Biomedical Signal and data processing

INTRODUCTION

Part 1. INTRODUCTION TO BIOMEDICAL SIGNALS AND DATA

1.1 BIOMEDICAL SIGNAL

A biomedical signal s(t) is a function continuous in time (t) and in

amplitude (s), analytically written as f (t, s) =0 or s=f(t), used in

medicine to monitor the functionality of an organ or of a part of it, for

diagnostic and treatment purposes . They are typically classified on their

nature or modality of occurrence. Based on its nature, the signal is classified

Electrical: Magnetic:

as: ECG, EMG, EEG; magneto cardiogram,

Impedentiometric: Chemical:

magnetoencephalogram; pneumogram; partial-

Acoustic: Mechanical:

pressure signal; phonocardiogram; pressure signal. All

signal, independently by their nature are transduced in electrical signal.

Based on its modality of occurrence, s(t) is classified as:

- Spontaneous: human body continually generated signals. Also, that comes

from voluntary muscles are classified as spontaneous because the impulse

come from the body and not from the extern.

- Induced: artificially generated as a response to the interaction between an

external energy sent to the tissue and the tissue itself.

A biomedical signal is always corrupted (often hidden) by external noise or

other biological signals of no interest interferences or crosstalk (the

interference comes from other electromedical devices)

Biomedical signal processing consists in the removal (filtering) of noise and

interferences and in the reduction of the biomedical signal of interest in few

significant parameters (data reduction) from which to derive clinical

information

1.2 TYPES OF BIOMEDICAL SIGNALS

Signal: s=s(t), where t=time is independent variable and s=amplitude is the

dependent variable. Depending on the nature of the domain and codomain,

signals are divided into:

- Analog signals f (t, s): continuous time and

continuous amplitude;

- Sampled signals f (t, s): discrete time and continuous

amplitude;

- Quantizated signals f (t, kQ): continuous time and

discrete amplitude;

- Digital (numerical) signals f (nT, kQ): discrete time and discrete

amplitude

Biomedical signals may also be divided (the difference is based on the different

tool that we can use for different signals) into:

- Deterministic signals: perfectly known and representable at each time

instant, and thus studied and analysed through mathematical analytical

methods; 1 INTRODUCTION

- Stochastic or random signals: they are not completely known a priori

and thus are studied through statistical methods

In reality, no signal is perfectly stochastic or deterministic: we cannot perfect

control the activity of any signal, i.e. heart depends on temperature, other

activity, emotion, so I can't control those parameters and as consequence I

cannot perfectly control heart I can only approximate the signal to a

deterministic one. In the other case, in the stochastic case, when we speak

about EEG or EMG seems to be noise, we can't recognise immediately some

ways that characterize the signal, but there are those ways that identifies the

signal. Also, in this case in it not all stochastic, it is not random but has some

periodical repetition. Deterministic signals are studied in time, instead

stochastic in the frequency domain.

Deterministic signal - Signals that could approximate the biomedical signals

CONTINUOUS DIGITAL SIGNALS

SIGNALS

s(t)= s(t+kP) k=0, ±1, s(nT)=s((n+kN ) T) k=0,

0

Periodic ±2 ±1, ±2

Even s(t)=s(-t) s(nT)=s(-nT)

Odd s(t)=-s(-t) s(nT)=-s(-nT)

Signal for processing or experimental setting but that are not biomedical

signals CONTINUOUS SIGNALS DIGITAL SIGNALS s(nT)=

s(t)=

CONSTAN = K = K

T

SINUSOID = Acos (ωt + φ) =

Acos(2π(n-

n ) t/N T)

0 0

EXPONENT = Ae =Ae

- -ωnT

IAL ωτ

STEP = K = K

t≥t n≥n

0 0

= 0 =0 n<n 0

t<t 0

RECTANGU = K |t- t | ≤ T =K |n- n | ≤ N

0 1 0 1

LAR = 0 |t- t | > T =0 |n- n | > N

0 1 0 1

IMPULSE

The importance of the above-mentioned signals derives from their use in the

solution of practical problems. In particular: the step signal used to represent

a quantity that varies rapidly in the neighbourhood of the point t=0. Periodic

2 INTRODUCTION

signals are used to represent quantities that are repeated many times. The

exponential signal allows to represent some damping phenomena.

Types of biological signals classified into two main groups: the deterministic

and stochastic (or statistical) signals. The deterministic group is subdivided into

periodic (for ),

processing or experimental setting but are not biomedical signals

quasiperiodic, transient

and signals; the stochastic signals are subdivided into

stationary nonstationary

(same mean value but different amplitude) and

signals.

1.3 The four fundamental stages of the biomedical signal

processing:

a) SIGNAL ACQUISITION - Process that brings the signal of interest into

a memory devise to allow automatic (by means of a computer) analysis.

analog,

By their nature, biomedical signals are while automatic processing is

digital. Acquisition consists in:

- Detection and, possibly, signal transduction. Electrodes (for electrical

signals) or transducers (for non-electrical signals) are used. Entropy must be

kept low in order to have a high signal-to-noise ratio

- Signal conditioning (pre-filtering). For example, use of a hardware filter

for an initial powerline-noise reduction

- Analogs to digital conversion. It consists in the numerical transformation

of the biomedical signal for subsequent automatic processing

- Digital storage as row data.

b) SIGNAL TRANSFORMATION - It may include the following procedures:

- Signal cleaning: removal or reduction of noise and interference through

numerical filtering 3 INTRODUCTION

- First data-redundancy reduction: identification of significant signal

components and removal of the others. Also performed through numerical

filtering time

- Domain transformation: transformation of the signal from the

domain frequency domain

(original) to the (Fourier’s analysis) for an

efficient information extraction

- Characteristic waves identification: it is performed in the analysis

domain and allows:

To discriminates abnormalities (pathologies)

 A second data-redundancy reduction



c) PARAMETER IDENTIFICATION (from the signal to the data) - The identified

parameters have to be ‘features’, that is they have to be characterized by

the following:

- have semantic content, that is provide information of the analysed

biological system;

- usable as input to subsequent procedures of clinical decision making;

- have discriminant power, that is allow identification of a pathology or of

its trend during development

- allow a second data-redundancy reduction

d)SIGNAL CLASSIFICATION - It consist in searching for links between the

event classes and characteristics identified in the previous stage,

which must be interpreted and classified by means of methods similar to those

of pattern recognition (based on heuristic reasoning, logic statistic, or a

combination them). A strict collaboration between the biomedical

engineer and the physician is needed

1.4 INTRODUCTION TO DIGITAL IMAGES

A biomedical image i(x,y) is a bidimensional function in space (x,y)

and in “amplitude” (i), analytically written as f(x,y,i)=0 or i=f(x,y),

used in medicine to monitor the functionality of an organ or of a part

of it, for diagnostic and treatment purposes. “Amplitude” may refer to

grey level or colour. Based on the acquisition technique, they are classified as:

XR, Fluoroscopy, MRI, US, Endoscopy, Elastography, Tactile imaging,

Thermography, Medical photography and nuclear imaging techniques. Body

regions appears completely different when altering the imaging modality.

Difference with signal: there is no time, it is fixed, characterized by 2

dimensions. Another thing that is no present is the continuity, sometimes it is

continuous, sometimes no. if it is continuous, we must process it line a

biomedical signal. An image can be digitally represented by a matrix.

Depending on the nature of their domain and codomain, images are

divided into:

Analog images f(x, y,i):

- continuous space and continuous amplitude;

Pixeled images f(nTx,nTy,i):

- discrete space and continuous amplitude;

4 INTRODUCTION

Quantized images f(x,y,kQ):

- continuous space and discrete amplitude;

- Digital (numerical) images f(nTx,nTy,kQ): discrete time and discrete

amplitude.

STAGES IF IMAGE PROCESSING - More complex than a signal but the basic

concept is the same: from the acquisition to the visualization through the

processing (made by a computer)

1.5 Biomedical data, strictly, measures and features obtained

by analysing biomedical signal, can be divided into:

Dynamic data: expressed as function of time. For example, signals

 (ECG, EEG, EMG) or tracings (action potential, glycaemic curve);

Static data. For example, biochemical data, temperature, short-time

 heart rate. 5 PHYSIOLOGY

I. CARDIAC SIGNALS

The heart id an involuntary muscle the size of a fist, located in the centre of

the chest cavity and divided into a right and left section, separated by a

septum. Each of the two section consists of two cavities (chamber), the upper

id termed atrium, and lower ventricle. Each atrium communicates with

corresponding ventricle through the atrioventricular orifice equipped with

valves: the tricuspid valve between the right cavities, and the mitral valve

between the left cavities.

The orifices that put in communication the chambers of the heart with the

efferent vessels are also protected by valves that prevent reflux: the pulmonary

semilunar valve into the right ventricle for the pulmonary artery, and the aortic

semilunar valve into the left ventricle of the aorta.

Cardiac excitability

The heart is constituted by a set of excitable and

contractile cells and is equipped with its own

automatism. In other words, the contraction capacity of

cardiac cell is an intrinsic property. The heart beats

even in the absence of nerve stimuli with a

characteristic frequency that corresponds to the mean

heart rate.

Even if the heart is isolated the sinoatrial node can send an electrical signal

able to contract atriums and so let hear beat. After that the signal passes to the

atrioventricular node that spread the contraction signal to the ventricles.

The cyclic pseudo-periodic contraction of the heart id ensured by an

uninterrupted transition of myocardial cells from the resting state to the state

of arousal, due to cellular bioelectric phenomena.

Phases of cardiac conduction and contraction

1. The sinus node, whose cells depolarize automatically, triggers

action potential in the myocardium

2. The depolarization impulse begins to spread through the atria

to reach the atrioventricular node

3. Through the His bundle contraction shifts to the cardiac apex

4. Thanks to the Purkinje fibres, the depolarization wave is

transmitted to the ventricular myocardium.

CARDIOVASCULAR

SIGNALS

One organ could generate

very different kind of signals

(each cell makes a signal; our

signal is the integration of all

of them). It is a phenomenon

that occurs simultaneously,

different aspects of the same 6 PHYSIOLOGY

phenomenon, same x axis and same amplitude but different nature of

investigation.

THE ELECTROCARDIOGRAM - The machine for recording the ECG was

invented in 1887 by the German Augustus Waller and improved later by the

physiologist William Einthoven

The electrocardiogram (ECG) is a graphical representation of the cardiac

electrical activity so the action potential generated by cardiac cells. This is

quite short and has a different morphology by the ecg that is recorded outside

the body, so it is the sum of the activity of all cardiac cells. It is usually

recorded through surface electrodes located in the body surface at

standardized positions.

The ECG reflects the spatio-temporal integration of the continuous change of

all action potentials in relation to the cardiac cycle and constitutes the most

important clinical investigation in the cardiac diagnostics since is simple, non-

invasive and cheap.

ECG RECORDING TECNIQUES - is done through electrodes placed at various

points of the body:

- Surface ECG: ECG recording made using electrodes placed in the body

surface and thus is innovative and commonly performed.

- Internal ECG: ECG recording made with electrodes placed directly on

epicardium. This invasive technique is performed only in a few occasional

experimental circumstances.

12 Lead ECG

The standard ECG has 12 leads. Six of the leads are considered “limb leads”

because they are placed on the arms and/or legs of the individual. The other

six leads are considered “precordial leads” because they are placed on the

torso (precordium). The six limb leads are called lead I, II, III, aVL, aVR and aVF.

The letter “a” stands for “augmented,” as these leads are calculated as a

combination of leads I, II and III. The six precordial leads are called leads V1,

V2, V3, V4, V5 and V6. Below is a normal 12-lead ECG tracing.

7 PHYSIOLOGY

We have some standard in order to have the same king of results for all

subject, in we perform a random acquisition there no way of compatibility

between subjects. depending where we put the electrodes, we can have a

different aspect of hear electrical activity under investigation. Another

comparison could be intrasubject, so a comparison of ECG made in a single

subject in different instant in time, maybe far one from each other. RA LA LL =

first three derivations. we put here because we have no muscles and no fat, so

we have no signal interference of muscles or the breath interference that we

could have in the chest. two recorded and the third geometrically calculated.

P wave: contraction of the right and left atria

 QRS complex: contraction of the right and left

 ventricles, which hides the atrial repolarization

T wave: ventricular repolarization

 PR interval: measuring the atrioventricular

 conduction time, some changes in this part are

the first alarms for a myocardial infarct

QT interval: measuring the total duration of

 systole, it is the most important and very little

variation (10, 15 milliseconds) could be very

dangerous, prolonged is more common.

TP segment: baseline

 Amplitude order: mV

 Frequency bandwidth: 0.05-100 Hz



THE TACHOGRAM - Is the sequence of R-R intervals as a function of

continuous number of bit. We construct it from ECG, identify the R pick, and

compute the distance beetwen two peack. The R interval of a pick in the

difference in time between the actual beat and the previous one. It is a digital

signal by construction, because takes intervals. They are not perfectly

constant, because it is a real representation and two time intervals are never

the same, so to have a periodic sempling, it is expressed in a progresssion og

beats, so a progression of natural number on x and no time. Express the

8 PHYSIOLOGY

tagogram with respect to consecutive number of bit means that the distance

between two samples id 1. On the x axis we will have the distance between

two sampres (mean R - R), so the interval is constant; instead in the y axis we

plot the real R-R intervals that oscillate around the manx. (NB it is an

approximation)

The tacogram could be consituted from any cardiovascular signal, but the best

is the ECB because from its morphology the R pic is easy to detect (fast and

hogh in amplitude).

Since each heart has it’s hown frequency, if we can isolate this freqency we can

have a costant rate, and we can measure some variation. The variation around

the mean valieu are not caracteristic of hear but of nervous system, so it in an

indirect non invasive measuere of its funcions. It appear in any machine and it

is a plot of what appear after an holter measurement (for example). Then we

have a premature bit it least longher than other, so is simple to detect aritmias.

THE PHONOCARDIOGRAM – The phonocardiogram is a mechanical signal,

the recording of the heart sounds: it is a PSEUDO-periodic and PSEUDO-

stochastic signal. It represents the closure of atrioventricular valves (the

bigger one), and after the closure of aortic valve (smaller one).

It is very important to detect it because it is not so affected by noise and

extremely easy to obtain and could be recorded alco in moving condition.

The locations of best auscultation for each heart valve are

labelled with:

“M”: mitralic, “T”: tricuspid, “A”: aortic, and “P”: pulmonary.

9 PHYSIOLOGY

THE FIRST AND THE SECOND HEART SOUND (normal condition)

 THE TIRD AND THE FOURTH HEART SOUNDS (pathologic condition)

 a. Third Heart sounds: S3 also called a protodiastolic gallop, ventricular

gallop, or informally the “Kentucky” gallop, is associated with heart

failure

b. Fourth Heart sounds: S4 when audible in an adult is called a

presystolic gallop or atrial gallop. This gallop is produced by the sound of

blood being forced into a stiff or hypertrophic ventricle

OTHER ABNORMAL COUNDS (pathologic condition)



FETAL ELECTROCARDIOGRAPHY – it is a technique used to analyse the

foetal condition during pregnancy. There are two different method:

- Indirect method – implies the use of standard electrodes placed on the

maternal abdomen according to a particular configuration. It is non-invasive

and applicable from 37° 38° week of pregnancy. There are two main

problem: it records both the mother and foetus heart, and mother signal has

a higher amplitude, the second problem is that the position of the electrodes

with respect the foetus. We will have also a processing problem because the

extracted signal is difficult to analyse than direct foetal electrocardiogram

and has a low quality and amplitude: sometimes the ECG is completely

covered by the mother’s one.

- Direct method: implies the use of a spiral electrode inserted through the

cervix of the pr