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Transcript
BE 581 Intro to MRI What is MRI? • Magnetic Resonance Imaging • Based on NMR: Nuclear Magnetic Resonance • Chapters 14 (NMR) and 15 (MRI) What is MRI? • An imaging modality that uses a magnetic field and radio frequency to image soft tissue • Non ionizing radiation - not enough energy to remove electrons from atoms • Non ionizing radiation - may have enough energy for excitation to a higher energy state What can we see with MRI? • In general soft tissue – Internal Organs – Muscles – Brain – Tumors – Inflammation What can we see with MRI? • With a contrast agent (MRAngiography) – Gadolinium + cherate – Blood vessels – Aneurisms – Blockage What can we see with MRI? • FunctionalMRI (FMRI) – Hemodynamic response of brain/spinal cord – Uses oxygenated hemoglobin as a marker – Response to a stimulus MRI video • http://www.imrser.org/PatientVideo.html • Lucas Parra lecture at City College NY • http://www.youtube.com/watch?v=4uzJ PpC4Wuk&feature=related MRI process • Patient in magnetic field – Precession of protons • Send radio frequency – Precession is in phase (synchronization) • Turn off radio signal – Decay of synchronization • Collection of resonance signal – Coherent precession induces current in detection coil NMR NMR Nuclear Magnetic Resonance Hydrogen Nuclei Hydrogen Nuclei (Protons) Axis of Angular Momentum (Spin), Magnetic Moment Hydrogen Nuclei Spins PRECESS at a single frequency (f0), but incoherently − they are not in phase External Magnetic Field Hydrogen Nuclei Irradiating with a (radio frequency) field of frequency f0, causes spins to precess coherently, or in phase Magnetic Field I magnetic field lines S By staying in the interior region of the field, we can ignore edge effects. But how do we describe magnetic fields and field strengths quantitatively? N Magnetic Field II S B If the charge is crossing magnetic field lines, it experiences a force F. v F An electric charge q moves between the N and S poles with velocity v. q F = qv x B N Thus F is perp both v and B. Magnetic Field III • • • • F[N] = q[A.s]v[m.s-1]B For consistency, units of B must be N.(A . m)-1 1 N.(A.m)-1 1 T (tesla) Kg (A s2)-1 If a current of 1 A flows in a direction perpendicular to the field lines of a 1 T magnetic field, each one-meter length of moving charges will experience a magnetic force of 1 N Magnetic Field B • B goes by several different names in physics literature: – Magnetic field – Magnetic induction – Magnetic induction vector – Magnetic flux density Nuclear Spin • Spin: subatomic property of the nucleus – Quantized (Hydrogen proton I=1/2) • Angular momentum J of spinning mass I spin energy level mI magnetic quantum number can be +1/2 or -1/2 Magnetic moment • The spinning of the charge generates magnetic moment µ is the gyromagnetic ratio and it’s an intrinsic property of each nucleus µ = J Material NMR properties spin • Only non zero spin atoms generate an MRI signal • 1H, 13C, 31P etc. 1H (proton) • MRI is based on the abundance of this proton in the human body Precession • A second order motion- the rotation of a rotating object (~ wobble) Precession • A spin in a uniform magnetic field Bo precesses at a frequency o (Larmor frequency) o= Bo • Quantum mechanics dictates that µz and Jz can only be µz= Jz= hmI / 2 mI= +/- 1/2 (for I=1/2) Spin Energy states • Due to the quantization of the spin there are only 2 possible energy states for the proton - parallel and antiparallel Zeeman effect -loss of a degenerate state E= µzBo= +/- hBo / 4 Degenerate state anti parallel parallel B=0 B B>0 Boltzman distribution • It’s the relative population difference between two energy states • nupper/nlower = exp(-E/KbT) • Kb Boltzman constant =1.38 1023 J/K • T temperature -> this is the reason why it’s hard to to MRI, you need a lot of ENERGY and low temp -> freeze patients? Magnetization • The Boltzman distribution characterizes the number of parallel and antiparallel spin • When B=1.5T applied to 1 million protons there are only 5 more parallel than antiparallel • Typical volume for MRI is 1021 protons Magnetization • This difference generates bulk magnetization Mo in z direction (N nuclei) Classical physics interpretation • valid when E << KbT B Nuclear magnetic moment is a bar magnet • When placed in a magnetic field it is forced to align Classical physics interpretation • Spin provides angular momentum, interaction with Bo -> Torque -> precession • The small difference in population of energy levels produces a small net magnetization Mz Larmor frequency • When proton are irradiated with EM radiation at a frequency fo we have resonance E = hfo= (h/2)Bo The Larmor frequency is o= Bo angular f o= Bo/2 linear • Larmor frequency ->wobbling frequency Use of RF pulse • Bulk magnetization Mz • A pulse of frequency o is able to flip M Use of RF pulse • A pulse of frequency o is able to flip M • The flip angle depends on amplitude and length of the pulse 90 degrees Flip Mz = My 180 degrees flip Mz = -Mz Use of RF pulse • It is fundamental that the RF pulse is applied at the resonant frequency o • Nothing would happen otherwise RESONANT FREQUENCY • Quantum mechanics: A photon with energy equal to E can promote lower energy protons to higher energy Block Equation • Bulk magnetization M=[Mx,My,Mz] Exponential decay with T2 time constant • Magnetization over time Exponential decay with T1 time constant Block Equation - T2 decay • A RF pulse generate the transverse Mx My component • When RF is off Mx and My will decay exponentially (tc=T2) back to Mz Block Equation - T2 decay Damped oscillation Induced on a receiver coil Free precession -T2 decay • Why does this happen? 1 Spin - Spin relaxation – Each spin sees other magnetic field generated by other spins (decay T2) 2 Bo is not perfectly homogeneus (T+2) shorter than T2 (100 times) TOTAL EFFECT Block Equation - T1 decay 90 pulse 180 pulse t M z t M o 1 e T1 t M z t M o 1 2e T1 Free precession - T1 decay • The spin give/loose energy to the environment (lattice) • Spin-lattice relaxation • The system return to equilibrium state after a pulse • Time necessary to recover 63% of longitudinal magnetization Mz Free precession - T1 decay • Water has long T1 • Adding protein reduces T1 length • Contrast agents are sometime used to decrease T1 Free Induction Decay (FID) • We can measure these relaxation state with a R coil tuned at the resonant frequency (o = 3.87 MHz for 1H) s(t)= • Mxy(0) is magnitude of Mx, My at t=0 Homework 1 (due 10/6) • Research values of Mo, T2 and o and trace the T2 relaxation in Matlab Homework 2 (due 10/6) • Do the same for T1 relaxation Homework 3 • Find the energy difference between low and high energy state of a proton in a 5 Tesla magnetic field Homework 4 • What kind of magnets (How many Tesla?) are the basis of commercially available MRI? • Consider clinical MRI, small (arm/leg MRI) and animal MRI Images References • Wikipedia.org • http://www.radiologyinfo.org/en/info.cfm ?pg=angiomr&bhcp=1 • MRI physics class by Lucas Parra CCNY