Transcript MBI-Machiraju-lecture8x - Ohio State Computer Science and

Inferences with fMRI,
Atlas Construction
A Big Thanks To 
Istavan (Pisti) Morocz, Firdaus Janoos,
Prof. Jason Bohland
OSU/Harvard,MIT/Exxon
Harvard,
MNI
Quantitative Neuroscience Laboratory
Boston University
Sources
http://neufo.org/lecture_events
Classical fMRI Pipeline
SPM-type approach
Time-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
y  t    xi  t  linear
 i    t model:
,   t  N  0, 2 
i
y  X  
design matrix: encodes predicted response and
covariates
Per Voxel Design Matrix
Constructed contains explanatory variables / regressors
(columns)
– For each column, a regression coefficient (beta) is
- Regressors
are convolved
estimated
with anticipated HRF to better
fit observed data
x  t   s  t   h  
- highly correlated or linearly
dependent regressors will
impact model estimability
- one design matrix per voxel,
usually identical
Design matrix X
Convolution With HRF
Estimation
Parameter estimation:

ˆ  X T X

1
XT y
ordinary least squares
– 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:
ˆ  Y  ˆ X
Inference
y  t    xi  t   i    t  ,   t 
N  0, 2 
i
y  X  
Contrasts:
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]
cT ˆ
Calculate one-tailed
t-statistic (N-rank(X) d.o.f.)
cT ˆ
Ratio of
to estimate of its standard error
(based on residual
sum of squared error)
cT ˆ



ˆ ˆ  N  p  c ˆ X T X
T
T

1
c
A (uncorrected) p-value is obtained at each voxel
Also derive F test: does xi model anything?
Statistical Threshold
B
A
t = 2.10, p < 0.05 (uncorrected)
C
t = 3.60, p < 0.001 (uncorrected)
t = 7.15, p < 0.05,
Bonferroni
Corrected
Multiple comparisons
Multi-subject Studies
 Combining results across subjects is made difficult by individual
brain variability
MR images obtained from http://www.oasis-brains.org
Multi-subject Studies
Inter-subject averaging typically takes one of 2
forms:
1. Spatial normalization – warping of each (hi-resolution, T1weighted 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 method
6 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 Studies
2. 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 Normalization
One 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
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.
The assumption here is that
registering size, shape, voxel
intensity, curvature profiles, etc.
will bring the local effect of
interest into alignment across
subjects
Talairach’ing
User-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
Talairach’ing
User-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 models
Real 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
Registration
Following 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 studies
Group inference:
Correct inferences about the population require a 2nd level
analysis (treat individuals as random variables)
Perform statistical test across individual summary statistics
cT ˆ
(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
distribution
see Nichols and Holmes (2002) and SnPM toolbox.
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
Brain Voyager
http://gallantlab.org/semanticmovies/
Human Brain Atlases
“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
Harvard Whole Brain Atlas http://www.med.harvard.edu/AANLIB/
Brain Parcellation
There are multiple bases for parcellating cortex, e.g.
1.
2.
3.
4.
Cytoarchitecture
Chemoarchitecture
Connectivity profiles
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)
CytoArchitectonic Parcellations
Colorized version of Brodmann (1909)
http://spot.colorado.edu/~dubin/talks/brodmann/brodmann.html
Adaptation of von Economo and Koskinas (1925)
From Triarhou (2007)
http://www.brain-map.org
Template space brain
atlases
• 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)
Examples: Automated anatomical labeling (Tzourio-Mazoyer, 2002); ICBM Template
Probabilistic Brain Atlases
LPBA40
ANATOMY TOOLBOX
• 56 structures manually outlined in
40 normal subjects, registered to
ICBM452 space (with different
methods)
• Cytoarchitectonic regions
determined from 10 post-mortem
brains, non-linearly morphed into
ICBM152 space
Image from Art Toga, LONI
Eickhoff et al. (2002).
Brain Atlas Concordance
The nomenclature problem is long-standing in
neuroscience
 People tend to think (and report) in regions, not coordinates
In fMRI, we have a chance to address this quantitatively
by comparing different atlases delineated in a common
template (MNI-305) space
Atlas
# Regions (LH) Brief Description
AAL
62
Manual parcellation of Colin27 atlas
CYTO
29
Maximum likelihood cytoarchitectonic atlas in MNI space
H-O
56
Maximum likelihood atlas from manually labeled scans
ICBM
49
Individual parcellation of Colin27 atlas
LPBA
29
Maximum likelihood from manually labeled scans (SPM registered)
T&G
65
Freesurfer-classified individual atlas, tweaked by human expert
TALc
68
Brodmann’s area labels mapped to MNI space with icbm2spm
TALg
49
Gyrus-level Talairach atlas mapped to MNI as above
Bohland et al. (2009), PLoS ONE
Parcellations As Sets
What is a parcellation system?
- a partitioning of the brain into a finite set of disjoint “regions”
R = {r1,r2 ,… ,rn }
where each region is itself a set of locations (e.g. voxels, vertices,
triangles, etc.)
ri = { x1, x2 ,… , xn }
cf. elementary micro-area (Stephan, Zilles, Kötter, 2000)
Compare with Reference
Atlas
Similarity index (S)
Reference atlases here are “flat” parcellations
with 12 or 94 regions



min  r , r 

X ij  max Pij , Pji
U ij
Wij 
i


j
0
if X ij  0
otherwise
U ij
U
ij
W X 1  X 
S  1 4
ij
ij
ranges from 0-1
ij
ij
Overlap saturating at K > 30
Clusters for large K are subdivisions of those for low K
Comparison methods
Multiple measures of region overlap may be defined:
Non-symmetric: Cij =
ri Ç rj
i
j
ri
e.g. the proportion of region i from parcellation R contained in region j
from parcellation R’
'
P( x  rj | x  ri )
Symmetric: Oij = O ji =
ri Ç rj
ri rj
= Cij C ji
e.g. the spatial overlap relative to the geometric mean of the 2 region
sizes
Both measures are normalized and bounded ( between 0 and 1 )
Cij
This matrix has non-zero entry for any pair of regions (from 8 atlases) that overlap
Single example:
“Superior Temporal”
region from the
ICBM atlas
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%)
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%)
Bohland et al. (2009). PLoS ONE
All connections
LPBA40 ATLAS
HARVARD OXFORD ATLAS
Edges encode max(Cij, Cji)
After pruning
LPBA40 ATLAS
HARVARD OXFORD ATLAS
Eij < 0.25 pruned
Global Atlas Similarity



min  r , r  if X

X ij  max Cij , C ji
U ij
Wij 
i


j
0
ij
0
otherwise
U ij
U
ij
W X 1  X 
S  1 4
1000 random pairs used in simulations
Green values are similarity scores above 95th percentile
ij
ij
ij
ij
SuperiorOccipitalGyrus
cerebellum
hOC5-V5-MT+
ITO
AngularGyrus
MTO
SupramarginalGyrus
Brodmannarea39
avSTs
aMTg
pvSTs
○
○
○
○
○
AAL
TAL AAL
T&GTAL
T&G
ICBM
ICBM
CYTO
CYTO
Occipital_Inf InferiorOccipitalGyrus
Brodmannarea17
InferiorTemporalGyrus
pMTg
AngularINFERIOR_PARIETAL_LOBULE
INFERIOR_OCCIPITAL_GYRUS
MIDDLE_OCCIPITAL_GYRUS
Brodmannarea42
CulmenofVermis
aITg
Brodmannarea37
adSTs
Tuber
Vermis_6
MiddleOccipitalGyrus
pSTg pdSTs
MiddleTemporalGyrus
Brodmannarea18
Occipital_Mid
InferiorParietalLobule
hiP2
Brodmannarea40
Temporal_Mid
FusiformGyrus
Brodmannarea41
Occipital_Sup
TOF
AG
Brodmannarea19
aSTg
INFERIOR_TEMPORAL
Cuneus
Dentate DecliveofVermis
Cerebelum_Crus1
Brodmannarea20
TE-1.1
MIDDLE_TEMPORAL_GYRUS
Temporal_Inf
TransverseTemporalGyrus
SPL Parietal_Inf
Brodmannarea21
pITg
OC
Declive
Uvula
SuperiorParietalLobule
pSMg
OccipitalLobe
aTF
PT
SupraMarginal
LateralGeniculumBody
Cerebelum_6
Pyramis
pTF
Brodmannarea36
SUPRAMARGINAL_GYRUS
CUNEUS
Brodmannarea22
Parietal_Sup
Brodmannarea1
Cerebelum_Crus2
CuneusTemporal_Pole_Mid Area-17 FUSIFORM_GYRUS
Vermis_7
aSMg
Fusiform
Temporal_SupSUPERIOR_TEMPORAL
Area-18
Brodmannarea2
Hippocampus
Calcarine
LINGUAL_GYRUS
LingualGyrus
TE-1.0
OP-1
PosteriorLobe
Area-2
ENTORHINAL_AREA
Cerebelum_4_5
Precuneus
PRE-CUNEUS
PO Brodmannarea5
Brodmannarea7
InferiorSemi-LunarLobule
SuperiorTemporalGyrus
SUPERIOR_PARIETAL_GYRUS
ParietalLobe
Brodmannarea23
CBctx
PostcentralGyrus
Brodmannarea30
CEREBELLUM
PosteriorCingulate
Culmen
CBw m CerebellarTonsil Cerebelum_7b
TemporalLobe
LG Lingual
aPH
Area-1
TE-1.2
AnteriorLobe
TP
Vermis_4_5
Cerebelum_8
OP-4
Heschl
PCN
PP
Brodmannarea38 Amyg-LB
H
pCO
Hipp-EC
Brodmannarea35
Brodmannarea3
CerebellarLingual
Brodmannarea28
Rolandic_Oper
Area-3b
vSSCPostcentral
POSTCENTRAL
Brodmannarea43
pPH
Precuneus
Brodmannarea29
Nodule
Amygdala
HIPPOCAMPUS
Vermis_9
OP-2
dSSC
MedialGeniculumBody
pINS
Cerebelum_3
LATERAL_GENICULATE_NUCLEUS
Uncus
Temporal_Pole_Sup
Vermis_8
TuberofVermis
ParahippocampalGyrus
Cerebelum_9
Insula
ParaHippocampal
PARAHIPPOCAMPAL_GYRUS
Hipp-SUB
Area-3a OP-3
INSULAR_CORTEX
Area-4p
Brodmannarea31 Cingulum_Post
Brodmannarea4
Vermis_3
Hipp-CA
Brodmannarea13
ilVent
Hippocampus
Cerebelum_10
Fastigium
pCG
Insula
Hipp
Area-4a aCO
PrecentralGyrus
ParacentralLobule
PONS
PyramisofVermis
AMYGDALA
Amygdala
Pons
Vermis_10
lVent
vMC
Claustrum
aINS
Frontal-TemporalSpace
Hipp-FD
Paracentralobule
LimbicLobe
Amyg
Midbrain
BrSt
LateralVentricle
Brodmannarea27
dMC
Pulvinar
PRECENTRAL_GYRUS
Hypothalamus
Vermis_1_2
BRAIN_STEM
Brodmannarea6
FrontalLobe
Extra-Nuclear
vPMC
Cingulum_Mid
CorpusCallosum
Brodmannarea44
Area-44
Amyg-SF
MEDULLA
CINGULATE_GYRUS
FourthVentricle
Hipp-HATA
CingulateGyrus
Precentral
Brodmannarea34
pdPMC
AnteriorCommissure
CaudateTail
UvulaofVermis
Area-6
PUTAMEN
Amyg-CM
Medulla
INFERIOR_FRONTAL_GYRUS
InferiorFrontalGyrus
Brodmannarea47
iFo
OpticTract
vDC
Frontal_Inf_Oper
Brodmannarea33
MedialGlobusPallidus
DORSO-MEDIAL_NUVENTRAL
Put
Putamen
MEDIAL_GENICULATE_NUCLEUS
Thalamus
FO
Brodmannarea9 Supp_Motor_Area
CENTROMEDIAN_NUCLEUS
FOC
aSMA pSMA
Frontal_Inf_Orb
SubcallosalGyrus
Area-45 aCG
SubstaniaNigra
VENTRAL_ANTERIOR_NUCLEUS
iFt
MIDDLE_FRONTO-ORBITAL_GYRUS Caudate
Frontal_Inf_TriLATERAL_FRONTO-ORBITAL_GYRUS
SEPTAL_NUCLEI
Olfactory
Tha
MedialFrontalGyrus
LateralGlobusPallidus
mdPMC pMFg
SubthalamicNucleus
Thalamus
LentiformNucleus
Putamen
MiddleFrontalGyrus
SUPERIOR_FRONTAL_GYRUS
RedNucleusVENTRAL_POSTEROLATERAL_NUCLEUS
MAMMILLARY_BODIES
Frontal_Mid
RED_NUCLEUS
Brodmannarea24
Brodmannarea45
Cingulum_Ant
VENTRAL_LATERAL_NUCLEUS VentralLateralNucleus
Brodmannarea8
Caud
SUBCALLOSAL_AREA
MIDDLE_FRONTAL_GYRUS
AnteriorCingulate
CAUDATE_NUCLEUS CaudateBody
Caudate
Frontal_Sup
SFg
MedialDorsalNucleus
FP
ANTERIOR_NUCLEUS
GLOBUS_PALLIDUS_PARS_INTERNA
SuperiorFrontalGyrus Frontal_Sup_Orb
RectusSCC
Pal
aMFg
ThirdVentricle
Acc
Frontal_Sup_Medial
Brodmannarea32
MammillaryBody
GLOBUS_PALLIDUS_PAR_EXTERNA
LATERAL_POSTERIOR_NUCLEUS
Pallidum
GYRUS_RECTUS
adPMC
VENTRAL_POSTERIO-MEDIAL_NUCLEUS
VentralPosteriorLateralNucleus
FMC
Frontal_Mid_Orb Frontal_Mid_Orb
Brodmannarea46
Brodmannarea25 CaudateHead
hiP1
Brodmannarea10
Brodmannarea11
VentralAnteriorNucleus
LATERO-DORSAL_NUCLEUS
VentralPosteriorMedialNucleus
AnteriorNucleus
RectalGyrus
MidlineNucleus
LateralPosteriorNucleus
OrbitalGyrus
LateralDorsalNucleus
subcortical