Computational Biology - Computer Science Departmentfeng/teaching/compbio_2015_I.pdf ·...

Computational Biology

Jianfeng Feng

Warwick University

(many slides are from Dr. M. Lindquist)

http://www.dcs.warwick.ac.uk/~feng/Comp_Biol.html

Brain Science with Big Data:

Data Acquisition, machine learning and networks

International brain projects: EU HBP, 1 B Euros

USA BRAIN, 4.5 B Dollars

Module Purposes

• Learn how to deal with big data in a concrete

example: a nice piece of work to demonstrate

the power and trouble of big data

• Understand how to tackle the most complex

organ in the universe

• Transfer skills: apply the same techniques to

other areas with big data

Outline (week 1 and 2)

1. Introduction

2. Basic MRI

3. Image Formation

4. K-space


1. Introduction

2. Basic MRI

3. Image Formation

4. K-space

5. fMRI signal and noise

6. fMRI data structure

7. Pre-processing


1. Introduction

2. Basic MRI

3. Image Formation

4. K-space

5. fMRI signal and noise

6. fMRI data structure

7. Pre-processing Able to use SPM to extract signals

first

secondthird

fouth?

Brain research

1831

1785

1970s

2020？AI

Are we facing another revolution?

Google brain

Apple Siri

Google NowDeepMind

Deep face

(Facebook)

Deep medicine

（J Rothberg & T Xu）

Google brain

(Andrew Ng)

Google

Automatic drive on Motoway

IBM

Watson

Microsoft

Automatic translations

Eugene Goostman

Past Turing test

Applications：Smart city, financial markets, medicine……

Foundations: This module

Brain-like AI：new revolution

2011

2012

2013

2014

Introduction to fMRI

behaviourbrainregionsmicorcircuitsNeuronssynapsesProtein

Genetics

Environments

Neuron

Neuron

The Architecture of the Neuron

Neuronal Activities

Vertical white bar: spike

soma

Dendrite

axon

synapse

Brain works in this way: Spiking neuronal network

Black dot: neuron

White dot: spike

The average of spikes is

called local field potential which is the signal we can measure

= average activity

of one time window

Rossoni E. et al. (2008), Plos Comp Biol.

Local field potential =

Can we understand our brain?

Can we observe neuronal activity?

Multi-billion Dollars Question

Brain Imaging

• In recent years there has been explosive interest

in using imaging techniques to explore the inner

workings of the human brain.

• Brain imaging data has found applications in a

wide variety of fields, such as psychology,

neuroscience, economics, political science,

and medicine.

• Brain imaging can be separated into two

major categories:

– Structural brain imaging

– Functional brain imaging

• There exist a number of different modalities

for each category.

Brain Imaging

Structural Brain Imaging

• Structural brain imaging deals with the study

of brain structure and the diagnosis of

disease and injury.

• Modalities include:

– computed axial tomography (CAT),

– magnetic resonance imaging (MRI),

– positron emission tomography (PET), and

– Diffusion tensor image (DTI)

MRI: your brain structure

Proton Density T1 T2

Principle: Different materials have different magnetic fields

real One modality another one

Functional Brain Imaging

• Functional brain imaging can be used to

study both cognitive and affective processes.

• Modalities include:

– functional magnetic resonance imaging (fMRI),

– electroencephalography (EEG), and

– magnetoencephalography (MEG).

fMRI: activation of your brain

Properties

• Each functional imaging modality provides a

different type of measurement of the brain.

• They also have their own pros and cons with regards

to spatial resolution, temporal resolution and

invasiveness.

• Functional MRI provides a nice balance between these

properties and has become the dominant functional

imaging modality in the past decade.

Functional MRI

• Functional magnetic resonance imaging (fMRI) is a

non-invasive technique for studying brain activity.

• During the course of an fMRI experiment, a

series of brain images are acquired while the

subject performs a set of tasks or at resting.

• Changes in the measured signal between

individual images are used to make inferences

regarding (task-related) activations or construct

networks in the brain.

fMRI Data

• Each image consists of ~100,000 'voxels' (cubic

volumes that span the 3D space of the brain).



fMRI Data



• Each voxel corresponds to a spatial location and

has a number associated with it that represents

its intensity (density or activity).

39

fMRI Data

• During the course of an experiment several

hundred images are acquired (~ one every 2s).

fMRI Data

2s 2s 2s

• Tracking the intensity over time gives us a time series.

TASK vs

fMRI Data

• Tracking the intensity over time gives us a time series.

TASK vs

fMRI Data

Sagittal view

BOLD fMRI

• The most common approach towards fMRI uses the

Blood Oxygenation Level Dependent (BOLD) contrast.

• BOLD fMRI measures the ratio of oxygenated to

deoxygenated hemoglobin in the blood.

• It is important to note that BOLD fMRI doesn’t measure

neuronal activity directly, instead it measures metabolic

demands (oxygen consumption) of active neurons.

fMRI Data

• fMRI data analysis is a massive data problem.

– Each brain volume consists of ~100,000 voxel measurements.

– Each experiment consists of hundreds of brain volumes.

– Each experiment may be repeated for multiple subjects

(e.g.,1000) to facilitate population inference.

• The total amount of data that needs to be analyzed isstaggering.

Statistical and Machine learning Analysis

• The statistical and machine learning

analysis of fMRI data is challenging.

– It is a massive data problem.

– The signal of interest is relatively weak.

– The data exhibits a complicated temporal and

spatial noise structure.

Our module

Preprocessing Data Analysis

Raw Data

Acquisition

Slice-time Correction

Motion Correction,Co-registration & Normalization

Spatial Smoothing

LocalizingBrain Activity

Applications:

Clinical

Imaging genetics

……..

Reconstruction

DTI

Data Processing Pipeline

Connectivity

Experimental

Design

Linear Model

Grangercausality

Localization (task)

• Determine which regions of the brain are active

during a specific task.

Connectivity (task or resting)

• Determine how different brain regions are

connected with one another.

Applications: Discriminations

• Use a person’s brain activity to diagnose

his/her disease status.

Classifier Pattern

Brain Activity

Predicted brain

disease

Cross-

product

Fun: DTI (diffusion tensor image)

• Determine how each brain region is connected via fibers (not covered)

Fun: male vs. female brain

Fun: Decoding dream (Horikawa et al. Science, 2013)

2: Basic MR Physics

1946 MR phenomenon - Bloch & Purcell*1952 Nobel Prize - Bloch & Purcell

1950-1970 NMR developed as analytical tool1972 Computerized Tomography-Hounsfield

1973 Back projection MRI - Lauterbur1975 Fourier Imaging (phase encording and frequency encording) - Ernst 1977 Echo-planar imaging - Mansfield

1980 FT MRI demonstrated - Edelstein 1986 Gradient Echo Imaging NMR Microscope 1987 MR Angiography - Dumoulin

*1991 Nobel Prize - Ernst

1992 Functional MRI 1994 Hyperpolarized 129Xe Imaging

*2003 Nobel Prize - Lauterbur & Mansfield

Magnetic Resonance Imaging


Pauli WE1945 Nobel PrizePhysics

Purcell EM1952 Nobel PrizePhysics

Bloch F1952 Nobel PrizePhysics

Isidor Rabi1944 Nobel PrizePhysics

1946 MR phenomenon - Bloch & Purcell 1952 Nobel Prize - Bloch & Purcell

1950-1970 NMR developed as analytical tool1972 Computerized Tomography-Hounsfield

1973 Back projection MRI - Lauterbur1975 Fourier Imaging (phase encording and frequency encording) - Ernst 1977 Echo-planar imaging - Mansfield

1980 FT MRI demonstrated - Edelstein 1986 Gradient Echo Imaging NMR Microscope 1987 MR Angiography - Dumoulin

1991 Nobel Prize - Ernst

1992 Functional MRI 1994 Hyperpolarized 129Xe Imaging

2003 Nobel Prize - Lauterbur & Mansfield



NATURE 242:190-191 IMAGE FORMATION BY INDUCED LOCAL INTERACTIONS -EXAMPLES EMPLOYING NUCLEAR MAGNETIC-RESONANCE

2003: Lauterbur and Mansfield won Nobel prize in Medicine

1977 MANSFIELD PJOURNAL OF PHYSICS C-SOLID STATE PHYSICS 10:L55-L58 MULTI-PLANAR IMAGE-FORMATION USING NMR SPIN ECHOES

1973 Lauterbur PC

/


An MR scanner consists of an electromagnet with a very strongmagnetic field (1.5 - 9.0 Tesla)

Earth’s magnetic field = 0.00005 Tesla

3 Tesla is 60,000 times stronger than the Earth’s magnetic field.

What MRI Measures

• MRI is an extremely versatile imaging modality thatcan be used to study both brain structure andbrain function.

• Both structural and functional MRI images are acquired using the same scanner.

• Different types of brain images can be generatedto emphasize contrast related to different tissuecharacteristics.

Principles of MRI

• All magnetic resonance imaging techniques rely

on a core set of physical principles.

• To understand we must begin by studying a

single atomic nuclei and illustrate its impact on

the generated MR signal.

• In particular we focus on hydrogen atoms

consisting of a single proton.

Protons can be viewed as positively charged spheres

which are always spinning. They give rise to a net

magnetic moment along the axis of the spins.

Principles of MRI

• We cannot measure the magnetization of a single

proton using MR, instead we measure the net

magnetization of all nuclei within a volume.

• The net magnetization M can be viewed as a

vector with two components.

– A longitudinal component parallel to the magnetic field.

– A transverse component perpendicular to the field.

Net Magnetization

Net Magnetization

A longitudinal component

A transverse component

an external magnetic field

In the absence of an external magnetic field, the

nuclear magnetic moments are randomly oriented.

There is no net magnetization.

Net Magnetization

When placed in a strong magnetic field, the nuclei align

with the field. This creates a net longitudinal

magnetization in the direction of the field.

Net Magnetization

The nuclei process about the field with an angular

frequency determined by the Larmor frequency but

at a random phase.

Net Magnetization

A radio frequency (RF) pulse is used to align the

phase and ‘tip over’ the nuclei. This causes the

longitudinal magnetization to decrease, and

establishes a new transversal magnetization.

Net Magnetization

• After the RF pulse is removed, the system seeks

to return to equilibrium.

• The transverse magnetization starts to disappear

(transversal relaxation),

and the longitudinal magnetization grows back

to its original size (longitudinal relaxation).

• During this process a signal is created that can

be measured using a receiver coil.

Relaxation

• Longitudinal Relaxation is the restoration of net

magnetization along the longitudinal direction as

spins return to their parallel state.

– Exponential growth described by time constant T1

• Transverse Relaxation is the loss of net

magnetization in the transverse plane due to loss

of phase coherence (resonance).

– Exponential decay described by time constant T2

Relaxation

Mz

Mo

tT1

63%

The restoration of longitudinal magnetization is

described by a time constant T1.

Longitudinal Relaxation Time

30002000100000.0

0.2

0.4

0.6

0.8

1.0

TR (msec)

Sig

na

l

white matter: T1 = 600gray matter: T1 = 1000Cerebrospinal fluid (CSF) : T1 = 3000

Longitudinal Relaxation Time

White matter and Gray matterWhite matter is a component of the central nervous system, in the brain and superficial spinal cord, and consists mostly of glial cells and myelinated axons that transmit signals from one region of the cerebrum to another and between the cerebrum and lower brain centers.

White matter tissue of the freshly cut brain appears pinkish white to the naked eye because myelin is composed largely of lipid tissue veined with capillaries. Its white color in prepared specimens is due to its usual preservation in formaldehyde.

Grey matter (or gray matter) is a major component of the central nervous system, consisting of neuronal cell bodies, neuropil (dendrites and myelinated as well as unmyelinated axons), glial cells (astroglia and oligodendrocytes) and capillaries.

Grey matter is distinguished from white matter, in that grey matter contains numerous cell bodies and relatively few myelinated axons, while white matter is composed chiefly of long-range myelinated axon tracts and contains relatively very few cell bodies.[1]

The color difference arises mainly from the whiteness of myelin. In living tissue, grey matter actually has a very light grey color with yellowish or pinkish hues, which come from capillary blood vessels and neuronal cell bodies.[2]

http://en.wikipedia.org/wiki/Central_nervous_system

http://en.wikipedia.org/wiki/Glial

http://en.wikipedia.org/wiki/Myelinated

http://en.wikipedia.org/wiki/Axons

http://en.wikipedia.org/wiki/Cerebrum

http://en.wikipedia.org/wiki/Myelin

http://en.wikipedia.org/wiki/Lipid

http://en.wikipedia.org/wiki/Capillaries

http://en.wikipedia.org/wiki/Formaldehyde

http://en.wikipedia.org/wiki/Central_nervous_system

http://en.wikipedia.org/wiki/Neuron

http://en.wikipedia.org/wiki/Soma_(biology)

http://en.wikipedia.org/wiki/Neuropil

http://en.wikipedia.org/wiki/Dendrites

http://en.wikipedia.org/wiki/Myelin

http://en.wikipedia.org/wiki/Axons

http://en.wikipedia.org/wiki/Glial_cell

http://en.wikipedia.org/wiki/Astroglia

http://en.wikipedia.org/wiki/Oligodendrocytes

http://en.wikipedia.org/wiki/Capillary

http://en.wikipedia.org/wiki/White_matter

http://en.wikipedia.org/wiki/Grey_matter#cite_note-Purves-1

http://en.wikipedia.org/wiki/Capillary

http://en.wikipedia.org/wiki/Grey_matter#cite_note-2

White matter and Gray matterWhite matter = fibers = axons which connect neurons

Grey matter (or gray matter)= neurons

CSF = something else

Mxy

37%

tT2

The decay of magnetization due to interaction

between nuclei is described by a time constant T2.

Transverse Relaxation Time

• By altering how often we excite the nuclei

(TR: repetition time) and how soon after

excitation we begin data collection (TE:

echo time) we can control which

characteristic is emphasized.

• The measured signal is approximately

where T1 and T2 depend tissue properties.

Image Contrast

)/exp())/exp(1( 210 TTETTRM

3. Image Formation

Image Formation

• The goal of MRI is to construct an image, or a matrix of numbers that correspond to spatial locations.

• The image depicts the spatial distribution of someproperty of the nuclei within the sample.

• This could be the density of nuclei of the tissuesin which they reside.

TR

Lo

ng

Sh

ort

Short Long

TE

ProtonDensity

T1

T2

Image Contrast

TE (echo time) -

the time between

excitation and

data collection.

)/exp())/exp(1( 210 TTETTRM

Signal Formation

• The subject is placed into the MR scanner.

– Nuclei of 1H atoms align with the magnetic field.

– The nuclei precess about the field at similar

frequencies, but at a random phase.

– Net longitudinal magnetization in the direction of field.

• Within a slice, a radio frequency (RF) pulse is used to align the phase and ‘tip over’ the nuclei.

– Causes the longitudinal magnetization to decrease,

and establishes a new transversal magnetization.

Signal Formation

• After the RF pulse is removed, the system seeks to returnto equilibrium.

– The transverse magnetization disappears (transversal

relaxation), and the longitudinal magnetization grows back to

its original size (longitudinal relaxation).

– Longitudinal relaxation: exponential growth described by

time constant T1.

– Transverse relaxation: exponential decay described by time

constant T2.

• During this process a signal is created that can be

measured using a receiver coil (MRI).

Signal Formation

fMRI Contrast T2*

• The image we are really interested in is called

T2* image

• T2* is the combined effect of T2 and local

inhomogeneities in the magnetic field.

• The scanner can be programmed to eliminate the

effects of these inhomogeneities, or alternatively

emphasize them.

• The latter types of procedures form the basis ofBOLD fMRI (Seiji Ogawa, another Nobel prize?)

Image Contrast

• Images can be produced that are sensitive

primarily to T1, T2 (T2*).

• Because T1 vary with tissue type, it is able to

represent boundaries between CSF, gray

and white matter.

• Because T2* is sensitive to flow and

oxygenation, it is can be used to image brain

function.

T1 and T2* Images

•From now on, we will concentrate these two types of images

•T1 will tell us about the anatomy(give an example to explain the use of it?)

•T2* will tell us the activity of a specific region

(give an example to explain the use of it?)

TRTR

TE

t

…

…

T1-weightedshort TR & TE

T2-weighted

long TR & TE

T1 and T2* Images

TE TE

T1 and T2* Images

By using different sequence of (TR, TE) in experiments, we can have different images

For example:

T1 (TR= 2000 msec, TE = 20 msec) : due to different T1 for different materials (gray matter or white matter), we can read out the gray matter density in each voxel

T2* (TR=2500 msec, TE = 25 msec) : will explain a bit more in details next week

))(/exp())(/exp(1()1(

))(/exp())(/exp(1(

210

210

matterwhiteTTEmatterwhiteTTRM

mattergrayTTEmattergrayTTRMM

Intensity (percentage) of gray matter

Slice Selection

• Most structural MRI and fMRI scans involve the

construction of a three dimensional image from a

set of two-dimensional slices.

Image Formation

• Imagine a brain slice split into a number of

equally sized volume elements or voxels.

ρ(x,y)

K-space

• The measurements are acquired in the

frequency-domain (k-space).

FT

IFT

k-space

k2

k1

Image space

y

x

Image Formation

K-space

• The measurements are acquired in the

frequency-domain (k-space).

• By making measurements for multiple values of

(k1, k2) we can gain enough information to

solve the inverse problem and reconstruct (x,

y).

• We can use the inverse Fourier transform (IFT):

(x, y) S(k1 ,k2 )ei2 (k1 xk2 y)

dkFdkP

K-space Measurements

• In practice, data measurements are made

discretely over a finite region.

– Use discrete Fourier transforms.

• The number of k-space measurements we make

influences the spatial resolution of the image.

– Need enough measurements to solve inverse problem.

16 unknowns 4 unknowns

4: K-space

FT

IFT

k-space

k1

k2

Image space

y

x

Image Formation

K-space

Each individual point in image space depends on all of the points contained in the k-space

It is important to note that there is not a one-to-one relationship between image and k-space.

Superposition of curves

Period: T

Frequency: =T-1

=

1 Dimension

K-space

2 Dimensions

Example

Example

Low passfilter

High passfilter

Example

Information content in k-space

• Low spatial frequencies represent parts ofthe object that change in a spatially slowmanner (Contrast).

• High spatial frequencies represent small structures whose size is on the same order as the voxel size (Tissue boundaries).

Spatial Resolution

32 32 image

1024 points sampled in k-space

64 64 image

4096 points sampled in k-space

128 128 image

16,384 points sampled in k-space

Seminar I

Question 1. Get familiar with your matlab

Question 2. 2-D Fourier transform

For a given image h(n,m) with N columns and N rows, the FT is defined as

1) For H (k,l) = H(1,-3)=1, and 0 otherwise, work out the image of exp(- j(kn+lm)) on the (n,m) plane

1

0

1

02

1

0

1

0

),())(exp(1

),(

),())(exp(),(

N

n

N

m

N

n

N

m

lkHlmknjN

nmh

mnhlmknjlkH

2) For H(k,l) = H(7,1)=1, and 0 otherwise, work out the image of exp(- j(kn+lm)) on the (n,m) plane

Seminar I

Seminar I

• 3) load a brain image and work out its Fourier transform using fft2

• 4) play with ifft2 and see the effect of high pass and low pass filters

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