Biomedical Engineering Reference
In-Depth Information
3.1.1.4 Factors Influencing the Appearance of Flowing Blood
on MR Images
The magnetization
M
xy
, after application of 90
◦
nutation pulse in an SE experi-
ment, can be explained as:
M
xy
=
F
{
v,
a
,...
}
H
{
1
−
exp (
t
/
T1)
}
(exp(
−
t
/
T2))
(3.7)
where the expressions in parentheses characterize longitudinal (T1) and trans-
verse (T2) dependent magnetizations and are known as relaxation times.
H
is proton density. The factor
F
(
v,
a
,...
) is flow factor which depends on spin
isochromats. Velocity (
v
), acceleration (
a
), slice transition, spin phase phenom-
ena, and high-order motion terms are the main variables.
3.1.2 Flow Physical Principles
Let us discuss the basic flow patterns in blood vessels and related MRA signal
magnitudes. Mathematical models of laminar and plug flow for signals from
spin echo pulses are well established. Flow causes a physical displacement of
spins between successive excitations. This time-of-flight effect leads to different
series of RF pulses producing different echo amplitudes for a number of different
spin populations. The fraction volume of each population can be expressed as
a function of the interpulse interval length during which each population enters
the slice. So, the total signal is the sum of the echo amplitudes from each spin
population. Different pulse sequences generate image signal intensity (SI) as a
function of velocity, TR, T I, TE and slice thickness.
Fractional volume segments.
The cylindrical volume of the vessel cut by a
slice is equal to fraction of flowing blood volume of imaging (VOI).
MRA image signal.
The evolution of magnetization for each spin popula-
tion can be described by Bloch equations. For simplicity, magnetization may be
expressed for transforming to a reference rotating frame at Larmor frequency
(
−
γ
H
0
) according to Bloch equations as follows:
M
x
(
t
)
=
M
0
x
exp
(
−
t
/
T2)
(3.8)
M
y
(
t
)
=
M
0
y
exp
(
−
t
/
T2)
(3.9)
M
z
(
t
)
=
M
0
[1
−
exp
(
t
−
t
/
T1)
]
+
M
0
z
exp
(
−
t
/
T
1)
(3.10)
