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Navigating the Brain. Mark P. Wachowiak, Ph.D. Department of Computer Science and Mathematics Nipissing University April 27, 2007. Outline. Basic brain anatomy Brain imaging Magnetic resonance imaging (MRI) Computed tomography (CT) Functional imaging Brain navigation Future directions.

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navigating the brain

Navigating the Brain

Mark P. Wachowiak, Ph.D.

Department of Computer Science and Mathematics

Nipissing University

April 27, 2007

  • Basic brain anatomy
  • Brain imaging
    • Magnetic resonance imaging (MRI)
    • Computed tomography (CT)
    • Functional imaging
  • Brain navigation
  • Future directions
interdisciplinary nature of brain research
Interdisciplinary Nature of Brain Research
  • Neuroscientists
  • Physicians
  • Psychologists
  • Mathematicians
  • Biologists
  • Engineers
  • Computer scientists
  • Electrically excitable cells in the nervous system.
  • Transmit and process information.
  • Dendrites
    • Conduct electrical impulses from other neurons or cells towards the cell body.
  • Axons
    • Conduct impulses away from the cell body to other neurons.

hodgkin huxley model of neurons
Hodgkin-Huxley Model of Neurons
  • First mathematical model of neurons (1952).
  • Models electrical characteristics of the cells
  • Based on systems of nonlinear ordinary differential equations.
  • Starting point for modern, advanced neuron models.

Alan Lloyd Hodgkin

Andrew Fielding Huxley

  • Largest part of the brain.
  • Higher brain functions:
    • Thought
    • Action
    • Vision
    • Memory

  • Associated with the regulation and coordination of movement, posture, and balance.
medulla oblongata
Medulla Oblongata
  • Relays nerve signals between the brain and the spinal cord.
  • Involuntary functions:
    • Breathing
    • Blood pressure
    • Heart rate
    • Reflexes
sulci and gyri
Sulci and Gyri
  • Sing. sulcus, gyrus
  • Sulcus
    • Fissure in the brain tissue.
    • Interhemispheric fissure – divides the brain into left and right hemispheres.
  • Gyrus
    • Elevated “hill” areas between sulci.




white matter
White Matter
  • Found in the brain and spinal cord.
  • Consists of insulated (myelinated) nerve fibers (axons).
  • Responsible transmitting and conducting information.

grey matter
Grey Matter
  • Consists of the bodies of neurons.
  • Responsible for information processing.
  • Generates responses to stimuli.

types of neuroimaging
Types of Neuroimaging
  • Structural
    • Magnetic resonance imaging
    • Computed tomography
    • Ultrasound
  • Functional
    • Functional MRI
    • Positron emission tomography
    • Single photon emission computed tomography
magnetic resonance imaging
Magnetic Resonance Imaging
  • Excellent for clearly visualizing structures in soft tissues, such as the brain.
  • Very commonly used in:
    • Diagnosis
    • Image-guided surgery and therapy
  • By adjusting scanning settings, specific features can be detected.
  • MRI images are 2D slices through the body at a specific location.
mri scanner
MRI Scanner

proton precession
Proton Precession

Hydrogen protons precess about an axis, like a “wobbling” spinning top.

proton precession in tissue
Proton Precession in Tissue

Randomly-oriented hydrogen protons precess.

application of magnetic field
Application of Magnetic Field

Magnetic field

A strong magnetic field is applied in a specified direction.

The protons align with the magnetic field.

application of rf pulse
Application of RF Pulse

A strong, sudden RF (radiofrequency) pulse is applied in a direction orthogonal to the magnetic field.

Magnetic field

Protons are briefly placed into a high-energy state.

RF pulse

rf pulse is turned off
RF Pulse is Turned Off

Energy is released as the protons return to their low-energy orietation within the magnetic field.

Magnetic field

mri image formation
MRI Image Formation
  • When the RF pulse is turned off, the hydrogen protons return to their natural alignment within the magnetic field.
  • Energy is released.
  • The coil detects this signal and sends it to a computer for processing.
  • The signal consists of complex values which have real and imaginary components.
complex numbers
Complex Numbers

Imaginary number

Complex number


fourier transform
Fourier Transform
  • Determine the frequency components of a signal.
  • From a complex frequency representation, recover the original signal.
  • Involves calculus and integration of complex-valued functions.

Jean Baptiste Joseph Fourier


fast fourier transform
Fast Fourier Transform
  • A very efficient method to compute the Fourier transform of a signal.
  • Developed in 1965 by J.W. Cooley and John Tukey (AT&T Labs).
  • One of the “top ten” algorithms of the 20th century.

James W. Cooley

John W. Tukey,

mri image formation27
MRI Image Formation

Fourier Transform

Magnitude information from signal

Phase information from signal

mri visualization
MRI Visualization
  • A series of 2D MRI images can be combined together to form a 3D volume.
  • This volume can then be used to generate realistic visualizations and models.
ms lesions
MS Lesions

computed tomography ct
Computed Tomography (CT)
  • Tomography
    • Imaging in sections, or slices.
  • Computed
    • Geometric processing used to reconstruct an image.
    • Computerized algorithms
computed tomography 2
Computed Tomography (2)
  • Uses X-rays
    • Dense tissue, like bone, blocks x-rays.
    • Gray matter weakens (attenuates) the x-rays.
    • Fluid attenuates even less.
  • A computerized algorithm (filtered backprojection) reconstructs an image of each slice.
ct image formation
CT Image Formation

X-ray tube


X-ray detector

computed tomography
Computed Tomography

ct image formation34
CT Image Formation


  • Functional MRI – used to investigate brain function.
  • Enables watching brain activity in vivo.
  • Measures haemodynamic response.
    • Changes in oxygen content of the blood occur as the result of neuronal activity.
interdisciplinary nature of fmri
Interdisciplinary Nature of fMRI
  • Physics
    • Hardware tools
  • Electrophysiology
    • Neuronal behaviour
  • Psychology
    • Cognitive psychology
  • Statistics
    • Making sense of observations
  • Neuroanatomy
blood oxygen level dependent fmri bold
Blood Oxygen Level Dependent fMRI (BOLD)

Signal increase

Signal decrease


Active areas while subjects remembered information presented visually

Active areas while subjects remembered information presented aurally

Active areas for both types

complementary imaging techniques
Complementary Imaging Techniques




mathematical challenges in neuroimaging
Mathematical Challenges in Neuroimaging
  • Segmentation
    • Identifying structures or abnormalities from 2D or 3D brain images.
    • Development of models to help plan surgery and therapy.
    • Concepts from computer graphics, geometry, topology, probability theory.
mathematical challenges in brain imaging
Mathematical Challenges in Brain Imaging
  • Registration
    • Aligning and combining images from the same or different type of image.
    • Useful in simulation, modeling, and in planning surgical procedures.
    • Employs concepts from probability theory, information theory, geometry, topology, optimization, parallel computing, and many other areas.
segmentation differential geometry
Segmentation – Differential Geometry

Automatically computed network of 3D curves lying deep in the cortex (sulcal fundi), color-coded according to the curvature.

G. Sapiro, SIAM News, Volume 40, Number 2, March 2007

registration and fusion
Registration and Fusion





Histology cryosection

MRI + Ultrasound

brain warping
Brain Warping
  • Nonlinear registration.
  • Used to match features in structurally different brains.
  • Uses:
    • Geometry
    • Topology
    • Probability
    • Calculus

segmentation and registration
Segmentation and Registration

Segmentation of the brain surface from MRI scans

Registration of fMRI onto segmented brain surface to display activation areas

neurosurgery planning
Neurosurgery Planning

3D models generated from MRI and CT images.


surgical planning with mri and fmri
Surgical Planning with MRI and fMRI

MRI and fMRI registration, and the 3D reconstruction of a tumour.

Tumour segmentation is carried out prior to the surgery.

Neurosurgeons now have complex information available to decide the best strategy for removing the tumour.

future areas
Future Areas
  • Functional imaging for to relieve acute and chronic pain.
  • Modeling to develop better therapies for:
    • Alzheimer’s disease
    • Multiple sclerosis
    • Brain tumours
    • Strokes
    • Psychiatric disorders
    • Other neurological and brain diseases
other areas of cross fertilization
Other Areas of Cross-fertilization
  • Electroencephalography (EEG)
  • Electroencephalography (EEG)
  • Electroencephalography (EEG)

other areas of cross fertilization57
Other Areas of Cross-fertilization
  • Electroencephalography (EEG)
  • Artificial neural networks

other areas of cross fertilization58
Other Areas of Cross-fertilization
  • Electroencephalography (EEG)
  • Artificial neural networks
  • Dynamical systems

other areas of cross fertilization59
Other Areas of Cross-fertilization
  • Electroencephalography (EEG)
  • Artificial neural networks
  • Dynamical systems
  • Modeling of brain processes
moving through the visual cortex
Moving Through the Visual Cortex

thank you

Thank You.