INVESTIGATION OF CHANGES IN KINETIC TREMOR

THROUGH ANALYSIS OF HAND-DRAWING MOVEMENTS

Differences between Physiological and Essential Tremors

Maria Fernanda S. Almeida, Guilherme L. Cavalheiro, Adriano O. Andrade

Biomedical Engineering Laboratory, Faculty of Electrical Engineering, Federal University of Uberlândia, Campus Santa

Mônica, Bloco 1E, Av. João Naves de Ávila, 2121, Uberlândia, Minas Gerais, 38.408-100, Brazil

Daniel A. Furtado, Adriano A. Pereira

Biomedical Engineering Laboratory, Faculty of Electrical Engineering

Federal University of Uberlândia, Uberlândia, Brazil.

Keywords: Physiological tremor, Essential tremor, Tremor detection, Tremor analysis, Archimedes' spiral.

Abstract: Tremor is the most common movement disorder characterized by repetitive and stereotyped movements.

Tremor can be classified in many ways, depending on its phenomenology, frequency and location. The data

collection conducted under kinetic conditions and while performing a voluntary movement highlights the

kinetic tremor. The analysis of hand-drawing movements is commonly used in the evaluation of patients

with tremor. In this study, a number of features extracted from tremor activity, obtained from digitized

drawings of Archimedes’ spirals, were analysed. The analyses followed the sequence bellow: 1 –

Linearization of the spiral of Archimedes; 2 – Estimate of tremor activity; 3 – Data pre-processing; and 4 –

Feature extraction from the tremor activity. The statistical analysis of the extracted features was able to

prove the differences between physiological and essential tremors collected under kinetic conditions.

1 INTRODUCTION

Tremor is an involuntary, rhythmic, oscillatory

movement of a body part that can be classified in

many ways, depending on is aetiology,

phenomenology, frequency and location. (Mansur et

al., 2007, Smaga, 2003) The movement caused by

tremor can be associated to factors such as

neurological disorders and natural processes. (De

Lima et al., 2006, Deuschl et al., 1995) The former

is called pathological tremor whereas the latter is

often referred as physiological tremor. (Almeida et

al., 2010) The physiological tremor occurs normally

in healthy individuals and, generally, it cannot be

observed by the naked eye. (Almeida et al., 2010)

An example of pathological tremor is the

essential tremor. This type of tremor is a visible

postural tremor of hands and forearms that may

include kinetic component. (Smaga, 2003) Essential

tremor is the most common movement disorder in

the world.

In both essential and physiological tremors, the

amplitude of tremor increases with stress, fatigue,

certain medications and voluntary activities. (Smaga,

2003) Although this, both types of tremor presents a

kinetic component that can be accessed through the

analysis of hand-drawing movements.

Hand-drawing patterns are commonly assessed

by means of visual rating scales. (Almeida et al.,

2010, Louis et al., 1998) However, scales provide

only crude subjective estimates of tremor amplitude.

The use of digitizing tablets is common and provides

the possibility of tremor activity detection under

kinetic conditions. (Almeida et al., 2010) Although

this, the use of this method for tremor detection is

simply, versatile, non-invasive and can provide an

electronically measure of tremor, reducing the

subjectivity and limitation of some methods based

on visual scales. (Almeida et al., 2010)

The digitizing tablet is able to inform the

coordinates (x and y) of the tip of the pen on its

surface while the subjects perform the drawing. In

393

S. Almeida M., L. Cavalheiro G., O. Andrade A., A. Furtado D. and A. Pereira A..

INVESTIGATION OF CHANGES IN KINETIC TREMOR THROUGH ANALYSIS OF HAND-DRAWING MOVEMENTS - Differences between Physiologi-

cal and Essential Tremors.

DOI: 10.5220/0003121703930398

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 393-398

ISBN: 978-989-8425-35-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

this study, a standard drawing pattern was fixed on

the surface of the device and the subjects were asked

to follow it. The selected drawing pattern is the

spiral of Archimedes, used in other studies for being

smooth and easily understood by subjects.

There are many studies concerning the

employment of digitizing tablets for the

quantification of physiological and pathological

tremors. (Elble et al., 1996, Feys et al., 2007, Liu et

al., 2005, Mergl et al., 1999) However, no study

focusing in the use of this device for investigation of

kinetic changes between physiological and essential

tremor was found in our literature survey.

In order to contribute to the understanding of

changes in kinetic tremor between physiological and

essential tremors, this study proposes to quantify

tremor by means of the analysis of digitized hand-

draw drawings of a clinically healthy individual and

an individual diagnosed with essential tremor.

2 MATERIALS AND METHODS

Two subjects participated in our experiments. The

first subject did not present clinical evidences of

suffering from any neurological disorder. The

second subject was diagnosed with essential tremor.

Prior to data collection the subjects signed a

Consent Form approved by the Ethical Committee of

the Federal University of Uberlândia, Brazil.

The subjects were asked to sit in a comfortable

chair with their feet flat on the floor and with their

back straight. The digitizing tablet, shown in Figure

1, was placed on a table properly positioned in front

of the subjects.

Figure 1: Digitizing tablet with the standard drawing

pattern fixed on its surface. In this study, the selected

drawing pattern is the spiral of Archimedes.

After verbal and written explanation about the

exam the subjects were asked to draw two samples

of a Spiral of Archimedes with their dominant hand.

The arms of the subjects were not supported during

the execution of the task. The first sample was

collected with the subject drawing the spiral from its

centre to its extremity (outgoing spiral - OS),

whereas for the second sample the subject drew the

spiral from its extremity to its centre (ingoing spiral

- IS). This procedure was repeated three times for

each subject. The subjects were asked to draw the

spiral at their natural speed. The collected spirals

were digitized at 64 Hz through a digitizing tablet

(Trust, model TB-4200) with resolution of 120

lines/mm.

2.1 Data Analysis

The analysis followed, for each data sample, the

sequence of steps below:

 Linearization of the spiral;

 Estimate of the tremor activity;

 Data pre-processing;

 Feature extraction from the tremor activity.

2.1.1 Linearization of the Spiral

The spiral of Archimedes is a geometrical shape that

has a uniform distance between its turns equal to

2πb. This kind of spiral can be represented by Eq.

(1) in polar coordinates, where r is the radius, θ the

angle, a and b are constants.

=+

(1)

The step of linearization consists in representing

the original  and  coordinates of the spiral in

terms of radius () and angle () as shown from Eqs.

(2) to (4).(Pullman, 1998) The linearization of a

perfect spiral results in a straight line as shown in

Eq. (5) and depicted in Figure 2, where  is the

slope of the straight line.

=sin()

(2)

 =  cos ()

(3)

=







+



(4)

=

(5)

2.1.2 Estimate of the Tremor Activity

The estimate of the tremor activity  is carried out

by Eq. (6), where 



is the ideal spiral (template)

and 



is the spiral drawn by the subject.

=



−



(6)

Figure 3A shows spirals obtained from the

subjects that participated on the study. In the figures

the template spiral and its linearized version (Figure

3B) are in black, whereas the actual spiral and its

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

394

linearization are in red. The tremor activity  (Figure

3C) is also presented for each case. Note that  is a

random time-series and, therefore, it is possible to

employ standard techniques for time-series analysis

in order to extract information from it.

Figure 2: Illustration of the process of linearization of an

ideal spiral of Archimedes. The spiral in the left panel is

converted into a straight line in polar coordinates, which is

shown in the right panel. This transformation eases the

process of tremor estimate from hand-drawn spirals.

Figure 3: Example of the application of the process of

linearization for an ideal spiral and two typical patterns

obtained from hand-drawn spirals of normal subject and

subject diagnosed with essential tremor. In (A) the spiral

drawn by each subject is compared against the ideal spiral.

In (B) the system coordinates are converted into polar

coordinates and the results of each subject are contrasted

to the ideal straight line, which represents the spiral in

polar coordinates. In (C) the tremor activity obtained for

each subject is shown. This activity is obtained by

subtracting the ideal spiral from the hand-drawn spiral in

polar coordinates.

2.1.3 Data Pre-processing

The tremor activity may be composed of: (i) the

inherent noise of the digitizing tablet, which is a

low-frequency noise (<0.1 Hz) as suggested by the

manufacturer; (ii) voluntary movement whose

energy is mostly limited to frequencies below 1 Hz;

(Feys et al., 2007, Liu et al., 2005, Ulmanová et al.,

2007) (iii) and the specific-task physiological

tremor which is characterized by involuntary

movements and energy mostly between 4 Hz and 10

Hz or the essential tremor with energy between 4 Hz

and 12 Hz. (Elble et al., 1996, Miralles et al., 2006,

Elble et al., 1990, Pullman, 1998, Smaga, 2003,

Bhagwath, 2001)

Therefore, we applied a linear filter in order to

obtain the tremor activity signals for analysis. This

activity was filtered by using a fourth-order digital

band-pass Butterworth filter. As the frequency

response of the filter is not ideal we set its lower and

upper cutoff frequencies to 2.5 Hz and 20 Hz with

the aim of preserving the bandwidth of interest. This

bandwidth was carefully defined to capture the full

tremor component in task-specific tremor, typically

in the frequency range between 4 and 12 Hz (Elble

et al., 1996, Miralles et al., 2006, Elble et al., 1990,

Pullman, 1998, Smaga, 2003, Bhagwath, 2001), and

also to avoid major influence of voluntary

movements whose energy is normally concentrated

in frequencies below 1 Hz. (Feys et al., 2007, Liu et

al., 2005, Ulmanová et al., 2007)

Frequency analysis (energy estimate) was

performed on the filtered signal by using the

Welch’s method with a 32 data point Hanning

window. Figure 4 illustrates the signal before and

after filtering. Figures 4a and 4b show, respectively,

a signal collected from the normal subject and the

subject diagnosed with essential tremor before

filtering. Figures 4c and 4d are filtered versions of

the signals shown in Figures 4a and 4b, respectively.

The waveform depicted in Figure 4d shows an

increase in amplitude when compared to the one in

Figure 4c.

2.1.4 Feature Extraction from the Tremor

Activity

In order to assess and quantify the tremor activity a

number of traditional features were used. Each

feature is described below:

 Frequency domain features: from the power

spectrum of the signal, obtained from the

Fourier Transform, the following features were

estimated: mean frequency, peak frequency,

frequency of 50% and frequency of 80%.

 Detrended fluctuation analysis (DFA): is a tool

for analysis of random signals that estimates the

 exponent which may characterize the nature

of time-series. (Delignieres D, 2003, Norris et

al., 2005)

INVESTIGATION OF CHANGES IN KINETIC TREMOR THROUGH ANALYSIS OF HAND-DRAWING

MOVEMENTS - Differences between Physiological and Essential Tremors

395

Figure 4: Illustration of the effect of filtering applied to

collected signals from normal subject (a, c) and subject

diagnosed with essential tremor (b, d). The non-filtered

signals are depicted in (a, b) whereas their filtered versions

are depicted in (c, d), respectively.

 Mean speed: is the average of the instantaneous

velocity.

 Total displacement: is calculated by summing

up all the distances from two consecutive

samples.

 Root mean square: also known as quadratic

mean, the Root Mean Square (RMS) is a

statistical measure of the magnitude of a

varying quantity.

 Approximate entropy: is a tool used to quantify

the regularity of a signal.

 First order smoothness: This tool can

characterize imperfections in spirals drawn by

the subjects. The calculation of this feature is

based on the overall deviation of the spiral, in

such a way that an ideal spiral results in a value

of the first order smoothness equal to zero.

(Pullman, 1998)

 Second order smoothness: the second order

smoothness can be defined as the rate of change

of first order smoothness.

 Residual: this feature reflects the total distance

between the spiral after the process of

linearization and a line of best fit on the radius

vs. angle graph. The larger this value is the

more spiral changes its shape in an irregular

way. (Pullman, 1998)

 Zero crossing rate: is a measure of irregularity

of the signal and shows how frequently values

cross their own  value.

3 RESULTS

Table 1 shows the values of extracted features for

two data collection protocols, i.e., Ingoing spiral (IS)

and Outgoing spiral (OS). The analysis of variance

(ANOVA) was applied for each protocol and

feature. A probability value (p-value) less than 0.05

( < 0.05) was considered as a threshold for

significance analysis. A 95% confidence bound were

used on the value of the statistic. Features that

yielded significant differences between the subjects

are highlighted with an asterisk (*) in Table 1.

Table 1: Mean values obtained for each feature and

protocol (ingoing and OS).

Feature

Physiological Tremor Essential Tremor

Outgoing

Spiral

Ingoing

Spiral

Outgoing

Spiral

Ingoing

Spiral

Frequency of 50% *

4.417 4.417 5.750 5.667

Frequency of 80%

6.833 7.083 6.750 6.667

Mean Frequency *

4.818 4.883 5.711 5.660

Peak Frequency *

3.167 3.250 5.750 5.667

Total Displacement *

0.064 0.071 1.339 1.219

Standard Deviation *

0.007 0.007 0.165 0.163

Approximate Entropy *

0.351 0.329 0.282 0.286

First Order Smoothness

10.099 13.751 16.043 17.534

DFA *

1.661 1.652 2.024 2.030

Mean

-4.9x10

-6

-4.1x10

-5

1.2x10

-4

5.9x10

-5

Residual *

0.069 0.066 0.236 0.257

RMS Mean *

0.007 0.007 0.165 0.163

Second Order Smoothness

27.398 38.438 37.647 40.271

Variance *

4.5x10

-5

5.4x10

-5

0.027 0.027

Mean Speed *

0.175 0.195 4.077 4.055

Zero Crossing Rate

488.667 450.667 587.333 462.667

4 DISCUSSION

The linearization of the espiral of Arquimedes was

performed as the first step in the data analysis.

Although the linearization step does not offer any

new information, it is extremely useful in the

analysis of the spiral, as it is responsible for

replacing the coordinates  and  by new ones,

giving rise to a linear relationship between them.

(Pullman, 1998)

Through this transformation, the mathematical

computational operations become easier and faster,

making it possible to analyze crucial aspects of the

drawing of the spiral. When comparing the straight

line obtained by means of the radius-angular

transformation of the ideal spiral with that generated

from an actual spiral, drawn by a subject, it is

possible to detect irregularities. (Pullman, 1998)

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

396

After the linearization step, a linear filter was

applied in order to obtain the tremor activity signals

for analysis. The definition of the linear filter’s

bandwidth (2.5 Hz and 20 Hz) was an important step

to preserve the bandwidth of interest and to avoid

major influence of voluntary movements, whose

energy is normally concentrated in frequencies

below 1 Hz. (Feys et al., 2007, Liu et al., 2005,

Ulmanová et al., 2007)

According to Elble et al.,(Elble et al., 1996) the

acts of writing and drawing constrict the range of

tremor frequencies. Furthermore, the frequency of

physiological tremor quoted in several studies (8-12

Hz) refers to tremor signals collected by

accelerometry. (Timmer et al., 1998, Raethjen et al.,

2000, Morrison et al., 2006) Moreover, the

frequency of essential tremor may suffer a

constriction either, since most studies face this type

of tremor as essentially postural. In both cases, the

data collection made under a postural tremor

protocol will present differences in frequency when

compared to kinetic paradigm.

From the analysis of Table 1 is possible to

conclude that the features that provided a significant

difference between the two individuals in analysis,

for the Outgoing Spiral (OS) and Ingoing Spiral (IS)

protocols, are: frequency of 50%, mean frequency,

peak frequency, total displacement, standard

deviation, DFA, approximate entropy, residual,

RMS mean, variance and mean speed.

The values of RMS, variance and standard

deviation show that the essential tremor activity had

larger displacement amplitude compared to the

physiological tremor activity. As in probability

theory the variance of a random variable is a

measure of statistical dispersion and the results show

that the essential tremor activity presented a larger

value of variance, it is possible to conclude that the

distribution of the essential tremor activity is more

spread out than that of the physiological tremor

activity.

The mean speed values were smaller for the

physiological tremor signals and, consequently, the

total displacement of the tremor activity was larger

in the essential tremor activity. Additionally,

through the analysis of the DFA and Approximate

Entropy, we can observe a change in the randomness

of the signal, i.e., the essential tremor activity has

higher predictability than that obtained for the

physiological tremor activity as suggested by the

increase of the DFA coefficients and the reduction

of the Entropy values.

The analysis of the features First Order

Smoothness and Second Order Smoothness in Table

1 allow us to conclude that in general subjects

presented more difficulty to draw the spiral towards

its centre. This is based on the fact that these

features can characterize imperfections in the traces

made by subjects, i.e., the larger their amplitudes the

more imperfect the trace is. The results depicted in

Table 1 support this assumption by showing an

increase in the feature amplitudes.

The main limitation of the obtained results is

with regard to the number of studied subjects.

However, the results show that is possible to

discriminate physiological and essential tremors

through the analysis of hand-draw movements, i.e.,

under kinetic conditions. Despite this limitation, this

research introduced a way of analyzing kinetic

tremor activity for the characterization of

physiological and essential tremors.

5 CONCLUSIONS

In this study, different from other researches, we

addressed the issues of quantifying physiological

and essential tremors under kinetic conditions. For

this, we investigated the tremor activity obtained

from a normal subject and a subject diagnosed with

essential tremor.

The study showed that digitizing tablets can be

used to make the evaluation of hand-drawing

movements. Moreover, the analysis of these

drawings makes possible the differentiation between

healthy subjects and that diagnosed with a type of

pathological tremor.

The analysis of physiological and essential

kinetic tremors of individuals may be an important

tool for the characterization of tremors. The results

obtained through this technique may be evaluated in

the context of the patient’s history and correlated

with neurological exams.

The early diagnosis of a pathological tremor can

lead to appropriate treatment, which can provide a

better condition of life for individuals.

The use of this method and paradigm may be an

important tool for the characterization of different

types of tremors.

ACKNOWLEDGEMENTS

The authors would like to thank the Brazilian

government for supporting this study (Project

PPSUS/FAPEMIG 2006 Nr. 3300/06).

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MOVEMENTS - Differences between Physiological and Essential Tremors

397

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