Large, High-Dimensional Data Sets in Functional Neuroimaging

©2012 Mark Cohen, all rights reserved www.brainmapping.org

Large, High-Dimensional Data Sets in Functional Neuroimaging

1www.brainmapping.org©2012 Mark Cohen, all rights reserved

Goals of Functional Neuroimaging■ Identify Regional Specializations of the Brain

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www.brainmapping.org©2012 Mark Cohen, all rights reserved

Goals of Functional Neuroimaging■ Identify Regional Specializations of the Brain

❏ Basic Science Questions❏ Medical or Surgical Intervention

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Language

Topology

Velocity

Location

Color

Identity

Direction

Texture

Vision


Goals of Functional Neuroimaging■ Identify Regional Specializations of the Brain■ Understand Network Connectivity

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Physical Temporal Information



■ Understand Multiple Levels of Organization

5 www.brainmapping.org©2012 Mark Cohen, all rights reserved

Levels of Understanding

fMRI-EEG

Fiber Tracingregional connectivity

fMRI - functional nuclei or processing centers

EEG & Autoradiographycell assemblies

Multi-unit Recordinglocal circuits: columns, retina…

Single Unit Electrophysiologyaction potentials, chemomodulation

Crystallography, Chromatography (etc…)transmitters, ion channels, membrane proteins

fMRI-EPhys

The Big Problem isn’t sparse...



■ Understand Multiple Levels of Organization■ Understand the Structure of Human Cognition


Neuroimaging Tools

■ Positron Emission Tomography (PET)■ functional MRI (fMRI)

■ Electro-encephalography (EEG)■ Magneto-encephalography (MEG)

■ Near Infrared Spectroscopy (NIRS)■ …

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Positron Emission Tomography (PET)

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outside inside

Note: Recon similar to CT


Positron Emission Tomography (PET)

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Phelps, Mazziotta, et al.

–

=


Tractography

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40 µm

up to 1m

www.brainmapping.org©2012 Mark Cohen, all rights reserved 12

fMRI

explores intensity variations in MR signal

intensity variations reflect venous [O2]


Traditional MRI Analysis - Model Driven

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Task Timing

Observed Signals


Traditional MRI Analysis - Model Driven

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HemodynamicResponse Model

z=5

z=1.5

Signal Model

Task Model


Model-Free MRI Analysis


Independent Components Analysis (ICA)

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http://www.fmrib.ox.ac.uk/fslcourse/lectures/melodic.pdf

Spatial ICA for fMRI

# ICs

Time

# ICs Location (space)

IC Spatial Maps

Time

Location (space)

Scan #k

fMRI ImageData

impose spatialindepedencedata are decomposed into a set of

spatially-independent maps and a set of time courses.


ICA Exposes Functional Networks


EEG: Hans Berger

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EEG vs. Magnetoencephalogaphy (MEG)


EEG vs. Magnetoencephalogaphy (MEG)

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EEG

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Creutzfeld Jacob (prion) disease Left parieto-posterior temporal spikes during drowsiness


EEG

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with Steve Sands and Massoud Akhtari

Somatosensory Evoked Potentials


EEG/MEG■ EEG/MEG is generally difficult to interpret■ Physicians frequently fail to detect abnormalities

■ Electrical features are ambiguous■ Estimation of electrical sources from scalp Voltage is

underconstrained

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Near Infrared Spectroscopy (NIRS)


Neuroimaging Tools - Data Size/subject

■ Positron Emission Tomography (PET)❏ 128 x 128 x 12 ≈ 2E5 samples

■ functional MRI (fMRI)❏ 64 x 64 x 20 x 200 ≈ 1.6E7 samples, but...

■ Electro-encephalography (EEG)

■ & Magneto-encephalography (MEG)❏ 256 x 250samples/s x 600s ≈ 3.8E7 samples

■ Near Infrared Spectroscopy (NIRS)❏ 32 x 250 samples/s x 600s ≈ 4.8E6 samples

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Brain Reading

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Postulate: All interesting behavioral, affective, mental or cognitive states are the expression of, or reflected in, neural “activity”


Machine Learning in fMRI

Haxby, et al., Science 293:2426

Resulting maps are difficult to interpret.


Optimal Basis Selection

■ Efficient Machine Learning Dimensions Are:❏ Independent Measures (foot size + shoe size adds little)❏ Sparse - Ideally the minimum number needed to

categorize the data❏ Too Many Dimensions Results in Errors!

■ For Scientific Applications Dimensions Ideally Reflect Real Sample Properties and are Explanatory

■ What are the Right Dimensions for Neuroscience?


A (perhaps naïve) Model of Cognition

■ Multiple Networks are Concurrently Active■ Many Such Networks are Common Across People

■ Current Cognitive State Reflects the Contributions of all Currently Active Networks

■ Perhaps:❏ Current Cognitive State is the sum of Active Network Activity

CS = α1N1 +α2N2 +α 3N3 +…+α j N j .Where:

CS is the current cognitive stateNk is one among many networksαk is the “activity” level of the corresponding network CS and α are functions of time

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ICA Exposes Functional Networks


IC Dictionary Elements

“Categorization and Generation of group-wide independent components in fMRI using clustering.” A Anderson1, J Bramen, A Lenartowicz, P Douglas, C Culbertson, A Brody, MS Cohen. OHBM 2010

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IC’s as Classifier Dimensions

Network 3

Cognitive State Instance Network 1

Network 2

CS = α1N1 +α2N2 +α 3N3 +…+α j N j .


“I believe that the infidels must die.”

Belief

Why should belief and disbelief gate emotion and behavior in this way?

Why should uncertainty not do so?

“I believe a sandwich would be tasty now”

Beliefs are actions in potentia

Sam Harris


“I believe that the infidels must die.”

Belief

Beliefs are actions in potentia

Sam Harris


Operationalized Belief■ Autobiographical

You own a toaster oven.

■ Ethical

It is good to help people in need.

■ Factual

Sugar is sweet.

■ Geographical

Nevada borders California.

■ Mathematical

(45/3) + 25 = 40

■ Religious

Jesus was actually born of a virgin.

■ Semantic

“gigantic” means “huge”

S Harris, SA Sheth and MS Cohen, Annals of Neurology, 63(2): p. 141-147. 2008

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Belief Detector

PK Douglas, S Harris, A Yuille and MS Cohen, “Performance comparison of machine learning algorithms and number of independent components used in fMRI decoding of belief vs. disbelief.” NeuroImage, 56(2): p. 544-553. 2011.

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Disbelief

Channel 8 Channel 200Channel 19 Channel 145Belief

Disbelief

Belief

Diagnostic Non-informative


Wavelet Spectrogram: Optimal Sampling Schedule

■ Spectrogram Power Sampled at 20 ms Intervals■ Highly Ranked Channels Determine Feature Time Points■ Optimal “disbelief” Time Point 500 ms After Belief

❏ Consistent with Behavioral Data

time

frequency

time time time

frequency

Belief

Disbelief

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1 sec

Pamela Douglas, Edward LauAgatha Lenartowicz, Wei Li

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Concurrent EEG and fMRI

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1 sec


Observable signals

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Activity Observablewith fMRI

Activity Observablewith EEG

fMRI Signal

EEG Signal

Filter Processe.g. hrf

Noise Noise

Noise

CommonNeural

Substrate

Noise

Filter Processe.g. coherentactivity only

based on a figure by Dan Ruan


Multimodal Imaging

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α

β

■ The observed EEG is the linear sum of the underlying electrical activity:❏ Synchronous Activity (SA)❏Asynchronous Activity (AA)

■ The magnitude signal, |EEG|, is:

■ fMRI signal is (probably) a function of the sum:


EEG & fMRI Signal Strength

EEG = k SA + AA( )

fMRI = f SA+AA( ).

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EEG-fMRI Coupling - A Variety of Mechanisms?

Xia HongjingOrganization for Human Brain Mapping 2012

5s

5s


Tomographic EEG Projection

Wei Li, Edward LauPamela Douglas, Agatha Lenartowicz,

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What is Sparse in Functional Neuroimaging?


What is Sparse in Functional Neuroimaging?■ Pixel-level analysis■ Axonal (fiber) connections

■ Number of Brain States■ Blood flow responses w.r.t. driving functions

■ Resolvable Electrical Sources■ Number of “meaningful” networks

■ Shared Sources in Multimodal data

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Documents

Large, High-Dimensional Data Sets in Functional Neuroimaging