Advances in Magnetic Resonance Angiography and Physical Principles - Biomedical Image Analysis - page 119

follows:

δ = γ [( G x S x + G x V x t + G x A x t 2 / 2) + (higher order terms)] δ t

(3.2)

The phases of precession and motion under the influence of gradient G x
may be explained to generate spin echo and even echo refocusing phenomena.
Gradient field G x is turned on. Precession phase of moving spin isochromat is in-
tegrated over different time intervals on a precession circle. It will show station-
ary spin isochromat pointing along the x direction at the first echo. Moving spin
isochromats will point in any direction in the xy plane. Let us consider the basis
of 'even echo refocusing phenomenon' in these spin isochromats. The phase an-
gle in these spin isochromats is proportional to the velocity and gradient field
strength G x . However, the second and other even echoes ( n = 2 , 4 , 6 ,... ) have
phase angle zero. The phase angles of even echoes are independent of velocity
in the case of constant-velocity motion and symmetrical echoes.
These concepts explain the behavior of phase and motion. Variations in phase
and motion of flowing blood inside vessels appear with variable spin-phase
appearance of flowing blood. Similarly for accelerated motion, the phase angle is
proportional to acceleration. In this case, even echo refocusing does not happen.
Interestingly, velocity-induced phase changes are proportional to the time t p . t p
is defined as the time during which the gradient field G x is switched on, and is a
function of the echo time ( T = TE/2). Acceleration-induced phase changes are
functions of the echo time TE and t p .

3.1.1.2 Flow Information in Spin Isochromats

In spin echo pulse sequence, gradient vectors are represented in the x , y , and z
directions as G x , G y , and G z gradient fields. In an earlier section, motion in the
gradient field G x was explained. Let us consider the case of motion along the
other gradient fields G y and G z . Similar spin isochromat effects and relationship
may be explained. These flow effects are stronger along the slice-selected gra-
dient. These flow effects are negligible along phase encoding gradient. For read
gradient, area under G z , before and after 180 ◦ refocusing pulse are equal. On
the contrary, for GRE sequence, read gradient is opposite. This read gradient is
equal to 1, just prior to read-out gradient. So, the refocusing effect is generated.
For it, during read-out, gradient is turned on for twice as long as that at the
beginning of the pulse sequence.