[001] Introduction to Parkinsons disease and other motor disorders.

5 Parkinson's disease (PD) and other neurological motor disorders (Dystonias, Dyskinesias, Huntington's disease, Essential Tremor. Multiple System Atrophy (MSA), etc), attacking principally the motor capacity of a person, affects worldwide more than 5 million persons, where the highest percentage is in the ageing population. The πsk of developing Parkinson's disease increases with age, and afflicted individuals are usually adults over 40. In io consequence, Parkinson's disease is a public problem of high relevance; a device that detects and evaluates the degree of this disease is desirable.

Parkinson's disease (PD) is a progressive degenerative disease of the central nervous system. Parkinson's disease occurs in all parts of the world.

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While the primary cause of Parkinson's disease is not known, it is characterized by degeneration of dopaminergic neurons of the substantia nigra. The substantia nigra is a portion of the low er brain, or brain stem, that helps control voluntary movements. The shortage of dopanine in the brain caused by the loss of these neurons is believed to cause the 20 observable disease symptoms.

Today the assessment is carried out by clinical signs which correct interpretation depends on the experience of the doctor doing the test, rendeπng this test highly subjective.

25 The shown method evaluates the existence and the degree of the motor capacity in an objective way, so its application to PD would help the diagnosis and the followιng-up of different treatments.

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[002] Introduction Rotational devices

Maintenances of rotational devices are normally subject to fixed time intervals but it would be convenient to have a method to detect on time when the efficiency is decreasing or the machine exhibits any problem showed as a deviation from its pure periodic movement

This method and apparatus gives an early warning that maintenance is needed The accelerometer is placed on the chassis and acceleration signal is acquired and analyzed on time, using the spectrum and the Hilbert Transform of the acceleration signal to evaluate the efficiency

[003] Apparatus description

The apparatus consists of two units

Unit 1 (Acquisition unit) Consists of an accelerometer, amplifier, A/D-converter with a micro processor and a Radio Frequency system (as for example Blue-tooth transmitter)

Unit 2 (Computer unit) Consists of a computer based system (such as a Personal Computer, Hand Held computer, Laptop ) containing a Radio Frequency system (such as a Blue-tooth receiver)

The computer unit will receive the acceleration signal acquired by the accelerometer sent by Unit 1 and will process the data using the described algorithm based on the Hilbert Transform

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According to figure 1 , the accelerometer (2), is attached to the hand or finger ( 1 ) of the subject for the study of Parkinson disease (PD) and on the chassis or rotor in the mechanical device The analogue signal is converted to a digital signal via an AD-converter (3) A microprocessor or other calculation unit executes the analysis of the recorded acceleration signal (4), which is then shown on a display (5) The acceleration signal is bandpass filtered (6). An Empeπcal Mode Decomposition (EMD) generate a seπes of intrinsic mode frequencies (IMF) which are Hilbert transformed (7) and a set of N parameters (8) are extracted for the calculation of the index ( 1 1) A spectral analysis (9) is earned out as well from which M parameters are extracted (10) The index is defined as a combination of both parameter set ( 1 1 )

[004] Subject movement tests

The test for Parkinson's disease and Effect site evaluation are carried out the following way The accelerometer in unit 1 is attached with a Velcro strap to the hand of the patient The patient is asked to perform circular like movements

The main and shared feature of all the movements is their intrinsic periodicity These movements, some of them accepted as a clinical criteria by the doctors as representative of Parkinson disease, are

(1 ) Tapping The patient moves alternatively the hand between two fix points

(2) Circular movement around the face (washing-face like) (3) Finger tapping The accelerometer is placed on the index finger while it is draws near and far from the thumb As picking up or leaving something with both fingers (4) Transversal finger movement from the nose The hand of the patient approaches and comes far from the nose alternatively

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(5) Hand trembling The patient must try to keep the hand still while the accelerometer is positioned

Independent of the application, unit 1 sends the acceleration of the movements trajectories to unit 2 via a radio link Unit 2 has a built in radio leceiver and a CPU to analyze the acceleration signal with the Hilbert transformation combined with the spectrum of the acceleration subsequently calculate the movement index (MI) The MI is a unitless scale ranging from 0 to 100 achieved by combining a set of sub-parameters of the Hilbert Transform and the power spectrum

[005] Brief Description of the algorithm

The algorithm, applied to the acceleration signal, consists of the following steps, Figure 1

( 1 ) The acceleration signal is acquired with the apparatus described before

(2) The spectrum of the acceleration signal is calculated Via a parametnc method (as for example Autoregressive analysis ) or non parametric method ( as for example the FFT)

(3) The acceleration signal is filtered through a band pass filter The empirical mode decomposition (EMD), producing a collection of intrinsic mode functions (IMF), to which the Hilbert Transform is applied

(4) A set of parameters, described below, are extracted from the spectrum analysis and the Hilbert Transform

(5) All parameters have significant information about the recorded acceleration and are combined to get the best performance The combination methods are a Fuzzy logic inference system and different statistical methods such as ordinal regression

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[006] Description of the parameters

The acceleration signal is a real signal, captured with the accelerometer

An EMD is earned out on the acceleration signal which produces a collection of IMF, on which the Hilbert transform is carried out, producing a complex signal

As any complex signal it can be written as a Real (H _R (t)) and Imaginary (H ι(t)) parts or into a Modulus (| H(t) |) and Phase signal (φ _H (0)

Henceforth φ _H '(t) is defined as the deπvative of φ _H (t), being this signal one of the most important source of information about the movement performance The radian phase signal φ _H (0 has been unwrapped by changing absolute jumps greater than π to their 2π complement, before applying the deπvative, to make the phase continuous across 2π phase discontinuities

The information of the acceleration extracted with the Hilbert Transform is complemented by the evaluation of the frequency contents if the acceleration signal, by means of it spectrum (calculated by parametric or non-parametπc methods)

A set of N parameters extracted from the Hilbert Transformed signal gives information of the deviation of the discontinuities

(1 ) Number of peaks of the deπvative of the Hilbert phase higher than a threshold (normalized to time length of the signal and sampling frequency)

Number peaks φ _H '(l) ≥ threshold

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(2) Vanance or standard deviation of the denvative of the Hilbert phase, φ' π(t)

(3) Fractal dimension (D _F ) of the curve (H _R (t), H|(t)), Hilbert plane

From the power spectrum estimate of the acceleration signal, the M parameters used are

( 1 ) Mean frequency

(2) Frequencies of the N main components

[007] Example of application

This section presents an example of the Hilbert Transform performance applied to Parkinson Disease and Rotational devices to show why this transform was selected to be used in these applications

Figure 2 a shows the acceleration signal from a normal subject doing one of the test movements (washing face like movement) with the accelerometer placed on the πght hand The spectrum of the acceleration signal is depicted in Figure 2c

The acceleration signal is filtered through a band pass filter, Figure 2b, and then the Hilbert Transform is applied Figure 2d and Figure 2e contain the curve of the Hilbert plane (H _R (t), H|(t) ) and the deπvative of the phase Hilbert Transform, respectively

Figure 3 shows the signals and transforms for the same test, as in Figure 2, collected from a Parkinson disease patient

As an another example, Figure 4, shows the effect of treatment with drugs (in this case L- Dopamine) on Parkinson disease, expressed on the derivative of Hilbert Transform's phase

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[008] Combined methods description

Each of the subparameters as single parameters has prediction capacity of Parkinson's disease, correlates to the effect site concentration, and the description of the rotational device 5 performance

However, by combining the parameters, sensitivity and specificity are increased

From the set of parameters detailed in section 006 several indexes are created from their combinations using one of these methods

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( 1 ) Combining indexes using a Fuzzy Inference System The adjustment of the Fuzzy is done by means of an ANFIS (Artificial Neural Fuzzy Inference System) algoπthm

(2) Ordinal logistic regression

(3) Discriminate Analysis is (4) Artificial Neural Network

For the study of the Parkinson, different indexes will be created

20 ■ Combining the information from the power spectrum and the Hilbert Transform, relating this information with the corresponding medical criteria (physician cπteπa based on several tests and scores) about the existence of a neurological motor disorder

25 ■ Combining information to get the best correlation with the concentration of different treatment drugs (as L-dopamine) to control neurological motor system disorders

An other posible application of the method is an evaluation of the effect site concentration (ES) of drugs on the subjects motoric system for people driving or manipulating machines

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The parameters will be combined based on a database adjusting with the before mentioned parameters versus different concentrations of alcohol and medical cπteπa about the control of the subject on their voluntary movements

The application of the EMD has been descπbed m the article (Dl) "Empirical mode decomposition a novel technique for the study of tremor time series by E Rocon de Lima et al, Med Bio Eng Comput (2006) 44 569-582 This article describes how the EMD is applied to data recorded from gyroscopes attached to the arm of the patient

The present method is significantly different from the method descπbed in D l First of all the method assesses the deviation from a sinusoidal movement Secondly, the number of peaks of the derivative of the Hilbert phase higher than a threshold is a used as a main mput parameter to one of the functions used to define the index of tremor The methods used for combining the parameters are for example, but not limited to, an ANFIS or a multiple logistic regression

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[009] Hubert Transformation description

The Hubert Transform of an infinite continuous signal f(t) is defined as:

The implementation of the Hubert Transform of finite length digital signal can be calculated by means of the FFT (Fast Fourier Transform) as shown schematically below.

N/2

H{xn} = H _R {x _n }+H,{xn} = |H{xn}| . φ _H {xn}

H{x _n } = FFT ^" ' (FFT (x _n ) * W _n ) where

Function H _n

[2 + yO; « = 0, n = N/2

W _n = J 1 + yO; \<n≤N 12-X

[0 + yO; NI2 + \≤n≤N-\ where j = V-T

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(010) Description of figures.

Fig. 1. Block diagram of method and apparatus

5 Fig. 2 Acceleration signal and Transformed signals NORMAL SUBJECT

(a) Acceleration signal

(b) Filtered acceleration signal

(c) Spectrum of acceleration signal

(d) Hilbert Plane (H _R (t), H,(t) Acceleration signal io (e) Hilbert Phase derivative φ H '(0 acceleration signals

Fig. 3. Acceleration signal and Transformed signals PARKINSON PATIENT

(a) Acceleration signal

(b) Filtered acceleration signal i s (c) Spectrum acceleration signal

(d) Hilbert Plane (H _R (t), H|(t) Acceleration signal

(e) Hilbert Phase derivative φ _H '(t) of acceleration signals

Fig. 4 φ _H " (t) of acceleration signal of a Parkinson patient making a tapping movement 20 (a) before administering L-Dopamine

(b) 20 min after administering L-Dopamine

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