The partial Fourier technique is a modification of the
Fourier transformation imaging method used in
MRI in which the symmetry of the
raw data in
k-space is used to reduce the
data acquisition time by acquiring only a part of
k-space data.
The symmetry in
k-space is a basic property of
Fourier transformation and is called
Hermitian symmetry. Thus, for the case of a
real valued function g, the data on one half of
k-space can be used to generate the data on the other half.
Utilization of this symmetry to reduce the
acquisition time depends on whether the
MRI problem obeys the assumption made above, i.e. that the function being characterized is
real.
The function imaged in
MRI is the distribution of
transverse magnetization Mxy, which is a
vector quantity having a
magnitude, and a direction in the transverse plane. A convenient mathematical notation is to use a complex number to denote a
vector quantity such as the
transverse magnetization, by assigning the x'-component of the
magnetization to the
real part of the number and the y'-component to the
imaginary part. (Sometimes, this mathematical convenience is stretched somewhat, and the
magnetization is described as having a
real component and an
imaginary component. Physically, the x' and y' components of Mxy are equally 'real' in the tangible
sense.)
Thus, from the known symmetry properties for the
Fourier transformation of a
real valued function, if the
transverse magnetization is entirely in the x'-component (i.e. the y'-component is zero), then an image can be formed from the data for only half of
k-space (ignoring the effects of the imaging gradients, e.g. the readout- and
phase encoding gradients).
The conditions under which
Hermitian symmetry holds and the corrections that must be applied when the assumption is not strictly obeyed must be considered.
There are a variety of factors that can change the
phase of the transverse magnetization:
Off
resonance (e.g.
chemical shift and
magnetic field inhomogeneity cause local
phase shifts in
gradient echo pulse
sequences. This is less of a problem in
spin echo pulse
sequences.
Flow and motion in the presence of gradients also cause
phase shifts.
Effects of the
radio frequency RF pulses can also cause
phase shifts in the image, especially when different coils are used to transmit and receive.
Only, if one can assume that the
phase shifts are slowly varying across the object (i.e. not completely independent in each
pixel) significant benefits can still be obtained. To avoid problems due to slowly varying
phase shifts in the object, more than one half of
k-space must be covered. Thus, both sides of
k-space are measured in a low
spatial frequency range while at higher frequencies they are measured only on one side. The fully sampled low
frequency portion is used to characterize (and correct for) the slowly varying
phase shifts.
Several
reconstruction algorithms are available to achieve this. The size of the fully sampled region is dependent on the
spatial frequency content of the
phase shifts.
The partial Fourier method can be employed to reduce the number of
phase encoding values used and therefore to reduce the
scan time. This method is sometimes called half-NEX, 3/4-NEX imaging, etc. (NEX/NSA).
The
scan time reduction comes at the expense of
signal to noise ratio (
SNR).
Partial
k-space coverage is also useable in the readout direction. To accomplish this, the
dephasing gradient in the readout direction is reduced, and the duration of the
readout gradient and the data acquisition window are shortened.
This is often used in
gradient echo imaging to reduce the
echo time (TE). The benefit is at the expense in
SNR, although this may be partly
offset by the reduced
echo time.
Partial Fourier imaging should not be used when
phase information is eligible, as in
phase contrast angiography.
See also
acronyms for 'partial Fourier techniques' from different manufacturers.
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