Computational Biology - dcs.warwick.ac.ukfeng/teaching/compbio_2015_II.pdf · Computational Biology...
Transcript of Computational Biology - dcs.warwick.ac.ukfeng/teaching/compbio_2015_II.pdf · Computational Biology...
Computational Biology
Jianfeng Feng
Warwick University
(many slides are from Dr. M. Lindquist)
http://www.dcs.warwick.ac.uk/~feng/Comp_Biol.html
http://venturebeat.com/2014/11/02/jonathan-rothbergs-butterfly-network-has-raised-100m-for-medical-imaging-tech/
By choosing short TR and TE, T1 weighted image is obtained
T1-weightedshort TR & TE
T2-weighted
long TR & TE
Last week
By choosing short TR and TE, T1 weighted image is obtained
T1-weightedshort TR & TE
T2-weighted
long TR & TE
Useful to access how many neurons are in your brain
Last week
By choosing long TR and TE, T2 or T2* weighted image is obtained
T1-weightedshort TR & TE
T2-weighted
long TR & TE
Useful to access the activity in your brain
Last week
MRI
• MRI studies brain anatomy.
– Structural (T1) images
– High spatial resolution
– Can distinguish different types of tissue
fMRI
• fMRI studies brain function.
– Functional (T2*) images
– Lower spatial resolution/ Higher temporal resolution
– Relate changes in signal to experimental manipulation
Functional MRI
• An fMRI experiment consists of a sequence of
individual MR images, where one can study
oxygenation changes in the brain across time.
BOLD fMRI
• The most common approach towards fMRI uses
the Blood Oxygenation Level Dependent (BOLD)
contrast.
• It allows us to measure the ratio of oxygenated to
deoxygenated hemoglobin in the blood.
• It doesn’t measure neuronal activity directly,
instead it measures the metabolic demands
(oxygen consumption) of active neurons.
BOLD Contrast
• Hemoglobin exists in two different states each
with different magnetic properties producing
different local magnetic fields. (Pauling 1936)
– Oxyhemoglobin is diamagnetic.
– Deoxyhemoglobin is paramagnetic.
• BOLD fMRI takes advantage of the difference in
T2* between oxygenated and deoxygenated
hemoglobin
(Seiji Ogawa, another Nobel prize?).
CellO2
Glucose
Cell
Capillary huge flowNeural activation
excitation reception
MR
sig
nal
(S)
TE t
RestActivation
T2*
Oxygenated Hb
BOLD Signal
BOLD Signal
• The change in the MR signal triggered by
instantaneous neuronal activity is known as the
hemodynamic response function.
• As neural activity increases, so does metabolic
demand for oxygen and nutrients.
• As oxygen is extracted from the blood, the
hemoglobin becomes paramagnetic which
creates distortions in the magnet field that cause
a T2* decrease (i.e. a faster decay of the signal).
• An over-compensation in blood flow
dilutes the concentration of
deoxyhemoglobin and tips the
balance towards oxyhemoglobin.– This leads to a peak in BOLD
signal about 4-6 s following
activation.
• After reaching its peak, the BOLD
signal decreases to an amplitude
below baseline level.– This poststimulus undershoot is due to a
combination of reduced blood flow and
increased blood volume.
BOLD Signal
HRF: hemodynamic
response function.
The strongest signal appears
5-6 seconds after activation.
HRF Properties
• Magnitude of signal changes is quite small
– 0.1 to 5%
– Hard to see in individual images
• Response is delayed and quite slow
– Extracting temporal information is tricky, but possible
– Even short events have a rather long response
• Exact shape of the response has been shown to
vary across subjects and regions.
Interpretation
• How well does BOLD signal reflect increases in
neural firing?
• The BOLD signal corresponds relatively closely
to the local electrical field potential surrounding a
group of cells.
• Demonstrations have shown that high-field BOLD
activity closely tracks the position of neural firing
and local field potentials.
• In plain words, the higher the fMRI signals, the
higher the neuronal firings.
LT I System
• The relationship between stimuli and the BOLD response
is often modeled using a linear time invariant (LTI) system.
– Here the neuronal activity acts as the input or impulse and the HRF acts as the impulse response function.
• In this framework the signal at time t, x(t), is modeled as theconvolution of a stimulus function v(t) and thehemodynamic response h(t), that is,
• In particular, if
t
dssthsvthvtx0
)()())(*()(
• The measured fMRI signal is corrupted by
random noise and various nuisance components
that arise due to hardware reasons and the
subjects themselves.
• Sources of noise:– Thermal motion of free electrons in the system.– Patient movement during the experiment.– Physiological effects, such as the subject’s heartbeat
and respiration.
– Low frequency signal drift.
fMRI Noise
• Slow changes in voxel intensity over time (low-
frequency noise) is present in the fMRI signal.
• Scanner instabilities and not motion or
physiological noise may be the main cause of the
drift, as drift has been seen in cadavers.
• We need to include drift parameters in our future
models.
Drift
Issues
• Drift can have serious consequences:– Experimental conditions that vary slowly may be confused
with drift.
– Experimental designs should use high frequencies (more rapid alternations of stimulus on/off states).
• Bad Design: 2 min. rest 2 min. active
Typical Drift Pattern & Magnitude
Typical Signal Magnitude
... you’ll never detect this signal, due to the drift
A cautious note
• Neuroscientist Craig Bennett purchased a whole Atlantic salmon, took it to a lab at Dartmouth, and put it into an fMRI machine used to study the brain. The beautiful fish was to be the lab’s test object as they worked out some new methods.
• So, as the fish sat in the scanner, they showed it “a series of photographs depicting human individuals in social situations.” To maintain the rigor of the protocol (and perhaps because it was hilarious), the salmon, just like a human test subject, “was asked to determine what emotion the individual in the photo must have been experiencing.”
• The salmon, as Bennett’s poster on the test dryly notes, “was not alive at the time of scanning.”
• The result is completely nuts — but that’s actually exactly the point. Bennett, who is now a post-doc at the University of California, Santa Barbara, and his adviser, George Wolford, wrote up the work as a warning about the dangers of false positives in fMRI data. They wanted to call attention to ways the field could improve its statistical methods.
• IgNobel Prize in Neuroscience: The dead salmon study 2012
A cautious note
• MRI images are typically acquired in axial
slices- one at a time.
•This can be performed in either a sequential or interleaved manner.
•Together the slices make up a 3 dimensional brain volume.
Terminology
•An experiment studies many subjects.
•Each subjects many be scanned during multiple
sessions.
•Each session consists a several runs.
•Each run consists of a series of brain volumes.
•Each volume is made up of multiple slices.
•Each slice contains many voxels.
•Each voxel has an intensity associate with it.
Terminology
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
•Prior to analysis, fMRI data undergoes a series of Preprocessing steps aimed at identifying and removing artifacts and validating model assumptions.
•The goals of preprocessing are – To minimize the influence of data acquisition and
physiological artifacts;
– To check statistical assumptions and transform the data to
meet assumptions;
– To standardize the locations of brain regions across
subjects to achieve validity and sensitivity in group analysis.
Pre-Processing
Preprocessing is performed both on the fMRI data and structural scans collected.
Pre-Processing Pipeline
•1. Visualization and Artifact Removal
•2. Slice Time Correction
•3. Motion Correction
•4. Physiological Corrections
•5. Co-registration
•6. Normalization
•7. Spatial Filtering
•8. Temporal Filtering
Pre-Processing Steps
•The first part of the preprocessing pipeline is to use exploratory techniques to investigate the raw image data and detect possible problems and artifacts.
• fMRI data often contain transient spike artifacts and slow drift over time.
•An exploratory technique (eye checking) can be used to look for spike-related artifacts.
Visualization and artifacts removing
•We often sample multiple slices of the brain during each individual repetition time (TR) to construct a brain volume.
•Typically each slice is sampled at a slightly different time points (i.e., 2D imaging; not 3D).
•Slice time correction shifts each voxel's time series so that they all appear to have been sampled simultaneously.
Slice time correction
Temporal Interpolation
•Use information from nearby time points to
estimate the amplitude of the MR signal at the
onset of the TR.
•Use a linear function for example.
Slice time correction
•Very small movements of the head during an experiment can be a major source of error if not treated correctly.
•When analyzing the time series associated with a voxel, we assume that it depicts the same region of the brain at every time point – Head motion may make this assumption incorrect.
•Can be corrected using a rigid body transformation.
Head motion
•The goal is to find the best possible alignment between an input image and some target image.
•To align the two images, one of them needs to be transformed.
•A rigid body transformation is used.
• It could involve 6 variable parameters, 3 sets of translations and 3 sets of rotations (6 DOF).
Motion correction
Linear transformations
•Rigid body (6 DOF) – translation and rotation
•Similarity (7 DOF) – translation, rotation and a single global scaling
•Affine(12 DOF) – translation, rotation, scaling and shearing.
Warping
Transformations where the equations relating the
coordinates of the images are non-linear.
Transformations
• The target image is usually defined to be the first (or mean) image in the fMRI time series.
•The goal is to find the set of parameters which minimizes some cost function that assesses similarity between the image and the target.
•Examples of cost functions include the sum of squared differences or mutual information.
Motion correction
•Next, a structural MRI collected in the beginning of the session is registered to the fMRI images in a process referred to as coregistration.
– Allows one to visualize single-subject task activations
overlaid on the individual’s anatomical information.
– Simplifies later transformation of the fMRI images to a
standard coordinate system.
Coregistration
•There are certain key differences between co-registration and motion correction. – Functional and structural images do not have the same
signal intensity in the same areas.
– Their shapes may differ.
• Use at least an affine transformation to perform
co-registration and the mutual information cost
function.
Coregistration
•All brains are different. The brain size of two subjects can differ in size by up to 30%.
•There may also be substantial variation in the shapes of the brain.
•Normalization allows one to stretch, squeeze and warp each brain so that it is the same as some standard brain.
Normalization
The structural MR image used in the coregistration procedure is
warped onto a template image.
Normalization
Pros
•Spatial locations can be reported and interpreted in a consistent manner.
•Results can be generalized to larger population
•Results can be compared across studies.
•Results can be averaged across subjects
Cons
•Reduces spatial resolution.
• Introduces potential errors.
Normalization
• Talairach space (Talairach and Tournoux,1988)
– Based on single subject (A cadaver of a 60 year old female)
– Based on a single hemisphere.
– The origin (0,0,0) is set at the Anterior Commisure.
– Oriented so that a line joining the Anterior
Commissure (AC) and the Posterior Commisure (PC) is
horizontal.
Brain atlases
• Montreal Neurological Institute (MNI)
– Combination of many MRI scans on normal
controls (152 in current standard).
– All right-handed subjects.
– More representative of population.
Brain Atlases
• In fMRI it is common to spatially smooth the
acquired data prior to statistical analysis.
•Can increase signal-to-noise, validate
distributional assumptions and remove artifacts.
Spatial Filtering
Pros
•May overcome limitations in the normalization by blurring any residual anatomical differences.
•Could increase the signal-to-noise ratio (SNR).
•May increase the validity of the statistical analysis.
•Required for Gaussian random fields.“
Cons
•The image resolution is reduced.
Spatial Filtering
The size of the kernel is determined by the
full width at half maximum (FWHM), which measures the width of the kernel at 50% of its peak value.
Spatial Filtering
•Typically, the amount of smoothing is chosen a priori and independently of the data.
•Furthermore, the same amount of smoothing is applied throughout the whole image.
•Adaptive smoothing could be an option.
– Non-stationary spatial Gaussian Markov random field.
– Smoothing varies across space and time.
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