Principles of MRI: Image Formation Allen W Song Brain Imaging and Analysis Center Duke University What is image formation? To define the spatial location of the sources that contribute to the detected signal But MRI does not use projection, reflection, or refraction mechanisms commonly used in optical imaging methods to form image So how are the MR images formed? Frequency and Phase Are Our Friends in MR Imaging ω θ = ωt θ The spatial information of the proton pools contributing MR signal is determined by the spatial frequency and phase of their magnetization Gradient Coils z z z y y x x X gradient y Y gradient x Z gradient Gradient coils generate spatially varying magnetic field so that spins at different location precess at frequencies unique to their location, allowing us to reconstruct 2D or 3D images 0.8 A Simple Example of Spatial Encoding Constant Magnetic Field w/o encoding Varying Magnetic Field w/ encoding Spatial Decoding of the MR Signal Frequency Decomposition Steps in 3D Localization ♦Can only detect total RF signal from inside the “RF coil” (the detecting antenna)  Excite and receive Mxy in a thin (2D) slice of the subject The RF signal we detect must come from this slice  Reduce dimension from 3D down to 2D   Deliberately make magnetic field strength B depend on location within slice Frequency of RF signal will depend on where it comes from  Breaking total signal into frequency components will provide more localization information   Make RF signal phase depend on location within slice  Exciting and Receiving Mxy in a Thin Slice of Tissue Excite: Source of RF frequency on resonance Addition of small frequency variation Amplitude modulation with “sinc” function RF power amplifier RF coil Electromagnetic Excitation Pulse (RF Pulse) Fo t FT Time Fo Fo+1/ t Frequency Fo t FT Fo ∆F= 1/ t The k-space Trajectory Equations that govern k-space trajectory: Kx = γ /2π ∫ 0t Gx(t) dt Ky = γ /2π ∫ 0t Gy(t) dt Gx (amplitude) Kx (area) t time A typical diagram for MRI frequency encoding: A k-space perspective 90o Excitation Slice Selectio n Frequency Encoding readout Readout Exercise drawing its k-space representation The k-space Trajectory A typical diagram for MRI frequency encoding: A k-space perspective 90o 180o Excitation Slice Selectio n Frequency Encoding readout Readout Exercise drawing its k-space representation The k-space Trajectory A typical diagram for MRI phase encoding: A k-space perspective Excitation 90o Slice Selectio n Frequency Encoding Phase Encoding readout Readout Exercise drawing its k-space representation The k-space Trajectory A typical diagram for MRI phase encoding: A k-space perspective 90 o Excitation 180o Slice Selectio n Frequency Encoding Phase Encoding readout Readout Exercise drawing its k-space representation The k-space Trajectory Sampling in k-space kmax ∆k = γ G∆t ∆k = / FOV A FOV: 10 cm Pixel Size: cm B 10 cm FOV: Pixel Size: cm A FOV: 10 cm Pixel Size: cm B FOV: Pixel Size: cm cm A FOV: 10 cm Pixel Size: cm B 20 cm FOV: Pixel Size: cm K-space can also help explain imaging distortions: Original image K-space trajectory Distorted Image