KINEMATIC FEATURES OF REACH AND GRASP MOVEMENTS IN

STROKE REHABILITATION USING ACCELEROMETERS

Julien Stamatakis

, Adriana Gonzalez

, Benoit Caby

, Stephanie Lefebvre

2,3

Yves Vandermeeren

2,3

and Benoit Macq

Institute of Information and Communication Technologies, Electronics and Applied Mathematics

Universit

e catholique de Louvain, Louvain-la-Neuve, Belgium

Institute of NeuroSciences, Universit

e catholique de Louvain, Brussels, Belgium

Department of Neurology, Cliniques Universitaires de Mont-Godinne, Universit

e catholique de Louvain, Yvoir, Belgium

Keywords:

Accelerometers, Codamotion, Kalman Filter, Kinematic Analysis, Stroke.

Abstract:

Rehabilitation is an essential process to recover impaired motor functions after stroke. Typically, visual

marker-based systems such as the Codamotion are used, as kinematic analyses seem to be an excellent tool

to quantify objectively the effects of rehabilitation processes. However, this solution remains expensive. A

low-cost accelerometer-based system has been developed and its performances were compared to those of the

Codamotion system, used as a gold standard. Thanks to a model for prediction and an error model Kalman

ﬁlter, the recorded signals were broken up into gravity and dynamic accelerations components that were placed

in a global frame and compared to the Codamotion signals. The vertical z-axis was well reconstructed and

used as a basis for kinematic analyses. Different features expressing movement speed, control strategy or

movement smoothness have been computed from both systems and compared. Despite the fact that some of

them showed differences between both systems, the accelerometer-based system computed features with a

discriminant power comparable to the ones derived from the Codamotion. In conclusion, this accelerometer-

based system is a low-cost alternative to expensive visual marker-based systems that could be extensively used

for rehabilitation processes in routine clinical practice or even at home.

1 INTRODUCTION

Stroke is one of the leading causes of brain function

impairment, affecting motor, visual and speech abili-

ties. The inability to perform motor tasks has major

consequences on daily-life activities, leading to dis-

ability and loss of autonomy. Although some of those

motor functions may be recovered spontaneously, a

rehabilitation therapy is needed in most cases (Zhou

et al., 2008). It has been shown that targeted reha-

bilitative strategies can help the patient to regain and

relearn the impaired motor skills (Zhou et al., 2008;

Cirstea and Levin, 2007; Caimmi et al., 2008). To de-

velop and reﬁne such strategies, the patient motions

need to be monitored, in order to follow the evolu-

tion of the treatment, to supervise the correct perfor-

mances of the rehabilitation and to help correcting

some movements (Zhou and Hu, 2008). Rehabilita-

tion has to focus on daily-life tasks such as reach-

ing and grasping an object. This relatively complex

task involves the selection and control of the ﬁnger

grip aperture according to the size and shape of an

object, as well as the transport of the hand towards

the target. Several studies have been dedicated to

the evaluation of revalidation methods and treatments

(Caimmi et al., 2008; Wu et al., 2000). Kinematic

analyses seem to be an excellent and very sensitive

tool to quantify the effects of rehabilitation processes

on motor performances (Caimmi et al., 2008). Fea-

tures representing speed, accuracy or efﬁciency can

be extracted all along the rehabilitation process (Lang

et al., 2006) in order to assess the evolution of the re-

covery. Several systems have been developed over the

past decade in order to track human motion for kine-

matic analyses (Zhou and Hu, 2008). Visual marker-

based tracking systems such as VICON or Codamo-

tion are often used as gold standards because of their

accuracy. However, these systems are expensive and

cannot currently be applied at home or in the daily-life

environment of the patients. Other systems based on

inertial sensors like accelerometers and gyroscopes

(Kavanagh and Menz, 2008) have also been devel-

199

Stamatakis J., Gonzalez A., Caby B., Lefebvre S., Vandermeeren Y. and Macq B..

KINEMATIC FEATURES OF REACH AND GRASP MOVEMENTS IN STROKE REHABILITATION USING ACCELEROMETERS.

DOI: 10.5220/0003711701990205

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 199-205

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

oped. They are small, low-cost and well adapted for

portable devices. These systems are widely used in

the medical ﬁeld to detect physical activity, to pre-

vent falls of the elderly or to track upper limb motions

(Zhou et al., 2008). Multiple inertial sensors can be

combined but the size is then increased and the cali-

bration method becomes more complex.

In this paper, the development of a low-cost inertial

system based exclusively on accelerometers for kine-

matic analyses is proposed. Such a system is physi-

cally compact and can be used in daily-life environ-

ments. Few studies have focused on the exclusive

use of accelerometers. Indeed, since the measure-

ment contains gravitational, kinematic and noise com-

ponents, the dynamic acceleration is difﬁcult to ex-

tract without some extra information. The extraction

of the dynamic acceleration in each sensor frame is

based on the frequential properties of the movements,

as proposed in Luinge and Veltink (2004). These ac-

celerations are then placed in a global frame through

a frame transformation. This system is used to ex-

tract kinematic features from reach and grasp move-

ments that are compared to those extracted from the

Codamotion system, used as ground truth.

2 MATERIAL AND METHODS

The Codamotion system (Charnwood Dynamics,

Rothley, UK) is based on active markers and in-

frared cameras, allowing the 3-D measurement of

each marker position. In the global Codamotion

frame, the horizontal x axis is parallel to the move-

ment direction, the horizontal y axis is perpendicu-

lar to x and z is the vertical axis. At a 3 m distance,

the accuracy is ±1.5 mm in x and z axes, and ±2.5

mm in y axis for peak-to-peak deviations from ac-

tual position (Zhou and Hu, 2008). The sampling fre-

quency is set to 200 Hz. The low-cost accelerome-

ter system is composed of three 3-axis accelerome-

ters, recording ±2.5 g accelerations at the sampling

rate of 66.67 Hz (1g = 9.81m/s

). In each sensor

frame, the x axis is tangent to the limb, y is horizon-

tally perpendicular to x and z is the normal axis to

the limb. The accuracy on the accelerations is ±0.01

g. Accelerometers have been calibrated using a min-

imization function based on the norm and direction

of the gravity ﬁeld. All data have been processed

with Matlab (MathWorks, Natick, MA, USA). Sub-

jects were recruited at Cliniques Universitaires UCL

de Mont-Godinne; they provided written informed

consent. This research protocol has been approved by

the local ethical committee. Two hemiparetic stroke

patients (mRS = 2) and three healthy volunteers have

been included. Each subject had to execute 15 reach

and grasp movements at comfortable speed. They

were seated on a chair in front of the target, which was

placed at a comfortable reaching distance, i.e. 90% of

the total arm length. Each movement began with the

hand resting on the legs. Sensors and active markers

were placed on the index nail, thumb nail and on the

wrist of the most affected arm for the patients and on

the dominant hand for the healthy volunteers, as illus-

trated in Figure 1. The results are presented for the

sensor and the marker that were placed on the wrist.

In order to extract kinematic features of the reach

and grasp movements, the dynamic accelerations due

to movements were extracted from the accelerom-

eter signals using a Complementary Kalman Filter.

The dynamic accelerations were expressed in the Co-

damotion global frame, instead of the sensor frame,

to compare the reconstructed signal to the Codamo-

tion signal in each axis. Then, some of the most

commonly used features were computed for both sys-

tems and compared. The ﬁrst feature is the Total

Movement Time (TMT) (Trombly, 1993; Chang et al.,

2005; Caimmi et al., 2008), computed as the time nec-

essary to operate the whole reach and grasp move-

ment; it is supposed longer for hemiparetic patients

(Lang et al., 2006; Michaelsen et al., 2004). The

second one is the number of Movement Units (MU),

which allows to evaluate the smoothness of the move-

ment (Trombly, 1993; Wu et al., 2007). A MU rep-

resents an increase of more than 10% of the maxi-

mum velocity between adjacent minimum and maxi-

mum in the velocity proﬁle; it is supposed higher for

pathological patients (Chang et al., 2005) since they

have numerous, corrective and small movements. The

third feature is the Normalized Jerk (NJ), deﬁned in

(1), where T is the total movement time, j is the jerk,

i.e. the derivative of the acceleration, and D is the

total distance of the reach and grasp movement path

in space. This represents another feature to evaluate

the smoothness of the movement, that is supposed to

be lower for healthy subjects (Caimmi et al., 2008;

Chang et al., 2005).

NJ =

stop

start

(t) dt (1)

The other features are the Peak Wrist Velocity

(PWV) and the percentage time to reach this value

(TPWV) (Trombly, 1993; Michaelsen et al., 2004;

Lang et al., 2006; Chang et al., 2005). PWV is usu-

ally used to reﬂect the level of force generation (i.e. a

high PWV is indicative of a high level of force genera-

tion) while TPWV reﬂects the control strategy (Chang

et al., 2005) (i.e. TPWV will express whether the

peak velocity is generated early or late in the move-

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

200

Figure 1: A. The accelerometers are placed on the ﬁnger

nail, thumb nail and on the wrist. B. The active markers are

placed above the accelerometers; the other markers are not

used here.

ment). Both are supposed to be lower for the hemi-

paretic patients.

3 COMPLEMENTARY KALMAN

FILTER

Although accelerometers do not depend on any exter-

nal reference, they are bound to the gravity ﬁeld and

therefore their output signal is dependent of both the

tilt angle and the actual acceleration. The ﬁrst step in

order to recover the accelerations due to movements

(a) is thus to remove the gravity (g) components from

the recorded signals (y). The signal is also affected by

the bias (b), an intrinsic parameter of the accelerome-

ter, that is reﬂected by an offset in the output signal.

a = y − g − b (2)

Luinge and Veltink (2004) have worked on the ex-

traction of the gravity and offset components from the

accelerometer signal, considering as noise the accel-

eration component caused by movement. They stated

that when the movement acceleration is sufﬁciently

small in comparison to the gravity, the accelerometer

can be used as an inclinometer. To perform such an

extraction, they used a Complementary Kalman Fil-

ter. In this paper, the design is based on their method

but instead of extracting the gravity and the offset,

the idea is to extract the dynamic acceleration and the

gravity.

The Complementary Kalman Filter or error-state

Kalman Filter enables to combine two media (Hig-

gins, 1975). It takes one as reference, works with

the estimation of the difference between them and

uses this estimation to update the other one (Welch

and Bishop, 2001). It is often used to combine two

sensors but, in this case, it combines one sensor and

one prediction step as described in Figure 2. Further-

more, it allows the use of a linear Kalman ﬁlter while

Figure 2: Complementary Kalman Filter with sensor and

prediction values as inputs. The superscript − reprensents

an a priori value and the superscript + represents an a pos-

teriori value. A hat on the top of a symbol is used to indi-

cate an estimation. k represents the current value and k − 1

the one of the previous time step. The superscript S means

that values are expressed in the Sensor frame while the su-

perscript G means that values are expressed in the Global

frame (Codamotion).

non-linear processes can be used during the predic-

tion step. Here, an autoregressive (AR) model is set

up.

The a posteriori estimates of the acceleration

and gravity (

S,k−1

k−1

S,k−1

k−1

) from the previous

time step are used to make an a priori estimation of

the acceleration and gravity, and thus to predict the

sensor output vector

−

. The difference y

−

ε,k

between

the a priori predicted accelerometer output

−

and

the actual output y

represents the a priori prediction

error of the acceleration and gravity (

S,k

−

ε,k

S,k

−

ε,k

Then, the Kalman ﬁlter uses y

−

ε,k

and the variance

of the predicted components Q

to generate the a

posteriori prediction error (

S,k

ε,k

S,k

ε,k

) that will

be used for the update of the acceleration and gravity

predictions, resulting in their a posteriori estimations

(

S,k

This model is only valid if the accelerometer out-

put signal meets the conditions exposed by Luinge

and Veltink (2004). As shown in Figure 2, the Com-

plementary Kalman Filter is composed by two phases

: one for the prediction and the other for the error

model Kalman ﬁlter. The prediction phase consists

in modeling the behaviour of acceleration and gravity

signals for speciﬁc movement, as presented for grav-

ity in Luinge and Veltink (2004). The acceleration

is modeled as an AR process, which is a time se-

ries analysis model based on the previous weighted

outputs of the system (3). The AR modeling pro-

cess is based on the spectrum of the signal, thus the

coefﬁcients of the AR model describe the frequency

changes of the signal.

S,k−1

−

= −

∑

i=1

S,k−i

k−i

+ ε

(3)

The error model Kalman ﬁlter consists in the estima-

KINEMATIC FEATURES OF REACH AND GRASP MOVEMENTS IN STROKE REHABILITATION USING

ACCELEROMETERS

201

tion of the a posteriori prediction errors of the ac-

celeration and gravity from their a priori values and

the error covariance via Kalman ﬁltering (Luinge and

Veltink, 2004). The state vector x

ε,k

is deﬁned with

the state variables a

ε,k

and g

ε,k

, corresponding to the

prediction errors of acceleration and gravity, respec-

tively (4).

ε,k



ε,k



(4)

The bias b

is considered as noise and not as a state

variable because the system is not able to distinguish

between a

and b

, since both of them are unknown.

Therefore, the extracted acceleration components will

contain an offset due to this bias, that will be removed

by high-pass ﬁltering.

As the accelerometers do not have any exter-

nal reference, their signals are referred to the sen-

sor frame. Although the reconstructed acceleration

signal norms can be directly compared between sys-

tems, both systems must have the same reference to

compare the reconstructed signals to the Codamotion

output for each axis. It is thus necessary to put the

extracted accelerations, expressed in the local sensor

frame, into the global Codamotion frame via a frame

transformation. In order to do so, the constant expres-

sion of the gravity in the global frame

g is used. The

matrix M

, called the Rotation Matrix, is deﬁned as

the rotation between each

S,k

(gravity expressed in

the sensor frame) and

g. Using M

, it is possible

to change the reference frame of the accelerations, in

order to formulate it in the global frame.





x,k

y,k

z,k





= M







S,k

x,k

S,k

y,k

S,k

z,k







(5)

Once the extracted accelerations are referenced in the

global coordinate frame, they need to be multiplied

by the constant of gravity g

= 9.81 m/s

in order to

have values in the MKS system of units.

4 EXPERIMENTAL VALIDATION

The ﬁrst step was to set up a model for the predic-

tion of the dynamic accelerations. This model has

been built with the data recorded by the Codamo-

tion for one healthy volunteer who was not part of

the experimental group (pilot data). The parameters

of the prediction step have been chosen experimen-

tally. The recorded accelerations from the Codamo-

tion were then down-sampled to match the accelerom-

eters sampling frequency, i.e. 66,67 Hz.

Once extracted, the dynamic accelerations were

high-pass ﬁltered (cut-off frequency of 0.4 Hz) in or-

A B

Figure 3: Accelerations and velocities for the wrist sensor.

The dashed curve is the Codamotion signal while the con-

tinuous one represents the reconstructed signal from the ac-

celerometers. Figures A and B represent the accelerations

and velocities in the global z axis for a healthy volunteer,

while Figures C and D represent the accelerations and ve-

locities for a hemiparetic patient.

der to remove the remaining bias. Then, they were in-

tegrated to obtain the velocities, which have also been

high-pass ﬁltered to remove the drift. All signals were

also low-pass ﬁltered at the cut-off frequency of 5 Hz.

As the features are usually extracted on the sig-

nal norms, the reconstructed acceleration norms and

the Codamotion acceleration norms have been com-

pared, as well as axis-by-axis. The correlation coefﬁ-

cients (r) and the mean square error (MSE) between

signals have been computed, for accelerations and ve-

locities respectively, and are presented in Table 1 and

2. Even if the norms are correlated, the reconstruc-

tion is not precise enough for feature extraction. The

main observation is that the best reconstruction is in

the z axis, whose signals are presented in Figure 3 for

a healthy volunteer and a hemiparetic patient. The x

and y axes are poorly reconstructed. This is due to

two different causes. The ﬁrst one is the frame trans-

formation. Indeed, only the z direction, the direction

of the gravity, is known; whatever the orientation of

the x and y axes,

g will remain the same. So, the

accelerations are transformed to match the correct z

direction, but not to match the directions of x and y.

This problem remains for the velocities, as velocities

are obtained from the integration of the acceleration

signals. Secondly, according to the signals compar-

ison, the reconstructed norm is affected by a poorly

reconstruction in the x and y axes, as the z axis is

very well reconstructed. The y axis gives the worst

reconstruction. This direction is not really part of the

movement as it is performed in the x − z plane. There

are only small displacements along this axis, giving

an unprecise model for the accelerations in that par-

ticular direction.

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202

Table 1: Performances of accelerations reconstruction.

Healthy Hemiparetic

Group Group

Sensor axis r MSE r MSE

Wrist norm 0.608 0.790 0.675 0.374

x 0.736 1.359 0.572 0.773

y -0.150 2.462 0.625 0.686

z 0.934 0.284 0.899 0.239

Table 2: Performances of velocities reconstruction.

Healthy Hemiparetic

Group Group

Sensor axis r MSE r MSE

Wrist norm 0.437 0.092 0.635 0.063

x 0.314 0.174 0.258 0.087

y -0.375 0.149 0.440 0.046

z 0.949 0.008 0.875 0.010

According to these observations, the feature ex-

traction will not be performed on the signal norms, as

it is done for the Codamotion system. Indeed, the er-

rors on the x and y axes are too large to lead to accept-

able approximations of the signal norms. Instead, the

feature extraction will be based on the z axis for the

accelerometer-based system. Section 5 will demon-

strate that the two extraction methods have the same

discriminant power.

5 FEATURE EXTRACTION

The extracted features have already been shown dis-

criminant between hemiparetic and healthy subjects

when extracted with an optical system (Lang et al.,

2006; Michaelsen et al., 2004; Chang et al., 2005;

Caimmi et al., 2008). The purpose is to demon-

strate that these discriminant features have the same

behavior when extracted on the z axis of the recon-

structed accelerations and velocities. In order to do

so, random effect models (Brown and Prescott, 1999)

were built using the computing environment R (Ihaka

and Gentleman, 1996) and the NLME (Nonlinear and

Linear Mixed Effects models) package (Pinheiro and

Bates, 2006). For each feature and for each system,

a random effect model was built with one ﬁxed ef-

fect (state, i.e. healthy or hemiparetic) and one ran-

dom effect (subject). The p-value associated with the

ﬁxed effect state determines if the output is signif-

icantly different between the two states for a given

feature and a given system. As subject is ﬁtted as a

random effect in the models, inference is not speciﬁc

to the observed subject but can be applied to the full

population of subjects. For each feature, a random

effect model was also built with three ﬁxed effects

(state, system, state × system) and two random effects

(subject, trial). In this case, the p-value associated

to the ﬁxed interaction effect (system × state) deter-

mines whether the differences between the two states

are signiﬁcantly different for both systems. If not, an-

other model without the ﬁxed interaction effect was

built to determine if the extracted features were sig-

niﬁcantly different between the two systems (system

effect). All data have been transformed through a log

function to meet the homoscedasticity hypothesis.

TMT (Total Movement Time) has ﬁrst been extracted.

The correlation between sensors is statistically sig-

niﬁcant (r = 0.967, p < 0.001 for the healthy group

and r = 0.729, p < 0.001 for the hemiparetic group).

For both sensors, TMT is signiﬁcantly shorter for the

healthy group (p < 0.05). There is neither interaction

nor system effect.

The MU (Movement Unit) has then been computed on

the velocities. There is no correlation between sys-

tems for the healthy group but a low signiﬁcant one

for the hemiparetic group (r = 0.479, p < 0.05). MU

is signiﬁcantly lower for the healthy group for both

systems (p < 0.001 for the Codamotion and p < 0.05

for the accelerometer-based system) and there is no

interaction effect. There is a signiﬁcant system effect

(p < 0.001).

For the computation of the NJ (Normalized Jerk), the

reach and the grasp distances have been approximated

by half the arm length as those values were not avail-

able for the accelerometer-based system. For both

groups, the values are correlated between systems

(r = 0.594, p < 0.01 and r = 0.621, p < 0.01). NJ is

signiﬁcantly shorter for the healthy group (p < 0.05

and p < 0.01). There is no interaction effect but a

signiﬁcant system effect (p < 0.001).

PWV (Peak Wrist Velocity) shows a signiﬁcant cor-

relation between the values of the two systems for the

hemiparetic group (r = 0.661, p < 0.001) but not for

the healthy group. There is no signiﬁcant difference

between the groups for any system but there is a sys-

tem effect (p < 0.001).

TPWV (percentage Time to Peak Wrist Velocity)

does not show any signiﬁcant difference or effect be-

tween groups or systems but the values are corre-

lated between systems, for both groups (r = 0.695,

p < 0.001 and r = 0.938, p < 0.001).

6 DISCUSSION

Discriminant kinematic features have been extracted

from both systems in order to compare the perfor-

mances of the accelerometer-based system to the Co-

KINEMATIC FEATURES OF REACH AND GRASP MOVEMENTS IN STROKE REHABILITATION USING

ACCELEROMETERS

203

Table 3: Mean features values.

Healthy Hemiparetic

Feature Accel. Coda. Accel. Coda.

TMT (s) 2.134 2.094 3.613 3.624

MU (-) 3.194 2.027 6.625 4.875

NJ (-) 69.33 54.95 297.3 229.2

PWV (m/s) 0.557 0.865 0.465 0.599

TPWV (%) 33.78 30.01 30.45 27.06

damotion, used as ground truth. These kinematic fea-

tures, i.e. TMT, MU, NJ, PWV and TPWV have been

extracted on the z axis of the reconstructed signals

for the accelerometer-based system and on the signal

norms for the Codamotion. All features were signif-

icantly correlated between systems, for both groups,

except for MU and PWV in the healthy group. TMT,

MU and NJ have been found to be discriminant fea-

tures, as expected, while PWV and TPWV have not.

However, the important observation is that both sys-

tems are discrimant for TMT, MU and NJ, and not

discriminant for PWV and TPWV, leading to the same

discriminant and non-discriminant features. There is

no interaction effect for any feature, which means that

the discriminant power of the features does not de-

pend on the system used. For features based on time,

i.e. TMT and TPWV, there is no system effect, which

means that their value does not depend on the sys-

tem used to acquire the data. There is a system effect

for MU, NJ and PWV, suggesting that the measured

value depends on the system used. Indeed, those fea-

tures are not extracted on the same signals, one being

extracted on the z dimension while the other is on the

norm. The values can thus not be similar, which leads

to a system effect; however, once again, this effect has

no impact on the discriminant faculty of the features.

7 CONCLUSIONS

Some evident limitations of visual marker-based sys-

tems are that they are expensive and not usable in

the daily clinical practice. However, their preci-

sion is valuable for the extraction of kinematic fea-

tures, that are essential to quantify stroke rehabilita-

tion processes. A low-cost accelerometer-based sys-

tem has been developed to address these drawbacks.

A Complementary Kalman Filter has been set up in

order to separate the recorded signals from the ac-

celerometers in dynamic accelerations due to move-

ments and gravity components. The dynamic acceler-

ations were placed into a global frame, instead of the

sensor frame, in order to draw a direct comparison

with the accelerations recorded by the Codamotion

system, used as ground truth. The 3-axis accelerations

and velocities have been compared between healthy

and hemiparetic subjects performing reach and grasp

movements, showing the best reconstruction in the z

axis, while the reconstructed norms were not precise

enough to be used for kinematic analyses. Feature

extraction was thus performed on the reconstructed

z axis for the accelerometer-based device and on the

norm for the Codamotion signals. Despite of that,

the accelerometer system allowed the computation of

features with a discriminant power comparable to the

ones derived from the Codamotion. Similar results

were obtained for the sensors and markers placed on

the index nail and on the thumb nail of the subjects.

This accelerometer-based device is a promising alter-

native to expensive visual marker-based systems for

rehabilitation processes, that could be used during re-

habilitation sessions or at home.

A larger set of patients should be formed, as well

as multiple recordings, in order to assess the evolu-

tion of the features all along the rehabilitation pro-

cess. Other features could also be extracted to allow a

deeper quantiﬁcation of the movements. For example,

the Peak Wrist Acceleration (PWA) and the percent-

age time to reach this value (TPWA) could be used as

more sensitive features to evaluate force generation

and control strategy. Indeed, the accelerometer-based

system records accelerations, that are directly related

to force generation. Marker-based systems use veloc-

ities for the evaluation of force generation and control

strategy because this measure is more accurate as it is

the ﬁrst derivative of the recorded position while the

acceleration is the second derivative.

ACKNOWLEDGEMENTS

The work of JS was supported by a FRIA grant.

The work of YV and the purchase of the Codamo-

tion system was supported by the following grants:

Fonds de la Recherche Scientiﬁque M

edicale (FRSM)

3.4.525.08.F 2008 & 2010; Universit

e catholique de

Louvain (UCL) Fonds Sp

ecial de Recherche (FSR)

2008 & 2010. The work of SL was supported by UCL

FSR grants 2008 & 2010.

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