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BME 595 - Medical Imaging ApplicationsPart 2: INTRODUCTION TO MRI
Lecture 2 Basics of Magnetic Resonance Imaging
Feb. 23, 2005
James D. Christensen, Ph.D.IU School of Medicine
Department of RadiologyResearch II building, E002C
References
Online resources for introductory review of MRI physics:Robert Cox’s book chapters online
http://afni.nimh.nih.gov/afni/edu/See “Background Information on MRI” section
Mark Cohen’s intro Basic MR Physics slideshttp://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/MiscShared.html
Douglas Noll’s Primer on MRI and Functional MRIhttp://www.bme.umich.edu/~dnoll/primer2.pdf
Joseph Hornak’s Web Tutorial, The Basics of MRIhttp://www.cis.rit.edu/htbooks/mri/mri-main.htm
Books covering basics of MRI physics:E. Mark Haacke, et al. Magnetic Resonance Imaging: Physical Principles and Sequence
Design, 1999.
D. Shaw. Fourier Transform NMR Spectroscopy, 1976.
R. N. Bracewell. The Fourier Transform and its Applications, 1965.
Fourier Transform
Discrete case
Fourier Transform Pairs
Convolution Theorem
Signal Detection:Real & Image Components
X channel (0 phase - Real)
Y channel (90 phase - Imaginary)
Single-Channel Detection
X channel (0 phase - Real) Y channel (90 phase - Imaginary)
Problem: positive & negative frequencies cannot be distinguished!
Quadrature Detection
+ and - frequencies can be distinguished. The entire bandwidth can be utilized
Signal ADC With sufficient sampling rate
Signal ADC Insufficient sampling rate causes aliasing
K-Space EncodingUsing an Applied Gradient
Where ρ is the spin density and k is the spatial frequency
Frequency-Encoding2-Spin Example
Dirac Delta function (line with width=0)
Phase-Encoding
2D K-Space -> Image Space
Slice Selection
Slice Selection
Slice Selection
Slice Selection
Oblique Slice Selection
Spin-Echo Pulse Sequence
Homework