Inferences with fMRI, Atlas Construction

A Big Thanks To

Prof. Jason BohlandQuantitative Neuroscience LaboratoryBoston University

Istavan (Pisti) Morocz, Harvard, MNI

Firdaus Janoos, OSU/Harvard,MIT/Exxon

Sources

http://neufo.org/lecture_events

Classical fMRI Pipeline

SPM-type approachTime-domain linear models dominate fMRI analysis

- Massively univariate approach - estimate model parameters at each voxel

- Compute test statistic at each voxel- threshold, controlling for error rate

- Yields statistical parametric maps (SPMs) across voxels

Time-domain linear model: 2, 0,i ii

y t x t t t N

y X

design matrix: encodes predicted response and covariates

Per Voxel Design MatrixConstructed contains explanatory variables / regressors

(columns)– For each column, a regression coefficient (beta) is

estimatedDesign matrix X

- Regressors are convolved with anticipated HRF to better fit observed data

- highly correlated or linearly dependent regressors will impact model estimability- one design matrix per voxel, usually identical

x t s t h

Convolution With HRF

EstimationParameter estimation:

– Assumes ε is independently and identically distributed ~ N(0,σ2I)

– Regressors are linearly independent– Effects of interest are independent of random error

Betas alone tell us very little without an estimate of error

Residual error is computed at each voxel:

1ˆ T TX X X y

ordinary least squares

ˆˆ Y X

InferenceContrasts:

A contrast - a linear combination of the parameters based on a particular hypothesis – is used to infer effects of interest

“Did some voxels show a larger effect for condition A than condition B”- use contrast vector c = [1 -1]

Calculate one-tailed t-statistic (N-rank(X) d.o.f.)Ratio of to estimate of its standard error

(based on residual sum of squared error)

A (uncorrected) p-value is obtained at each voxelAlso derive F test: does xi model anything?

ˆTc

ˆTc

1

ˆ

ˆˆ ˆ

T

T T T

c

N p c X X c

2, 0,i ii

y t x t t t N

y X

Statistical Threshold

Slide from Duke University course notes

A B C

t = 2.10, p < 0.05 (uncorrected) t = 3.60, p < 0.001 (uncorrected) t = 7.15, p < 0.05, Bonferroni Corrected

Multiple comparisons

Multi-subject Studies

MR images obtained from http://www.oasis-brains.org

Combining results across subjects is made difficult by individual brain variability

Multi-subject StudiesInter-subject averaging typically takes

one of 2 forms:1. Spatial normalization – warping of each (hi-resolution,

T1-weighted anatomical) brain volume to a standard template– Attempts to align same areas across subject (to voxel

level?)– Adds argument for utility of spatial smoothing– By far the most commonly used method6 different brains registered using 12-parameter affine

transformation with least squares cost function

From Ashburner and Friston (2003) in Human Brain Function, Volume 2

Multi-subject Studies2. Region of interest (ROI) analysis

– Effects from voxels in pre-defined ROIs are collapsed to a small set of components (e.g. Fourier coefficients)

– Comparison across subjects is at the region level– Sidesteps problems w/ spatial normalization– still assumes function follows anatomy

Nieto-Castanon et al., 2002

Spatial NormalizationOne often wants to understand properties of a

population:Approach: Register or spatially normalize the subjects such that

they are in a common coordinate space (reduce individual variability)

Typically warp each subject to a template image in stereotactic space

The assumption here is that registering size, shape, voxel intensity, curvature profiles, etc. will bring the local effect of interest into alignment across subjects

Approach 1 (landmark-based):• Identify (perhaps manually) some

set of corresponding features in each brain

• Scale individual brains in order to bring those landmarks into alignment

Approach 2 (intensity-based / densitometric):

• Optimize the parameters of a registration model s.t. the intensities of a (template) target image and the transformed source image match well.

Talairach’ingUser-defined landmarks (subjective)• xy plane defined by the superior extent of the anterior commissure (AC) and

the inferior extent of the posterior commissue (PC) • yz plane defined by hemispheric midline• Lateral, anterior, and posterior extents of brain• Origin: intersection of AC-line, midsagittal plane, and AC-PC plane

AC PC

Talairach’ingUser-defined landmarks (subjective)• xy plane defined by the superior extent of the anterior commissure (AC) and

the inferior extent of the posterior commissue (PC) • yz plane defined by hemispheric midline• Lateral, anterior, and posterior extents of brain• Origin: intersection of AC-line, midsagittal plane, and AC-PC plane

Surface-Based modelsReal geometry of cortex is essentially a 2-D sheet Volumetric approaches do not use this information!

TOOLS: CARET, FREESURFER, BRAINVISA, SUMA

From Fischl et al., 1999

Free Surfer Spherical RegistrationFollowing surface extraction, each hemisphere can be inflated to

a unit sphere while:– Preserving topological structure (local connectedness)– Minimizing metric distortion– Maintaining average curvature indices

Subjects are then aligned to an average in the spherical space s.t. mean squared convexity differences are minimized while also minimizing metric distortions.

– Considers entire curvature profile (not specific gyri / sulci)– But emphasizes consistent curvature features “for free”

Fischl et al., 1999

Multi-subject studiesGroup inference:

Correct inferences about the population require a 2nd level analysis (treat individuals as random variables)

Perform statistical test across individual summary statistics (e.g. “contrast images” computed at 1st level for each subject)

Non-parametric tests may be preferred for low N• Much weaker assumptions than SPM• Permute condition labels• Compute test statistic (e.g. mean effect) for

each permutation• Compare observed test statistic to random

distributionsee Nichols and Holmes (2002) and SnPM

toolbox.

ˆTc

What else ?Atlases – Can we build Atlases for

populations ?

Network analysis – what does the correlation structure across brain space tell us?

Analysis of spontaneous BOLD signals (“resting state”)

Machine Learning – do evoked BOLD patterns predict stimulus, behavior, etc?

Brain Voyagerhttp://gallantlab.org/semanticmovies/

Harvard Whole Brain Atlas http://www.med.harvard.edu/AANLIB/

“A bound collection of maps”In practice it tells you where you

are

Provide a common reference frame

Unify multiple diverse data modalities

Allow for dimensionality reduction / clustering of data

Establish a language / taxonomy of brain parts

Usually created from a single studied brain

Often take the form of cartoon labels and arrows

Human Brain Atlases

There are multiple bases for parcellating cortex, e.g.1. Cytoarchitecture2. Chemoarchitecture3. Connectivity profiles4. Folding patterns

MRI is the vehicle for most modern neuroanatomy…which features are identifiable from typical T1-weighted

structural MRI images?typically ~256x256x128 voxel volumes (~1mm resolution)

Brain Parcellation

Colorized version of Brodmann (1909)http://spot.colorado.edu/~dubin/talks/brodmann/brodmann.html

Adaptation of von Economo and Koskinas (1925) From Triarhou (2007)

CytoArchitectonic Parcellations

http://www.brain-map.org

Template space brain atlases

Examples: Automated anatomical labeling (Tzourio-Mazoyer, 2002); ICBM Template

•Deform individual anatomy to atlas (MNI-space)•“read off” anatomical labels from a parcellation of a single

subject in that space (assumes corresponding structures are aligned)

Probabilistic Brain AtlasesLPBA40

• 56 structures manually outlined in 40 normal subjects, registered to ICBM452 space (with different methods)

ANATOMY TOOLBOX• Cytoarchitectonic regions

determined from 10 post-mortem brains, non-linearly morphed into ICBM152 space

Eickhoff et al. (2002). Image from Art Toga, LONI

Brain Atlas ConcordanceThe nomenclature problem is long-standing in

neuroscience People tend to think (and report) in regions, not

coordinatesIn fMRI, we have a chance to address this

quantitatively by comparing different atlases delineated in a common template (MNI-305) space Atlas

AAL

ICBMLPBA

H-O

T&GTALcTALg

CYTO

# Regions (LH) Brief Description

Manual parcellation of Colin27 atlas

Maximum likelihood cytoarchitectonic atlas in MNI space

Maximum likelihood atlas from manually labeled scans

Individual parcellation of Colin27 atlas

Maximum likelihood from manually labeled scans (SPM registered)

Freesurfer-classified individual atlas, tweaked by human expert

Brodmann’s area labels mapped to MNI space with icbm2spm

Gyrus-level Talairach atlas mapped to MNI as above

6229564929656849

Bohland et al. (2009), PLoS ONE

Parcellations As SetsWhat is a parcellation system? - a partitioning of the brain into a finite set of disjoint

“regions”

where each region is itself a set of locations (e.g. voxels, vertices, triangles, etc.)

cf. elementary micro-area (Stephan, Zilles, Kötter, 2000)

Compare with Reference Atlas Reference atlases here are “flat” parcellations

with 12 or 94 regionsSimilarity index (S)

max ,ij ij jiX P P

min , if 0

0 otherwisei j ij

ij

ijij

ij

r r XU

UW

U

1 4 1ij ij ijij

S W X X

ranges from 0-1

Overlap saturating at K > 30

Clusters for large K are subdivisions of those for low K

Comparison methodsMultiple measures of region overlap may be defined:

Non-symmetric:

e.g. the proportion of region i from parcellation R contained in region j from parcellation R’

Symmetric:

e.g. the spatial overlap relative to the geometric mean of the 2 region sizesBoth measures are normalized and bounded ( between 0 and 1 )

i j

'( | )ijP x r x r

Cij

ICBM: superior temporal gyrus (100%)T&G: aSTg (94%)T&G: pdSTs (88%)CYTO: TE-1.2 (87%)H-O: STG anterior division (86%)T&G: adSTs (83%)T&G: pSTg (82%)

ICBM: superior temporal gyrus (100%)LPBA: superior temporal gyrus (72%)TALg: superior temporal gyrus (47%)AAL: middle temporal gyrus (36%)AAL: superior temporal gyrus (33%)AAL: temporal pole (22%)TALg: middle temporal gyrus (17%)

Single example:“Superior Temporal” region from the ICBM atlas

This matrix has non-zero entry for any pair of regions (from 8 atlases) that overlap

Bohland et al. (2009). PLoS ONE

HARV

ARD

OXFO

RD A

TLAS

LPBA40 ATLAS

All connectionsEdges encode max(Cij, Cji)

HARV

ARD

OXFO

RD A

TLAS

LPBA40 ATLAS

Eij < 0.25 pruned

After pruning

1000 random pairs used in simulations

Green values are similarity scores above 95th percentile

Global Atlas Similarity

max ,ij ij jiX C C

min , if 0

0 otherwisei j ij

ij

ijij

ij

r r XU

UW

U

1 4 1ij ij ijij

S W X X

Precentral

Frontal_Sup

Frontal_Sup_Orb

Frontal_Mid

Frontal_Mid_Orb

Frontal_Inf_Oper

Frontal_Inf_Tri

Frontal_Inf_Orb

Rolandic_Oper

Supp_Motor_Area

Olfactory

Frontal_Sup_Medial

Frontal_Mid_Orb

Rectus

Insula

Cingulum_Ant

Cingulum_Mid

Cingulum_PostHippocampus

ParaHippocampal

Amygdala

Calcarine

Cuneus

Lingual

Occipital_SupOccipital_Mid

Occipital_Inf

Fusiform

Postcentral

Parietal_Sup

Parietal_Inf

SupraMarginal

Angular

Precuneus

Paracentralobule

Caudate

Putamen

Pallidum

Thalamus

Heschl

Temporal_Sup

Temporal_Pole_Sup

Temporal_Mid

Temporal_Pole_Mid

Temporal_Inf Cerebelum_Crus1

Cerebelum_Crus2

Cerebelum_3

Cerebelum_4_5

Cerebelum_6

Cerebelum_7bCerebelum_8

Cerebelum_9

Cerebelum_10

Vermis_1_2

Vermis_3

Vermis_4_5

Vermis_6

Vermis_7

Vermis_8Vermis_9

Vermis_10

Amygdala

AnteriorCommissure

AnteriorNucleus

Brodmannarea1

Brodmannarea10Brodmannarea11

Brodmannarea13

Brodmannarea17

Brodmannarea18

Brodmannarea19

Brodmannarea2

Brodmannarea20Brodmannarea21

Brodmannarea22

Brodmannarea23

Brodmannarea24

Brodmannarea25

Brodmannarea27

Brodmannarea28Brodmannarea29

Brodmannarea3

Brodmannarea30

Brodmannarea31

Brodmannarea32

Brodmannarea33

Brodmannarea34

Brodmannarea35

Brodmannarea36

Brodmannarea37

Brodmannarea38

Brodmannarea39

Brodmannarea4

Brodmannarea40Brodmannarea41

Brodmannarea42

Brodmannarea43

Brodmannarea44

Brodmannarea45

Brodmannarea46

Brodmannarea47

Brodmannarea5

Brodmannarea6

Brodmannarea7

Brodmannarea8

Brodmannarea9

CaudateBody

CaudateHead

CaudateTail

CorpusCallosum

Dentate

Hippocampus

Hypothalamus

LateralDorsalNucleus

LateralGeniculumBody

LateralGlobusPallidus

LateralPosteriorNucleus

MammillaryBody

MedialDorsalNucleus

MedialGeniculumBody

MedialGlobusPallidus

MidlineNucleus

OpticTract

Pulvinar

PutamenRedNucleus

SubstaniaNigra

SubthalamicNucleus

VentralAnteriorNucleus

VentralLateralNucleus

VentralPosteriorLateralNucleus

VentralPosteriorMedialNucleus

AngularGyrus

AnteriorCingulate

Caudate

CerebellarLingual

CerebellarTonsil

CingulateGyrus

Claustrum

Culmen

CulmenofVermis

Cuneus

Declive

DecliveofVermis

Extra-Nuclear

Fastigium

FourthVentricle

FusiformGyrus

InferiorFrontalGyrus

InferiorOccipitalGyrus

InferiorParietalLobule

InferiorSemi-LunarLobule

InferiorTemporalGyrus

Insula

LateralVentricle

LentiformNucleus

LingualGyrus

MedialFrontalGyrus

MiddleFrontalGyrus

MiddleOccipitalGyrusMiddleTemporalGyrus

Nodule

OrbitalGyrus

ParacentralLobule

ParahippocampalGyrus

PostcentralGyrus PosteriorCingulate

PrecentralGyrus

Precuneus

Pyramis

PyramisofVermis

RectalGyrus

SubcallosalGyrus

SuperiorFrontalGyrus

SuperiorOccipitalGyrus

SuperiorParietalLobule

SuperiorTemporalGyrus

SupramarginalGyrus

Thalamus

ThirdVentricle

TransverseTemporalGyrus

Tuber

TuberofVermisUncus

Uvula

UvulaofVermis

AnteriorLobe

FrontalLobe

Frontal-TemporalSpace LimbicLobe

Medulla

Midbrain

OccipitalLobe

ParietalLobe

Pons

PosteriorLobe

TemporalLobe

AG

aCG

pCGaCO

SFg

aMFg

iFo

iFt

FMC

FO FOC

FP

H

aINS

pINS

pSMA

LG

OC

PCNaPH

pPH

PO

PP

PT

SCC

aSMg

pSMgSPL

aSTg

aMTg

aITgpSTg

pMTg

pITgaTF

pTF

MTOITO

TOF

TP

aSMA

vMC

dMC

adPMC

mdPMC

pdPMC

vPMC

adSTs

avSTs

pdSTs

pvSTs

vSSCpCO

dSSC

pMFg

lVent

ilVent

CBw mCBctx

Tha

Caud

Put

Pal

BrSt

Hipp

Amyg

Acc

vDC

VENTRAL_ANTERIOR_NUCLEUS

DORSO-MEDIAL_NUVENTRAL

LATERO-DORSAL_NUCLEUS

LATERAL_GENICULATE_NUCLEUS

LATERAL_POSTERIOR_NUCLEUS

GLOBUS_PALLIDUS_PARS_INTERNA

PUTAMEN

GLOBUS_PALLIDUS_PAR_EXTERNA

CENTROMEDIAN_NUCLEUS

VENTRAL_LATERAL_NUCLEUS

PARAHIPPOCAMPAL_GYRUS

VENTRAL_POSTEROLATERAL_NUCLEUS

SUPRAMARGINAL_GYRUS

SUPERIOR_FRONTAL_GYRUS

PRECENTRAL_GYRUS

CINGULATE_GYRUS

MIDDLE_FRONTAL_GYRUS

SUPERIOR_TEMPORAL

INFERIOR_FRONTAL_GYRUS

INFERIOR_OCCIPITAL_GYRUS

MEDIAL_GENICULATE_NUCLEUS

CUNEUS

LATERAL_FRONTO-ORBITAL_GYRUS

ANTERIOR_NUCLEUS

INSULAR_CORTEX

SUPERIOR_PARIETAL_GYRUS

CAUDATE_NUCLEUS

PRE-CUNEUS

BRAIN_STEM

MIDDLE_TEMPORAL_GYRUS

CEREBELLUM

LINGUAL_GYRUS

VENTRAL_POSTERIO-MEDIAL_NUCLEUS

POSTCENTRAL

MIDDLE_FRONTO-ORBITAL_GYRUS

GYRUS_RECTUS

HIPPOCAMPUS

FUSIFORM_GYRUS

SEPTAL_NUCLEI

ENTORHINAL_AREA

MIDDLE_OCCIPITAL_GYRUSINFERIOR_PARIETAL_LOBULE

INFERIOR_TEMPORAL

SUBCALLOSAL_AREAMAMMILLARY_BODIES RED_NUCLEUS

MEDULLA

AMYGDALA PONS

Hipp-CA

OP-1

Area-45

hiP2

Amyg-CM

Area-4a

TE-1.0

Hipp-ECArea-3b

Area-17

Amyg-SF

OP-3

Area-44

hOC5-V5-MT+

Hipp-FD

Area-4p

Area-1

hiP1

Area-18

TE-1.1

Hipp-HATA

OP-2

Area-6

Amyg-LB

Area-3a

Area-2

TE-1.2OP-4

Hipp-SUB

AALTALT&GICBMCYTO

subcortical

cerebellum

○ AAL○ TAL○ T&G○ ICBM○ CYTO