Functional Magnetic Resonance Imaging (fMRI)
Modelling: Observing the brain in action
Peter Drysdale
Complex Systems, School of Physics, University of Sydney
Brain Dynamics Center, Westmead Millennium Institute, Westmead
Hospital and Western Clinical School of the University of Sydney
How Physics led to Brain Dynamics
Honours in theoretical wave physics in plasmas.
Ph.D. in theoretical wave physics including statistical phase changes
and random diffusion.
Prof. Peter Robinson walked into my office and asked me to do
some contour integrals for fMRI analysis.
Leads to research in fMRI and then Postdoc in Brain Dynamics.
Where have other people come from?
Over 20 people researching Brain Dynamics in Physics.
They have come from a variety of areas including: Physics,
Applied and Pure Mathematics, Psychology, Psychiatry,
Computer Science, Medicine, Bioinformatics, Engineering.
What is Magnetic Resonance Imaging
MRI is the medical name for Nuclear Magnetic Resonance (NMR) imaging
(from Hoiting 2005)
1.5T fMRI machine of collaborators at FIL,
London (N.B. Earth’s B field is 30-60µT)
Structural MRI and Functional MRI
Structural MRI
Image:- Jezzard et al. (2001)
Functional MRI superimposed on model brain
Image:- Williams, Brain Dynamics Centre.
What is the Blood Oxygen Level Dependent
signal?
Indirect measure of neuronal activity:
Neuronal activity depletes metabolic reserves.
Localised increase in blood flow to active region mediated by
astrocytes.
Localised change in blood volume and oxygenation of blood.
Deoxygenated hemoglobin (deHB) is paramagnetic as opposed to
diamagnetic which changes magnetic environment of H nuclei.
Change in deHb volume and concentration alters detected MRI signal.
Who uses it? Researchers who want to observe
brain’s functioning!
Several thousand neuroscientists around the world. Huge diversity of
worldwide research applications including:- visual perception, Alzheimer's,
schizophrenia, emotional processing, language processing, motor function,
audio and music perception, cognitive origins of decision making.
Why do we need to model?
BOLD Signal is 2-4% over baseline MRI signal.
“Noise” fluctuations are typically 1-2% of baseline MRI signal.
The indirect process of BOLD generation is not well understood.
Linearized Frequency Response
Linearizing the hemodynamic model yields the transfer
function.
BOLD response is weakly
resonant low-pass filter
Peak response at ~ 0.07 Hz
Optimized stimulation patterns by exploiting
resonance
Optimal stimulus pattern which is superior to stimulating
every 12-14s can be derived.
The optimal stimulus pattern
stimulates repeatedly for ~7s
and then rests for ~7s.
This is analogous to pushing a
swing.
Examples of nonlinear model response
Balloon Model
Friston et al. (2003), Obata et al. (2004)
Models blood vessel as extensible balloon which can
temporarily store blood.
Models each region as containing a single large blood vessel.
Models are voxel based where voxels span entire cortical
thickness (voxels are instrument dependent volume pixels).
Temporal only – no spatial terms.
Does not conserve blood between adjacent cortical points.
Balloon Models are still being refined.
brain matrix
blood flow
Cortical thickness
Balloon model of cerebral vasculature.
Vessel is a single inflatable balloon with
voxel the full thickness of cortex.
A new approach – a porous elastic model
Poroelastic models describe a fluid-saturated
porous elastic medium and originated in
geophysics.
Advantages:
Image: Ziokovic & Apuzzo (1998)
imposes continuity of fluid flow.
allows instrument independent (non-voxel) description of
hemodynamics.
models vasculature as pores in the cortical matter rather than as a
single vessel in each voxel.
A porous elastic model allows voxels
of smaller scale than capillary length,
facilitating study of intervoxel
dependence and blood flow in more
than one direction.
Structure of porous elastic model
Blood mass
conservation
Neural activity
z
Neuronal
signal
equation
BOLD response
y
Momentum
conservation
Hemoglobin
conservation
The structure of the porous elastic model is built from components
using basic physical principles and physiological observations.
Brain Dynamics is more than BOLD fMRI
My research also includes:
Development of computational models of EEG and ERP in the brain.
Understanding the transitions between wake and sleep in a corticothalamic model of the brain.
Other people in the Brain Dynamics group research:
Development of analytic models of EEG and ERP in brain,
Visual rivalry,
Transition to epileptic states in the brain,
Effect of neurotransmitters on EEG and ERP,
Network and stability characteristics of the brain,
Visual Hallucinations,
Sleep/Wake switch.