Highlights of Introductory MRI Course I

　

　

Content:

  1. Structure of an atom
  2. Atomic nucleus
  3. Proton
  4. Magnetic moment
  5. Protons in an external magnetic field
  6. Resonance
  7. Signal generation

　

　

Structure of an atom

The atom consists of a central nucleus and orbiting electrons.

The nucleus contains protons and neutrons.

Protons are positively charged, neutrons have no charge, and electrons are negatively charged.

The atomic number is the number of the protons in the nucleus, and the mass number is the number of the protons and neutrons in the nucleus.

3 types of motion are present within an atom.  These are:

　

(1) electrons spinning on their own axes,

(2) electrons orbiting the nucleus,

(3) the nucleus itself spinning about its own axis.

　

　

　

　

　

　

　

Atomic nucleus

　

lNucleus: odd no. of protons or odd no. of neutrons (or both) => magnetic moment.
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Magnetic moment, m = gIh/2p

                                    
   where     g = gyromagnetic ratio of the nucleus,
                   h = Planck’s constant, and
                   I = nuclear spin.
　

Atomic nuclei which which contain an odd number of protons or an odd number of neutrons (or both) possess magnetic moments, meaning that they behave like tiny bar magnets. 

　

Unit of m is nuclear magneton (nm).

　

Atomic nuclei consist of an even number of protons and even number of neutrons have zero spin (i.e. I =0) and thus zero magnetic moment.

                                       
Common atomic nuclides that can be used for MRI :-

　

lHydrogen is most abundant element, the magnitude of its magnetic moment is comparatively large.
　

　

　

Proton

　

lNucleus of hydrogen = ‘single proton’ 

   

Like the earth, a proton is constantly turning, or spinning around an axis.  It possesses a spin.
The positive electrical charge, being attached to the proton, naturally spins around with it.
Where there is an electrical current, there is also a magnetic field.  The proton has its own magnetic field and it can be seen as a little bar magnet.
　

　

　

　

Magnetic moment

　

The axial magnetic field created by a spinning hydrogen nucleus (or proton) is known as magnetic moment.
　

It should be stressed that MR signals are created by the magnetic moments of the protons and not the protons themselves.

　

　

　

　

　

　

　

　

　

Protons in an external magnetic field

　

　

　   

　

In the absence of a magnetic field, spins are randomly oriented.

　

Exposed to an external magnetic field, each spin or magnetic moment can assume two different orientations, denoted “parallel” (spin up) (at a lower energy state) and “anti-parallel” (spin down) (at a higher energy state), respectively.

　

There is a slight preference for the parallel orientation since lower energy state is more stable.

On equilibrium, the ratio of the number of magnetic moments in  parallel direction (Npara) to the number of magnetic moments in anti-parallel direction (Nanti) is given by Boltzmann Distribution.

Boltzman Distribution

Npara/Nanti = exp(- mBo/kT)
           where m = magnetic moment of proton
                            Bo = external magnetic field strength
                            T = absolute temperature
                             k = Boltzmann’s constant   
At ~ 0°K, the vast majority of the spins are in the lower energy state.
At body temperature and at 1 Tesla, the equilibrium ratio » 1 ppm
(i.e. about 1 excess magnetic moments in // direction per one million magnetic moments of protons)

Precession

　

In the presence of a strong static external magnetic field, the magnetic moments of protons rotate (or precess) around the magnetic field with a well-defined frequency as given by the Larmor Equation.

　

　

　

Larmor Equation

fo = g Bo/2p       or      wo = g Bo

where
                fo = Resonance or Larmor frequency (MHz)
            wo = Larmor angular frequency
                g = Gyromagnetic ratio of the nucleus (MHz/T)
                Bo = Magnetic field strength (T)
e.g. for hydrogen nucleus, Bo = 1 T => wo = 42.6 MHz.
                                              Bo = 1.5 T => wo = 63.9 MHz.

Macroscopic Tissue Magnetisation

　

Each magnetic moment of proton is resolved into longitudinal and transverse components.  The transverse components cancel each other while the longitudinal components add up to form the net tissue magnetisation M.

　

　

When a group of tissue is exposed to an external magnetic field, a net tissue magnetisation of the patient in the direction of the external field is produced.

　

It would be nice if we could measure this magnetisation of the patient, but there is a problem: we cannot measure this magnetic force directly, as it is in the same direction, parallel to the external magnetic field.  So, we need a magnetisation not longitudinal, but transversal to the external magnetic field.

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Resonance

　

Tranverse magnetisation is induced by a radio frequency field B1 rotating synchronously with the precessing magnetic moment.  If the duration of the B1 field and its strength are sufficient to nutate the magnetisation by an angle of 90°, the entire magnetisation ends up in the transverse plane.

　

 i.e. Radio frequency pulse – to resonate magnetic moment
　

The angle of rotation f (known as the RF flip angle) produced by B1 field, is approximated by :

    f = g B1 tp

              where g = gyromagnetic ratio of the proton
                          B1 = RF magnetic field strength
                          tp = RF magnetic field pulse duration
How it works?

We send in a radio wave, which is an electromagnetic wave in the frequency range of the waves which we receive in our radio.  We send into the patient a short burst of radio frequency (RF) pulse.  We need a special RF pulse, which precesses with the same frequency as that of the proton (i.e. same g), so that the proton can pick up some energy from the RF pulse.  By changing the strength and duration of the RF magnetic field pulse, we can flip the net tissue magnetisation vector M through any angle f until it has attained an angle of 90° or p/2 to the external magnetic field.

When RF pulses of frequency equal to the Larmor Frequency of the protons (i.e. 63.9 MHz at 1.5 T) is applied vertical to the external magnetic field, the magnetic moments of protons resonate and absorb maximum amount of energy from the RF pulses.

　

　

　

　

　

　

Signal generation

　

　

 

　

　

When a bar magnet is rotated perpendicular to a coil connected to a cathode ray oscilloscope, an alternating voltage is  generated and displayed on the oscilloscope.
According to Faraday’s law of induction, a changing magnetic field will generate a alternating voltage and current in a conductor directly proportional to dB/dt.
The bar magnet produces a magnetic field B and when it sweeps across the face of the coil, there is a change in magnetic flux linked with the coil and an alternating voltage of frequency equal to the rotational frequency of the bar magnet is induced in the coil.  The magnitude of the induced voltage depends on the strength of the magnetic field and the rate of rotation, since both determine the rate of change of magnetic flux through the coil.
lTransverse magnetisation Mxy rotates at Larmor Frequency => alternating voltage with Larmor Frequency induced in receiver coil => MR signal used in image reconstruction.

　

　

References:

1.  Chan JHM.  Basic Physics of Magnetic Resonance Imaging.  Hong Kong: Bondman Publishing Company, 1994.
2.  General Electric Company.  NMR – A perspective on Imaging.  London: General Electric Co., 1984.
3.  Schild HH.  MRI made easy.  Berlin: H Heenemann GmbH & Co, 1990.
4.  Westbrook C, Kaut C.  MRI in Practice.  Oxford: Blackwell Scientific Publications, 1993.