Introduction to MRI

Spin in QM and Magnetic resonance imaging X-rays. EM wave with enough energy to kick electron off atom or molecule (“ionize”). Molecular damage. e X-ray Harmless Methods (if low power, just slight warming) MRI- uses radio waves, very low frequency/energy electromagnetic radiation. How many had an MRI? Low dose damage DNA  cancer Balance of risks

MRI- like optical spectroscopy to selectively detect atoms, But uses radiofrequency transitions between quantum levels. What are these different quantum states? How can they be used to tell different atoms apart? What physics determines signal strength and selectivity of MRI signal? Why do they put you inside that giant can for MRI? Why does it make so much noise? MRI entirely the creation of quantum mechanics. 1. understood the QM of magnetism in basic particles (atoms, electrons, protons, atomic nuclei) 2. Figured out how it could be useful: determine composition of materials, and medical imaging.

Bunch of ideas- none hard, but put lot of them together: 1. Angular momentum of electron makes magnet (strength given by “magnetic moment,  ”. 2. Orientation of angular momentum is quantized (L z quantized). 3. #1&2 show up/are proved in experiment looking at how atoms are deflected in spatially varying magnetic field (Stern-Gerlach). 4. Atoms with electron in S state (L=0) shows deflection and other stuff  Surprise, electron has magnetic moment even if in state with angular momentum = 0. Unexpected intrinsic property the particle (“spin”). Orientation is quantized-- “up” or “down”. 5. #4 implies that there are additional quantized energy levels for electron in uniform magnetic field. “up energy, down energy”.

6. Can make transitions between these spin levels, like between N,L levels in atoms, but uses oscillating magnetic fields rather than EM fields. Also level separation depends on applied mag. field, but much smaller than for atomic N,L levels. 7. Nuclei of atoms have spin and associated magnetic moments just like electrons, except magnetic moments times smaller. Each different type of atom has different moment. “nuclear fingerprint”. 8. Looking at nucleus spin flip transitions, can identify different types of atoms, similar to optical spectroscopy in a gas, but this nuclear spin spectroscopy (“nuclear magnetic resonance”, NMR) will also work in a solid, including living tissue. 9. Can use NMR to measure distribution of H atoms in human body, and chemical environment = “magnetic resonance imaging, MRI”.

History- putting atoms in magnetic fields to see what happens. Putting atoms in magnetic fields to look at forces. a. What happens to regular magnet in uniform B field? ans b. Homogeneous field makes magnet rotate, not move. Force pulling N up, equal force pulling S end down. Torque but no net force. a. moves upward, b. rotates so N up, c. rotates so N down d. both a and b. e. moves downward red end is North pole

History- putting atoms in magnetic fields to see what happens. Putting atoms in magnetic fields to look at forces. (regular magnet in uniform B field makes magnet rotate, torque, not force) (inhomogeneous field )stronger on top a. rotate, b. move up, c. move down, d. move to right, e. move to left ans. b. stronger force up on N than force down on S. Up wins. If magnet was pointing opposite direction, force is down.

History- putting atoms in magnetic fields to see what happens. Send beam of atoms through uniform B field, see no effect. Doesn’t mean very much because bar magnets would do same. (inhomogeneous field )stronger on top atoms bend up or down by precise small amounts, or no deflection. Never anything in between. (homogeneous field ) no deflection

History- putting atoms in magnetic fields to see what happens. Putting atoms in magnetic fields to look at forces. (inhomogeneous field )stronger on top Experimental observation (Stern and Gerlach) atoms bend up or down by precise small amounts. Never anything in between. L =1, up, middle, down. like book If corresponding experiment with a beam of bar magnets sent fast (so no time to rotate) through an inhomogenous B field would see: smeared out over range of paths, according to orientation.

spinning disc of charge, has angular momentum. Produces magnetic dipole moment. Similar to electron wave function with angular momentum. So no great surprise. What seems strange is that only can have specific orientations in space. Spatial orientation quantized! Seems weird, but already assumed when said L z is quantized.

History- putting atoms in magnetic fields to see what happens. Send beam of H atoms in 1 S state (L=0) through inhomogenous field. Would see what? a. deflect up, b. deflect down, c. no deflection, d. would go up, down, or nondeflected, e. only up or down. e. L=0 state H atoms bend only up or down. Never anything in between.

Putting atoms (H) in magnetic fields to look at forces. (inhomogeneous field )stronger on top Experimental discovery. Always oriented completely up or down! In addition to magnetic moment associated with L, electron has intrinsic magnetic moment (“spin”). Spin ½, Only up or down. New quantum label (in addition to n, l, m)

Bunch of ideas- none hard, but put lot of them together. 1. Angular momentum of electron makes magnet (strength given by “magnetic moment,  ”. 2. Orientation of angular momentum is quantized (L z quantized). 3. #1&2 show up/are proved in experiment looking at how atoms are deflected in spatially varying magnetic field (Stern-Gerlach). 4. Atoms with electron in S state (L=0) shows deflection and other stuff  Surprise, electron has magnetic moment even if in state with angular momentum = 0. Unexpected intrinsic property the particle (“spin”). Orientation is quantized-- “up” or “down”. 5. #4 implies that there are additional quantized energy levels for electron in uniform magnetic field. “up energy, down energy”.

Quantization of magnetic orientation. “Spin” Electron has magnetic moment, can point only up or down. “Spin ½” New quantum label (in addition to n, l, m when in atom) e e Two “types” of electrons. Can have 2 per level without violating Pauli exclusion principle. Not identical. Apply uniform magnetic field- turns into quantized energy levels. For any magnet, E =-µ  B, where µ is magnetic moment, but now only points up or down, so only two possible E’s. Energy ΔE = 2µB B B µ µ

Quantization of magnetic orientation. “Spin” When we apply uniform magnetic field- turns into quantized energy levels. For any magnet, E =-µ  B, where µ is magnetic moment, but now only points up or down, so only two possible E’s. Energy ΔE = 2µB B B µ µ What is fundamentally different about this quantization of energy compared to energy levels in atom? We control it!! Energy depends on B we apply! also energy splitting tiny compared to levels in atom!

Protons and neutrons also have spin and magnetic moments. proton spin=+½, so also only point up or down, but magnetic moment much smaller than for electron (and points in opposite direction). ep m.m.

 each atomic nucleus has particular spin and magnetic moment. Depends on how all the protons and neutrons are hooked together (and quarks inside them, not understood, but well measured) magnet moment µ in units (H = 8.8 x eV/T  42.5 MHz/T to flip) µ H - “1”, µ N = 1/14, µ Na =¼ etc. for others so each type of nucleus has different energy splitting, proportional to B field Energy in applied B field

magnet moment µ in units (H = 8.8 x eV/T  42.5 MHz/T to flip) µ H - “1”, µ N = 1/14, µ Na =¼ etc. for others Put chunk of material in a really big magnetic field (2 Tesla = 4000 G). Separation of nuclear spin energy levels is: a. bigger than thermal energy, and > normal separation of levels in atom observed in optical spectrum. b. > thermal energy, < separation of atom levels. c. ~ thermal energy, < separation of atom levels. d. > thermal energy, ~ separation of atom levels. e. << thermal energy, < < separation of atom levels.

magnet moment µ in units (H = 8.8 x eV/T  42.5 MHz/T to flip) µ H - “1”, µ N = 1/14, µ Na =¼ etc. for others (2 Tesla ) ΔE = 2µB, for H nucleus ~ 2 x eV Atomic levels separated by 2-10 eV thermal energy kT=1/40 eV = eV. So ans. e. spin energy levels split by << kT, <<< atom levels in 2 T field, ΔE = 2µB =h  85 MHz to flip proton (radio wave)

Bunch of years go by. Physicists understand all about atomic, --electron, and nuclear magnetic moments. Measure energy levels, magnetic moments super precisely. Everything checked and tested incredibly precisely in isolated atoms.

Take a container filled with blob of stuff. Apply 2 T magnetic field (big!), measure absorption of radio waves over large frequency range. Would see B = 2T Det stuff looking inside materials RF generator show simplified MRI simulation, only H atoms. B current 50 A, 6.5 x 10 7 Hz a. absorption at only one frequency. b. absorption at one frequency for each kind of atom. c. absorption at many frequencies for each kind of atom. d. no absorption

Take a solid made up of molecules, apply 2 T B field, measure absorption of radio waves at different frequencies. B = 2T Det stuff MHz = Na RF generator Na nuclei res. freq.(= 42.5 MHz/T x ¼ x 2T = MZ = ¼ H) freq. 0 absorption MHz = H 6.07 MHz =1/14 H = ?? three elements, ratios as shown below

magnet moment µ in units (H = 8.8 x eV/T = 42.5 MHz/T) H- “1”, N = 1/14, Na ¼, etc. Brilliant idea: Have a glob of unknown stuff. Find out what it is by putting in mag. field and look at amount of radio waves absorbed at each frequency corresponding to flipping magnetic moment of each type of nucleus.  Nuclear magnetic resonance- analysis of materials Multibillion $$$ industry. 1) Each atomic nuclei has a distinct signature that is not messed up by surroundings. 2) Radio waves go through almost everything pretty easily.

Bunch of ideas- none hard, but put lot of them together. 1. Angular momentum of electron makes magnet (strength given by “magnetic moment,  ”. 2. Orientation of angular momentum is quantized (L z quantized). 3. #1&2 show up/are proved in experiment looking at how atoms are deflected in spatially varying magnetic field (Stern-Gerlach). 4. Atoms with electron in S state (L=0) shows deflection and other stuff  Surprise, electron has magnetic moment even if in state with angular momentum = 0. Unexpected intrinsic property the particle (“spin”). Orientation is quantized-- “up” or “down”. 5. #4 implies that there are additional quantized energy levels for electron in uniform magnetic field. “up energy, down energy”.

6. Can make transitions between these spin levels, like between N,L levels in atoms, but uses oscillating magnetic fields rather than EM fields. Also level separation depends on applied mag. field, but much smaller than for atomic N,L levels. 7. Nuclei of atoms have spin and associated magnetic moments just like electrons, except magnetic moments times smaller. Each different type of atom has different moment. “nuclear fingerprint”. 8. Looking at nucleus spin flip transitions, can identify different types of atoms, similar to optical spectroscopy in a gas, but this nuclear spin spectroscopy (“nuclear magnetic resonance”, NMR) will also work in a solid, including living tissue. 9. Can use NMR to measure distribution of H atoms in human body, and chemical environment = “magnetic resonance imaging, MRI”.

Magnetic resonance imaging. (MRI) Detect density of H atoms throughout body. More H than anything else, and magnetic moment biggest of common stuff. Different tissues have different molecules = different # H atoms. H atoms--tiny magnets

One of most challenging engineering problems ever faced: detect small power at radio frequencies- little photon energies tiny fraction of atoms absorb because of thermal energy need extremely uniform B field want to get good spatial resolution solutions- 1) make B big as possible-- win twice: i) increase ΔE/kT, more absorb, ii) photon energies get bigger. 2) Design really uniform, constant in time magnets so atoms not shifting in and out of resonance. 3) Develop way beyond state-of-art electronics and detectors. 4) Use a bunch of detection and signal processing tricks so more complicated than my description, but basic physics same. Why giant can

Make magnetic field different across body. Use magnetic field dependence of resonance. B x Resonant frequency (radio wave frequency) to flip spin of H nucleus at left ear (LE) right ear (RE), and nose (N). a. same at all three places. b. RE most, nose second, LE least c. LE most, nose second, RE least d. nose least, RE and LE same and higher. e. nose most energy, RE and LE less. Good for detecting amount of H through whole body, but how to look at details in particular location, like part of brain?? 1.0 T 1.1 T B LE B RE ans. c, E = 2µB, mri sim

B x h =2µB x Power absorbed tells you how many H atoms only in slice of head where h =2µB. same, vary B gradients. matches only at one B = one slice. Tells how many H in that slice! B x x change B, now energy matches at different slice. Power absorbed tells you how many H atoms only in new slice of head.

Change B variation over time. Get number of H atoms at each different slice. Change B by changing currents through wires. Move a little, makes lots of noise! To get measure of each spot (not just slope) make B vary in 3 D. Slices of slices Have B varying in x,y, z. Measure power absorbed. Change B's and repeat over and over. Map out H atom distribution in entire head/body. Takes a while. Makes lots of noise turning on and off big magnet coils and RF pulses.

Getting even fancier!! If measure frequency really really carefully, can tell what type of molecule the H atom is in. Other atoms change the B field a little. H C C C H C C C O Hemoglobin without oxygen. Hemoglobin with oxygen. Oxygen shifts magnetic field. H atom flips at slightly different frequency! Can tell difference. proton spectra in CDCl3

Take a solid made up of molecules, want to look at sodium (Na) nuclei. Apply 2 T B field, measure absorption of radio waves at Na nuclei resonant frequency. (= 42.5 MHz/T x ¼ x 2T = MZ = 8.8 x eV) a. Would have one radio photon absorbed by each Na nuclei. b. Would have one photon absorbed for every few Na nuclei. c. Would have a few photons absorbed for every million Na atoms. d. would have no photons absorbed. B = 2T Det stuff ans. c. Energy gap small compared to thermal energy kT (=.025 eV). Population difference between upper and lower differ by e -ΔE/kT ~ 1-ΔE/kT ~ 1- 9 x eV/.025 eV = x So bottom has tiny bit more. That fraction (3.5/10 6 ) absorbs photons. E