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Biomedical Signal Processing and Biomedical Signal Processing and ComputationComputationProf. Zoran Nenadic

OutlineOutline

•What are biomedical signals?

•How are they generated? What are biomedical systems?

•How do we model/simulate/analyze biological and medical systems?

•How do we analyze/process biomedical signals?

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Biomedical SignalsBiomedical Signals

Biomedical signals are measurements of characteristic variables of biomedical systems.

Example 1 Electrocardiogram (ECG)

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01

Time [sec]

EC

G [

mV

]

Note: 1-D signal

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Example 2 Electroencephalogram (EEG)

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1110987654321

Time [ms]

Ele

ctro

de

#

(data from human brain)

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Example 3 Aortic blood velocity

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−10

0

10

20

30

40

50

Time [sec]

Vel

ocity

[cm

/sec

]

(data from pig aorta)

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Example 4 Intra-cranial pressure (ICP)

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Time [sec]

Pre

ssur

e [m

m/H

g]

(human data)

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Example 5 Neuronal action potentials (APs)

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−0.5

0

0.5

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Time [ms]

Vo

ltag

e

action potential →

(data from monkey brain)

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Example 6 Magnetic resonance imaging (MRI)

Note: 2-D signal

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Example 7 Functional MRI (fMRI)

Note: 3-D signal

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Example 8 Computer axial tomography (CAT)

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Example 9 Positron emission tomography (PET)

(human brain)

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What generates biomedical signals?

biomedicalsystem

sensor(measuring

device)

biomedicalbiomedicalvariablevariable

biomedicalbiomedicalsignalsignal

environmental/externalenvironmental/externalvariable(svariable(s))

Answer: biomedical systems.

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Biomedical SystemsBiomedical SystemsSystem: a collection of units (elements, parts, devices, organs) , funct ional ly organized to accomplish certain goals by consuming, transforming and exchanging energy, matter and/or information.Biomedical System: a system that describes biological and medical processes (e.g. photosynthesis, respiration) and objects (e.g. cells, tissues, organs).Important to remember:

(A) A system often consists of smaller systems (called subsystems), which work together toward a common function.

(B) No system is isolated, i.e. a system always interacts with the environment and other systems.

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Example 10 Digestive system

Environment Environment

smallsmallintestineintestine

liverliver

stomachstomach

Digestive systemDigestive system(A)

(B)

Digestive Digestive systemsystem

CardioCardio--vascular vascular systemsystem

Nervous Nervous systemsystem

Endocrine Endocrine systemsystem

Respiratory Respiratory systemsystem

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Therefore, it makes sense to adopt systems approach to biology and medicine.

System science Traditional (experimental) science

systematic approach reductionist approach

study all pieces simultaneously

study one piece at a time

examine interactions(with other systems)

no interactions (system in isolation)

can make forecasts that cannot be extrapolated from data (measurements)

cannot make predictions

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System theory is about applying mathematical formalism(symbols, relations, operations, etc.) to describe a systemat hand.

Mathematical model is an abstract mathematical description of a system.

This abstraction leads to the representation of a system with a box, with inputs and outputs:

System (*)Input Output

Think of (*) as a system of equations.Finding equation(s) (*) amounts to mathematical modeling.

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Examples of mathematical models.

Example 11 Eye movements

motorneurons

synapses

muscles

θ

eyeball

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Example 12 Metabolic process in a cell

membrane

cytoplasm

mitochondria

Cc

RoCm

Demo: cellular_dynamics.m

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Example 13 Firefly synchronization

Demo: firefly_synch_neighbor.m

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What can system theory do for us?

- What can be said about the behavior of the system base on the model. Are the outputs oscillatory, aperiodic? How quickly do they reach the steady state? What frequencies is the system tuned to, etc? (analysis)

- Can we figure out how inputs affects outputs? Can we find a set of inputs so that outputs have certain behavior. (control)

- How are the parameters affecting the behavior of the system. (sensitivity analysis)

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Example 14 Disease outbreak (foot and mouth disease, UK 2001, Ferguson et al., Science, 2001)

y(x, y, t) - degree of infection at place (x, y) at time t.

u(x, y, t) - control variable (slaughter, vaccinate, quarantine, etc.)

What is the best control strategy?

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Population dynamics

N(t) - population at year tB - birth rate (US: 1 person in 7 sec.)D - death rate (US: 1 person in 13 sec.)I - immigration rateE - emigration rate

Solution: - exponential growth

Does not quite fit the census data! Can we make better predictions?

Example 15

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Time-varying system: B = B(t), D = D(t), I = I(t), E = E(t)

year λ (source: US Census Bureau)1999 0.90%1992 1.14%1950 2.05% (baby boomers)

Tweaking the parameters B(t), I(t), etc., we can control the growth of population.

These manipulations are performed with the model, and predictions are made.

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Example 16 Blood pressure dynamics

QL(inflow from the left heart)

Qs(outflow to

systemic tissues)

P

Psa(T) – diastolic pressure

Psa(0) – systolic pressure

tT 3T2T

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Example 17 Drug delivery dynamics

C - drug concentration in blood [kg/m3]KL - liver constant [1/s]VB - blood volume [m3]Rin - rate of injection [kg/s]

00

1/VB

δ(t) − bolus injection

g(t) = exp(−KL t)/V

B

00

Co

Ro

R0/(V

B K

L)

Rin

(t)

C(t)

I.V. drip bolus injection

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Example 18 The diffusion of oxygen in a living tissue

- y(ξ,η,ζ,t) ∈ R is the oxygen concentration at a point (ξ,η,ζ) and time t

- D is the diffusion constant

- k is the oxygen uptake constant

If the diffusion constant is known, can make predictions as to how far the oxygen penetrates the tissue.

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Example 19 Predator-prey equations (Lotka-Volterra)

x - the size of prey population at time t; y - the size of predator population at time t;α, β, γ, δ - parameters representing the interaction of the two species.

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Example 20 Dynamics of emotions (S. Strogatz, Mathematics Magazine, 1988)

R(t) – Romeo’s love (R>0)/hate (R<0) for JulietJ(t) – Juliet’s love (J>0)/hate (J<0) for Romeo a,b > 0

Romeo is a fickle lover. Juliet’s love echoes Romeo’s. Their ill-fated romance consists of a never-ending cycle of love and hate.

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−1

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Time

R(t)J(t)

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Analysis of Biomedical SignalsAnalysis of Biomedical Signals

Recall: Biiomedical signals are generated by biomedical systems, therefore their properties are largely determined by the properties of the generating (biomedical systems) systems:

- non-stationary (time varying)- noisy (stochastic)- limited bandwidth (frequency content)- some of them are periodic- multiple signaling pathways (redundancy)

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What can engineers do?

- denoising (remove the noise from signals)- spectral analysis(what are the important

frequencies)- compression (squeeze out the redundancy)- pattern recognition (e.g. FBI fingerprint

database, National DNA index system)- and many other things

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Image denoising (filtering)Example 21

An image of a celebrity scientist garbled beyond recognition and successfully restored.

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Sound analysisExample 22

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0 1024 2048 3072 40960

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Frequency [Hz]

time domaintime domain

frequency domainfrequency domain

Demo: handel.mtimetime--frequency domain?frequency domain?

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JPEG compression (wavelets)Example 23

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Face recognition (from Olivetti Research Laboratory, Cambridge, UK)

Example 24

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(person B)(person B)(person A)(person A)

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eigenface 1 eigenface 2 eigenface 3 eigenface 4

Eigen-faces: representation of images in low-dimensional space (e.g. 4-D)

These two persons can be recognized in such a space.

By projecting original images to eigen-faces, one obtains a cluster of points

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C2

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(person A)(person A) (person B)(person B)

Question to ponder: How is the human brain doing this?