Contents

• • Today's Focus
  • Classical Model of the 1H proton
    • The Magnetic Piece
    • The Angular Momentum Bit
    • Combine Angular Momentum and Magnetism to get an Equation of Motion
  • Representations of the Precession
  • In-Class Questions
  
  
• Introducing the RF Field
  • Summary of Last Week's Class and Today's Focus
  • Rotating Reference Frames
    • Physical Picture Requiring Mathematical Model
    • Rotating Reference Frame
    • Rotating Reference Frame AND Magnetic Moment
    • Linear and Quadrature $B_1$
  • In-Class Questions
  
  
• Magnetizatgion, Bloch Equations, and Relaxation
  • Summary
  • Magnetization Vector
  • Longitudinal Spin Behavior and Spin-Lattice Relaxation
    • .
    • Spin-Spin (transverse) Relaxation
  • Little Summary of Bloch Equations and Magnetization
  • RF and Static Fields
  
  
• Quantum Mechanics and Precession
  • Summary
  • Proton in a Magnetic Field: Discreteness
    • Quantized Spin and Angular Momentum
  • The Schrödinger Equation and Describing the Proton's State
  • Quantum Mechanics to Precession
  • In-Class Questions
  
  
• Quantum Mechanics and Longitudinal Relaxation
  • Summary
  • Boltzmann Picture
  • Quantum Mechanical Examination of Longitudinal Relaxation
  
  
• Basics of Signal Detection
  • Summary
  • Faraday's Law of Induction and MR
  • The MRI Signal and Reciprocity
  • Signal from the Precessing Magnetization
  • Demodulation: very briefly
  • Relative Signal Strength
  
  
• Basics of Signal Acquisition
  • Signal for an FID Experiment
  • Sequence Diagrams and the FID Experiment
  • The Mighty, Mighty Spin(RF)-Echo
  • Repeated MR Experiment: Signal Effects (gonna be, signal reduction, you know it)
  • The Not-so-Mighty, but pretty Handy Inversion Recovery Experiment
  • Spectroscopy: The Once and Future King of MR
  • In-Class Questions
  
  
• Introduction to Imaging
  • Today's Focus
  • Starting Simple: The Two Spin Example
  • What really makes up a ``1D'' MRI Signal?
  • The Imaging Equation
    • Constant Gradient
  • Couple of Important Mathematical Functions (and their Fourier transforms)
    • Revisit the 2 Spins
  • What about a distribution of Spins (real world)?
  • The Gradient (or Field) Echo and k-space Diagrams
    • Re-Thinking the Experiment in k-space
  • Combine the Gradient Echo with the Spin Echo
  • IN-CLASS PROBLEMS
  
  
• Imaging in More Dimensions
  • Introduction to Imaging in More Dimensions
  • Imaging in More Dimensions
  • N-D Imaging and Sequence Diagrams
  • Selecting a Slice or Slab of Spins
    • Conventional Slice Orientations
  • 2D Imaging (interleaving is the name of the game)
  • Spectroscopic Imaging (MRI is so cool ...)
  • In-Class Questions
  
  
• Introduction to Fourier transform
  • Today's Focus
  • Brief Review of Imaging and Hardware
  • Spectroscopic Imaging (MRI is so cool ...)
  • Continuous Fourier Transform Properties
    • Fourier Transform Shift Theorem
    • Phase Imaging and Phase Aliasing
    • Convolution Theorem
    • Fourier Transform Derivative Theorem
    • Fourier Transform Symmetries
  • Fourier Transform: Effects of Sampling
    • What does all of this mean to the measured MRI ``signal''?
  • The Discrete Fourier transform Pair
  • IN-CLASS PROBLEMS
  
  
• More Fourier Transform: Sampling and Aliasing
  • What to do?
  • What Does Sampling Imply for the Reconstructed Image?
    • Nyquist Sampling Criterion
  • Truncating the MRI Signal
    • Resolution and the Discrete Fourier Transform
  • IN-CLASS PROBLEMS
  
  
• More Fourier Transform(2): Sampling and Aliasing
  • Today's Focus
  • RF Probe and Noise Effects
  • Non-Uniform Sampling
    • What if you don't have enough DAC resolution?
  
  
• Filtering and Resolution
  • Overview
  • Point Spread Function
    • Additional Filters
  • Resolution
    • Additional Filtering
  • Gibbs Ringing and Filters
    • Applications of Filtering Concepts Applied to Other MRI Methods
  • MID-TERM NOTES
  • Instructions
  • Questions
  
  
• Signal, Noise, and Contrast
  • Summary
  • Signal and Noise
    • Signal: Review
    • Noise in MRI
    • Assumptions and Associated Properties of the Noise in MRI
    • Effect of Averaging in MRI
  • SNR and Imaging Parameters: The Master Equation
    • Imaging Parameters and SNR
  • Contrast and Noise
    • Why is Contrast a Big Deal?
    • Contrast to Noise
  • The Big Three MRI Image Contrasts
    • spin-density weighting
    • $T_{2}$ or $T_{2}^{*}$-weighting
    • $T_{1}$-weighting
  • Contrast Agents
  • Partial Voluming
  • In-Class Questions
  
  
• Fast Imaging in the Steady State
  • Why Fast Imaging?
  • Introduction to Fast Imaging in the Steady State
  • Introduction to Short-$T_R$, Spoiled, Gradient Echo Imaging
    • Can force Equilibrium
    • RF Non-uniformity Effects can be Magnified
  • Introduction to Short-$T_{R}$, Coherent Gradient Echo Imaging (SSFP)
  • SSFP Signal Formation Mechanisms
  • With all of these Spin Pathways Floating Around, How Will Spoiling be Achieved?
  • In-Class Questions
  
  
• Segmented k-space Imaging and Single-Shot Techniques
  • Steady State Imaging???
  • How do you select Acquisitions in MRI?
  • Introduction to Methods for Collecting Multiple $k$-space Lines after Each Excitation
    • Introduction to Segmented $k$-space acquisitions
  • Introduction to Single-Shot EPI
    • Alternative Ways to Cover $k$-space
  • Repeated Spin Echoes to Collect Multiple $k$-space Lines
  
  
• Effect of Flow on the Transverse MRI Signal: Velocity Encoding
  • Please Don't Forget
  • Today's Focus
  • Effects on Spin Phase from Motion along the Read Direction
    • Constant Velocity Flow at Different Velocities in the same Voxel
  • Velocity Compensation along Read
    • Importance of the Time Origin
  • Velocity Compensation along PE
  • Velocity Encoding
  
  
• Effect of Flow on the Longitudinal Magnetization Signal: Time-of-Flight Effects
  • Time-of-Flight Effects
    • Contrast Agents
  • Visualizing Vasculature: MIPs
  • Beyond Flow: Translational Anatomical Motion
  • In-Class Questions
  
  
• Sequence Zoo
  • State of the Class
  • Choosing an Imaging Methodology
  • Sequence Zoo
    • Common Contrast Methods not Covered in Class, but detailed in Book
    • Spin Echoes
    • Spin Echo with Multiple FEs and Phase Encoding
    • Gradient Echo
    • Short-$T_{R}$ Gradient Echo
    • Single Shot, Single-Excitation Methods (excluding fast spin echo, and ``single-shot'' GE methods)
  • Most Methods can be Combined with ...
  • Common Artifacts
  • In-Class Questions
  
  
• About this document ...

HWS 2.2, 2.4, 2.6