# SDSU Foundations of Neuroimaging (PSY 596)

### [formerly UCSD Cog Sci 276]

Course Flyer:
PSY596-flyer.pdf

Professor:
Marty Sereno — email: msereno - AT - sdsu
time: Mon/Wed/Fri 1:00-1:50 PM (grad session: Fri 12:00-12:50)
location: SSW 2667 (Learning Glass Studio, Student Services West)

Resources:
Learning Glass lecture recordings
Sereno Lecture Notes (73-page PDF [11MB] — single-page links below)
Huettel, S., A.W. Song, G. McCarthy (2014) Functional Magnetic Resonance Imaging, 3rd ed.

Assignments:
Homework #1 (due 09/29/2017, paper printout, incl. code and graphs)
Homework #2 (due 11/17/2017, paper printout, incl. code and graphs, brain image is here)
Final Paper: 10 page literature review on narrow methodological topic (start search in
Magnetic Resonance in Medicine, Neuroimage, Human Brain Mapping)

Learning Objectives:
Students will be able to do the following:
(1) explain excitation/recording/contrast of magnetic resonance signals and echoes using the Bloch equation
(2) compute Fourier transform, use to explain how RF stimulation, gradients, and RF coil signals generate brain images
(3) describe origin/localization of EEG/MEG signals, cortical surface-based methods, how to combine them w/fMRI
N.B.: consult with me if a disability hinders your performance so we can use University resources to maximize learning

Description and Prerequisites:
This course covers the physical and mathematical foundations of structural, functional, diffusion, and perfusion MRI, fMRI time series analysis, cortical-surface based reconstruction and data analysis, and the neural basis, recording, and localization of EEG and MEG signals. Although this course does not assume a background in linear algebra, vector calculus, differential equations, electromagnetism, the Fourier transform, and convolution, students will be expected to develop a solid grasp of a number of key equations underlying the different neuroimaging methods and solve simple Matlab problems. We will go slower than a typical engineering class and there will be plenty of time for questions. Here are two neuroimaging courses at UCSD for reference. Tom Liu's Bioengineering 280A — Principles of Biomedical Imaging (Fall 2015), provides a stronger mathematical foundation in the fundamentals of the Fourier transform and linear systems theory and covers ultrasound and CT in addition to MRI. David Dubowitz and Rick Buxton teach a two-quarter SOMI 276 — School of Medicine fMRI Course (2016/2017) in the Radiology Department.

Lecture Topics — Fall 2017 (pdf)

Week of Aug 28 (Mon/Wed/Fri)Introduction

• Introduction to Neuroimaging — MRI, fMRI, EEG, MEG
• MRI hardware
• Spin and Precession

Week of Sep 04 (Wed/Fri)Bloch Equation

• [no class Mon, Sep 04]
• Bloch Equation
• Dot/Cross/Complex Products
• Precession Solution
• Initial-Value Solutions to Differential Equation
• Verify T1 Re-Growth Solution
• T1, T2 Solutions
• Bloch Equation, Solution — Matrix Version

Week of Sep 11 (Mon/Wed/Fri)Signal Equation

• RF Excitation
• Signal Equation
• Phase-Sensitive Detection

Week of Sep 18 (Mon/Wed/Fri)Echoes

• Free Induction Decay
• Spin Echo
• Spin Echo Equations
• Stimulated Echo, Spin Echo Trains

Week of Sep 25 (Mon/Wed/Fri)Using the Bloch Equation

• Saturation-Recovery Signal
• Inversion Recovery Signal
• Spin Echo Signal
• Generalized MDEFT Signal
• Gray-White Contrast
• Signal-to-Noise

Week of Oct 02 (Mon/Wed/Fri)Fourier transform

• Complex Algebra
• Fourier Transform
• Negative Exponents, Orthogonality
• Spatial Frequency Space (k-Space)
• One k-Space Point
• One k-Space Point — 3 representations
• 1st Take-Home Due

Week of Oct 09 (Mon/Wed/Fri)Gradients, Slice Selection

• Slice Selection
• RF Pulse Details

Week of Oct 16 (Mon/Wed/Fri)MRI Image Formation

• Frequency-Encoding—A Misnomer
• Frequency-Encoding—Avoid This Intuition
• Frequency-Encoding—Correct Intuition (=Phase-Encoding)
• Imaging Equation (1D)
• Phase Encoding
• 3D Imaging (2nd Phase-Encode)
• Spin Phase in Image Space
• Gradients Move Signal in k-Space

Week of Oct 23 (Mon/Wed/Fri)Image Reconstruction

• Image Space and k-space (311K MPEG, R.-S. Huang)
• Image Reconstruction
• Aliasing and FOV
• Under/Over Sample
• Replicas, FTs
• General Linear Inverse for MRI Reconstruction

Week of Oct 30 (Mon/Wed/Fri)Practical Pulse Sequences

• Fast Spin Echo
• Quantitative T1/PD/T2*
• Spin Echo EPI
• Spin Echo Size Selectivity
• Single-Shot Spiral
• 3D Spiral Inversion-recovery FSE
• SENSE and GRAPPA (rough draft)
• Simultaneous Multi-Slice ("multiband")
• 3D Echo Volume Imaging

Week of Nov 06 (Mon/Wed)Image Artifacts

• Fourier Shift Artifacts
• EPI vs. Spiral Artifacts
• Image-space View Localized B0 Defect
• Effect Local B0 Defect on Reconstruction
• Shimming and B0-Mapping
• Motion-detection with Navigator Echoes
• RF Field Inhomogeneities
• [no class Fri, Nov 10]

Week of Nov 13 (Mon/Wed/Fri)Diffusion and Perfusion Imaging

• Diffusion-Weighted Imaging and Tract Tracing
• Perfusion Imaging (Arterial Spin Labeling)
• Combining Spectroscopy with Imaging
• 2nd Take-Home Due

Week of Nov 20 (Mon-only)Block Design, Phase-Encoded Design

• Phase-Encoded Stimulus and Mapping
• Convolution
• General Linear Model and Solution
• General Linear Model — Geometric Picture
• Cluster Correction — 3D and Surface-Based
• [no class Wed/Fri, Nov 22/24]

Week of Nov 27 (Mon/Wed/Fri)Cortical Surface Based methods

• Normalize, Strip Skull
• Spring Force in Detail
• Non-isotropic Filter, Region-Growing
• Tessellation: 3D -> 2D
• Energy Functional for Smooth/Inflate/Final
• Cortical Unfolding and Flattening
• Automatic Topology Repair
• Sulcus-Based Alignment
• Cortical Thickness Measurement
• Mapping Cortical Visual Areas

Week of Dec 04 (Mon/Wed/Fri)Source of EEG/MEG

• Source of EEG/MEG (rough draft)
• 1D/2D/3D Current Source Density
• Intracortical Circuits (rough draft)
• Intracortical Basis of EEG (rough draft)
• Maxwell Equations — Low Frequency Limit
• Why We Can Ignore Magnetic Induction
• Monopole, Dipole (rough draft)

Week of Dec 11 (Mon/Wed)Neuroimaging EEG/MEG

• Forward Solution — Analytic, Boundary Element (incomplete)
• Matrix Formulation of the Linear Forward Solution
• Derivation of Ill-Posed Minimum Norm Linear Inverse
• Two Equivalent Formulations — One Is Easier to Compute
• Using Spatiotemporal Covariance of Sensors (MUSIC)
• Noise-Sensitivity Normalization of Mininum Norm (rough draft)
• Noise-Sensitivity Normalization — Intuition
• Surface-Normal Constraint and its Problems
• Non-linear Fitting of Moveable Dipoles
• fMRI-weighted Inverse Solutions
• [no class Fri, Dec 15]

Week of Dec 18 Final Paper/Exam

Final paper/exam due Dec 20