U.S. patent application number 09/906310 was filed with the patent office on 2002-02-21 for method of measuring the magnetic resonance (=nmr) by means of spin echos.
Invention is credited to Hennig, Jurgen.
Application Number | 20020021127 09/906310 |
Document ID | / |
Family ID | 7649599 |
Filed Date | 2002-02-21 |
United States Patent
Application |
20020021127 |
Kind Code |
A1 |
Hennig, Jurgen |
February 21, 2002 |
Method of measuring the magnetic resonance (=NMR) by means of spin
echos
Abstract
A method of NMR spectroscopy or tomography, wherein a sequence
of temporarily offset radio frequency pulses is applied onto a spin
ensemble, is characterized in that after a sequence of pulses with
flip angles .alpha..sub.1 . . . .alpha..sub.n (with .alpha..sub.1 .
. . .alpha..sub.n.gtoreq.0.degree.) and phases .PHI..sub.1 . . .
.PHI..sub.n between which spins are dephased by .phi..sub.1 . . .
.phi..sub.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
.alpha..sub.n+2 . . . .alpha..sub.2n+1 and phases .PHI..sub.n+2 . .
. .PHI..sub.2n+1 of the pulses have, in comparison with the
mirror-symmetrical pulses with .alpha..sub.n . . . .alpha..sub.1
and .PHI..sub.n . . . .PHI..sub.1, negative sign with respect to
amplitude and phase and the dephasings .phi..sub.n+2 . . .
.phi..sub.2n+1 which are also mirror-symmetrical to the central
refocusing pulse in the sequence are equal to the respective
mirror-symmetrical dephasings .phi..sub.n . . . .phi..sub.1 such
that at the end of the pulse sequence, an output magnetization
M.sub.A(Mx,My,Mz) of the spin ensemble is refocused with respect to
the central refocusing pulse through application of rotation
corresponding to the symmetrical relation
M.sub.R(-Mx,My,-Mz)=Rot.sub.y(180.degree.)*M.sub.A(Mx,My,Mz) into a
final magnetization M.sub.R=(-Mx,My,-Mz) (=hyperecho formation). In
this fashion, even after application of refocusing pulses of any
flip angles, the occurring signal losses can be cancelled and the
complete signal amplitude can be regained with respect to dephasing
through chemical shift, susceptibility and field inhomogeneity.
Inventors: |
Hennig, Jurgen; (Freiburg,
DE) |
Correspondence
Address: |
Walter A. Hackler
Suite B
2372 S.E. Bristol
Newport Beach
CA
92660
US
|
Family ID: |
7649599 |
Appl. No.: |
09/906310 |
Filed: |
July 16, 2001 |
Current U.S.
Class: |
324/307 ;
324/309 |
Current CPC
Class: |
G01R 33/5613 20130101;
G01R 33/5617 20130101 |
Class at
Publication: |
324/307 ;
324/309 |
International
Class: |
G01V 003/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 18, 2000 |
DE |
10035319.3 |
Claims
I claim:
1. Method of NMR (=nuclear magnetic resonance) spectroscopy or NMR
tomography, wherein a sequence of radio frequency pulses is applied
to a spin ensemble, characterized in that for at least 2n+1
consecutive pulses within the sequence, where n>1, with flip
angles .alpha..sub.1 . . . .alpha..sub.2n+1 and phases .PHI..sub.1
. . . .PHI..sub.2n+1, of the pulses, between which spins are
respectively dephased by .phi..sub.1 . . . .phi..sub.2n, the
following conditions are fulfilled: The central and (n+1)st pulse
is used as a refocusing pulse with a preferred flip angle of
180.degree., Corresponding pulses placed symmetrically around the
central and (n+1)st refocusing pulse have opposite phase and
amplitude, consequently for the i-th pulse with i between 1 and
2n+1 the following relations hold
.alpha..sub.(n+1)-i=-.alpha..sub.(n+1)+i(the flip angle of the
(n+1-i)th the pulse is equal to the opposite of the flip angle of
the (n+1+i)th pulse) and .PHI..sub.(n+1)-i=.PHI..sub.(n+1)-i(the
phase of the (n+1-i)th the pulse is equal to the opposite of the
flip angle of the (n+1+i)th pulse) Dephasing intervals following
the i-th pulse are-symmetrical around the central and (n+1)st
refocusing pulse according to the relation:
.phi..sub.(n+1)-i=.phi..sub.n+i,(the dephasing interval after the
(n+1-i)th pulse is identical to that after the (n+i)th pulse) such
that at the end of the pulse sequence, the vector describing the
initial magnetization M.sub.A(Mx,My,Mz) of the spin ensemble will
appear to be rotated to M.sub.R(-Mx,My,-Mz) by 180.degree. around
the axis of the radiofrequency field of the central refocusing
pulse (=hyper-echo formation):
M.sub.R(-Mx,My,-Mz)=Rot.sub.y(180.degree.)* M.sub.A(Mx,My,Mz)
2. Method according to claim 1, characterized in that the
hyper-echo sequence is preceded by a further rf-pulse used for
excitation with a flip angle of optimally 90.degree., which leads
to the formation of coherent magnetization M.sub.A and which will
accordingly then form M.sub.R as fully coherent magnetization.
3. Method according to claim 2, characterized in that after the
sequence leading to hyper-echo formation a further radio frequency
pulse is applied the phase of which is orthogonal to the phase of
M.sub.R and the flip angle such that M.sub.R is transformed into z
magnetization , wherein the time until adjustment of the thermal
equilibrium of the excited spin system is shortened or when
repeating the sequence with constant recovering time, the intensity
of the signals which contribute to the hyper echo, is
increased.
4. Method according to claim 2, characterized in that after the
sequence leading to hyper-echo formation a further radio frequency
pulse is applied the phase of which is orthogonal to the phase of
M.sub.R and the flip angle such that M.sub.R is transformed into -z
magnetization, wherein the time until adjustment of the thermal
equilibrium of the excited spin system is prolonged or when
repeating the sequence with constant recovering time, the intensity
of the signals which contribute to the hyper echo, is
shortened.
5. Method according to claim 1, characterized in that a pulse
sequence is applied, corresponding to the hyper-echo formation,
onto z magnetization such that at the end of the sequence, z
magnetization is inverted.
6. Method according to claim 5, characterized in that a hyper-echo
sequence is applied to the spin system with pure z magnetization,
wherein magnetization is transferred into -z magnetization,
followed by an inversion pulse, which again transfers the spin
system into +z magnetization, thereby reducing the time until
adjustment of the thermal equilibrium of the excited spin system or
increasing the intensity of the signals which contribute to the
hyper-echo when the sequence is repeated with constant recovering
time.
7. Method according to claim 1, characterized in that a pulse
sequence is applied to transverse magnetization corresponding to
hyper-echo formation such that transverse magnetization is
refocused at the end of the sequence.
8. Method according to claim 1, characterized in that the measuring
sequence consists of an excitation pulse with subsequent multiple
refocusing in the sense of a multi-echo sequence, such that
hyper-echo formation is carried out once or several times during
the multi-echo sequence thereby forming one or more hyper-echos
during each multi-echo train.
9. Method according to claim 1, characterized in that the symmetry
required for hyper-echo formation is disturbed through a modulation
step E such that merely spins whose phase is not disturbed by the
modulation step contribute to hyper-echo formation whereas spins
for which the modulation step effects a phase change, form a
correspondingly attenuated hyper-echo.
10. Method according to claim 1, characterized in that spin
selection is carried out such that the phase of signals of spins
with J-coupling, zero and multiple-quantum coherences differs from
the phase of spins in uncoupled signals such that a hyper-echo is
formed only for uncoupled spins.
11. Method according to claim 1, characterized in that a spin
selection is carried out such that the phase of the radio frequency
pulses follows the phase development of spins with J-coupling, zero
or multiple-quantum coherences etc. such that a hyper-echo is
formed only for those spins for which the conditions for hyper-echo
formation are met.
12. Method according to claim 1, characterized in that hyper-echo
formation is carried out on the basis of an imaging sequence,
preferably RARE, GRASE, Echo Planar Imaging, FLASH, or Spiral
Imaging.
13. Method according to claim 1, characterized in that a hyper-echo
is formed after excitation of the spin system and subsequently the
signal of the hyper echo is read.
14. Method according to claim 13, characterized in that an imaging
sequence, preferably RARE, Echo Planar Imaging, Snapshot-FLASH or
Spiral Imaging is used for reading out a signal.
15. Method according to claim 1, characterized in that a measuring
sequence is applied to several nuclei with different gyromagnetic
relationship, wherein the partial sequence acting on at least one
nucleus, effects hyper-echo formation.
Description
[0001] 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.
[0002] Method of measuring the magnetic resonance (=NMR) by means
of spin echos
BACKGROUND OF THE INVENTION
[0003] 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.
[0004] In the following, reference is made to the accompanying
literature list ("D" and corresponding numbers in round
brackets).
[0005] A nuclear magnetic resonance signal is frequently measured
by means of the spin echo method known from (D1). 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.degree.. 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.degree..
[0006] 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 (D2) wherein by an appropriate
displacement of the pulse phase between excitation and refocusing
pulses, partial automatic compensation of the refocusing pulses is
effected.
[0007] It could be shown that with such a sequence with long echo
trains, high echo amplitudes could be achieved (D3) even with small
refocusing flip angles.
[0008] When using different flip angles across the first refocusing
periods of the multi-echo train, the echo amplitude can be further
increased (D4)(D5).
[0009] In applications of analytical NMR spectroscopy, improvements
through different phase cycles such as MLEV16 or XY16 are used
(D6). These serve mainly for compensating residual small errors in
refocusing pulses with a flip angle of approximately
180.degree..
[0010] All methods known from literature include that in case of
deviation of the flip angle of only one single refocusing pulse by
180.degree., signal loss occurs which can, at best, be reduced
through corresponding design of the subsequent refocusing
pulses.
[0011] 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
[0012] In accordance with the invention, this object is achieved in
a effective manner in that after a sequence of pulses with flip
angles .alpha..sub.1 . . . .alpha..sub.n (with .alpha..sub.1 . . .
.alpha..sub.n.gtoreq.0.degree.) and phases .PHI..sub.1 . . .
.PHI..sub.n between which spins are dephased by .phi..sub.1 . . .
.phi..sub.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
.alpha..sub.n+2 . . . .alpha..sub.n+1 and phases .PHI..sub.n+2 . .
. .PHI..sub.n+1 of the pulses have, in comparison with the
corresponding pulses with .alpha..sub.n . . . .alpha..sub.1 and
.PHI..sub.n . . . .PHI..sub.1, negative sign with respect to
amplitude and phase and the dephasings .phi..sub.n+2 . . .
.phi..sub.2n+1 which are also mirror-symmetrical to the central
refocusing pulse in the sequence are equal to the
mirror-symmetrical dephasings .phi..sub.n . . . .phi..sub.1 such
that at the end of the pulse sequence, an output magnetization
M.sub.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.sub.R(-Mx,My,-Mz)=Rot.sub.y(180.degree.)* M.sub.A(Mx,My,Mz)
[0013] into a final magnetization M.sub.R=(-Mx,My,-Mz) and thereby
refocused neglecting relaxation effects.
[0014] Refocusing, effected by the inventive pulse sequence, of the
initial magnetization M.sub.A is characterized as hyper echo
formation.
[0015] Method
[0016] The main idea is based on the observations of symmetry
relations with respect to vector rotation: We observe rotations of
vectors which hold:
[0017] Rotation about the z axis by an angle .phi.: 1 Rot z ( n ) =
cos ( n ) sin ( n ) 0 - sin ( n ) cos ( n ) 0 0 0 1 [ 1 ]
[0018] Rotation about the y axis by an angle .alpha.: 2 Rot y ( n )
= cos ( n ) 0 - sin ( n ) 0 1 0 sin ( n ) 0 cos ( n ) [ 2 ]
[0019] Rotation Rot.sub..PHI.(.alpha.) about a rotary axis which is
tilted in the x-y plane about an angle .PHI. with respect to the y
axis can be described as:
Rot.sub..PHI.(.alpha.)=Rot.sub.z(.PHI..sub.n)Rot.sub.y(.alpha..sub.n)Rot.s-
ub.z(-.PHI..sub.n) [3]
[0020] Corresponding to the conventions of the matrix
multiplication, calculation is effected from the right to the
left.
[0021] Observation of two vectors V(x,y,z) and V*(-x,y,-v) which
are disposed symmetrically with respect to rotation about
180.degree. about the y axis, facilitates representation (FIGS.
1A-1C):
[0022] L1: Rotation Rot.sub.z(.phi.) of a vector V(x,y,z) about the
z axis at an angle .phi. 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.degree., the point V*'(-x',y',-z) corresponding to V'
results from V* through rotation by -.phi. (FIG. 1A).
[0023] Accordingly V can be transferred by rotation about z with a
turning angle of .PHI., subsequent rotation about y with a turning
angle of 180.degree. and subsequent rotation about z with .PHI. in
V*:
V*(-x,y,-z)=Rot.sub.z(.phi.)*Rot.sub.y(180.degree.)*Rot.sub.z(.phi.)*V(x,y-
,z)=Rot.sub.y(180.degree.)V(x,y,z). [4]
[0024] L2: Rotation Rot.sub.y(.alpha.) of V about the y axis by an
angle .alpha. generates the resulting vector V'(x',y,z'). The
corresponding symmetrical point V*'(-x',y',-z) also results from V*
through rotation by .alpha..
[0025] A trivial addition of the turning angle (FIG. 1B) thus
obtains:
V*(-x,y,-z)=Rot.sub.y(.alpha.)*Rot.sub.y(180.degree.)*Rot.sub.y(-.alpha.)-
*V(x,y,z)=Rot.sub.y(180.degree.)V(x,y,z). [5]
[0026] From L1 and L2 together with equation [3] one obtains:
[0027] L3: Rotation Rot.sub..phi. (.alpha.) by an angle .alpha., of
V about an axis, tilted with respect to the y axis by .PHI.
produces the resulting vector V'(x',y,z'). The corresponding
symmetrical point V*'(-x',y',-z) results from V* through rotation
Rot.sub..PHI. (.alpha.) about a rotational axis tilted with respect
to the y axis by -.PHI.. Therefore (FIG. 1C):
V*(-x,y,-z)=Rot.sub..PHI.(-.alpha.)*Rot.sub.y(180.degree.)*Rot.sub..PHI.(.-
alpha.)*V(x,y,z)
[0028] And with equations [3]-[5]:
V*(-x,y,-z)=Rot.sub.z(.PHI..sub.n)*Rot.sub.y(-.alpha..sub.n)*Rot.sub.z(-.P-
HI..sub.n)*Rot.sub.y(180.degree.)*Rot.sub.z(-.PHI..sub.n)*Rot.sub.y(.alpha-
..sub.n)*Rot.sub.z(.PHI..sub.n)*V(x,y,vz)=Rot.sub.y(180.degree.)V(x,y,z).
[6]
[0029] Rotation with -.alpha. about an axis -.phi. corresponds to
rotation with .alpha. about 180.degree.-.phi.:
Rot.sub..PHI.(-.alpha.)=Rot.sub.180.degree.-.PHI.(.alpha.) [7]
[0030] Both nomenclatures are equivalent and are used in the
following depending on their practicability.
[0031] These initially purely mathematical symmetrical relations
can be converted into pulse sequences of NMR spectroscopy or MR
tomography. Equation [4] is the basis of the spin echo experiment
by Hahn, which says:
[0032] Dephasing Rot.sub.z(.phi.), applied to magnetization
M.sub.A(-Mx,My,-Mz), defined as 3 M A ( M x , My , Mz ) = M x My
Mz
[0033] and subsequent refocusing by a 180.degree. pulse
Rot.sub.y(180.degree.) and further phase development corresponding
to Rot.sub.z(.phi.) produces magnetization M.sub.R(-Mx,My,-Mz)
which is rotationally symmetrical with respect to M.sub.A.
[0034] Corresponding to equation [4] thus results:
M.sub.R(-Mx,My,-Mz)=Rot.sub.z(.phi.)*Rot.sub.y(180.degree.)*Rot.sub.z(.phi-
.)*M.sub.A(-Mx,My,-Mz)=Rot.sub.y(180.degree.)*M.sub.A(Mx,My,Mz)
[8]
[0035] which means that spins are refocused by a 180.degree. pulse
independent of their phase development .phi..
[0036] The phase development about .phi. can thereby be effected
either through temporally constant mechanisms such as chemical
shift, inhomogeneities etc., wherein dephasing is then
characterized by an off resonance frequency .omega. and .phi.
becomes proportional to the respective time intervals corresponding
to .phi.=.omega.. .phi. may also be determined through variables
such as magnetic field gradients or movement in inhomogeneous
fields. In terms of NMR, the rotation about a rotational axis in
the x-y plane described in equations [5]-[7] corresponds to
application of a radio frequency pulse with flip angle .alpha..
[0037] Starting from the spin echo sequence corresponding to [8]
same can be symmetrically extended according to L1-L3, equations
[4]-[7] thereby maintaining the rotational symmetry, wherein the
sequence in both cases is extended either by one dephasing interval
corresponding to equation [4] or a pulse corresponding to equations
[5]-[7].
[0038] Usually pulse sequences in MR are represented as alternating
sequence of pulses and subsequent time intervals which is also the
convention followed in the following examples of implementation.
All statements are, of course, also true for sequences, wherein
several radio frequency pulses directly follow one another or
contain several dephasing steps between 2 radio frequency
pulses.
[0039] The temporal development between two pulses may be
arbitrary. Decisive is merely the total dephasing between
subsequent pulses. Therefore, the inventive method can be
formulated as follows:
[0040] Multiple pulse sequence in NMR spectroscopy or MR
tomography, wherein a sequence of 2n+1 radio frequency pulses is
applied to a spin system with magnetization M.sub.A(Mx,My,Mz) is
characterized in that at first n radio frequency pulses
R(.alpha..sub.n, .PHI..sub.n) are applied with respective temporal
separation t.sub.n which effect rotation
Rot.sub..PHI.n(.alpha..sub.n) of the spins, wherein the spins
experience, in the time intervals I.sub.n between the pulses, a
phase development about .phi..sub.n corresponding to a rotation
Rot.sub.z(.phi..sub.n) about z, and subsequently a refocusing pulse
R(.alpha..sub.n+1, .PHI..sub.n+1)=R(180.degree., 0.degree.)
followed by n radio frequency pulses R(.alpha..sub.n+2,
.PHI..sub.n+2) . . . R(.alpha..sub.n2+1, .PHI..sub.2n+1) in a
temporally reversed order and corresponding to the relation given
in equations [5]-[7]
R(.alpha..sub.n+2,.PHI..sub.n+2) . . .
R(.alpha..sub.2n+1,.PHI..sub.2n+1)=- R(-.alpha..sub.n,-.PHI..sub.n)
. . . R(-.alpha..sub.1,-.PHI..sub.1)=R(.alp-
ha..sub.n,180.degree.-.PHI..sub.n) . . .
R(.alpha..sub.1,180.degree.-.PHI.- .sub.1) [10]
[0041] and
.phi..sub.n-1 . . . .phi..sub.2n=.phi..sub.n . . . .phi..sub.1
[10]
[0042] thereby obtaining magnetization M.sub.R which holds:
M.sub.R(-Mx,My,-Mz)=Rot.sub.y(180.degree.)*M.sub.A(Mx,My,Mz),
[11]
[0043] which means that the initial magnetization M.sub.A is
refocused independently of .alpha..sub.n, .PHI..sub.n and
.phi..sub.n.
[0044] This sequence is illustrated in FIG. 2.
[0045] According to the basic principle, that radio frequency
pulses having a complicated amplitude and phase profile (as used
e.g. for slice selection in NMR tomography) can be represented as a
sequence of short pulses with discrete flip angle, equations
[9]-[11] are valid analogously also for pulse sequences with
amplitude and/or phase-modulated pulses. Additionally, it should be
noted that the phase of the central refocusing pulse was defined to
be 0.degree. and does not necessarily need to correspond to the
reference phase of magnetization. Coordination transformation of
equations [9]-[11] corresponding to equation [3] makes the
refocusing relation of equation [11] also valid for any phases of
the central pulse if corresponding transformation is carried out
also for the other pulses.
[0046] For a central pulse having a phase .xi. which effects
rotation corresponding to (180.degree.,.xi.) equation [9] results
in:
R(.alpha..sub.n+2,.PHI..sub.n+2) . . .
R(.alpha..sub.2n+1,.PHI..sub.2n+1)=-
R(-.alpha..sub.n,-.PHI..sub.n+2.xi.) . . .
R(-.alpha..sub.1,-.PHI..sub.1+2-
.xi.)=R(.alpha..sub.n,180.degree.-.PHI..sub.n+2.xi.) . . .
R(.alpha..sub.1,180.degree.-.PHI..sub.1+2.xi.) [12]
[0047] For completion it should be noted that the central
refocusing pulse may also have a flip angle of <180.degree.. The
amplitude of the formed refocused magnetization is then
correspondingly weakened.
[0048] Such a pulse sequence refocuses all spins independent of
their respective and optionally different phase development and
form a coherent spin echo. This refocusing process through a pulse
sequence is called below hyper-echo formation.
[0049] Relaxation proceedings were not taken into consideration in
this derivation which lead to relaxation-based signal
attenuation.
[0050] It is possible to derive a series of realizations on the
basis of known pulse sequences from the basic sequence shown in
FIG. 2A. Introduction of a hyper-echo formation into an existing
sequence can thereby be effected in different ways:
[0051] As shown in FIG. 2B, an existing sequence (in the present
case a simple spin echo sequence having a 90.degree. excitation
pulse and a 180.degree. refocusing pulse) can be modified through
introduction of further pulses corresponding to equations [9]-[11]
into a hyper-echo sequence. Sequences where the temporal sequence
of pulses already meets the dephasing conditions for hyper-echo
formation thereby require optionally only modification of the flip
angle and pulse phases (see below).
[0052] FIG. 2C shows the principle of integration of the hyper-echo
formation through supplementation: Any pulse sequence (in this case
consisting of an excitation pulse with subsequent n radio frequency
pulses) is converted to a hyperecho sequence by adding a refocusing
pulse and subsequent pulses according to equations [9]-[11] to form
a hyper-echo.
[0053] Finally, FIG. 2D shows application of a hyper-echo for
preparing magnetization as hyper-echo which is subsequently read
with any pulse sequence (in the present case a simple spin
echo).
[0054] Of course, these different types of introduction of a
hyper-echo can be arbitrarily combined. Formation of several
hyper-echos within one sequence can also be advantageous.
[0055] Some examples of application are shown below. It must be
stated that the NMR literature describes an extremely large number
of different multiple pulse sequences which can only be exemplarily
described below. The expert can easily apply the method of
symmetrization described in equations [9]-[11] for forming a
completely refocused spin echo such that the following examples do
not represent a limitation but merely show the general application
possibilities of the basic principle.
[0056] The following application classes seem to be
advantageous:
[0057] 1. Multi-echo sequences
[0058] Application of the principle described in equation [11] to
transverse magnetization recovers complete magnetization--when
relaxation effects are neglected--(corresponding to the continuous
use of refocusing pulses having a flip angle of 180.degree.) for
any values of .alpha..sub.1 . . . .alpha..sub.n. While the
amplitude is <<1 after each echo produced by .alpha..sub.n,
the complete amplitude is recovered after the inventive
sequence.
[0059] A special case of equations [9]-[11] is given when the
magnetization vector M.sub.A is oriented parallel to the central
refocusing pulse R(180.degree.,0). In this case M.sub.R=M.sub.A,
i.e. magnetization is converted into itself (except for relaxation
effects during the sequence). This is the case e.g. in the CPMG
multi echo methods (D2) wherein magnetization is generated by a
90.degree. pulse. In the subsequent multiple refocusing,
180.degree. pulses are applied with a phase which is perpendicular
to the excitation pulse and thus parallel to the excited
magnetization.
[0060] Clinical application of such sequences often requires
selection of the flip angle of the refocusing pulse <180.degree.
to limit the radio frequency output (D3). Modification of a CPMG
method according to the inventive method can be realized as
below:
[0061] If M.sub.A is magnetization directly after excitation and
possible phase effects during the excitation pulse are neglected,
the condition M.sub.A parallel to R(180.degree.,0) is met for all
subsequent refocusing pulses. For all .PHI..sub.n thus holds:
.PHI..sub.n=.PHI..sub.0=0.
[0062] Due to the equidistant refocusing pulses in CPMG sequences
(and when using symmetrical conditions corresponding to magnetic
field gradients for dephasing caused thereby) it is furthermore
true for all .phi..sub.n:
.phi..sub.n=.phi..sub.1
[0063] The symmetry of the inventive sequence is achieved in this
case through inversion of the respectively applied flip angles. The
phases always remain zero (FIG. 3):
R(.alpha..sub.n+2,0) . . .
R(.alpha..sub.2n+1,0)=R(-.alpha..sub.n,0) . . . R(-.alpha..sub.1,0)
[13]
[0064] With this modification, the amplitude of the (2n+1)th echo
can be reproduced to the completely refocused value (=1) for any
.alpha..sub.1. . . .alpha..sub.n. When using such a sequence in MR
tomography corresponding to the RARE method, the contrast of the
image is essentially given by the intensity of the echo which
represents the center of the k space in the phase encoding
direction.
[0065] In a preferred implementation of the inventive method, it is
therefore reasonable to recover complete refocusing for exactly
this echo. Towards this end, in a first approximation, the signal
intensity of the image becomes independent of a.sub.1 . . .
.alpha..sub.n. Selection of .alpha..sub.1 . . .
n.sub.n<180.degree. only slightly changes the sharpness of the
image. It is advisable thereby to chose values for .alpha..sub.1 .
. . .alpha..sub.n which generate a possibly high and homogeneous
echo amplitude as described e.g. in (D4) and (D5).
[0066] In particular, for so-called multi-contrast methods wherein
phase encoding is carried out such that at least the center of the
k space is read several times and at different echo times, the
principle according to equation [12] can be repeated several times
even during an echo train such that several hyper-echos can be
formed in one echo train.
[0067] The chosen example of application to a RARE sequence merely
has illustrative character. Hyper-echos can be integrated also in
other imaging sequences such as GRASE, BURST etc. to improve the
signal behavior through refocusing of magnetization.
[0068] 2. Driven Equilibrium sequences
[0069] A further particularly preferred application of the
inventive method deals with recovery of z magnetization in
so-called driven equilibrium (DEFT) sequences. Application of DEFT
to spin echo sequences for MR imaging was described already in 1984
(D7). It is based on the application of a so-called flip back pulse
at the time of echo formation, i.e. when all transverse
magnetization is refocused. This flip back pulse converts the
remaining transverse magnetization into z magnetization. Same is
thus closer to the thermal equilibrium which achieves higher signal
intensity with identical recovering time.
[0070] In a hyper-echo sequence, such conversion of the spin system
in the direction of balanced magnetization can be realized in two
ways: If the entire sequence is designed according to the
principles of hyper-echo formation and applied to z magnetization,
magnetization at the time of hyper-echo formation according to [11]
will be z magnetization. Same can be converted into z magnetization
through a directly following 180.degree. pulse (FIG. 4A). The same
effect can be achieved if the 90.degree. pulse is phase-inverted at
the end of the hyper-echo sequence thereby acting as a flip back
pulse which converts magnetization directly into +z magnetization
(FIG. 4B).
[0071] RARE (TSE . . .) sequences having small refocusing flip
angles (see above) permit rotation back to the z axis only of part
of the magnetization by means of a flip back pulse due to
incomplete refocusing. Application of the inventive method,
however, allows regaining of the entire transverse magnetization
through formation of a hyper-echo for the time of the flip back
pulse and conversion into z magnetization through flip back.
[0072] This application is mainly (but not exclusively) useful for
application in high field systems wherein on the one hand, often
small refocusing flip angles are used due to the increased radio
frequency absorption, and furthermore long repeating times are
required due to the generally longer T1 relaxation times with
increasing field strength without flip back to balance out
magnetization as well as possible before the next excitation.
[0073] The method is thereby particularly preferred for
applications which offer an inherently short repeating time, such
as e.g. recordings with three-dimensional local encoding or rapidly
repeated recordings for observing temporally changing
processes.
[0074] It is also possible to refocus gradient echo sequences
through hyper-echo formation by introducing a 180.degree. pulse
into the sequence after reading out m excitation intervals, in
which one gradient echo is generated in each case, followed by
further m excitation intervals with pulses corresponding to
equation [11]. FIG. 5A shows a hyper-echo sequence based on a
gradient echo sequence. Therein, the temporal succession of the
entire sequence was converted after the 180.degree. pulse and the
pulses were changed corresponding to [9]-[11]. To simplify matters,
FIG. 5A shows a sequence with constant flip angle .alpha.. Taking
into consideration equations [9]-[11] hyper-echo formation is
effected also for sequences with variable .alpha..
[0075] As shown, the signals recorded in the second half of the
sequence correspond to the signal parts refocused by the
180.degree. pulse. Since the symmetry condition for the hyper-echo
formation holds true merely for the entire spin dephasing between
two subsequent radio frequency pulses in each case, the sequence
shown in FIG. 5B also leads to hyper-echo formation. In contrast to
FIG. 5A, in this case, merely the read gradient GR was temporally
inverted (and the slice selection gradient GS was made symmetrical)
such that now, the gradient echos directly generated by the
respectively preceding radio frequency pulse, were formed also in
the second half of the sequence. Considering [9]-[11] with respect
to total dephasing between the pulses, a hyper-echo is also formed
in this case.
[0076] Suitable selection of the gradients allows reading out of
both possible signal groups (FIG. 5C). Same may either be generated
and read separately. When the reading gradient GR is designed such
that the entire surface below GR between 2 refocusing pulses
becomes zero, these signals overlap to form one single signal
corresponding to the principle of the FISP sequence.
[0077] The measuring methods shown in FIGS. 5A-C can be carried out
either such that the signals used for imaging are recorded in one
single hyper-echo train. This can be carried out also such that a
data set required for image construction is achieved only after
multiple repetition of the corresponding sequences. In particularly
preferred implementations, inversion of the initial z magnetization
caused by hyper-echo formation--as already shown in the multi-echo
method in FIG. 4--is inverted before the recovering time tr through
a 180.degree. pulse and thus brought closer to an equilibrium (FIG.
5D).
[0078] It should finally be noted that formation of several
hyper-echos is possible also for gradient echo sequences (FIG.
5E).
[0079] When the excitation pulse is started with a flip angle of
generally, but not necessarily 90.degree., the hyper-echo can also
be formed as signal with transverse magnetization (FIG. 5F) which
can again be converted into z magnetization corresponding to the
description for multi-echo sequences through a flip back pulse
(FIG. 5G) before the recovering time tr. In the variants shown in
FIGS. 5D-G, the generic sequence (FIG. 5A) was taken as a basis but
also the variants corresponding to FIGS. 5B,C (inclusive FISP) can
be used.
[0080] To optimize steady-state magnetization in continuous methods
such as FIG. 5E, it may also be useful to realize the initial
excitation pulse and the refocusing pulse used for hyper-echo
formation not as pulses having a flip angle of 90.degree. and
180.degree. but as pulses with correspondingly smaller flip angles
.beta. (excitation) or 2.beta. (refocusing), wherein the phase of
the refocusing pulses alternates with repeated application
according to the principle of a true FISP sequence.
[0081] Hyper-echos can be integrated also in other imaging
sequences, such as echo planar imaging, spiral imaging etc. to
modify the contrast behavior e.g. corresponding to the formation of
the driven equilibrium.
[0082] The application, as described, onto measuring methods in MR
imaging are merely illustrative. A large number of measuring
sequences in analytical NMR--mainly multiple-dimensional Fourier
spectroscopy--such as COSY, NOESY, INEPT, INADEQUATE etc.--to name
only some of the current sequences, is based on a plurality of
repetitions of multi-pulse sequences. With all these sequences,
balanced magnetization can be achieved more rapidly through
formation of a hyper-echo with subsequent flip back pulse and thus
reduction of the measuring time and/or increase of the
signal-to-noise ratio. If in such sequences, pulses are applied to
different nuclei, formation of hyper-echos onto all nuclei
concerned is advantageous.
[0083] The use of hyper-echos in driven equilibrium sequences is
particularly advantageous mainly for observing nuclei with long T1
since in this case, magnetization with a suitable sequence (e.g.
imaging) can be read and subsequently re-stored as z magnetization
to be read out again at a later time.
[0084] A preferred application in this case is the measurement
using hyper-polarized magnetization (e.g. through corresponding
preparation of hyper-polarized inert gases). Therein, the
longitudinal magnetization is prepared in a state far beyond from
the thermal equilibrium. The prepared spin system thus produces a
signal intensity which is in factors of several thousand above that
of the balanced magnetization. Such hyper-polarized substances are
applied e.g. in MR tomography using hyper-polarized helium for
illustrating the lung. A problem produced in this connection is
that magnetization, once it has been excited, relaxes into the
balanced state and thus loses polarization. The use of flip back
sequences allows regaining of the polarized magnetization without
the relaxation losses caused by T2 and can thus be re-used several
times.
[0085] 3. Spin selection
[0086] Hyper-echo sequences may be used for selecting a sub-amount
of the originally excited spins if modification is carried out such
that the symmetrical condition of equation [11] leading to
hyper-echo formation is fulfilled only for part of the spin. A
large number of such applications can be derived from the plurality
of sequences known in NMR literature which can be described only
illustratively and not completely below.
[0087] 3.1. Spin selection through variation of symmetrical
conditions for hyper-echo formation
[0088] Spin selection in a hyper-echo experiment can be realized by
selecting the pulse sequence such that the symmetrical conditions
of equation [11] are met only for part of the initially excited
spins. This can be achieved e.g. with application of
slice-selective pulses in that the individual pulses act in each
case only onto spins within a certain frequency range through
selection of corresponding pulse profiles. With corresponding
selection of the respective frequency ranges, it is possible to
filter out signals from a partial range of the excitation profile
of each pulse. With simultaneous application of magnetic field
gradients during the pulses, one can observe spins from
corresponding spatial volumes.
[0089] FIG. 6 shows in this connection a simple example of
application, wherein the profiles of the corresponding pulses which
are symmetrical with respect to the central 180.degree. pulse are
displaced with respect to one another such that hyper-echo
formation is effected only in the overlapping central spectral
range (grey) whereas the signals of the outer regions appear to be
dephased depending on phase and flip angle of the pulses.
[0090] A particularly effective type of this hyper-echo formation
results when the phase of the pulses 1 . . . n is continuously
alternated since spins in the outer regions are submitted only to
the pulses with the identical phase used in a Carr-Purrcel sequence
which is known to produce a rapid signal loss and thus signal
suppression for .alpha.<180.degree..
[0091] Other implementations are also possible which have the
common feature that the condition for hyper-echo formation is
fulfilled only in the region of the desired excitation window. A
particularly simple implementation can be achieved also in that
merely the central refocusing pulse has a different selectivity
(e.g. chemical shift selectivity) with respect to the other pulses
of the hyper-echo sequence.
[0092] A generalization of this principle is schematically shown in
FIG. 7, which shows that a complex excitation window can be
obtained through application of a pulse sequence with simple
excitation profiles.
[0093] Spin selection is also possible through modification of the
temporal order of the pulse sequence before and/or after the
central 180.degree. pulse through an additional modulation step
E(.phi..sub.E). In case of introduction before the central
180.degree. pulse, the effect of the pulse sequence is then
according to equations [9]-[11] described as
M.sub.R(Mx,My,Mz)=R(.alpha..sub.1,180.degree.-.PHI..sub.1,.phi..sub.1)
. . .
*R(.alpha..sub.n-1,180.degree.-.PHI..sub.n-1,.phi..sub.n-1)*R(.alpha..s-
ub.n,180.degree.-.PHI..sub.n,.phi..sub.n)*R(180.degree.,0,0)*E(.phi..sub.E-
)*R(.alpha..sub.n,.PHI..sub.n,.phi..sub.n) . . .
*R(.alpha..sub.2,.PHI..su-
b.2,.phi..sub.2)*R(.alpha..sub.1,.PHI..sub.1,.phi..sub.1)M.sub.A(Mx,My,Mz)
[14]
[0094] Hyper-echo formation occurs only for that part of the spins
for which magnetization remains unchanged, corresponding to the
vectorial disintegration, this is M.sub.RCOS(.phi..sub.E). The
corresponding orthogonal component M'.sub.R"sees" pulses which are
phase-shifted by 90.degree. after the interval E(.phi..sub.E) and
therefore develops:
M'.sub.R(Mx,My,Mz)=R(.alpha..sub.1,90.degree.-.PHI..sub.1,.phi..sub.1)*R(.-
alpha..sub.n-1,90.degree.-.PHI..sub.n-1,.phi..sub.n-1)*R(.alpha..sub.n,90.-
degree.-.PHI..sub.n,.phi..sub.n)*R(180.degree.,90.degree.,0)*E(.phi..sub.E-
)*R(.alpha..sub.n,.PHI..sub.n,.phi..sub.n) . . .
*R(.alpha..sub.2,.PHI..su-
b.2,.phi..sub.2)*R(.alpha..sub.1,.PHI..sub.1,.phi..sub.1)M.sub.A(Mx,My,Mz)
[15]
[0095] With corresponding selection of .PHI..sub.1 . . .
.PHI..sub.n, this signal portion is suppressed. In the most simple
case, this can be achieved for .PHI..sub.1 . . .
.PHI..sub.n=0.degree. and .alpha..sub.1 . . .
.alpha..sub.n<180.degree..
[0096] If E is represented as an additional time interval t.sub.d
(FIG. 8A) the symmetry of the hyper-echo sequence for resonant
spins is not disturbed. Spins having a certain off-resonance
frequency .omega.>0 experience in contrast thereto a phase
change .DELTA..phi. corresponding to .DELTA..phi.=.omega.t.sub.d.
Same causes distortion of the symmetry of the hyper-echo sequence
and the signals of said spins are suppressed. E(.phi..sub.E) may
also be designed much more complex.
[0097] FIG. 8B shows as further example introduction of an
additional spin echo interval with symmetrical strong magnetic
field gradients. Moving spins are dephased by these gradients. When
all spins move uniformly as in vascular flow, this leads to
velocity-dependent phase changes of the observable magnetization
which impairs the symmetry condition of hyper-echo formation and
thus causes attenuation of the hyper-echo signal.
[0098] Spin ensembles which move incoherently due to molecular
diffusion experience an amplitude change due to the incoherent
dephasing, which depends on the diffusion constant and will also
attenuate the amplitude of the subsequent hyper-echo. Formation of
the hyper-echo per se will not be influenced by diffusion.
[0099] In a conventional spin echo sequence, spins moving at a
constant velocity are represented without signal loss but with
altered signal phase. In a hyper-echo sequence, in which the signal
portion M'.sub.R(Mx,My,Mz) represented in equation [14] is dephased
and therefore does not contribute to the total signal, phase
effects do not occur.
[0100] Change of the signal phase depending on the motion and thus
loss of the hyper-echo formation will occur merely through
switching a bipolar magnetic field gradient by one (or several) of
the refocusing pulses with otherwise constant time scheme (FIG.
8C).
[0101] The embodiments shown in FIGS. 8A through 8C of a modified
hyper-echo sequence are again exemplarily. Literature (see e.g.
(D9), (D10)) shows a large number of method steps which include
concrete change of the signal phase and/or amplitude and can be
applied also in a hyper-echo sequence.
[0102] It is to be noted that all modifications which, when applied
to conventional spin echo or gradient echo sequences, lead to phase
change, effect a signal intensity loss in the hyper-echo formation.
Phase effects will depend on the fate of the magnetization
component orthogonal to that leading to hyperecho-formation.
[0103] 3.2 Hyper-echos for suppressing of signals of coupled
spins
[0104] As initially mentioned, hyper-echo refocusing according to
equation [11] is true for mechanisms, such as chemical shift,
susceptibility etc., i.e. spin states which are characterized by a
temporal development of the phase and which are inverted by a
180.degree. pulse. Other mechanisms such as zero and
multiple-quantum coherences and J-coupling show a different
refocusing behavior and thus do not follow the same conditions for
hyper-echo formation.
[0105] On the other hand, following the general symmetry relations
described in Eq.[1]-[5] can also be applied to such mechanisms,
such that a hyper-echo is then selectively formed for coupled
systems, however, not for uncoupled spins. Corresponding selection
of .alpha..sub.n, .PHI..sub.n, .phi..sub.n, permits discrimination
of the corresponding spin states.
[0106] Some typical applications for coupled spins are exemplarily
shown below. This representation, too, is only exemplarily and not
complete. Further applications for other states such as zero and
multiple quantum coherences can be easily derived from the basic
equation [11].
[0107] Spin systems comprising J-coupling have a different
refocusing behavior than coupled spin systems which is shown by an
AX system below. Extension to other systems is easily possible. An
AX system is characterized as weakly coupled system wherein the
difference of the chemical shifts of the A and X nuclei is larger
than the coupling constant J. Such a system is characterized by two
doublets. If a refocusing pulse is applied to such a system,
magnetizations are refocused on the one hand and on the other hand,
the corresponding coupling partners are simultaneously exchanged
which means that after this double inversion, the spin system
behaves with respect to J-coupling as if no refocusing had taken
place.
[0108] When refocusing pulses having a flip angle of exactly
180.degree. are applied, this causes that the phase of the echos of
coupled spins develops differently than that of uncoupled spins.
This is the basis of methods such as COSY etc.
[0109] When several pulses are applied which have a flip angle
other than 180.degree., this phase development causes increasingly
destructive interference and thus signal loss. In particular, with
CPMG sequences, there is a positive interference loss of the
different signal contributions corresponding to ref. (D3) if the
pulse separation with respect to J and .DELTA..sigma. is
sufficiently large (D8). It is therefore possible to suppress the
signals of coupled spins through a corresponding multi-pulse
sequence. Although the principle is known, such a method is not
often used in practice since the required condition of using flip
angles <180.degree. leads to signal loss of the observed
uncoupled spins and this method is disadvantageous compared to
other discrimination methods.
[0110] In contrast thereto, a sequence which forms a hyper-echo
with respect to the signals of uncoupled spins results in full
signal intensity, whereas signals of coupled spins are suppressed
since they effectively .sub."see" another phase of the refocusing
pulses. Towards this end, we observe such a doublet signal and
assume that the reference frequency is in the center of the
doublet. The doublet signal will then experience a phase
development according to cos(J/2*tn) wherein tn is the time after
excitation (FIG. 9).
[0111] A particularly advantageous feature of this application is
given in that with corresponding selection of .alpha..sub.n,
.PHI..sub.n, .phi..sub.n signals of spins of systems having
different coupling constants can be simultaneously suppressed.
[0112] Suppression of the signals of coupled spins is prevented by
selecting the time of the central 180.degree. pulse=1/J (FIG. 9
below). This is true, of course, only for spins having particular
coupling constants J.
[0113] This principle of different phase development can be also
used for the reversed purpose of specifically selecting coupled
spins. This is achieved in that the phase development according to
J-coupling in the phases .phi..sub.n of the refocusing pulses is
taken into consideration. Modification of a hyper-echo sequence
according to equation [11] leads to incrementation of each pulse
phase .PHI..sub.n about arcsin(J/2*t.sub.n) and shows that
formation of a hyper-echo can be achieved only for the
corresponding signal whereas for signals with different coupling
constants and also for signals with uncoupled spins, the symmetry
relation according to equation [11] is not met and same thus appear
attenuated, wherein already a few refocusing pulses achieve
attenuation leading to a practically complete suppression of said
signals.
[0114] Corresponding to this simple example, a large number of
pulse sequences can be devised which have the same feature, i.e.
that the symmetrical relation for hyper-echo formation is met in
each case only for the spins to be observed, however not for
others. This is true in particular also for zero and
multiple-quantum coherences for which a hyper-echo method with
corresponding selection or suppression of the differently
associated signals can be easily derived from the description with
respect to J-coupling.
[0115] The observation that when the symmetry of the phase
development according to the above chapter 3 is not fulfilled, only
the cosine contribution of the magnetization contributes to the
hyper-echo formation, there is the possibility of using the
hyper-echo formation as polarization filter which allows passage
only of signals with a symmetry following the hyper-echo sequence
and deletes the signal contributions which are orthogonal thereto.
Application of several such polarizations, optionally with
selection under different polarization angles, permits specific
selection of signals whose dephasing follows corresponding and
precise handicaps.
[0116] 4. Spin inversion
[0117] Application of a sequence according to equation [11] to pure
z magnetization leads to spin inversion as used for so-called
inversion recovery sequences for T1 measurements or also in the
field of imaging for achieving T1 weighted images. Application of a
hyper-echo sequence in contrast to conventional inversion with one
single 180.degree. pulse thereby permits use of methods for
selective spin inversion described under chapter 3. On the one
hand, one can obtain complex inversion profiles, on the other hand,
selective inversion corresponding to chemical shift, J-coupling,
different zero and multiple-quantum coherences etc. is
possible.
[0118] Considerations for Implementation
[0119] In implementing hyper-echoes, one has to differentiate that
formation of hyper-echos can be integrated either in the course of
the measurement with a certain pulse sequence which is advantageous
mainly for the sequences mentioned above in chapters 1 and 2.
Implementation is also possible or even advantageous, wherein
formation of a hyper-echo initially serves for special preparation
of the spin system, and data acquisition is carried out
subsequently using any appropriate sequence (according to FIG.
2D).
[0120] The acquisition module can thereby be formed from any
appropriate signal generation sequence. Mainly in applications in
MR tomography, the acquisition module may consist of a
corresponding imaging module (gradient echo, echo planar imaging,
RARE(TSE, . . .) spiral scan etc.) such that images are produced
which have a contrast which corresponds to the characteristic of
the hyper-echo.
[0121] There are further applications wherein hyper-echos are used
in a different context than up to now. Literature discloses (D3)
that in multi-pulse sequences, a number of possible refocusing
paths for transverse magnetization, which increases with the
3.sup.rd power of the number of pulses, is generated of which often
only part is used to contribute to signal read-out. When such a
sequence is repeated with a repetition time which is smaller than
the longitudinal relaxation time T1, undesired signals may be
formed which can be prevented through hyper-echo formation since
thereby all refocusing paths are combined again. Such a
.sub."clean-up" function may be reasonable in particular also when
using NMR in quantum computing since hyper-echo formation can serve
here as deleting function of the information stored in the spin
system as transverse magnetization.
[0122] Further advantages of the invention can be extracted from
the description and the drawing. The features mentioned above and
below may be used in accordance with the invention either
individually or collectively in any arbitrary combination. The
embodiments shown and described are not to be understood as
exhaustive enumeration but rather have exemplary character for
describing the invention.
[0123] The invention is shown in the drawing and is further
explained by means of embodiments.
BRIEF DESCRIPTION OF THE DRAWING
[0124] FIG. 1A through 1C show a demonstration of the symmetry
relations with respect to rotation;
[0125] FIG. 2A shows a hyper-echo sequence;
[0126] FIG. 2B shows the principle of application of a hyper-echo
sequence through integration into a known sequence;
[0127] FIG. 2C shows the principle of application of a hyper-echo
sequence through supplementation;
[0128] FIG. 2D shows the principle of application of a hyper-echo
sequence as preparation sequence;
[0129] FIG. 3 shows a pulse sequence of a modified CPMG sequence
corresponding to the inventive method;
[0130] FIG. 4 shows the principle of application of the hyper-echo
mechanism;
[0131] FIGS. 5A through 5G show the hyper-echo sequences on the
basis of gradient echo sequences;
[0132] FIG. 6 shows a schematic representation of the principle of
spin selection;
[0133] FIG. 7 shows a generalized scheme of the principle of FIG. 6
for demonstration how a complex excitation window can be realized
from a hyper-echo sequence with pulses with shifted excitation
profile;
[0134] FIGS. 8A through 8C show modified hyper-echo sequences;
[0135] FIG. 9 shows the effect of J-coupling on the hyper-echo
formation; and
[0136] FIG. 10 shows a generalized scheme of a measuring sequence
with hyper-echo preparation module and subsequent acquisition
module.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0137] FIG. 1A shows the symmetry with respect to rotation about
the z axis corresponding to equations [4] and [8] i.e.
perpendicular to the image plane, from which follows that the
vector V* obtained from V through rotation about z with .phi.,
subsequent rotation about y by 180.degree. and subsequent renewed
rotation about z with .phi. (arrows) is identical to a rotation of
V about y by 180.degree. (arrow shown in broken lines). The y axis
which is perpendicular to the image plane marks the zero point of
the x-z plane.
[0138] FIG. 1B shows the symmetry with respect to rotation about
the y axis corresponding to equation [5] wherein trivially a
sequence of rotations about y with .alpha. 180.degree. and -.alpha.
is identical to rotation about 180.degree..
[0139] FIG. 1C shows the symmetry with respect to rotation about a
rotational axis tilted with respect to the y axis by .PHI.
corresponding to equation [6]. Corresponding to the representation
in top view, the pole of the rotational axis is shifted with
respect to the zero point defined by the y axis about
sin(.PHI.).
[0140] The radio frequency pulses with a flip angle (.alpha..sub.1
. . . .alpha..sub.n and the respective phase .PHI..sub.1 . . .
.PHI..sub.n are separated from the dephasing intervals be
.phi..sub.1 . . . .phi..sub.n in FIG. 2A. After a central
refocusing pulse, the sequence is applied in reversed order with
pulses of opposite phase and amplitude. The order of the dephasing
intervals is also reversed, however, the dephasings .phi..sub.1 . .
. .phi..sub.n remain identical. Independent of the type of
magnetization at the start of the sequence, same is refocused
through the pulse sequence about the rotational axis of the
refocusing pulse.
[0141] In FIG. 2B, additional pulses corresponding to the basic
principle of FIG. 2A are introduced into an existing sequence (in
this case: a simple spin echo experiment with a 90.degree. and a
180.degree. pulse (broad lines)) such that a hyper-echo is formed
instead of a normal spin echo.
[0142] In FIG. 2C, an existing sequence (in this case a multi-echo
experiment with n refocusing pulses) is supplemented by a
180.degree. pulse and the reversed pulse sequence to form a
hyper-echo. The initial excitation pulse (most often a 90.degree.
pulse) is usually not included in the supplementation such that the
hyper-echo is generated as signal of transverse magnetization
corresponding to magnetization generated by the 90.degree.
pulse.
[0143] In FIG. 2D, a hyper-echo sequence precedes a conventional
sequence (in this case again a spin echo) to modify the contrast
behavior corresponding to the hyper-echo sequence, which may also
be modified for spin selection according to the principles
described above.
[0144] The refocusing pulse flip angles .alpha..sub.n according to
FIG. 3 are generally <180.degree. and may be different from each
other. Refocusing to a complete echo amplitude may occur once
(above) or several times (below). Application in imaging involves
additional magnetic field gradients which are correspondingly
switched (e.g. according to (D3)) in order to encode spatial
information into the signal.
[0145] At the time of formation of the hyper-echo, a 90.degree.
pulse is applied according to FIG. 3. During the multi-echo train,
the transverse magnetization Mtr decays according to spin
relaxation, z magnetization Mz recovers with T1. The relaxation
curves are shown only schematically. The fully refocused transverse
magnetization at the time of the hyper echo formation is
transferred into z magnetization M.sub.DE. It is much closer to the
equilibrium value M.sub.0 than z magnetization M.sub.sat without
flipback (broken lines).
[0146] In FIGS. 5A through 5D, Rf, GS, GR and GP designate the
radio frequency pulses, and the slice selection, read and phase
encoding gradients respectively. First, in FIG. 5A a number of m
gradient echos are generated through m-fold repetition, wherein the
flip angle .alpha. and phase .PHI. of the used pulses can be freely
selected and are constant in the most simple case (however, not
necessarily preferred case). Subsequently, the refocusing pulse (in
the simplest case a 180.degree. pulse) is applied and finally the
gradient echo sequence is repeated m times, wherein flip angle and
phase of the used pulses are determined by equation [11]. The
number of repetitions m can thereby be selected freely such that a
complete data set required for image reconstruction is produced
through single application or repeated application of this
sequence.
[0147] When applied to z magnetization, the hyper-echo mechanism
leads to inversion. To realize a hyper-echo as transverse
magnetization, the sequence can be preceded by an excitation pulse
with a 90.degree. flip angle in the simplest case, as shown in FIG.
5B.
[0148] FIG. 5C shows a section from a gradient echo sequence
comprising several hyper echos, wherein also in this case, signal
preparation can be preceded by a 90.degree. pulse like in FIG.
5B.
[0149] FIG. 5D shows a driven equilibrium sequence, wherein the
formed hyper-echo is transferred by a corresponding flip back pulse
in the z magnetization.
[0150] The pulses used for hyper-echo formation in accordance with
FIG. 6 have excitation profiles which are shifted with respect to
one another, such that the condition for forming a hyper-echo is
met only for spins whose resonance frequency is within the
overlapping region (grey). Signals of spins which are detected only
by part of the pulses and for which the condition for hyper-echo
formation is not met, are suppressed. The dephasing intervals .phi.
between the pulses are not shown.
[0151] The pulses in FIG. 7 show different excitation profiles
(dark grey). The hyper-echo conditions are met merely for
individual spectral windows (light grey).
[0152] FIG. 8A shows a sequence derived from the CPMG hyper-echo
sequence shown in FIG. 3 wherein an additional interval td was
introduced before the central 180.degree. pulse. For spins whose
signal phase changes during td, the hyper-echo refocusing mechanism
is no longer met.
[0153] FIG. 8B shows a sequence, wherein a motion-dependent change
of the signal phase is effected through an additional spin echo
interval with symmetrical magnetic field gradient G which also
produces hyper-echo formation loss.
[0154] FIG. 8C shows that a motion-dependent change of the signal
phase and thus change of the amplitude of the hyper-echo can be
effected already merely through corresponding magnetic field
gradients alone in an otherwise unchanged hyper-echo sequence.
[0155] For coupled spins, a periodic phase change .PHI. of the two
signals of the doublet occurs due to J-coupling, whose spectrum
S(.omega.) is characterized by a doublet as shown in FIG. 9. If a
hyper-echo sequence is applied to such a doublet, the phase
.PHI..sub.n of each pulse is formally changed by
.+-.arcsin(t.sub.n*J/2), wherein t.sub.n is the time of the pulse.
In general, the symmetry of the hyper-echo formation is disturbed
and the signals of coupled spins are not refocused. If the time of
the central 180.degree. pulse is 1/J, the symmetry remains
unchanged. These doublets are illustrated.
[0156] FIG. 10 finally shows a measuring sequence wherein at first
magnetization is generated via hyper-echo formation (optionally
with one of the modifications described) and is subsequently read
with any read-out sequence.
[0157] Literature:
[0158] (D1) Hahn E L, Spin Echoes, Phys.Rev. 80:580-594 (1950)
[0159] (D2) Meiboom S, Gill D, Modified Spin-Echo Method for
Measuring Nuclear Relaxation Times, Review of Scientific
Instruments, 29:688-691 (1958)
[0160] (D3) Hennig J, Multiecho Imaging Sequences with Low
Refocusing Flip Angles, J.Magn.Reson., 78:397-407 (1988)
[0161] (D4) Le Roux P, Hinks R S, Stabilization of echo amplitudes
in FSE sequences, Magn Reson Med. 30:183-90 (1993)
[0162] (D5) Alsop D C, The sensitivity of low flip angle RARE
imaging, Magn Reson Med. 37:176-84 (1997)
[0163] (D6) Gullion T, Baker D E, Conradi M S., J.Magn.Reson. 89,
479 (1990)
[0164] (D7) van Uijen C M, den Boef J H, Driven-equilibrium
radiofrequency pulses in NMR imaging, Magn Reson Med. 1984
Dec;1(4):502-7.
[0165] (D8) Hennig J, Thiel T, Speck O, Improved Sensitivity to
Overlapping Multiplet Signals in in vivo Proton Spectroscopy Using
a Multiecho Volume Selective (CPRESS-) Experiment, Magn Reson Med.
37: 816-20 (1997)
[0166] (D9) Haase A, Snapshot FLASH MRI. Applications to T1, T2,
and chemical-shift imaging, Magn Reson Med. 13:77-89 (1990)
[0167] (D10) Norris D G, Ultrafast low-angle RARE: U-FLARE, Magn
Reson Med. 17: 539-542 (1991)
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