978-1-4244-9352-4/11/$26.00 ©2011 IEEE 693

2011 4th International Conference on Biomedical Engineering and Informatics (BMEI)

Comparison of methods for tremor frequency analysis for patients with Parkinson’s disease

K.Niazmand, A. Kalaras, H. Dai, T.C. Lueth

Dept. of Micro Technology and Medical Device Technology

Technische Universitaet Muenchen, Garching, Germany

Abstract — Tremor is described as involuntary rhythmic oscillations of one or more body parts. It is a symptom of Parkinson’s disease (PD). The severity of tremor is based on its frequency. Using acceleration sensors, one can detect tremor of the limbs or other body parts. Data from sensors can be processed using spectral analysis. The most common methods for the investigation of tremor are Fast Fourier Transformation (FFT), Short Time Fourier Transform (STFT) and power spectral density analysis (PSD). In this paper we investigate these methods together with peak detection and pattern recognition methods. We compare the various approaches with each other with respect to frequency. A visual frequency analysis using an optical tracking system is used as a reference. The experiments were performed with a measuring glove with integrated acceleration sensors on the middle finger and thumb joint. We examined the accuracy of the various methods for the analysis of tremor in PD patients. Keywords – frequency analysis; tremor; peak detection; pattern recognition; Fast Fourier Transformation (FFT); Short Time Fourier Transform (STFT); power spectral density (PSD);

I. INTRODUCTION Parkinson’s disease (PD) is a neurodegenerative disorder

causing progressive loss of dopamine-producing brain cells. The loss of dopamine in the midbrain often induces tremor of one or more body parts. Tremor is an involuntary rhythmic oscillation and the main symptom of PD.

The predominant method for evaluating the status of tremor is the Unified Parkinson’s Disease Rating Scale (UPDRS) [1]. Rating results can vary from neurologist to neurologist with limited reproducibility [2]. A quantifiable and objective data acquisition providing information for the tremor could improve diagnosis and therapy. The main parameter, which characterizes the tremor, is its frequency. On the basis of the frequency the evaluation of tremor is possible.

Using accelerometers to detect specific movements and activities is a well-known approach [3]. The sensors are either fixed with bandages to the limbs [4] or they are integrated into clothing [5, 6]. The sensors deliver acceleration values several times per second. A change of these values is the effect of a movement [5]. By means of different mathematical methods, movement and activity as well as the frequency of changes in the movement can be detected and displayed.

II. STATE OF THE ART There are many systems which assess the severity of

tremor taken based on its spectrum. The main methods for the calculation of frequency are the Fast Fourier Transformation (FFT), the Short Time Fourier Transform (STFT) [7, 8] or wavelet Transform [9,10].

Fourier analysis breaks down a signal into sinusoids of different frequencies. It is a mathematical technique for transforming a signal from the time domain to the frequency domain. The drawback of the Fourier transform is that all time information is lost after the transformation [11]. When looking at the Fourier transform of a signal, it is impossible to tell when a particular event took place. Tremor signals contain numerous non-stationary or transitory characteristics such as drift, trends, and abrupt changes. These characteristics are often the most important part of a signal like tremor, and Fourier analysis is not suited to detecting them.

Tremor is defined as an oscillatory, involuntary motion. Because of its oscillatory characteristic, tremor is suited for spectral analysis. The idea is to calculate the power spectral density function which indicates the signal power at different frequencies across the spectrum. The dominant frequency of tremor is evident from a visible peak in the power spectral density, while the average tremor amplitude can be determined from the area under the peak [12, 13].

For tremor analysis specific FFT-based power estimation techniques are often used [14, 15, 16, and 17]. In [14] an FFT-based power estimation of the signal in a specific frequency area is calculated rather than the tremor frequency. The acceleration data are filtered with a high pass filter with a cut-off frequency of 3Hz and the signal power is calculated for frequencies greater than 3Hz. In [17] power spectral density vs. frequency is estimated by the “Welch” method of averaging periodograms (Fast Fourier Transform length 128, Kaiser windowed segments overlapping 50%). The dominant power density of signal is not necessarily the frequency of tremor; it can also be the power of noise. In [15] two FFT-based spectral estimation techniques are used: the “Blackman-Tukey” method and the periodogram method. These methods have a limited performance for finite data records. In circumstances where only short data records are available, it may be difficult to manage the bias-variance trade-off satisfactorily and produce spectral estimates with an acceptable resolution. Moreover the windowing method in FFT imposes a spectral leakage. It is a leakage of power from

This work has received funding from the Bavarian Research Foundation (BFS) under contract number AZ-780-07. The views expressed here are thoseof the authors only. The BFS is not liable for any use that may be made of the information contained therein.

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the spectral peaks of the desired spectrum to surrounding frequencies.

On the other hand, the Short-Time Fourier Transform (STFT) analyzes only a small section of the signal at a time (windowing the signal). The STFT represents a signal as a two-dimensional function of time and frequency. The STFT is a compromise between the time- and frequency-based views of a signal. It provides some information about both when and at what frequencies a signal event occurs. Thus, one can obtain this information with only limited precision. That precision is determined by the size of the window. In [7] acceleration sensors are fastened with bands to the skin of PD patients. Time signals are transformed into time frequency signals. For each data point a STFT is calculated using an interval of 2 seconds counting backwards from this point, whereby the interval length determines frequency steps of 0.5Hz in the spectrum. The main drawback is that if one chooses a particular size for the time window, then that window is the same for all frequencies. But the tremor signal requires a more flexible approach, i.e., a variation of the window size is desirable to obtain either better time or frequency resolution. By contrast the wavelet transform window is scaled. Thus, the same resolution is obtained for multiple frequency bands. A summary of the state of the art is shown in table I.

So far there is no method to estimate the frequency of the tremor (stochastic signal) over a specific, either short or long time period. The accuracy of these methods in a discrete signal is strongly dependent on the sampling frequency. The higher the signal is sampled the more accurate the frequency analysis. At a low sampling frequency, however, these methods are not accurate because the fundamental frequency in the waveform is not dominant as the noise frequency or frequency of body vibrations. Moreover, these methods are generally unsuitable for the analysis of stochastic signals. The estimation of the frequency could help to evaluate the severity of tremor.

III. TASK AND APPROACH A new method is needed to estimate the tremor

frequency using acceleration sensors. This method should not be based on FFT or STFT because of the drawbacks previously described. The new method should also calculate the frequency over brief periods of time and should deliver good results even at low sampling rates. The accuracy of such a method should be demonstrated. Using a reference measurement with alternative methods of tremor frequency analysis (e.g. optical measurement), one can compare and evaluate all methods.

In [18] we have described the function and set-up of the “MiMed-Glove”, a textile integrated measurement device, which identifies clearly movement disorders such as tremor, bradykinesia and rigidity from recorded sensor data. The glove integrates acceleration sensors and a unit for data acquisition and processing. The glove can be washed in a washing machine. Data acquisition is provided by wireless communication. This measuring system is used for recording of transaction data.

IV. CONCEPT DESCRIPTION We developed and evaluated two methods for the estimation of tremor frequency.

TABLE I. SUMMARY OF THE STATE OF THE ART

The first method is based on peak detection and the second on pattern recognition (correlation of tremor signal with sinus signals).

A. Peak detection: In [19] we developed a sensor based garment to detect and

classify the tremor. The acceleration values (X[k]) from eight sensors integrated in a garment are captured with a frequency of 20Hz. The relative accelerations X[k]’ based on the absolute acceleration X[k] are calculated as follows (equ. 1-3):

(1) ∑ (2) , , (3)

where gm is the acceleration of gravity and NTHLD refers to the maximum noise level caused by the electronics.

The frequency of the tremor can be the number of peaks of relative acceleration per second. We developed two techniques for the detection of peaks. The first one – “offline method” - detects the peaks and calculates the frequency if the sensor values are available. This means that we need to first capture the sensor values and afterwards apply the algorithm. The second one –“online method”- detects the peaks and calculates the frequency in real time with a delay of 0.05s (period between sensor values acquisition=1/20Hz).

1) Offline methode The relative accelerations of a movement are calculated at

first. The time points of the maximum values of the relative accelerations are detected. Therefore, an upper (form. 1) and a lower threshold (form. 2, red lines in fig. 1) are calculated.

Figure 1. Calculation of the frequency

Ref. Spectral Analysis

Method Power vs. Frequency

Estimation [7] Short Time Fourier Transform Maximum peak in STFT [8] Short Time Fourier Transform STFT-Spectrogram [9] wavelet Transform -

[10] wavelet Transform -

[12, 13] Fast Fourier Transformation Power Spectral Density [14] Fast Fourier Transformation -

[15] Fast Fourier Transformation Blackman-Tukey, Periodogram

[16] Fast Fourier Transformation FFT squared,Statistical methods [17] Fast Fourier Transformation Welch method

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The maximum, which is obtained during this process, is defined as a signal peak. For the calculation of the upper and lower threshold, the mean value (equ. 6) and the standard deviation (equ. 7) of the relative accelerations are taken into account, in order to detect all the peaks of the signal, even if the peaks have different amplitudes. (4) (5) ∑ (6)

∑ ² (7)

where Xi(+) and Xi

(-) refers to the ith positive and negative acceleration and n+ and n- the number of the positive and negative values.

When the time points of the peaks are detected, the distances between these points are calculated (ΔΤ1, ΔΤ2 ...). The frequency of the signal is calculated as follows (equ. 8):

·∑ ∆ (8)

Where ΔΤ is the distance between the points of time of the peaks and N is the number of the distances.

2) Online methode This method is a modification of the first technique. The

purpose is to calculate the frequency in real time. The upper and lower thresholds are calculated over a period of 2s. Thus this algorithm needs a buffer time of 2s at the beginning of a measurement. During this time the frequency cannot be estimated. After this time period the frequency is calculated each time when the sensors receive a new value. Thus, the frequency is calculated 20 times per second. The acceleration values of the last 2s are taken into account for the peak detection and calculation of the frequency each time.

B. Pattern recognition: In this technique the tremor signals are compared with

periodical sample signals with a known frequency. These signals are sinusoidal signals with time span of two seconds and frequencies from 0 to 7Hz with a step of 0.1Hz. Each time when the sensors receive a new value the relative accelerations of the last two seconds are correlated with the sinusoidal signals. The frequency of the signal equates with the frequency of the sinusoidal signal with the maximal correlation.

In fig. 2 we can see a tremor signal (red line) and the most suitable sinusoidal signal (blue dashed line) from 71 sample signals. The signal has a frequency of 6Hz. The tremor signal is not a periodical signal. Using this method we will try to find repetitions in the tremor signal and its frequency.

Figure 2. Tremor signal and the most suitable sinus signal

V. EVALUATION OF PEAK DETECTION AND PATTERN RECOGNITION METHODS

A. Materials and Methods: The “smart glove”, described in [18], was used for our

experiments as a test instrument. The glove includes inter alia two integrated triaxial acceleration sensors fixed on the middle finger and on the dorsal wrist. The data of the 3D acceleration sensors were recorded with a sampling rate of 20 Hz.

B. Peak Detection Experiment: 1) Setup:

To assess the reliability of the two techniques of peak detection, 3 patients with PD executed the two tasks according to UPDRS. First, hands and arms were kept at rest, afterwards stretched out (fig. 3). During the first task the “rest tremor” can be assessed, while during the second task the “postural tremor” of the hand is obtained.

Using the first technique the system calculated the frequency over a time of 15s for each executed task. The frequencies were compared with the estimated frequencies. The estimated frequencies were calculated using an optical measurement of the signal. We detected visually the duration between the peaks and estimated the frequency from this.

To assess the reliability of the second technique, we calculated the frequencies with the second technique and determined the average of the frequency every 5 seconds during the execution of the tasks for rest and postural tremor.

Figure 3. Two tasks according to UPDRS [18]

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At the end we compared the average meaof the system with the estimated average freqsame period.

2) Results: The average deviation of measured freq

estimated frequency according to the offline 0.34Hz. The average deviation of measaccording to online method from the estima0.44±0.51Hz. The large deviation comes intonon-repeatable processes.

C. Pattern recognition Experiment: 1) Setup: For the evaluation of this method we tdata from a patient with PD for 30s andfrequency of the signal for intervals of 2sestimated the frequency of signal repetitions aa low frequency (a) and a high frequencydisplayed. 2) Results:

The average deviation of measured frequepattern recognition from the estimated0.62±0.76Hz.

VI. EVALUATION OF COMPARISON BEDIFFERENT METHODS

In order to compare the different methods(PD), pattern recognition (PR), Fast Fourier(FFT) and power spectral density (PSD)), wfollowing experiment.

A. Materials and Methods: A measurement was performed on a subje

for 90 seconds. The subject (fig. 5.1) wore (fig. 5.2) during the measurement.

Figure 4. A) Low frequency and b) High frequ

a)

b)

asured frequency quency during the

quency from the method is 0.31±

sured frequency ated frequency is o because of the

took acceleration d calculated the s. After that we as above. In fig.4 y (b) signal are

ency according to d frequency is

ETWEEN THE

s (peak detection r Transformation

we performed the

ect (28 years old) the smart glove

uency signal

Figure 5. Experiment setup: subject (1), middle finger (3) and on the dorsal wrist (camera (6).

The forearm and middle fingerOnly one movement around thOscillating movements with lofrequencies each for 10 seconds afive seconds of rest with a highsimulated. We fixed additionally asmart glove and measured with a Ithe position of the glove duringcalculated visually the frequenciesThe distance to the IR-Marker is and the frequency of movememanually. These frequencies are thfrequencies. Additionally, we calcuvalues the frequencies of the signduring 90 seconds. The measured methods were compared with the ta

B. Results: In table II the difference is p

frequencies from the four methfrequencies. We can see that theprecise than the other three methoand target frequencies are displayed

VII. CONCL

Frequency analysis of tremor iused to diagnose and monitor the p(Fast Fourier transformation), STtransform) and PSD (power spectrused for spectral analysis of tremmotion is a stochastic signal resulvalues, the Fourier transformation itwo new methods were presentefrequency.

smart glove (2), sensor on the

(4), IR-Marker (5) and IR- stereo

r of the subject was fixed. he forearm was allowed. ow, medium and high

are first low and then after h intensity movement was a marker (fig. 5.5) on the IR- stereo camera (fig. 5.6) g the tremor activity. We s of the position changes. measured with the camera

ent change is calculated he target simulated tremor

ulated from the acceleration nal with the four methods

frequencies from the four rget frequencies.

resented for the measured hods from the estimated e peak detection is more ds. In fig. 6 the calculated

d from 50 to 90s.

LUSION n patients with PD can be progress of treatment. FFT TFT (short time Fourier ral density) are most often mor. As the frequency of lting from the acceleration s not reliable. In this work,

ed for the calculation of

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TABLE II. EVALUATION OF THE 4 METHODS

The first method calculates the frequency based on the number of detected peaks in the motion signal. The second method correlates the motion signal with 71 pre-defined pattern signals of different frequencies. The frequency of the pattern signal with the highest correlation corresponds to the signal frequency. These methods were compared and evaluated with common methods of the state of art with the help of an experiment. The activity signal is equivalent to the body movement. The sensor that detects the movement sits on the skin surface. With each change of movement caused several oscillations that are dependent on the position of the sensor and the skin elasticity. These oscillations are high frequency and are superimposed on the signal activity. These oscillations by a PD patient can hardly distinguished from the actual activity and distort the analysis. The frequency change can be detected very well by all methods but the peak-detection method has the highest correlation with the estimated frequency of tremor with a deviation of 1 ± 0.88Hz. The accuracy of peak detection method can be improved through better threshold value calculation. The methods should be evaluated and improved in further studies in a clinical setting. With a larger number of participants the peak detection should be adapted and tested for various applications (e.g. intra operative diagnosis by deep brain stimulation). In pattern recognition the recognition should be improved by means of adjusting the pattern signal to the shape of the tremor signal. The effect of sampling frequency on the accuracy of frequency calculation should also be investigated.

VIII. ACKNOWLEDGMENT We thank the patients and physician of the Schoen Klinik

Muenchen Schwabing, especially Dr. U. M. Fietzek, for their support and cooperation. Within the research consortium of the Bavarian Research Foundation (BFS) „FitForAge“ a team of scientists and engineers works together with 25 industrial partners on the development of products and services for the aging society.

Figure 6. Comparison between the PD, PR, FFT and PSD

Eventually not only elderly people but also all social groups should profit from these solutions.

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Method Difference from target frequency [Hz]

Peak Detection 1±0.88 Pattern Recognition 2.39±1.92 Power Spectral Density 2.97±2.38 Fast Fourier Transformation 2.29±1.94