University:
University of Michigan
Course:
PHYSICS 250 | Fundamental Physics for the Life Sciences II
Academic year:

2020
Views:

222

Pages:

19
Author:

K Moody

MRI Physics: Frequency and Phase Encoding Spatial Localization B0 MR signals + + = N S w = g B0 Spatial Localization Fourier transform MR signals + + = Raw data Gx 𝜔(𝑥) = 𝛾𝐵(𝑥) = 𝛾(𝐵! + 𝐺" $ 𝑥) Frequency Encoding B=B0-xGx B=B0 B=B0+xGx Gx time FT x Signal (t) OR Summed Signal from all vials (t) 1D “Image” freq x Gradients alter frequency and phase of spins x Gx Frequencyàhow fast spins precess Phaseàrelative orientation with respect to one another Phase EncodingàJust Encoding like Freq Encoding y Phase Encoding works just like Frequency Encoding àImparts spatial dependent frequency which can be extracted using Fourier Transform No Gy Weak Gy Stronger Gy Spins in Constant Magnetic Field Frequency Encoding Phase Encoding Frequency Encoding Signal Equation and Fourier MRI Signal measured in Time OMG, No FT Gradient Gradient k-space “position” Freq FT Spatial Position Traversal of k-Space with Gradients RF Gy Gx ACQ Traversal of K-Space with Gradients RF Gy Gx ACQ Traversal of K-Space with Gradients ACQ RF Gy Gx TE TR Fundamental Imaging Time Time = TR × N PE × NA • TR: Amount of time needed to acquire one line (3 ms – 5 sec) • NPE: Number of lines to acquire (32 – 512) • NA: Averages of each line (1 - ∞) Summary • Magnetic field gradients used to link precession frequency to position à spatial encoding • Frequency encoding: gradient on during data acquisition • Phase encoding: gradient on to accumulate phase, then gradient off during data acquisition • Application of gradients over time dictates k-space trajectory • The need for multiple lines of k-space data leads to long acquisition times

MRI Physics - Frequency and Phase Encoding

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