Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
2001-07-16
2002-09-24
Lefkowitz, Edward (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
C324S309000, C324S311000
Reexamination Certificate
active
06456071
ABSTRACT:
This application claims Paris Convention priority of German patent application number 100 35 319.3 filed on Jul. 18, 2000, the complete disclosure of which is hereby incorporated by reference.
BACKGROUND OF THE INVENTION
The invention concerns a method of NMR spectroscopy or nuclear magnetic resonance tomography, wherein a sequence of temporally offset radio frequency pulses is applied onto a spin ensemble, at least one of which is designed as refocusing pulse.
In the following, reference is made to the accompanying literature list (“D” and corresponding numbers in round brackets).
A nuclear magnetic resonance signal is frequently measured by means of the spin echo method known from (D
1
). The excited magnetization is thereby after a period te/2 submitted to a refocusing pulse and a spin echo is formed after a further time period te/2. At the time of the spin echo, effects acting on the spins, such as chemical shift, susceptibility, field inhomogeneity, are refocused such that all spins have a coherent signal phase with respect to these effects. The signal maximum is achieved if the flip angle of the refocusing pulse is exactly 180°. In practice, such an ideal flip angle can only approximately be realized such that, in particular with methods based on formation of many spin echos, one obtains signal losses due to deviation of the flip angle of the refocusing pulses by 180°.
Such a deviation can occur either through technical facts or be artificially produced, e.g. in applications on human beings for keeping the values of the radiated radio frequency energy within tolerable limits (SAR=specific absorption rate). Literature proposed a series of measures for limiting the corresponding signal losses. This includes on the one hand the so-called Carr-Purrcell-Meiboom-Gill method (D
2
) wherein by an appropriate displacement of the pulse phase between excitation and refocusing pulses, partial automatic compensation of the refocusing pulses is effected.
It could be shown that with such a sequence with long echo trains, high echo amplitudes could be achieved (D
3
) even with small refocusing flip angles.
When using different flip angles across the first refocusing periods of the multi-echo train, the echo amplitude can be further increased (D
4
)(D
5
).
In applications of analytical NMR spectroscopy, improvements through different phase cycles such as MLEV16 or XY16 are used (D
6
). These serve mainly for compensating residual small errors in refocusing pulses with a flip angle of approximately 180°.
All methods known from literature include that in case of deviation of the flip angle of only one single refocusing pulse by 180°, signal loss occurs which can, at best, be reduced through corresponding design of the subsequent refocusing pulses.
In contrast thereto, it is the object of the present invention to present a method for reversing the occurred signal losses even after application of refocusing pulses of any flip angle, and reproduce the complete signal amplitude with respect to dephasing through chemical shift, susceptibility and field inhomogeneity.
SUMMARY OF THE INVENTION
In accordance with the invention, this object is achieved in a effective manner in that after a sequence of pulses with flip angles &agr;
1
. . . &agr;
n
(with &agr;
1
. . . &agr;
n
≧0 °) and phases &phgr;
1
. . . &phgr;
n
between which spins are dephased by &phgr;
1
. . . &phgr;
n
, a central refocusing pulse is applied as (n+1)th pulse, followed by a pulse sequence which is mirror-symmetrical to the central refocusing pulse, wherein the flip angles &agr;
n+2
. . . &agr;
2n+1
and phases &phgr;
n+2
. . . &phgr;
2n+1
of the pulses have, in comparison with the corresponding pulses with &agr;
n
. . . &agr;
1
and &phgr;
n
. . . &phgr;
1
, a negative sign with respect to amplitude and phase and the dephasings &phgr;
n+2
. . . &phgr;
2n+1
which are also mirror-symmetrical to the central refocusing pulse in the sequence are equal to the mirror-symmetrical dephasings &phgr;
n
. . . &phgr;
1
such that at the end of the pulse sequence, an output magnetization M
A
(Mx,My,Mz) of the spin ensemble is transferred with respect to the central refocusing pulse through application of rotation corresponding to the symmetrical relation
M
R
(−
Mx,My,−Mz
)=Rot
y
(180°)*
M
A
(
Mx,My,Mz
)
into a final magnetization M
R
=(−Mx,My,−Mz) and thereby refocused neglecting relaxation effects.
Refocusing, effected by the inventive pulse sequence, of the initial magnetization M
A
is characterized as hyper echo formation.
Method
The main idea is based on the observations of symmetry relations with respect to vector rotation: We observe rotations of vectors which hold:
Rotation about the z axis by an angle &phgr;:
Rot
z
(
ϕ
n
)
=
&LeftBracketingBar;
cos
(
ϕ
n
)
sin
(
ϕ
n
)
0
-
sin
(
ϕ
n
)
cos
(
ϕ
n
)
0
0
0
1
&RightBracketingBar;
[1]
Rotation about the y axis by an angle &agr;:
Rot
y
(
α
n
)
=
&LeftBracketingBar;
cos
(
α
n
)
0
-
sin
(
α
n
)
0
1
0
sin
(
α
n
)
0
cos
(
α
n
)
&RightBracketingBar;
[2]
Rotation Rot
&phgr;
(&agr;) about a rotary axis which is tilted in the x-y plane about an angle &phgr; with respect to the y axis can be described as:
Rot
&phgr;
(&agr;)=Rot
z
(&phgr;
n
)Rot
y
(&agr;
n
)Rot
z
(−&phgr;
n
) [3]
Corresponding to the conventions of the matrix multiplication, calculation is effected from the right to the left.
Observation of two vectors V(x,y,z) and V*(−x,y,−v) which are disposed symmetrically with respect to rotation about 180° about the y axis, facilitates representation (
FIGS. 1A-1
c
):
L
1
: Rotation Rot
z
(&phgr;) of a vector V(x,y,z) about the z axis at an angle &phgr; produces the resulting vector V′(x′,y′,z). For a vector V*(−x,y,−z) rotated with respect to V about the y axis by 180°, the point V*′(−x′,y′,−z) corresponding to V′ results from V* through rotation. by −&phgr; (FIG.
1
A).
Accordingly V can be transferred by rotation about z with a turning angle of &phgr;, subsequent rotation about y with a turning angle of 180° and subsequent rotation about z with &phgr; in V*:
V*
(
−x, y, −z
)=Rot
z
(&phgr;)*Rot
y
(180°)*Rot
z
(&phgr;)
*V
(
x, y, z
)=Rot
y
(180°)
V
(
x, y, z
). [4]
L
2
: Rotation Rot
y
(&agr;) of V about the y axis by an angle &agr; generates the resulting vector V′(x′,y,z′). The corresponding symmetrical point V*′(−x′,y′,−z) also results from V* through rotation by &agr;.
A trivial addition of the turning angle (
FIG. 1B
) thus obtains:
V*
(
−x, y, −z
)=Rot
y
(&agr;)*Rot
y
(180°)
*Rot
y
(−&agr;)
*V
(
x, y, z
)=
Rot
y
(180°)
V
(
x, y, z
). [5]
From L
1
and L
2
together with equation [3] one obtains:
L
3
: Rotation Rot
&phgr;
(&agr;) by an angle &agr;, of V about an axis, tilted with respect to the y axis by &phgr; produces the resulting vector V′(x′,y,z′). The corresponding symmetrical point V*′(−x′,y′,−z) results from V* through rotation Rot
&phgr;
(&agr;) about a rotational axis tilted with respect to the y axis by −&phgr;. Therefore (FIG.
1
C):
V*
(
−x, y, −z
)=Rot
&phgr;
(−&agr;)*Rot
y
(180°)*Rot
&phgr;
(&agr;)
*V
(
x, y, z
)
And with equations [3]-[5]:
V*
(
−x, y, −z
)=Rot
z
(&phgr;
n
)*Rot
y
(−&agr;
n
)*Rot
z
(−&phgr;
n
)*Rot
y
(180°)*Rot
z
(−&phgr;
n
)*Rot
y
(&agr;
n
) *Rot
z
(&phgr;
n
)
*V
(
x, y, vz
)=Rot
y
(180°)
V
(
x, y, z
). [6]
Rotation with −&agr; about an axis −&phgr; corresponds to rotation with &agr; about 180°−&phgr;:
Rot
&phgr;
(−&agr;)=Rot
180 °−&phgr;
(&agr;) [7]
Both no
Hackler Walter A.
Lefkowitz Edward
Shrivastav Brij B
Universitatsklinikum Freiburg
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