references introduction: what is medical...

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Stat 233, UCLA, Ivo Dinov Slide 1

UCLA STAT 233Statistical Methods in Biomedical

Imaging

Instructor: Ivo Dinov, Asst. Prof. In Statistics and Neurology

University of California, Los Angeles, Spring 2004http://www.stat.ucla.edu/~dinov/

Stat 233, UCLA, Ivo DinovSlide 2

Basic fMRI Physics


References

“Foundation of Medical Imaging,” Z.H. Cho, J.P. Jones, M. Singh, John Wiley & Sons, Inc., New York 1993, ISBN 0-471-54573-2

“Principles of Medical Imaging,” K.K. Shung, M.B. Smith, B. Tsui, Academic Press, San Diego 1992, ISBN 0-12-640970-6

“Handbook of Medical Imaging,” Vol. 1, Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter (eds.), SPIE Press 2000, ISBN 0-8194-3621-6


Introduction: What is Medical Imaging?Goals:

Create images of the interior of the living human body from the outside for diagnostic purposes.

Biomedical Imaging is a multi-disciplinary field involvingPhysics (matter, energy, radiation, etc.)Math (linear algebra, calculus, statistics)Biology/PhysiologyEngineering (implementation)Computer science (image reconstruction, signal processing)


BMI methods: X-Ray imaging

Year discovered: 1895 (Röntgen, NP 1905)

Form of radiation: X-rays = electromagnetic radiation (photons)

Energy / wavelength of radiation: 0.1 – 100 keV / 10 – 0.01 nm(ionizing)

Imaging principle: X-rays penetrate tissue and create "shadowgram" of differences in density.

Imaging volume: Whole body

Resolution: Very high (sub-mm)

Applications: Mammography, lung diseases,orthopedics, dentistry, cardiovascular, GI


Electromagnetic Spectrum

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BMI methods: X-Ray Computed Tomography

Year discovered: 1972 (Hounsfield, NP 1979)

Form of radiation: X-rays

Energy / wavelength of radiation: 10 – 100 keV / 0.1 – 0.01 nm(ionizing)

Imaging principle: X-ray images are taken under many angles from which tomographic ("sliced") views are computed


Resolution: High (mm)

Applications: Soft tissue imaging (brain, cardiovascular, GI)




BMI methods: Nuclear Imaging (PET/SPECT)

Year discovered: 1953 (PET), 1963 (SPECT)

Form of radiation: Gamma rays

Energy / wavelength of radiation: > 100 keV / < 0.01 nm(ionizing)

Imaging principle: Accumulation or "washout" of radioactive isotopes in the body are imaged with x-ray cameras.


Resolution: Medium – Low (mm - cm)

Applications: Functional imaging (cancer detection, metabolic processes, myocardial infarction)




Functional Brain Imaging - Positron Emission Tomography (PET)



http://www.nucmed.buffalo.edu

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Isotope Energy (MeV) Range(mm) 1/2-life Appl’nC 0.96 1.1 20 min receptor studiesO 1.7 1.5 2 min stroke/activationF 0.64 1.0 110 min neurologyI ~2.0 1.6 4.5 days oncology

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C:\Ivo.dir\LONI_Viz\LONI_Viz_MAP_demo\runNoArgs.batLoad Volumes:

C:\Ivo.dir\LONI_Viz\data.dir\A1_Global.imgC:\Ivo.dir\LONI_Viz\data.dir\R12_Global.img

Subsample 2-2-2 VolumeRenderer + 2D Section + Change ColorMap


BMI methods: Magnetic Resonance Imaging

Year discovered: 1945 ([NMR] Bloch, NP 1952)1973 (Lauterburg, NP 2003)1977 (Mansfield, NP 2003) 1971 (Damadian, SUNY DMS)

Form of radiation: Radio frequency (RF)(non-ionizing)

Energy / wavelength of radiation: 10 – 100 MHz / 30 – 3 m (~ 10-7 eV)

Imaging principle: Proton spin flips are induced, and the RF emitted by their response (echo) is detected.



Applications: Soft tissue, functional imaging




BMI methods: Ultrasound Imaging

Year discovered: 1952 (clinical: 1962)

Form of radiation: Sound waves (non-ionizing)

Frequency / wavelength of radiation: 1 – 10 MHz / 1 – 0.1 mm

Imaging principle: Echoes from discontinuities in tissue density/speed of sound are registered.

Imaging volume: < 20 cm


Applications: Soft tissue, blood flow (Doppler)




BMI methods: Optical Tomography

Year discovered: 1989 (Barbour)

Form of radiation: Near-infrared light (non-ionizing)

Energy / wavelength of radiation: ~ 1 eV/ 600 – 1000 nm

Imaging principle: Interaction (absorption, scattering) of light w/ tissue.

Imaging volume: ~ 10 cm

Resolution: Low (~ cm)

Applications: Perfusion, functional imaging

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BMI methods: Optical Tomography




Recipe for MRI

1) Put subject in big magnetic field (leave him/her there)2) Transmit radio waves into subject [about 3 ms]3) Turn off radio wave transmitter4) Receive radio waves re-transmitted by subject

– Manipulate re-transmission with magnetic fields during this readoutinterval [10-100 ms: MRI is not a snapshot]

5) Store measured radio wave data vs. time– Now go back to 2) to get some more data

6) Process raw data to reconstruct images7) Allow subject to leave scanner

Source: Robert Cox’s web slides Stat 233, UCLA, Ivo DinovSlide 23

History of NMR

NMR = nuclear magnetic resonanceFelix Block and Edward Purcell

1946: atomic nuclei absorb and re-emit radio frequency energy1952: Nobel prize in physics

nuclear: properties of nuclei of atomsmagnetic: magnetic field requiredresonance: interaction between magnetic field and radio frequency

Bloch PurcellNMR → MRI: Why the name change?

most likely explanation: nuclear has bad connotations

less likely but more amusing explanation: subjects got nervous when fast-talking doctors suggested an NMR


History of fMRI

MRI-1971: MRI Tumor detection (Damadian)-1973: Lauterbur suggests NMR could be used to form images-1977: clinical MRI scanner patented-1977: Mansfield proposes echo-planar imaging (EPI) to acquire images faster

fMRI-1990: Ogawa observes BOLD effect with T2*

blood vessels became more visible as blood oxygen decreased

-1991: Belliveau observes first functional images using a contrast agent-1992: Ogawa et al. and Kwong et al. publish first functional images using BOLD signal

Ogawa


Necessary Equipment

Magnet Gradient Coil RF Coil

Source: Joe Gati, photos

RF Coil

4T magnet

gradient coil(inside)

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The Big Magnet

Very strong

1 Tesla (T) = 10,000 Gauss

Earth’s magnetic field = 0.5 Gauss4 Tesla = 4 x 10,000 ÷ 0.5 = 80,000 times Earth’s magnetic field

Continuously onMain field = B0

x 80,000 =

Robarts Research Institute 4T

B0


Magnet Safety - The whopping strength of the magnet makes safety essential. Things fly – Even big things!

Screen subjects carefullyMake sure you and all your students & staff are aware of hazardsDevelop strategies for screening yourself every time you enter the magnet

Source: www.howstuffworks.com Source: http://www.simplyphysics.com/flying_objects.html


Subject SafetyAnyone going near the magnet – subjects, staff and visitors – must be thoroughly screened:

Subjects must have no metal in their bodies:• pacemaker• aneurysm clips• metal implants (e.g., cochlear implants)• interuterine devices (IUDs)• some dental work (fillings okay)

Subjects must remove metal from their bodies• jewellery, watch, piercings• coins, etc.• wallet• any metal that may distort the field (e.g., underwire bra)

Subjects must be given ear plugs (acoustic noise can reach 120 dB)

C:\Ivo.dir\Research\Data.dir\LianaApostolova_AD\FrontalVolumes2Groups\MRI_ToothMetal_Defect.img.gz (Show-VolumeRenderer)C:\Ivo.dir\LONI_Viz\LONI_Viz_MAP_demo\runNoArgs.bat

This subject was wearing a hair band with a ~2 mm copper clamp. Left: with hair band. Right: without.

Source: Jorge Jovicich


Protons

Can measure nuclei with odd number of neutrons

1H, 13C, 19F, 23Na, 31P1H (proton) - Human body 70+% H2O

abundant: high concentration in human body high sensitivity: yields large signals

Both protons and neutrons possess spins, i.e. they revolve round their own axis, much as earth does. If the nucleus has just one proton, it would spin on its axis and would impart a net spin to the nucleus as a whole. One would imagine that two protons would double up the spin for the nucleus but it doesn’t happen that way; the spins of the two protons tend to cancel out, with the result that the nucleus has no net spin. A nucleus with three protons again has a net spin (as there is one unpaired proton) and a nucleus with four protons again would have no spin. The same is true for neutrons; an odd number of neutrons imparts a net spin to the nucleus, an even number doesn’t. So out of protons or neutrons if any one of these (or both) are in odd number, the nucleus would have a net spin. If both are even, the nucleus would not have any net spin.


What nuclei exhibit this magnetic moment (and thus are candidates for NMR)?

Nuclei with: odd number of protonsodd number of neutronsodd number of both

Magnetic moments: 1H, 2H, 3He, 31P, 23Na, 17O, 13C, 19F

No magnetic moment: 4He, 16O, 12C


Outside magnetic field – random orientation

In Mag Field - Protons align with field

Inside magnetic field• randomly oriented

• spins tend to align parallel or anti-parallel to B0• net magnetization (M) along B0• spins precess with random phase• no net magnetization in transverse plane• only 0.0003% of protons/T align with field

M

M = 0

Source: Mark Cohen’s web slidesSource: Robert Cox’s web slides

longitudinalaxis

transverseplane

Longitudinalmagnetization

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As its name implies, NMR is a resonance phenomenon. This means that it will occur only if the applied RF pulse is tuned to the natural resonance frequency of the nucleus in question. The natural resonance frequency of any given nucleus depends on the strength of the applied main magnetic field; more strength higher frequency.

To locate each atom within the sample make the main magnetic field graded so that it is not of uniform strength but rather increases slightly in strength from one side of the sample to the other, the resonance frequencies of different nuclei would differ.


Larmor FrequencyLarmor equation

(frequency) f = γ B0 (field strength)γ = 42.58 MHz/T (constant for each Atom).

For example for Hydrogen: At 1.5T, f = 63.76 MHz

At 4T, f = 170.3 MHz

Field Strength (Tesla)

ResonanceFrequency for 1H

170.3

63.8

1.5 4.0


RF Excitation

Excite Radio Frequency (RF) field• transmission coil: apply magnetic field along B1 (⊥ to B0) for ~3 ms• oscillating field at Larmor frequency• frequencies in range of radio transmissions• B1 is small: ~1/10,000 T• tips M to transverse plane – spirals down• analogies: guitar string, swing• final angle between B0 and B1 is the flip angle

B1

B0

Source: Robert Cox’s web slides

Transversemagnetization


Relaxation and Receiving

Receive Radio Frequency Field• receiving coil: measure net magnetization (M)• readout interval (~10-100 ms)• relaxation: after RF field turned on and off, magnetization returns to normal

longitudinal magnetization↑ → T1 signal recoverstransverse magnetization↓ → T2 signal decays



T1 and TR

Source: Mark Cohen’s web slides

T1 = recovery of longitudinal (B0) magnetization• used in anatomical images• ~500-1000 msec (longer with bigger B0)

TR (repetition time) = time to wait after excitation before sampling T1


Spatial Coding: GradientsHow can we encode spatial position?

• Example: axial slice

Use other tricks to get other two dimensions• left-right: frequency encode

• top-bottom: phase encode

excite only frequencies

corresponding to slice plane

Field Strength (T) ~ z position

Freq

Gradient coil

Add a gradient to the main magnetic field

Gradient switching – that’s what makes all the beeping & buzzing noises during imaging!

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How many fields are involved after all?

In MRI there are 3 kinds of magnetic fields:1. B0 – the main magnetic field2. B1 – an RF field that excites the spins3. Gx, Gy, Gz – the gradient fields that provide localization


Precession In and Out of Phase


• Protons precess at slightly different frequencies because of (1) random fluctuations in local field at the molecular level affect both T2 and T2*;

(2) larger scale variations in the magnetic field (such as the presence of deoxyhemoglobin!) that affect T2* only.

• Over time, the frequency differences lead to different phases between the molecules (think of a bunch of clocks running at different rates – at first they are synchronized, but over time, they get more out of sync until they are random)

• As the protons get out of phase, the transverse magnetization decays • This decay occurs at different rates in different tissues


T2 and TE


T1 = recovery of longitudinal (B0) magnetizationTR (repetition time) = time to wait after excitation before sampling T1T2 = decay of transverse magnetizationTE (time to echo) = time to wait to measure T2 or T2* (after refocussing with spin echo or gradient echo)


Echos


Echos – refocussing of signal

Spin echo – use a 180 degree pulse to “mirror image” the spins in the transverse plane when “fast” regions get ahead in phase, make them go to the back and catch up

-measure T2

-ideally TE = average T2

Gradient echo – flip the gradient from negative to positive make “fast” regions become “slow” and vice-versa

-measure T2*

-ideally TE ~ average T2*

Pulse sequence: series of excitations, gradient triggers and readouts

Gradient echopulse sequence

t = TE/2

A gradient reversal (shown) or 180 pulse (not shown) at this point will lead to a recovery of transverse magnetization

TE = Time to Echo – wait to measure refocussed spins


T1 vs. T2


RepetitionTime:

Time to Echo


T1 vs. T2 – contrast and noise


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Properties of Body Tissues

Tissue T1 (ms) T2 (ms)

Grey Matter (GM) 950 100

White Matter (WM) 600 80

Muscle 900 50Cerebrospinal Fluid (CSF) 4500 2200

Fat 250 60

Blood 1200 100-200

MRI has high contrast for different tissue types!Stat 233, UCLA, Ivo DinovSlide 46

MRI of the Brain - Sagittal

T1 ContrastTE = 14 msTR = 400 ms


Proton DensityTE = 14 msTR = 1500 ms


MRI of the Brain - Axial



Proton DensityTE = 14 msTR = 1500 ms


Rel

ativ

e SN

R

Field of View

MRI Quality Determinants

•Echo Time (TE)•Slice Thickness•Slice Order•Averaging•Bandwidth•Imaging Matrix•Patient Motion•Surface Coils

•Repetition Time(TR)•Interslice Gap•Field of View•Number of Echos•Motion Comp•Window Level•Photography•Equipment Performance

Mark Cohen


MRI Quality Determinants –period = 1/frequency

.FOV ½ Y and FOV ½ X ifoccur not will

aliasing and k1 FOV and

k1 FOV :spacing sample space-K

over the one as defined typicallyisn acquisitioan of viewof field Thealiasing).(or images in the overlap spatial be wille then thersatisfied,not is thisIf

. k21 Y is Yin position spatialhighest theand

k21 X is

Xin position spatialhighest theif image original theoverlapnot willimagesreplicated The .k & k :is directions k & k in the spacing sample

domainFourier where),k,1/k(1/ isct image/obje replicated theof Spacingdomain. image in then replicatio toleadsdomain Fourier in the Sampling

YmaxXmax

YY

XX

Ymax

Xmax

YXYX

YX

<<∆

=∆

=

∆≤

∆≤

∆∆∆∆


K-Space –an MRI literature fancy name for Fourier space

Source: Traveler’s Guide to K-space (C.A. Mistretta)http://www.cis.rit.edu/htbooks/mri/

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A Walk Through (sampling from ) K-space

K-space can be sampled in many “shots”(or even in a spiral)

2 shot or 4 shot• less time between samples of slices• allows temporal interpolation

both halves of k-space in 1 sec

1st half of k-spacein 0.5 sec

2nd half of k-spacein 0.5 sec

vs.

single shot two shot

1st volume in 1 sec interpolatedimage

Note: The above is k-space, not slices

1st half of k-spacein 0.5 sec

2nd half of k-spacein 0.5 sec

2nd volume in 1 sec


T2*

Source: Jorge Jovicich

time

MxyMo sinθ

T2

T2*

T2* relaxation - Sequences without a spin echo will be T2*-

weighted rather than T2-weighted. The longer the echo time (TE) the greater the T2 contrast.

- dephasing of transverse magnetization due to both:- microscopic molecular interactions (T2)- spatial variations of the external main field ∆B

(tissue/air, tissue/bone interfaces)• exponential decay (T2* ≈ 30 - 100 ms, shorter for higher Bo)


Susceptibility


Adding a nonuniform object (like a person) to B0 will make the total magnetic field 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 nonuniformmagnetic 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-spins become dephased so quickly (quick T2*), no signal can be measured

sinuses

earcanals

Susceptibility variations may be seen around blood vessels where deoxyhemoglobinaffects T2* in nearby tissue


Signal-to-Noise Ratio (SNR)

Pick a region of interest (ROI) outside the brain free from artifacts (no ghosts, susceptibility artifacts). Find mean (µ) and standard deviation (SD).

Pick an ROI inside the brain in thearea you care about. Find µ and SD.

SNR = µbrain/ µoutside = 200/4 = 50

Alternatively SNR = µbrain/ SDoutside = 200/2.1 = 95(should be 1/1.91 of above because µ/SD ~ 1.91)

When citing SNR, state which denominator you used. Head coil should have SNR > 50:1Surface coil should have SNR > 100:1

e.g., µ=4, SD=2.1

e.g., µ = 200


Motion Correction

Gradual motions are usually well-corrected

Abrupt motions are more of a problem (esp. if related to paradigm

SPM outputraw data

linear trend removal

motion corrected in SPM

Caveat: Motion correction can cause artifacts where there were none!!!

references introduction: what is medical...

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