Basics of Magnetic Resonance Imaging Angular Momentum Orbital Angular Momentum P

Basics of Magnetic Resonance Imaging Angular Momentum Orbital Angular Momentum P

Ramirez, Andy, Managing Editor has reference to this Academic Journal, PHwiki organized this Journal Basics of Magnetic Resonance Imaging Angular Momentum Orbital Angular Momentum Principles of Medical Imaging  Shung, Smith in addition to Tsui Angular Momentum Spin Angular Momentum Spin is an intrinsic property of the nucleons (protons in addition to neutrons) in a nucleus HOWEVER  The name doesnt mean that spin results from the nucleons rotating about an axis!!! http://svs.gsfc.nasa.gov/vis/a000000/a001300/a001319/

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Spin Angular Momentum Spin is quantized  it can only take certain values Here I is the total spin quantum number of the nucleus. The proton has I = ½. Lz is the angular momentum due to that spin. Spin Angular Momentum To get the total spin of a nucleus we add up (separately) the spins of the protons in addition to neutrons Only nuclei with an odd number of protons or neutrons will be visible to MRI We do pairwise addition: 7 protons 8 neutrons Note: 14N has spin 1. 15N has spin ½ . Alignment of Spins in a Magnetic Field, B0 Principles of Medical Imaging  Shung, Smith in addition to Tsui The spin angular momentum yields a magnetic moment

Energy Levels of Spins in addition to B0 Principles of Medical Imaging  Shung, Smith in addition to Tsui E1 = B0 E2 = -B0 Energy Levels in addition to Spin E = E1 – E2 = 2 B0 = (h/2) B0 as long as spin-1/2 particles B0 is the main magnetic field Energy Level Population in addition to Field Strength Spins are distributed according to the Boltzmann distribution

Larmor Frequency Principles of Medical Imaging  Shung, Smith in addition to Tsui Excitation Energy in addition to Frames of Reference x z y x z lab frame y rotating frame B0 = main magnetic field B1 = applied field (pulse) Beff = vector sum B0+B1 Net Magnetization, M, in addition to the Rotating Frame B1 M M y x z y x z B0 0 B1 = 0 B0 0 B1 0 While B1 0, M precesses around B1

Net Magnetization, M, in addition to the Rotating Frame We turn B1 on by a applying radiofrequency (RF) to the sample at the Larmor frequency. This is a resonant absorption of energy. If we leave B1 on just long enough as long as M to rotate into the x – y plane, then we have applied a 90 pulse. In this case, Nupper = Nlower. If we leave B1 on just long enough as long as M to rotate along the -z axis, then we have applied a 180 pulse (inversion). In this case, Nupper = Nlower + M. Free Induction Decay What is the effect of applying a 90 pulse RF /2 time Free Induction Decay The effect of a 90 pulse is to rotate M into the x – y (transverse) plane. If we place a detection coil (a loop of wire) perpendicular to the transverse place, we will detect an induced current in the loop as M precesses by (in the lab frame). Principles of Medical Imaging  Shung, Smith in addition to Tsui

Signal Processing of Free Induction Decay Principles of Medical Imaging  Shung, Smith in addition to Tsui We can characterize the signal by its: Amplitude Phase Frequency Fourier Trans as long as m Signal Processing of Free Induction Decay We see that after a 90 pulse, we get a cosinusoidal signal. To quantitatively describe the signal we calculate its Fourier trans as long as m. (think: Larmor frequency) Principles of Medical Imaging  Shung, Smith in addition to Tsui http://www.med.harvard.edu/JPNM/physics/didactics/improc/intro/fourier3.html Fourier Trans as long as m of Time Domain Data

Image Contrast (I) We can detect the signal from water molecules in the body. Can we make an image Will it be a useful image Relaxation Processes Fortunately as long as us, the signal we get from water molecules in the body depends on their local environment. Spins can interact by exchanging or losing energy (or both). As in all spectroscopy methods, we put energy into the system in addition to we then detect the emitted energy to learn about the composition of the sample. We then use some variables to characterize the emission of energy which (indirectly) tell us about the environment of the spins. Image Contrast! Relaxation Processes (T2) 1. Spin-spin relaxation time (T2): when spins interact With each others magnetic field, they can exchange energy (per as long as m a spin flip). They can lose phase coherence, however. Only affects Mxy. Signal without T2 interaction between spins Signal including T2 interactions between spins http://irm-francophone.com/htm/signal.htm T2 T2

T2 in addition to T2 T2 is an intrinsic property of the sample. This is what we are interested in to use as long as contrast generation. T2 is the time constant of the decay of the free induction decay. It is related to the intrinsic T2 in the following way: T2 in addition to T2 Not a r in addition to om process r in addition to om process Inhomogeneity term – dephasing due to magnet (B0) imperfections depends upon position Susceptibility term – dephasing due to the interaction of different sample regions with B0 (depends upon position) /2 pulse (delay) Relaxation Processes (T2)

T2 Effect of Spin Coherence on Signal http://irm-francophone.com/htm/signal.htm Reverse Start Irreversible versus Reversible http://www.cchem.berkeley.edu/demolab/images/HahnEchoSpinRes.htm Hahn Spin Echo Pulse Sequence http://www.chem.queensu.ca/FACILITIES/NMR/nmr/webcourse/t2.htm http://www.esr.ethz.ch/intro/spinecho.html

Hahn Spin Echo in addition to T2 Echo spacing , Signal We can calculate T2 by changing the echo spacing, , in addition to recording the signal at 2. http://spiff.rit.edu/classes/phys273/exponential/exponential.html Spin-Lattice Relaxation, T1 To look at the behavior of the longitudinal component of M (Mz), we start by putting M along the -z axis in addition to then read it out with a 90 pulse. Spin-Lattice Relaxation, T1 Energy levels in addition to Inversion Equilibrium Net Magnetization: After Inversion = =

low spatial frequencies high spatial frequencies all frequencies http://www.indyrad.iupui.edu/public/lectures/mri/iu-lectures/mri-homepage.htm FT http://www.jsdi.or.jp/~fumipon/mri/K-space.htm k-space data image data Structure of MRI Data: k-space

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