The document discusses several topics related to magnetism and resonance in MRI: 1) All substances are magnetic to some degree due to the spin and motion of charged subatomic particles like protons and electrons, which generate small magnetic fields and dipoles even in non-magnetic materials. 2) Materials fall into classes like diamagnetic, paramagnetic, and ferromagnetic based on their magnetic susceptibility, or how they respond to an external magnetic field. 3) Resonance is the absorption of energy from an oscillating field that matches the natural precessional frequency of protons in a magnetic field, which is the basis for MRI signal generation.

1. M R I Physics Course

2. M R I Physics course Chapter 2 Basic Physical Properties Magnetism & Resonance The “M” and “R” in MRI.

3. Magnetism “ Magnetized” objects exert forces of repulsion or attraction on one another, resulting from electric currents.

4. Magnetic Properties All substances are magnetic (to various degrees). Magnetic susceptibility is the ability of a substance to become magnetized. Q: If all substances are magnetic, do all substances have “electric currents” running in them? A: We’ll examine this question shortly…

5. Magnetic Properties (continued) External field is applied  object becomes magnetized, according to susceptibility. Most standard materials fall into one of these classes (defined by the susceptibility): Diamagnetic Paramagnetic Super-paramagnetic Ferromagnetic

6. Magnetic Properties (continued) Diamagnetic - develop a small magnetic field in opposition to an applied field (and have a small negative magnetic susceptibility). Non-Magnetic - very weakly diamagnetic No field applied Field applied

7. Magnetic Properties (continued) No field applied Field applied Paramagnetic -develop a small magnetic field in alignment with an applied field (and have a small positive magnetic susceptibility). Super-paramagnetism is ascribed to small particles of iron oxide that can be used as MRI contrast agents.

8. Magnetic Properties (continued) No field applied Field applied Ferromagnetic - strongly paramagnetic Fe, Co, Ni, Gd. Magnetism induced by an applied magnetic field may be retained. Ferromagnetic substances have a strong positive magnetic susceptibility.

9. Magnetic Properties (continued) Stainless Steel: can be ferromagnetic (exterior surface of the downtown VAMC) or non-magnetic (most surgical steel) depending upon the particular alloy (Fe, Cr, Ni, Mn). Fortunately, most ( not all ) surgical appliances (staples, clips, etc.) are an alloy that is non-magnetic.

10. A ferromagnetic substance in an applied magnetic field will develop a magnetic field hundreds of times as strong as the applied field. A spherical iron ball at a distance of 1.6 m from a 1.0 T unshielded magnet will experience equal attractive forces from gravity and the magnet. This phenomenon is the basis for the “projectile hazards” in MRI. Induced Magnetism

11. Induced Magnetism (continued) An electrical conductor wrapped around a ferromagnetic iron rod induces a very useful magnetic field when an electric current is flowing: Electromagnets, Transformers, and Motors have iron cores. The induced field is much larger than the magnetic field created by the current flow in the conductor.

12. Magnetism in Our World Magnetic fields are all around us: Average field in Milky Way: 5x10 -6 Gauss Average field in Solar Wind: 5x10 -5 Gauss Average field at Moon: 1x10 -2 Gauss Average field at Jupiter: 2x10 4 Gauss 1 Tesla = 10,000 Gauss = 1x10 4 Gauss 1 T = 10,000 G

13. The Earth’s magnetic field is 0.5 - 1.0 Gauss at 15° with axis of Earth’s rotation. A 1.5 Tesla (15,000 Gauss) field is 15,000 to 30,000 times greater than the Earth’s magnetic field. Magnetism in Our World (continued)

14. Origins of Magnetism “ Stationary” electrical charges have an electric field (“E-field”). “ Moving” electrical charges develop a magnetic field (“B-field”). The basis for ALL MAGNETISM is the motion of electrical charges.

15. Relationship of E- and B-fields Stationary observer of stationary charge sees E-field E Stationary observer of moving charge also sees B-field E` B

16. Because of the inseparability of electric charges and magnetism, we refer to these phenomena in general as “Electromagnetism”. Phenomena of stationary charges  “Electrostatics” Relationship of E- and B-fields

17. tungsten target on X-ray tube anode Bremsstrahlung photon high speed electron Remember: an accelerating or decelerating point electric charge radiates electromagnetic radiation. “ Acceleration” of electrons as they are deflected by the nucleus of a tungsten atom in the target produces Bremsstrahlung photons for diagnostic x-ray applications. -

18. Electric Field Lines (arrows) represent the direction of the fields “ Stationary” Point Electrical Charges Electric Fields (in this case, an “electrostatic field”) - +

19. Origins of Magnetism (continued) The “ right hand rule ” describes the direction of the magnetic field relative to the direction of movement of electric charges. Fingers : direction of magnetic field Thumb : direction of positive charges

20. A moving point electric charge develops a magnetic field Movement of a positive particle into the page + Movement of a positive particle out of the page Magnetic Fields +

21. Movement of an electron into the page Movement of an electron out of the page A moving point electric charge develops a magnetic field Magnetic Fields - -

22. + Direction of magnetic field depends on: 1) particle charge, and 2) direction of motion . - - Movement of a positive particle out of the page Movement of a positive particle into the page Movement of an electron out of the page - - Movement of an electron into the page +

23. Topology of B-field Charges moving in straight lines form circular field. Charges moving in a circle form a linear field in the center of circle. E` B B

24. Magnetic Properties Q: If all substances are magnetic, do all substances have “electric currents” running in them? Let’s examine this question…

25. electrons mass = ~0.0005 amu charge = -1 electrostatic unit(esu) protons mass = ~1.0 amu charge = +1 esu neutrons mass = ~1.0 amu charge = neutral All Observable Matter is Composed of Subatomic Particles + -

26. + Proton 2 Up quarks (+2/3 esu) and 1 Down quark (-1/3 esu) = +1 esu net charge Nucleons (or protons, neutrons) are composed of charged “quarks” Neutron 2 Down quarks (-1/3 esu) and 1 Up quark (+2/3 esu) = no net charge + + + - - -

27. Magnetic Properties Subatomic particles have a property called “spin”. They behave as if they are spinning on their axis. So, let’s think about little regions on the surface of the particle, shown as boxes.

28. Magnetic Properties Each box contains charged particle material. Therefore, as the particle rotates, the boxes act like moving charges. So, our particle behaves like a collection of currents, and we generate a magnetic field. B

29. + Spinning of the subatomic particles generates a magnetic field, called a “magnetic moment” or “magnetic dipole”. Electron magnetic moment Proton magnetic moment Neutron magnetic moment For both protons and neutrons, the spinning of the charged quarks produces the magnetic moment. So, although the neutron is electrically “neutral”, its spinning quarks give it a magnetic moment . -

30. Magnetic Properties Q: If all substances are magnetic, do all substances have “electric currents” running in them? A: Yes, at the subatomic level. But the currents are a result of particle “spin”.

31. Resonance Stimulated oscillation at the natural or normal frequency

32. E E A Classical demonstration using tuning forks: Tuning Fork 1 Tuning Fork 2 Sound waves from tuning fork 1 stimulate a non-vibrating tuning fork 2, with same resonant frequency, to RESONATE. It will absorb and give off energy readily at this frequency. ) ) ( ( ) ) ( ( D F

33. Tuning Fork 1 Tuned string The same is true of a guitar string tuned to the frequency of the tuning fork. But, if you detune the string, it will (essentially) not resonate anymore. ) ) ( ( ) ) ( (

34. In MRI, resonance relates to the stimulation of proton magnetic moments (hydrogen nuclei) by RF energy of the appropriate resonant frequency. So, the protons will readily absorb and release RF energy at this frequency. The resonant frequency is “tunable” by the strength of the magnetic field in which the protons are spinning, as we shall see in a later lecture. Resonance (cont.)

35. Radio Frequency Energy (RF) - oscillating magnetic and electric fields (I.e., “electromagnetic” fields) having frequencies between 3 kilohertz (kHz) and 30 Gigahertz (GHz). Examples Radio waves(AM: 535-1605 kHz; FM: 88-108 MHz ) MRI (21,43,64,128 MHz  protons in 0.5,1T,1.5T,3T; lower for spectroscopy) Cellphones (824-848 MHz) TV transmission (50-900 MHz; Ch.2-4  54-72 MHz ) Microwave Ovens (2.45 GHz) Radar (3-30 GHz)

36. Radio Frequency Energy In MRI, magnetic fields oscillating at the appropriate resonant frequency are used to stimulate nuclei to either absorb energy or to release energy (spin flip transitions; phase coherence).

37. Summary All magnetism originates in the movement of electric charge. Magnetic susceptibility describes to what extent a material increases or decreases an applied magnetic field. Resonance: periodic stimulation at the natural frequency can cause energy exchange.