Introduction: from image to inference

• Chris Rorden
• fMRI strengths and limitations.
• fMRI signal: tiny, slow, hidden in noise.
• fMRI processing: a sample experiment.
• fMRI anatomy: stereotaxic space.

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Taylor

John

Chris

Alex

Natalie

Samaneh

Roger

A brief history of Nobel prizes for MRI

1937 - Isidor I Rabi, a professor at Columbia University observed the quantum phenomenon dubbed nuclear magnetic resonance (NMR). He recognized that the atomic nuclei show their presence by absorbing or emitting radio waves when exposed to a sufficiently strong magnetic field.

1952 Felix Bloch and Edward Purcell win Nobel for nuclear magnetic resonance (NMR)

1973 Paul Lauterbur uses gradients to encode space, creating 2D MRI ex-vivo images

1970’s Sir Peter Mansfield develops phase and frequency encoding, pioneers echo planar imaging. Makes MRI viable.

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A brief history of MRI

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1977/1978 - Raymond Damadian builds the first human MRI scanner by hand.

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1993 - Functional MR imaging of the brain is introduced.

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Damadian with 1st human MRI: Indomitable

No wonder Dr. Freeman Cope, an NMR collaborator of Dr. Damadian's on other NMR studies, told Dr. Damadian, "Your cancer paper contains a second discovery. No one has ever reported a comparison study of the healthy tissues. There are major differences here as well."

Sir Peter Mansfield (with Lauterbur), 2003 Nobel Prize Development of MRI Obituary, Feb 9, 2017

MRI as Art

The Many Flavors of MRI

MRI in the Media

Scary examples from House, Grey’s Anatomy, Terminator Genesys, etc.

Modern neuroscience

• Different tools exist for inferring brain function.
• No single tool dominates, as each has limitations.
• This course focuses on fMRI.

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Temporal resolution

good (millisecond)

poor (months)

good

(neuron)

poor

(whole brain)

scr

erp

fmri

pet

tms

nirs

lesions

eeg

iap

Spatial resolution

Brain Imaging Methods

Modern neuroscience techniques

Single Cell Recording (SCR)

• Directly measure neural activity
• Exquisite timing/spatial information
• Example
• Cells in monkey V1 have brief response starting ~50 ms after visual stimuli is displayed.
• Limitations
• Invasive: Hard to infer human cognition from animals
• Poor field of view: only sample small brain region

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fMRI signal sluggish

• Unlike single cell recordings (SCR), in fMRI there is a huge delay between activity and signal change.
• Response in visual cortex shows peak response ~5s after visual stimuli.
• Thus, fMRI is an indirect measure of brain activity

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What is the fMRI signal?

• fMRI is ‘Blood Oxygenation Level Dependent’ measure (BOLD).
• Capillaries dilate
• Increased oxygenated versus deoxygenated blood.
• At first oxygen in blood dips (local consumption)
• Brain regions become oxygen rich after activity.
• Very indirect measure.

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Basal State

Stimulated State

• Dilation
• Increased flow
• More Hbr02 relative to Hbr
• Increased Signal

fMRI Processing

• We must heavily process fMRI data to extract a signal.
• The signal in the raw fMRI data is influenced by many factors other than brain activity.
• We need to filter the data to remove these artifacts.
• We will examine why each of these steps is used.

Processing Steps

• Motion Correct
1. Spatial
2. Intensity
• Physiological Noise Removal
• Temporal Filtering
• Temporal Slice Time Correct
• Spatial Smoothing
• Normalize
• Statistics

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Let’s conduct a study

• Anatomical Hypothesis: lesion studies suggest location for motor-hand areas (upside-down Omega shaped fold in motor cortex)
• Ask person to tap finger while in MRI scanner – predict contralateral activity in motor hand area..

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M1: movement

S1: sensation

Data Collection

• Participant Lies in scanner.
• Watch computer screen through mirror.
• Computer shows flashing arrows (up, left, right).
• Tap left/right finger after seeing left/right arrow, rest when up arrow is shown.
• Collect 302 3D volumes of data, one every 1.92s (total time = ~10min).

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Raw Data

• The scanner reconstructs 302 3D volumes.
• Each volume = 64x64x36 voxels
• Each voxel is 3x3x3.6mm.

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• We need to process this raw data to detect task-related changes.

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Motion Correction

• Unfortunately, people move their heads a little during scanning.
• We need to process the data to create motion-stabilized images.
• Otherwise, we will not be looking at the same brain area over time.

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Spatial smoothing

• Each voxel is noisy
• By blurring the image, we can get a more stable signal (neighbors show similar effects, noise spikes attenuated).

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Predicted fMRI signal

• We need to generate a statistical model.
• We convolve expected brain activity with hemodynamic response to get predicted signal.
• Since the HRF is sluggish, convolution blurs the rapid neural signal across many seconds.
• Note that predicted signal at any moment is often influenced by several previous events.

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Predicted fMRI signal

=

Event Onset and

Neural Signal

HRF

Predicted fMRI signal

• We generate predictions for neural responses for the left and right arrows across our dataset.
• Statistics will identify which areas show this pattern of activity.
• Several possible statistical contrasts (crucial to inference):
1. Activity correlated with left arrows: visual cortex, bilateral motor.
2. More activity for left than right arrows: contralateral motor.

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fMRI signal change is tiny, noise is high

• Right motor cortex is brighter after movement of left hand.
• Note signal increases from ~12950 to ~13100, only 1.2%!
• And this is after all of our complicated processing to reduce noise.

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Coordinates - normalization

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• Different people’s brains look different
• ‘Normalizing’ adjusts overall size and orientation

Raw Images

Normalized Images

Why normalize?

• Benefits of warping individuals brains to stereotaxic space
• Universal description for anatomical location
• Allows other to replicate findings
• Allows between-subject analysis: crucial for inference that effects generalize across humanity.

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Group analysis

Subject1

Subject2

Subject3

Subject4

Subject5

Goals for this course

• fMRI is notoriously difficult technique
• Sluggish signal
• Poor signal/noise
• Must find meaningful statistical contrasts

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• This seminar reveals how to
• Devise meaningful contrasts
• Maximize signal, minimize noise
• Control for statistical errors

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Reporting findings

• How do we describe anatomy to others?
• We could use anatomical names, but often hard to identify.
• We could use Brodmann’s Areas, but this requires histology – not suitable for invivo research.
• Both show large between-subject variability.
• Requires anatomical coordinate system.

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Ambiguous Coordinates

• Human brain rotated relative to spine
• Ambiguous coordinates
• Dorsal/ventral
• Rostral/caudal
• Unambiguous coordinates
• Head/Foot
• Superior/Inferior
• Anterior/Posterior

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V

D

V

D

V

D

Rat

Human

Anatomy – Common Terms

• Radiological convention: Left on right side
• Neurological convention: Left on left side

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Posterior <> Anterior

Posterior <> Anterior

Inferior <> Superior

lateral < medial > lateral

sagittal

coronal

axial

Oblique Slices

• Slices that are not cut parallel to an orthogonal plane are called ‘oblique’.

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Ax

Cor

Oblique

• Thickness of gray matter impossible to determine using any 2D view.
• Tissue appears thinner if cut is perpendicular to slice, thicker if cut is angled.

Brain Coordinates

• On Earth: North, South, East and West.
• 0˚N/S explicitly defined by spheres rotation (equator).
• 0˚E/W arbitrary (Greenwich by convention).
• For brain: Left/Right, Sup./Inf., Ant./Post.
• Origin of L/R explicitly defined (brain symmetry)
• Origin of S/I and A/P arbitrary.

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Coordinates - Talairach

• Anterior Commissure (AC) is the origin for neuroscience.
• We measure distance from AC
• 57x-67x0 means ‘right posterior middle’.
• Three values: left-right, posterior-anterior, ventral-dorsal

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Coordinates - Talairach

• Axis for axial plane is defined by anterior commissure (AC) and posterior commissure (PC).
• Both are small regions that are clear to see on most scans.

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 PC

 AC

Y-

Y+

Z+

Z-

Recognizing the cortical lobes

• NB Insula (hidden) is also a lobe.

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The major sulci

• Postcentral easy to find: becomes intraparietal. Precentral easy to find- attached to superior frontal. Between these is the Central (Rolandic).

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Interhemispheric (Longitudinal) fissure

Sylvian (lateral) fissure

Major sulci

• You can usually find the central suclus’ motor hand area (omega shape on axial slice)

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Gyri and sulci

• Naming of most gyri (ridges) and sulci (valleys) follows simple pattern of position (superior, middle, inferior) and lobe name.

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Subcortical structures

• With a bit of practice, it is easy to find subcortical structures such as caudate nucleus, globus pallidus, putamen.

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Image Center/Width

• How do we view an image that has higher resolution than our computer screen?
• Panning changes the ‘image center’.
• We will not see some of the image.
• Zooming changes the ‘image width’.
• We may lose details.

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Pan

Zoom

Intensity Center/Width (Brightness/Contrast)

• Computers show 256 shades of gray, most scans have thousands.
• Adjust brightness ‘window center’
• E.G. range -64..124 makes muscles gray, 114..302 shows kidneys
• C/W 30/188 vs C/W 208/188
• Adjust contrast ‘window width’
• E.G. range -64..124 shows muscles, �-400..596 shows full range.
• C/W 30/188 vs C/W 98/996
• CT intensity is calibrated (kidneys always ~208 Hounsfield units)
• MRI intensity values vary from scan to scan.

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Pan

Zoom

Brain research prerequisites?

What skills do you need to do MRI research?

• Probability and Statistics
• Computer Programming
• Linear Algebra
• Magnetic Resonance Imaging
• Neurophysiology and biophysics
• Signal and image processing

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Viewing images with MRIcroGL

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Click on the image to move crosshair position

Right-drag over region to adjust intensity range

File/OpenTemplates to view a different image.

Window/Render to see volume rendering.

View/FlipLR changes between radiological and neurological view

x1 Zoom Scale

Intensity range �>49=black >133=white

Crosshair at 43x15x16 Talairach: intensity of 109

L,A,S remind us of left, anterior and superior direction

Basic MRI Safety

Magnetism

• All substances have some form of magnetism.
• The degree of magnetism exhibited depends on the atoms that form the material.
• Magnetic susceptibility: the ability of a substance to become magnetized.
• Ferromagnetic substances have large magnetic susceptibility (i.e. iron). These substances can be easily magnetized and will become a magnet itself.
• All magnets have a North and a South pole.
• All magnets have a “fringe” field which extends to the surrounding area.

Bioeffects

• Burn Hazards are caused by damaged hardware or by electrical currents produced in conductive loops of material.
• It is important to not let the patient cross their legs or intertwine their fingers during the exam because it creates a closed circuit and can increase the heating in the subject

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• Localized heating is caused by RF energy absorption to a volume of tissue. FDA limits the amount of absorption we can give to the subject.

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Specific Absorption Rate (SAR)

• The rate the subject absorbs the RF energy is described in terms of Specific Absorption Rate (SAR), measured in watts/kg.

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• SAR is calculated by the patient’s weight, height and the expected increase in body temperature for each imaging pulse sequence.
• scan.

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Forces in the MR Environment

• There are two types of effects the magnet will have on Ferromagnetic substances

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• Translation:
• The “Missile Effect”

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• Rotation/Torque:
• The “Rotational Effect”

MRI Safety - Projectiles

• Projectile effects of metal objects seriously compromise safety.
• This potential harm cannot be over emphasized.
• For example, paper clips can travel at a velocity of 40mph @ 3T.
• Larger objects travel at a higher velocity and may be fatal.

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• *If you question the ferromagnetic qualities of your equipment please ask the MRI technologist *

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Items that can be Damaged by the magnet

• The magnetic field can seriously damage or impair the following personal items:
• Cameras
• Watches
• Credit /Bank cards
• Hearing Aids
• Hair Accessories, Belt Buckles, Shoes
• I-pods
• Memory Sticks / USB Drives

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Careful screening is a must!

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What can you take into the magnet??

• Some items may contain metal and be safe.
• Examples of non-ferrous metals are:
• Brass
• Aluminum
• Plastic
• If you have any questions we can check an object with a hand held magnet
• If item is implanted in body must have information card on implant. Check www.mrisafety.com.

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Noise

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• The MR scanner can produce very high acoustic noise levels (up to 130 dB).

Pregnancy considerations

“MR imaging may be used in pregnant women if other non-ionizing forms of diagnostic imaging are inadequate or if the examination provides important information that would otherwise require exposure to ionizing radiation (e.g., fluoroscopy, CT, etc.). It is recommended that pregnant patients be informed that, to date, there has been no indication that the use of clinical MR during pregnancy has produced deleterious effects. However, as noted by the FDA, the safety of MR during pregnancy has not been proved.”

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• -SMRI Safety Committee

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Tatoos

• There have been some documented cases of unusual sensation or tingling from a tattoo site during the procedure to receiving burns or raised skin at the site.  
• If the subject complains of any unusual sensation during the exam the study will be immediately stopped.
• If the area becomes red or irritated a hand cold compresses will be applied (these can be found in the bathroom storage container at the center)

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MRI Physics 1: Image Acquisition

• Chris Rorden & Paul Morgan
• Magnetic Resonance
• Radio frequency absorption
• Relaxation: Radio frequency emission
• Gradients
• Increases signal/noise: antenna selection, field strength.

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• Excellent references:
• www.cis.rit.edu/htbooks/mri/
• www.mikepuddephat.com/Page/1603/Principles-of-magnetic-resonance-imaging

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Anatomy of an atom

• Atoms are the building blocks of our world.
• Composed of 3 components
• Electrons: tiny negatively charged particles.
• Protons: heavy positively charged particles.
• Neutrons: heavy particles without charge.
• Electrons are often thought of like planets: tiny objects distantly orbiting a massive core.
• Neutrons and protons form the dense nucleus of an atom.

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Atomic Nuclei

• Nuclei are composed of protons and neutrons.
• Protons determine the element.
• Neutrons determines the isotope
• Hydrogen: always one proton
• Usually no neutrons (‘Proton’ ¹H ); Rarely one (Deuterium ²H) or two (Tritium ³H : radioactive, spontaneous decay).
• Helium: always two protons
• Usually two neutrons (⁴He); Rarely only one (³He).

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³H

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Nuclear Magnetic Resonance

• Felix Block and Edward Purcell
• 1946: the nuclei of some elements absorb and re-emit radio frequency energy when in magnetic field
• 1952: Nobel prize in physics
• Atoms with odd number of protons/neutrons spin in a magnetic field
• Nuclear: properties of nuclei of atoms
• Magnetic: magnetic field required
• Resonance: interaction between magnetic field and radio frequency
• Analogy: atoms precess in a magnetic field like tops spin in gravitational field

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Resonant Frequency of Nuclei

• We will focus on ¹H
• Most abundant in body (63% of atoms).
• Elements with even numbers of neutrons and protons have no spin, so we can not image them (⁴He, ¹²C).
• ²³Na and ³¹P are relatively abundant, so can be imaged.
• Larmor frequency varies for isotope:
• ¹H = 42.58 Mhz/T
• ²H = 6.54 Mhz/T
• ³H = 45.41 Mhz/T
• ¹³C = 10.7 Mhz/T
• ¹⁹F = 40.1 Mhz/T
• ³¹P = 17.7 Mhz/T
• Therefore, by sending in a RF pulse at a specific frequency we can selectively energize ¹H.

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Field Strength (Tesla)

298

40

1.0

7.0

1H Larmor Frequency (MHz)

At 1.5T, f = 63.76 MHz

At 3.0T, f = 127.7 MHz

At 7.0T, f = 298.0 MHz

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Radiofrequency Pulses

• Align
• Nuclei align to static magnetic field.
• Nuclei precesses at Larmor frequency.
• Flip
• We transmit a radiofrequency (RF) pulse at the Larmor frequency will be absorbed.
• Degree of spin tilted (flipped).
• Relax
• Nuclei re-aligns to to static field.
• As spin returns to low energy state it emits a RF signal at the Larmor frequency.
• We can measure this signal with an antenna.

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Electromagnetic Spectrum

• MRI signals are in the same range as FM radio and TV (30-300MHz).
• Unlike X-rays, MRI is non-ionizing radiation.
• Specific absorption rate (SAR):
• Absorbed RF warms tissue
• Increases ~ with square of field strength.
• FDA limits SAR, and is a limiting factor for some protocols
• For head, limit is 3 W/kg averaged over 10 minutes.
• Problem for light individuals (children)
• Tune sequence, or alternate between high and low energy sequences

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Ionizing Radiation

Breaks Bonds

Non-Ionizing Radiation

Heating

Excites Electrons

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Excites Nuclei

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Making a spatial image

• To create spatial images, we need a way to cause different locations in the scanner to generate different signals.
• To do this, we apply gradients.
• Gradients make the magnetic field slightly stronger at one location compared to another.
• Lauterbur: first MRI: 2003 Nobel Prize.

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Slice Selection Gradient

• Gradients: field stronger at one location compared to another.
• Larmor frequency different along this dimension.
• RF pulse only energizes slice where field strength matches Larmor frequency.

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127 Mhz

RF pulse

Larmor Freq

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126 Mhz

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127 Mhz

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128 Mhz

Slice Selection Gradient

Gradual gradients select thick slices, steep gradients select thinner slices.

• Rapid changes in field strength (dB/dt) induce electrical currents.
• For MRI, FDA limits dB/dt - some protocols elicit peripheral nerve stimulation (mild tingling, muscle twitches).
• Transcranial Magnetic Stimulation (TMS) intentionally employs extreme dB/dt to stimulate brain activity.

Position of gradient determines which 2D slice is selected.

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Field Strength

Z Position

Field Strength

Z Position

Field Strength

Z Position

Field Strength

Z Position

❶

❷

❶

❷

Phase encoding gradient

• Orthogonal gradient between RF pulse and readout
• This adjusts the phase along this dimension.
• Analogy: Phase encoding is like timezones. Clocks in different zones will have different phases.

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Frequency encoding gradient

• Apply final orthogonal gradient when we wish to acquire image.
• Slice will emit signal at Lamour frequency, e.g. lines at higher fields will have higher frequency signals.
• Aka ‘Readout gradient’.

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RF emission

Reconstruction

• Raw MRI data is 2D fourier image
• Modern scanners automatically convert k-space to image space (reconstruction).
• Images with even number of rows/columns faster to reconstruct
• This is why most image matrices are a power of 2 (64,128,256)
• Modern scanners allow other values (e.g. 96) but not primes (97)

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Reconstruction

MRI scanner anatomy

• Superconducting magnet generates static field.
• Always on: only quench field in emergency.
• niobium titanium wire.
• Coils allow us to
• Make static field homogenous (shims: metal [permanent] and solenoids [adjustable])
• Briefly adjust magnetic field (gradients: solenoid coils)
• Transmit, receive RF signal (body and head RF coils: antennas)

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Magnet

Body Coil

Gradients

Permanent Shims (16)

MRI terminology

• Orientation: typically coronal, sagittal or axial, can be in-between these (oblique)
• Matrix Size:
• Voxels in each dimension
• Field of view:
• Spatial extent of each dimension.
• Resolution:
• FOV/Matrix size.

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Axial Orientation

64x64 Matrix

192x192mm FOV

3x3mm Resolution

Sagittal Orientation

256x256 Matrix

256x256mm FOV

1x1mm Resolution

Volumes

• 3D volumes are composed of stacks of 2D slices, like a loaf of bread.
• Each slice has a thickness.
• Thicker slices have more hydrogen, so more signal
• Volume of 1x1x1mm voxel is 1mm³
• Volume of 1x1x2mm voxel is 2mm³
• Thinner slices provide higher resolution.
• Optional: gap between slices.
• Reduces RF interference
• Allows fewer slices to cover whole brain.

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1mm Gap

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2mm Thick

3mm

EPI

• In conventional MRI, we collect one line of our matrix with each RF pulse.
• So a 64x64 matrix with a TR of 2s will be generated in 128s.
• Problem: this is unacceptable if the object changes rapidly:
• Heart motion.
• Brain activity.
• Echo Planar Imaging (EPI): By rapidly applying the frequency gradient, we can collect a 2D slice with a single RF pulse.
• Benefit: Collect entire 2D slice with each TR
• Disadvantage: spatial warping and signal dropout due to slow encoding (spatial processing lecture).

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EPI

Multishot

n.b. 4x4 matrix shown

Signal to Noise

• Signal To noise is given by the formula

Signal = V√N

• Where V is the volume and N is the number of samples averaged (referred to as ‘Nex’, as in ‘number of excitations’).
• For example, to get the same SNR as a single 3x3x3mm scan (27mm³) we would need to collect 12 2x2x2mm (8mm³) scans or 768 1x1x1mm (1mm³) scans.

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Signal to Noise: Antennas

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Head coil

Surface coil

• The MRI antenna is called a coil.
• We use different coils for different body parts.
• For brains, the most common antenna is the head coil, which is a volume coil: it shows the whole brain.
• We can also use a surface coil: it gives great signal for a small field of view.

Parallel Imaging (SENSE, iPat)

• Parallel imaging: use multiple surface coils to generate a volume image.
• Dramatically reduces spatial distortion and increases signal.
• Optionally, you can acquire images more rapidly by only collecting a portion of k-space.
• Reduces spatial distortion and increases speed of acquisition. Some loss in signal.
• E.G. SENSE R=2 collects half of the lines.

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8-channel

array

Parallel Imaging (SENSE, iPat)

• Increasing SENSE reduction factor decreases acquisition time and spatial distortion, but high values lead to reduced signal.

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Effects of SENSE factor (R) on EPI

R=1

R=2

R=3

Signal and Field Strength

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Outside magnetic field

• Spins randomly oriented

In magnetic field:

• Spins align parallel or anti-parallel to magnetic field.
• At room temperature, ~4 parts per million more protons per Tesla align with versus against field.
• As field strength increases, there is a bigger energy difference between parallel and anti-parallel alignment (faster rotation = more energy).
• A larger proportion will align parallel to field.
• More energy will be released as nuclei align.
• MR signal increases with square of field strength.

Signal and Field Strength

• 1.5-3.0T typical clinical; 3.0T typical research
• NbTi max ~11.7T (~9.4T at atmospheric pressure)
• NbSn max ~22T (brittle, hard to manufacture)
• Increasing field strength yields
• Faster Larmor frequency
• Larger ratio of nuclei aligned
• More signal as nuclei realign
• T1 increases;T2 decreases (contrast lecture)
• Signal: square of field strength
• Noise: ~linear with field strength
• In theory, 3T twice SNR of 1.5T (Less in practice)
• Benefits: better SNR
• Costs: Artifacts, Money, SAR, wavelength effects, auditory noise

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Magnetic attraction

• MRI field measured in Tesla.
• 10,000 Gauss per Tesla
• Compass needle moved by Earths field ~0.5 Gauss
• 3T MRI ~30,000 Gauss
• Force in magnetic field (1.8T, unit dynes)
• Water: -22
• Copper: -2.6
• Copper Chloride: +280
• Iron: +400,000
• Diamagnetic material repelled (e.g. H2O).
• Paramagnetic material attracted (e.g. CuCl, Gd).
• Ferromagnetic material strongly attracted (Fe).
• Even without magnetic field, magnetic moments aligned
• Dangerous near MRI scanner

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MRI Physics 2: Contrasts and Protocols

• Chris Rorden, Paul Morgan
• Types of contrast: Protocols
• Static: T1, T2, PD
• Endogenous: T2* BOLD (‘fMRI’), DW
• Exogenous: Gadolinium Perfusion
• Motion: ASL

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www.fmrib.ox.ac.uk/~karla/

www.hull.ac.uk/mri/lectures/gpl_page.html

www.cis.rit.edu/htbooks/mri/chap-8/chap-8.htm

www.e-mri.org/cours/Module_7_Sequences/gre6_en.html

Contrast in XRays

• Xrays (and CT) have a single contrast mechanism: how well does tissue attenuate rays.
• Air ~transparent
• bone ~opaque
• soft tissue ~translucent
• The only way to influence Xray contrast is to change tissue. E.G. injection of radio-opaque Gd into bloodstream.

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Analogy: overhead projector ~ Xray

CT: reconstructed from series of Xrays

MR Contrast – a definition

• Contrasts influence the brightness of a voxel.
• E.G. water (CSF) dark in a T1-weighted scan, bright in a T2 scan.
• Unlike X-rays, with MR we can manipulate many contrast mechanisms. This provides tremendous versatility.
• Types of MR contrasts:
1. Static Contrast: Sensitive to relaxation properties of the spins (T1, T2)
2. Endogenous Contrast: Contrast that depends on intrinsic property of tissue (e.g. fMRI BOLD)
3. Exogenous contrast: Contrast that requires a foreign substance (e.g. Gadolinium)
4. Motion contrast: Sensitive to movement of spins through space (e.g. perfusion).

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T1

T2

Anatomy of an MRI scan

• Place object in strong static magnetic field, then.
1. Transmit Radio frequency pulse: atoms absorb energy
2. Wait
3. Listen to Radio Frequency emission due to relaxation
4. Wait, Goto 1
• Time between set 1 and 3 is our Echo Time (TE)
• Time between step 1 being repeated is our Repetition Time (TR).
• TR and TE influence image contrast.

T1 and T2 definitions

• After RF is absorbed, emitted RF signal decays with time.
• Two simultaneous but independent reasons for signal loss: recovery and dephasing.
• T1-Relaxation: Recovery
• Recovery of longitudinal orientation.
• ‘T1 time’ refers to interval where 63% of longitudinal magnetization is recovered.
• T2-Relaxation: Dephasing
• Loss of transverse magnetization.
• ‘T2 time’ refers to interval where only 37% of original transverse magnetization is present.

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Contrast: T1 and T2 Effects

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• T1 effects measure recovery of longitudinal magnetization.
• T2 refers to decay of transverse magnetization.
• T1 and T2 vary for different tissues. For example, hemoglobin has very different T1/T2 than CSF. This difference causes these tissue to have different image contrast.
• T1 is primarily influenced by TR, T2 by TE.

CSF: Long T2

Blood: Medium T2

TR and T1: saturation

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• Consider very short TR:
• Fat: rapid recovery, each RF pulse will generate strong signal.
• Water: slow recovery, little net magnetization to tip. Later pulses generate little signal

T1 effects explain why we discard the first few fMRI scans: the signal has not saturated, so these scans show more T1 than subsequent images.

Before first pulse:�1H in all tissue �strongly magnetized.

CSF

Fat

After several rapid pulses: CSF has little net magnetization, so these tissue will not generate much signal.

T2 Relaxation

• After RF absorption ends, protons begin to release energy
• Emission at Larmor frequency.
• Emissions amplitude decays over time.
• Different tissues show different rates of decay.
• ‘Free Induction Decay’ (FID).
• Analogy: tuning fork – initially loud, quieter over time, always at resonant frequency.
• Strongest signal immediately after transmission.
• Most signal with short TE.
• Why not always use short TE?

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TE and T2 contrast

• Signals from all tissue decays with time.
• Signal decays faster in some tissues relative to others.
• Optimal contrast between tissue when they emit relatively different signals.

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Optimal GM/WM contrast

Optimal contrast

• Optimal TE will depend on which tissues you wish to contrast
• Gray matter �vs White matter
• CSF �vs Gray matter

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T2: Dephasing

• RF pulse sets phase.
• Initially, everything in phase: maximum signal.
• Signals gradually dephase = signal is reduced.
• Some tissue shows more rapid dephasing than other tissue.

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T1 and T2 contrasts

• Every scan is influenced by both T1 and T2.
• However, by adjusting TE and TR we can determine which effect dominates:
• T1-weighted images use short TE and short TR.
• Fat bright (fast recovery), water dark (slow recovery)
• T2-weighted images use long TE and long TR: they are dominated by the T2
• Fat dark (rapid dephasing), water bright (slow dephasing).
• Proton density images use short TE and long TR: reflect hydrogen concentration. A mixture of T1 and T2

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T1

T2

T2 vs T2*

• T2 only one reason for dephasing:
• Pure T2 dephasing is intrinsic to sample (e.g. different T2 of CSF and fat).
• T2* dephasing includes true T2 as well as field inhomogeneity (T2m) and tissue susceptibility (T2ms).
• Due to these artifacts, Larmor frequency varies between locations.
• T2* leads to rapid loss of signal: images with long TE will have little coherent signal.

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0.2

Signal

TE (s)

0

0

1

T2

T2*

Susceptibility artifacts

• Magnet fields interact with material.
• Ferromagnetic (iron, nickel, cobalt)
• Strongly attracted: dramatically increases magnetic field.
• all steel has Iron (FE), but not all steel is ferromagnetic (try putting a magnet on a austenitic stainless steel fridge).
• Paramagnetic (Gd)
• Weakly attracted: slightly increases field.
• Diamagnetic (H₂O)
• Weakly repelled: slightly decreases field.

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Field Strength

Field strength increases near some tissues, decreases around others

Tissue Susceptibility

• Due to spin-spin interactions, hydrogen’s resonance frequency differs between materials.
• E.G. hydrogen in water and fat resonate at slightly different frequencies (~220 Hz; 1.5T).
• Macroscopically: These effects can lead spatial distortion (e.g. ‘fat shift’ relative to water) and signal dropout.
• Microscopically: field gradients at boundaries of different tissues causes dephasing and signal loss.

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Field Inhomogeneity Artifacts

• When we put an object (like someone’s head) inside a magnet, the field becomes non-uniform.
• When the field is inhomogeneous, we will get artifacts: resonance frequency will vary across image.
• Prior to our first scans, the scanner is ‘shimmed’ to make the field as uniform as possible.
• Shimming is difficult near tissue boundaries that have very different density (e.g., sinuses have air-bone-soft tissue boundaries).
• Shimming artifacts more intense at higher fields.

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Fieldmap showing

inhomogeneity

fMRI image

Spin Echo Sequence

• Spin echo sequences apply a 180º refocusing pulse halfway between initial 90º pulse and measurement.
• This pulse eliminates phase differences due to artifacts, allowing measurement of recovery of true T2.
• Spin echo dramatically increases signal.

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Signal

Time

0

1

T2

T2*

0.5 TE

0.5 TE

Actual Signal

Analogy for Spin Echo

• Consider two clocks.
• Clock 1: minute hand takes 240 minutes to make a revolution.
• Clock 2: minute hand takes 60 minutes to make a revolution.
• Simultaneously,set both clocks to read 12:00. (~send in 90º RF pulse).
• Wait precisely 20min
• Minute hands now differ: out of phase.
• Reverse direction of each clock (~send in 180º RF pulse).
• Wait precisely 20min
• Minute hands now identical: both read noon.
• They are briefly back in phase

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Minute hand rotation

0

160º

20min

20min

BOLD effect

• Deoxyhemoglobin (Hbr) acts as contrast agent
• Frequency spread causes signal loss over time
• Effect increases with delay (TE = echo time)

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• But, overall signal reduces with TE.
• Optimal BOLD TE ~60ms for 1.5T, ~30ms at 3T.

Fera et al. (2004) J MRI 19, 19-26

0.2

TE (s)

0

Optimal fMRI scans

• More observations with shorter TR, but slightly less signal per observation (due to T1 effects and temporal autocorrelation).
• When you have a single anatomical region of interest use the fewest slices required for a very short TR.
• For exploratory group study, use a scan that covers whole brain with minimal spatial distortion (for good normalization).
• Typical 3T: 3x3x3mm 64x64 matrix, 36 slices, SENSE r=2, TE=32ms, TR= 2000ms
• Typical 1.5T: 3x3x3mm 64x64 matrix, 36 slices, TE=60ms, TR= 3500ms.

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• Shorter TR yields better SNR
• Diminishing returns
• G.H. Glover (1999) ‘On Signal to Noise Ratio Tradeoffs in fMRI’

Diffusion Imaging

• Diffusion imaging is an endogenous contrast.
• Apply two gradients sequentially with opposite polarity.
• Stationary tissue will be both dephased and rephased, while spins that have moved will be dephased.
• Sensitive to acute stroke (DWI, see lesion lecture)
• Multiple directions can measure white matter integrity (diffusion tensor imaging, see DTI lecture)

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water diffuses faster in unconstrained ventricles than in white matter

Gadolinium Enhancement

• Gd Perfusion scans are an example of an exogenous contrast.
• intravenously-injected.
• Gd not detected by MRI (1H).
• Gd has an effect on surrounding 1H.
• Gd shortens T1, T2, T2* of surrounding tissue.
• makes vessels, highly vascular tissues, and areas of blood leakage appear brighter.
• Very rare side effect: allergic reaction.
• Gd can help measure perfusion.
• Useful for clinical studies: how much blood is getting to a region, how long does it take to get there?

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Arterial Spin Labelling

• ASL is an example of a motion contrast
• IMAGE_perfusion = IMAGE_uninverted – IMAGE_inverted
• Perfusion is useful for clinical studies: how much blood is getting to a region, how long does it take to get there?

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White matter = low perfusion

Gray matter = high perfusion

Time of Flight

• ToF is a motion contrast.
• In T1 scans, motion of blood between slices can cause artifacts.
• ToF intentionally magnifies flow artifacts.
• Several Protocols of ToF, E.G:
1. Use very short TR, so signal in slice is saturated. External spins flowing into slice have full magnetization.
2. Conduct a Spin Echo Scan: 90º and 180º inversion pulses applied to different slices. Only nuclei that travel between slices show coherent signal.

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Advanced Physics Notes

• T1/T2 vary based on tissue type and scanner field strength.

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From Atlas ISBN-10: 0781720362

Advanced Physics Notes

• Optimum flip angle (‘Ernst angle’) may not be 90 degrees. Ernst angle determined by TR, and T1 of tissue.

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Figure shows optimal flip angles for TI=1400ms, which is a good choice for the brain at 3T (Mark Cohen)

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For fMRI see PMID 21073963

Advanced Physics Notes

• Field strength influences T1 and T2: influences TR/TE
• Higher Field = Faster T2 decay: Typically, TE decreases as field increases = faster imaging.
• Higher Field = Slower T1 recovery: TR increases with field strength. Influences T1 contrast: e.g. time of flight improves dramatically with field strength.
• N.B. Different tissues have different relative T1/T2 changes with field strength.

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1.5T Scanner

3.0T Scanner

Signal

TE (s)

0

.2

Magnetization

0

6

TR (s)

100%

100%

T2

T1

Designing a behavioral experiment

• Chris Rorden
• Designing fMRI studies
• fMRI signal is sluggish and additive.
• Efficient designs maximize predictable changes in HRF.
• Efficient designs are often very predictable
• Participant may anticipate events.
• Techniques for balancing efficiency and psychological validity.

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The BOLD timecourse

Hemodynamic response function

• The HRF is very sluggish
• Delay between brain activity and changes in fMRI images (~5s).
• The HRF is additive
• Doing a task twice causes about twice as much change as doing it once.

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0 6 12 18 24

Image Brightness

Time (seconds)

BOLD effects are additive

• Three stimuli presented rapidly result in almost 3 times the signal of a single stimuli (e.g. Dale & Buckner, 1997).
• Crucial finding for experimental design.
• Note there are limits to this additivity effect, but the basic point is that more stimuli generate more signal (see Birn et al. 2001)

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Assumed (linear) responses

Temporal Properties of fMRI Signal

• We predict the HRF by convolving the neural signal by the HRF.
• We want to maximize the amount of predictable variability.

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Convolved Response

=

Neural Signal

HRF

Comparing predictable HRF

Consider 3 paradigms:

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• Fixed ISI: one stimuli every 16 seconds.
• Inefficient
• Fixed ISI: one stimuli every 4 seconds.
• Insanely inefficient: virtually no task-related variability
• Block design: cluster five stimuli in 8 seconds, pause 12 seconds, repeat.
• Very efficient.
• Cluster of events is additive. Note peak amplitude is x3 the 16s design.

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Block Designs

• Block designs are optimal (aka ‘Epoch’, ‘Box Car’).
• Present trials as rapidly as possible for ~12..30 sec
• Summation maximizes additive effect of HRF
• Consider experiment:
• Three conditions, each condition repeated 14 times (once every 900ms)
• Press left index finger when you see ←
• Press right index finger when you see ➔
• Do nothing when you see ↑

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Block design limitations

• While block designs offer statistical power, they are very predictable.
• E.G. our participants will know they will press the same finger 14 times in a row.

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• Many tasks not suitable for block design
• E.G. Novelty detection, memory, etc.
• Your can not post-hoc sort data from block designs, e.g. Konishi, et al., 2000 examine correct rejection vs hits on episodic memory task.

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Block designs

• Strengths
• Optimal design for detect (where)
• Weaknesses
• Poor for estimation (when)
• Predictable
• Limited number of psychological questions
• Notes
• Optimal block length ~12s
• Avoid long blocks (>40s):
• Reduced signal variability
• Low frequency signal will be hard to distinguish from low frequency signals such as drift in MRI signal.

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Estimation

Detection

Event related designs

• Much less power than block designs.
• Simply randomizing trial order of our block design, the typical event related design has one quarter the efficiency.
• Here, we ran 50 iterations and selected the most efficient event related design.
• Still half as efficient as the block design.
• Note this design is not very random: runs of same condition make it efficient.

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Permuted Blocks

• Permuted block designs (Liu, 2004):
• Start with block design
• Transpose fixed number of trials
• Can offer a balance of power and predictability.

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Block after 10 permutations

Jittered Inter-Stimulus Interval

• Dale et al. suggest using exponential distribution for inter-trial intervals.
• Exponential Distribution:
• Many trials have short duration
• A few trials have long duration
• Efficient because jittering makes events block-like

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1 condition, fixed ISI = little variability

1 condition, exponential ISI = more variability

Should you use variable ISIs?

• In practice, variable ISIs often reduce power.
• Most experiments have more than one condition, so fixed ISI designs also have temporal variability.
• Unless you are looking at low-level processes (e.g. early vision), trials must be separated by a couple seconds.
• For multi-condition studies, the minimum time between trials is crucial.
• People are faster to respond to fixed ISI than variable ISI
• Therefore, fixed ISI are often more powerful
• However, variable ISI may help us reconstruct the true shape of the HRF measured.

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Tips

• For event related designs – helpful if TR is either variable or a not evenly divisible by the interstimulus interval.
• Allows you to accurately estimate whether conditions influence the latency of response.

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TR divisible by ISI

TR not divisible by ISI

Generate your own experiments…

• Set the TR (time per volume)
• Set the number of volumes
• Set minimum ISI – this will be time between trials for block designs.
• Set the mean ISI – this will be the average time between trials for event related designs.
• Set the number of conditions.
• You can select permutations for block designs, or iterations for event related designs to trade of predictability and power.
• Measures approximate power (variance). Value relative (for given number of volumes and TR).

• Drop-down menu selects design
1. Block
2. Permuted Block
3. Fixed ISI Event
4. Exponential ISI Event
5. Random ISI Event

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Response Suppression Designs

• Show two stimuli in rapid succession.
• See if a brain region can discriminate if these stimuli are the same or different.
• Classically, regions show adaptation – less time to process same information twice in a row.
• E.G. Fusiform gyrus shows more response to two photos of different faces than identical faces: this region can discriminate between these stimuli.

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Sparse fMRI

• Standard fMRI acquires data continuously.
• Loud noises can make it difficult to examine auditory stimuli.
• Sparse imaging includes a delay between each fMRI volume, so stimuli can be presented while scanner is silent.

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Time (sec)

0

10

Continuous

Time (sec)

0

10

Sparse

General guidelines (Nichols et al)

1. If possible, use block design
• Keep blocks <40s (temporal processing lecture describes why)
2. Limit number of conditions
• Pairwise comparisons far apart in time may be confounded by low frequency noise.
3. Randomize order of events that are close to each other in time.
4. Randomize ISI between events that need to be distinguished.
5. Run as many people as possible for as long as possible.
6. Have testable anatomical prediction

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Statistics – Modelling Your Data

• Modelling data:
• Signal, Error and Covariates
• Parametric Statistics
• Thresholding Results:
• Statistical power and statistical errors
• The multiple comparison problem
• Familywise error and Bonferroni Thresholding
• Permutation Thresholding
• False Discovery Rate Thresholding
• Implications: null results uninterpretable

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Calculating statistics

• Consider analysis of task where someone moves hand for 12s, rests for 12s.
• We can model (predict) the hemodynamic response.
• Our statistics will test how well our model predicts the observed data.
• Statistics: does model predict substantial amount of variability in observed data.
• Does this brain area change brightness when we do the task?
• Top panel: model very good predictor for observed data (very little error)
• Lower panel: mediocre predictor

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General Linear Model

• The observed data is composed of a signal that is predicted by our model and unexplained noise.

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Observed Data

Amplitude (solve for)

Design Model

Noise (Error, unexplained variance)

Y = αM + ε

cf Boynton et al., 1996

What is your model?

• Model is predicted effect.
• Consider Block design experiment:
• Three conditions, each for 11.2sec
1. Press left index finger when you see ←
2. Press right index finger when you see ➔
3. Do nothing when you see ↑

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Intensity

FSL/SPM display of model

• Analysis programs display model as grid.
• Each column is regressor
• e.g. left / right arrows.
• Each row is a volume of data
• for within-subject fMRI = time
• Brightness of row is model’s predicted intensity.

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Intensity

Time

Statistical Contrasts

• fMRI inference based on contrast.
• Consider study with left arrow and right arrow as regressors
1. [1 0] identifies activation correlated with left arrows: we could expect visual and motor effects.
2. [1 –1] identifies regions that show more response to left arrows than right arrows. Visual effects should be similar, so should select contralateral motoric.
• Choice of contrasts crucial to inference.

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Statistical Contrasts

• t-Test is one tailed, F-test is two-tailed.
• T-test: [1 –1] mutually exclusive of [-1 1]: left>right vs right>left.
• F-test: [1 –1] = [-1 1]: difference between left and right.
• Choice of test crucial to inference.

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How many regressors?

• We collected data during a block design, where the participant completed 3 tasks
• Left hand movement
• Right hand movement
• Rest
• We are only interested in the brain areas involved with Left hand movement.
• Should we include uninteresting right hand movement as a regressor in our statistical model?
• I.E. Is a [1] analysis the same as a [1 0]?
• Is a [1 0] analysis identical, better, worse or different from a [1] analysis?

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=?

Meaningful regressors decrease error

• Meaningful regressors can explain some of the variability.
• Adding a meaningful regressor can reduce the unexplained noise from our contrast.

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Meaningful regressors decrease error

• Consider voxel that responds strongly to left movement and weakly to right movement.
• Note that observed and left are identical for both models.
• Yet, ratio left/error changes.
• Inclusion of right movements can describe variability that would otherwise be counted as error.

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Correlated regressors decrease signal

• Each explanatory variable (EV) should be independent.
• If two EVs are highly correlated, each will predict the others’ variability.
• Example: consider a task where someone is asked to press a button after they see a left arrow stimuli.
• Responses happen ~0.5-1.5s after arrow onset (with some variability).
• These two events are highly correlated.
• We will have little power if we add both stimuli onset and button press times to our model.

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Single factor…

• Consider a test to see how well height predicts weight.

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Small t-score

height only weakly predicts weight

High t-score

height strongly predicts weight

Adding a second factor…

• How does an additional factor influence our test?
• E.G. We can add waist diameter as a regressor.
• Does this regressor influence the t-test regarding how well height predicts weight?
• Consider ratio of cyan to green.

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Increased t

Waist explains portion of weight not predicted by height.

Decreased t

Waist explains portion of weight predicted by height.

Weight

Height

Waist

Regressors and statistics

• Our analysis identifies three classes of variability:
1. Signal: Predicted effect of interest
2. Noise (aka Error): Unexplained variance
3. Covariates: Predicted effects that are not relevant.
• E.G. Regressors with a weight of zero
• Statistical significance is the ratio:

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• Covariates will
• Improve sensitivity if they reduce error (explain otherwise unexplained variance).
• Reduce sensitivity if they reduce signal (explain variance that is also predicted by our effect of interest).

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Signal�Noise

t =

Summary

• Regressors should be orthogonal
• Each regressor describes independent variance.
• Variance should not be explained by more than one regressor.
• N.B. Adding a regressor reduces our degrees of freedom. This is a big issue for many techniques. In low-level fMRI statistics we have hundreds of DoF, so not much of a concern.
• E.G. we will see that including temporal derivatives as regressors tend to help event related designs (temporal processing lecture).

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Group Analysis

• We test inferences about the general population
• Conduct time course analysis on many people.
• Identify which patterns are consistent across group.

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Group analysis

Subject1

Subject2

Subject3

Subject4

Subject5

Statistical thresholding example

• Erythropoietin (EPO) doping in athletes
• EPO improves endurance ~ 10%
• Races won ~1%
• Without testing, athletes forced to dope
• Dangers: Carcinogenic and can cause heart-attacks
• Therefore: Measure haematocrit
• Problem: threshold to expel

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hematocrit

30%

50%

If we set the threshold too low, we will accuse innocent people (high rate of false alarms).

If threshold set too high, we fail to detect dopers (high rate of misses).

hematocrit

30%

50%

Statistical thresholding

• We need to choose a threshold that balances the benefits of finding effects with the cost of making false alarms.
• α is our statistical threshold: it measures our chance of Type I error.
• A 5% alpha level (Z>1.64) means only 1/20 chance of false alarm (p < 0.05).
• A 1% alpha level (Z>2.3) means only 1/100 chance of false alarm (p< 0.01).

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Z>0.5

Z>1

Z>2

Z>4

Z>8

Fewer peaks survive as we apply a more stringent threshold.

Liberal, conservative, power

• With noisy data, we will make mistakes.
• Statistics allows us to
• Estimate our confidence
• Bias the type of mistake we make (e.g. we can decide whether we will tend to make false alarms or misses)
• We can be liberal: avoiding misses
• airport weapons detection (X-ray often leads to innocent cases being opened).
• We can be conservative: avoiding false alarms.
• criminal conviction: avoid sending innocent people to jail.

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Type II error

Correct rejection

Accept Ho

Hit (‘Power’)

Type I error

Reject Ho

Ho false

Ho true

Decision

Reality

• ‘Power’ refers to our chance of detecting real effects. There are four ways we can influence power….

Concrete Example

• Consider a drug candidate to treat cancer.
• Drug either does or does not treat cancer.
• Null hypothesis (Ho): Drug has no effect.
• Hit: We correctly detect that the drug works!
• Correct rejection: We correctly determine the drug has no effect.
• Type I error: We claim drug treats cancer when it does not.
• Type II error: We decide drug is not effective when it is (miss).

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Type II error

Correct rejection

Accept Ho

Hit (‘Power’)

Type I error

Reject Ho

Ho false

Ho true

Decision

Reality

• ‘Power’ refers to our chance of detecting real effects. There are four ways we can influence power….

1.) Alpha and Power

• By making alpha less strict, we can increase power.�(e.g. p < 0.05 instead of 0.01)
• In other words, we can become more liberal
• However, we increase the chance of a Type I error!

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Power

Type I Error

α

Control Condition (e.g. non-dopers)

Experimental Condition (e.g. dopers)

Hits (dopers expelled)

False alarms (innocent athletes expelled)

2.) Effect Size and Power

• Power will increase if the effect size increases. (e.g. higher dose of drug, 3T instead of 1.5T MRI).
• Unfortunately, effect sizes are often small and fixed.

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3.) Variability and Power

• Reducing variability increases the relative effect size.
• Most measures of brain activity noisy.
• N.B. Statistically what is important is ratio of effect size to variability, SNR.

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4.) Sample Size

• A final way to increase our power is to collect more data.
• We can sample a person’s brain activity on many similar trials.
• We can test more people.
• The disadvantage is time and money.
• Increasing the sample size is often our only option for increasing statistical power.

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Multiple Comparison Problem

• Olympics: 10500 athletes
• At 1% α and all innocent we will wrongly accuse ~105
• Neuroimaging: gray matter 900cc, fMRI voxels 27mm³, >33333 tests
• At 1% α, we will make ~333 false alarms.
• Many tests means many chances to make mistakes: the multiple comparison problem.
• Probability of at least one error is 1- (1- α)^C: familywise error (FWE).

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Bonferroni Correction

• Bonferroni Correction: controls FWE.
• For example: if we conduct 10 tests, and want a 5% chance of any errors, we will adjust our threshold to be p < 0.005 (0.05/10).
• Benefits: Controls for FWE.
• Problem: Very conservative = very little chance of detecting real effects = low power.

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Random Field Theory

• We spatially smooth our data – peaks due to noise should be attenuated by neighbors.
• Worsley et al, HBM 4:58-73, 1995.
• RFT uses resolution elements (resels) instead of voxels.
• If we smooth our data with 8mm FWHM, then resel size is 8mm.
• SPM uses RFT for FWE correction: only requires statistical map, smoothness and cluster size threshold.
• Euler characteristic: unsmoothed noise will have high peaks but few clusters, smoothed data will be have lower peaks but show clustering.
• RFT has many unchecked assumptions (Nichols)
• Works best for heavily smoothed data (x3 voxel size)

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Permutation Thresholding

• Gold standard to control FWE.
• Alternative hypothesis (H₁): Label ‘Group 1’ and ‘Group 2’ mean something.
• Null Hypothesis (H₀): Labels are meaningless.
• If Ho true, randomly scrambled orders will generate similar t-values as observed.
• Alternative H₀ suggests observed t-values unusually high.

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• Method:
1. Permute (randomize) labels
2. Compute maximum T-score for entire 3D volume
3. Repeat steps 1 and 2 at least 1000 times.
4. Find 5^th Percentile max T.
5. Any voxel in our observed dataset that exceeds this threshold has only 5% probability of being noise.

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Max T

Percentile

0 100

0

5

5%

T= 3.9

Permutation Thresholding

• Observed, max T = 4.1

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Group 1

Group 2

1. Permutation 1, max T = 3.2�
2. Permutation 2, max T = 2.9�
3. Permutation 3, max T = 3.3

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• Permutation 4, max T = 2.8

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• Permutation 5, max T = 3.5

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...

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1000. Permutation 1000, max T = 3.1

…

…

H₁ : Young (solid) participants have more gray matter than old (dotted).

H₀ : Label (young versus old) does not influence gray matter.

Permutation Thresholding

• Permutation Thresholding offers the same protection against false alarms as Bonferroni.
• Typically, much more powerful than Bonferroni.
• Implementations include SnPM, FSL’s randomise, NPM.
• Disadvantage: computing 1000 permutations means it takes x1000 times longer than typical analysis!
• Permutation thresholding has been used (Nichols et al) to validate other techniques: Bonferroni conservative,
• Random Fields only accurate with high DF and heavily smoothed.

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False Discovery Rate

• Traditional statistics attempts to control the False Alarm rate.
• ‘False Discovery Rate’ controls the ratio of false alarms to hits.
• It often provides much more power than Bonferroni correction.
• Some issues with neuroimaging. Solution is ‘topological FDR’ which requires a priori cutoff.

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• As a thought experiment, consider an Olympics where no one doped on EPO: population would show normally distributed hematocrit levels:

• However, distribution looks different if 20% dope. The shape of the distribution demonstrates there are different groups here:

Hematocrit Z-Scores: normal distribution

Hematocrit Z-Scores: bimodal/skewed distribution

Controlling for multiple comparisons

• Bonferroni correction
• We will often fail to find real results.
• RFT correction
• Typically less conservative than Bonferroni.
• Requires large DF and broad smoothing.
• Permutation Thresholding
• Offers same inference as Bonferroni correction.
• Typically much less conservative than Bonferroni.
• Computationally very slow
• FDR correction
• At FDR of .05, about 5% of ‘activated’ voxels will be false alarms.
• If signal is only tiny proportion of data, FDR will be similar to Bonferroni.

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Alternatives to voxelwise analysis

• Conventional fMRI statistics compute one statistical comparison per voxel.
• Advantage: can discover effects anywhere in brain.
• Disadvantage: low statistical power due to multiple comparisons.
• Small Volume Comparison: Only test a small proportion of voxels. (Still have to adjust for RFT).
• Region of Interest: Pool data across anatomical region for single statistical test.

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SVC

ROI

Voxels

Example: how many comparisons on this slice?

• Voxelwise: 1600
• SVC: 57
• ROI: 1

ROI analysis

• In voxelwise analysis, we conduct an independent test for every voxel
• Each voxel is noisy
• Huge number of tests, so severe penalty for multiple comparisons
• Alternative: pool data from region of interest.
• Averaging across meaningful region should reduce noise.
• One test per region, so FWE adjustment less severe.
• Region must be selected independently of statistical contrast! (‘voodoo correlations’)
• Anatomically predefined
• Defined based on previous localizer session
• Selected based on combination of conditions you will contrast.

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M1: movement

S1: sensation

Inference from fMRI statistics

• fMRI studies have very low power.
• Correction for multiple comparisons
• Poor signal to noise
• Variability in functional anatomy between people.
• Null results impossible to interpret. (Hard to say an area is not involved with task).
• Between group inference require significant interactions (positive effect in one group and null result in other is not a demonstration that groups differ).

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Spatial Processing

• Chris Rorden
• Spatial Registration
• Motion correction
• Coregistration
• Normalization
• Interpolation
• Spatial Smoothing
• Advanced notes:
• Spatial distortions of EPI scans
• Image intensity distortions

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Why spatially register data?

• Statistics computed individually for voxels.
• Only meaningful if voxel examines same region across images.
• Therefore, images must be in spatially registered with each other.

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Spatial Registration

We use spatial registration to align images

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• Motion correction (realignment) adjusts for an individual’s head movements.
• Coregistration aligns two images of different modalities from the same individual.
• Normalization aligns images from different people.

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Within-subject registration

• Within subject registrations
• Assumption: same individual, so there should be a good linear solution.

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Motion correction

Coregistration

Registration of the fMRI scans (across time)

Registration across modality (e.g. T2* and T1 image)

Rigid Body Transforms

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Translation

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Rotation

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• By measuring and correcting for translations and rotations, we can adjust for an object’s movement in an image.
• 6 Parameters: translation and rotation, each in 3 dimensions.

Motion Correction

• Motion correction aligns all in time series.
• Translations and rotations only
• 6 parameters (X,Y,Z; yaw, pitch, roll)
• ‘rigid body registration’
• Assumes brain size and shape identical across images.

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Motion correction cost function

• Motion correction uses least squares to check if images are a good match (aka minimum sum of squares).
• Smaller difference² = better match (‘least squares’).
• Notes about difference²
• Any number squared is positive: does not care about direction of error.
• Large error penalized much more than small error (e.g. 2²=4, 3²=9), whereas using absolute value as cost function would not be so biased between large and small errors.
• Iterative: moves image a bit at a time until match is worse.

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Image 1

Image 2

Difference

Difference²

|Difference|

Local Minima

• Search algorithm is iterative:
• Adjust image a little bit.
• Test cost function
• Repeat until cost function does not get better.
• Problem: local minima
• Solution: ensure starting estimate is accurate
• For motion correction: only small head movements
• For coregistration: both images start in good alignment
• For normalization: similar origin and rotation as template

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Value of Cost Function

Local Minimum

Global Minimum

Translation in X (mm)

Starting Estimate

0

10

Coregistration

• Coregistration is more complicated than motion correction
• Rigid body not enough:
• Size differs between images (must rescale: zooms).
• fMRI scans often have spatial distortion not seen in other scans (must skew: shears).
• Least squares cost function will fail: relative contrast of gray matter, white matter, CSF and air differences between images.

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Affine Transforms (aka linear, geometric)

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Translation

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Rotation

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Zoom

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Shear

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12 Parameters: translation, rotation, zoom and shear each in 3 dimensions.

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Translation

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Rotation

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Zoom

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Shear

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Coregistration

• Coregistration is used to align images of different modalities from the same individual

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• Uses ‘mutual information cost function’: Note unaligned images have messy joint histograms.
• Uses entropy reduction instead of variance reduction as cost function.

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Coregistration

• Note original joint histogram (prior to coregistration) is noiser than the final joint histogram (after coregistration).
• Used within individual, so linear transforms should be sufficient.
• Typically 12 parameters (translation, rotation, zooms, shear each in 3 dimensions).
• Though note that different MRI sequences create different non-linear distortions.

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T1 reference

Aligned T2

Between-subject: Normalization

• Normalization: align images from different people (align everyone to a template image)

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Subject 2

Subject 1

Template

Average activation

Normalization

Why normalize?

• Stereotaxic coordinates analogous to longitude
• Universal description for anatomical location
• Allows others to replicate findings
• Allows between-subject analysis: crucial for inference that effects generalize across humanity.

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Group analysis

Subject1

Subject2

Subject3

Subject4

Subject5

Normalization

• Normalization attempts to register scans from different people.
• We align each person’s brain to a template.
• Template often created from multiple people (so it is fairly average in shape, size, etc).
• We typically use template that is in the same modality as the image we want to normalize
• Therefore, variance cost function.
• If different groups use similar templates, they can talk in common coordinates.

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Popular MNI Template�based on T1-weighted scans �from 152 individuals.

Common templates

• SPM uses modality specific template
• MNI T1 template, plus custom templates
• By default, FSL uses MNI T1 template for all modalities
• Requires intra-modal cost functions (e.g. mutual information)

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T1 T2* PET

Templates

• Our coordinate system using anterior commissure as origin developed by Talairach and Tournoux (1988) who created atlas based on histological slices from one 69-year old woman.
• Single brain may not be representative
• No MRI scans from this woman
• Modern templates are generated from a group of MRI scans that are approximately aligned to images from the Montreal Neurological Institute.
• MNI space slightly different from T&T atlas (larger in every dimension).
• Therefore, proper to refer to “Talairach and Tornoux” coordinates and “MNI space”.

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Affine Transforms

• Co-linear points remain co-linear after any affine transform.
• Transform influences entire image.

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Spatial Processing

• Non-linear transforms can match features that could not aligned with affine transforms.
• SPM uses basis functions.

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Nonlinear functions and normalization

Linear Only

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Linear + Nonlinear

Scans from 5 people: nonlinear helps alignment

Regularization

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Regularization

• Regularization is a parameter that you can adjust that influences non-linear normalization

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http://www.fmri.ox.ac.uk/fsl/fnirt/

Medium Regularization

Little Regularization

Affect of Regularization on Normalization

Advanced Normalization

• Affine transforms (e.g. FSL’s FLIRT): 12 degrees of freedom
• Translation, Rotation, Scaling, Shear *3 dimensions
• Nonlinear basis functions (SPM5) thousands of DoF
• Diffeomorphic algorithms (SPM8’s DARTEL, ANT) millions DoF
• Not yet suggested for fMRI (due to spatial distortions/dropout)

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www.fil.ion.ucl.ac.uk/spm/course/

www.pubmed.com/19195496/

Affine

template

DARTEL

template

Advanced Normalization

• SPM’s unified normalization-segmentation uses information about different tissue types.
• Ensures that normalization is driven by brain tissue (gray matter) not scalp.
• Can be combined with Diffeomorphic.
• See VBM lecture.

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An example from AFNI

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Alternatives

• SPM and FSL normalize overall brain shape.
• Individual sulci largely ignored.
• What are different normalization strategies?
• Sulci are crucial for some tasks (Herschl’s gyrus and hearing)
• Sulci are formed by experience.
• Perhaps less so for others (e.g. Amunts et. al 2004 with Broca’s variability)

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Probability (%) of region being Brodmann Area 44 based on histology. Note that the location of this brain region varies across people.

Sulcal matching

• Normalization conducted on smoothed images.
• Not precisely matching sulci (avoid local distortion).
• Sulcal location still varies between people after normalization, especially in parietal lobe.

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Copyright Pierre Fillard, INRIA http://www-sop.inria.fr/asclepios/projects/UCLA/

The Brain with No Folds

Lissencephaly

Alternatives

• SPM/FSL normalization will roughly match orientation and shape of head.
• Good if function is localized to proportional part of brain
• Poor if function is localized to specific sulci (e.g. early visual area V1 tied to calcarine fissure).
• Alternatively, use sulci as cost function (Goebel et al., 2006).
• Image below: mean sulcal position for 12 people after standard normalization followed by sucal registration.
• Note: This technique improves sulcal alignment, but distorts cortical size.

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Individual Sulci Image

Individual Sulci Map

Sulcal maps of group following standard normalization

Sulcal maps of group following using sulci as cost function

No perfect solution

• Analogy: creating 2D map of spherical earth
• Mercator projection distorts area but preserves navigation rhumb lines and local shape.
• Gall-Peters projection preserves area but has severe shape distortions.
• Different normalization methods have different priorities.
• SPM/FSL attempt to preserve overall volume and avoid local distortions.
• Diffeomorphic normalization aligns sulci better but at the cost of local distortion.
• Brain Voyager and flat map techniques use sulci as the cost function, and can provide very good alignment of the major sulci, but cause local distortions and tend to disregard finer and more variable sulci.

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Interpolation

Each lower image rotated 12º.

Left looks jagged, right looks smooth.

Different reslicing interpolation.

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1D Interpolation

• How do we estimate values that occur between discrete samples?
• Three popular methods:
1. Nearest neighbor (‘box’)
2. Linear (‘tent’, ‘triangle’)
3. Spline/Sinc

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❶

❷

❸

Weather analogy: it was 25º at 9am, and 31º at 12am, what would you estimate the temperature was at 10am?

2D Interpolation

• How do we estimate values that occur between discrete samples?
• Three popular methods:
1. Nearest neighbor (‘box’)
2. Linear (‘tent’, ‘triangle’)
3. Spline/Sinc

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❶

❷

❸

Nearest Neighbor Interpolation

• Nearest neighbor interpolation is simple.
• Always based on single sample.
• Quick to compute.
• Generally a lousy estimate for continuous data.

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1D Box Interpolation

Nearest sample

2D Box Interpolation

Nearest sample

3D Box Interpolation

Nearest sample

Linear Interpolation

• For neuroimaging we usually use linear interpolation.
• Much more accurate than nearest neighbor.
• There is some loss of high frequencies.
• Since we spatially smooth data after spatial registration, we will lose high frequencies eventually.

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1D Linear Interpolation

Weighted mean of 2 samples

2D Bilinear Interpolation

Weighted mean of 4 samples

3D Trilinear Interpolation

Weighted mean of 8 samples

Sinc Interpolation

• Sinc interpolation retains more high frequency information.
• Computation very time consuming (in theory, infinite extent)
• FSL: Windowing option limits extent
• SPM: Splines are used for rapid approximation
• Not necessary if you will heavily blur your data with a broad smoothing kernel.

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Windowed 2D Sinc Function

Asymmetric

1D Sinc Function

Symmetric

Resampling

• Reslicing always loses information.
• Nearest neighbor has severe artifacts
• Linear interpolation gets blurry.
• Windowed sinc functions often show subtle ringing near edges.

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Source

1x10°

2x10°

Nearest Neighbor

36x10°

Linear

Sinc�(Lanczos)

• Cumulative: consecutive reslicing leads to more dramatic artifacts.
• Solution: whenever possible, apply transforms to image matrix (lossless) rather than reslicing data (lossy).
• Solution: use sinc interpolation if high frequencies important.

Palette indexed images

• Nearest Neighbor
• Never use with MRI scans (or any continuous data).
• Useful for atlases that use indexed palette.
• E.G. For Brodmann Atlas, a region at the border of areas 37 and 39 should not be labelled ‘area 38’

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Source

Zoomed �(Linear Interpolation)

Continuous

Palette

n.b. errors at edges

Interpolation summary

• Nearest Neighbor
• Paletted images
• Linear interpolation
• Default option
• Sinc/Spline interpolation
• When edges are critical

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1D kernels

2D kernels

Nearest Neighbor

Linear

Sinc

Interpolation versus smoothing

• Interpolation kernel is always 100% at 0 and 0% at all other integers.
• This means that interpolated estimates always cross through control points (observations).
• Smoothing kernels blur an observation with its neighbors thereby lowering intensity maxima.

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Interpolation

Smoothing

Kernel

Observations

Spatial Smoothing

• Each voxel is noisy. However, neighbors tend to show similar effect. Smoothing results in a more stable signal.
• Smoothed data more normal – fits our assumptions. Also, allows RFT thresholding (statistics lecture). Minimizes sulcal variability between individuals (group analysis)

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=

Gaussian Smoothing

How much to smooth - FWHM

• Smoothing is a form of convolution: the output intensity based on weighted-influence of neighbors.
• The most popular kernel is the gaussian function (a normal distribution).
• The ‘full width half maximum’ adjusts the amount of gaussian smoothing.
• FWHM is a measure of dispersion (like standard deviation, standard error or variance)
• Large FWHMs lead to more blurry images.
• For fMRI, we typically use a FWHM that is ~x2..x3 our original resolution (e.g. 8mm for 3x3x3mm data).
• However, the FWHM tunes the size of region we will be best able to detect.
• E.G. If you want to look for a brain region that is around 10mm diameter, use a 10mm FWHM.

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Dispersion Differs

Smoothing Limits Inference

• Consider a study that observes ‘increased’ activation for strong versus weak motor movements.
• After smoothing we can not distinguish between:
• Recruitment of more neighboring neurons (bar on right)
• Increased activation of the same population of neurons (bar on left)

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2D

1D

Example: note that after smoothing broad low contrast looks line looks like focused high contrast line.

None 10pixel 20pixel

Smoothing Amount

Smoothing Alternatives

• Gaussian smoothing is great for ‘normal’ (Gaussian) noise: lots of small errors, very few outliers.

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• Gaussian poor for spike noise
• Outlier contaminates neighbors
• Alternatives if your data has spikes:
• Median filters
• FSL’s SUSAN

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Gaussian

Median Filter

Gaussian Noise

Gaussian Smooth

Spike Noise

FSL SUSAN: preserve edges, reduce noise

Spatial unwarping

• Objects distort magnetic field strength
• Shim attempts to create homogeneous field
• Impossible for regions with tissue interfaces: e.g. bone, air (sinuses) and brain all near orbital frontal cortex.
• Errors in shim (inhomogeneity) lead to spatial distortion & signal dropout.
• We can measure field homogeneity.
• Fieldmap can unwarp images (FSL’s B0 unwarping, SPM’s FieldMap).
• We can recover shape, but not lost signal.

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Intensity unwarping

• Motion correction creates a spatially stabilized image.
• However, head motion also changes image intensity – some regions of the brain will appear brighter/darker.
• SPM: EPI unwarping corrects for brightness changes (right)
• FSL: You can add motion parameters to statistical model (FEAT stats page).
• Problem: We will lose statistical power if head motion is task related, e.g. pitch head every time we press a button

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Above: motion related image intensity changes.

Image Matrices

• As noted, reslicing data to a grid will lose information.
• A matrix with 12 numbers can store the consequences of an infinite number of affine transforms without requiring any reslicing.
• Each NIfTI image records its own transformation matrix.
• Understanding matrix math is useful for neuroimaging (e.g. it is the ‘Mat’ in SPM’s Matlab).

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Example NIfTI Affine transform viewed with MRIcron.

Vectors

• Vectors have a direction and a length
• The 2D vector [1,0] points East and has a length of 1
• The 2D vector [0,1] points North and has a length of 1
• The 2D vector [1,2] points North-East and has a length of 2.23
• 2D: two values [x,y], 3D: three values [x,y,z]

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1, 0

0, 1

1, 2

2D Rotation matrix

• 2D rotation matrix as two vectors (horizontal and vertical)
• Can be described by four numbers

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1, 0

0, 1

1, 0

0, 2

.7,-.7

.7, .7

Original

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Zoom: ‘Scale’

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Rotation

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1, 0

1, 1

Shear

-1, 0

0, 1

-Zoom: ‘Flip’

2D Transformation matrix

• Transformation matrix is a rotation matrix plus translation values (encodes x,y origin of vectors)

n.b. for computations we use 9 values, final row is always 0 0 1 (must have as many rows as columns).

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1, 0, 0

0, 1, 0

0, 0, 1

Original

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1, 0, 1

0, 1, 0

0, 0, 1

2, 0, .2

0, 1, .2

0, 0, 1

Translated+Zoom

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Translated

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All affine transforms can be combined into a single matrix

3D Matrices are 4x4

• We can generate 4x4 matrices that will allow us to work with 3D images.
• A 4x4 matrix, but the last row always ‘0 0 0 1’

fx = (x*i)+(y*j)+(z*k)+l

fy = (x*m)+(y*n)+(z*o)+p

fz = (x*q)+(y*r)+(z*s)+t

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Matrices and 3D space

• 3D matrices work just like 2D matrices
• The identity matrix still has 1’s along the diagonal
• Translations are the values in the final column (constants)
• Zooms are done by scaling values of a row.
• Shears are values added to the relevant orthogonal value
• Rotations use sine/cosine in dimensions of plane.
• Our twelve numbers can store all of the possible rotations, shears, translations and scaling.
• Simply multiply previous matrix with our transform.
• ‘Not commutative’: order crucial: to undo operations we need to put opposite values in reverse order (e.g. 30° rotation followed by X shear 1.2 can be undone by X shear of -1.2 followed by -30° rotation.

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Transform Matrix and Filtering Demo

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Select your operation: shear, zoom, rotate and translate.

Order crucial: e.g. 30° rotate: X shear 1.2: -30 ° rotate: X shear -1.2 does not return to source

Add up to 8 successive transforms

Choose an interpolation or smoothing filter.

Filter Kernel

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Transformation Matrix

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Settings for Current Transform

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Source Image

Transformed Image

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Specify Additional Transforms

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Transformed

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Source

​

Amount

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Function

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Select function: gaussian blur, perspective, intensity gradient, gaussian noise, median filter, fisheye.

‘Combine’ overlays two images (mean, difference, absolute difference, difference²).

Select amount, e.g. blur with 10-pixel FWHM.

Save results to create new source images.

E.G. save gaussian noise, clean up with blur.

E.G. Save blur, use combine for difference with source – result is edge map (unsharp mask)

‘Rotation’ illustrates consequence of successive reslicing (e.g. linear vs sinc filter).

Transformed 2D image and 1D cross-section shown in the right column

Temporal Processing

• Chris Rorden
• Temporal Processing can reduce error in our model
• Slice Time Correction
• Temporal Autocorrelation
• High and low pass temporal filtering
• Temporal Derivatives

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Slice Timing Problem

• 3D EPI volume composed of a stack of 2D slices.
• Each slice acquired at a different timepoint.

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Time

TR

The slice timing problem

• Each 2D slice like a photograph.
• Each 2D slice within a 3D volume taken at different time.
• Hemodynamic response changes with time.
• Therefore, we need to adjust for slice timing differences.

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Why slice time correct?

• Consider 3D volumes collected as ascending axial slices
• For each volume, we see inferior slices before superior slices

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Statistics assume all slices are seen simultaneously…

Time

Time

Slice timing correction

• Timing of early slices weighted with later image of same slice
• Timing of late slices is balanced with previous image of same slice
• Result: each volume represents single point in time
• Typically, volume corrected to mean volume image time (estimate time of middle slice in volume)

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Timef