Larmor Frequency

-


Larmor Frequency


The Larmor frequency and equation are named after the Irish physicist and mathematician Joseph Larmor (1857-1942).
Protons and neutrons pair up in nuclei causing the cancellation of their individual angular momentum. All nuclei also have a spin; those with an odd number of protons and/or neutrons will have a property called a magnetic (dipole) moment. Magnetic moment is characterized by its alignment with an external magnetic field analogous to a small bar magnet. These particular nuclei are also called dipoles because they have two poles like the north and south pole of a bar magnet. H-1 and P-31 are examples of nuclei with an unpaired proton. N-14 is an example of a nucleus with both an unpaired proton and neutron.
In addition to alignment of nuclei with a magnetic moment, application of an external magnetic field will produce a secondary spin or wobble (precession) of nuclei around the main or static magnetic field. The precessional path around the magnetic field is circular like a spinning top.
The Larmor or precessional frequency in MRI refers to the rate of precession of the magnetic moment of the proton around the external magnetic field. The frequency of precession is related to the strength of the magnetic field, B0.
The precessional frequency of nuclei of a substance placed in a static magnetic field B0 is calculated from the Larmor Equation:

ω = γB

where ω is the Larmor frequency in MHz, γ is the gyromagnetic ratio in MHz/tesla and B is the strength of the static magnetic field in tesla. Note that the gyromagnetic ratio is defined in different ways by different authors. See the article on gyromagnetic ratio. In this case a useful, simplified version is shown representing the Larmor frequency when B0=1.
  • The gyromagnetic ratio (MHz/T) for a few commonly measured or imaged isotopes are :
    • H-1                   42.58
    • F-19                 40.05
    • Na-23               11.26
    • P-31                 17.24

B0



The B0 in MRI refers to the main static magnetic field and is measured in teslas. The majority of MRI systems in clinical use are 1.5 T, with increasing numbers of 3 T systems being installed.
Altering the field strength will affect the Larmor frequency at which the protons precess.

Comments

Post a Comment

Popular posts from this blog

MRI Physics

-
Image
THE BASIC PROCESS The way MR images are generated is complicated and is much harder to understand than plain radiography, CT and ultrasound. It has strong underpinnings in physics which must be understood before any real sense of 'how it works' is gained. What follows is a very abbreviated, 'broad strokes' description of the process. Essentially, the process can be broken down into four parts: 1. Preparation 2. Excitation 3. Spatial encoding 4. Signal acquisition Preparation The patient is placed in a static magnetic field produced by the magnet of the MR scanner. In living tissues there are a lot of hydrogen atoms included in water molecules or in many different other molecules. The proton, the nucleus of hydrogen, possesses an intrinsic magnetisation called spin. The spin magnetization vector precesses (rotates) around the magnetic field at a frequency called the Larmor frequency, which is proportional to the magnetic field intensity. The
Read more

Echo Time

-
Image
ECHO TIME The echo time (TE) refers to the time between the application of the radiofrequency excitation pulse and the peak of the signal induced in the coil. It is measured in milliseconds. The amount of T2 relaxation is controlled by the TE.
Read more

Relaxation

-
Image
Relaxation MRI image contrast is influenced by several characteristics of tissues and other materials including: T1, T2 and T2* relaxation as well as spin density, susceptibility effects and flow effects. This page and the following detailed pages on relaxation parameters will introduce properties and effects on imaging contrast, time and signal-to-noise ratio (SNR). Relaxation  is the process in which spins release the energy received from a radiofrequency pulse. T1 and T2 relaxation rates affect the SNR in an image. Improvement in the SNR is seen when the TR is increased significantly to about 3-5 T1 times. Changing the TR time will also affect the T1 weighting of the image and the acquisition time. T1 weighting occurs in a short TR spin echo sequence because of incomplete recovery of longitudinal magnetization. The effect of TR on SNR can be shown graphically by a T1 relaxation curve as illustrated in the exponential growth curve in figure 1. As the TR is increased to
Read more