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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
Stat 233, UCLA, Ivo DinovSlide 4
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
Stat 233, UCLA, Ivo DinovSlide 5
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)
Stat 233, UCLA, Ivo DinovSlide 6
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
Stat 233, UCLA, Ivo DinovSlide 7
Electromagnetic Spectrum
2
Stat 233, UCLA, Ivo DinovSlide 8
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
Imaging volume: Whole body
Resolution: High (mm)
Applications: Soft tissue imaging (brain, cardiovascular, GI)
Stat 233, UCLA, Ivo DinovSlide 9
Electromagnetic Spectrum
Stat 233, UCLA, Ivo DinovSlide 10
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.
Imaging volume: Whole body
Resolution: Medium – Low (mm - cm)
Applications: Functional imaging (cancer detection, metabolic processes, myocardial infarction)
Stat 233, UCLA, Ivo DinovSlide 11
Electromagnetic Spectrum
Stat 233, UCLA, Ivo Dinov Slide 12
Functional Brain Imaging - Positron Emission Tomography (PET)
Stat 233, UCLA, Ivo Dinov Slide 13
Functional Brain Imaging - Positron Emission Tomography (PET)
http://www.nucmed.buffalo.edu
3
Stat 233, UCLA, Ivo Dinov Slide 14
Functional Brain Imaging - Positron Emission Tomography (PET)
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
11
1518
124
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
Stat 233, UCLA, Ivo DinovSlide 15
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.
Imaging volume: Whole body
Resolution: High (mm)
Applications: Soft tissue, functional imaging
Stat 233, UCLA, Ivo DinovSlide 16
Electromagnetic Spectrum
Stat 233, UCLA, Ivo DinovSlide 17
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
Resolution: High (mm)
Applications: Soft tissue, blood flow (Doppler)
Stat 233, UCLA, Ivo DinovSlide 18
Electromagnetic Spectrum
Stat 233, UCLA, Ivo DinovSlide 19
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
4
Stat 233, UCLA, Ivo DinovSlide 20
BMI methods: Optical Tomography
Stat 233, UCLA, Ivo DinovSlide 21
Electromagnetic Spectrum
Stat 233, UCLA, Ivo DinovSlide 22
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
Stat 233, UCLA, Ivo DinovSlide 24
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
Stat 233, UCLA, Ivo DinovSlide 25
Necessary Equipment
Magnet Gradient Coil RF Coil
Source: Joe Gati, photos
RF Coil
4T magnet
gradient coil(inside)
5
Stat 233, UCLA, Ivo DinovSlide 26
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
Stat 233, UCLA, Ivo DinovSlide 27
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
Stat 233, UCLA, Ivo DinovSlide 28
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
Stat 233, UCLA, Ivo DinovSlide 29
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.
Stat 233, UCLA, Ivo DinovSlide 30
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
Stat 233, UCLA, Ivo DinovSlide 31
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
6
Stat 233, UCLA, Ivo DinovSlide 32
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.
Stat 233, UCLA, Ivo DinovSlide 33
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
Stat 233, UCLA, Ivo DinovSlide 34
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
Stat 233, UCLA, Ivo DinovSlide 36
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
Source: Robert Cox’s web slides
Stat 233, UCLA, Ivo DinovSlide 37
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
Stat 233, UCLA, Ivo DinovSlide 38
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!
7
Stat 233, UCLA, Ivo DinovSlide 39
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
Stat 233, UCLA, Ivo DinovSlide 40
Precession In and Out of Phase
Source: Mark Cohen’s web slides
• 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
Stat 233, UCLA, Ivo DinovSlide 41
T2 and TE
Source: Mark Cohen’s web slides
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)
Stat 233, UCLA, Ivo DinovSlide 42
Echos
Source: Mark Cohen’s web slides
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
Stat 233, UCLA, Ivo DinovSlide 43
T1 vs. T2
Source: Mark Cohen’s web slides
RepetitionTime:
Time to Echo
Stat 233, UCLA, Ivo DinovSlide 44
T1 vs. T2 – contrast and noise
Source: Mark Cohen’s web slides
8
Stat 233, UCLA, Ivo DinovSlide 45
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
T2 ContrastTE = 100 msTR = 1500 ms
Proton DensityTE = 14 msTR = 1500 ms
Stat 233, UCLA, Ivo DinovSlide 47
MRI of the Brain - Axial
T1 ContrastTE = 14 msTR = 400 ms
T2 ContrastTE = 100 msTR = 1500 ms
Proton DensityTE = 14 msTR = 1500 ms
Stat 233, UCLA, Ivo DinovSlide 48
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
Stat 233, UCLA, Ivo DinovSlide 49
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
9
Stat 233, UCLA, Ivo DinovSlide 51
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
Stat 233, UCLA, Ivo DinovSlide 52
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)
Stat 233, UCLA, Ivo DinovSlide 53
Susceptibility
Source: Robert Cox’s web slides
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
Stat 233, UCLA, Ivo DinovSlide 54
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
Stat 233, UCLA, Ivo DinovSlide 55
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!!!