Adiabatic pulse design

Details Adiabatic pulse design Adiabatic pulse design

1998-01-07

2002-09-10

Oda, Christine K. (Department: 2862)

Electricity: measuring and testing

Particle precession resonance

Using a nuclear resonance spectrometer system

C324S309000, C324S314000

Reexamination Certificate

active

06448769

ABSTRACT:

FIELD OF THE INVENTION
The present invention relates to the design of adiabatic pulses for MRI (Magnetic Resonance Imaging) and in particular to adiabatic pulses which do not fulfill an adiabatic condition, as defined in a frequency frame.
BACKGROUND OF THE INVENTION
Magnetic resonance imaging is based on the process of inverting the spins of atoms which are situated in a strong axial magnetic field and then measuring the electromagnetic radiation of the atoms, as the spins return to a more relaxed state. A practical MRI device requires the ability to selectively invert a narrow slice of a subject, in a short period of time and using a low dose of RF radiation. A laboratory frame of reference is customarily defined such that the z axis coincides with the direction of the static magnetic field and the x and y axes are perpendicular thereto. The usual manner of inversion includes applying a z-gradient magnetic field to the subject so that each x-y plane of the subject has a different Larmor frequency and irradiating the subject with a RF radiation pulse, so that only the spins contained in a limited range of Larmor frequencies are inverted. As higher strength magnetic fields are used for MRI imaging, the amount of RF energy absorbed by the body is higher. It is therefore important to limit the amount of radiation to which the subject is exposed. Furthermore, in practical MRI devices, the peak RF amplitude is limited. Usually, there is a tradeoff made between the pulse duration and the RF amplitude.
The relationship between the RF radiation, the magnetic field and the inversion of the spins is governed by the Bloch equations.
When a RF electromagnetic field is applied to a spin which is already in a strong static magnetic field, the RF magnetic field affects the spin. The RF field is very much smaller than the static field, so the RF field is usually described as rotating in the plane perpendicular to the direction of the static magnetic field (the effect of the component in the direction of the static field is negligible). The effect of the RF field on the spins is most conveniently described in a rotating frame of reference, having three perpendicular axes, z′, y′ and x′, known as the “frequency frame” or “FM frame”. The z′ axis is aligned with the main magnetic field denoted by M
z
. The x′ axis is, by convention, aligned with the transverse RF field and the y′ axis is perpendicular to both the x′ and z′ axes. The entire frame of reference rotates around the z′ axis at the instantaneous angular frequency of the RF pulse. Both x′ and z′ axes use units of angular frequency, such that all magnetic fields {right arrow over (B)} are represented by vectors &ggr;{right arrow over (B)}, where &ggr; is the gyro-magnetic ratio of the spin (type of species thereof). For this reason, magnitudes of magnetic fields are described hereafter in units of angular frequency.
The effective magnetic field to which a spin is subjected as a result of the RF field is preferably defined as a vector in the rotating frame of reference. The magnitude of the z′ component of the vector is equal to the frequency difference between the RF field frequency and the Larmor frequency of the spin. The magnitude of the x′ component is equal to the instantaneous amplitude of the RF field. It should be appreciated that in a uniform z′ directed field, all the spins are located at the same z′ coordinate. When a gradient magnetic field is applied, each spin has a different Larmor frequency and, hence, a different z′ coordinate.
Typically, the net magnetization of a group of spins is treated as a single vector value, called the magnetization vector. Thus, the effect of an inversion pulse is to invert the magnetization vector in a slice of tissue.
FIG. 1
is a graph of a typical inverted slice profile. The slice includes an in-slice region, which is inverted by the inversion pulse, an out-of-slice region which is not inverted by the pulse and a transition region in which the post-inversion magnetization varies between +1 (not inverted) and −1 (inverted). The magnetization values are normalized to the equilibrium magnetization, M
0
. For convenience, the in-slice region is usually depicted as centered around the magnetization axis, by defining the off-resonance to be &OHgr;
0
=&ohgr;
0
−&ohgr;
c
, where &ohgr;
c
is the Larmor frequency at the slice center. The width of the slice (SW) is usually measured between the two points SW/2 and SW/2 where the post-inversion (M
z
) magnetization is zero. The slice width is measured in units of frequency. The transition width is defined as twice c
0
(half a transition width).
One important type of inversion pulse is an adiabatic pulse. Inversion by an adiabatic pulse is less affected by inhomogenities of the RF field amplitude than are inversions by other types of inversion pulses. An adiabatic pulse uses the following mechanism: An effective field vector of the RF radiation field is initially aligned with the main field magnetization axis (+M
z
) direction and its direction is slowly changed until it is aligned in the direction opposite the main field magnetization, (−M
z
). If the rate of change of the effective field vector is gradual enough, the magnetization vector will track the effective field vector of the RF field and will be inverted when the effective field vector becomes aligned with the −z′ axis. The adiabatic condition (described below) describes the conditions under which the rate of change of the vector is sufficiently gradual to permit tracking. The motion of the effective field vector is characterized by its “trajectory”, which is the path of the tip of the effective field vector and its “velocity profile”, which describes the instantaneous rate of motion of the effective field vector, along its trajectory.
FIG. 2
is a graph showing the trajectory of a typical adiabatic pulse in the z′−x′ plane. The effective field vector of the pulse starts out at SW/2 aligned with the +z′ direction and moves along a half ellipse in the z′−x′ plane until SW/2 where it becomes aligned with the −z′ direction. It should be noted that the trajectory shown in
FIG. 2
is depicted for spins at the center of the slice. For all other spins, the trajectory shown is effectively shifted along the z′ axis by an amount equal to the difference between the Larmor frequency of the spin and the Larmnor frequency at the slice center, i.e., the off-resonance frequency &OHgr;
0
. Each point P along the trajectory, defined by a time tp, designates an instantaneous position of the effective field vector. The projection of the point P on the X′ axis is shown as X, where X=&ohgr;
1
(t
P
) is the instantaneous RF amplitude and which is &ohgr;
1
max and occurs when the point P is on the X′ axis. The projections of P on the Z′ axis is &Dgr;&ohgr; where &Dgr;&ohgr;=(&ohgr;(t
P
)−&ohgr;
0
) &Dgr;&ohgr;=(&ohgr;(t
P
)−&ohgr;
0
) is the difference between the instantaneous RF synthesizer frequency and the Larmor frequency of the spin we are inspecting. For each spin which is affected by the adiabatic pulse, a vector connecting the spin and point P is the effective field vector, having a magnitude r. &thgr; is defined as the angle between r and the x′ axis. In order for the rate of change of the vector to be sufficiently gradual to permit tracking, the motion must satisfy the following (adiabatic) condition, &Ggr;=r/|{dot over (&thgr;)}|>>1, where &Ggr; is an adiabatic parameter which describes the ratio between r and {dot over (&thgr;)}. For the pulse defined by the modulation functions &ohgr;
1
(t) and &ohgr;(t), different spins will see different angular velocities. Since r and {dot over (&thgr;)} are different for each spin, the adiabatic parameter may ensure tracking for one group of spins but not for another, even at

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