6720 Lecture 10_MRI - Lecture X 1. 2. 3. 4. 5. MRI X-1...

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1 PHYS 6720 - Lecture X 1 Lecture X MRI 1. Magnetism of nuclear spin 2. A single spin in a DC field 3. A spin system in a DC field 4. Detection with an RF field 5. Magnetic Resonance Imaging PHYS 6720 - Lecture X 2 • The source of magnetic field: electric current or EM fields. • The forms of magnetic source: magnetic dipole m , quadruple Q, … • The origin of m in an atom: (i) spin: nuclear spin and electronic spin; - its existence can only be explained by QM. (ii) orbital motion of electrons. - can be modeled by either classical EM or QM. X-1 Magnetism of nuclear spin Magnetism and nuclear spin PHYS 6720 - Lecture X 3 • Magnetic dipole moment m (could also be written as μ ) and angular momentum j are related as m = γ j γ = gyromagnetic ratio where j can be either the classical angular momentum for electornic orbital motion (= r x p ) or quantum angular momentum for nuclear spin • The term MRI evolves from Nuclear Magnetic Resonance (NMR) which detects magnetic dipole moment m in atomic nuclei of tissues X-1 Magnetism of nuclear spin Magnetism and nuclear spin PHYS 6720 - Lecture X 4 The rules for determining nuclear spin quantum number: (i) If the number of neutrons and the number of protons are both even, then the nucleus has NO spin. (ii) If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin (1/2, 3/2, 5/2, …) (iii) If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin (1, 2, 3, …) Æ Hydrogen nucleus has only one proton so the spin quantum number is 1/2 X-1 Magnetism of nuclear spin Magnetism and nuclear spin PHYS 6720 - Lecture X 5 Nuclear spins measured by NMR X-1 Magnetism of nuclear spin Magnetism and nuclear spin nucleus 1 H 13 C 17 O 19 F 23 Na 31 P Spin # 1/2 1/2 5/2 1/2 3/2 1/2 Isotopic abundance 100% 1.11% 0.04% 100% 100% 100% Relative physiologic concentration 100 50 4x10 -6 8x10 -2 7.5x10 -2 PHYS 6720 - Lecture X 6 • MRI image signals are acquired from tissues that are magnetized • Understanding MRI requires one to consider (i) how does a single nuclear spin m interact with an “magnetization” field B 0 and (ii) how does its environment affects this interaction • For a single spin in an external field B 0 , the equation of motion for the angular momentum of the spin is given by or X-2 A single spin in a DC field Motion of a spin in a constant field B 0 0 d dt = × j mB 0 d dt γ m
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2 PHYS 6720 - Lecture X 7 • Spin precession and Lamor frequency f 0 Let use a cartesian coordinate system with z-axis being parallel to the magnetic field direction: m =(m x , m y , m z ) and B 0 =(0, 0, B 0 ). Then the equation of motion becomes X-2 A single spin in a DC field Motion of a spin in a constant field B 0 0 ˆˆ ˆ ˆ () 00 xyz x y z x yz d mx my mz m m m dt B γ ++ = PHYS 6720 - Lecture X 8 • Spin precession and Lamor frequency f 0 Separate the equation into different components, take time derivative on both sides and substitute the 1 st -order differential equations on x and y components into each other, assuming B 0 is a static field, we find X-2 A single spin in a DC field
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This note was uploaded on 04/25/2010 for the course PHYS 6720 taught by Professor Hu during the Spring '10 term at East Carolina University .

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6720 Lecture 10_MRI - Lecture X 1. 2. 3. 4. 5. MRI X-1...

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