SDSU Foundations of Neuroimaging (PSY0569, PSY0769)

FALL 2021

Course Flyer:

Marty Sereno — email: msereno - AT - sdsu
lecture recording times: Mon/Wed/Fri 9:00-9:50 AM (grad session: Fri 8:00-8:50 AM)
lecture recording location: SSW 2667 (Learning Glass Studio, Student Services West)

Learning Glass lecture recordings
Sereno Lecture Notes (124-page PDF [19MB] — single-page links below, last update: 9 Nov 2021)
Huettel, S., A.W. Song, G. McCarthy (2014) Functional Magnetic Resonance Imaging, 3rd ed.
Additional background reading

Homework #0 (warm-up, no need to turn in)
Homework #1 (due 10/11/2021, paper printout, incl. code and graphs)
Homework #2 (due 11/22/2021, paper printout, incl. code and graphs, brain image is here)
Final Paper: (ugrad=5pg, grad=10pg) 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 precession/excitation/recording/contrast of magnetic resonance signals and echoes using the Bloch equation
   (2) compute Fourier transform, use to explain RF stim, gradients, signals generate k-space data, how recon. works
   (3) diagram main classes anatomical/functional pulse sequences
   (4) describe diffusion, perfusion, and spectroscopic imaging
   (5) describe origin/localization of EEG/MEG signals, cortical surface-based methods, and how to combine 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 recently taught neuroimaging courses at UCSD for reference. Tom Liu's Bioengineering 280A — Principles of Biomedical Imaging (Fall 2015), provides a strong mathematical foundation in the fundamentals of the Fourier transform and linear systems theory and covers ultrasound and CT in addition to MRI. Tom Liu et al. teach an fMRI Course (Cognitive Science 260) (2020) in the Cognitive Science Department.

Lecture Topics — Fall 2021 (pdf)

Week of Aug 23 (Mon/Wed/Fri)Introduction

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

    Week of Aug 30 (Mon/Wed/Fri)Bloch Equation

  • Dot/Cross/Complex Products
  • Bloch Equation
  • Precession Solution
  • Effects of Change (M, B, Angle) On Precession Freq
  • Initial-Value Solution to T2 Differential Equation
  • Verify T1 Re-Growth Solution
  • Simple Matrix Operations
  • Bloch Equation, Solution — Matrix Version
  • Bloch Equation: Excitation In Rotating Frame
  • Bloch Equation: Summary

    Week of Sep 06 (Wed/Fri)Signal Equation

  • [no class Mon, Sep 06]
  • RF Excitation
  • Signal Equation
  • Phase-Sensitive Detection

    Week of Sep 13 (Mon/Wed/Fri)Echoes

  • Free Induction Decay
  • Spin Echo
  • Spin Echo Equations
  • Stimulated Echo, Spin Echo Trains
  • Extended Phase Graphs
  • 3-Pulse Echo Amplitudes
  • HyperEcho Train
  • Gradient Echo, Gradient Echo Trains

    Week of Sep 20 (Mon/Wed/Fri)Using the Bloch Equation

  • Saturation-Recovery Signal
  • Imperfect 90 deg Approach to State State
  • Inversion Recovery Signal
  • Spin Echo Signal
  • Gradient Echo Signal
  • Generalized MDEFT Signal
  • Magnetization Transfer Contrast
  • SNR/tSNR/CNR (e.g., Gray/White)
  • Signal-to-Noise

    Week of Sep 27 (Mon/Wed/Fri)Fourier transform

  • Complex Algebra
  • Fourier Transform
  • Negative Exponents, Orthogonality
  • Inverse Fourier as Correlation w/Cos,Sin
  • Spatial Frequency Space (k-Space) — 3 Equivalent Representations
  • One k-Space Point
  • Simple Image (1 Freq), Shifted Simple Image
  • Center of k-Space, Complex Image
  • Kx plus Ky Rotates, Special Case Sum of Reals

    Week of Oct 04 (Mon/Wed/Fri)Gradients, Slice Selection

  • Gradient Fields
  • Gradient Combination
  • Slice Selection
  • RF Pulse Details
  • Slice Select RF Pulses
  • Introduction to Frequency-Encoding —It's A Misnomer
  • Frequency-Encoding—Avoid This Intuition
  • Frequency-Encoding—Correct Intuition (=Phase-Encoding)

    Week of Oct 11 (Mon/Wed/Fri)MRI Image Formation

  • 1st Take-Home Due
  • Imaging Equation (1D)
  • Phase Encoding
  • 3D Imaging (2nd Phase-Encode)
  • Spin Phase in Image Space
  • Gradients Move Signal in k-Space

    Week of Oct 18 (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
  • Point-Spread Function
  • General Linear Inverse for MRI Reconstruction

    Week of Oct 25 (Mon/Wed/Fri)Practical Pulse Sequences

  • Fast Spin Echo
  • 3D Multi-Slab Fast Spin Echo
  • 3D Single-Slab Fast Spin Echo (SPACE)
  • Fast Gradient Echo
  • Quantitative T1 (Intro, Other Methods)
  • Quantitative T1 (2-Flip-Angle Method)
  • Gradient Echo EPI
  • Spin Echo Size Selectivity
  • Spin Echo EPI
  • Coil Fall-Off, Undersampling, GRAPPA, SENSE
  • Simultaneous Multi-Slice (blipped CAIPI)
  • SMS cont.: slice-GRAPPA, split-slice-GRAPPA
  • 3D Echo Volume Imaging
  • Single-Shot Spiral
  • 3D Spiral Inversion-recovery FSE

    Week of Nov 01 (Mon/Wed/Fri)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

    Week of Nov 08 (Mon/Wed/Fri)Diffusion, Perfusion, and Spectroscopy

  • Diffusion-Weighted Imaging and Tract Tracing
  • Practical Diffusion-Weighted Sequences
  • Perfusion Imaging (Arterial Spin Labeling)
  • pCASL
  • Off-Resonance RF Excitation
  • Combining Spectroscopy with Imaging

    Week of Nov 15 (Mon/Wed/Fri)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
  • Why Use Surfaces?
  • 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
  • Sulcus-Based Alignment

    Week of Nov 22 (Mon-only)Cortical Surface Based methods

  • 2nd Take-Home Due
  • Cortical Thickness Measurement
  • Mapping Cortical Visual Areas
  • [no class Wed/Fri, Nov 24/26]

    Week of Nov 29 (Mon/Wed/Fri)Source of EEG/MEG

  • Neural Source of EEG/MEG
  • Intracortical Circuits and EEG/MEG
  • Grad, Div, Curl
  • 1D/2D/3D Current Source Density
  • 1D/2D Current Source Density Experiments
  • Intracortical Basis of EEG
  • Maxwell Equations — Low Frequency Limit
  • Why We Can Ignore Magnetic Induction
  • Monopole, Dipole Current Sources

    Week of Dec 06 (Mon/Wed)Neuroimaging EEG/MEG

  • Forward Solution — Analytic, Boundary Element (incomplete)
  • Matrix Formulation of the Linear Forward Solution
  • Why Localize?
  • Derivation of Ill-Posed Minimum Norm Linear Inverse
  • Minimum Norm: Why It Appropriately 'Devalues' Deeper Sources
  • Two Equivalent Formulations — One Is Easier to Compute
  • Surface-Normal Constraint and its Problems
  • fMRI-weighted Inverse Solutions
  • Noise-Sensitivity Normalization of Mininum Norm
  • Noise-Sensitivity Normalization — Intuition
  • Point-Spread/Crosstalk, Conclusions
  • Using Spatiotemporal Covariance of Sensors (MUSIC)
  • Sensor Covariance: Calculate Weights
  • Sensor Covariance: Insert Weights into Inverse
  • Sensor Covariance: How it Helps
  • Non-linear Fitting of Moveable Dipoles
  • [no class Fri, Dec 10]

    Week of Dec 13 Final Paper/Exam

    Final paper/exam due Dec 17

    website last modified: 19 Jul 2021
    Scanned/video'd class notes (pdf, links above) © 2020 Martin I. Sereno
    Supported by NSF 0224321, NIH MH081990, Royal Society Wolfson