Physics, Techniques and ProceduresQ factor
in radiology, the term relates to 1) the efficieny of an MR
radiofrequency coil (the "
coil quality factor"), or 2) the "quality" of sound emanating from an
ultrasound transducer after being struck by a short voltage pulse.
MR imaging
In any resonant system, Q relates to the energy stored in that system to the rate at which energy is lost by dissipative processes such as electrical resistance. In a parallel tuned circuit (such as used in an MR
coil), Q is defined as:
Q = vL/R
where L is the coil inductance, R is the circuit resistance, and v is the angular frequency. Increasing Q results in improving the signal to noise ratio SNR by a factor ÖQ and also produces a sharper frequency response (decreased band width). Of several available methods for determing Q, a plot of the coil's frequency response is usually the simplest way to make the measurement. In MR, the coil Q is often dominated by the electrical losses in the human body which limit the improvements that are achievable by better coil design.
Ultrasound
The Q factor of an
ultrasound transducer is defined as:
Q = f0 / (f2 - f1)
where f0 is the resonant frequency (centre frequency) of the transducer crystal, f2 is the frequency above resonance at which the intensity is reduced by half, and f1 is the frequency below resonance at which the intensity is reduced by half. f2 - f1 is thus an expression of the band width of the sound.
The Q factor refers to two characteristics of the transducer: the "purity" (bandwidth) of the sound and the persistence of the sound (the ring down time). Bandwidth and sound duration are related. Theoretically, only infinite sine waves have a single frequency. The beginning and end of an ultrasound pulse introduce a range of frequencies; the shorter the pulse, the wider its frequency spectrum. A "high Q" transducer will respond to a short voltage pulse with a relatively long lasting vibration, emitting ultrasound with a narrow bandwidth (nearly "pure" sound). A "low Q" transducer, on the other hand, will vibrate for ony a short time period, emitting a short pulse of ultrasound consisting of a broad range of frequencies. Adding a backing block to an ultrasound transducer reduces the Q factor by shortening the ringdown time and consequently the pulse duration, which increases the bandwidth of the ultrasound pulse. "Low Q" transducers are preferable in ultrasound imaging systems where a small spatial pulse length is needed for high axial resolution. Doppler ultrasound applications require transducers with higher Q factor to produce narrow bandwidth ultrasound which is needed for detection of the frequency changes caused by blood flow.
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