Biomedical Signal Processing Lectures 2011-12

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Biomedical

Signal

Processing

Lecture 0

INTRODUCTIONDr.R.B.Ghongade

Department of E&TC

Vishwakarma Institute of Information Technology, Pune

INDIA



Syllabus1)Introduction: cell structure, basic cell function, origin of bio

‐potentials,

electric activity of cells.

2)Bio‐transducers: Physiological parameters and suitable transducers for its

measurements, operating principles and specifications for the transducers to

measure parameters like blood flow, blood pressure, electrode sensor,temperature, displacement transducers.

3)Cardiovascular system: Heart structure, cardiac cycle, ECG

(electrocardiogram) theory (B.D.), PCG (phonocardiogram).EEG, X‐Ray,

Sonography, CT‐Scan, The nature of biomedical signals.

4)Analog signal processing of Bio‐signals, Amplifiers, Transient Protection,

Interference Reduction, Movement Artifact Circuits, Active filters, Rate

Measurement. Averaging and Integrator Circuits, Transient Protection

circuits.

5)Introduction to time‐frequency representations

‐ e.g. short

‐time Fourier

transform, spectrogram , wavelet signal decomposition.

6)Biomedical applications: Fourier, Laplace and z‐transforms,

autocorrelation, cross‐correlation, power spectral density.

7)Different sources of noise, Noise removal and signal compensation.

8)Software based medical signal detection and pattern recognition.



Texts/References

1. Handbook of Biomedical Instrumentation,secondedition,R S Khandpur,TMH Publication,2003

2. E. N. Bruce, Biomedical signal processing and

signal modelling, New York: John Wiley, 2001.

3. Wills J. Tompkins, biomedical digital signalprocessing, PHI.

4. M.Akay, Time frequency and wavelets in

biomedical signal processing, Piscataway, NJ:

IEEE Press, 1998.5. Biomedical instrumentation and measurements

by Cromwell, 2nd edition, Pearson education.



Additional

Texts/References

1. Jaakko Malmivuo; Robert Plonsey; “Bioelectromagnetism :

Principles and

Applications

of

Bioelectric

and

Biomagnetic

Fields”, Oxford University Press

2. Antoun Khawaja ; “Automatic ECG Analysis using Principal

Component Analysis and Wavelet Transformation”, Karlsruhe

Transactions on Biomedical Engineering, 2006

3. John L. Semmlow; “Biosignal and Biomedical Image Processing:

MATLAB‐Based Applications”, Marcel Dekker, Inc., 2004

4. Rezaul Begg; Joarder Kamruzzaman; Ruhul Sarker; “Neural

networks in healthcare: potential and challenges”, Idea Group

Publishing, 2006

5. Lief Sornmo; Pablo Laguna; “Bioelectrical Signal Processing in

Cardiac and Neurological Applications”, Elsevier, 2005, First

Edition



Lecture Plan

Lecture 1: Introduction to Biomedical Instrumentation and safety

considerations

Lecture 2: Bio‐potentials

Lecture 3:

Bio

‐electrodes

and

Physical

Measurements

Lecture 4a: Cardiovascular System

Lecture 4b:Phonocardiography, EEG

Lecture 5: X‐Ray Imaging , Computed Tomography , Diagnostic Ultrasound

ImagingLecture 6: Analog Signal Processing of Bio‐signals (NO PPT)

Lecture 7: Digital signal processing of Biosignals

Lecture 8: Software based medical signal detection and pattern recognition –

Case Study (NO PPT)



Assignments

PART I

Assig. 1: Survey of Bio‐medical sensors

Assig.2: Design and simulation of instrumentation amplifier

Assig.3: Design and simulation of Active Filters

PART II

Assig.4: MATLAB

exercise

( basic

operations,

commands…)

Assig.5: ECG Signal processing using FFT and Wavelets

Assig. 6:ECG Pattern classification



Lecture 1PART I:Introduction to Biomedical

Instrumentation

PART II: Safety considerations

Dr.R.B.Ghongade

Department of E&TC,

V.I.I.T., Pune‐411048



Bio‐medical Instrumentation

• A medical device is

– “any item promoted for a medical purpose that does not rely on chemical action to achieve its intended effect”

• Difference from any conventional instrument – source of signals is living tissue

– energy is applied to the living tissue

• How does this impact design requirements? – Reliability, Reliability, Reliability !!!



Timeline of major inventions



Generalized instrumentation system



• Physical quantity, property or condition that the

system measures

• Types of measurands

• Internal –Blood pressure

• Body surface –ECG or EEG potentials

•

Peripheral –Infrared radiation• Offline –Extract tissue sample, blood or biopsy

• Categories of measurands

• Bio‐potential, pressure, flow, dimensions

(imaging), displacement (velocity, acceleration

and force), impedance, temperature and

chemical concentration

Measurand



Sensor• A sensor converts physical measurand to an

electrical output

• Sensor requirements

• Selective – should respond to a specific form

of energy in the measurand

• Minimally invasive – should not affect the

response of the living tissue

• Most important types of sensors in biomedical

systems• displacement

• pressure



Signal Conditioning

• Signal Conditioning: Amplification and filtering

of the signal acquired from the sensor to make it suitable for processing/display

• General categories

• Analog, digital or mixed‐signal• Time domain processing

• Frequency domain processing

•

Spatial domain processing



Operational Modes•

Direct vs. Indirect• Direct mode: measure desired measurand directly

• if the sensor is invasive, direct contact with the

measurand is possible but expensive, risky and least

acceptable• Indirect mode: measure a quantity that is accessible and

related to the desired measurand

• assumption: the relationship between the measurands is

already known

• often chosen when the measurand requires invasive

procedures to measure directly

•

Example indirect mode• Cardiac output (volume of blood pumped per minute by the

heart)can be determined from measurement of respiration,

blood gas concentration & dye dilution

• Organ morphology can be determined from x‐ray shadows



Operational Modes

• Sampling vs. Continuous mode• Sampling: for slow varying measurands that are sensed

infrequently like body temperature & ion concentrations

• Continuous: for critical measurements requiring constant monitoring like electro‐cardiogram and respiratory gas

flow

• Generating vs. Modulating• Generating: also known as self ‐powered mode derive

their operational energy from the measurand itself

• Example: piezoelectric sensors, solar cells

•

Modulating: measurand modulates the electrical signal which is supplied externally modulation affects output of

the sensor

• Example: photoconductive or piezoresistive sensor



Measurement Constraints• Other than device functionality, the signal to be measured

imposes constraints on how it should be acquired and

processed

• Measurement and frequency ranges

• Most medical measurands are typically much lower than

conventional sensing parameters (microvolts, mm Hg, low frequency)

• Interference and cross‐talk

• Not possible to isolate effects of other measurands

• Cannot measure EEG without interference from EMG

• Placement of sensors and compensation/calibration

process play a key role in any bio‐instrumentation design



Measurement Constraints• Measurement variability is inherent at molecular, organ and body level

• Primary cause

• interaction between different physiological systems

•

existence of numerous feedback loops whose properties are poorly understood

• Therefore evaluation of biomedical devices rely on probabilistic/statistical

methods (biostatistics)

• SAFETY

• Due to interaction of sensor with living tissue, safety is a primary

consideration in all phases of the design & testing process the

damage caused could be irreversible

• In many cases, safe levels of energy is difficult to establish

• Safety of medical personnel also must be considered

• Operator constraints

• Reliable, easy to operate, rugged and durable



Classification of biomedical instruments• Quantity being sensed

• pressure, flow or temperature

• makes comparison of different technologies easy

• Principle of transduction

• resistive, inductive, capacitive, ultrasonic or

electrochemical

•

makes development of new applications easy• Organ systems

• cardiovascular, pulmonary, nervous, endocrine

• isolates all important measurements for specialists

who need to know about a specific area• Clinical specialties

• pediatrics, obstetrics, cardiology or radiology

• easy for medical personnel interested in specialized

equipment.



Measurement Input Sources• Desired inputs

• measurands that the instrument is

designed to isolate

• Interfering inputs

• quantities that inadvertently affect the

instrument as a consequence of the

principles used to acquire and process

the desired inputs

• Modifying inputs

• undesired quantities that indirectly

affect the output by altering the

performance of the instrument itself

• ECG example

• Desired input – ECG voltage

• Interfering input – 50 Hz noise voltage,

displacement currents

• Modifying input – orientation of the patient

cables

• when the plane of the cable is

perpendicular to the magnetic

field the magnetic interference is

maximal

• Interfering inputs generally not

correlated to measurand

• often easy to remove/cancel

• Modifying inputs may be correlated to

the measurand• more difficult to remove



Design Criteria and Process



Regulation of Medical Devices• Regulatory division of medical devices: class I, II and III

• more regulation for devices that pose greater risk

• Class I (General controls)

• Manufacturers are required to perform registration,

premarketing notification, record keeping, labeling,

reporting of adverse experiences and good

manufacturing practices• Class II (Performance standards)

• 800 standards needed to be met!

• Class III (Premarketing approval )

• Manufacturers have to prove the safety of these devices prior to market release

• Implanted devices (pacemakers etc.) are typically

designated class III

• Investigational devices are typically exempt



Compensation Techniques

• Compensation: elimination or reduction of interfering and

modifying inputs

•

Techniques• Altering the design of essential instrument components

• simple to implement

• Adding new components to offset the undesired inputs

• Methods• Reduce sensitivity to interfering and modifying inputs

• Example: use twisted cables and reduce number of

electrical loops

• Signal Filtering• temporal, frequency and spatial separation of signal

from noise



Compensation: Negative Feedback• When modifying input cannot be avoided, negative feedback is used

to make the output less dependent on the transfer function of the

device

• Feedback devices must be accurate and linear



Feedback



Other Compensation Techniques

• Opposing inputs or noise cancellation• When interfering and modifying inputs

cannot be filtered • additional inputs can be used to cancel

undesired output components• similar to differential signal representation



Biostatistics• Used to design experiments and clinical

studies:• To summarize, explore, analyze and present data

• To draw inferences from data by estimation or by

hypothesis testing

• To evaluate diagnostic procedures

• To assist clinical decision making

• Medical research studies can be classified as:• Observational studies: Characteristics of one or more

groups of patients are observed and recorded.

• Experimental intervention studies: Effect of a medical

procedure or treatment is investigated.



Biostatistics Studies• Observational studies – case‐series studies

• Case‐control studies

• use of individuals selected because they have some

outcome or disease

• then look backward to determine possible causes

• Cross‐sectional studies:• Analyze characteristics of patients at one particular time

to determine the status of a disease or condition.

• Cohort observational studies:•

A particular characteristics is a precursor for an outcome or disease

• Controlled studies:• If procedures compared to the outcome for patients

given a placebo or other accepted treatment



Biostatistics Studies II

• Concurrent control:• Patients are selected in the same way and for the same

duration

• Double‐blind study:• Randomized selection of patients to treatment options

to minimize investigator or patient bias



Biostatistics: Data Analysis• Distributions of data reflect the values of a variable /

characteristic and frequency of occurrence of those values

•

Mean: (X )average of N values (arithmetic or geometric mean)

• Median: middle of ranked values

• Mode: most frequent value



Biostatistics: Data Analysis

• Standard deviation:(s) spread of data

• 75% of values lie between

• Coefficient of Variation: (CV)

•

permits comparison of different scales

• Percentile

• Percentage of distribution that is less than or

equal to the percentile number



More Biostatistics• Correlation coefficient(r)

• Measure of the relationship

between two numerical variables

for paired observations

• values between +1 and ‐1 (+1means strong correlation)

• Estimation and Hypothesis Testing

• Confidence intervals• indicates the degree of confidence that data contains the true mean

• Hypothesis testing

• reveals whether the sample gives enough evidence for us to reject the

null hypothesis(statement expressing the opposite of what we think is

true)

• P‐value:

• how often the observed difference would occur by chance alone



More Biostatistics• Methods for measuring the accuracy of a diagnostic

procedure:

• Sensitivity: probability of the test yielding positive results in patients who actually have the disease

• opposite: false‐negative rate

• Specificity: probability of the test yielding negative results in patients

who do not have the disease

• opposite: false‐positive rate



Instrument Characterization• Enable comparison of available instruments

• Permit evaluation of new instrument designs

• Generalized static characteristics• Static characteristics:

• performance of instruments for dc or very low

frequency inputs

• some sensors respond only to time‐varying inputs and

have no static characteristics

•

Dynamic characteristics:• require temporal relationships to describe the quality

of measurements



Static Characteristics• Accuracy

• Difference between the true value and the measured value

normalized by the magnitude of the true value• Several ways to express accuracy

• most popular is in terms of percentage of full‐scale

measurement

•

Precision• Expresses number of distinguishable alternatives from which a given

result is selected

• High‐precision does not mean high accuracy.

•

Resolution• Smallest incremental quantity that can be measured with certainty

• Reproducibility• Ability of an instrument to give the same output for equal inputs

applied over some period of time



Statistical Control and Static Sensitivity

• Measurement conditions have to take into account randomness introduced by

environmental conditions

• If the source of variation can not be removed, then use averaging

• Statistic sensitivity (dc‐gain)

• To perform calibration between output and input

• For linear calibration

•

A static calibration is performed by holding all inputs (desired, interfering, and modifying) constant except one

• This one input is varied incrementally over

the normal operating range, resulting in a

range of incremental outputs.

• The static sensitivity of an instrument or system is the ratio of the incremental

output quantity to the incremental input

quantity



Static Characteristics• Zero drift (offset error)

• When all measurements

increases or decrease by the

same absolute amount

• Causes: manufacturing

misalignment, variations in

ambient temperature,

hysteresis vibration, shock, dc‐

offset voltage at electrodes

• Sensitivity drift (gain error)• When the slope of the

calibration curve changes as a

result of interfering or

modifying input• Causes: manuf acturing

tolerances, variations in power

supply, non‐linearity

• Example: ECG amplifier gain changes

due to dc power‐supply variation



Linearity• Linearity: A system that demonstrates superposition principle

• Measure of linearity:a) maximal deviation of points from the regression line

expressed as percentage of the full‐range or

b) harmonic distortion measure.



More Static Characteristics• Input ranges

• Constraints on linearity imposes an operational range for the input

parameters

• Input range is also applicable to interfering inputs (used for shielding of instruments)

• Input impedance(Z)• Measures the degree to which instruments

disturb the quantity being measured

• effort variable: examples voltage, pressure,

force

• flow variable: examples current, flow, velocity

• when measuring effort variables, input impedance

should very large

• when measuring flow variables, input impedance

should very small



Dynamic Characteristics• Quantify response of medical equipment with respect to

time‐varying inputs

• Many engineering instruments can be described by ordinary

linear differential equations

• Most practical instruments have a first or second order

response

• Practical evaluation of a system

• Apply input as a unit‐step function, sinusoidal function or

white noise



Dynamic Characteristics• Operational transfer function:

• Frequency response of a system

• For a sinusoidal input

• the output is a sinusoid with different magnitude and

phase

• Magnitude:

•

Phase:



Zero‐order Instrument

• Linear

potentiometer is an

example of a zero

order instrument

• In practice, at high

frequencies

parasitic

capacitance and

inductance will

cause distortion



First‐order Instrument

• First‐order instrument contains a single energy‐storage

element

• Static sensitivity (dc‐gain):

• Time‐constant of the system:

• A frequency transfer function is given by



First‐order Instrument



Second‐order Instrument• Second‐order instrument contains a minimum of two

energy‐storage element

• Static sensitivity (dc‐gain):

• Un‐damped natural frequency:

• Damping ratio:



Second‐order Instrument



Medical Instrument Electrical Safety



Significance of safety• Tens of thousands device related patient

injuries in U.S every year.• Even a single harmful event can lead to

significant damage in terms of reputation and

legal action.

• Different level of protection required as

compared to household equipment.• Minimum performance standards introduced

in 1980s –relatively new practice.

Ph i l i l Eff t f El t i it



Physiological Effects of Electricity

• Experiments from 160lb human with 60Hz current



Susceptibility Parameters

• Mean “threshold of perception”

– 1.1mA for men

– 0.7mA for women

• Minimum threshold of perception 500 μA

– 80 μA with gel electrodes(reduces skin impedance)

• Mean “let‐go current”

– 16.5 mA for men

– 10.5 mA for women

• Let‐go current vs. frequency

– Minimal let‐go current occurs at commercial power‐line frequencies of

50‐60 Hz



From experiments performed by Charles Dalziel (1940 to 1950



Susceptibility Factors• Shock (stimulation) duration

– Fibrillation current is inversely proportional to the shock pulse duration

– longer pulses ‐>lower current does damage

• Body weight – Fibrillation current increases with body weight

•

50 mA RMS for 6 Kg dogs• 130 mA RMS for 24 Kg dogs

• Points of entry – Skin impedance varies: 15 kΩ to 1 MΩ

• Resistive barrier that limits current flow

– Tissue (beneath skin) has low impedance

Macro vs Micro Shock



Macro vs. Micro Shock • Macroshock

– externally applied current

– spreads through the body so less concentrated

• Microshock

– applied current is concentrated at an invasive point

– accepted safety limit is only 10 μA

– generally only dangerous if current flows through the heart

Macroshock Hazards



Macroshock Hazards• Most probable cause of death due to macroshock

– ventricular fibrillation

• Factors

– skin/body resistance

– design of electrical equipment

• Skin and body resistance

– dry skin has high resistance (~15k‐1M ohm)

• limits current through body

• wet/broken skin has low resistance (~1% that of dry skin)

– internal body resistance

– ~200 ohm for each limb

–

~100 ohm for trunk of body – resistance between two limbs = ~500 ohm

• procedures that bypass skin resistance can be dangerous

• example: gel electrodes, surgery, oral/rectal thermometers

Microshock Hazards



Microshock Hazards

• Main causes

– leakage currents in line‐operated equipment

• undesired currents through insolated conductors at different

potentials – differences in voltage between grounded conductive surfaces

• Leakage currents

– if low resistance ground is available ‐>no problem

– if ground is broken ‐>current flows through patient



Conductive Paths• Direct connection to an internal organ (during

measurement or surgery) makes patients susceptible

to mircoshock – External electrodes of temporary cardiac pacemakers

– Electrodes for intra‐cardiac measuring devices

– Liquid filled catheters placed in the heart• liquid filled catheters have much greater resistance than

electrodes

• Worst ! danger! – currents flowing through the heart

• Electrode current density – experiments suggest smaller electrode are more dangerous



Power Distribution • Electrical power system in Healthcare Facility

– must control available power (fuse/breaker to set max current)

– must provide good ground

– Patient’s Electrical Environment –Grounding

– NEC code: max potential between two surfaces

• general care areas: 500mV under normal operation

• critical care areas: 40mV under normal operation

• Isolated Power Systems – Ground fault

• short circuit between hot conductor and ground

• injects large current into grounding system

•

can create hazardous potentials on grounded surfaces – Isolation transformer

• isolates conductors against ground faults

• may include ground fault monitor/alarm

Ground Loops



Ground Loops• Differences in ground

potential: major source of

microshock

– all intensive care units must

have single ground for each

patient isolated from

hospital ground

– 40mV limit on potential of

any conductive surfaces

• Example: current due to

ground loop flows through

patient

Electrical Isolation



Electrical Isolation

• Isolation amplifiers – devices that break ohmic continuity of

electric signals between input and

output of the amplifier

– different supply voltage sources and different grounds on each side of the

barrier

• Barrier isolation

–

transformer, optical or capacitive isolation

• no current across barrier

• Implants

–

proper insulation required to prevent



Review questions1. Draw the block diagram of a typical biomedical

instrumentation system.

2. Enlist the design criteria for biomedical instrumentation

system.

3. Classify biomedical instruments.

4. Enlist various physiological processes/parameters and their ranges.

5. What do you mean by “biostatistics”?

6. What are the characteristics of a biomedical instrumentation system?

7. Comment on the safety aspects of a biomedical system.



Next Class Bio‐potentials

(It has a lot of potential!)



Lecture 2

Bio‐

potentials

Dr.R.B.Ghongade

Department

of

E&TC,V.I.I.T., Pune‐411048

Cells



• Cell‐the basic unit of living tissue

• Specialized in their anatomy and physiology to perform different

tasks

• All cells exhibit a voltage difference across the cell membrane.

• Nerve cells and muscle cells are excitable• Their cell membrane can produce electrochemical impulses and

conduct them along the membrane.

• In muscle cells, this electric phenomenon is also associated with the

contraction of the cell

• In other cells, such as gland cells, it is believed that the membrane

voltage is important to the execution of cell function

• The

origin

of

the

membrane

voltage

is

the

same

in

nerve

cells

as

in

muscle cells.

• In both cell types, the membrane generates an impulse as a

consequence of excitation.

• This impulse propagates in both cell types in the same manner



Structure of Nerve Cell



• The body of a nerve cell is similar to that of all other cells.• The cell body generally includes the nucleus, mitochondria, endoplasmic reticulum,

ribosomes, and other organelles.

• Nerve cells are about 70 ‐ 80% water; the dry material is about 80% protein and 20% lipid.

• The cell volume varies between 600 and 70,000 µm³

• The short processes of the cell body, the dendrites, receive impulses from other cells andtransfer them to the cell body (afferent signals).

• The effect of these impulses may be excitatory or inhibitory .

• A neuron may receive impulses from tens or even hundreds of thousands of neurons

• The long nerve fiber, the axon, transfers the signal from the cell body to another nerve or to a

muscle cell

• Mammalian axons are usually about 1 ‐ 20 µm in diameter.

• Some axons in larger animals may be several meters in length.

• The axon may be covered with an insulating layer called the myelin sheath, which is formed

by Schwann cells (named for the German physiologist Theodor Schwann, 1810‐1882, who

first observed the myelin sheath in 1838).

• The myelin sheath is not continuous but divided into sections, separated at regular intervals

by the nodes of Ranvier (named for the French anatomist Louis Antoine Ranvier, 1834‐1922,

who observed them in 1878).

The Cell Membrane



• The

cell

is

enclosed

by

a

cell

membrane

whose

thickness

is

about

7.5 ‐

10.0

nm• Its structure and composition resemble a soap‐bubble film , since one of its major

constituents, fatty acids, has that appearance

• The fatty acids that constitute most of the cell membrane are called

phosphoglycerides

• A phosphoglyceride consists of phosphoric acid and fatty acids called glycerides

• The head of this molecule, the phosphoglyceride, is hydrophilic (attracted to

water)

• The fatty acids have tails consisting of hydrocarbon chains which are hydrophobic

(repelled

by

water)• If fatty acid molecules are placed in water, they form little clumps, with the acid

heads that are attracted to water on the outside, and the hydrocarbon tails that

are repelled by water on the inside.

The Cell Membrane



• If these molecules are very carefully placed on a water surface, they orient themselves so that all acid heads are in the water and all hydrocarbon tails protrude from it.

• If another layer of molecules were added and more water put on top, the

hydrocarbon tails would line up with those from the first layer, to form a double

(two molecules thick) layer.

• The acid heads would protrude into the water on each side and the hydrocarbons would fill the space between.

• This bilayer is the basic structure of the cell membrane.

• From the bioelectric viewpoint, the ionic channels constitute an important part of the cell membrane

• These are macromolecular pores through which sodium, potassium, and chloride

ions flow through the membrane.

• The flow of these ions forms the basis of bioelectric phenomena.

The Cell Membrane



• The construction of a cell membrane• The main constituents are two lipid layers, with the hydrophobic tails pointing inside the

membrane (away from the aqueous intracellular and interstitial mediums).

• The macromolecular pores in the cell membrane form the ionic channels through which

sodium, potassium, and chloride molecules flow through the membrane and generate the

bioelectric phenomena

The Synapse• The junction between an axon and the next cell with which it communicates is called the



j

synapse.• Information proceeds from the cell body uni‐directionally over the synapse, first along

the axon and then across the synapse to the next nerve or muscle cell.

• The part of the synapse that is on the side of the axon is called the presynaptic terminal ;

that part on the side of the adjacent cell is called the postsynaptic terminal

• Between these terminals, there

exists a gap, the synaptic cleft, with a

thickness of 10 ‐ 50 nm

• The fact that the impulse transfers

across the synapse only in onedirection, from the presynaptic

terminal to the postsynaptic

terminal, is due to the release of a

chemical transmitter by the

presynaptic cell• This transmitter, when released,

activates the postsynaptic terminal

• The synapse between a motor nerve and the muscle it innervates is called the

neuromuscular junction

Muscle Cell



Muscle Cell

• Three types of muscles in the body

– smooth muscle

– striated muscle (skeletal muscle)

– cardiac muscle

• Smooth

muscles

• They are involuntary (i.e., they cannot be controlled voluntarily)

cells have a variable length but are in the order of 0.1 mm exist, for

example, in the digestive tract, in the wall of the trachea, uterus,

and bladder

• The contraction of smooth muscle is controlled from the brain

through the autonomic nervous system

• Striated muscles

– also called skeletal muscles because of their anatomical location, are formed from a

large number of muscle fibers, that range in length from 1 to 40 mm and in diameter



from 0.01 to 0.1 mm.

– Each fiber forms a (muscle) cell and is distinguished by the presence of alternating dark

and light bands.

– The striated muscle fiber corresponds to an (unmyelinated) nerve fiber but is

distinguished electrophysiologically from nerve by the presence of a periodic transverse

tubular system (TTS), a complex structure that, in effect, continues the surface

membrane into the interior of the muscle.

– Propagation of the impulse over the surface membrane continues radially into the fiber

via the TTS, and forms the trigger of myofibrillar contraction.

– The presence of the TTS affects conduction of the muscle fiber so that it differs

(although only slightly) from propagation on an (unmyelinated) nerve fiber.

– Striated muscles are connected to the bones via tendons.

– Such muscles are voluntary and form an essential part of the organ of support and

motion.

• Cardiac muscle

– also striated, but differs in other ways from skeletal muscle

– Not only is it involuntary, but also when excited, it generates a much longer electric

impulse than does skeletal muscle, lasting about 300 ms

– Correspondingly, the mechanical contraction also lasts longer

– cardiac muscle has a special property: The electric activity of one muscle cell spreads to

all other surrounding muscle cells, owing to an elaborate system of intercellular

junctions.

Structure of Muscle Cell



Structure of Muscle Cell

Bio‐potentials



Bio potentials

• Certain systems of the body create their own "monitoring"

signals, which convey useful information regarding the

functions they represent.

• These signals are the Bio‐ potentials “BP” associated with the

conduction along the sensory and motor nervous system,

muscular contractions, brain activity, heart contractions, etc.

• These potentials are a result of the electrochemical activity

occurring in certain classes of cells within the body

Excitable

Cells.

• Measurements of these Bio‐potentials can provide clinicians

with invaluable diagnostic information

Bio‐potentials



• From the biological cell, electrical potentials are generated due to the

electrolytes inside and outside of the cell

• A bioelectric potential may be defined as the difference in potential

between the inside and the outside of a cell; there exists a difference in

potential

existing

across

the

cell

wall

or

membrane.• A cell consists of an ionic conductor separated from the outside

environment by a semi permeable or selectively permeable cell

membrane

• Human

cells

may

vary

from

1

micron

to

100

microns

in

diameter,

from

1

millimeter to 1 meter in length and have a typical membrane thickness of

100 Angstrom units

• Bioelectricity is studied both from the viewpoint of the source of electrical

energy within the cell and also from the viewpoint of the laws of

electrolytic current flow relative to the remote ionic fields produced

currents by the cell.

• We make measurements external to a group of cells while these cells are

supplying electrolytic current flow.

Cell Potential Genesis



Cell Potential Genesis• Experimental investigations with microelectrodes have shown

that the internal resting potential within a cell is ‐60 mV to ‐90

mV (typically ‐ 70 mV) with reference to the outside of the cell

• By convention, the outside is defined as 0mV (ground)

• This potential changes to approximately + 20 mV for a short

period during cell depolarisation

• Cell activity results from some form of stimulation

Cell Membrane Potentials



• Cell membranes in

general,

and

membranes

of

nerve

cells

in

particular,

maintain a small voltage or "potential" across the membrane in its normal

or resting state.

• In the rest state, the inside of the nerve cell membrane is negative with

respect to the outside (typically about ‐70 millivolts).

• The voltage arises from differences in concentration of the electrolyte

ions K+ and Na+.

• There is a process which utilizes ATP (adenosine triphosphate ‐ Active

transport of ions against an established electrochemical gradient ) to

pump out three Na+ ions and pump in two K+ ions. The collective action of

these mechanisms leaves the interior of the membrane about ‐70 mV with

respect to the outside.

• If the equilibrium of the nerve cell is disturbed by the arrival of a suitable

stimulus dynamic changes in the membrane potential in response to

the stimulus is called an Action Potential.

• After the action potential the mechanisms described above bring the cell

membrane back to its resting state

Excitable Cells



• Excitable cells are a class of cells that produce bioelectric

potentials as a result of electrochemical activity.

• At any given time, these cells can exist in one of two states,

resting and active.

• Chemical

and

electrical

stimuli

can

force

an

excitable

cell

from

the resting to the active state.

• While there are numerous ionic species present both inside

and

outside

the

cell,

only

three

ions

(for

which

the

cell

membrane in its resting state is permeable) play a key role in

the behavior of these cells: K+, Na+ and Cl‐.

Resting Potential, Ionic Concentrations, and Channels



• The neuron cell membrane is approximately 10nm thick and, because it consists of a lipid

bilayer (i.e., two plates separated by an insulator), has capacitive properties.

• The extracellular fluid is composed of primarily Na+ and Cl‐, and the intracellular fluid

(cytoplasm) is composed of primarily K+ and A‐

• The large organic anions (A) are primarily amino acids and proteins and do not cross the

membrane.• Almost without exception, ions cannot pass through the cell membrane except through a

channel

• Channels allow ions to pass through the membrane, are selective, and are

either passive or active



• Passive channels are always open and are ion specific

• A particular channel allows only one ion type to pass through the

membrane and prevents all other ions from crossing the membrane

through that channel.

• Passive channels exist for Cl‐, K+, and Na+

• Active channels, or gates, are either opened or closed in



response

to

an

external

electrical

or

chemical

stimulation.• The active channels are also selective and allow only specific

ions to pass through the membrane.

• Typically, active gates open in response to neurotransmitters

and an appropriate change in membrane potential.

Active State



• If adequately stimulated , either electrically or chemically, the excitable cell will enter into the active

state.

• The trans‐membrane potential varies with time and

position within the cell in this state, and is called an

action

potential .• The following sequence of events occurs when the

cell enters the active state:

₋ The chemical or electrical stimuli increases the

permeability of the membrane to Na+

₋ Na+ rushes into the cell due to the large concentration

gradient.

Active State (cont.)



• These positively charged ions entering the cell cause the

trans‐membrane potential to become less negative, and

eventually slightly positive

• This change is often referred to as a depolarization• A short time ( tenths of microseconds) later the membrane’s

permeability to K + increases, which results in an outflow of K+

• The outflow of K + causes the trans‐membrane potential to

decrease

• This decrease in potential causes the membrane’s permeability to both Na +, and eventually K +, to decrease to

their resting levels

• There is only a relatively small (immeasurable) net flow of ions across the membrane during an action potential.

• The Na‐K pump restores the concentrations (pumps Na out

and K in) of the ions to their resting levels.

• The result of the transition from the resting to the

active state is the Action Potential



• In response to the appropriate stimulus, the cell

membrane of a nerve cell goes through a sequence of

depolarization from its rest state to the active state

followed by repolarization to the rest state once again

• The cell membrane actually reverses its normal polarity

for

a

brief

period

before

re‐

establishing

the

rest

potential

• The action potential sequence is essential for neural

communication.• The simplest action in response to thought requires

many such action potentials for its communication and

performance



The process summary



1. A stimulus is received by the dendrites of a nerve cell. This causes the Na+

channels to open. If the opening is sufficient to drive the interior potential from ‐70 mV up to ‐55 mV, the process continues.

2. Having reached the action threshold, more Na+ channels (sometimes called

voltage‐gated channels) open The Na+ influx drives the interior of the cell membrane up to about +30 mV. The process to this point is called

DEPOLARIZATION.

3. The Na+ channels close and the K+ channels open. Having both Na+ and K+

channels open at the same time would drive the system toward neutrality

and prevent the creation of the action potential.

4. With the K+ channels open, the membrane begins to REPOLARIZE back

toward its rest potential.

5. The repolarization typically overshoots the rest potential to about ‐90 mV.

This

is

called

hyperpolarization. Hyperpolarization prevents

the

neuron

from

receiving another stimulus during this time.

6. After hyperpolarization, the Na+/K+ pumps eventually bring the membrane

back to its resting state of ‐70 mV .



Absolute & Relative Refractory Period

ARP & RRP• During the initial portion of the Action potential



• During the initial portion of the Action potential

membrane does not respond Absolute refractory

period

• During the Relative Refractory Period “RRP” the action

potential takes action

• The refractory period limits the frequency of a

repetitive excitation procedure

₋ e.g. ARP=1ms → upper limit of repetitive discharge

< 1000 impulses/s

Absolute & Relative Refractory Period

ARP & RRP (cont.)



v : action pot.

Nernst equil. Pot for Na

Nernst equil. Pot for K

Electrical Circuit Model of Nerve Membrane



Alan Hodgkin and Andrew Huxley Neural Model

Nobel

Prize

in

1963

Bioelectric phenomena



Lecture 3



Lecture 3Bio‐transducers

Part I: Bio‐ElectrodesPart II: Physical Measurements

Dr.R.B.Ghongade

Department of E&TC,

V.I.I.T., Pune‐411048

Introduction



• Biomedical sensors are used routinely in clinical medicine and biological research for measuring a

wide range of physiological variables• Often called biomedical transducers and are the

main building blocks of diagnostic medical instrumentation

• Used in vivo to perform continuous invasive and noninvasive monitoring of critical physiological variables

• Also used in vitro to help clinicians in various diagnostic procedures

• Some sensors are used primarily in clinical

laboratories to measure in vitro physiological



laboratories to measure in vitro physiologicalquantities such as electrolytes, enzymes, and other biochemical metabolites in blood

• Other biomedical sensors for measuring pressure, flow, and the concentrations of

gases such as oxygen and carbon dioxide are used in vivo to follow continuously (monitor) the condition of a patient

Requirements of Biomedical Sensors• Stringent requirements



g q• Assess in vitro the

– accuracy, –

operating range – response time – Sensitivity – Resolution –

Reproducibility• Later, depending on the intended application, similar in

vivo tests may be required to confirm the specifications of the sensor and to assure that the measurement remains – Sensitive – Stable – Safe – cost‐effective

Sensor Classifications



• Physical sensors – Geometric – Mechanical – Thermal – Hydraulic – Electric – Optical

• Chemical sensors – Gas – Electrochemical – Photometric – Other physical chemical methods – Bioanalytic

Sensor Classifications• Classified according to the quantity to be measured and are

typically categorized as physical, electrical, or chemical



yp y g p y , ,depending on their specific applications

• Biosensors are a special sub‐classification of biomedical

sensors• They have two distinct components:

– a biological recognition element such as a purified enzyme, antibody, or receptor, (which functions as a mediator and provides the selectivity

that

is

needed

to

sense

the

chemical

component (usually referred to as the analyte) of interest)

– a supporting structure, which also acts as a transducer and is in intimate contact with the biological component. (The purpose of the

transducer

is

to

convert

the

biochemical

reaction

into

the

form

of

an

optical,

electrical,

or

physical

signal

that

is

proportional

to

the

concentration

of

a

specific

chemical)

Another way of classifying biomedical transducers!

•

One can also look at biomedical sensors from the standpoint of their applications



pp

• These can be generally divided according to whether a sensor is used for

– diagnostic

– therapeutic *purposes

• Sensors for clinical studies such as those carried out in the

clinical chemistry laboratory must be standardized in such a way that errors that could result in an incorrect diagnosis or inappropriate therapy are kept to an absolute minimum

• These sensors must not only be reliable themselves, but appropriate methods must exist for testing the sensors that are a part of the routine use of the sensors for making biomedical measurements

*Having or exhibiting healing powers

One more way of classifying biomedical transducers!



• Standpoint of how they are applied to the patient or research subject

– Non‐contacting (noninvasive)

– Skin surface (contacting)

–

Indwelling (minimally invasive) – Implantable (invasive)



Part I: Bio‐Electrodes

BIOPOTENTIAL MEASUREMENTS



• Biopotential measurements are made using different kinds of specialized electrodes

• The function of these electrodes is to couple the ionic potentials generated inside the body

to an electronic instrument• Biopotential electrodes are classified either as

– noninvasive (skin surface)

– invasive (e.g., microelectrodes or wire electrodes)

Bioelectric Signals Sensed by Biopotential Electrodesand Their Sources



The Electrolyte/Metal Electrode

Interface



• A metal when placed in an electrolyte (i.e., anionizable) solution, develops a charge distribution

is created next to the metal/electrolyte interface

• This localized charge distribution causes an electric potential, called a half ‐cell potential , to be developed across the

interface between the metal and the electrolyte solution



• Biopotential measurements are made by utilizing two similar electrodes composed of the same metal.

•

Therefore, the two half ‐cell potentials for these electrodes would be equal in magnitude.



• For example, two similar biopotential electrodes can be taped to the chest near the heart to measure the electrical potentials generated by the heart (electrocardiogram, or ECG)

• Ideally, assuming that the skin‐to‐electrode interfaces are electrically identical , the differential amplifier attached to these two electrodes would amplify the biopotential (ECG) signal but the half ‐cell potentials would be canceled out

• In practice disparity in electrode material or skin contact resistance could cause a significant DC of fset voltage that would cause a current to flow through the two electrodes.

• This current will produce a voltage drop across the body

• The offset voltage will appear superimposed at the output of the amplifier and may cause instability or base line drift in the recorded biopotential

Electrode – Electrolyte InterfaceGeneral Ionic Equations

a)



a) If electrode has same material as cation, then this material gets oxidized and enters the electrolyte as a cation and electrons remain at the electrode and flow in the external circuit.

b) If anion can be oxidized at the electrode to form a neutral atom, one or two electrons are given to the electrode.

a)

b)

Current flow from electrode to electrolyte : Oxidation (Loss of e‐)Current flow from electrolyte to electrode : Reduction (Gain of e‐)

The dominating reaction can be inferred from the following :

Half Cell Potential

A characteristic potential difference established by the electrode and its



c a acte st c pote t a d e e ce estab s ed by t e e ect ode a d tssurrounding electrolyte which depends on the metal, concentration of ions in solution and temperature (and some second order factors) .

Half cell potential cannot be measured without a second electrode.

The half cell potential of the standard hydrogen electrode has been

arbitrarily set to zero. Other half cell potentials are expressed as a potential difference with this electrode.

Reason for Half Cell Potential : Charge Separation at Interface

Oxidation or reduction reactions at the electrode‐electrolyte interface lead to a double‐

charge layer, similar to that which exists along electrically active biological cell membranes.

Measuring Half Cell Potential



Note: Electrode material is metal + salt or polymer selective membrane

Polarization

If there is a current between the electrode and electrolyte, the observed half cell i l i f l d d l i i



potential is often altered due to polarization.

OverpotentialDifference between observed and zero‐current half cell

potentials

Resistance

Current changes resistance of electrolyte and thus, a voltage drop results.

Concentration

Changes in distributionof ions at the electrode‐

electrolyte interface

ActivationThe activation energy

barrier depends on the direction of current and

determines kinetics

Note: Polarization and impedance of the electrode are two of the most important electrode properties to consider.

Nernst Equation

When two aqueous ionic solutions of different concentration are separated by an ion‐selective semi‐permeable membrane an electric potential exists across the membrane



selective semi permeable membrane, an electric potential exists across the membrane.

For the general oxidation‐reduction reaction

The Nernst equation for half cell potential is

where E0 : Standard Half Cell Potential E : Half Cell Potential

a : Ionic Activity (generally same as concentration)

n : Number of valence electrons involved

Note: interested in ionic activity at the electrode

(but note temp dependence

Polarizable and Non-Polarizable

Electrodes

Use for recording



Perfectly Polarizable Electrodes

These are electrodes in which no actual charge crosses the electrode‐electrolyte interface when a current is applied. The current across the interface is a displacement current and the electrode behaves like a capacitor. Example : Ag/AgCl Electrode

Perfectly Non‐Polarizable Electrode

These are electrodes where current passes freely across the electrode‐electrolyte interface, requiring no energy to make the transition. These electrodes see no overpotentials. Example : Platinum electrode

Example: Ag‐AgCl is used in recording while Pt is use in stimulation

Use for stimulation

Ag/AgCl Electrode

Relevant ionic equations



Ag

+

Cl

‐

Cl2 Governing Nernst Equation

Solubility

product of AgCl

Fabrication of Ag/AgCl electrodes1. Electrolytic deposition of AgCl

2. Sintering process forming pellet electrodes

Equivalent Circuit



Cd : capacitance of electrode‐eletrolyte interfaceRd : resistance of electrode‐eletrolyte interface

Rs : resistance of electrode lead wireEcell : cell potential for electrode

Frequency Response

Corner frequencyRd+Rs

Rs

Electrode Skin Interface

Ehe



Sweat glandsand ducts

Electrode

Epidermis

Dermis andsubcutaneous layer

Ru

Rs

RdCd

Gel

Re

Ese EP

RPCPCe

Stratum Corneum

Skin impedance for 1cm2 patch:200kΩ @1Hz

200 Ω @ 1MHz

Alter skin

transport (or deliver drugs) by:

Pores produced by

laser, ultrasound or by iontophoresis

100

100

Nerve endings Capillary

Motion Artifact

Why



When the electrode moves with respect to the electrolyte, the distribution of the double layer of charge on polarizable electrode interface changes. This changes the half

cell potential temporarily.

What

If a pair of electrodes is in an electrolyte and one moves with respect to the other, a potential difference appears across the electrodes known as the motion artifact.

This is a source of noise and interference in biopotential measurements

Motion artifact is minimal for non‐polarizable electrodes

Body Surface Recording ElectrodesElectrode metal

Electrolyte



1. Metal Plate Electrodes (historic)

2. Suction Electrodes

(historic interest)

3. Floating Electrodes

4. Flexible Electrodes

Think of the

construction of electrosurgical electrode

And, how does

electro‐surgery work?

Commonly Used Biopotential Electrodes

M t l l t l t d



Metal plate electrodes

– Large surface: Ancient,

therefore still used, ECG

– Metal disk with stainless steel;

platinum or gold coated

–

EMG, EEG – smaller diameters

– motion artifacts

– Disposable foam-pad: Cheap!

(a) Metal‐plate electrode used for application to limbs. (b) Metal‐disk electrode applied with surgical tape. (c)Disposable foam‐pad electrodes, often used with ECG

Commonly Used Biopotential

ElectrodesSuction electrodes



Suction electrodes

‐ No straps or adhesives required‐ precordial (chest) ECG‐ can only be used for short periods

Floating electrodes

‐ metal disk is recessed‐ swimming in the electrolyte gel‐ not in contact with the skin

‐ reduces motion artifact

Suction Electrode

Insulatingpackage

Metal disk

Commonly Used Biopotential

Electrodes



Double‐sided

Adhesive‐tapering Electrolyte gel

in recess

(a) (b)

(c)

Snap coated with Ag‐AgCl External snap

Plastic cup

Tack

Plastic disk

Foam padCapillary loops

Dead cellular material

Germinating layer

Gel‐coated sponge

Floating Electrodes

Reusable

Disposable

Commonly Used Biopotential Electrodes



(a) Carbon‐filled silicone rubber electrode. (b) Flexible thin‐film neonatal electrode.(c) Cross‐sectional view of the thin‐film

electrode in (b).

Flexible electrodes

‐ Body contours are often irregular

‐ Regularly shaped rigid electrodesmay not always work.‐ Special case : infants ‐ Material : ‐ Polymer or nylon with silver

‐ Carbon filled silicon rubber(Mylar film)

Internal Electrodes

Needle and wire electrodes for



percutaneous measurement of biopotentials

(a) Insulated needle electrode. (b) Coaxial needle electrode. (c) Bipolar coaxial electrode.

(d) Fine‐wire electrode connected to hypodermic needle, before being inserted.

(e) Cross‐sectional view of skin

and muscle, showing coiled fine‐wire electrode in place.

Biopotential microelectrodes:(a) capillary glass microelectrode(b) insulated metal microelectrode

(c) solid‐state multisite recording microelectrode



Fetal ECG Electrodes



Electrodes for detecting fetal electrocardiogram during labor, by means of intracutaneous needles (a) Suction electrode. (b) Cross‐sectional view of suction electrode in place, showing penetration of probe through epidermis. (c) Helical electrode, which is attached to fetal skin by corkscrew type action.

Electrode Arrays

ContactsInsulated leads

Ag/AgCl electrodes

Ag/AgCl electrodesContacts



Examples of microfabricated electrode arrays. (a) One‐dimensional plunge electrode array, (b) Two‐dimensional array, and (c) Three‐dimensional array

(b)

Base

BaseInsulated leads

(a)

(c)

Tines

Base

Exposed tip

Microelectrodes

Why

M t ti l diff ll b



Measure potential difference across cell membrane

Requirements – Small enough to be placed into cell

– Strong enough to penetrate cell membrane

–

Typical tip diameter: 0.05 – 10 micronsTypes

– Solid metal -> Tungsten microelectrodes

– Supported metal (metal contained within/outside glass needle)

– Glass micropipette -> with Ag-AgCl electrode metal

Intracellular

Extracellular

Metal Microelectrodes

C



Extracellular recording – typically in brain where you are interested in recording the firing of neurons (spikes).

Use metal electrode+insulation ‐> goes to high impedance amplifier…negative capacitance amplifier!

Microns!

R

Metal Supported Microelectrodes



(a) Metal inside glass (b) Glass inside metal

Glass Micropipetteheat

pull

Ag‐AgCl wire+3M

KCl has very low junction potential and hence very accurate for dc

measurements (e.g. action potential)



A glass micropipet electrode filled with an electrolytic solution (a) Section of fine‐bore glass capillary.

(b) Capillary narrowed through heating and stretching. (c) Final structure of glass‐pipet microelectrode.

Intracellular recording – typically for recording from cells, such as cardiac myocyteNeed high impedance amplifier…negative capacitance amplifier!

Fill with intracellular fluid or 3M KCl

Electrical Properties of

MicroelectrodesMetal Microelectrode



Metal microelectrode with tip placed within cell

Equivalent circuitsUse metal electrode+insulation ‐> goes to high impedance amplifier…negative capacitance amplifier!

Electrical Properties of Glass Intracellular

Microelectrodes

Glass Micropipette Microelectrode



Stimulating Electrodes

– Cannot be modeled as a series resistance and capacitance (there is no single useful model)

Features



(there is no single useful model) – The body/electrode has a highly nonlinear response to

stimulation – Large currents can cause

– Cavitation – Cell damage – Heating

Types of stimulating electrodes

1. Pacing

2. Ablation3. Defibrillation

Platinum electrodes:Applications: neural stimulation

Modern day Pt‐Ir and other exotic metal combinations to reduce polarization, improve conductance and long life/biocompatibility

Steel electrodes for pacemakers and defibrillators

Intraocular Stimulation Electrodes



Microelectronic technology

for MicroelectrodesBonding pads

SiO2 insulatedAu probes

Exposed

Insulatedlead vias



Si substrateExposed tips

Lead viaChannels

Electrode

Silicon probe

Silicon chip

Miniatureinsulatingchamber

Contactmetal film

Hole

Silicon probe

electrodes

(b)

(d)

(a)

(c)

Different types of microelectrodes fabricated using microfabrication/MEMS technology

Beam‐lead multiple electrode. Multielectrode silicon probe

Multiple‐chamber electrode Peripheral‐nerve electrode

• Ensure that all parts of a metal electrode that will touch the

electrolyte

are

made

of

the

same

metal.

– Dissimilar metals have different half ‐cell potentials making an electrically unstable, noisy junction.

– If the lead wire is a different metal, be sure that it is well insulated.

Practical Hints in Using ElectrodesPractical Hints in Using Electrodes



If the lead wire is a different metal, be sure that it is well insulated.

– Do not let a solder junction touch the electrolyte. If the junction must touch the electrolyte, fabricate the junction by welding or mechanical clamping or crimping.

• For differential measurements, use the same material for each electrode.

– If the half ‐cell potentials are nearly equal, they will cancel and minimize the saturation effects of high‐gain, dc coupled amplifiers.

• Electrodes attached to the skin frequently fall off.

– Use very flexible lead wires arranged in a manner to minimize the force

exerted on the electrode. – Tape the flexible wire to the skin a short distance from the electrode,

making this a stress‐relief point.

Practical Hints in Using ElectrodesPractical Hints in Using Electrodes

• A common failure point in the site at which the lead wire is attached to the

electrode. – Repeated flexing can break the wire inside its insulation.

– Prove strain relief by creating a gradual mechanical transition between the wire and the electrode.



– Use a tapered region of insulation that gradually increases in diameter from that

of the wire towards that of the electrode as one gets closer and closer to the electrode.

• Match the lead‐wire insulation to the specific application.

– If the lead wires and their junctions to the electrode are soaked in extracellular fluid or a cleaning solution for long periods of time, water and other solvents can

penetrate the polymeric coating and reduce the effective resistance, making the lead wire become part of the electrode.

– Such an electrode captures other signals introducing unwanted noise.

• Match your amplifier design to the signal source.

– Be sure that your amplifier circuit has an input impedance that is much greater than the source impedance of the electrodes.



Part II: Physical Measurements

Primary Transducers

• Conventional Transducers – large, but generally reliable, based on older technology



• thermocouple: temperature difference• compass (magnetic): direction

• Microelectronic Sensors• millimeter sized, highly sensitive, less robust

– photodiode/phototransistor: photon energy (light)• infrared detectors, proximity/intrusion alarms

– piezoresisitve pressure sensor: air/fluid pressure – microaccelerometers: vibration, Δ‐velocity (car crash)

– chemical sensors: O2, CO2, Cl, Nitrates (explosives)

– DNA arrays: match DNA sequences

Direct vs. Indirect Measurement

• Direct Measurement: – When sensor directly measures parameter of interest



–

Example, displacement sensor measuring diameter of blood vessel

• Indirect Measurement: – When sensor measures a parameter that can be

translated into the parameter of interest – Example, displacement sensor measuring movement

of a microphone diaphragm to quantify blood movement through the heart

Physical Variables and Sensors



Displacement Measurements

• Many biomedical parameters rely on measurements of size, shape, and position of organs, tissue, etc.– require displacement sensors



– require displacement sensors

• Examples(direct) diameter of blood vessel – (indirect) movement of a microphone diaphragm to quantify

blood movement through the heart

• Primary Transducer Types – Resistive Sensors (Potentiometers & Strain Gages) – Inductive Sensors – Capacitive Sensors – Piezoelectric Sensors

Displacement Sensors



Variable Resistance Sensor(Potentiometer)• A potentiometer is a resistive‐type transducer that converts either

linear or angular displacement into an output voltage by moving a

sliding contact along the surface of a resistive element

• Potentiometers produce output potential (voltage) change in response to input ( d l ) h



(e.g., displacement) changes• typically formed with resistive

elements e.g. carbon/metal film• ΔV = I ΔR

• produce linear output in response to

displacement• Example potentiometric displacement

sensors• Translational: small (~mm) linear

displacements• Vo increases as xi increases

• Single‐Turn: small (10‐50º) rotational displacements

• Vo increases as φ increases

xi

• Strain gauges are displacement‐type transducers that measure changes in the length of an object as a result of an applied force

• These transducers produce a resistance change that is proportional to the fractional change in the length of the object also called strain

Variable Resistance Sensor(Strain Gauge)



fractional change in the length of the object, also called strain• The relative sensitivity of this device is given by its gauge factor, γ

Where ΔR is the change in resistance when the structure is stretched by an amount Δl

(a)Bonded‐type strain gauge transducer



(b) Resistive strain gauge (un‐bonded type) blood pressure transducer

Strain gauges on a cantilever structure to provide temperature compensation

(a) cross‐sectionalview of the cantilever



(b) placement of the strain gauges in a half bridge or full bridge for temperature compensation and enhanced sensitivity

Liquid metal strain gauge• Instead of using a solid electric conductor such as the wire or metal foil,

mercury confined to a compliant, thin wall, narrow bore elastomeric tube

is used – The compliance of this strain gauge is determined by the elastic

properties of the tube

– Since only the elastic limit of the tube is of concern this sensor can be



Since only the elastic limit of the tube is of concern, this sensor can be

used to detect much larger displacements than conventional strain gauges

– Its sensitivity is roughly the same as a foil or wire strain gauge, but it is not as reliable

• Elastic‐resistance strain gages are extensively used in biomedical applications, especially in cardiovascular and respiratory dimensional and plethysmographic (volume‐measuring) determinations

• Elastic strain gage is typically linear with 1% for 10% of maximal extension thus, strain gages are only good measuring small displacements

Mercury‐in‐rubber strain‐gage plethysmography



(a) Four‐lead gage applied to human calf (b) Bridge output for venous‐occlusion plethysmography(c) Bridge output for arterial‐pulse plethysmography

Semiconductor strain gauge

– These devices are frequently made out of pieces of silicon with strain gauge patterns formed using



semiconductor microelectronic technology. – The principal advantage of these devices is that

their gauge factors can be more than 50 times

greater than that of the solid and liquid metal devices



Strain Gauge:

Materials



• G for semiconductor materials ~ 50‐70 x that of metals due to stronger piezo‐resistive effect

• semiconductors have much higher TCR, requires temperature compensation in strain gauge

Disposable blood‐pressure sensor



• Made of clear plastic so that air bubbles can be seen• Saline flows from intravenous bag through clear IV tube and the sensor to

the patient• This flushes blood out of the tip of the catheter to prevent clotting•

A lever can open or close the flush valve• The silicon chip has silicon diaphragm with four‐resistor Wheatstone bridge

diffused to it• Its is isolated electrically by a silicone elastomer gel

Inductive Sensors

• An inductance L can be used to measure displacement by varying any three of the coil



parameters:

where

n = number of turns of coilG= geometric form factorµ = effective permeability of the

medium

• Each of these parameters can be changed by mechanical means

Inductive displacement sensors



(a) self ‐inductance, (b) mutual inductance, (c) differential transformer

LVDT

• The linear variable differentialtransformer (LVDT) is widely used inphysiological research and clinicalmedicine to measure pressure,



displacement, and force• The LVDT is composed of a primary coil

and two secondary coils connected inseries

• The coupling between these two coils ischanged by the motion of a high‐permeability alloy slug between them

• The two secondary coils are connectedin opposition in order to achieve awider region of linearity

• The primary coil is sinusoidally excited,with a frequency between 60 Hz and 20kHz.

• The alternating magnetic field induces nearly equal voltages and in the secondary coils

• The output voltage = ‐

• When the slug is symmetrically placed, the two secondary voltages are equal and the output signal is zero

• Linear variable differential transformer characteristics



include linearity• over a large range, a change of phase by 180° when the

core passes through the center position, and saturation on the ends

• Specifications of commercially available LVDTs include sensitivities on the order of 0.5 to 2 mV for a displacement of 0.01 mm/V of primary voltage, full‐scale displacement of 0.1 to 250 mm, and linearity of 0.25%

•

Sensitivity for LVDTs is much higher than that for strain gauges

(a) As moves through the null position, the phase changes 180°,while the magnitude of is proportional to the



magnitude of (b) An ordinary rectifier demodulator cannot distinguish between (a) and (b), so a phase‐sensitive

demodulator is required

Electromagnetic blood‐flow transducer

• Blood flow through an exposed vessel can

be measured by means of an electromagnetic flow transducer

• Consider a blood vessel of diameter filled with blood flowing with a uniform velocity



• Blood vessel is placed in a uniform

magnetic field that is perpendicular to the direction of blood flow

• Negatively charged anion and positively charged cation particles in the blood will

experience a force that is normal to both the magnetic field and blood flow

directions )

• where q is the elementary charge (1.6 x 10 C)

• These charged particles will be deflected in opposite directions and will move along the diameter of the blood vessels according to the direction of the force

vector

• This movement will produce an opposing force

which is equal to



• where is the net electrical field produced by the displacement of the charged particles and is the potential

produced across the blood vessel• At equilibrium, these two forces will be equal, hence the

potential difference is given by

• is proportional to the velocity of blood through the vessel

Electromagnetic flowmeter



Capacitive Sensors• The capacitance between two parallel plates of area A separated by

distance is

Where is the dielectric constant of free space and is the relative dielectric constant of the insulator

….(1)



• The sensitivity K of a capacitive sensor to changes in plate separation is found by differentiating (1)

Note that the sensitivity increases as the plate separation decreases

• The percent change in C about any neutral point is equal to the per‐unit change in for small displacements is

Capacitance sensor for measuring dynamic displacementchanges and pressure



• Compliant plastics of different dielectric constants may

be placed between foil layers to form a capacitive mat to be placed on a bed

• Patient movement generates charge, which is amplified and filtered to display respiratory movements from the

lungs and ballistographic movements from the heart

Piezoelectric Sensors

• Piezoelectric sensors are used to measure physiological displacements and record heart sounds

• Piezoelectric materials generate an electric potential when



mechanically strained, and conversely an electric potential can cause physical deformation of the material• The principle of operation : when an asymmetrical crystal

lattice is distorted, a charge reorientation takes place, causing a relative displacement of negative and positive charges

• The displaced internal charges induce surface charges of opposite polarity on opposite sides of the crystal

• Surface charge can be determined by measuring the difference in voltage between electrodes attached to the surfaces

• Assume infinite leakage resistance, the total induced charge is directly proportional to the applied force

Where is the piezoelectric constant, /

• The change in voltage can be found by assuming that the



system acts like a parallel‐plate capacitor where the voltage across the capacitor is charge divided by capacitance

• Typical values for are 2.3 pC/N for quartz and 140 pC/N for barium titanate

• For a piezoelectric sensor of 1 cm area and 1 mm thickness

with an applied force due to a 10 g weight, the output voltage v is 0.23 mV and 14 mV for the quartz and barium titanatecrystals, respectively

• There are various modes of operation of piezoelectric sensors, depending on the material and the crystallographic orientation of the plate

• These modes include the thickness or longitudinal compression, transversal compression, thickness‐shear action, and face‐shear action

•

Al il bl i l t il i fil h



Also available are piezoelectric polymeric films, such as polyvinylidene fluoride (PVDF)

• These films are very thin, lightweight and pliant(easily flexed or bent), and they can be cut easily

and adapted to uneven surfaces

(a) Equivalent circuit of piezoelectric sensor, where Rs = sensor leakage resistance, Cs =

sensor capacitance, Cc = cable capacitance, Ca = amplifier input capacitance, Ra = amplifier input resistance, and q = charge generator

(b) Modified equivalent circuit with current generator replacing charge generator

Temperature Measurements

• Temperature is extremely important to human physiology

l l i di f



– example: low temperature can indicate onset of problems, e.g., stroke

– example: high temperature can indicate infection

• Temperature sensitive enzymes and proteins can be destroyed by adverse temperatures

•

Temperature measurement and regulation is critical in many treatment plans

Temperature Sensor Options• Thermoelectric Devices

– most common type is called Thermocouple – can be made small enough to place inside catheters or hypodermic needles

• Resistance Temperature Detectors (RTDs) – metal resistance changes with temperature

– Platinum, Nickel, Copper metals are typically used

ff



– positive temperature coefficients

• Thermistors(“thermally sensitive resistor”) – formed from semiconductor materials, not metals

– often composite of a ceramic and a metallic oxide (Mn, Co, Cu or Fe)

– typically have negative temperature coefficients

• Radiant Temperature Sensors – photon energy changes with temperature

– measured optically (by photo detector)

• Integrated Circuit(IC) Temperature

Sensors

– various temperature effects in silicon manipulated by circuits

– proportional to absolute temperature (PTAT) circuit: Si bandgap=

Properties of Temperature Sensors



Metallic Resistance Thermometers

• The electric resistance of a piece of metal or wire generally increases as the temperature of that electric conductor increases

• A linear approximation to this relationship is given by



• A linear approximation to this relationship is given by

Where

is the resistance at temperature

, is the temperature coefficient of resistance, and is the temperature at which the resistance is being measured

• It is important to make sure that the electronic circuit does

not pass a large current through the resistance thermometer to provide self ‐heating due to the Joule conversion of electric energy to heat

Temperature Coefficient of Resistance for Common Metals and Alloys



Thermocouples• Thermoelectric thermometry is based on the discovery of

Seebeck – dissimilar metals at diff. temps. ‐>signal

– electromotive force (emf) is established by the contact of two dissimilar metals at different temperatures

• Empirical calibration data are usually curve fitted with a



Empirical calibration data are usually curve fitted with a power series expansion that yields the Seebeck voltage

…

where is in degrees Celsius and the reference junction is maintained at 0°

• Thermocouple features:• rugged and good for very high temperatures• not as accurate as other Temp sensors (also non‐linear and drift)

Thermocouple Circuits



(a) Peltier emf

(b)The first law, homogeneous

circuits, states that in a circuit composed of a single homogeneous metal, one cannot maintain an

electric current by the application of heat alone

• In (b) the net emf at c–d is the same as in (a), regardless of the fact that a temperature distribution (T3) exists along one of the wires (A)



• The second law, intermediate metals, states that the

net emf in a circuit consisting of an interconnection of a number of unlike metals, maintained at the same

temperature, is

zero

• The practical implication of this principle is that lead wires may be attached to the thermocouple without

affecting the accuracy of the measured emf, provided that the newly formed junctions are at the same temperature



• The third law, successive or intermediate temperatures, is illustrated in (d), where emf E1 is generated when two dissimilar metals have junctions at

temperatures T1 and T2 and emf E2 results for temperatures T2 and T3.• It follows that an emf E1 + E2 results at c–d when the junctions are at

temperatures T1 and T3• This principle makes it possible for calibration curves derived for a given

reference‐ junction temperature to be used to determine the calibration

curves for another reference temperature

• The thermoelectric sensitivity α (also called the thermoelectric power or the Seebeck coefficient) is

⋯



• Using thermocouple with cold junction compensator LT1025

Common Thermocouples



Thermistors

• Heavily used in biomedical applications

– base resistivity: 0.1 to 100 ohm‐meters

– can be made very small ~500um diameter



can be made very small, 500um diameter – large sensitivity to temperature (3‐4% / ºC)

– excellent long‐term stability

• Resistance vs. temperature

– keep current low to avoid self ‐heating



•

The diagonal lines with a positive slope give linear resistance values and show the degree of thermistor linearity at low currents.• The intersection of the thermistor curves and the diagonal lines with negative slope

give the device power dissipation

Semiconductor Thermometers• The

PTAT

Voltage

and

Electronic

Thermometry

– The well‐defined temperature dependence of the diode voltage is actually used as the basis for most digital thermometers

– We can build a simple electronic thermometer in

which two identical diodes are biased by current sources and



ysources and

• If we calculate the difference between the diode voltages using

we discover a voltage that is directly proportional t o absolute t emperature (PTAT), referred to as the PTAT voltage V PTAT



• The PTAT voltage has a temperature coefficient given by

• By using two diodes, the temperature dependence of has been eliminated from the equation

• For example, suppose T = 295 K,

= 250 µA, and

= 50 µA , then VPTAT = 40.9 mV with a temperature coefficient of +0.139 mV/K.

Electromagnetic Radiation

Spectrum

•

Visible light wavelength – ~400‐700nm

• Shorter wavelengths

– ultraviolet, ~100nm

– x‐ray, ~1nm~0 1 ( 1Å)



– gamma rays, ~0.1nm (=1Å)

• Longer wavelengths

– infrared IR: broad spectrum

• near IR, ~1000nm = 1μm

• thermal IR, ~100μm

• far IR, ~1mm

• microwave, ~1cm

• radar, ~1‐10cm

• TV & FM radio, ~1m

• AM radio, ~100m

Radiation Thermometry• There is a known relationship between the surface temperature of

an object and its radiant power• possible to measure the temperature of a body without physical

contact with it• At body temperatures, radiant spectrum in far infrared

•

Medical thermography is a technique whereby the temperature distribution of the body is mapped with a sensitivity of a few tenths



y pp yof a kelvin.

• It is based on the recognition that skin temperature can vary from place to place depending on the cellular or circulatory processes

occurring at each location in the body.• Thermography has been used for the early detection of breast

cancer, but the method is controversial• It has also been used for determining the location and extent of

arthritic disturbances, for gauging the depth of tissue destruction from frostbite and burns, and for detecting various peripheral circulatory disorders (venous thrombosis, carotid artery occlusions)



(a) Spectral radiant emittance versus wavelength for a blackbody at 300 K on the left

vertical axis; percentage of total energy on the right vertical axis(b) Spectral transmission for a number of optical materials(c) Spectral sensitivity of photon and thermal detectors

Human Temperature Measurement

• Radiation thermometry is good for determining internal (core body) temperature

―measures magnitude of infrared radiation from tympanic

membrane & surrounding ear canal• tympanic membrane is perfused by the same vasculature as the



tympanic membrane is perfused by the same vasculature as the hypothalamus, the body’s main thermostat

– advantages over thermometers, thermocouples or

thermistors• does not need to make contact to set temperature of the sensor

• fast response time, ~0.1sec

• accuracy ~ 0.1°C

•

independent of user technique or patient activity• requires calibration target to maintain accuracy



• radiation thermometry is an instrument that determines the internal or core body temperature of the human by measuring the magnitude of infrared radiation emitted from the tympanic membrane and surrounding ear canal

Fiber‐optic Temperature Sensor

• Sensor operation – small prism‐shaped sample of single‐crystal undoped GaAs attached to

ends of two optical fibers – light energy absorbed by the GaAs crystal depends on temperature

– percentage of received vs. transmitted energy is a function of temperature



• Can be made small enough for biological implantation

Optical Measurement

• Widely used in medical diagnosis – clinical‐chemistry lab: blood and tissue analysis – cardiac catheterization: measure oxygen saturation of hemoglobin

• Optical system components – source

– filter – detector

C i l i l



• Conventional optical system

• Solid‐state (semiconductor) optical system – miniaturize and simplify

Optical/Radiation Sources

• Tungsten lamp

– very common radiation source

– emissivity is function of wavelength, λ

• ~40% for λ< 1μm (1000nm)

– output varies significantly with temperature

• note 2000K and 3000K spectra on next slide

• higher temperature shortens life of lamp filament

• Arc discharge lamps

fl l fill d i h b di



– fluorescent lamps filled with, e.g., carbon, mercury, sodium, xenon

– more compact w/ high output per unit area

• Light emitting diodes (LED)

– silicon band gap ~1.1eV not very efficient for detection

– GaAs, higher energy (lower wavelength), fast (~10ns) switching

– GaP & GaAsP have even higher energy

• LASER

– common lasers: He‐Ne, Argon (high power, visual spectrum), CO2 – semiconductor laser not preferred; energy too low (infrared)

– lasers also used to mend tears, e.g., in retina

Spectral characteristics of sources, filters, detectors

(a) Light sources: 1. tungsten (W) at 3000 K has a broad

spectral output. At 2000 K, output is lower at all wavelengths and peak output shifts to longer wavelengths

2. Light‐emitting diodes yield a narrow

spectral output with GaAs in the infrared, GaP in the red, and GaAsP in the green

3. Monochromatic outputs from common lasers are shown by dashed lines



(b) Filters1. A Corning 5‐56 glass filter passes a

blue wavelength band

2. A Kodak 87 gelatin filter passes infrared and blocks visible wavelengths.

3. Germanium lenses pass long wavelengths that cannot be passed by glass

4. Hemoglobin Hb and Oxyhemoglobin HbO pass equally at 805 nm and have maximal difference at 660 nm

Spectral characteristics of sources, filters, detectorsc) Detectors

1. The S4 response is a typical

phototube response. 2. The eye has a relatively

narrow response, with colors indicated by VBGYOR.

3. CdS plus a filter has a

response that closely matches that of the eye.

4 Si p n junctions are widely



4. Si p–n junctions are widely used.

5. PbS is a sensitive infrared detector.

6. InSb is useful in far infrared

d) Combination

Indicated curves from (a), (b), and

(c) are multiplied at each

wavelength to yield (d), which shows how well source, filter, and detector are matched

Optical Transmitter & Filters

• Geometrical Optics: Lenses – focus energy from source into smaller area

– placed to collimate radiation (rays are parallel)

– focus energy from target into detector

• Fiber Optics– efficient transmission of optical signals over



efficient transmission of optical signals over distance

– example medical application: endoscope

• Filters – control transmitted power

– determine wavelengths (colors) transmitted

– produce wavelength spectrum (diffraction grating)

Radiation Sensors

• Spectral response

– Si, no response above 1100nm

– special materials (InSb)

• monitor skin radiation (300K)

• Thermal sensors

– transforms radiation into heat

– flat spectral response but slow

– subject to error from changes in ambient temperature

– example thermal sensors: thermistors thermocouples



– example thermal sensors: thermistors, thermocouples

• Quantum sensors

– transform photon energy into electron release

– sensitive over a limited spectrum of wavelengths

– example quantum sensors: eye, photographic emulsion, sensors below

– Photoemissive sensors, e.g. phototube

– Photoconductive cells

– Photojunction sensors – Photovoltaic sensors

Photoemissive Sensors• Construction & Operation

– photocathode coated with alkali metal – incoming photons (with enough energy, >1eV or 1200nm) release

electrons from photocathode – released electrons attracted to anode and form a current proportional

to incoming photon energy

• Example: phototube, like the S4 in the spectrum plots• Photomultiplier: phototube combined with electron amplifier

– very (the most?) sensitive photodetector



very (the most?) sensitive photodetector• cooled to prevent thermal excitation of electrons• can count individual photons

–

fast response, ~10ns – compare to the eye, which can detect ~6photons within 100ms

Solid‐State

Photoelectric

Sensors

• Photoconductive cells

– Photoresistor

• photosensitive crystalline material such as CdS or PbS• incoming radiation causes electrons to jump band gap and

produce electron‐hole pairs ‐>lower resistance

• Photojunction sensors

– incoming radiation generates electron‐hole pairs in diode depletion region



– minimum detectable energy based on band gap of the diode substrate (e.g., Si)

– can be used in photovoltaic modechange in open‐circuit voltage is monitored

• Photon coupler

– LED‐photodiode combination

• used to isolate electrical circuits• prevent current from leaking out of equipment and into the heart

of a patient

MEMS Transducers

• MEMS = micro‐electro‐mechanical system – miniature

transducers created using IC fabrication processes

•

Microaccelerometer – cantilever beam– suspended mass



– suspended mass

• Rotation – gyroscope

• Pressure

Sensor Calibration

• Sensors can exhibit non‐ideal effects – offset: nominal output ≠ nominal parameter value

– nonlinearity: output not linear with parameter changes

– cross parameter sensitivity: secondary output variation with, e.g.,

temperature• Calibration= adjusting output to match parameter

– analog signal conditioning



– analog signal conditioning

– look‐up table

– digital calibration

• T = a + bV +cV2, T= temperature; V=sensor voltage;

• a,b,c = calibration coefficients

• Compensation

– remove secondary sensitivities

– must have sensitivities characterized

– can remove with polynomial evaluation

– P = a + bV + cT + dVT + e V2, where P=pressure, T=temperature

End of Lecture 3



Lecture

4

aCardiovascular System

I. Heart structure & Cardiac Cycle

II. Heart

conduction

system

&

ECG



Dr.R.B.Ghongade

Department of E&TC,

V.I.I.T., Pune

‐411048

The Cardiovascular System

• Heart: One of the most important organ in the

human body

• Function:– Supply oxygen to all the parts (cells , tissues ,



Supply oxygen to all the parts (cells , tissues ,

muscles ,vital organs) of the human body

– Collect the

excreted

CO2

from the

organs

• Described mostly by comparing it with a fluid

pump

Motivation

• Heart disease

– Major cause of deaths in developed and developing

countries

•

Use

of

engineering

methods

and

the

development

of

instrumentation have contributed substantially to

progress made in recent years in reducing death from



progress made in recent years in reducing death from

heart diseases

•

Blood pressure , flow , and volume are measured byusing engineering techniques

• The electrocardiogram , echocardiogram and

phonocardiogram are measured and recorded with

electronic instruments

The Heart and the cardiovascular system

• A functional cardiovascular system is vital for supplyingoxygen and nutrients to tissues and removing wastesfrom them.

• The heart

is

the

strongest

muscle

in

the

body

• The heart must pump blood throughout the body day



& night

•

The heart

is

2 pumps

working

side

by

side;

on

your

right side is the heart that pumps blood to your lungs

where it picks up O2; on your left side is the heart that pumps this O2‐soaked blood out to your body; pumps

45 million

gallons

blood

in

a lifetime

Location of

the

Heart

• The heart is located in the chest

between the lungs behind the

sternum

and

above

the

diaphragm

• It is surrounded by the

pericardium

• Its size is about that of a fist, and

its weight

is

about

250

‐300

g

• Located above the heart are the

great vessels:



great vessels:

• the superior

•

inferior

vena

cava• the pulmonary artery

• the pulmonary vein, a

• the aorta

• The aortic

arch

lies

behind

the

heart

• The esophagus and the spine lie further behind the heart

Anatomy of

the

Heart

• The walls of the heart are composed of

cardiac muscle, called myocardium

• It also has striations similar to skeletal

muscle

• It consists of four compartments:

the right and left atria and ventricles

• The heart is oriented so that the anterior

aspect is the right ventricle while the

posterior aspect shows the left atrium

• The atria form one unit and the

ventricles another



• This has special importance to the

electric function of the heart

• The left ventricular free wall andthe septum are much thicker than the

right ventricular wall

• This is logical since the left ventricle

pumps blood to the systemic circulation,

where the pressure is considerablyhigher than for the pulmonary

circulation, which arises from right

ventricular outflow

Anatomy of

the

Heart

• The cardiac muscle fibers are oriented spirally and are divided into four groups

• Two groups of fibers wind around the outside of both ventricles

• Beneath these fibers a third group winds around both ventricles

• Beneath these fibers a fourth group winds only around the left ventricle

• The fact that cardiac muscle cells are oriented more tangentially than radially,

and that the resistivity of the muscle is lower in the direction of the fiber has

importance in electrocardiography

• The heart has four valves

– Tricuspid valve: between the right atrium and ventricle lies



– Mitral valve : between the left atrium and ventricle

– Pulmonary valve : between the right ventricle and the pulmonary artery,

– Aortic valve lies in

the

outflow

tract

of

the

left

ventricle

(controlling

flow

to

the

aorta)

• The blood returns from the systemic circulation to the right atrium and from

there goes through the tricuspid valve to the right ventricle

• It is ejected from the right ventricle through the pulmonary valve to the lungs

• Oxygenated blood

returns

from

the

lungs

to

the

left

atrium,

and

from

there

through the mitral valve to the left ventricle

• Finally blood is pumped through the aortic valve to the aorta and the systemic

circulation

Anatomy of

the

Heart



Path of

Blood

through

the

Heart

• Blood that is low in O2 and high in CO2 enters the right atrium through

the venae cavae & coronary sinus

•

next

is

pumped

into

the

pulmonary

circulation

after

blood

is

oxygenated

in the lungs & some of the CO2 is removed, it returns to the left side of

the heart through the pulmonary veins from the left ventricle

• it moves into the aorta

• gas exchanges occur between the blood in the capillaries and the air in

the alveoli

of

the

lungs

• ORDER IN WHICH BLOOD FLOWS:

1. venae cavae & coronary sinus



1. venae cavae & coronary sinus

2. right atrium ‐> tricuspid valve

3. right

ventricle ‐

>

pulmonary

valve ‐

>

pulmonary

trunk4. pulmonary artery

5. pulmonary vein

6. left atrium ‐> bicuspid (mitral) valve

7. left ventricle ‐> aortic valve

8. aorta

• Both pumps are divided into two spaces called

chambers so your heart is actually a 2‐barreled, 4‐

chambered pumper

• The two

sides

do

not

work

independently;

they

are

precisely timed as a team to make the best use of their pumping power (quite efficient!)

• As the heart pumps it makes a variety of clicks and

thumps; these are the sounds of the heart valves asthey click open & shut; each sound has a specialmeaning



meaning – (lubb‐dupp)

• lubb is the

sound

of

the

tricuspid

&

mitral

(bicuspid)

heart

valves

(on the top chambers) shutting;

• dupp is the sound of the semi‐lunar heart valves closing (these

heart valves shut off the big vessels leaving the heart)

• The heart hangs in the center of the chest (mediastinum)

The cardiovascular

system



The

cardiovascular

system



syste

Terminology

• Pulmonary circulation

– The circulatory path for blood‐flow through the lungs

(function of right side heart)

– Pressure difference between the arteries and the veins is

small, low

resistance

– Can be considered as volume pump

S t i i l ti



• Systemic circulation –

The

circulatory

system

that

supplies

oxygen

and

nutrients

to the cells of the body (function of left side of the heart)

– This system is a high resistance circuit with a large pressure

gradient between the arteries and veins

– Can be considered as a pressure pump

• The muscle contraction of the left heart is larger and

stronger than the right heart, because of the greater

pressures

required

for

systemic

circulation• However the volume of the blood delivered per unit time

by the two sides is same when measured over a sufficiently

long interval of time

•

The

left

heart

develops

a

pressure

head

sufficient

to

cause

blood flow to all extremities of the body

• The pumping action itself is performed by contraction of th h t l di h h b f th h t



the heart muscles surrounding each chamber of the heart

•

These

muscles

receive

their

own

blood

supply

from

the

coronary arteries , which surround the heart like a crown( corona)

• The coronary arterial system is a special branch of the

systemic circulation

Pitfall!

• Why we

cannot

indiscriminately

approximate

the

system

with a pump and a hydraulic system? – The pipes, the arteries and the veins are not rigid but flexible

– They are capable of helping and controlling blood circulation by

their own

muscular

action

and

their

own

valve

and

receptor

system

– Blood is not a pure Newtonian fluid; rather it possesses

ti th t d t l ith th l i h d li



properties that do not comply with the laws governing hydraulic

motion

– Also the

blood

requires

help

from

the

lungs

for

O2 and

it

interacts with the lymphatic system

– Many chemicals and hormones affect the operation of the

system

Cardiovascular

circulation



Functioning

• Blood enters the heart on the right side through

– Superior vena cava (coming from upper body

extremities)

– Inferior vena cava (coming from lower body

extremities)



• Incoming blood fills the storage chamber, right

atrium

• Coronary sinus also empties into right atrium

(blood

that

circulates

through

the

heart

itself)

• When right atrium is full, it contracts and

forces blood through the tricuspid valve into

right ventricle• Right ventricle contracts to pump blood into

pulmonary circulation system

• Tricuspid valve closes when pressure in

ventricle exceeds atrial pressure



ventricle exceeds atrial pressure

• Semi ‐lunar valve opens and

blood

is

forced

into pulmonary artery and into the two lungs

• In the alveoli of lungs red blood cells are

recharged with

O2

and CO2 is

expelled

• Pulmonary artery divides many times into

smaller arteries (arterioles), which supply

blood to

alveolar

capillaries,

where

the

exchange of O2

and CO2 takes place

• On the other side of the lung mass is a similar

construction where

capillaries

feed

into

tiny

veins (venules), which in turn form larger veins



and ultimately terminate into pulmonary vein

• This pulmonary vein returns the oxygenated

blood to the heart



Heart’s pumping Cycle

•

Systole – Is defined as the

period of

contraction of the

heart muscles, specifically the

t i l



ventricular

muscles, at

which

time, blood is

pumped into the

pulmonary

artery

and the aorta

Heart’s pumping Cycle

• Diastole

– Period of

dilation of

the heart

cavities as



they fill will

blood

• Once the blood has been pumped into the

arterial system, the heart relaxes, pressure in

chambers

decreases,

the

outlet

valve

close

and in a short time the inlet valves open again

to restart the diastole and initiate new cycle in

the heart

• After passing through many bifurcations of arteries, the blood reaches vital organs, the



brain

and

the

extremities• The last stage of arterial system divides into

smallest arterioles

• These arterioles

feed

into

capillaries

where

O2

is supplied to cells and CO2

is received

• In turn capillaries join into venules and these

finally form inferior and superior vena cava

• Blood supply to the heart itself is from aorta

through coronary arteries into a similar

capillary system

to

the

cardiac

veins

• This blood returns to heart chambers by the

way of coronary sinus



way of coronary sinus

Some facts!

• Average heart

beat

rate

– 75 bpm

– May vary from 60 to 85 (sitting , standing position)

– Infant heart rate may be as high as 140 bpm

– HR increases with heat exposure , physiological and



psychological factors

• Heart pumps about 5 liters of blood per minute

• 75 to 80 % of blood volume in veins, 20% in

arteries , remaining

in

capillaries

Blood Supply to the Heart

• Heart muscle

(myocardium)

needs

blood

• Coronary arteries branch off from systemic

circulation &

feed

capillaries

that

permeate

the heart muscle (myocardium)

• When blockage of to heart muscles occur



• When blockage of to heart muscles occur

cardiac muscles

begin

to

die

&

a heart

attack

(myocardial infarction) can occur if blockage is

extensive



The Conduction System of the Heart

• Electrical stimulus

needed

to

cause

heart

muscle contractions (systole)



ECG Summary



Although representation of an ECG recording as a scalar trace is illustrated in

Figure , several

other

techniques

for

cardiac

electrical

representation,

usually

closely linked to the recording technique, exist

Various Components of the ECG Waveform

• Genesis of ECG

waveform and

timing of

different action

potentials from

different regions

and specialized

cells of the heart and the

corresponding

d l f



cardiac cycle of the

ECG

as

measured on the

body surface

manifest as

P,Q,R,S and T

points

The Application

Areas

of

ECG

Diagnosis

1. The electric axis of the heart

2. Heart rate monitoring

3. Arrhythmias

a. Supraventricular arrhythmias

b. Ventricular arrhythmias

4. Disorders in the activation

sequence

a. Atrioventricular conduction

defects (blocks)

b. Bundle‐branch block

c. Wolff‐Parkinson‐White

6. Myocardial ischemia and infarction

a. Ischemia

b. Infarction

7. Drug effect

a. Digitalis

b. Quinidine

8. Electrolyte imbalance

a. Potassium

b. Calcium

9. Carditis

i di i



c. Wolff Parkinson White

syndrome

5. Increase in wall thickness or size

of the atria and ventricles

a. Atrial enlargement

(hypertrophy)

b. Ventricular enlargement (hypertrophy)

a. Pericarditis

b. Myocarditis

10. Pacemaker monitoring

The Application

Areas

of

ECG

Diagnosis



ECG Lead Systems

• The Conventional

12

‐lead

System

– Bipolar Limb Leads

–

Wilson

Central

Terminal

(WCT) – Goldberger Augmented Leads

– Precordial Leads



– Mason and

Likar Lead

System

(Modified

leads)

• The Corrected Orthogonal Leads (Frank lead

system)

Bipolar Limb

Leads

• Force vectors: – The major sequences of depolarization of the heart and

the relative

voltages

encountered

can

be

explained

by

drawing a series of summation vectors

– It is also useful to describe the direction in which these

vectors are traveling by superimposing our drawing on a

360‐degree

compass

rose

There are there important things that are the

underlying concepts of the lead systems:

1 The principle that impulses coming toward



1. The principle that impulses coming toward

an electrode produce positive deflections,whereas impulses going away from an

electrode produce negative deflections.

2. The positions from which the various

electrodes “look” at the heart.

3. The sequence, direction, and relativemagnitude of the four major vectors of

cardiac depolarization and repolarization.

Einthoven limb

leads

and

Einthoven

triangle

• In the

year

1913,

Einthoven

et

al.

developed

a method

of studying the electrical activity of the heart by

representing it graphically in a two‐dimensional geometric figure, namely, an equilateral triangle

• Based on several oversimplifying assumptions

– The body is a homogeneous volume conductor

– The mean of all electrical forces can be considered as



The mean of all electrical forces can be considered as

originating in

an

imaginary

dipole

located

in

the

electrical

center of the heart

– Electrodes placed on the right arm (RA), left arm (LA) and

left foot (LF) are used to pick up the potential variations on

these extremities

to

form

an

equilateral

triangle

Einthoven triangle

• The Einthoven limb leads

(standard

leads)

are

defined in the following

way

where,

V I= voltage of lead I



V II=

voltage

of

lead

IIV III= voltage of lead III

φL=potential of left arm

φR=potential of right arm

φF =potential of left foot

• The limb

leads

describe

the

cardiac

electrical activity in three different

directions of the frontal plane

Wilson Central

Terminal

(WCT)

• Frank Norman Wilson (1890‐1952) investigated

how electrocardiographic unipolar potentials

could be defined

• Measured with respect to a remote reference

(infinity)

• Formed by connecting a 5 k resistor from each

terminal of the limb leads to a common point called the central terminal

• Wilson suggested that unipolar potentials

should be

measured

with

respect

to

this

terminal which approximates the potential at infinity

• The Wilson central terminal is the average of the limb potentials



•

The

total

current

into

the

central

terminal

from

the limb leads must add to zero to satisfy the

conservation of current (KCL)

Hence,

Circuit of WCT and the location image space and the

location of WCT



Goldberger Augmented

Leads

• Three additional limb leads, VR, VL, and VF are obtained by measuring the

potential between each limb electrode and the Wilson central terminal

• For

instance,

the

measurement

from

the

left

foot

gives

• Goldberger observed that these signals can be augmented by omitting

that resistance from the Wilson central terminal, which is connected to

the measurement electrode

• Three leads may be replaced with a new set of leads that are called

augmented leads because of the augmentation of the signal



• The equation

for

the

augmented

lead

aVF is

• Augmented signal to be 50% larger than the signal with the Wilson central

terminal chosen

as

reference

Goldberger Augmented

Leads

• Note that the three augmented leads, aVR, aVL, and aVF, are fully

redundant with respect to the limb leads I, II, and III



Precordial Leads

• For measuring the potentials close to

the heart, Wilson introduced the

precordial

leads

(chest

leads)

in

1944• These leads, V1‐V6 are located over

the left chest

• The points V1 and V2 are located at the fourth intercostal space on the

right and left side of the sternum

• V4 is located in the fifth intercostal space at the midclavicular line

• V3 is located between the points V2

and V4

•



•

V5

is

at

the

same

horizontal

level

as

V4 but on the anterior axillary line

• V6 is at the same horizontal level as

V4 but at the midline

Precordial chest leads are used to record the voltage difference

between these electrodes and Wilson’s Central Terminus



Mason and

Likar Lead

System

(Modified

leads)

• Mason and Likar recommended moving

the limb electrodes used to record the 12‐

lead ECG from the limbs to the thorax for

exercise electrocardiography

(1966)

• The 12 lead system is usually used for just long enough to record a few heart cycles or beats (10‐15) seconds

• The recorded information is represented as

12 scalar

traces

depicting

the

heart’s

electrical activity at the various sample

sites.

• Interpretation of the 12‐lead ECG is based

upon examination of the shape and size, or



amplitude and

duration,

of

the

various

components of each scalar trace

• The increased number of sample sites, six

of which are on the chest close to the

heart, allows an expert to not only

determine the

presence

of

disease,

but

also the chambers or areas of the heart that are affected

The Corrected

Orthogonal

Leads

• This lead system is known also as Frank

lead system

• Seven electrodes placed on the chest,back,

neck and

left

foot

are

used

to

view

the

heart from the left side, from below and

from the front

• This kind of lead system reflects the

electrical activity in the three perpendicular

directions

X,

Y,

and

Z

and

traces

out

a

three‐

dimensional loop for every cardiac cycle by

means of the time‐variant cardiac

dominant vector

• The three projections of this loop onto XY,

XZ and YZ planes are also recorded



• The morphology of the loops, their direction of rotation and their areas are the

main spatial quantities that improve ECG‐

based diagnosis of some cardiac

pathologies, like myocardial infarction

• This particular

type

of

recording

is

referred

to as a vectorcardiogram (VCG).

Electrocardiograph Block

Diagram Right

leg

electrode

Microcomputer

Operatordisplay

Drivenright legcircuit

Amplifierprotection

circuit

Leadselector

Sensingelectrodes

Lead‐faildetect

Preamplifier

Autocalibration

Baselinerestoration

Isolatedpower

supply

Isolationcircuit

Driveramplifier

Recorder‐printer

ADC Memory

Parallel circuits for simultaneous recordings from different leads

• Sensing electrodes

• Lead fail

detect

• Amplifier protection

circuit

• Lead selector

• Auto calibration

• Preamplifier

• Baseline restoration

• Driven right leg circuit

• Isolation circuit

•



Controlprogram

ECG analysisprogram

Keyboard

ADC

&

Memory

system• Driver amplifier

• Recorder‐printer

• Microcomputer

• Control software

Frequent Problems

• Frequency distortion

– High‐frequency loss rounds the sharp edges of the QRS complex.

– Low‐frequency loss can distort the baseline (no longer horizontal) or cause

monophasic waveforms to

appear biphasic.

• Saturation/cutoff distortion

– Combination of input amplitude & offset voltage drives amplifier into

saturation

– Positive case: clips off the top of the R wave

– Negative case:

clips

off

the

Q,

S,

P and

T waves

• Ground loops

– Patients are connected to multiple pieces of equipment; each has a ground

(power line or common room ground wire)

– If more that one instrument has a ground electrode connected to the patient,



a ground loop exists. Power line ground can be different for each item of equipment, sending current through the patient and introducing common‐

mode noise.

• Open lead wires

– Can be detected by impedance monitoring.

Artifacts

Effect of a voltage transient on an

ECG recorded on an

electrocardiograph in which the

transient causes the amplifier to

, and a finite period of

• Unwanted voltage

transients

– Patient movement

– Electrical stimulation

signals, like defibrillation

l f



saturatetime is required for the charge to

bleed off enough to bring the ECG

back into the amplifier’s active

region of operation. This is

followed

by

a

first ‐

order

recovery

of the system.

• Amplifier saturates

• First‐order recovery to

baseline

– Recovery time set by low‐

frequency corner of

the

bandpass amplifier

Artifacts

•U fi li f 50H /60 H li i



Upper figure:

coupling

of

50Hz/60

Hz

power

line

noise

– Electric‐field coupling between power grid, instrument, patient, and

wiring.

• Lower figure: coupling of electromyographic (EMG) noise

– Example of tensing chest muscles while ECG is being recorded.

Power‐Line

Coupling

Electro-

cardiograph

A

Power line 230 V

B

G

C 3

C 1

Z 1

Z 2

Z G

C 2

I d1

I d2

I d1+ I d2

• Small parasitic capacitors connect the

power line to the RA and LA leads,

and the

grounded

instrument

case

• Small ac displacement currents Id1 and

Id2 are generated

• The body impedance is about 500

and can be neglected

vA ‐ vB = id1 Z1 ‐ id2 Z2 (6.3)

• If Id1 and Id2 are approximately equal:

vA ‐ vB = id1 (Z1 ‐ Z2) (6.4)

= (6 nA) (20 K )

= 120 µV

• Remedies

– Shield electrodes & connect to



A mechanism of electric‐field pickup of an

electrocardiograph resulting from the power

line. Coupling capacitance between the hot

side of

the

power

line

and

lead

wires

causes

current to flow through skin‐electrode

impedances on its way to ground.

G – Shield electrodes

&

connect

to

electrocardiograph (grounding

tree) to reduce id

– Reduce or match the electrode

skin impedances (minimize Z1 ‐ Z2

)

Power‐Line Coupling

Electrocardiograph

Power line 230V

A

Z in

Z 1

C b

idb

Z 2

cm

B

G

Z in

cm

cm

• Power line is coupled into the body

• Small ac displacement current Idb is

generated, which produces a common

mode voltage

vcm = idb ZG (6.6)

= (0.2 µA) (50 K )

=

10 mV

• At the amplifier inputs:

vA ‐ vB = vcm (Z1 ‐ Z2)/ Zin (6.9)

= (10 mV) (20 K / 5 M

40 µV



Current flows from the power line through the body

and ground impedance, thus creating a common‐

mode

voltage

everywhere

on

the

body.

Z in is

not

only

resistive but, as a result of RF bypass capacitors at

the amplifier input, has a reactive component as

well.

Z G idb

=

40 µV

• Remedies:

– Reduce or match the electrode skin

impedances (minimize Z1 ‐ Z2

)

– Increase Zin

Magnetic Field

Coupling

• Sources

– Power lines

– Transformers

and ballasts

in

fluorescent lights

• Remedies

– Shielding

–

Route

leads

fM i fi ld i k b h l di h ( ) L d



Route leadsaway from

potential sources

– Reduce the

effective area of

the single

‐turn

coil (twist the

lead wires)

Magnetic‐field pickup by the elctrocardiograph (a) Lead

wires make a closed loop (shaded area) when patient and

electrocardiograph are considered in the circuit. The

change in magnetic field passing through this area induces

a current in the loop.

(b) This effect can be minimized by twisting the lead wires

together and keeping them close to the body in order to

subtend a much smaller area.

Lecture 4 bCardiovascular System

III. Phonocardiogram (PCG)

IV. Electroencephalogram(EEG)

D R B Gh d



Dr.R.B.GhongadeDepartment of E&TC,

V.I.I.T., Pune‐411048

Introduction• Heart sounds result from the interplay of the dynamic events associated

with the contraction and relaxation of the atria and ventricles, valve

movements, and blood flow.

• Can be heard from the chest through a stethoscope, a device commonly used for screening and diagnosis in primary health care

• Auscultation is the term for listening to the external sounds of the body,

usually using a stethoscope

• The art of evaluating the acoustic properties of heart sounds and

murmurs, including the intensity, frequency, duration, number, and quality

of the sounds, are known as cardiac auscultation.

• One of the oldest means for assessing the heart condition, especially the

function

of

heart

valves



function of heart valves• The stethoscope (from the Greek word stethos, meaning "chest" and

skopein, meaning "to examine") invented during the early twentieth

century, was one of the most primitive devices designed to aid a doctor in

listening to heart sounds

• Traditional auscultation involves subjective judgment by the clinicians,

which introduces variability in the perception and interpretation of the

sounds, thereby affecting diagnostic accuracy

PHONOCARDIOGRAPHY ‐

TECHNIQUE

• The auscultation of the heart gives the clinician valuable

information about the functional integrity of the heart

• Additional details can be gathered when the temporal

relationships between the heart sounds and the electrical

and mechanical events of the cardiac cycle are compared

• This approach to the analysis of heart sounds using a

study of the frequency spectra is known as

phonocardiography

•

The

phonocardiogram is

a

device

capable

of

obtaining

h l h b l h



The phonocardiogram is a device capable of obtainingheart sounds and displaying the obtained signals in the

form of a graph drawn with the signal amplitude in one

axis and with time in the other

Block diagram of the general biomedical signal processing and analysis, as an integrative

approach for computer‐aided diagnosis system



CARDIOVASCULAR PHYSIOLOGY (revisited)

• The heart can be classified from a hemodynamics point of view as a simple reciprocating pump

• The pumping chambers have a variable volume and input and output ports

• A one‐way valve in the input port is oriented such that it opens only when

the pressure in the input chamber exceeds the pressure within the pumping chamber

• Another one‐way valve in the output port opens only when pressure in

the pumping chamber exceeds the pressure in the output chamber

•The rod and crankshaft will cause the diaphragm to move back and forth



The rod and crankshaft will cause the diaphragm to move back and forth• The chamber’s volume changes as the piston moves, causing the pressure

within to rise and fall

• In the heart, the change in volume is the result of contraction and

relaxation of the cardiac muscle that makes up the ventricular walls



• The mechanical activity of the heart involves contraction of myocardial cells, opening/closing of valves, and flow of blood to and from the heart chambers

•

This

activity

is

modulated

by

changes

in

the

contractility

of

the heart, the compliance of the chamber walls and

arteries and the developed pressure gradients

• The mechanical activity can be also examined using ultrasound imaging

• The peripheral blood flows in the arteries and veins is also

modulated by mechanical properties of the tissue

• The flow of blood can be imaged by Doppler‐echo, and the pulse‐wave can be captured in one of the peripheral arteries



arteries

• The dif ferent types of signals give us various pieces of information about the cardiac activity. Integrating this information may yield a better ability to assess the

condition of the cardiovascular system

Cardiac Sounds• Audible sounds are produced from the opening and the closing of

the heart valves, the flow of blood in the heart, and the vibration of heart muscles

• Heart sounds are short‐lived bursts of vibrational energy having a transient character

• They are primarily associated with valvular and/or ventricular

vibrations• Both their site of origin and their original intensity governs the

radiation of the heart sounds to the surface of the chest

• There are four separate basic sounds that occur during the

sequence

of

one

complete

cardiac

cycle



q p y

Cardiac Murmurs

•

Murmurs are vibrations caused by turbulence in the blood as it flows through some narrow orifice or tube.

• A murmur is one of the more common abnormal phenomena that can be detected with a stethoscope ‐a somewhat prolonged 'whoosh' that can be described as blowing, rumbling, soft, harsh, and so on

•

Murmurs

are

sounds

related

to

the

non‐

laminar

flow

of

blood

in

the

heart

and the great vessels

• They are distinguished from basic heart sounds in that they are noisy and

have a longer duration

• While heart sounds have a low frequency range and lie mainly below 200

Hz,

murmurs

are

composed

of

higher

frequency

components

extending

up

to 1000 Hz



p g q y p g p

• Most heart murmurs can readily be explained on the basis of high velocity flow or abrupt changes in the caliber (the diameter of the inside)of the vascular channels

• Typical conditions in the cardiovascular system, which cause blood flow

turbulence, are local obstructions, shunts, abrupt changes in diameter, and valve insufficiency(valve is not strong enough to prevent backflow )

S1• The first heart sound (S1) occurs at the onset of ventricular systole

• It can be most clearly heard at the apex and the fourth intercostal spaces along the left sternal border

•

It is characterized by higher amplitude and longer duration in comparison with other heart sounds

• It has two major high frequency components that can be easily heard at bedside

• Although controversy exists regarding the mechanism of S1, the most compelling evidence indicates that the components result from the closure of the mitral and

tricuspid valves and the vibrations set up in the valve cusps, chordate, papillary, muscles, and ventricular walls before aortic ejection

• S1 lasts for an average period of 100–200ms

• Its frequency components lie in the range of 10‐200 Hz

• The acoustic properties of S1 are able to reveal the strength of the myocardial

systole and the status of the atrioventricular valves’ function• As a result of the asynchronous closure of the tricuspid and mitral valves the



• As a result of the asynchronous closure of the tricuspid and mitral valves, the

two components of S1 are often separated by a time delay of 20‐30 ms

• This delay is known as the (split) in the medical community and is of significant diagnostic importance

• An abnormally large splitting is often a sign of heart problem

S2• The second heart sound (S2) occurs within a short period once the ventricular diastole starts.

• It coincides with the completion of the T‐wave of the electrocardiogram (ECG)

• S2 consists of two high‐frequency components, one because of the closure of the aortic valve and the other because of the closure of the pulmonary valve

• At the onset of ventricular diastole, the systolic ejection into the aorta and the pulmonary artery declines and the rising pressure in these vessels exceeds the pressure in the respective ventricles, thus reversing the flow and causing the closure of their valves.

• The second heart sound usually has higher‐frequency components as compared with the

first

heart

sound• As a result of the higher pressure in the aorta compared with the pulmonary artery, the

aortic valve tends to close before the pulmonary valve, so the second heart sound may have an audible split

• In normal individuals, respiratory variations exist in the splitting of S2

• During expiration phase, the interval between the two components is small (less than 30

ms)H d i i i ti th litti f th t t i id t



• However, during inspiration, the splitting of the two components is evident

• Clinical evaluation of the second heart sound is a bedside technique that is considered to

be a most valuable screening test for heart disease

• Many heart diseases are associated with the characteristic changes in the intensities of

or the time relation between the two components of S2• S1 and S2 were basically the main two heart sounds that were used for most of the

clinical assessment based on the phonocardiography auscultation procedure

S3 &S4• The third and fourth heart sounds, also called gallop sounds, are low‐

frequency sounds occurring in early and late diastole, respectively, under highly variable physiological and pathological conditions

• Deceleration of mitral flow by ventricular walls may represent a key mechanism in the genesis of both sounds

• The third heart sound (S3) occurs in the rapid filling period of early diastole

• It is produced by vibrations of the ventricular walls when suddenly distended by the rush of inflow resulting from the pressure difference

between ventricles and atria

• The audibility of S3 may be physiological in young people or in some adults, but it is pathological in people with congestive heart failure or ventricular dilatation

• The fourth heart sound (S4) occurs in late diastole and just before S1

• It is produced by vibrations in expanding ventricles when atria contract.



• Thus, S4 is rarely heard in a normal heart

• The abnormally audible S4 results from the reduced distensibility (the capability of being stretched under pressure ) of one or both ventricles

•

As a result of the stiff ventricles, the force of atrial contraction increases, causing sharp movement of the ventricular wall and the emission of a prominent S4



LUPP DUBBLUPP

DUBBMURMUR



Cardiac cycle events occurring in the left ventricle

Pressure profile of the

ventricle andatrium

Volume profile of the

left ventricle

Phonocardiographgy

signals



• The ECG, PCG (low and high

filtered), carotid pulse,

apexcardiogram, and logic states

(high = open) of left heart valves,

mitral and aortic valve, and right

heart valves, tricuspid and

pulmonary

valve• Left heart mechanical intervals

are indicated by vertical lines:

isovolumic contraction (1),

ejection (2), isovolumic relaxation

(3), and filling (4) (rapid filling,

slow filling, atrial contraction)• The low frequency PCG shows the

four normal heart sounds (I, II, III,

and IV)

• In the high frequency trace III and

IV have disappeared and splitting

is visible in I [Ia and Ib (and even a

small Ic due to ejection)] and in II



small Ic due to ejection)] and in II

[IIA (aortic valve) and IIP

(pulmonary valve)]

• Systolic intervals LVEP (on carotid

curve) and Q ‐IIA (on ECG and PCG) are indicated



Phonocardiography trace with 8 successive S1–S2 waveform.



PCG signal recording with different filtering coefficient for different

corresponding heart sound class



PCG SIGNAL SPECTRAL ANALYSIS

•

Heart sounds are complex and highly non‐stationary signals in their nature and have been known to be quasi‐stationary signals for a long time

• The “heart beats” associated with these sounds are reacted

in the signal by periods of relatively high activity and

rhythmic energy style, alternating with comparatively intervals of low activity

• Accordingly, PCG Spectrometric properties can be extracted

by different methods using (e.g., Short‐Time Fourier Transformation (STFT)), as it estimates the power spectral density (PSD) of successive waveform and computed these



density (PSD) of successive waveform and computed these transformation will lead to periodic estimation of energy spikes within the acoustical waveform

Classes of spectral analysis used• Two broad classes of spectral analysis approaches

– nonparametric methods

– parametric (model‐based) methods.

• The nonparametric methods—such as periodogram, Blackman‐

Tukey, and minimum variance spectral estimators—do not impose any model assumption on the data, other than wide‐sense stationarity

• The parametric spectral estimation approaches, on the other hand,

assume that the measurement data satisfy a generating model by which the spectral estimation problem is usually converted to that of determining the parameters of the assumed signal model

• Two kinds of models are widely assumed and used within the parametric methods, according to different spectral characteristics of the signals: the rational transfer function (RTF) model and the sinusoidal signal model



sinusoidal signal model

• The RTF models, including autocorrelation (AR),moving average (MA), and autocorrelation moving average (ARMA) types are

usually

used

to

analyze

the

signals

with

continuous

spectra,

while

the sinusoidal signal model is a good approximation of signals with

discrete spectral patterns



ELECTROENCEPHALOGRAM(EEG)

• The electroencephalogram (EEG) measures the activity of

large numbers (populations) of neurons.

• First recorded by Hans Berger in 1929.

• EEG recordings are noninvasive, painless, do not interfere

much with a human subject’s ability to move or perceivestimuli, are relatively low-cost.

• Electrodes measure voltage-differences at the scalp in themicrovolt (μV) range.

• Voltage-traces are recorded with millisecond resolution



EEG

• Spontaneous activity is measured on the scalp or on the brain and is called the electroencephalogram

•

The

amplitude

of

the

EEG

is

about

100

µV

when

measured

on

the

scalp, and about 1‐2 mV when measured on the surface of the brain

• The bandwidth of this signal is from under 1 Hz to about 50 Hz

• As the phrase "spontaneous activity" implies, this activity goes on

continuously in the living individual

• Evoked potentials are those components of the EEG that arise in

response to a stimulus (which may be electric, auditory, visual, etc.)

• Such signals are usually below the noise level and thus not readily

distinguished,

and

one

must

use

a

train

of

stimuli

and

signal

averaging to improve the signal‐to‐noise ratio



• Single‐neuron behavior can be examined through the use of microelectrodes which impale the cells of interest. Through studies

of the single cell, one hopes to build models of cell networks that will reflect actual tissue properties

Frequency spectrum of normal EEG



EEG

LEAD

SYSTEMS• The internationally standardized 10‐20 system is usually employed to record the spontaneous

EEG

• In this system 21 electrodes are located on the surface of the scalp

• The positions are determined as follows

– Reference points are nasion, which is the delve at the top of the nose, level with the eyes;

– inion, which is the bony lump at the base of the skull on the midline at the back of the head

• From these points, the skull perimeters are measured in the transverse and median planes

• Electrode locations are determined by dividing these perimeters into 10% and 20% intervals

•

Three

other

electrodes

are

placed

on

each

side

equidistant

from

the

neighboring

points



• In addition to the 21 electrodes of the international 10‐20 system, intermediate 10% electrode positions are also used

• The locations and nomenclature of these electrodes are standardized by the American Electroencephalographic Society

• In this recommendation, four electrodes have different names compared

to the 10‐20 system; these are T7, T8, P7, and P8. These electrodes are drawn black with white text in the figure



EEG



Standard placements of electrodes on the human scalp: A, auricle; C, central;F, frontal; Fp, frontal pole; O, occipital; P, parietal; T, temporal.

EEG



EEG



Many neurons need to sum their activity in order to be detected by EEG electrodes.

The timing

of

their

activity

is

crucial.

Synchronized

neural

activity

produces

larger

signals.

THE BEHAVIOR OF THE EEG SIGNAL

•

It

is

possible

to

differentiate

alpha

(α

),

beta

( ),

delta

(), and theta () waves as well as spikes associated with

epilepsy

• The alpha waves have the frequency spectrum of 8‐13

Hz and can be measured from the occipital region in an awake person when the eyes are closed

• The frequency band of the beta waves is 13‐30 Hz; these are detectable over the parietal and frontal lobes

• The delta waves have the frequency range of 0.5‐4 Hz and are detectable in infants and sleeping adults



• The theta waves have the frequency range of 4‐8 Hz and are obtained from children and sleeping adults



EEG and the Brain State

EEG potentials are good indicators of global brain state. Theyoften display rhythmic patterns at characteristic frequencies



EEG

EEG suffers from poor current source localization and the “inverse problem”



EEG

Power spectrum:



• Schematic of amplifier inputs for analog EEG for a longitudinal bipolar montage

• One additional electrode input—the ground—is omitted for simplicity

• Since an EEG voltage signal represents a difference between the voltages at two



electrodes, the display of the EEG for the reading encephalographer may be set up in

one of several ways

• The representation of the EEG channels is referred to as a montage• A typical adult human EEG signal is about 10µV to 100 µV in amplitude when measured

from the scalp

EEG OF A

NORMAL

HUMAN

ADULT



EEG OF A

HUMAN

ADULT

SUFFERING

FROM

EPILEPSY



Lecture 5I.X

‐Ray

Imaging

II. Computed Tomography

III. Diagnostic Ultrasound Imaging

Dr.R.B.GhongadeDepartment of E&TC,



V.I.I.T., Pune‐411048

I.X‐Ray Imaging



INTRODUCTION TO X‐RAY IMAGING

• X‐ray imaging is a well‐known imaging modality that has

been used

for

over

100

years

since

Roentgen

discovered

X‐

rays based on his observations of fluorescence

• X‐rays are high‐energy photons

• Their generation creates incoherent beams that experience

insignificant scatter

when

passing

through

various

media

• As a result, X‐ray imaging is based on through transmission

and analysis of the resulting X‐ray absorption data

• X‐

rays

are

detected

through

a

combination

of

a

phosphor

screen and

a light

‐sensitive

film



Typical Imaging Chain forMedical X‐ray Systems

X-ray source

Collimator

Object Film

processing

Image



Electromagnetic Radiation

• EM radiation can be thought of as oscillating electric field

which generates oscillating magnetic field which generates

oscillating electric

field…and

so

on.

• Can also be thought of as photons (particles), as in CCD

d i f i ibl li h



detection of visible light.

• This is

called

the

“wave

‐particle

duality”

of

EMR.

Wavelength• (lambda) is called wavelength, the

distance between two identical points

on a wave

• =

, where v is called the phase

speed (magnitude of the phase

velocity) of the wave and f is the

wave's frequency

• In the case of EM radiation, the

equation becomes =

, where c is

the speed of light: 3 x 108m/s

• (nu) is called frequency, the number of cycles per unit of time.



• It is inversely proportional to the wavelength.

Photons: review

• Photons are

little

“packets”

of

energy.

• Each photon’s energy is proportional to its

frequency.

• A photon’s

energy

is

represented

by

“h”

E = hEnergy = (Planck’s constant) x (frequency of photon)



X‐Rays

• Usually detected as particles of energy (photons).

10-9 m (1 nm)10-11 m (0.01 nm)

“soft”“hard”



• Discovered in 1895 by Wilhelm Conrad Roentgen.

X‐Ray Production

• Electrons are

accelerated

from

cathode

to

anode.

• When high energy electrons hit atoms of heavy

metals, the atoms produce X‐ray photons.

e-

e-

h

Anode (+)

Cathode(-)

h



metals, the atoms produce X ray photons.

X‐Ray

Tube



Generation

of

X‐

rays

• Depends on thermionic emission and acceleration of electrons from

a heater filament

• During that process, electrons emitted from cathode are

accelerated by anode voltage

• Kinetic energy loss at an anode is converted to X‐rays

• The relative position of an electron with respect to the nucleus determines the frequency and energy of the emitted X‐ray

• X‐rays produced in an X‐ray tube contain two types of radiation

– Bremsstrahlung – characteristic radiation

• The word Bremsstrahlung is retained from the German language to

describe the radiation that is emitted when electrons are

decelerated

• It is characterized by a continuous distribution of X‐ray intensity and

shifts toward higher frequencies when the energy of the

bombarding electrons is increased



• Characteristic X‐rays, on the other hand, produce peaks of intensity

at particular

photon

energies

Generated

X‐

Ray

spectrum• In practice, emitted radiation is filtered, intentionally or not, producing high‐pass filter response as low‐energy

radiation is completely attenuated

• As a result,

the

final

X‐ray

spectrum

has

band

‐pass

type characteristics with several local peaks

superimposed on it



Schematic representation

of

a standard X‐ray system



Object

• What can happen to an X-ray when itencounters the object to be imaged?

Passes right through the object.

Absorbed completely by the object.

Scattered by the object



Attenuation Coefficient

5

10 50 100 150

1

0.1

Attenuation

Coefficient

Photon Energy (keV)

500

Bone

MuscleFat



Attenuation coefficients tell you the “x-ray blocking power” of a material.

Photon Energy (keV)

Attenuation Coefficient

• Coefficient depends

on

the

property

of

the

material.

– Density (Bone has a high density compared to soft

tissues) – Chemical Make‐up (Lead blocks x‐rays; lead

screening used to protect patient & technicians)



Detector

• A special

photographic

film

is

used

to

capture the x‐ray photons which passed

through the object.

• The film is then processed.

• Film turns dark where it was exposed to x‐

Exposure

(Capture)Processing Image



p

ray photons.

Typical X‐Ray

Images

X-ray image of hand

Dental X-ray



Mammogram

Image Quality

Factors

• Source

– Energy of

the

photons

– Collimation

• Object

– Attenuation coefficient

– Source‐object geometry

• Detector

– Object‐

detector

geometry – Efficiency



Advantages of

Standard

Diagnostic

Medical X‐ray Imaging Systems

• Readily available

• Reasonably cheap

• Simple systems to maintain

• Many experienced and trained personnel due

to the fact that technology has existed for a

while



Disadvantages of

Diagnostic

Medical X‐ray Imaging Systems

• Exposure to

harmful

radiation.

• Not much contrast between different soft

tissues.

• Image is

a shadowgram

(projection

image)

with no depth information.



II. Computed Tomography



Basic Concepts• All x‐ray imaging systems consist of an x‐ray source, a collimator, and an x‐ray

detector

• Diagnostic medical x‐ray systems utilize externally generated x‐rays with energies

of 20–150 keV

• The “shadow graph” images obtained are the results of the variations in the

intensity of

the

transmitted

x‐ray

beam

after

it

has

passed

through

tissues

and

body fluids of different densities

• Advantages – high‐resolution

– high‐contrast images

– relatively small patient exposure

– permanent record

of

the

image

• Disadvantages – significant geometric distortion

– inability to discern depth information

– incapability of providing real‐time imagery

• Conventional radiography

(X

‐Ray

imaging)

is

the

imaging

method

of

choice

for

such tasks as dental, chest, and bone imagery

• When this procedure is used to project three‐dimensional objects into a two‐

dimensional plane, however, difficulties are encountered

• Structures represented on the film overlap, and it becomes difficult to distinguish

b t ti th t i il i d it



between tissues that are similar in density.

• Conventional x‐ray

techniques

are

unable

to

obtain

distinguishable/

interpretable

images of the brain, which consists primarily of soft tissue

X‐

ray

technique

for

visualizing

three‐

dimensionalstructures

• Known as plane tomography

• The imaging of specific planes or cross sections within the body became

possible

• The x‐ray source is moved in one direction, while the photographic film

(which is placed on the other side of the body and picks up the x‐rays) is

simultaneously moved in the other direction

• X‐rays

travel

continuously,

changing

paths

through

the

body,

each

ray

passes through the same point on the plane or cross section of interest

throughout the exposure

• Structures in the desired plane are brought sharply into focus and are

displayed on

film,

whereas

structures

in

all

the

other

planes

are

obscured

and show up only as a blur

• Better than conventional methods in revealing the position and details of

various structures and in providing three dimensional information by such



a two‐dimensional presentation

Tomography• Limitations – does not really localize a

single plane, since there is

some error in

– the depth

perception

obtained

– large contrasts in radio

density are usually

required in order to obtain

high‐quality

images

that

are easy to interpret

– x‐ray doses for tomography are higher

than

routine

radiographs,

and because the

exposures are longer, patient motion may

degrade the image

• A tomogram is made by having the x‐ray

source move in one direction during the

exposure

and

the

film

in

the

other

direction• In the projected image, only one plane in

the body remains stationary with respect to

the moving film

• In the picture, all other planes in the body



content are blurred

Computerized Tomography• Consists

of

a scanning

and

detection

system, a computer, and a display

medium

• Combines image‐reconstruction

techniques with x‐ray absorption

measurements in

such

a way

as

to

facilitate the display of any internal organ in two‐dimensional axial slices

or by reconstruction in the Z axis in

three dimensions

• A collimated

beam

of

x‐rays

is

directed through the section of body

being scanned to a detector that is

located on the other side of the

patient

• With a narrowly

collimated

source

and

detector

system,

it

is

possible

to

send

a

narrow beam of x‐rays to a specific detection site

• Some of the energy of the x‐rays is absorbed, while the remainder continues to

the detector and is measured

I i d h h d ll i f l



• In computerized tomography, the detector system usually consists of a crystal

(such as cesium iodide or cadmium tungstate) that has the ability to scintillate

or emit light photons when bombarded with x‐rays

• The intensity of these light photons or “bundles of energy” is in turn

measured by

photo

‐detectors

and

provides

a measure

of

the

energy

absorbed (or transmitted) by the medium that is penetrated by the x‐

ray beam

• Since the x‐ray source and detector system are usually mounted on a

frame or

“scanning

gantry,”

they

can

be

moved

together

across

and

around the object being visualized

• In early designs, for example, x‐ray absorption measurements were

made and

recorded

at

each

rotational

position

traversed

by

the

source and detector system creating an absorption profile for that

angular position

• To obtain another absorption profile, the scanning gantry holding the

x‐ray

source

and

detector

was

then

rotated

through

a small

angle

and

an additional set of absorption or transmission measurements was

recorded

• Each x‐ray profile or projection obtained in this fashion is basically



• Each x‐ray profile or projection obtained in this fashion is basically

one‐dimensional

• It is as wide as the body but only as thick as the cross section

Example 160 x 160 picture matrix• Exact

number

of

these

equally

spaced

positions determines the dimensions to

be represented by the picture elements

that constitute the display

• Absorption measurements from 160

equally

spaced

positions

in

each

translation are required

• Each one‐dimensional array constitutes

one x‐ray profile or projection

• To obtain the next profile, the scanning

unit is rotated a certain number of

degrees around

the

patient,

and

160

more linear readings are taken at this

new position

• Process is repeated again and again

until the unit has been rotated a full

180°• When all the projections have been

collected, 160 x 180, or 28,800,

individual x‐ray intensity measurements

are available to form a reconstruction

• Each of the measurements obtained by the

preceding procedure enters the resident

computer and

is

stored

in

memory

• Once all the absorption data have been

obtained and located in the computer’s

memory, the software packages developed to

analyze the data by means of image‐



of a cross

section

of

the

patient’s

head

or body

y y g

reconstruction algorithms

are

called

into

action

Image reconstruction• Computer

initially

establishes

a grid

consisting

of

a number

of

small

squares for the cross section of interest, depending on the size of the

desired display

• Since the cross section of the body has thickness, each of these squares

represents

a

volume

of

tissue,

a

rectangular

solid

whose

length

is

determined by the slice thickness and whose width is determined by the

size of the matrix

• Such a three‐dimensional block of tissue is referred to as a “voxel” (or “volume element”) and is on the display in two dimensions as a “pixel”

(or “picture

element”)

• During the scanning process, each voxel is irradiated by a narrow beam

of x‐rays up to 180 times

• The absorption caused by that voxel contributes to up to 180 absorption

measurements, each measurement part of a different projection

• Each voxel

affects

a unique

set

of

absorption

measurements

to

which

it

has contributed, the computer calculates the total absorption due to

that voxel

• Using the total absorption and the dimension of the voxel, the average



absorption

coefficient

of

the

tissues

in

that

voxel

is

determined

precisely

and displayed

in

a corresponding

pixel

as

a shade

of

grey

• The cross section of interest can be considered to be

made up of a set of blocks of material

• Each block has an attenuating effect upon the

passage of the x‐ray energy or photons, absorbing

some of the incident energy passing through it

• The first block absorbs a fraction A1 of the incident

photons, the

second

a fraction

A2,

and

so

on,

so

that

the n‐th block absorbs a fraction An

• The total fraction “A” absorbed through all the blocks

is the product of all the fractions, while the

logarithm of this total absorption fraction is defined

as the

measured

absorption

• Only the measured absorption factors A(1), A(2), A(3),

and A(4) would be known, but this can be solved since

4 simultaneous equations and 4 unknowns

• To reconstruct a cross section containing n rows of



blocks and

n columns,

it

is

necessary

to

makeat least

n individual absorption measurements from at least n

directions

“Back‐projection” method of Image Reconstruction• A parallel beam of x‐rays is directed past and

through a cylinder

‐absorbing

substance

• a shadow of the cylinder is cast on the x‐ray film

• density of the exposed and developed film along the

line AA can be regarded as a projection of the object

• If

a

series

of

such

radiographs

are

taken

at

equally

spaced angles around the cylinder, these

radiographs then constitute the set of projections

from which the cross section has to be

reconstructed

• An

approximate

reconstruction

can

be

reproduced

by directing parallel beams of light through all the

radiographs in turn from the position in which they

were taken

• The correct cross section can be reconstructed by

back‐projecting the original shadow and subtracting

the result of back‐projecting two beams placed on

either side of the original shadow

• Mathematically, this is the equivalent of taking each

transmission value in the projection and subtracting

from it a quantity proportional to adjacent values



from it a quantity proportional to adjacent values

• This process is called convolution and is actually used

to modify projections

Back‐projection



• A file, usually known as the picture file,

is

created

in

the

computer

memory• Contains an absorption coefficient or density reading for each element of the

final picture

• Resultant absorption coefficients for

each element

of

the

image

calculated

in

this manner can then be displayed as

gray tones or color scales on a visual display

• Each element or “pixel” of the picture

file has

a value

that

represents

the

density (or more precisely the relative

absorption coefficient) of a volume in

the cross section of the body being

examined

• The scale developed by Hounsfield

demonstrates the values of absorption

coefficients that range from air (–1,000) at the bottom of the scale to bone at



the

top

CT Technology

• CT scanners are usually integrated units consisting of

three major elements:

1. The scanning

gantry ,

which

takes

the

readings

in

a suitable form and quantity for a picture to be

reconstructed

2. The

data‐

handling

unit ,

which

converts

these

readings

into intelligible picture information, displays this picture

information in a visual format, and provides various

manipulative aids to enhance the image and thereby

assist the

physician

in

forming

a diagnosis

3. A storage facility , which enables the information to be

examined or reexamined at any time after the actual



scan

The Scanning Gantry• The

objective

of

the

scanning

system

is

to

obtain

enough

information

to

reconstruct an image of the cross section of interest

• CT scanners have undergone several major gantry design changes

• Four generations

of

scanning gantry designs.

With modern slip ring

technology, third‐ or

fourth‐generation

geometry allows spiral

volumetric scanning using

slice widths from 1 to 10

mm and pixel matrixes to

10,242• Typically, a 50‐cm volume

can be imaged with a

single breath hold



CT scanner



Mathematical algorithms for taking the

attenuation projection

data

• Can be classified into two categories: – iterative

– Analytic

• The iterative

techniques

(also

known

as

the

algebraic

reconstruction

technique [ART]), such as the one used by Hounsfield in the first‐generation scanner, require an initial guess of the two‐dimensional pattern of x‐ray absorption

• The attenuation projection data predicted by this guess are then

calculated and

the

results

compared

with

the

measured

data

• The difference between the measured data and predicted values is used in

an iterative manner so the initial guess is modified and that difference

goes to zero

• In general, a large number of iterations are required for convergence, with

the process

usually

halted

when

the

difference

between

the

calculated

and the measured data is below a specified error limit

• A number of different versions of the ART were developed and used with

first‐ and second‐generation CAT scanners

• Later‐generation scanners used analytic reconstruction techniques, since



the iterative

methods

were

computationally

slow

and

had

convergence

problems in the presence of noise

Analytic Algorithm

• Analytic techniques

include

the

Fourier

transform,

back

‐projection,

filtered

back

‐projection, and convolution back‐projection approaches

• All of the analytic methods differ from the iterative methods in that the image is

reconstructed directly from the attenuation projection data

• Analytic techniques

use

the

central

section

theorem

and

the

two

‐dimensional

Fourier transform

Given an image , , a single projection is taken along the direction, forming a

projection described by

This projection represents an array of line integrals

The two dimensional Fourier transform of , is

given by

In the Fourier domain, along the line 0, this

transform becomes



• which can be rewritten as

where 1 represents a one‐dimensional Fourier transform

• It can

be

shown

that

the

transform

of

each

projection

forms

a radial

line

in

, , and therefore , can be determined by taking projections at many

angles and taking these transforms

• When , is completely described, the reconstructed image can be found

by

taking

the

inverse

Fourier

transform

to

obtain

,



CT scanners may be compared with one another by considering

the following

ten

factors:

1. Gantry design, which affects scan speed, patient processing time, and cost‐effectiveness

2. Aperture size, which determines the maximum size of the patient along with the weight

carrying capacity of the couch

3. The type of x‐ray source, which affects the patient radiation dose and the overall life of the scanning device

4. X‐ray fan beam angle and scan field, which affects resolution

5. The slice thickness, as well as the number of pulses and the angular rotation of the

source, which are important in determining resolution

6. The number and types of detectors, which are critical parameters in image quality

7. The type of minicomputer employed, which is important in assessing system capability

and flexibility

8. The type of data‐handling routines available with the system, which are important user

and reliability considerations

9. The storage capacity of the system, which is important in ascertaining the accessibility of

the stored data

10. Upgradeability and connectivity—that is, they should be capable of modular

upgradeability and should communicate to any available network



III. Diagnostic

Ultrasound

Imaging



Introduction

• Ultrasound is a non-ionizing method which uses sound waves of

frequencies (2 to 10 MHz) exceeding the range of human hearing for

imaging

• Medical diagnostic ultrasound uses ultrasound energy and the

acoustic properties of the body to produce an image from stationary

and moving tissues

• Ultrasound is used in pulse-echo format, whereby pulses of

ultrasound produced over a very brief duration travel through various

tissues and are reflected at tissue boundaries back to the source• Returning echoes carry the ultrasound information that is used to

create the sonogram or measure blood velocities with Doppler

frequency techniques

• Along a given beam path, the depth of an echo-producing structure

is determined from the time between the pulse-emission and the

echo return, and the amplitude of the echo is encoded as a gray-

scale value

• In addition to 2D imaging, ultrasound provides anatomic distance

d l t ti t di bl d l it



and volume measurements, motion studies, blood velocitymeasurements, and 3D imaging

• Returning echoes carry the ultrasound information that is used to

create the sonogram or measure blood velocities with Doppler

frequency techniques

•

• Along a given beam path, the depth of an echo-producing structure

is determined from the time between the pulse-emission and the

echo return, and the amplitude of the echo is encoded as a gray-

scale value

•

• In addition to 2D imaging, ultrasound provides anatomic distance

and volume measurements, motion studies, blood velocity

measurements, and 3D imaging



Characteristics of SoundFrequency

Frequency (f) is the number of times the wave oscillates

through a cycle each second (sec) (Hertz: Hz or cycles/sec)Infra sound < 15 Hz

Audible sound ~ 15 Hz - 20 kHzUltrasound > 20 kHz; for medical usage typically 2-10 MHz withspecialized ultrasound applications up to 50 MHz

period () - the time duration of one wave cycle: = 1/f



Characteristics of Sound Speed

The speed or velocity of sound is the distance traveled by the wave

per unit time and is equal to the wavelength divided by the period

(1/f)speed = wavelength / period

speed = wavelength x frequency

c = f

c [m/sec] = [m] * f [1/sec]

Speed of sound is dependent on the propagation medium and varieswidely in different materials



Characteristics of Sound

Speed

• A highly compressible medium such as air, has a low speed of

sound, while a less compressible medium such as bone has ahigher speed of sound

• The difference in the speed of sound at tissue boundaries is a

fundamental cause of contrast in an ultrasound image



fundamental cause of contrast in an ultrasound image

Characteristics of Sound Wavelength, Frequency

and Speed• The ultrasound frequency is unaffected by

changes in sound speed as the acousticbeam propagates through various media

• Thus, the ultrasound wavelength isdependent on the medium (c = f )

• A change in speed at an interface betweentwo media causes a change in wavelength

• Higher frequency sound has shorterwavelength

• Ultrasound wavelength determines thespatial resolution achievable along thedirection of the beam

• A high-frequency ultrasound beam (smallwavelength) provides superior resolutionand image detail than a low-frequency beam

• However, the depth of beam penetration isreduced at high frequency and increased atlow frequencies

• For thick body parts (abdomen), a lowerfrequency ultrasound wave is used (3.5 to 5 MHz)to image structures at significant depth

• For small body parts or organs (thyroid breast) a



For small body parts or organs (thyroid, breast), ahigher frequency is employed (7.5 to 10 MHz)

Characteristics of SoundPressure, Intensity and the dB scale

• The amplitude of a wave is the size of the wave displacement

• Larger amplitudes of vibration produce denser compression bands and,hence, higher intensities of sound

• Intensity of ultrasound is the amount of power (energy per unit time)

per unit area proportional to the square of the pressure amplitude, I

P2

units of milliwatts/cm2

or mW/cm2

• Measured in decibels (dB) as a relative intensity

dB = 10 log10 (I2/I1) or dB = 20 log10 (P2/P1) since I P2

I1 and I2 are intensity values

P1 and P2 are pressure or amplitude variations

(1 B = 10 dB where B is bels)



Interactions of Ultrasound with Matter

• Ultrasound interactions are determined by the acoustic properties ofmatter

• As ultrasound energy propagates through a medium, interactionsthat occur include

• reflection• refraction

• scattering

• Absorption (attenuation)

• Acoustic Impedance, Zis equal to density of the material times speed of sound in thematerial in which ultrasound travels, Z = c

= density (kg/m3) and c = speed of sound (m/sec)measured in rayl (kg/m2sec)

• Air and lung media have low values of Z, whereas bone and metalhave high values• Large differences in Z (air-filled lung and soft tissue) cause

reflection, small differences allow transmission of sound energy• The differences between acoustic impedance values at an interface

determines the amount of energy reflected at the interface



determines the amount of energy reflected at the interface

Reflection

• A portion of the ultrasound beam is reflected at tissue interface• The sound reflected back toward the source is called an echo and

is used to generate the ultrasound image

• The percentage of ultrasound intensity reflected depends in part onthe angle of incidence of the beam

• As the angle of incidence increases, reflected sound is less likely toreach the transducer



• Sound reflection occurs at tissue boundaries with differences inacoustic impedance

• The intensity reflection coefficient, R = Ir /Ii = ((Z2 – Z1)/(Z2 + Z1))2

• The subscripts 1 and 2 represent tissues proximal and distal to theboundary.

• Equation only applies to normal incidence• The transmission coefficient = T = 1 – R

T = (4Z1Z2)/(Z1+Z2)2



Tissue reflections

• Air/tissue interfaces reflect virtually all of the incident ultrasound beam

• Gel is applied to displace the air and minimize large reflections• Bone/tissue interfaces also reflect substantial fractions of the incidentintensity

• Imaging through air or bone is generally not possible• The lack of transmissions beyond these interfaces results in an

area void of echoes called shadowing• In imaging the abdomen, the strongest echoes are likely to arise from

gas bubbles• Organs such as kidney, pancreas, spleen and liver are comprised of

sub-regions that contain many scattering sites, which results in a

speckled texture on images• Organs with fluids such as bladder, cysts, and blood vessels have

almost no echoes (appear black)



Refraction

• Refraction is the change in direction of an ultrasoundbeam when passing from one medium to anotherwith a different acoustic velocity

• Wavelength changes causing a change inpropagation direction (c = f)

• sin(t) = sin(i) * (c2/c1), Snell’s law;for small ≤ 15o: t = i * (c2/c1)

• When c2 > c1, t > i , When c1 > c2, t < i

• Ultrasound machines assume straight linepropagation, and refraction effects give rise toartifacts



Scatter

• Acoustic scattering arises from objects within a tissue that are about

the size of the wavelength of the incident beam or smaller, and

represent a rough or nonspecular reflector surface• As frequency increases, the non-specular (diffuse scatter)

interactions increase, resulting in an increased attenuation and lossof echo intensity

• Scatter gives rise to the characteristic speckle patterns of variousorgans, and is important in contributing to the gray-scale range in theimage



Attenuation

• Ultrasound attenuation, the loss of energy with distance

travelled, is caused chiefly by scattering and tissueabsorption of the incident beam (dB)

• The intensity loss per unit distance (dB/cm) is theattenuation coefficient

• Rule of thumb: attenuation in soft tissue is approx. 1dB/cm/MHz

• The attenuation coefficient is directly proportional toand increases with frequency

• Attenuation is medium dependent



Transducers

• A transducer is a device that can

convert one form of energy intoanother

• Piezoelectric transducers convert

electrical energy into ultrasonicenergy and vice versa

(Piezoelectric means pressure

electricity )

• High-frequency voltage

oscillations are produced by a

pulse generator and are sent to

the ultrasound transducer by atransmitter

• The electrical energy causes thepiezoelectric crystal to

momentarily change shape

(expand and contract dependingon current direction)



• This change in shape of the crystal increases and decreases

the pressure in front of the transducer, thus producingultrasound waves

• When the crystal is subjected to pressure changes by the

returning ultrasound echoes, the pressure changes are

converted back into electrical energy signals• Return voltage signals are transferred from the receiver to a

computer to create an ultrasound image

• Transducer crystals do not conduct electricity but are coated

with a thin layer of silver which acts as an electrode• The piezoelectric effect of a transducer is destroyed if

heated above its curie temperature limit

• Transducers are made of a synthetic ceramic

(peizoceramic) such as lead-zirconate-titanate (PZT) orplastic polyvinylidence difluoride (PVDF) or a composite

• A transducer may be used in either pulsed or continuous-wave mode

• A transducer can be used both as a transmitter and receiverof ultrasonic waves



of ultrasonic waves

• The thickness of apiezoelectric crystal

determines the resonant

frequency of the

transducer

• The operating resonant

frequency is determined

by the thickness of thecrystal equal to ½

wavelength (t=/2) of

emitted sound in the

crystal compound• Resonance transducers

transmit and receive

preferentially at a single

“centre frequency”



Damping Block

• The damping block absorbs the backward directed ultrasoundenergy and attenuates stray ultrasound signals from the housing

• It also dampens (ring-down) the transducer vibration to create an

ultrasound pulse with a short spatial pulse length, which is

necessary to preserve detail along the beam axis (axial resolution)



Q factor

• The Q factor is related to thefrequency response of the crystal

• The Q factor determines thepurity of the sound and length of

time the sound persists, or ringdown time

• Q = operating frequency (MHz) /bandwidth (width of thefrequency distribution)

• Q = f 0/BW

• High-Q transducers produce a

relatively pure frequencyspectrum

• Low-Q transducers produce awider range of frequencies



Matching Layer

• A matching layer of material is placed on the front surface of the

transducer to improve the efficiency of energy transmission into thepatient

• The material has acoustic properties intermediate to those of soft

tissue and the transducer material

• The matching layer thickness is equal to ¼ the wavelength of sound

in that material (quarter-wave matching)

• Acoustic coupling gel is used to eliminate air pockets that could

attenuate and reflect the ultrasound beam



Non-resonance (Broad-Bandwidth) “Multi-frequency” Transducers



Transducer Arrays

• Linear or curvilinear arraytransducers

• 256 to 512 elements

• Simultaneous firing of

a small group ofapprox. 20 elements

produces theultrasound beam

• Rectangular field of

view produced for

linear and trapezoidal

for curvilinear arraytransducers

• Phased array transducers

• 64 to 128 elements

• All are activated simultaneously

• Using time delays can steer and focus beam electronically



Ultrasound Beam Properties: Near Field and Far

Field

• Near (parallel) Field “Fresnelzone”

• Is adjacent to thetransducer face and has aconverging beam profile

• Convergence occursbecause of multipleconstructive anddestructive interferencepatterns of the ultrasoundwaves (pebble dropped ina quiet pond)

• Near Zone length = d2/4 =r 2/(d=transducer diameter,r=transducer radius )



• Unfocused transducer, Near Zone

length = d2/4 = r 2/• A focused single element

transducer uses either a curvedelement or an acoustic lens:

• Reduce beam diameter

• All diagnostic transducers arefocused

• Focal zone is the region overwhich the beam is focused

• A focal zone describes the

region of best lateral resolution



• The far field or Fraunhofer

zone is where the beamdiverges

• Angle of divergence

for non-focused

transducer is given by• sin() = 1.22 /d

• Less beam divergence

occurs with high-

frequency, large-

diameter transducers



Ultrasound Beam Properties - Side Lobes

• Side lobes are unwanted emissions of ultrasound energy directed

away from the main pulse

• Caused by the radial expansion and contraction of the transducerelement during thickness contraction and expansion

• Lobes get larger with transducer size• Echoes received from side lobes are mapped into the main beam,

causing artifacts



• For multielement arrays, side lobe emission occurs in a forward

direction along main beam• Grating lobes result when ultrasound energy is emitted far off-axis

by multielement arrays, and are a consequence of thenoncontinuous transducer surface of the discrete elements

• results in appearance of highly reflective, off-axis objects in

the main beam



Image Data Acquisition



Pulse Echo OperationPulse Repetition Frequency (PRF)

• Diagnostic ultrasound utilizes a pulse-echo format using a single

transducer to generate images• Most ultrasound beams are emitted in brief pulses (1-2 s duration)•

• For soft tissue (c = 1540 m/s or 0.154 cm/sec), the time delaybetween the transmission pulse and the detection of the echo is

directly related to the depth of the interface as• c = 2D / time• Time ( sec) = 2D (cm) / c (cm/ sec) = 2D/0.154• Time ( sec) = 13 sec x D (cm)• Distance (cm) = [c (cm/ sec) x Time ( sec)] / 2

• Distance (cm) = 0.077 x Time ( sec)



Spatial Resolution

Spatial resolution has 3 distinct measures: axial, lateral and slice

thickness (elevational)



Spatial Resolution - Axial

• Axial resolution (linear, range,

longitudinal or depth resolution) isthe ability to separate two objects

lying along the axis of the beam

• Achieving good axial resolution

requires that the returning echoesbe distinct without overlap

• The minimal required separation

distance between two boundaries

is ½ SPL (about ½ ) to avoid

overlap of returning echoes



Spatial Resolution - Lateral

• Lateral resolution - the ability

to resolve adjacent objectsperpendicular to the beam

direction and is determined by

the beam width and line

density

• Typical lateral resolution

(unfocused) is 2 - 5 mm, and is

depth dependent• Single focused transducers

restrain the beam to withinnarrow lateral dimensions at aspecified depth using lenses atthe transducer face



Spatial Resolution - Slice thickness (Elevational)

• Elevational resolution is dependent on the transducer element

height

• Perpendicular to the image plane

• Use of a fixed focal length lens across the entire surface of the arrayprovides improved elevational resolution at the focal distance,however partial volume effects before and after focal zone



Display

• Ultrasound scanners use time

gain compensation (TGC) to

compensate for increasedattenuation with depth

• TGC is also known as depth

gain compensation, time

varied gain, and swept gain• Images are normally displayed

on a video monitor or stored in acomputer

• Generally 512 x 512 matrix size

images, 8 bits deep allowing 256gray levels to be displayed, 0.25MB data



Display Modes: A-mode

• A-mode “amplitude” mode:

displays echo amplitude vs. time

(depth)

• One “A-line” of data per pulserepetition

• A-mode used in ophthalmology

or when accurate distance

measurements are required



Display Modes: B-mode

• B-mode (B for brightness) isthe electronic conversion of the

A-mode and A-line information

into brightness-modulated dots

on a display screen• In general, the brightness of

the dot is proportional to the

echo signal amplitude• Used for M-mode ad 2D gray-

scale imaging



Display Modes: M-mode

• M-mode (“motion” mode) or T-

M mode (“time-motion” mode):

displays time evolution vs.

depth

• Sequential US pulse lines are

displayed adjacent to each

other, allowing visualization of

interface motion

• M-mode is valuable forstudying rapid movement, suchas mitral valve leaflets



Scan Converter

• The function of the scan converter is to create 2D images from echo

formation received and to perform scan conversion to enable imagedata to be viewed on video display monitors

• Scan conversion is necessary because the image acquisition and

display occur in different formats

• Modern scan converters use digital methods for processing andstoring data

• For color display, the bit depth is often as much as 24 bits or 3 bytesof primary color



Lecture 7Digital signal processing of Biosignals

Dr.R.B.Ghongade

Department of E&TC,

V.I.I.T., Pune‐411048



Objectives

• Noise removal

• Clearly understand the nature (analysis)

• Diagnosis of the underlying pathology

• Aid in treatment (specific instances)



SOURCES OF VARIABILITY: NOISE

• Noise is a very general and somewhat relative

term: noise is what you do not want and signal is what you do want

• Noise is inherent in most measurement

systems and often the limiting factor in the performance of a medical instrument

• Many signal processing techniques are motivated by the desire to minimize the variability in the measurement



VARIABILITY

• In biomedical measurements, variability has four different

origins

(1) physiological variability

(2) environmental noise or interference(3) transducer artifact

(4) electronic noise

• Physiological variability is due to the fact that the information

you desire is based on a measurement subject to biological

influences other than those of interest

– For example, assessment of respiratory function based on

the measurement of blood pO2could be confounded by other physiological mechanisms that alter blood pO2

– can be a very difficult problem to solve, sometimes

requiring a totally different approach



• Environmental noise can come from sources

external or internal to the body

– example is the measurement of fetal ECG where the desired signal is corrupted by the mother’s ECG

– not possible to describe the specific characteristics of

environmental noise, typical noise reduction techniques such as filtering are not usually successful

– can be reduced using adaptive techniques

–

techniques do not require prior knowledge of noise characteristics



•

Transducer artifact is produced when the transducer responds to energy modalities

other than that desired

– For example, recordings of electrical potentials using electrodes placed on the skin are sensitive

to motion artifact , where the electrodes respond

to mechanical movement as well as the desired electrical signal

– Transducer artifacts can sometimes be

successfully addressed by modifications in transducer design



• Electronic noise has well‐known sources and

characteristics

• Electronic noise falls into two broad classes

–

thermal

or Johnson

noise, – shot noise

• Johnson noise is produced primarily in resistor or

resistance materials • Shot noise is related to voltage barriers associated

with semiconductors

• Both sources produce noise with a broad range of frequencies often extending from DC to 1012 –1013 Hz

• Such a broad spectrum noise is referred to as white

noise since it contains energy at all frequencies



Johnson Noise• Johnson or thermal noise is produced by resistance

sources, and the amount of noise generated is related to the resistance and to the temperature:

where R is the resistance in ohms, T the temperature in degrees Kelvin, and k

is Boltzman’s constant (k = 1.38 × 10−23 J/°K).* B is the bandwidth, or range of

frequencies, that is allowed to pass through the measurement system(The system bandwidth is determined by the filter characteristics in the system, usually

the analog filtering in the system)

• If noise current is of interest, the equation for Johnson noise

current can be obtained as:



•

Since Johnson noise is spread evenly over all frequencies, it is not possible to calculate a noise voltage or current without specifying B, the frequency range

• Since the bandwidth is not always known in advance, it is common to describe a relative

noise; specifically, the noise that would occur if the bandwidth were 1.0 Hz

• Such relative noise specification can be

identified by the unusual units required: or



Shot noise

• Shot noise is defined as a current noise and is

proportional to the baseline current through a

semiconductor junction

where q is the charge on an electron (1.662 × 10−19 coulomb), and Id is the

baseline semiconductor current

(In photo‐detectors, the baseline current that generates shot noise is termed the dark current, hence, the symbol Id)

• Noise is spread across all frequencies, the

bandwidth, BW, must be specified to obtain a specific value, or a relative noise can be specified in



Multiple Noise Sources

• When multiple noise sources are present, as is

often the case, their voltage or current contributions to the total noise add as the square root of the sum of the squares,

assuming that the individual noise sources are independent



Signal‐to‐Noise Ratio• Most waveforms consist of signal plus noise mixed together

• Signal and noise are relative terms, relative to the task at

hand: the signal is that portion of the waveform of interest

while the noise is everything else

• Goal of signal processing is to separate out signal from noise,

to identify the presence of a signal buried in noise, or to

detect features of a signal buried in noise

• The relative amount of signal and noise present in a waveform is usually quantified by the signal‐to‐noise ratio, SNR

• Is the ratio of signal to noise, both measured in RMS (root‐

mean‐squared) amplitude



It is difficult to detect

presence of the signal visually when the SNR is

−3 db, and impossible

when the SNR is −10 db

The ability to detect signals with low SNR is the goal and motivation for many of the

signal processing tools



ANALOG‐TO‐DIGITAL CONVERSION: BASIC

CONCEPTS• Converts an analog voltage to an equivalent digital number

• Analog or continuous waveform, x (t ), is converted into a

discrete waveform, x (n), a function of real numbers that are defined only at discrete integers, n

• Requires – slicing in time

– slicing in amplitude• Slicing the signal into discrete points in time is termed time

sampling or simply sampling

• Time slicing samples the continuous waveform, x (t ), at

discrete points in time, nTs, where Ts is the sample interval

• Since the binary output of the ADC is a discrete integer while the analog signal has a continuous range of values, analog‐to‐digital conversion also requires the analog signal to be sliced

into discrete levels, a process termed quantization



Quantization Error•

The number of bits used for conversion sets a lower limit on the resolution, and also determines the quantization error

• This error can be thought of as a

noise process added to the signal• If a sufficient number of quantization

levels exist (say N > 64), the distortion produced by quantization error may be modeled as additive independent white noise with zero mean with the variance determined by the quantization step size, δ = VMAX/2N

• Assuming that the error is uniformly distributed between −δ/2 +δ/2, the

variance, σ, is:

• Assuming a uniform distribution, the RMS value of the noise would be just twice the

standard deviation, σ



Noise Representation

• Noise is usually represented as a random variable, x (n)

• Describing noise as a function of time is not very useful

• More common to discuss other properties of noise such : – probability distribution – range of variability

– frequency characteristics

• Noise can take on a variety of different probability

distributions• Central Limit Theorem implies that most noise will have a

Gaussian or normal distribution

• The Central Limit Theorem states that when noise is

generated by

a large

number

of

independent

sources

it

will

have a Gaussian probability distribution regardless of the

probability distribution characteristics of the individual sources



(A) The distribution of

20,000 uniformly

distributed random

numbers.

(B) The distribution of

20,000 numbers, each of

which is the average of

two uniformly distributed

random numbers

(C) and (D) The

distribution obtained

when 3 and 8 random

numbers, still uniformly

distributed, are averaged

together

Although the underlying distribution is uniform, the averages of these

uniformly distributed numbers tend toward a Gaussian distribution



• The probability of a Gaussian distributed variable, x , is specified in the well‐known normal or Gaussian distribution equation

• Two important properties of a random variable are its mean, or

average value, and its variance, the term σ2

• The mean value of a discrete array of N samples is evaluated as:

• The sample variance, σ2, is calculated as

and the standard deviation, σ, is just the square root of the variance

• Normalizing the standard deviation or variance by 1/(N − 1) produces

the best estimate of the variance, if x is a sample from a Gaussian

distribution



• When multiple measurements are made, multiple random variables can be generated

• If these variables are combined or added together, the means add so that the resultant random variable is simply the mean, or average, of the individual means

• The same is true for the variance—the variances add and the average variance is the mean of the individual variances:

• But the standard deviation is the square root of the variance and the standard

deviations add as the times the average standard deviation

• Accordingly, the mean standard deviation is the average of the individual

standard deviations divided by

• Thus averaging noise from different sensors, or multiple observations from the

same source, will reduce the standard deviation of the noise by the square root

of

the

number

of

averages



Spectral characteristics of Noise• Energy distribution may vary with frequency

• Frequency characteristics of the noise are related to

how well, one instantaneous value of noise correlates with the adjacent instantaneous values: for digitized data how much one data point is correlated with its

neighbors

• If the noise has so much randomness that each point is independent of its neighbors, then it has a flat spectral

characteristic and vice versa, called as white noise• When white noise is filtered, it becomes bandlimited

and is referred to as colored noise



ENSEMBLE AVERAGING

• Averaging can be a simple, yet powerful signal processing technique for reducing noise when multiple observations of the signal are possible

• In many biomedical applications, the multiple observations come from repeated responses to the same stimulus

• In ensemble averaging, a group, or ensemble, of time responses are averaged together on a point‐by‐point basis; that is, an average signal is constructed by taking the average, for each point in time, over all signals in the ensemble

• Two essential requirements – the ability to obtain multiple observations

– reference signal closely time‐linked to the response



An ensemble of individual (vergence) eye movement

responses to a step change in stimulus



DATA FUNCTIONS AND TRANSFORMS

• In signal processing, most functions fall into two categories – waveforms, images, or other data

– entities that operate on waveforms, images, or other data • can be further divided into functions that modify the data, and

functions used to analyze or probe the data

• Example1: filter coefficients (modify the spectral content of a waveform)

• Example2: Fourier Transform uses functions (harmonically related sinusoids) to analyze the spectral content of a waveform

• Functions that modify data are also termed operationsor transformations

• A transform can be thought of as a re‐mapping of the

original data into a function that provides more information than the original



How transforms work!• Transforms are achieved by comparing the signal of interest with some

sort of probing function

• Comparison takes the form of a correlation (produced by multiplication)

that is averaged (or integrated) over the duration of the waveform, or

some portion of the waveform

where x (t ) is the waveform being analyzed, f m(t ) is the probing function and m is

some variable of the probing function, often specifying a particular member in a family of similar functions

• A family of probing functions is also termed a basis

• For discrete functions, a probing function consists of a sequence of values,

or vector, and the integral becomes summation over a finite range

where x(n) is the discrete waveform and f m(n) is a discrete version of the family

of probing functions. This equation assumes the probe and waveform functions are the same length



• When either x(t) or f m(t) are of infinite length, they must be truncated

• Also if the length of the probing function, f m(n), is shorter than the

waveform , x(n), then x(n) must be shortened in some way

• Can be shortened by simple truncation or by multiplying the function by

another function that has zero value beyond the desired length

• A function used to shorten another function is termed a window function

• Consequences of this artificial shortening will depend on the specific

window function used

where W(n) is the window function



Finite Support• If the probing function is of finite length ( finite support ) and this length is

shorter than the waveform, then it might be appropriate to translate or

slide it over the signal and perform the comparison (correlation, or

multiplication) at various relative positions between the waveform and

probing function

• The output would be a family of functions, or a two‐variable function, where one variable corresponds to the relative position between the two

functions and the other to the specific family member

where the variable k indicates the relative position between the two functions

and m is the family member as in the above equations

• Approach can be used for long—or even infinite—probing functions,

provided the probing function itself is shortened by windowing to a length that is less than the waveform

• The shortened probing function can be translated across the waveform in

the same manner as a probing function that is naturally short

Used in STFT



Projections•

All of the discrete equations (discussed so far) have one thing in common: they all feature the multiplication of two (or sometimes three) functions

and the summation of the product over some finite interval

• This multiplication and summation is the same as scalar product of the

two vectors

• When the probing function consists of a family of functions, then the scalar

product operations can be thought of as projecting the waveform vector

onto vectors representing the various family members

• In this vector‐based conceptualization, the probing function family, or basis, can be thought of as the axes of a coordinate system

• Hence the motivation behind development of probing functions that have

family members that are orthogonal or orthonormal so that the scalar

product computations (or projections) can be done on each axes (i.e., on

each family member) independently of the others



CONVOLUTION• Important concept in linear systems theory, solving the need for a time

domain operation equivalent to the Transfer Function

• Convolution can be used to define a general input–output relationship in

the time domain analogous to the Transfer Function in the frequency

domain

• The input, x(t), the output, y(t), and the function linking the two through

convolution, h(t), are all functions of time; hence, convolution is a time

domain operation

• Basic concept behind convolution is superposition

• The first step is to determine a time function, h(t ), that tells how the

system responds to an infinitely short segment of the input waveform

• If superposition holds, then the output can be determined by summing

(integrating) all the response contributions calculated from the short

segments



Impulse Response

• The way in which a linear system responds to an infinitely short

segment of data can be determined simply by noting the system’s response to an infinitely short input, an infinitely short pulse

• An infinitely short pulse (or one that is at least short compared to

the dynamics of the system) is termed an impulse or delta

function (commonly denoted δ(t )), and the response it produces is termed the impulse response, h(t ).

• Given that the impulse response describes the response of the system to an infinitely short segment of data, and any input can be

viewed as an infinite

• string of such infinitesimal segments, the impulse response can be used to determine the output of the system to any input

• Response produced by an infinitely small data segment is simply

this impulse response scaled by the magnitude of that data segment

• The contribution of each infinitely small segment can be summed, or integrated, to find the response created by all the segments



Mathematical Description of Convolution

• Stated mathematically, the output y (t ), to any input, x (t ) is given by:

• To determine the impulse of each infinitely small data segment, the

impulse response is shifted a time τwith respect to the input, then scaled

(i.e.,multiplied) by the magnitude of the input at that point in time

• It does not matter which function, the input or the impulse response, is

shifted

• Shifting and multiplication is sometimes referred to as the lag product

• For discrete signals, the integration becomes a summation and the

convolution equation becomes:



Correlation•

Word correlation conveys similarity: how one thing is like another• Mathematically, correlations are obtained by multiplying and normalizing

• Covariance and correlation use multiplication to compare the linear

relationship between two variables, but in correlation the coefficients are

normalized to fall between zero and one• Because of normalization correlation coefficients are insensitive to

variations in the gain of the data acquisition process or the scaling of the

variables

• Can be applied to

– two or more waveforms

– multiple observations of the same source

– multiple segments of the same waveform

• The correlation function is the lagged product of two waveforms:

Also called cross‐

correlation



Autocorrelation• Special case of the correlation function occurs when the

comparison is between two waveforms that are one in the same;

that is, a function is correlated with different shifts of itself

• Provides a description of how similar a waveform is to itself at

various time shifts, or time lags

• Autocorrelation function will naturally be maximum for zero lag (n =

0) because at zero lag the comparison is between identical

waveforms

• Usually the autocorrelation is scaled so that the correlation at zero

lag is 1

• Function must be symmetric about n = 0, since shifting one version

of the same waveform in the negative direction is the same as shifting the other version in the positive direction

• Related to the bandwidth of the waveform

• The sharper the peak of the autocorrelation function the broader

the bandwidth



Cross‐covariance• Same as cross‐correlation function except that the means

have been removed from the data before calculation

• The terms correlation and covariance, when used alone (i.e.,

without the term function result into a single number



Covariance and Correlation Matrices

• Can be applied to multivariate data where multiple responses,

or observations, are obtained from a single process

• The covariance and correlation matrices assume that the multivariate data are arranged in a matrix where the columns

are different variables and the rows are different observations

of those variables

• In signal processing, the rows are the waveform time samples, and the columns are the different signal channels or

observations of the signal

• The covariance matrix gives the variance of the columns of the

data matrix in the diagonals while the covariance between

columns is given by the off ‐diagonals



• Correlation matrix is related to the covariance matrix by the

equation:

• The correlation matrix is a set of correlation coefficients between waveform observations or channels and has a similar

positional relationship as in the covariance matrix

• Since the diagonals in the correlation matrix give the

correlation of a given variable or waveform with itself, they will

all equal 1 (rxx(0) = 1), and the off ‐diagonals will vary between

± 1



SAMPLING THEORY AND FINITE DATA

CONSIDERATIONS

• To convert an analog waveform into a digitized version:

– sampling the waveform at discrete points in time

– if the waveform is longer than the computer memory, isolating a segment of the analog waveform for the conversion‐(windowing)

• The “Shannon Sampling Theorem” states that any sinusoidal waveform can be uniquely reconstructed provided it is

sampled at least twice in one period

• The sampling frequency, f s, must be ≥ 2 f sinusoid

• Shannon’s Sampling Theorem states that a continuous waveform can be reconstructed without loss of information provided the sampling frequency is greater than twice the highest frequency in the analog waveform:



Sampling function

• The sampling process is equivalent to multiplying the analog waveform by a repeating series of short pulses

• This repeating series of short pulses is sometimes referred to

as the sampling function

• The sampling function can be stated mathematically using the

impulse response

where Ts is the sample interval and equals 1/f s

• For an analog waveform, x(t), the sampled version, x(n), is

given by multiplying x(t) by the sampling function:



Effects of sampling•

Multiplication in the time domain is equivalent to convolution in frequency domain (and vice versa)

• Hence, the frequency

characteristic of a sampled waveform is just the convolution of the analog waveform spectrum with the sampling function

spectrum• It would be possible to

recover the original spectrum simply by filtering the sampled data by an

ideal low‐pass filter with a bandwidth > f max

CONV



Aliasing

• Spectrum that results if the digitized data were sampled at f s < 2 f max, in this case f s = 1.5 f max

• The reflected portion of the spectrum has

become intermixed with the original

spectrum, and no filter can unmix them

• When f s < 2 f max, the sampled data suffers

from spectral overlap,better known as

aliasing

• The sampled data no longer provides a unique representation of the analog

waveform, and recovery is not possible

• Aliasing must be avoided either by :

• use of very high sampling rates—rates

that are well above the bandwidth of the

analog system

• or by filtering the analog signal before

analog‐to‐digital conversion

Anti‐aliasing filters



ExampleAn ECG signal of 1 volt peak‐to‐peak has a bandwidth of 0.01 to 100 Hz.

Assume that broadband noise may be present in the signal at about 0.1 volts

(i.e., −20 db below the nominal signal level). This signal is filtered using a four‐

pole low‐pass filter. What sampling frequency is required to ensure that the

error due to aliasing is less than −60 db (0.001 volts)?

The noise at the sampling frequency must be reduced another 40 db (20 * log (0.1/0.001)) by the four‐pole filter. A four‐pole filter with a

cutoff of 100 Hz (required to meet the fidelity requirements of the ECG signal) would attenuate the waveform at a rate of 80 db per decade. For a four‐pole filter the asymptotic attenuation is given as:

Attenuation = 80 log( f 2/ f c) db

To achieve the required additional 40 db of attenuation required by the problem from a four‐pole filter:

80 log( f 2/ fc) = 40 log( f 2/ fc) = 40/80 = 0.5

f 2/ fc = 10.5 =; f2 = 3.16 × 100 = 316 Hz

Thus to meet the sampling criterion, the sampling frequency must be at

least 632 Hz, twice the frequency at which the noise is adequately attenuated



• Unfortunately, in order for this impulse function to produce an ideal filter,

it must be infinitely long• However if fs >> f max, as is often the case, then any reasonable low‐pass

filter would suffice to recover the original waveform

• Recovery of a waveform when the sampling frequency is much muchgreater that twice the highest frequency in the sampled waveform (fs =

10fmax) is easier with practical LPF

• In this case, the low‐pass filter (dotted line) need not have as sharp a

cutoff.



Edge Effects• Advantage of dealing with infinite data is that one

need not be concerned with the end points• Finite data consist of numerical sequences having

a fixed length with fixed end points at the

beginning and end of the sequence• Some operations, such as convolution, may

produce additional data points while some operations will require additional data points to complete their operation on the data set

• How to add or eliminate data points?



Extending data length• Three common strategies for extending a data set when

additional points are needed:

– extending with zeros (or a constant), termed zero padding;

– extending using periodicity or wraparound ;

– extending by reflection, also known as symmetric extension

• In the zero padding approach, zeros are added to the end or

beginning of the data sequence

• This approach is frequently used in spectral analysis and is justified by the implicit assumption that the waveform is zero outside of the sample period anyway

• A variant of zero padding is constant padding, where the data sequence is extended using a constant value, often the last (or first) value in the sequence



• If the waveform can be reasonably thought of as one

cycle of a periodic function, then the wraparoundapproach is clearly justified data are extended by tacking on the initial data sequence to the end of the data set and visa versa

• This is quite easy to implement numerically: simply make all operations involving the data sequence index modulo N, where N is the initial length of the data set

• These two approaches will, in general, produce a

discontinuity at the beginning or end of the data set, which can lead to artifact in certain situations

• The symmetric reflection approach eliminates this discontinuity by taking on the end points in reverse order (or beginning points if extending the beginning of the data sequence)



S t l A l i Cl i l M th d



Spectral Analysis: Classical Methods• Many biological signals demonstrate interesting or diagnostically useful properties

when viewed in the so called frequency domain,

E.g. heart rate, EMG, EEG, ECG,

eye movements and other motor responses, acoustic heart sounds, and stomach

and intestinal sounds

• Determining the frequency content of a waveform is termed spectral analysis

• Methods can be divided into two broad categories

– classical methods based on the Fourier transform

– modern methods such as those based on the estimation of model parameters

• The accurate determination of the waveform’s spectrum requires that the signal

be periodic, or of finite length, and noise‐free

• But many biological signals are

– either infinite or of sufficient length that only a portion of it is available for

analysis

– often corrupted by substantial amounts of noise or artifact

• All spectral analysis techniques must necessarily be approximate; they are

estimates of the true spectrum

• The various spectral analysis approaches attempt to improve the estimation

accuracy of specific spectral features



• Two spectral features of potential interest are: – the overall shape of the spectrum, termed the spectral estimate,

and/or

– local features of the spectrum sometimes referred to as parametric estimates

• Techniques that provide good spectral estimation are poor

local estimators and vice versa

THE FOURIER TRANSFORM FOURIER SERIES ANALYSIS



THE FOURIER TRANSFORM: FOURIER SERIES ANALYSIS

• Classical Fourier transform (FT) method is the most straightforward for spectral

estimate

• Any periodic waveform can be represented by a series of sinusoids that are at the

same frequency as, or multiples of, the waveform frequency

• If a waveform can be broken down into a series of sines or cosines of different

frequencies, the amplitude of these sinusoids must be proportional to the frequency component contained in the waveform at those frequencies

• Consider the case where sines and cosines are used to represent the frequency

components: to find the appropriate amplitude of these components it is only

necessary to correlate (i.e., multiply) the waveform with the sine and cosine family,

and average (i.e., integrate) over the complete waveform (or one period if the waveform is periodic)

where T is the period or time length of the

waveform , f T = 1/T , and m is set of

integers, possibly infinite: m = 1, 2, 3, . . . ,

defining the family member.

This gives rise to a family of sines and cosines

having harmonically related frequencies,

mf T

F i i l i bi f i i hi h h f il



• Fourier series analysis uses a probing function in which the family consists of harmonically related sinusoids

• The sines and cosines in this family have valid frequencies only at values of m/T , which is either the same frequency as the waveform (when m = 1) or higher multiples (when m > 1) that are termed harmonics

• Since this approach represents waveforms by harmonically related

sinusoids, the approach is sometimes referred to as harmonic decomposition

• For periodic functions, the Fourier transform and Fourier series

constitute a bilateral transform: the Fourier transform can be applied to a waveform to get the sinusoidal components and the Fourier series sine and cosine components can be summed to reconstruct the original waveform:

…. (1)



Two periodic functions and their approximations constructed from a

limited series of sinusoids.

Upper graphs: A square wave is approximated by a series of 3 and 6 sine waves.

Lower graphs: A triangle wave is approximated by a series of 3 and 6 cosine

waves



• Spectral information is usually presented as a frequency plot,

a plot of sine and cosine amplitude vs. component number, or the equivalent frequency

• To convert from component number, m, to frequency, f , note

that f = m/T , where T is the period of the fundamental.

• In digitized signals, the sampling frequency can also be used

to determine the spectral frequency

• Rather than plot sine and cosine amplitudes, it is more

intuitive to plot the amplitude and phase angle of a sinusoidal wave using the rectangular‐to‐polar transformation



•

A triangle or sawtooth wave (left) and the first 10 terms of its Fourier series (right)

• Note that the terms become quite small after the second term

Symmetry



Symmetry• Some waveforms are symmetrical or anti‐symmetrical about t

= 0, so that one or the other of the components, a(k ) or b(k ) in

Eq. (1), will be zero

• If the waveform has mirror symmetry about t = 0, that is, x (t )

= x (−t ), then multiplications by a sine functions will be zero irrespective of the frequency, and this will cause all b(k ) terms

to be zeros

• Such mirror symmetry functions are termed even functions

• If the function has anti‐symmetry, x (t ) = − x (t ), a so‐called odd

function, then all multiplications with cosines of any

frequency will be zero, causing all a(k ) coefficients to be zero

• Functions that have half ‐wave symmetry will have no even

coefficients, and both a(k ) and b(k ) will be zero for even m

• These symmetries are useful for reducing the complexity of

solving for the coefficients when such computations are done

manually



Function Symmetries

R l Wi d



Rectangular Window

• The digitized waveform must necessarily be truncated at least

to the length of the memory storage array

• This process is called windowing

• The windowing process can be thought of as multiplying the

data by some window shape

• If the waveform is simply truncated and no further shaping is

performed on the resultant digitized waveform (as is often the case), then the window shape is rectangular by default

• Other shapes can be imposed on the data by multiplying the

digitized waveform by the desired shape

• Windowing creates some effects (to be discussed later!)

Another representation of Fourier series



p• The equations for computing Fourier series analysis of digitized data are

the same as for continuous data except the integration is replaced by summation

• Equations are presented using complex variables notation so that both the sine and cosine terms can be represented by a single exponential term using Euler’s identity

• Discrete Fourier transform becomes:

where N is the total number of points and m indicates the family member,

i.e., the harmonic number (m must now be allowed to be both positive

and negative when used in complex notation)

• The inverse Fourier transform can be calculated as:

• gives the magnitude for the sinusoidal representation



• gives the magnitude for the sinusoidal representation

of the Fourier series while the angle of X (m) gives the phase angle for this representation, since X (m) can also be written as

• The discrete Fourier transform produces a function of m

• To convert this to frequency note that:

where f 1 ≡ f T is the fundamental frequency, T s is the sample interval; f s is the

sample frequency; N is the number of points in the waveform; and T P = NT s is

the period of the waveform

• The equation for the discrete Fourier transform can also be written as:

Fourier Transform For Aperiodic Functions



Fourier Transform For Aperiodic Functions

• If the function is not periodic, it can still be accurately decomposed into sinusoids if it is

aperiodic; that is, it exists only for a well‐defined

period of time, and that time period is fully represented by the digitized waveform

• The sinusoidal components can exist at all

frequencies, not just multiple frequencies or harmonics

• The analysis procedure is the same as for a periodic

function, except that the frequencies obtained are really only samples along a continuous frequency

spectrum



• The frequency

spectrum of a

periodic triangle

wave for three

different periods• As the period

gets longer,

approaching an

aperiodic

function, the

spectral shape

does not change,

but the points get

closer together

Frequency Resolution



Frequency Resolution•

From the discrete Fourier series equation , the number of points produced by the operation is N, the number of points in the data set

• Since the spectrum produced is symmetrical about the midpoint, N/2 (or fs/2 in frequency), only half the points contain unique

information• If the sampling time is T s, then each point in the spectra represents

a frequency increment of 1/(NT s)

• As a rough approximation, the frequency resolution of the spectra will be the same as the frequency spacing, 1/(NT s)

• Frequency spacing of the spectrum produced by the Fourier transform can be decreased by increasing the length of the data, N

• Increasing the sample interval, T s, should also improve the frequency resolution, but since that means a decrease in f s, the

maximum frequency in the spectra, f s /2 is reduced limiting the spectral range

• One simple way of increasing N even after the waveform has been sampled is to use zero padding

Truncated Fourier Analysis: Data Windowing



Truncated Fourier Analysis: Data Windowing

• Often, a waveform is neither periodic or aperiodic, but a segment of a much longer—possibly infinite—time series (E.g.

ECG)

•

Only a portion of such waveforms can be represented in the finite memory of the computer, and some attention must be

paid to how the waveform is truncated

• Types of windowing used:

– Rectangular

– Barlett (Triangular)

– Hamming

– Hanning

– Truncated Gaussian



Window Functions (a.k.a. Tapering Functions)



Rectangular

Barlett (Triangular)

Hamming

Hanning

Gaussian

Effects of windowing



• When a data set is windowed, which is essential if the data set is larger than the memory storage, then the frequency characteristics of the window become part of the spectral result

• Thus all windows produce two types of artifact

• The actual spectrum is widened by an artifact termed the main lobe, and additional peaks are generated termed the side

lobes



Selecting the Window Function



Selecting the Window Function

• Selecting the appropriate window, depends on what spectral

features are of interest

• If the task is to resolve two narrowband signals closely spaced in

frequency, then a window with the narrowest mainlobe (the rectangular window) is preferred

• If there is a strong and a weak signal spaced a moderate distance

apart, then a window with rapidly decaying sidelobes is preferred to

prevent the sidelobes of the strong signal from overpowering the weak signal

• If there are two moderate strength signals, one close and the other

more distant from a weak signal, then a compromise window with

a moderately narrow mainlobe and a moderate decay in sidelobes

could be the best choice

• Often the most appropriate window is selected by trial and error

Power Spectrum



p

• The power spectrum is commonly defined as the Fourier

transform of the autocorrelation function

• In continuous and discrete notation, the power spectrum

equation becomes:

• Since the autocorrelation function has odd symmetry, the sine

terms, b(k) will all be zero

Power Spectrum (Direct Approach)



• The direct approach is motivated by the fact that the energy contained in

an analog signal, x (t ), is related to the magnitude of the signal squared,

integrated over time

• By an extension of Parseval’s theorem it is easy to show that

Parseval’s Theorem: The sum (or integral) of the square of a function is

equal to the sum (or integral) of the square of its transform

• Hence equals the energy density function over frequency, also

referred to as the energy spectral density, the power spectral density, or simply the power spectrum

• In the direct approach, the power spectrum is calculated as the

magnitude squared of the Fourier transform of the waveform of interest:

Periodogram



g• While the power spectrum can be evaluated by applying the

FFT to the entire waveform, averaging is often used,

particularly when the available waveform is only a sample of a

longer signal

• In such very common situations, power spectrum evaluation

is necessarily an estimation process, and averaging improves

the statistical properties of the result

• When the power spectrum is based on a direct application of the Fourier transform followed by averaging, it is commonly

referred to as an average periodogram

• Selection of data window and averaging strategy is usually

based on experimentation with the actual data

• Averaging is usually achieved by dividing the waveform into a

number of segments, possibly overlapping, and evaluating the

Fourier transform on each of these segments

Welch method of spectral analysis



Welch method of spectral analysis

• One of the most popular procedures to evaluate the average

periodogram is attributed to Welch and is a modification of

the segmentation scheme originally developed by Bartlett

• In this approach, overlapping segments are used, and a

window is applied to each segment

• By overlapping segments, more segments can be averaged for

a given segment and data length• Averaged periodograms obtained from noisy data traditionally

average spectra from half ‐overlapping segments; that is,

segments that overlap by 50%.



• A waveform is divided into three segments with a 50% overlap between each

segment

• In the Welch method of spectral analysis, the Fourier transform of each

segment would be computed separately, and an average of the three

transforms would provide the output

Digital Filters



• Filters are closely related to spectral analysis since the goal of filtering is to reshape the spectrum to one’s advantage

• Most noise is broadband (the broadest band noise being white noise with a flat spectrum) and most signals are

narrowband; hence, filters that appropriately reshape a waveform’s spectrum will almost always provide some improvement in SNR

• A basic filter can be viewed as a linear process in which the

input signal’s spectrum is reshaped in some well‐defined manner

• Filters differ in the way they achieve this spectral reshaping, and can be classified into two groups based on their

approach: – finite impulse response (FIR) filters

– infinite impulse response (IIR) filters

THE Z‐TRANSFORM



• Frequency‐based analysis introduced in the last chapter is a most useful tool for analyzing systems cannot be applied to transient responses of infinite length, such as step functions, or systems with nonzero initial conditions

• Motivated the development of the Laplace transform

in the analog

domain

• Laplace analysis uses the complex variable s (s = σ + j ω) as a representation of complex frequency in place of j ω in the Fourier

transform• The Z ‐transform is a digital operation analogous to the Laplace

transform in the analog domain, and it is used in a similar manner

• The Z‐transform is based around the complex variable, z, where z is

an arbitrary complex number, e j ω

• This variable is also termed the complex frequency, and as with its time domain counterpart, the Laplace variable s, it is possible to substitute e j ω for z to perform a strictly sinusoidal analysis

If is set to 1, then z = e jω

. This is called evaluating z on the unit circle

• The Z‐transform(similar to the Fourier transform equation) is:



where z = an arbitrary complex variable

• Probing function for this transform is simply z−n

• In any real application, the limit of the summation will be finite, usually the length of x (n)

• When identified with a data sequence, such as x (n) above, z−n

represents an interval shift of n samples, or an associated

time shift of nT s seconds

• This time shifting property of z−n can be formally stated as:

The time shifting characteristic of the Z‐

transform can be used to define a unit

delay process, z−1

Digital Transfer Function



Digital Transfer Function

• Most useful applications of the Z‐transform lies in its ability to define the digital equivalent of a transfer function

• By analogy to linear system analysis, the digital transfer function is defined as:

• Unlike analog systems, the order of the numerator, N, need

not be less than, or equal to, the order of the denominator, D, for stability

• In fact, systems that have a denominator order of 1 are more

stable that those having higher order denominators

• From the digital transfer function, H(z), it is possible to

determine the output given any input



determine the output given any input

• The input–output or difference equation analogous to the

time domain equation and can be obtained by applying the

time shift interpretation to the term z−n

equation assumes that a(0) = 1

• Filter design, then, is simply the determination of the

appropriate filter coefficients, a(n) and b(n), that provide the

desired spectral shaping

• If the frequency spectrum of H ( z) is desired, it can be

obtained from a modification substituting z = ejω as:



obtained from a modification ‐substituting z = e j ω as:

• Frequency can be obtained from the variable m by multiplying

by f s/N or 1/(NT s )

FINITE IMPULSE RESPONSE (FIR) FILTERS• FIR filters have transfer functions that have only numerator



y

coefficients, i.e., H(z) = B(z)• This leads to an impulse response that is finite

• Merits:

–

stable – linear phase shifts

– have initial transients that are of finite durations

– their extension to 2‐dimensional applications is straightforward

• Demerits:

– less efficient in terms of computer time and memory

• FIR filters are also referred to as nonrecursive because only

the input (not the output) is used in the filter algorithm• FIR filtering has also been referred to as a moving

average process

• The general equation for an FIR filter is: Similar to convolution



where b(n) is the coefficient function (also referred to as the weighting

function) of length L, x(n) is the input, and y(n) is the output

• Filter coefficients (or weights) of an FIR filter are the same as the

impulse response of the filter

• Since the frequency response of a process having an impulse

response h(n) is simply the Fourier transform of h(n), the frequency

response of an FIR filter having coefficients b(n) is just the Fourier

transform of b(n):

• The inverse operation, going from a desired frequency response to the coefficient function, b(n), is known as filter design

• Since the frequency response is the Fourier transform of the filter

coefficients, the coefficients can be found from the inverse Fourier

transform of the desired frequency response

FIR Filter Design



• The ideal lowpass filter is a rectangular window in

the frequency domain

• The inverse Fourier transform of a rectangular

window function is:

where f c is the cutoff frequency; T s is the sample interval in

seconds; and L is the length of the filter.The argument, n − L/2, is used to make the coefficient

function symmetrical giving the filter linear phase

characteristics

Filter function



•

FFT of this function is same as an impulse response

• This coefficient function must be infinitely long to produce

the filter characteristics of an ideal filter

• Truncating it will result in a

lowpass filter that is less than ideal

Effects of b(n) truncation with rectangular



window

• The weighting functions were abruptly truncated at 17 and 65 coefficients (rectangular window)

• The artifacts associated with this truncation are clearly seen

• The lowpass cutoff frequency is 100 Hz

Effects of b(n) truncation with



Hamming window

• The overshoot in the passband has disappeared and the oscillations

are barely visible in the plot

Highpass, Bandpass, and Bandstop



filters• Are derived in the same manner from equations generated by

applying an inverse FT to rectangular structures having the

appropriate associated shape



MATLAB Demo LPF FIR Design

Steps for Designing FIR Filters



p g g

• Given: f s,( f C or f H and f L)

• Choose the appropriate filter (LPF,HPF,BP,BS)

• Select the filter length L

• Compute b(n) using filter formula(length: L+1)

• Check the filter spectrum by using FT of b(n)

• Convolve the input x(n) with b(n) to obtain

the output y(n)

Derivative Operation



• The derivative is a common operation in signal processing and is particularly useful in analyzing certain physiological signals

• Digital differentiation is defined as Δ x /Δt and can be implemented by taking the difference between two adjacent points, scaling by 1/T s, and repeating this operation along the entire waveform

• As FIR filter this is equivalent to a two coefficient filter, [−1, +1]/T s,

•

The frequency characteristic of the derivative operation is a linear increase with frequency so there is

• Considerable gain at the higher frequencies

• Since the higher frequencies frequently contain a greater percentage of noise, this operation tends to produce a noisy

derivative curve hence we use two‐point central difference algorithm

The Two‐Point Central Difference Algorithm

•



• The two‐point central difference algorithm uses two

coefficients of equal but opposite value spaced L points apart,

as defined by the input–output equation:

where L is the skip factor that influences the effective bandwidth, and

T s is the sample interval

• The filter coefficients for the two‐point central difference

algorithm would be:

Frequency characteristic of the derivative



operationIdeal

FIR implementation



(A) The derivative was calculated by taking the difference in adjacent points and scaling by the sample frequency.

(B) The derivative was computed using the two‐point central difference algorithm with a skip factor of 4

Time‐Frequency Analysis• Spectral analysis techniques developed thus far represent powerful signal



processing tools if one is not especially concerned with signal timing• Classical or modern spectral methods provide a complete and appropriate

solution for waveforms that are stationary; that is, waveforms that do not

change in their basic properties over the length of the analysis

• Many waveforms—particularly those of biological origin–are not stationary, and change substantially in their properties over time

• Fourier analysis provides a good description of the frequencies in a

waveform, but not their timing

• Timing is encoded in the phase portion of the transform, and this

encoding is difficult to interpret and recover

• In the Fourier transform, specific events in time are distributed across all

of the phase components

•

A local feature in time has been transformed into a global feature in phase

• Timing information is often of primary interest in many biomedical signals,

and this is also true for medical images where the analogous inf ormation

is localized in space

Methods



• A wide range of approaches have been

developed to try to extract both time and frequency information from a waveform

• Basically they can be divided into two groups:

– time–frequency methods

– time–scale methods (wavelet analysis)

Short‐Term Fourier Transform: The



Spectrogram• The first time–frequency methods were based on the

straightforward approach of slicing the waveform of interest into a number of short segments and performing the analysis on each of these segments, usually using the standard Fourier transform

• A window function is applied to a segment of data, effectively isolating that segment from the overall

waveform, and the Fourier transform is applied to that segment

• This is termed the spectrogram or “short‐term Fourier transform” (STFT) since the Fourier Transform is applied to

a segment of data that is shorter, often much shorter, than the overall waveform

• Selecting the most appropriate window length can be critical

• The basic equation for the spectrogram in the continuous domain is:



where w(t‐τ) is the window function and τ is the variable that

slides the window across the waveform, x(t)

• The discrete version

• There are two main problems with the spectrogram:

(1) selecting an optimal window length for data segments

that contain several different features may not be possible,

(2) the time–frequency tradeoff: shortening the data length, N, to improve time resolution will reduce frequency

resolution which is approximately 1/(NTs)

• If window is made smaller to improve the time resolution, then the frequency resolution is degraded and visa versa

• Thi ti f t d ff h b t d t



• This time–frequency tradeoff has been equated to an uncertainty principle where the product of frequency resolution (expressed as bandwidth, B) and time, T , must be greater than some minimum

• STFT has been used successfully in a wide variety of problems, particularly those where only high frequency components are of interest and frequency resolution is not critical

• The area of speech processing has benefitted considerably from the application of the STFT

• Where appropriate, the STFT is a simple solution that rests on

a well understood classical theory (i.e., the Fourier transform) and is easy to interpret



Wavelet Analysis



• Inability of the Fourier transform to describe both time and frequency characteristics of the

waveform led to a number of different approaches

• The wavelet transform can be used as yet another way to describe the properties of a waveform that changes over time, but in this case the waveform is divided not into sections

of time, but segments of scale

THE CONTINUOUS WAVELET TRANSFORM

• A variety of different probing functions may be used, but the family always

consists of enlarged or compressed versions of the basic function as well



consists of enlarged or compressed versions of the basic function, as well as translations

• Continuous wavelet transform (CWT) equation is defined as:

where b acts to translate the function across x(t) just as t and the variable

a acts to vary the time scale of the probing function, ψ

• If a is greater than one, the wavelet function, ψ, is stretched along the time axis, and if it is less than one (but still positive) it contacts the

function

• Negative values of a simply flip the probing function on the time axis

•

Probing function ψ could be any of a number of different functions, but it always takes on an oscillatory form, hence the term “wavelet”

• The * indicates the operation of complex conjugation, and the

normalizing factor l/ ensures that the energy is the same for all values

of a (all values of b as well, since translations do not alter wavelet energy)

• If b = 0, and a = 1, then the wavelet is in its natural form,

which is termed the mother wavelet ; that is, ψ1,0 (t) ≡ ψ(t)



• The wavelet shown is the popular Morlet wavelet, named after a

pioneer of wavelet analysis, and is defined by the equation

• Wavelet coefficients, W (a,b), describe the correlation between the waveform and the wavelet at various

translations and scales: the

similarity

between

the

waveform

and the wavelet at a given combination of scale and position



translations and scales: the similarity between the waveformand the wavelet at a given combination of scale and position, a,b

• Coefficients provide the amplitudes of a series of wavelets,

over a range of scales and translations, that would need to be added together to reconstruct the original signal

• Wavelet analysis can be thought of as a search over the waveform of interest for activity that most clearly

approximates the shape of the wavelet• This search is carried out over a range of wavelet sizes: the

time span of the wavelet varies although its shape remains the same

• Wavelet coefficients respond to changes in the waveform, more strongly to changes on the same scale as the wavelet, and most strongly, to changes that resemble the wavelet

• If the wavelet function, ψ(t ), is appropriately chosen, then it is

possible to reconstruct the original waveform from the

wavelet coefficients just as in the Fourier transform



wavelet coefficients just as in the Fourier transform• As CWT decomposes the waveform into coefficients of two

variables, a and b, a double summation (or integration) is

required to recover the original signal from the coefficients

Wavelet Time–Frequency Characteristics

• Wavelets provide a compromise in the battle between time and frequency

localization: they are well localized in both time and frequency, but not precisely localized in either



y q y,precisely localized in either

• Measure of the time range of a specific wavelet, Δt ψ, can be specified by the square root of the second moment of a given wavelet about its time center (i.e., its first moment)

In mathematics, a moment is, loosely speaking, a quantitative measure of the shape of a

set of points. The "second moment", for example, is widely used and measures the

"width" (in a particular sense) of a set of points in one dimension or in higher dimensions measures the shape of a cloud of points as it could be fit by an ellipsoid. Other moments

describe other aspects of a distribution such as how the distribution is skewed from its

mean, or peaked. Any distribution can be characterized by a number of features (such as

the mean, the variance, the skewness, etc.), and the moments of a function describe the

nature of its distribution

where t 0 is the center time, or first moment of

the wavelet

• Similarly the frequency range, Δωψ, is given by:



where Ψ ( ω ) is the frequency domain representation (i.e., Fourier

transform) of ψ(t/a), and ω0 is the center frequency of Ψ ( ω )

• The time and frequency ranges of a given family can be

obtained from the mother wavelet

For Mexican hat wavelet



• The frequency range, or bandwidth, would be the range of the mother

Wavelet divided by a:

Δωψ(a) = Δωψ /

• If we multiply the frequency range by the time range, the a’s cancel and



e u t p y t e eque cy a ge by t e t e a ge, t e a s ca ce a d

we are left with a constant that is the product of the constants

• Product of the ranges is invariant to dilation and that the ranges are inversely

related; increasing the frequency range, Δωψ(a), decreases the time range,

Δtψ(a)

• These ranges correlate to the time and frequency resolution of the CWT• Decreasing the wavelet time range (by decreasing a ) provides a more

accurate assessment of time characteristics (i.e., the ability to separate out

close events in time) at the expense of frequency resolution, and vice versa

•

CWT will provide better frequency resolution when a is large and the length of the wavelet (and its effective time window) is long

• Conversely, when a is small, the wavelet is short and the time resolution is

maximum, but the wavelet only responds to high frequency components

x(t) Mother

wavelet



CWT



CWT representations allow

detecting the fiducial points for ECG

THE DISCRETE WAVELET TRANSFORM

• The CWT has one serious problem: it is highly redundant.

• The CWT provides an oversampling of the original waveform: many ffi i d h ll d d



more coefficients are generated than are actually needed to

uniquely specify the signal

• Will be costly if the application calls for recovery of the original

signal

• For recovery, all of the coefficients will be required and the

computational effort could be excessive

•

In applications that require bilateral transformations, we would prefer a transform that produces the minimum number of

coefficients required to recover accurately the original signal

• The discrete wavelet transform (DWT) achieves this by restricting

the variation in translation and scale, usually to powers of 2• When the scale is changed in powers of 2, the discrete wavelet

transform is sometimes termed the dyadic wavelet transform

• The DWT is often introduced in terms of its recovery transform



Here k is related to a as: a = 2k ; b is related to as b = 2k ; and d(k, ) is

a sampling of W(a,b) at discrete points k and

.

• New concept is introduced termed the scaling function, a function that

facilitates computation of the DWT

• To implement the DWT efficiently, the finest resolution is computed first

• The computation then proceeds to coarser resolutions, but rather than

start over on the original waveform, the computation uses a smoothed

version of the fine resolution waveform

• This smoothed version is obtained with the help of the scaling function

• Actually, the scaling function is sometimes referred to as the smoothing

function

• The definition of the scaling function uses a dilation or a two‐

scale difference

equation:



where c(n) is a series of scalars that defines the specific scaling

function

• In the DWT, the wavelet itself can be defined from the scaling

function:

where d(n) is a series of scalars that are related to the waveform x(t)

Filter Banks•

For most signal and image processing applications, DWT‐based analysis is best described in terms of filter banks



y

• The use of a group of filters to divide up a signal into various

spectral components is termed subband coding.

• The most basic implementation of the DWT uses only two

filters

• The waveform under analysis is divided into two components, y lp(n) and y hp(n), by the digital filters H0(ω) and H1(ω)

• The spectral characteristics of the two filters must be carefully chosen with H0(ω) having a lowpass spectral characteristic and H (ω) a highpass spectral characteristic



H1(ω) a highpass spectral characteristic

• The highpass filter is analogous to the application of the wavelet to the original signal, while the lowpass filter is analogous to the application of the scaling or smoothing function

• The original signal can often be recovered, but both subband signals will required

• A second pair of filters, G0(ω) and G1(ω), operate on the high and lowpass subband signals and their sum is used to reconstruct a

close approximation of the original signal, x ’(t )• The Filter Bank that decomposes the original signal is usually

termed the analysis filters while the filter bank that reconstructs the signal is termed the syntheses filters

• FIR filters are used throughout because they are inherently stable and easier to implement



• If the output is essentially the same, as occurs in some data compression applications, the process is termed lossless, otherwise it is a lossy operation

• Problem is that data samples get doubled hence we use downsamplingillustrated schemacally by the symbol ↓ 2

• If downsampling is used, then there must be some method for recovering the missing data samples (those with odd indices) in order to reconstruct the original signal

• An operation termed upsampling (indicated by the symbol ↑ 2) accomplishes this operation by replacing the missing points with zeros



Signal Decomposition

• For most of the signal analyses,

the DWT operation takes the



the DWT operation takes the

form of logarithmic tree

• The bandwidth of the signal is

halved after each level of decomposition also it is more

appropriate to describe the

frequency in radians in the

discrete domain

•

Effectively the resolution of the signal, which is the amount of

detail information in the signal,

is changed by the filtering

operations and the scale is

increased by downsamplingoperations

Denoising

• Processing is done on the subband signals before



• Processing is done on the subband signals before reconstruction

• The basic assumption in this application is that the noise is coded into small fluctuations in the higher resolution (i.e., more detailed) highpass subbands

• This noise can be selectively reduced by eliminating the smaller sample values in the higher resolution highpass

subbands• The two highest resolution highpass subbands are

examined and data points below some threshold are zeroed out

• The threshold is set to be equal to the variance of the highpass subbands

Biomedical Signal Processing Lectures 2011-12

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Transcript of Biomedical Signal Processing Lectures 2011-12