1!TT. Liu, BE280A, UCSD Fall 2009!Bioengineering 280A"Principles of Biomedical Imaging"Fall Quarter 2009"MRI Lecture 1"TT. Liu, BE280A, UCSD Fall 2009!Spin!• Intrinsic angular momentum of elementary particles -- electrons, protons, neutrons. !• Spin is quantized. Key concept in Quantum Mechanics. !TT. Liu, BE280A, UCSD Fall 2009!Magnetic Moment and " Angular Momentum!A charged sphere spinning about its axis!has angular momentum and a magnetic moment.!This is a classical analogy that is useful for understanding quantum spin, but remember that it is only an analogy! !Relation: µ = γ S where γ is the gyromagnetic ratio and S is the spin angular momentum. !TT. Liu, BE280A, UCSD Fall 2009!Nuclear Spin Rules!Number of Protons!Number of Neutrons! Spin! Examples!Even! Even! 0!12C, 16O!Even! Odd! j/2!17O!Odd! Even! j/2!1H, 23Na, 31P!Odd! Odd! j!2H!2!TT. Liu, BE280A, UCSD Fall 2009!Classical Magnetic Moment!I!A! € µ = IAˆ n TT. Liu, BE280A, UCSD Fall 2009!Energy in a Magnetic Field!Lorentz Force!B! € E = −r µ • B= −µzBMinimum Energy State!Maximum Energy State!TT. Liu, BE280A, UCSD Fall 2009!Energy in a Magnetic Field!www.qi-whiz.com/images/ Earth-magnetic-field.jpg!TT. Liu, BE280A, UCSD Fall 2009!Magnetic Field Units!€ 1 Tesla = 10,000 GaussEarth's field is about 0.5 Gauss 0.5 Gauss = 0.5x10-4 T = 50 µT3!TT. Liu, BE280A, UCSD Fall 2009!Boltzmann Distribution!B0!TT. Liu, BE280A, UCSD Fall 2009!Equilibrium Magnetization!Hansen 2009! € M0= Nµz≈ Nµz2B /(kT)= Nγ22B /(4kT)N = number of nuclear spins per unit volume!Magnetization is proportional to applied field. !TT. Liu, BE280A, UCSD Fall 2009!7T Human imager at U. Minn.!3T Human imager at UCSD.!7T Rodent Imager at UCSD!9.4T Human imager at UIC!Bigger is better!TT. Liu, BE280A, UCSD Fall 2009!Torque !B!µ"N!N = µ x B!Torque!For a non-spinning magnetic moment, the !torque will try to align the moment with !magnetic field (e.g. compass needle)!4!TT. Liu, BE280A, UCSD Fall 2009!Precession!N = µ x B!= N!dS!dt!µ = γ S"= µ x B!= µ x γB!dµ!dt!Torque!Change in !Angular momentum!Relation between magnetic moment and angular momentum!dS!dt!TT. Liu, BE280A, UCSD Fall 2009!Precession!B!µ"= µ x γB!dµ!dt!dµ"Analogous to motion of a gyroscope!Precesses at an angular frequency of!ω = γ Β"This is known as the Larmor frequency.!http://www.astrophysik.uni-kiel.de/~hhaertełmpg_e/gyros_free.mpg!TT. Liu, BE280A, UCSD Fall 2009!Magnetization Vector!€ M =1Vµiprotons in V∑€ dMdt=γM × BVector sum of the magnetic moments over a volume. !For a sample at equilibrium in a magnetic field, the transverse components of the moments cancel out, so that there is only a longitudinal component. !Equation of motion is the same form as for individual moments. !Hansen 2009!TT. Liu, BE280A, UCSD Fall 2009!Gyromagnetic Ratios!Nucleus! Spin! Magnetic Moment! γ/(2π)"(MHz/Tesla)"Abundance! 1H ! 1/2! 2.793! 42.58! 88 M! 23Na! 3/2! 2.216! 11.27! 80 mM! 31P! 1/2! 1.131! 17.25! 75 mM!Source: Haacke et al., p. 27!5!TT. Liu, BE280A, UCSD Fall 2009!Larmor Frequency!ω = γ Β"f = γ Β / (2 π)"Angular frequency in rad/sec!Frequency in cycles/sec or Hertz, !Abbreviated Hz!For a 1.5 T system, the Larmor frequency is 63.86 MHz!which is 63.86 million cycles per second. For comparison,!KPBS-FM transmits at 89.5 MHz. !Note that the earth’s magnetic field is about 50 µΤ, so that!a 1.5T system is about 30,000 times stronger. !TT. Liu, BE280A, UCSD Fall 2009!Notation and Units!€ 1 Tesla = 10,000 GaussEarth's field is about 0.5 Gauss 0.5 Gauss = 0.5x10-4 T = 50 µTγ= 26752 radians/second/Gaussγ=γ/2π= 4258 Hz/Gauss = 42.58 MHz/TeslaTT. Liu, BE280A, UCSD Fall 2009!Simplified Drawing of Basic Instrumentation. Body lies on table encompassed by coils for static field Bo, gradient fields (two of three shown), and radiofrequency field B1. Image, caption: copyright Nishimura, Fig. 3.15 TT. Liu, BE280A, UCSD Fall 2009!RF Excitation!From Levitt, Spin Dynamics, 2001!6!TT. Liu, BE280A, UCSD Fall 2009!RF Excitation!http://www.drcmr.dk/main/content/view/213/74/!TT. Liu, BE280A, UCSD Fall 2009!RF Excitation!Image & caption: Nishimura, Fig. 3.2 B1 radiofrequency field tuned to Larmor frequency and applied in transverse (xy) plane induces nutation (at Larmor frequency) of magnetization vector as it tips away from the z-axis. - lab frame of reference At equilibrium, net magnetizaion is parallel to the main magnetic field. How do we tip the magnetization away from equilibrium? http://www.eecs.umich.edu/%7EdnolłBME516/!TT. Liu, BE280A, UCSD Fall 2009!On-Resonance Excitation!Hanson 2009!http://www.drcmr.dk/JavaCompass/!TT. Liu, BE280A, UCSD Fall 2009!RF Excitation!http://www.eecs.umich.edu/%7EdnolłBME516/!7!TT. Liu, BE280A, UCSD Fall 2009!Rotating Frame of Reference!Reference everything to the magnetic field at isocenter. !TT. Liu, BE280A, UCSD Fall 2009!Images & caption: Nishimura, Fig. 3.3 a) Laboratory frame behavior of M b) Rotating frame behavior of M http://www.eecs.umich.edu/%7EdnolłBME516/!TT. Liu, BE280A, UCSD Fall 2009!RF Excitation!From Buxton 2002!TT. Liu, BE280A, UCSD Fall 2009!Free Induction Decay
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