Fund BioImag : Introduction to Magnetic Resonance 1.What are the components of an MR scanner ? 2.What is the basis of the MR signal ? 3.How is nuclear magnetization affected by an external magnetic field ? 4.How do we best describe the motion of magnetization (in the rotating frame of reference) ? After this week you 1.Are familiar with the prerequisites for nuclear spin 2.know the factors determining nuclear magnetization 3.Can compare magnetizations for different nuclei and magnetic field 4.Know the equation of motion for magnetization 5.Are able to describe the motion of magnetization in lab and rotating frame 6.Understand that MRI has complex mechanisms

Fund BioImag Magnetic resonance of animal models Control 3h 8h 24h 24h Blood vessels (contrast agents) Stroke (mouse) Mouse whole body microscopy Rat brain spectroscopy Brain function

Fund BioImag One magnet, many modalities (contrast mechanisms) Human brain

Fund BioImag mm Ca imaging using Mn-enhanced MRI Glutamate chemical shift imaging Phase imaging 1mm -6.25Hz 6.25Hz IV VI Cerebral blood flow using arterial spin labeling (rat,  -chloralose) 250 ml/100g/min 125 One magnet, many contrasts Rat brain

Fund BioImag What are the essential components of an MRI scanner ? Cut-open in real life It’s a complex machine … Schematic depiction of all MRI components This course focuses on the major elements of MRI : Nucleus Magnet RF coil Gradient coil

Fund BioImag What are the risks of the scanner being never off ? Superconducting wires cooled to lHe temperature (4K) Current stays for 1000 years … It’s a powerful magnet … Magnetic field B 0 [unit: Tesla, T] Earth’s magnetic field ~ T Electromagnets < 1.5 T MRI 1-7 T

Fund BioImag Is it dangerous to walk around a MRI magnet ? Effect of dB/dt on biological tissue TMS has (subtle) behavioral effects (transcranial magnetic stimulation - allowed in volunteers, rTMS is applied every s) Magnetic field B 0 : 0 → 2T in 100 µs = T/s (conservative) Situation: Let’s “walk” to 7T with the same dB/dt over 1.4m  B/  x = 5T/m v  B/  x=20000 T/s  v = 4000 m/s = km/h (10x earth rotational speed) Most B 0 is within the bore of the magnet Don’t start at 0 T, don’t end at 7 T… distance ~ 7m … Max. equivalent speed can be several-fold higher … Correct for surface area A TMS coil radius of 5cm : Area ~.008m 2 vs 0.5m 2 upper trunk  ~ 63 m/s (220km/h) Faraday’s law: (induced voltage  AdB/dt, Faraday)

Fund BioImag What is the basis of Nuclear Magnetism ? Classical and quantum-mechanical view Nucleus  angular momentum L (here called P)  Rotation of electrical charge (nucleus)  Rotating current  Dipole moment P nucleus Magnetic moment  of  individual spin in induction field B o  : gyromagnetic ratio (empirical constant) = N S P  Isotope Net Spin (I) gyromagnetic ratio  [MHz T -1 ] Abundance / % 1H1H1/ H2H P1/ Na3/ N1/ C1/ F 1/ NMR-active isotopes and their gyromagnetic ratio  The angular momentum P of a nucleus is quantized: P z has 2I + 1 values (m): Spin ½: P=h  3/4 

Fund BioImag What is the basis for nuclear magnetization ? Unequal population of Energy levels m=-1/2 (N 1 spins) m=1/2 (N 2 spins) Energy of a magnetic dipole in magnetic field B 0 (classical) Energy is minimal, when µ||B 0 (Where is that used ?) Quantum mechanical description: Boltzmann statistics/distribution: Unequal population of energy levels k : Boltzmann's constant (1.4x J/Kelvin) NB. At 310K : ~1 in 10 6 excess protons in low energy state (1Tesla) → N 1 ~N 2 ~N/2 (N = no of spins) m I =-I,…,I NMR Non-ionizing radiation Transitions between E 1 and E 2 induced by photons h =  E

Fund BioImag View each spin as a magnetic dipole µ (a tiny bar magnet).. Classically: torque  of a dipole µ in B Sum over all µ k → Magnetization 8-3. How to classically describe the Motion of Magnetization ? 2 nd law of rotations (P: angular momentum) Larmor equation What motion does the Larmor equation describe ? A brief tour back to rotational kinematics (arrghh!) v=  r =  r  /  t  r  =const r  →circulates  Precession of M about B with frequency  B/2  Describes a rotation of r about  with frequency f=  /2   valid for any vector entity M,L instead of r r

Fund BioImag What is precession ? A brief tour back to 1 st year, well… physics dL/dt M W,  r Observation: The motion of the axis of the wheel with mass M W is circular about O with constant angular velocity   to L dictated by  MWgMWg MWgMWg From Newton’s 2 nd law (rotations): O CM  Precession frequency string  L Precession frequency increases with 1.mass M W of the wheel → gyromagnetic ratio  2.gravitational pull g → magnetic field B 0 Just like a spinning Gyroscope in gravity What is the value of  ? L=I 

Fund BioImag What are the essentials of Magnetic Resonance ? nucleus & magnetic field Magnet to create magnetic field B 0 || z (N 2 -N 1 )µ z results in equilibrium magnetization M 0  E is small (~µeV)  Non-ionizing e.m. fields Convention in magnetic resonance: Static magnetic field B 0 || z x y z B0B0 Nucleus with non-zero spin and high gyromagnetic ratio  : 1 H M0M0 Nuclear equilibrium magnetization M 0 Magnetization is prop. to 1.No. of spins N (molecules) 2.magnetic field B 0 3.gyromagnetic ratio  Magnetization is prop. to 1.No. of spins N (molecules) 2.magnetic field B 0 3.gyromagnetic ratio  MRI: 1 H 2 O !  thermodynamic equilibrium: M 0 || z Larmor frequency f L =  B 0 /2   L  B 0 Larmor frequency f L =  B 0 /2   L  B 0 Edward M. Purcell Physics 1952 MR is safe, but insensitive N 2 ~N/2

Fund BioImag How can the sensitivity be increased ? magnetic field strength B 0 cle/research/38414 MRI of the breast (1.5 vs 3 Tesla) MRI of the lower abdomen MRI of the spinefMRI of the brain (1.5 vs 4 Tesla) maximum possible MR signal: determined by equilibrium nuclear magnetization M 0 maximum possible MR signal: determined by equilibrium nuclear magnetization M 0

Fund BioImag Why use a Rotating frame of reference to describe the motion of magnetization ? Rotating frame: A reference frame which rotate about z of the laboratory frame at frequency  RF Why use a rotating reference frame ? FfFFfF carrousel I am immobile but feel a force F f That pushes me against the chair...

Fund BioImag What are the consequences of using a rotating reference frame ? Fictitious forces Bird’s eye view (inertial reference frame) Still need proper description of motion Need to add 2 fictitious forces: Situation: A pendulum swings above a rotating disk with amplitude (Rsin  ) equal the disk radius and period equal to that of the disk Observation: While the pendulum swings along a straight line in the inertial reference frame it moves along a circle in the rotating reference frame. Centrifugal Force Coriolis

Fund BioImag x y z What is the equation of motion for magnetization in the rotating reference frame ? Larmor frequency in reference frame rotating with  RF :  =  L -  RF  =  B   B =  /  = B o -  RF /  [lab frame:  RF =0   =  L (  B=B 0 )] For  RF =  L  B = 0 (on–resonance): Off-resonance On-resonance:  =0 LL  RF   RF =  L BB (fictitious) magnetic field  RF /  is progressively subtracted from B 0  RF /  M

Fund BioImag Ex. Flipping magnetization over in the rotating reference frame Start with thermodynamic equilibriummagnetization M 0 Reference frame rotating with  L (on- resonance)Apply additional, constant magnetic field with magnitude B 1 (in xy plane) for time  x y z M0M0 B1B1  What motion can be observed for M ? M 0 precesses about B 1 Magnetization rotates about B 1 with angular velocity  B 1 Frequency  B 1 /2  → period T = 2  /  B 1 Definition Flip angle = angle of rotation  induced by B 1 applied for  seconds Special cases of  : 90 0 : Full excitation (all M 0 is rotated into transverse plane, xy, i.e. M 0 → M xy ) : Inversion (M z → -M z ) B 1 = radiofrequency (RF) field (why?) Rotating reference frame Lab frame: B 1 (t)=B 1 (cos  L t,sin  L t)  ~ 42MHz/Tesla →  L /2  ~ 100MHz

Fund BioImag Supplement: Why there is only equilibrium magnetization along B 0 ? Random Phase approximation Random phase approximation: Only prevails: Thermodynamic equilibrium magnetization M 0 =M z B0B0 Bulk Nuclear Magnetization: B0B0 Random… µ z <µ tot Individual spin is never aligned with B 0 … Quantized magnetic moment µ µzµz µ tot But … Equilibrium M 0 || B 0 = Phase  of µ xy is random (random phase approximation): No net µ xy Phase of µ xy 