mri 1 - BE101 Foundations of Biomedical Imaging Fall 2009...

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UCSD BE101 Fa06 Lecture 7 Slide 1 BE101 Foundations of Biomedical Imaging Fall 2009 David Hall, Ph.D. Department of Bioengineering University of California–San Diego Lecture: MRI I
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UCSD BE101 Fa06 Lecture 7 Slide 2 Physical Basis for Magnetic Resonance Spin Physics Relaxation Suetens’s: Chapter 6 (pages 99-108) Today’s Outline
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UCSD BE101 Fa06 Lecture 7 Slide 3 The Nitty gritty (concentrate!) ~ 30 slides Recap by analogy (easier) ~ 40 slides Summary ~ 6 slides Lecture Overview
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UCSD BE101 Fa06 Lecture 7 Slide 4 Nuclear Magnetic Resonance (NMR): Bloch 1940’s Nuclear Magnetic Resonance Imaging (NMRI) – Lauterbur 1973, aka MRI. “Spin angular momentum” requires theory of Quantum electrodynamics (QED) – special theory of relativity and quantum mechanics. Simplified discussion of NMR based on classical and quantum mechanics suffice for understanding MRI. Magnetic Resonance Imaging (MRI )
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UCSD BE101 Fa06 Lecture 7 Slide 5 Angular Momenta and Magnetic Moments Earth around Sun: 2 angular momenta: Rotation around the Sun, rotation about own axis (=spinning).
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UCSD BE101 Fa06 Lecture 7 Slide 6 Nuclei Unpaired Protons Unpaired Neutrons Net Spin (γ/2π) MHz/T 1 H 1 0 1/2 42.57 2 H 1 1 1 6.54 31 P 1 0 1/2 17.25 23 Na 1 2 3/2 11.27 14 N 1 1 1 3.08 12 C 0 0 0 0 16 O 0 0 0 0 adapted from: JP Hornak, www.cis.rit.edu/htbooks/mri Protons, Neutrons, and Electrons all have “spin”. Larmor Frequency
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UCSD BE101 Fa06 Lecture 7 Slide 7 Angular Momenta and Magnetic Moments Rutherford’s model of the atom (1911): Orbital angular momentum assigned to electron about the nucleus. Electron is a charged particle implies a current loop and a magnetic moment. Uhlenbeck and Goudsmit (1925) electron must have spin angular momentum (“spin”). BUT spin has no classical analogue – needs QED (Dirac, 1958).
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UCSD BE101 Fa06 Lecture 7 Slide 8 Classical Description NMR – Behavior of atomic nuclei with spin in an external magnetic field. J μ γ = G G 0 (0,0, ) B B = G Angular Momentum Magnetic Moment Gyromagnetic Ratio (constant of a given nucleus)
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UCSD BE101 Fa06 Lecture 7 Slide 9 00 . cos EB B J B μ μθ γ θ =− G G Potential Energy: Energy minimal when μ and B are parallel. Classically, J and θ can have any value, No restrictions on E and J z any value from [–J, +J]
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UCSD BE101 Fa06 Lecture 7 Slide 10 0 00 ( ) (0)cos( ) (0)sin( ) ) ) () (0 ) ) xx y yx y zz it xy xy J dJ dt B d B dt tt t t t B te ω μγ τ τμ μ μμ μω ωγ = = =+ =− + = = = G G G G G GG G G G Torque Cross Product of 2 vectors Combining 3 equations yields Magnetic Moment Solution: (0) xy x y xy x y i t and i μμμ = + note!
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UCSD BE101 Fa06 Lecture 7 Slide 11 0 () (0 ) it xy xy te ω μμ = Transverse (xy) component of μ rotates clockwise about z-axis with angular frequency ω 0 . Longitudinal (z) component is time independent. The motion of μ is a “precession” about z-axis. Rotating Reference Frame: x’,y’,z’ which rotates about z-axis at ω 0 : ' ' ' ) ) ) xx yy zz t t t μ = = = So μ stands still in time.
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This note was uploaded on 04/30/2010 for the course BENG 101 taught by Professor Silva,g during the Fall '08 term at UCSD.

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mri 1 - BE101 Foundations of Biomedical Imaging Fall 2009...

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