**Course Flyer:**- FlyerPsy569,769.pdf
**Professor:**- Marty Sereno — email: msereno - AT - sdsu
- lecture times: Mon/Wed/Fri 9:00-9:50 AM (advanced/grad session: Fri 8:00-8:50 AM)
- lecture location: SSW 2667 (Learning Glass Studio, Student Services West)
- Zoom QA/officehours/review as needed (Zoom address on Canvas)
**Resources:**- Learning Glass lecture recordings
- Sereno Lecture Notes (124-page PDF [19MB] — single-page links below, last update: 13 Nov 2022)
- Huettel, S., A.W. Song, G. McCarthy (2014)
*Functional Magnetic Resonance Imaging, 3rd ed.*(2nd ed. OK, too) - Additional background reading
**Assignments:**- Homework #0 (warm-up, no need to turn in)
- Homework #1 (due Oct 11, 2022, incl. code/graphs, turn in paper printout or email 1 PDF)
- Homework #2 (due Nov 22, 2022, incl. code/graphs, turn in paper printout or email 1 PDF), 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 2022**(pdf)-

*Week of Aug 22 (Mon/Wed/Fri)*—**Introduction**

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

*Week of Aug 29 (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 05 (Wed/Fri)*—**Signal Equation**

*[no class Mon, Sep 05]*- RF Excitation
- Signal Equation
- Phase-Sensitive Detection

*Week of Sep 12 (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 19 (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 26 (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 03 (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 10 (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 17 (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 24 (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 Oct 31 (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 07 (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
- PRESS, MEGA-PRESS
*[no class Fri, Nov 11]*

*Week of Nov 14 (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 21 (Mon-only)*—**Cortical Surface Based methods**

**2nd Take-Home Due**- Cortical Thickness Measurement
- Mapping Cortical Visual Areas
*[no class Wed/Fri, Nov 23/25]*

*Week of Nov 28 (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 05 (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 of Dec 12 (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/exam due Dec 16**

website last modified:*10 Mar 2023*

Scanned/video'd class notes (pdf, links above) © 2022 Martin I. Sereno

Supported by NSF 0224321, NIH MH081990, Royal Society Wolfson