Biomedical Engineering Reference
In-Depth Information
velocity as a change of phase. The phase accumulation associated with such a
gradient is expressed as:
φ
=
γ
V
·
T
·
A
(3.14)
where
φ
is phase shift induced by flow in the transverse spin magnetization,
γ
is the gyromagnetic ratio of the spin,
V
is the component of the spin's velocity
in the applied gradient's direction,
T
is the center-to-center time interval between
the two gradient lobes, and
A
is the area of each gradient lobe. This equation
describes only the phase shift induced by constant velocity flow when a bipolar
gradient is applied and not phase shifts due to such higher orders of motion as
acceleration or jerk. Since the flow-induced phase shift is directly proportional
to velocity, a stationary spin with zero velocity will have no net phase accumula-
tion. For subsequent acquisitions, this pulse sequence inverts the polarity of the
bipolar flow-encoding gradients. The polarity of the gradient (
A
) is now negative,
giving the equation for the second acquisition as
φ
=−
γ
VTA
. When the image
data from the first acquisition is subtracted from the second acquisition, the
remaining data is from the signal that is different in two acquisitions i.e., the
intravascular signal from moving blood. The procedural difference in these two
acquisitions is the negation of bipolar gradients. A stationary spin will have iden-
tical (zero) phase shifts for each polarity of the flow-encoding pulse, resulting
in a zero net phase shift. So, the subtraction of two vectors result in zero. The
vector subtraction of signals from the spins moving with constant velocity is
quite different.
Suppose two signals have the same magnitude but different phases. Con-
sequently, when the vectors are subtracted, the resulting vector is not zero.
The result is signal originating from vascular structures with nearly complete
elimination of stationary tissues from the MR angiogram. In MRA, the imager
acquires the equivalent of three raw data sets for three flow-encoding directions.
The magnitudes of these data sets are combined into a total flow angiogram.
3.2.4.2 Image Contrast
Image contrast in PC angiography is influenced by several factors such as flow
direction, velocity encoding and aliasing, phase dispersion and flow compensa-
tion, and saturation effects.
