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Quality Factor
 
The quality factor (Q) applies to any resonant circuit component; most often the quality factor of the coil determines the overall Q of the circuit.
Inversely related to the fraction of the energy in an oscillating system lost in one oscillation cycle. Q is inversely related to the range of frequency over which the system will exhibit resonance.
In a parallel tuned circuit (such as used in a MR coil), the quality factor is defined as:
Q = vL/R
where L is the coil inductance, R is the circuit resistance, and v is the angular frequency. Increasing quality factor results in improving the signal to noise ratio SNR by a factor √Q and also produces a sharper frequency response (decreased band width). The Q of a coil will depend on the circumstances under which it is measured, e.g. whether it is 'unloaded' (no patient) or 'loaded' (patient).
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Field of View
 
(FOV) Defined as the size of the two or three dimensional spatial encoding area of the image. Usually defined in units of mm². The FOV is the square image area that contains the object of interest to be measured. The smaller the FOV, the higher the resolution and the smaller the voxel size but the lower the measured signal. Useful for decreasing the scantime is a field of view different in the frequency and phase encoding directions (rectangular field of view - RFOV).
The magnetic field homogeneity decreases as more tissue is imaged (greater FOV). As a result the precessional frequencies change across the imaging volume. That can be a problem for fat suppression imaging. This fat is precessing at the expected frequency only in the center of the imaging volume. E.g. frequency specific fat saturation pulses become less effective when the field of view is increased. It is best to use smaller field of views when applying fat saturation pulses.
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Smaller FOV required higher gradient strength and concludes low signal. Therefore you have to find a compromise between these factors. The right choice of the field of view is important for MR image quality. When utilizing small field of views and scanning at a distance from the isocenter (more problems with artifacts) it is obviously important to ensure that the region of interest is within the scanning volume.
A smaller FOV in one direction is available with the function rectangular field of view (RFOV).

See also Field Inhomogeneity Artifact.
 
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Further Reading:
  Basics:
Image Characteristics and Quality
   by www.sprawls.org    
  News & More:
Optimizing Musculoskeletal MR
   by rad.usuhs.mil    
Path Found to a Combined MRI and CT Scanner
Wednesday, 20 March 2013   by spectrum.ieee.org    
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Rectangular Field of View
 
(RFOV) A different field of view (the scanned region) in the frequency and phase encoding directions that means the data acquisition with fewer measurement lines. Because there are fewer rows than columns, a rectangular image is obtained. To reduce the FOV in phase encoding direction (foldover direction) saves scan time by decreasing signal but invariable spatial resolution.
Also called HFI or undersampling.
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If the scanned object is oval, e.g. head or abdomen, a rectangular FOV is an easy to use scan parameter to reduce the scan time without loss of resolution.
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Gyromagnetic Ratio
 
A constant for any given nucleus that relates the nuclear MR frequency and the strength of the external magnetic field.
Definition: The ratio of the magnetic moment (field strength = T) to the angular momentum (frequency = ν) of a particle.
The gyromagnetic effect happens if a magnetic substance is subjected to a magnetic field. Upon a change in direction of the magnetic field, the magnetization of the substance must change. In order for this to happen, the atoms must change their angular momentum. Since there are no external torques acting on the system, the total angular momentum must remain constant. This mass rotation may be measured. The gyromagnetic ratio is different for each nucleus of different atoms. The value of the gyromagnetic ratio for hydrogen (1H) is 4,258 (Hz/G) (42.58 MHz/T).
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Further Reading:
  Basics:
Electron and proton gyromagnetic ratios
   by www.phys.au.dk    
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PhaseForum -
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In a periodic function (such as rotational or sinusoidal motion), the position relative to a particular part of the cycle. An angular relationship describing the degree of synchronism between two sinusoidal waveforms of the same frequency.
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