BME 595 - Medical Imaging Applications Part 2: INTRODUCTION TO MRI Lecture 2 Basics of Magnetic Resonance Imaging Feb. 23, 2005 James D. Christensen, Ph.D.

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Presentation transcript:

BME Medical Imaging Applications Part 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 Radiology Research II building, E002C

References Online resources for introductory review of MRI physics: Robert Cox’s book chapters online See “Background Information on MRI” section Mark Cohen’s intro Basic MR Physics slides Douglas Noll’s Primer on MRI and Functional MRI Joseph Hornak’s Web Tutorial, The Basics of MRI Books covering basics of MRI physics: E. Mark Haacke, et al. Magnetic Resonance Imaging: Physical Principles and Sequence Design, D. Shaw. Fourier Transform NMR Spectroscopy, 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 Encoding Using an Applied Gradient Where ρ is the spin density and k is the spatial frequency

Frequency-Encoding 2-Spin Example Dirac Delta function (line with width=0)

Phase-Encoding

2D K-Space -> Image Space

Slice Selection

Oblique Slice Selection

Spin-Echo Pulse Sequence

Homework