TREMOR CHARACTERIZATION

Algorithms for the Study of Tremor Time Series

E. Rocon, A. F. Ruiz, J. C. Moreno, J. L. Pons

Bioengineering group, IAI-CSIC, Ctra. Campo Real, km 0.200, Madrid, Spain

J. A. Miranda

Technaid S. L., Madrid, Spain

A. Barrientos

Grupo de Rob´otica y Cibern´etica, UPM, Madrid, Spain

Keywords:

Tremor, Empirical mode decomposition, Inertial sensors, Timefrequency analysis, Real-Time estimation.

Abstract:

This paper introduces the work developed by the authors in the study of tremor time series. First, it introduces

a novel technique for the study of tremor. The technique presented is a high-resolution technique that solves

most of limitations of the Fourier Analysis (the standard technique to the study of tremor time series). This

technique was used for the study of tremorous movement in joints of the upper limb. After, some conclusions

about tremor behaviour in upper limb based on the technique introduces are presented. Furthermore, an

algorithm able to estimated in real-time the voluntary and the tremorous movement was presented. This

algorithm was validated in two contexts with successful results. Finally, some conclusions and future work

are given.

1 INTRODUCTION

Tremor is a rhythmic, involuntary muscular contrac-

tion characterized by oscillations of a part of the body

(Anouti and Koller, 1998). The oscillatory activi-

ties are related to various combinations of four basic

mechanisms: (a)mechanically induced oscillations,

(b) oscillations due to reﬂexes, (c) oscillations gen-

erated by neuronal generators in the central nervous

system, (d) oscillations resulting from impaired feed-

forward and feedback loops.

It is well established that tremorous activity is

composed of deterministic and stochastic compo-

nents, (Timmer et al., 2000). The detection and quan-

tiﬁcation of tremor are of clinical interest for diag-

nosis of neurological disorders and objective evalu-

ation of their treatment, (Gao and Wen-wen, 2002).

Furthermore, the estimation of tremor is an important

stage in systems that aim to control limb oscillations,

and also in biofeedback studies. In this regard, es-

timation techniques have been developed for tremor

suppression. Methods based on the Fourier transform

(FT) are commonly employed for this purpose, spe-

cially because of the similarity between the tremor to

a sine wave, (Elble and Koller, 1990). For instance,

the weighted Fourier linear combiner (WFLC) char-

acterizes the tremor based on its approximation by a

sinusoidal waveform, (Riviere, 1995). Riviere also in-

vestigated the application of neural networks to aug-

ment manual precision by cancelling involuntary mo-

tion. Another example is the extraction of frequency

parameters from the power spectrum (based on the

FT) of the tremor for classiﬁcation purposes, (Rocon

et al., 2004).

This paper introduces an original study for tremor

characterization. First, experiments were performed

with 31 patients suffering from tremor diseases in

order to study tremor characteristics. The data col-

lected in this experiments were analyzed by means of

a novel methodology for the study of tremor time se-

ries based on Empirical Mode Decomposition. This

technique allows an automatic detection of tremorous

movement and the study of nonlinear and nonstation-

ary characteristics of tremor, (Rocon et al., 2006).

Based on the information provided by this study, a

novel algorithm able to estimate in real time and com-

posed by two stages, one for the detection of vol-

untary movements and other for the estimation of

355

Rocon E., F. Ruiz A., C. Moreno J., L. Pons J., A. Miranda J. and Barrientos A. (2008).

TREMOR CHARACTERIZATION - Algorithms for the Study of Tremor Time Series.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 355-360

DOI: 10.5220/0001058603550360

 SciTePress

Figure 1: Hilbert Spectrum of an Essential tremor patient

performing the task of Keeping the arms outstretched. The

high levels of energy activities are perceived when the pa-

tient is performing the task.

tremorous movements, is presented. Finally, exper-

iments for the validation of the algorithm presented

are given.

2 THE EXPERIMENTAL

PROTOCOL

In order to assess tremor characteristics we studied

its behavior in 31 patients suffering from different

pathologies. The average age of patients was 52.3

years old (ranging from 23 to 84 years old). All pa-

tients provided their written consent for the experi-

ments.

The diagnosis of the condition of patients was

given by the neurological staff of the General Hospi-

tal of Valencia (GHV, Spain) and the functional state

of patients was evaluated by means of the Faher scale,

(Fahn et al., 1998). Ethical approval for this research

has been granted by the Ethical Committee of the

GHV.

2.1 Sensors

The tremor was detected by a customized sensor,

which is based on the combination of two indepen-

dent gyroscopes placed distally and proximally to the

joint of interest. The joint angular speed is obtained

by subtraction of the angular speed measured by one

gyroscope from the angular speed measured by the

other one. The weight of the system is roughly 15

g, which is a low-mass system when compared to

other sensors used in the ﬁeld, (Rocon et al., 2004).

The use of a low-mass sensor is important to reduce

the effect of low-pass ﬁltering on the detected signal.

Gyroscopes were placed in order to estimate follow-

ing movements of the upper limb: 1) Elbow ﬂexion-

extension, 2) Forearm pronation-supination, 3) Wrist

ﬂexion-extension, and 4) Wrist deviation.

2.2 Tasks

Six different tasks were employed for excitation of

tremor: 1) Rest, 2) Reaching for an object, 3) Draw-

ing a spiral, 4) Arm outstretched, 5) Touching nose,

and 6) Moving a cup. In all tasks the patient was sit-

ting on a chair. This set of tasks aims to stimulate all

different types of tremor.

3 ANALYSIS OF TREMOROUS

MOVEMENT

In order to analyze the tremorous movement acquired

during the experiments, Empirical Mode Decomposi-

tion was used. This technique was proposed in (Ro-

con et al., 2006). This technique was identiﬁed as

a very useful tool for an automatic decomposition of

the signal into tremor and voluntary signal. Moreover,

this technique enables the representation of the ampli-

tude and the instantaneous frequency of the input sig-

nal as function of time in which the amplitude could

be contoured on the time-frequency plane. The tech-

nique presented is a high-resolution technique that

solves most of limitations of the Fourier Analysis (the

standard technique to the study of tremor time series).

This technique provides, in a time-frequency-energy

plot, a clear visualization of local activities of tremor

energy over the time, see ﬁgure 1.

Based on this technique, a study of the tremorous

movement at different joints of the upper limb was

developed. The study was performed with the data

collect from the experiments introduced in the previ-

ous section and aim at understanding tremorous be-

haviour. The main conclusions of this study are the

following: 1)the amplitude of the tremorous move-

ment is larger in distal joints than in proximal joints,

2)the frequency of tremorous movements is com-

prised in the bandwidth between 3 and 8 Hz, 3)tremor

frequencyat different joints of the upper limb has very

similar values, 4)tremor frequency is not related to

the task performed by the patient, 5)the frequency of

tremorous movement is constant during the execution

of a task, nevertheless it could change during repe-

titions of the same task, 6)tremor activity is not al-

ways present during the experiments. Patients showed

tremor activity just during 40% of the time measured,

7) sex and age does not inﬂuence tremor behaviour.

The main novelty of this study is that it is centered in

tremor at joint level while the majority of the studies

presented in the literature are centered in the study of

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

356

tremor at ﬁnger tip. The main drawback of this tech-

nique is the impossibility to implement it in real-time

(RT). In order to address this issue, next section de-

scribes the development of an algorithm able to dis-

tinguish in RT tremorous movement from voluntary

movement.

4 TREMOR ESTIMATION

A number of estimation algorithms have been devel-

oped for tremor suppression. As a ﬁrst approach,

we evaluated robust algorithms based on IEEE-STD-

1057, which is a standard for ﬁtting sine waves to

noisy discrete-time observations. In particular, the

weighted-frequencyFourier linear combiner (WFLC)

developed by Riviere, (Riviere, 1995), in the context

of actively counteracting physiological tremor in mi-

crosurgery was implemented. The WFLC is an adap-

tive algorithm that estimates tremor using a sinusoidal

model, estimating its time-varying frequency, ampli-

tude, and phase. The WFLC can be described by

equation 1. It assumes that the tremor can be mathe-

matically modelled as a pure sinusoidal signal of fre-

quency ω

plus M harmonics and computes the error,

, between the motion, s

, and its harmonic model.

= s

−

∑

r=1

sin(rω

k) + w

r+M

cos(rω

k)] (1)

In its recursive implementation, see equations 2

and 3, the WFLC can be used online to obtain estima-

tions of both tremor frequency and amplitude, (Riv-

iere, 1995).

k+1

= w

+ 2µ

∑

r=1

r(w

M+r

− w

M+r

) (2)

where,







sin(rω

k), 1 ≤ r ≤ M

cos((r− M)ω

k), M + 1 ≤ r ≤ 2M

(3)

The WFLC algorithm was evaluated with the sig-

nals measured in the experiments described in pre-

vious section. In the completed trials, the algorithm

was able to estimate the tremor movement of all the

patients with accuracy always lower than 2 degrees,

see ﬁgure 2. The main disadvantage of the WFLC

is the need for a preliminary ﬁltering stage to elimi-

nate the voluntary component of the movement, (Riv-

iere, 1995). This ﬁltering stage introduces an unde-

sired time lag for our system when estimating tremor

movement, this time lag introduces a time delay that

could considerably affect the implementation of the

control strategies for tremor suppression.

7 8 9

−3

−2

−1

Time (s)

Angular position (

)

Figure 2: Estimation of tremor, solid line, based on WFLC

algorithm, red dashed line.

4.1 Estimation of Voluntary Movement

The tremor literature indicates that voluntary move-

ments and tremor movements are considerably dif-

ferent, (Elble and Koller, 1990). Voluntary move-

ments are slower while tremor movements are brus-

quer. This indicates that adaptive algorithms to esti-

mate and track movement would be useful when sep-

arating the two movements with an appropriate de-

sign. The underlying idea is to design the ﬁlters so

that they only estimate the less dynamic component of

the input signal, which in our case we consider to be

voluntary movement, thereby ﬁltering out the tremor

movement.

A set of algorithms was considered for the estima-

tion of the voluntary motion: two point-extrapolator,

critically damped g-h estimator, Benedict-Bordner g-

h estimator, and Kalman ﬁlter. These algorithms im-

plement both estimation and ﬁltering equations. The

combination of these actions allows the algorithm to

ﬁlter out the tremorous movement from the overall

motion at the same time it reduces the phase lag intro-

duced, (Bar-Shalom and Li, 1998). The equation pa-

rameters were adjusted to track the movements with

lower dynamics (voluntary movement) since tremors

present a behaviour characterised by quick move-

ments. The performance of these algorithms were

compared based on their accuracy when estimating

voluntary movements of tremor time series from pa-

tients.

4.1.1 Two Points Extrapolator

It is the simplest tracking algorithm. This algorithm

uses the current position measured, y

, and the past

measured position, y

n−1

, to estimate the velocity, ˙x

∗

and the future position x

∗

n+1

˙x

∗

−Y

n−1

, (4)

TREMOR CHARACTERIZATION - Algorithms for the Study of Tremor Time Series

357

∗

n+1

= y

+ T ∗ ˙x

∗

, (5)

where T is the sample time and “∗” denotes an esti-

mated value.

4.1.2 Critically Damped G-h Estimator

This estimation algorithm is a g-h ﬁlter composed

by g-h track update equations and by g-h prediction

equations

update







˙x

∗

k,k

= ˙x

∗

k,k−1

+ h



−x

∗

k,k−1



∗

k,k

= x

∗

k,k−1

+ g



− x

∗

k,k−1



(6)

predict



˙x

∗

k+1,k

= ˙x

∗

k,k

∗

k+1,k

= x

∗

k,k

+ T ˙x

∗

k+1,k

(7)

The track update equations or estimation equa-

tions, 6, provide us the velocity and position of tremor

at time kT after the measurement of the angular posi-

tion of the joint, y

. The estimated position is based

on the use of the actual measurement as well as the

past prediction. As a consequence of ﬁltering, the

measured noise is reduced. The predicted position is

an estimate of x

n+1

based on past states and predic-

tion (equation 7), and take into account the current

measurement by means of updated states.

4.1.3 Benedict-Bordner G-h Estimator

This estimation algorithm have the same equations

that the Critically Damped g-h estimator but with dif-

ferent values in the parameters g-h, (Bar-Shalom and

Li, 1998). The Benedict-Bordner estimator is de-

signed to minimize the transient error. Filter g-h pa-

rameters are related by:

h =

2− g

(8)

4.1.4 The Kalman Filter

The Kalman ﬁlter is a g-h ﬁlter where the weights g

and h are a function of n and are updated recursively.

This ﬁlter has the advantage of allowing the optimum

use of the information if it is available. In addition,

permits the use of the target dynamics information

to optimize the ﬁlter parameters. More complete in-

formation about Kalman ﬁlter can be found in (Bar-

Shalom and Li, 1998).

4.2 Figure of Merit

In order to quantitative compare the estimators pro-

posed a metric, Cinematic Estimation Error (CEE),

was proposed. The equation that deﬁne this metrics

is:

CEE =

∗

+ σ

∗

, (9)

where ϕ

∗

is the mean square of errors of the esti-

mators: |b

∗

| = |x

− x

∗

k,k−1

|, and σ

∗

variance of the

estimation.

CEE quantiﬁes the transient response through

∗

and, at the same time, the averaging or ﬁlter-

ing capabilities of the ﬁlter through the term σ

∗

. The

accuracy and transient response of the estimation al-

gorithms are important. Another important parameter

taken into account in our analysis was the execution

time of each algorithm in view of the fact that the sys-

tem was designed to work in real time. The result

of such analysis indicated that Benedict-Bordner ﬁl-

ter presents the best results with the lowest computa-

tional cost.

4.3 Real-time Estimation of Voluntary

and Tremorous Movement

The solution adopted was the development of an algo-

rithm capable of estimating voluntary and tremorous

motion with a small phase lag based on a two-stage al-

gorithm. In the ﬁrst stage, the Benedict-Bordner ﬁlter

estimates the voluntary component of the movements.

In the second stage, the estimated voluntary motion is

removed from the overall motion and it is assumed

that the remaining movement is tremor. After this,

the WFLC was used in order to estimate tremor pa-

rameters. In this stage, the algorithm estimates both

the amplitude and the time-varying frequency of the

tremorous movement.

The algorithm proposed was evaluated with data

obtained from the patients measured in our experi-

ments. The estimation error of the ﬁrst stage was

1.4± 1.3 degrees. The second stage algorithm has a

convergence time always smaller than 2 s for all sig-

nals evaluated and the Mean Square Error (MSE) be-

tween the estimated tremor and the real tremor, after

the convergence, is smaller than 1 degree. The com-

bination of both techniques resulted in a very efﬁcient

algorithm with small processing cost for estimating in

real time the voluntary and the tremorous components

of the overall motion.

5 EXPERIMENTS AND RESULTS

The performance of the algorithm proposed was eval-

uated in two different contexts: 1)Tremor suppres-

sion based on exoskeleton devices, and 2)Filtering

tremorous movement from PC mouse cursor.

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

358

5.1 Tremor Suppression based on

Exoskeleton Devices

The algorithm for tremor estimation was incorpo-

rated to the WOTAS (Wearable Orthosis for Tremor

Assessment and Suppression) active exoskeleton for

tremor suppression, (Rocon et al., 2007). In order

to evaluate the performance of the device developed

to suppress tremor we have planned an experimen-

tal phase involving 10 patients suffering from differ-

ent tremor diseases. During the ﬁrst clinical trials the

algorithm was able to measure and estimate tremor

parameters, see Figure 3. The capacity of applying

dynamic internal forces to the upper limb for tremor

suppression (based on the information provided by

the tremor estimation algorithm) was also evaluated.

Based on this parameter it was found that the device

could achieve a consistent 30% tremor power reduc-

tion, with reduction peaks in the order of 80% in the

tremor power for patients exhibiting severe tremor,

see Figure 3. Moreover, patients related that they

felt small inﬂuence of the WOTAS device on their

intended motion, which indicates a proper function-

ing of the algorithms proposed in the precious section,

(Rocon et al., 2007).

5.2 Filtering Tremorous Movement

From PC Mouse Cursor

In these experiments the algorithm was integrated in

a device connected between the mouse and the com-

puter that should remove tremorous movements from

PC mouse cursor. These experiments were carried out

in cooperation with Spanish Foundation of Multiple

Sclerosis. Previously to the realization of the experi-

ment, the operation of the system was explained to the

user. After, the patient was asked to achieve a com-

fortable position in the chair and to grab and use the

mouse as natural as possible. After a time of adap-

tation and relaxation, roughly 10 minutes, the patient

was asked to perform 2 typical movements when us-

ing a computer mouse:

1. Draw a spiral - The patient was asked to follow

with the cursor of the mouse a path with the form

of a spiral drawn on the screen of the computer.

The trajectory described by the user is not illus-

trated in the screen; with this approach it is possi-

ble to avoid the attempts of the user to correct the

trajectory. The patient just has the reference of the

model spiral on the screen. During this tasks the

buttons are disabled and the trajectory described

by the user was recorded by the software.

6 7 8 9 10

−5

WOTAS: Monitoring mode

Time (s)

rad/s

6 7 8 9 10

−5

WOTAS: Damping mode (0.2 N.m.s/rad)

Time (s)

rad/s

0 5 10 15 20

100

200

300

400

500

600

Frequency (Hz)

Tremor Power (rad

)

0 5 10 15 20

100

200

300

400

500

600

Frequency (Hz)

Tremor Power (rad

)

Figure 3: The graphics illustrated the reduction in the

tremor power when WOTAS is applying viscosity to the

tremorous movement.

2. Goal and click - To move the cursor over 10 icons

that appear in a random sequence on the screen of

the computer.The patient was asked to click over

the picture every time he/she reaches it. In this

way, the next picture will appear just after the pa-

tient click on the actual one. The trajectories and

the number of erroneous clicks were recorded.

The total time of each experiment was 40 minutes

and the main objective was to quantify the effective-

ness of the device in tremor suppression. Each task

was repeated 3 times, one with the ﬁlter disabled, an-

other one with the ﬁlter activated and in the last trial,

the ﬁlter is deactivated again. The order of trials was

randomized. The ﬁgures of merit used to quantify the

improvement in the ability of the patient in the real-

ization of the tasks were:

1. The relation between the number of times the user

leaves the boundaries of the path deﬁned by the

spiral, with and withoutthe help of the algorithms,

in the task draw a spiral, e

2. The relation between the number of erroneous

clicks, with and without the help of the algo-

rithms, during the click and goal task, e

Table 1: Results of the experiments.

Patient e

1 20 % 44 %

2 33 % 100 %

3 30 % 28 %

4 50 % 33 %

Table 1 summarizes the results obtained in the

data analysis. The results show that all patients im-

proved their performance using the algorithm. In the

TREMOR CHARACTERIZATION - Algorithms for the Study of Tremor Time Series

359

Figure 4: Results of a patient performing the task of draw-

ing a spiral.

case of the draw a espiral task, the mean reduction in

the error during the realization of the task was in order

of 33,3%. This is a sign of a improvement of the pa-

tient ability in tracking a shape in the screen. The pa-

tients also presented a mean reduction of 52 % in the

number of erroneous clicks during the execution of

the goal and click task. These results indicates a con-

sistent improvement in the ability of the patient in the

execution of the tasks, see Figure 4. During the trials

it was noticed that feedback of a smooth movement

has a positive impact. Two patients spontaneously re-

lated that they felt a decrease in the amplitude of their

tremorous movement.

6 CONCLUSIONS

This paper summarizes the work developed by the au-

thors in the study of tremor time series. First, it in-

troduces a novel technique for the study of tremor.

The main advantage of this technique it that it allows

an automatic estimate of the tremulous movement for

different pathologies. The technique presented is a

high-resolution technique that solves most of limita-

tions of the Fourier Analysis (the standard technique

to the study of tremor time series). This technique

provides, in a time-frequency-energy plot, a clear vi-

sualization of local activities of tremor energy over

the time.

The technique was used for the study of tremorous

movement in joints of the upper limb. This study

generates some conclusions about tremor behaviour

in upper limb.

Furthermore, an algorithm able to estimated in

real-time the voluntary and the tremorous movement

was presented. This algorithm was validated in two

contexts with successful results. The algorithm in-

troduced presents a learning behavior that adapts to

personal characteristics of each user. This algorithm

was implemented in a novel device able to ﬁlter

tremorous movement from a mouse cursor before it

reaches computer interface. The device was success-

fully tested with patients. The results of the experi-

ments showed an improvement of the patient ability

in tracking a shape in the screen and a consistent im-

provement in the ability of the patient in the accom-

plishment of tasks, for instance, the number of erro-

neous clicks was reduced in 52%.

REFERENCES

Anouti, A. and Koller, W. (1998). Tremor disorders: di-

agnosis and management. The Western Journal of

Medicine, 162(6):523–530.

Bar-Shalom, Y. and Li, X. (1998). Estimation and Tracking:

Principles, Techniques, and Software. Artech House

Publishers.

Elble, R. and Koller, W. (1990). Tremor. The Johns Hopkins

University Press.

Fahn, S., Tolosa, E., and Marin, C. (1998). Clinical rat-

ing scale for tremor. In J. Jankovic, E. T., editor,

Parkinson’s disease and movement disorders. Urban

& Schwarzenberg, Baltimore.

Gao, J. B. and Wen-wen, T. (2002). Pathological tremors

as diffusional processes. Biological Cybernetics,

86:263–270.

Riviere, C. (1995). Adaptive suppression of tremor for im-

proved human-machine control. PhD thesis, Johns

Hopkins University.

Rocon, E., Andrade, A., J.L.Pons, Kyberd, P., and Nasuto,

S. (2006). Empirical mode decomposition: a novel

technique for the study of tremor time series. Med Bio

Eng Comput, 44:569–582.

Rocon, E., Belda-Lois, J., Ruiz, A., Manto, M., Moreno,

J., and J.L.Pons (2007). Design and validation of a re-

habilitation robotic exoskeleton for tremor assessment

and suppression. IEEE Transactions on Neural Sys-

tems and Rehabilitation Engineering, 15(3):367–378.

Rocon, E., Belda-Lois, J., Sanchez-Lacuesta, J., and

J.L.Pons (2004). Pathological tremor management:

Modelling,compensatory technology and evaluation.

Technology and Disability, 16:3–18.

Timmer, J., Haubler, S., Lauk, M., and Lucking, C. (2000).

Pathological tremors: Deterministic chaos or nonlin-

ear stochastic oscillators? Biological Cybernetics,

78:349–357.

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

360