Signal Processing for Medical Applications Frequency Domain - - PowerPoint PPT Presentation

Muthuraman Muthuraman

Christian-Albrechts-Universität zu Kiel Department of Neurology / Faculty of Engineering Digital Signal Processing and System Theory

Signal Processing for Medical Applications – Frequency Domain Analyses

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-2

1.Basics of Brain – i) Brain signals - EEG/ MEG; ii) Muscle signals - EMG; iii) Magnetic resonance imaging – MRI iv) Tremor disorders

• 2. Quantities measured from time series in frequency domain

i) Power spectrum ii) Modelling time series using AR2 processes ii) Coherence spectrum

• Different windows used for the estimation

iii) Phase spectrum iv) Delay between signals

• 3. Source analysis in the frequency domain
• Forward problem
• Inverse problem
• Different Solutions

Lecture 1 & 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6-10

Contents

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-3

• Basics of MRI

> Magnets > Hydrogen atoms

• Creating a image
• Visualization

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-4

• Magnets The biggest and the most important part component in a

MRI system is the magnet, unit-tesla. There is horizontal tube running through the magnet from front to back, this tube is the bore of the magnet.

• Superconducting Magnet Principle(Superconductivity) Metals and

ceramic materials cooled to temp. near absolute zero no electrical resistance electrons can travel through them freely carry large amounts

• f current long periods of time without losing energy as heat.
• Gradient Magnet There are 3 gradient magnets inside the MRI
• machines. These magnets are very, very low strength compared to the

main magnetic field, range-18 to 27 millitesla.

• The main magnet immerses the patient in a stable and very intense

magnetic field, and the gradient magnets create a variable field.

Basics Of MRI(Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-5

Magnets

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-6

• Hydrogen atoms- It is an ideal atom for MRI because its nucleus

has a single proton and a large magnetic moment

• When placed in a magnetic field, the hydrogen atom has a strong

tendency to line up with the direction of the magnetic field

Hydrogen atoms

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-7

Creating a Image

• Inside the bore of the scanner, the magnetic field runs straight down the center of

the tube in which we place the patient. The hydrogen protons in the body will lineup in the direction of either the feet or the head.

• The vast majority of protons will cancel each other only a couple remains which is

used to create images.

• The MRI machine applies an RF pulse that is specific only to hydrogen, the

system directs the pulse towards the area of the body we want to examine. The RF pulse causes the protons in that area to absorb the energy required to make them spin at a particular frequency in a particular direction. The specific frequency

• f resonance is the larmour frequency and is calculated based on the

particular tissue being imaged and the strength of the magnetic field.

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-8

• The three gradient magnets are arranged in such a manner inside the main

magnet that when they are turned on and off very rapidly in a specific manner, they alter the main magnetic field on a very local level, which means we can pick exactly which area we want a picture of the brain.

• The RF pulse is turned off, the hydrogen protons begin to slowly return to their

natural alignment within the magnetic field and release there excess stored

• energy. They give off a signal that the coil picks up and sends it to the

computer system. With the Fourier transform the mathematical data is converted into a picture to put on film.

Creating a Image

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-9

Visualization

• MRI works by altering the local magnetic field in the tissue being

examined.

• Normal and abnormal tissue will respond slightly altered, giving us

different signals.

• These varied signals are transfered to the images, allowing us to

visualize many different types of tissue abnormalities.

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-10

Review: Image Formation

• Data gathered in k-space (Fourier domain of image)
• Gradients change position in k-space during data acquisition (location in k-

space is integral of gradients)

• Image is Fourier transform of acquired data

k-space image space

Fourier

transform ky kx

Visualization

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-11

Sagittal Coronal Axial Magentic Resonance Imaging (MRI)

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-12

Magentic Resonance Imaging (MRI)

Lecture 2 – Magnetic resonance imaging (MRI)

Sagittal Axial / Horizontal Coronal / Frontal

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-13

Magentic Resonance Imaging (MRI)

Lecture 2 – Magnetic resonance imaging (MRI)

Sagittal Axial / Horizontal Coronal / Frontal

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-14

Magentic Resonance Imaging (MRI) Lecture 2 – Magnetic resonance imaging (MRI) Susceptibility and Susceptibility Artifacts Adding a nonuniform object (like a person) to B0 will make the total magnetic field B nonuniform This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming Susceptibility Artifact

• occurs near junctions between air and tissue
• sinuses, ear canals

sinuses ear canals

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-15

How Susceptibility Affects Signal Susceptibility  nonuniform precession frequencies RF signals from different regions that are at different frequencies will get out of phase and thus tend to

cancel out

Sum of 500 Cosines with Random Frequencies

Starts off large when all phases are about equal

Decays away as different

components get different phases

Magentic Resonance Imaging (MRI)

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-16

FMRI (Functional Magnetic Resonance Imaging)

• FMRI measures brain activity indirectly through changes in blood

vasculature that accompany neural activity An intial increase in oxygen consumption owing to increased metabolic demand After a delay of 2 secs, a large increase in local blood flow, which

• vercompensates for the amount of oxygen being extracted

Local increase in cereberal blood volume

• The increase in blood oxyhaemoglobin is what we measure in FMRI.

This is so called the BOLD (Blood oxygen level dependent) response.

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-17

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

The Bold effect BOLD: Blood Oxygenation Level Dependent Deoxyhemoglobin (dHb) has different resonance frequency than water dHb acts as endogenous contrast agent dHb in blood vessel creates frequency offset in surrounding tissue (approx as dipole pattern)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-18

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Frequency spread causes signal loss over time BOLD contrast: Amount of signal loss reflects [dHb] Contrast increases with delay (TE = echo time)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-19

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Vascular Response to Activation O2 metabolism dHb dHb HbO2 HbO2 dHb HbO2 HbO2 dHb dHb HbO2

blood flow [dHb]

dHb = deoxyhemoglobin HbO2 = oxyhemoglobin capillary

blood volume

neuron HbO2 HbO2 HbO2 HbO2 dHb dHb dHb dHb dHb dHb HbO2 HbO2 dHb HbO2 HbO2 dHb dHb HbO2

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-20

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Very indirect measure of activity (via hemodynamic response to neural activity)! Complicated dynamics lead to reduction in [dHb] during activation (active research area) Neuronal activity Metabolism Blood flow Blood volume [dHb] BOLD signal

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-21

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Hemodynamic Response Function

% signal change = (point – baseline)/baseline usually 0.5-3% initial dip

• more focal
• somewhat elusive so far

time to rise signal begins to rise soon after stimulus begins time to peak signal peaks 4-6 sec after stimulus begins post stimulus undershoot signal suppressed after stimulation ends

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-22

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI) The Canonical FMRI Experiment

Subject is given sensory stimulation or task, interleaved with control or rest condition Acquire timeseries of BOLD-sensitive images during stimulation Analyse image timeseries to determine where signal changed in response to stimulation

Predicted BOLD signal time Stimulus pattern

• n
• ff
• n
• ff
• n
• ff
• n
• ff
• ff

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-23

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

What is required of the scanner? Must resolve temporal dynamics of stimulus (typically, stimulus lasts 1-30 s) Requires rapid imaging: one image every few seconds (typically, 2–4 s) Anatomical images take minutes to acquire! Acquire images in single shot (or a small number of shots)

1 2 3 … image

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-24

High-resolution FMRI at 7T High-res 7T: 0.58 x 0.58 x 0.58 mm3 = 0.2 mm3 High-res 3T: 1 x 1 x 1 mm3 = 1 mm3 Conventional 3T: 3 x 3 x 3 mm3 = 27 mm3

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-25

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Diffusion Tensor Imaging (DTI) Water diffusion restricted along white matter Sensitize signal to diffusion in different directions Measure along all directions, infer tracts Diffusion direction

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-26

FMRI (Functional Magnetic Resonance Imaging)

Lecture 2 – Magnetic resonance imaging (MRI)

Complementary information to FMRI FMRI: gray matter, information processing DTI: white matter, information pathways Tractography: tracing white matter pathways between gray matter regions Tract-based connectivity Color-coded directions

x y z

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-27

Tremor Disorders

Tremor: Tremor is defined as rhythmic non-voluntary oscillatory activity of body parts. The body parts affected by this disorder are the hands, arms, head, face, vocal cords, trunk and legs. Parkinsonian tremor: The classical form of Parkinsonian tremor is the rest tremor which is present when the limb is at rest. But pure rest tremor is not so common; it is usually in combination of both rest and postural or kinetic tremors.

• 1% of the population above 50 years

Essential tremor: This tremor occurs while doing voluntary actions and remains constant till the action is performed, it usually disappears at rest.

• 4% of the population above 65 years

Lecture 2 – Tremor Disorders

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-28

PD ET PD and ET Tremor Patients

Lecture 2 – Tremor Disorders

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-29

Lecture 2 – Tremor Disorders

PD and ET Tremor Patients

STIM OFF STIM ON

Digital Signal Processing and System Theory| Signal Processing for Medical Applications | Introduction Slide I-30

Deep Brain Stimulation

Lecture 2 – Tremor Disorders