towards the target forces in the 2D control
experiments. With feedforward force control only, errors were
larger in stroke subjects, compared to healthy subjects.
However, with added feedback control, significant
differences in control performance had disappeared.
Therefore the methodology for multi-dimensional feedback
force control presented here has potential applicability
as part of post stroke rehabilitation techniques.
Especially when applied earlier after stroke and muscles are
The authors declare that they have no competing interests.
AW carried out the experiments, data analysis and drafting of the manuscript.
AS, PV ad HK made substantial contributions to the study design,
interpretation of the data and critical revision of the manuscript. All authors
have read and approved the final manuscript.
This study was part of the Interreg IV MIAS-ATD project, part of the European
regional development fund. We would like to acknowledge the support of all
project partners, which is greatly appreciated.
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