Basic magnetism and nuclear magnetic resonance

• Spins, Angular Momentum and Magnetization
• QM description of spin system: Energy in a static field
• Classical description of spins in a static magnetic field: vector model for spin 1/2 and motion equation
• Detection of NMR signal
• Magnetic interactions and relaxation times Bulk magnetization

1. Spins, Angular Momentum and Magnetization
   
   •  What is spin

     --- Spin is an intrinsic quantum mechanical property of electrons and some nuclei
     --- The spin acts as an internal angular momentum
     --- Spin has an associated magnetic moment
     u = rhI
     --- The angular momentum is described by
     J = u/r
     --- The direction of the spin angular momentum and magnetic moment are parallel.
     --- r = gyromagnetic constant (ratio)
     --- h = Plank's constant

     Quantum properties of spin
     --- In QM physical properties have discrete ("quantum") values
     --- For spin the direction and magnitude are quantized
     

   •  Spin 1/2 nucleus in an external magnetic field

     Water: ~ 110 mole proton (¹H) with highest NMR sensitivity.
     Tissue: ~60-90% water
     ===> Most MRI based on imaging of water proton

   
   

   [chapter top]

   
   

2. QM description of spin system:
   
   
   •  Energy in a static field

     
     

     
   •  Excitation and Detection of NMR signal:

     

   
   

   [chapter top]

   
   

3. Classical description of spins in a static magnetic field:
   
   
   •  vector model for spin 1/2 and motion equation

     
     
     
     

   •  Time dependent Bloch equations and rotating frame

     
     
     
     

   
   

   [chapter top]

   
   

4. Detection of NMR signal

   90o pulse --> the time-varying transverse magnetization --> induced voltage in the RF coil (Faraday's law):

   

   
   

   ==> Voltage induced at RF freq. ==> receiver electronically subtract carrier freq. from signal freq. ("Free Induction Decay" or FID).

   
   

   Often echo signals are detected:

   
   

   
   

   [chapter top]

   
   

5. Magnetic interactions and relaxation times
   
   
   •  Bulk magnetization:

     
     

     Nuclear spins constantly interacting with their environment and among themselves:

     

     ===>When magnetization is subject to static or radio-freq field, transitions take time: relaxation times T1, T2, T2*,... reflecting biological properties of tissues.

     

     We'll see below that the combination of spin-echo acquisition, magnetic field gradients, and the effective use of timing allow us:
     (1) to achieve spatial encode for imaging;
     (2) to obtain images with proper contrast based on differences in relaxation times.