Lecture01 CourseIntro MRIPhysicsece-research.unm.edu/vcalhoun/courses/fMRI_Spring...1 Sprint 2009...

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Sprint 2009 fMRI Analysis Course Sprint 2009 fMRI Analysis Course 1

Analysis Methods in Analysis Methods in Functional Magnetic Resonance ImagingFunctional Magnetic Resonance Imaging

ECE 595ECE 595--0808

•• Review Syllabus (check Feb 3Review Syllabus (check Feb 3rdrd class)class)

•• LectureLecture


OutlineOutline•• MR Basic PrinciplesMR Basic Principles

•• HardwareHardware

•• SpinSpin

•• SequencesSequences

•• Basics of BOLD fMRIBasics of BOLD fMRI•• Signal mechanismSignal mechanism

•• Sequences usedSequences used

•• ArtifactsArtifacts

•• A few tradeA few trade--offsoffs


Puzzle PiecesPuzzle Pieces

Helmholtz

Golay


The MagnetThe Magnet

•• Goal: align the protonsGoal: align the protons•• Coils Coils

•• Super conductance: Super conductance: HeliumHelium

•• 1.5T, 1.5T, 3T3T, 7T , 7T (Earth magnetic field = (Earth magnetic field = 0.0005T) 0.0005T)

•• Side Effects (FDA : <8T, Side Effects (FDA : <8T, neonates <4T )neonates <4T )•• NauseaNausea•• VertigoVertigo•• TinglingTingling•• HeadacheHeadache•• Pain in tooth fillingsPain in tooth fillings


Not harmful?Not harmful?


The Gradient CoilsThe Gradient Coils•• Goal: Goal:

•• Slice selectionSlice selection

•• Frequency encodingFrequency encoding

•• Phase encodingPhase encoding

Side EffectsSide Effects•• Induced currents (dynamo; small) Induced currents (dynamo; small)

•• Nerve stimulation Nerve stimulation

•• PhosphenesPhosphenes

•• Acoustic NoiseAcoustic Noise

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The RF CoilThe RF Coil•• Goal: Goal:

•• Turn longitudinal Turn longitudinal magnetization into magnetization into transverse magnetizationtransverse magnetization

•• Measure the signal Measure the signal generated by the precessing generated by the precessing spins. spins.

•• Side Effects Side Effects •• Induced currents: Specific Induced currents: Specific

Absorption Rate (SAR) Absorption Rate (SAR) limits limits

•• Heating: avoid loops.Heating: avoid loops.


CoilsCoils

Head coil•homogenous signal•moderate SNR

Surface coil•highest signal at hotspot•high SNR at hotspot


Basic TheoryBasic Theory

•• Protons have a property called spinProtons have a property called spin

•• LarmorLarmor Equation: Equation: ωω = = γγBB00

•• ωω = = LarmorLarmor frequencyfrequency

•• γγ = = gyromagneticgyromagnetic ratioratio•• 42MHz/T for protons (42MHz/T for protons (11H) H)

•• 11MHz/T for 11MHz/T for 1313CC

•• 176GHz/T for electrons (e176GHz/T for electrons (e--))







3



180°90°

z




Mo

Mz

t

63%

T1

Longitudinal Relaxation Time T1

Longitudinal Relaxation = Energy transfer between excited spins andTissue (Spin-Lattice-Relaxation)

Reestablishing of longitudinal magnetization with time constant T1

1-e-t/T1


Mxy

37%

T2

t

Transverse Relaxation Time T2

Transverse Relaxation = Decay of magnetization by interaction between nuclei (Spin-Spin-Relaxation)


Mz S

Tissue 1

Tissue 2

TRShort TE Medium TE Long TE

Longitudinal Relaxation Transverse Relaxation

Tissue 2

Tissue 1

Relaxation Times are Tissue Specific


30002000100000.0

0.2

0.4

0.6

0.8

1.0

TR (msec)

Sig

nal

gray matterT1 = 1000

CSFT1 = 3000

white matterT1 = 600

T1T1--relaxation timerelaxation time

•• Depends on tissue typeDepends on tissue type•• White matter: 70 msWhite matter: 70 ms•• Gray matter: Gray matter: 90 ms90 ms•• CSF: CSF: 400 ms400 ms

•• T2 << T1T2 << T1

•• Measure the signal Measure the signal 200 ms after the RF pulse. 200 ms after the RF pulse.

•• White matter: eWhite matter: e--200/70 200/70 = 5% = 5%

•• Gray matter: eGray matter: e--200/90 200/90 = 10%= 10%

•• CSF:CSF: ee--200/400 200/400 = 60= 60

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TR

Long

Short

Short Long

TE

ProtonDensity

T1 poor!

T2

Image contrastImage contrastNMR Signal

B0

z’ z’ z’

X’ X’ X’

y’ y’ y’

S(t) S(t) S(t)

M0

S(t)

t

S0≈M0 T2*

0

T0=1/f0

Spin refocusing

z’

X’

y’ y’

z’

X’

y’y’

B0

z’

X’

z’

X’

12

3

45

1

23

45

z’

X’

y’1

23

45

90°x 180°y

Hahn echo

CPMG (Carr-Purcell-Meiboom-Gill) modification : multiple

t = TEt = TE/2t = 0

Spin echo

90° 180°

t = TE/2

t = TE

2

Spin echo

FID Spin echo

readout

Signal

Gradient

TransversalMomentsPhase

+

-

0t

1

2

3

4

5

1

4

5

2

3

T2

T2*

90° 180°

Gradient echo

readoutGradient

FID gradientecho

Signal

TransversalMomentsPhase

t

T2*

5

Longitudinal Relaxation

B0

t=t0 t=t1Mz=0

t=t2Mz=a

t=t3Mz=b

t=Mz=1

….

t

Mz(t)

t0 t1 t2 t3

90°M0

Making an image1. Slice selection with a gradient field

B0

0

a) Set a z-gradient b) Choose the frequency of the RF pulsec) Switch off the z-gradient

Resonance at ω = γ(B0+ 1)

B0+1

B0+2

z

Making an image2. Frequency encoding with a gradient field

0x

Faster precession: fast changing signal

Slower precession: slow changing signal

Bx

a) When measuring the signal, set a gradientb) Measure only fast signals -> back of headc) Measure only slow signals -> front of head

Making an image3. Phase encoding with a gradient field

0y

By

a) After the RF pulse, set a gradient for a brief timeb) Measure the signal

The phase of the signal depends on the y-position : sin(…+y)c) Repeat, with ever stronger gradient

The signal : sin(…+2y), sin(…+3y), sin(…+4y)d) Signals that change rapidly with the repeat number have large ye) Signals that change slowly with the repeat number have small y

Phase advance


1 2 N

ky

kx

Raw Data Matrix (k-Space)

Raw data matrix or k-space is filled line by line by variation of the Phase Encoding Gradient

Line Information =Frequencies of the Readout Gradient


Fourier Transformation

K_x

K_y

x

y

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EPI imaging and kEPI imaging and k--spacespacex = frequency and y = phase or angle


Frequency and phase encoding merely Frequency and phase encoding merely plots a trajectory across kplots a trajectory across k--space.space.

frequ. encode

phase encode


EPI


EPI and SpiralsEPI and Spirals

kx

ky

Gx

Gy

kx

ky

Gx

Gy


EPI Spirals

Susceptibility: distortion, blurring,dephasing dephasing

Eddy currents: ghosts blurring

k = 0 is sampled: 1/2 through 1st

Corners of kspace: yes no

Gradient demands: very high pretty high


OutlineOutline•• MR Basic PrinciplesMR Basic Principles

•• HardwareHardware

•• SpinSpin

•• SequencesSequences

•• Basics of BOLD fMRIBasics of BOLD fMRI•• Signal mechanismSignal mechanism

•• Sequences usedSequences used

•• ArtifactsArtifacts

•• A few tradeA few trade--offsoffs

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Basics of BOLD fMRIBasics of BOLD fMRI


The MR roomThe MR room


Scanner InternalsScanner Internals


Macroscopic: Brain SystemsMacroscopic: Brain Systems


Microscopic: Neuronal FunctionMicroscopic: Neuronal Function

Action Potentials & Neurotransmitter TraffickingAction Potentials & Neurotransmitter Trafficking


Hemodynamic Measure of Brain Function (1881)Hemodynamic Measure of Brain Function (1881)

ArmArm

BrainBrain

Angelo Angelo MossoMosso

Pressure TracesPressure Traces ““BertinoBertino””

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Artery Vein

Arterioles Venules

1 - 3 cm

Capillary Bed

Neurons


Blood Oxygen Level Dependent (BOLD)Blood Oxygen Level Dependent (BOLD)

•• Neural activity Neural activity increasesincreases•• Blood flow Blood flow increasesincreases ((““reactive hyperemiareactive hyperemia””))•• DeoxyhemoglobinDeoxyhemoglobin concentration concentration decreasesdecreases•• Magnetic field homogeneity Magnetic field homogeneity increasesincreases•• Gradient echo EPI signal Gradient echo EPI signal increasesincreases

venulesvenulesarteriolesarterioles

BaselineBaseline

capillarycapillarybedbed

time

MxySignal

Mo

sin T2* taskT2* control

TEoptimum

Stask

ScontrolS

time

MxySignal

Mo

sin T2* taskT2* control

TEoptimum

Stask

ScontrolS

““ActivatedActivated””

venulesvenulesarteriolesarterioles

NeuronalNeuronalFiringFiring

capillarycapillarybedbed

HbOHbO22

DeoxyDeoxy--HbHb


Hemodynamic Response PropertiesHemodynamic Response Properties•• Magnitude of signal changes is quite small Magnitude of signal changes is quite small

•• 0.5 to 3% at 1.5 T (or smaller)0.5 to 3% at 1.5 T (or smaller)

•• Too small to see in individual imagesToo small to see in individual images

•• Always considering differences or timeAlways considering differences or time--course changes course changes in image intensityin image intensity

•• Response is delayed and quite slow (~10 seconds)Response is delayed and quite slow (~10 seconds)•• Extracting temporal information is tricky, but possibleExtracting temporal information is tricky, but possible

•• Even short events have a rather long responseEven short events have a rather long response


Blood Oxygen Level Dependent Blood Oxygen Level Dependent (BOLD) Contrast Activation(BOLD) Contrast Activation


TimeTime--Course Response in fMRICourse Response in fMRI•• Brief neuronal events can Brief neuronal events can

elicit a (positive) blood elicit a (positive) blood flow and oxygenation flow and oxygenation response.response.

•• Reponses to events as Reponses to events as brief as 50 ms have been brief as 50 ms have been recorded.recorded.

Functional MRI response to a Functional MRI response to a visual stimulus of duration 2svisual stimulus of duration 2s

Start of Start of EventEvent

SlowerSlowerNegativeNegativeResponseResponse

Rise andRise andFall in ~10 sFall in ~10 s


Response to periodic flashes of lightResponse to periodic flashes of light

Processed ImageProcessed Image Anatomic ImageAnatomic Image

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Typical Functional Image VolumeTypical Functional Image Volume


fMRI Experiment Stages: PrepfMRI Experiment Stages: Prep

1) Prepare subject• Consent form• Safety screening• Instructions

2) Shimming• putting body in magnetic field makes it non-uniform• adjust 3 orthogonal weak magnets to make magnetic field as homogenous as

possible

3) SagittalsTake images along the midline to use to plan slices


Slice Thicknesse.g., 6 mm

Number of Slicese.g., 10

SAGITTAL SLICE IN-PLANE SLICE

Field of View (FOV)e.g., 19.2 cm

VOXEL(Volumetric Pixel)

3 mm

3 mm6 mm

Slice TerminologySlice Terminology

Matrix Sizee.g., 64 x 64

In-plane resolutione.g., 192 mm / 64

= 3 mm


fMRI Experiment Stages: fMRI Experiment Stages: FunctionalsFunctionals5) Take functional (T2*) images

• images are indirectly related to neural activity• usually low resolution images (3x3x5 mm)• all slices at one time = a volume (sometimes also called an image)• sample many volumes (time points) (e.g., 1 volume every 2 seconds for 150

volumes = 300 sec = 5 minutes)• 4D data: 3 spatial, 1 temporal

first volume(2 sec to acquire)

…


MRI vs. fMRI

neural activity blood oxygen fMRI signal

MRI fMRI

one image

many images(e.g., every 2 sec for 5 mins)

high resolution(1 mm)

low resolution(~3 mm but can be better)

fMRIBlood Oxygenation Level Dependent (BOLD) signal

indirect measure of neural activity

…


Detection/Detection/EstimationEstimation

fMRI process chain

RegistrationRegistrationFunctional ImagesFunctional Images

Threshold/Threshold/OverlayOverlay

Phase FixPhase Fix

TimeTime 11 22 33 …… 750 750 (secs)(secs)

11 2233

0s0s .66s.66s.33s.33s

11 22

y Xβ e

NormalizationNormalization

11 22

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Statistical Mapsuperimposed on

anatomical MRI image

~2s

Functional images

Time

Condition 1

Condition 2 ...

~ 5 min

Time

fMRISignal

(% change)

ROI Time Course

Condition

Activation StatisticsActivation Statistics

Region of interest (ROI)


% s

igna

l cha

nge

images

Stimulation protocols in fMRI

baseline rest

stimulationhaemodynamic

response function

time courseof activation


Statistical Maps & Time CoursesStatistical Maps & Time Courses

Use stat maps to pick regions

Then extract the time course


2D 2D 3D3D


Design Jargon: RunsDesign Jargon: Runs

run (or scan): one continuous period of fMRI scanning (~5-7 min) session: all of the scans collected from one subject in one day

experiment: a set of conditions you want to compare to each othercondition: one set of stimuli or one task

4 stimulus conditions+ 1 baseline condition (fixation)

A session consists of one or more experiments.Each experiment consists of several (e.g., 1-8) runsMore runs/expt are needed when SNR is low or the effect is weak.Thus each session consists of numerous (e.g., 5-20) runs (e.g., 0.5 – 3 hours)


Design Jargon: Paradigm or ProtocolDesign Jargon: Paradigm or Protocol

paradigm (or protocol): the set of conditions and their order used in a particular run

Time

volume #1(time = 0)

volume #105(time = 105 vol x 2 sec/vol = 210 sec = 3:30)

runepoch: one instance of a condition

first “objects right” epochsecond “objects right” epoch

epoch 8 vol x 2 sec/vol = 16 sec

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Susceptibility in MRSusceptibility in MR

The good.The good.

The bad.The bad.

The ugly.The ugly.

All susceptibility effects increase with Bo field


Susceptibility in Temporal LobesSusceptibility in Temporal Lobes


What is the source of susceptibility?

The magnet has a spatially uniform field but your head is magnetic…

1) deoxyHeme is paramagnetic

2) Water is diamagnetic ( = -10-5)

3) Air is paramagnetic ( = 4x10-6)

Pattern of B field outside magnetic object in a uniform

field…

Bo


Bo

Ping-pong ball in H20:Field maps (TE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T)

1.5T 3T

Susceptibility effects occur near magnetically Susceptibility effects occur near magnetically disdis--similar materialssimilar materials


Bo map in head: it’s the air tissue interface…

Sagittal Bo field maps at 3T


Other Sources of Susceptibility You Should Other Sources of Susceptibility You Should Be Aware ofBe Aware of……

Those fillings might be a problem…

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Local susceptibility gradients:2 effects

• Local dephasing of the signal (signal loss) within a voxel, mainly from thru-plane gradients

• Local geometric distortions, (voxel location improperly reconstructed) mainly from local in-plane gradients (in PE direction).

Sagittal Bo field map at 3T


Bandwidth is asymmetric in EPI(Distortion is 100x more in phase direction)

The phase error (and thus distortions) are in the phase encode direction.

=

kx

ky

t=0.005ms

t=0.5ms


Susceptibility in EPI can give either a Susceptibility in EPI can give either a compression or expansioncompression or expansion

Altering the direction kspace is traversed causes either local compression or expansion.

choose your poison…

3T whole body gradients


Susceptibility Causes Image DistortionSusceptibility Causes Image Distortion

Field near sinus

z

Echoplanar Image, encode time 1/BW

Encode time = 34, 26, 22, 17ms

3T head gradients

Use shortest possible encoding


With fast gradients, add parallel imagingWith fast gradients, add parallel imaging

Acquisition: SM

AS

H

SE

NS

E

Reconstruction:

Folded datasets+

Coil sensitivity maps

Reduced k-space sampling

{

Folded images ineach receiver channel

FOVk

2


3T MAGNETOM Allegra 3T MAGNETOM Allegra ss EPI PATss EPI PAT

MAGNETOM Allegra. Courtesy Bruker Medical and USA Instruments.4 channel tx/rx array coil

Single shotTE = 30 ms

with PAT x2192x128

with PAT x2128x128

with PAT x264x64

Conventional64x64

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•• Good shimming (first & second order)Good shimming (first & second order)•• Thinner slices (Drawback: Takes more to cover the brain)Thinner slices (Drawback: Takes more to cover the brain)•• Shorter TE (Drawback: BOLD contrast is optimized for TE = T2*locShorter TE (Drawback: BOLD contrast is optimized for TE = T2*local)al)•• ““ZZ--shimmingshimming”” Repeat measurement several times with an applied z Repeat measurement several times with an applied z

gradients that rewind the gradients that rewind the dephasingdephasing, Pick the right gradient afterward on a , Pick the right gradient afterward on a pixel by pixel basis. (Drawback: multi shot or longer encode). pixel by pixel basis. (Drawback: multi shot or longer encode). Yang et al. Yang et al. MRM 39 p402, 1998.MRM 39 p402, 1998.

•• Use special RF pulse with builtUse special RF pulse with built--in in prephasingprephasing in just the right places. in just the right places. (Drawback: long RF pulse, pre(Drawback: long RF pulse, pre--phasing differs from person to person) phasing differs from person to person) Glover et al. Proceed. ISMRM p298, 1998.Glover et al. Proceed. ISMRM p298, 1998.

•• The The ““mouth shimmouth shim”” paramagnetic material in roof of mouth. paramagnetic material in roof of mouth. Wilson, Wilson, JenkinsonJenkinson, , JezzardJezzard, Proceed. ISMRM p205, 2002., Proceed. ISMRM p205, 2002.

•• Distortion correction based on a measured field map (drawback: cDistortion correction based on a measured field map (drawback: cannot annot recover signal dropout or fully correct recover signal dropout or fully correct ““overlappingoverlapping”” intensities)intensities)

•• MultiMulti--shot imaging methods (drawback: more motion sensitive)shot imaging methods (drawback: more motion sensitive)•• Fancy pulse sequences (best to have local physicist): 180 degreeFancy pulse sequences (best to have local physicist): 180 degree

refocusing pulses to reverse distortion (GRASE)/Multiple refocusrefocusing pulses to reverse distortion (GRASE)/Multiple refocusing ing pulsespulses…… singlesingle--shot FSE, Ushot FSE, U--FlareFlare

What can you do?What can you do?


SingleSingle--shot Gradient Echo EPIshot Gradient Echo EPI•• Parameters you can chooseParameters you can choose

•• TRTR

•• Slice thickness/gapSlice thickness/gap

•• Number of slices/slice acquisition orderNumber of slices/slice acquisition order

•• TETE

•• BandwidthBandwidth

•• Matrix sizeMatrix size

•• Field of viewField of view

•• Flip angleFlip angle

•• All of these parameters can be appropriately All of these parameters can be appropriately applied over a wide range of valuesapplied over a wide range of values


TR (repetition time)TR (repetition time)•• Determines how much magnetization is allowed to Determines how much magnetization is allowed to

recover before it is knocked over again by the next rf recover before it is knocked over again by the next rf pulsepulse

•• From a pure signal strength perspective, waiting for From a pure signal strength perspective, waiting for very long very long TRTR’’ss (5 seconds +) allows for maximal (5 seconds +) allows for maximal signalsignal--toto--noise (SNR)noise (SNR)

•• Noise is MR dominated by physiologic noise (not Noise is MR dominated by physiologic noise (not thermal noise)thermal noise)

•• Requires many images in both conditions to reliably Requires many images in both conditions to reliably distinguish activation (which requires shorter distinguish activation (which requires shorter TRTR’’ss))

•• fMRI can be performed as fast as TR=100msfMRI can be performed as fast as TR=100ms•• Bottom line: use as short a TR as you canBottom line: use as short a TR as you can


Flip AngleFlip Angle•• A given flip angle will maximize the SNR (Ernst A given flip angle will maximize the SNR (Ernst

Angle)Angle)……at long at long TRTR’’ss (> 3s) this is 90 degrees(> 3s) this is 90 degrees

•• This angle is dependent upon the TRThis angle is dependent upon the TR

•• Incorrect angles may sensitize your BOLD scans to inIncorrect angles may sensitize your BOLD scans to in--flow artifacts (bad) flow artifacts (bad) [Lu et al, NeuroImage 17, 943[Lu et al, NeuroImage 17, 943––955 (2002)]955 (2002)]

•• Bottom line: For TR of 1Bottom line: For TR of 1--2s, a flip angle of around 602s, a flip angle of around 60--70 degrees is optimal70 degrees is optimal

11cos exp /TR T


Number of slicesNumber of slices•• Separate slices in EPI are typically squeezed into a TR Separate slices in EPI are typically squeezed into a TR

intervalinterval

•• Many factors influence # of slices that fit in a TRMany factors influence # of slices that fit in a TR•• Length of TRLength of TR

•• TE (determines center of blue box)TE (determines center of blue box)

•• Matrix size (determines length of blue box)Matrix size (determines length of blue box)

•• Bandwidth (determines length of blue box)Bandwidth (determines length of blue box)

•• Bottom line: collect as many slices as you canBottom line: collect as many slices as you can


So farSo far•• Long TR maximized SNRLong TR maximized SNR•• Short TR maximizes fMRI statsShort TR maximizes fMRI stats•• Long TR provides many slicesLong TR provides many slices•• Short TR provides few slicesShort TR provides few slices

•• The above suggests imaging only brain regions of The above suggests imaging only brain regions of interest (to minimize slices)interest (to minimize slices)

•• But processing decisions also play a roleBut processing decisions also play a role•• Whole brain data is much easier to spatially normalizeWhole brain data is much easier to spatially normalize•• Motion correction works best with thin slicesMotion correction works best with thin slices•• In general In general TRTR’’ss between 1s and 2s are not too badbetween 1s and 2s are not too bad

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Slice ThicknessSlice Thickness•• SNR in MRI is proportional to voxel volume (thinner SNR in MRI is proportional to voxel volume (thinner

slices slices --> less SNR)> less SNR)

•• Thinner slices reduces partial volume effectsThinner slices reduces partial volume effects

•• Thinner slices reduces throughThinner slices reduces through--plan plan dephasingdephasing

•• What is the size of the structure of interest?What is the size of the structure of interest?

•• Isotropic voxel size is preferredIsotropic voxel size is preferred


TE (echo time)TE (echo time)•• Optimum TE is shorter at high field (say 30ms at 3T Optimum TE is shorter at high field (say 30ms at 3T

versus 50ms at 1.5T)versus 50ms at 1.5T)

•• Shorter TE reduces signal loss due to field Shorter TE reduces signal loss due to field inhomogeneities, but also reduces BOLD effect inhomogeneities, but also reduces BOLD effect


BandwidthBandwidth•• Rate at which points are sampled (the echoes are Rate at which points are sampled (the echoes are

digitized)digitized)

•• High bandwidth implies a high sampling rateHigh bandwidth implies a high sampling rate•• Sampling of the order of 128 kHzSampling of the order of 128 kHz

•• 128kHz/64matrix = 2000Hz/pixel128kHz/64matrix = 2000Hz/pixel

•• Noise is proportional to sampling rateNoise is proportional to sampling rate

•• High bandwidth means faster data acquisition (and High bandwidth means faster data acquisition (and more slices can be acquired, with less T2 blurring)more slices can be acquired, with less T2 blurring)


Matrix SizeMatrix Size•• Matrix size impact everythingMatrix size impact everything

•• Increasing matrix size decreases voxel size and thus SNRIncreasing matrix size decreases voxel size and thus SNR

•• Increasing matrix and FOV maintains constant voxel size, but Increasing matrix and FOV maintains constant voxel size, but increases N and therefore increases SNRincreases N and therefore increases SNR

•• IntravoxelIntravoxel dephasingdephasing reduced somewhat with smaller voxels reduced somewhat with smaller voxels (bigger matrix)(bigger matrix)


Field of View (FOV)Field of View (FOV)•• Voxel size determined by field of view and matrix sizeVoxel size determined by field of view and matrix size

•• FOV=200mm/64 matrix = 3.125mm voxel dimensionFOV=200mm/64 matrix = 3.125mm voxel dimension

•• Recall SNR proportional to voxel volumeRecall SNR proportional to voxel volume

x

x

FOVx

N y

y

FOVy

N

Lecture01 CourseIntro MRIPhysicsece-research.unm.edu/vcalhoun/courses/fMRI_Spring...1 Sprint 2009...

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Transcript of Lecture01 CourseIntro MRIPhysicsece-research.unm.edu/vcalhoun/courses/fMRI_Spring...1 Sprint 2009...