# 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.*
Additional background reading

**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
Gradient Echo, Gradient Echo Trains

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

Saturation-Recovery Signal
Inversion Recovery Signal
Spin Echo Signal
Gradient 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**

Gradient Fields
Gradient Combination
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
Fast Gradient Echo
Quantitative T1/PD/T2*
Gradient Echo EPI
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
Gradient Non-linearities
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)
Grad, Div, Curl
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
Point-Spread/Crosstalk, Conclusions
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**

last modified: *Sep 08, 2017*

Scanned class notes (pdf, links above) © 2017 Martin I. Sereno

Supported by NSF 0224321, NIH MH081990, Royal Society Wolfson