Foundations of Neuroimaging (online course)


Marty Sereno (homepage) — email: OR
Example lecture times: Mon/Wed/Fri, 9:00-9:50 AM
Example advanced/grad section: Fri, 8:00-8:50 AM
See also Systems Neuroscience (online course)

Course Description:
This course covers (1) the physical, biological, and mathematical foundations of data acquisition and reconstruction of structural, functional, diffusion, and perfusion MRI images, (2) fMRI time series analysis, (3) cortical surface-based reconstruction and data analysis, and (4) the neural basis, recording, and localization of EEG and MEG signals.
     Although we don't 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 go slower than a typical engineering class, but don't skip the math.
     Special thanks to SDSU Physics Professor Matt Anderson and the SDSU Instructional Technologies Services for the use of Matt's wonderful Learning Glass lecture recording system, and David Poddig and Stan Greene for inspiration and production. This course was developed and taught at UCSD, Birkbeck/UCL (London), and SDSU.

• Sereno lecture recordings: direct video links or youtube playlist (equivalent)
     (58 one-hour lectures: about one semester or two quarters)
• Sereno lecture notes PDF (124-page PDF [19MB]— single-page links below)
• References: background reading PDFs
• Reference texts:
     Huettel, S., A.W. Song, G. McCarthy (2014) Functional Magnetic Resonance Imaging
     Liang, Z.-P. and P.C Lauterbur (1999) Principles of Magnetic Resonance Imaging
     Nishimura, D.G. (1996) Principles of Magnetic Resonance Imaging
     Buxton, R., 2nd ed. (2009) Introduction to Functional Magnetic Resonance Imaging
     Haacke, E.M., R.W. Brown, et al. (2014) Magnetic Resonance Imaging
     Bernstein, M.A., K.F. King, and X.J. Zhou (2004) Handbook of MRI Pulse Sequences
     Nunez, P.L (1981) Electric Fields of the Brain

Homework #0 (warm-up)
Homework #1 (due end of 6th week as email PDF)
Homework #2 (due end of 12th week as email PDF, test brain image is here)
• Final Paper: (ugrad=5pg, grad=10pg) literature review on narrow methodological topic
     (start search: Magnetic Resonance in Medicine, Neuroimage, Human Brain Mapping)

Lecture Topics: (e.g., Fall semester course) (1-page PDF syllabus)

Week 1 (Mon/Wed/Fri)Introduction

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

    Week 2 (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 3 (Wed/Fri)Signal Equation

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

    Week 4 (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 5 (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 6 (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 7 (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 8 (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 9 (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 10 (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 11 (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 12 (Mon/Wed)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
  • [no class Fri]

    Week 13 (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 14 (Mon-only)Cortical Surface Based methods

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

    Week 15 (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 16 (Mon/Wed/Fri)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

    Week 17 (Mon-only)Final Paper/Exam

  • 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
    Final paper due

    last modified: Jul 2023
    Scanned/video'd class notes (pdf, links above) © 2023 Martin I. Sereno
    Supported by NSF 0224321, NIH MH081990, Royal Society Wolfson
    Back to Sereno homepage