Reconstruction of images from MR signals obtained in the presence of non-uniform fields

For MR image acquisition, a sequence of individual measurements that are each composed of an excitation phase and a read-out phase is implemented. In the read-out phase, a nuclear magnetic resonance signal is read out that is allocated to only one point in the k-space defined by a preceding phase-coding gradient. A phase-coding gradient remains activated during a group of individual measurements and changes in size from individual measurement-to-individual measurement. Switching this phase-coding gradient in every individual measurement is thus avoided, so that ramp times can be eliminated and the overall data acquisition procedure is considerably shortened.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention is directed to a method for reconstructing an image 
of an examination subject from MR (magnetic resonance) signals which are 
acquired in the presence of non-uniform fields. 
2. Description of the Prior Art 
Magnetic resonance image acquisition with a sequence of individual 
measurements, each composed of an excitation phase in which nuclear spins 
are excited with excitation pulses, a coding phase wherein the nuclear 
spins are phase-coded with at least one phase-coding gradient, a read-out 
phase wherein a nuclear magnetic resonance signal is read out, the 
magnetic resonance signal being allocated by the preceding phase-coding 
gradient to a specific point in the k-space. Each signal acquired in the 
read-out phase is entered into a k-space matrix, with the measuring 
sequence being implemented n times with respectively different phase 
coding for the complete scan of the k-space. 
A method of this type is disclosed, for example, in German OS 42 19 610 and 
German OS 42 32 731. 
As is known, inhomogeneities in the basic magnetic field lead to image 
distortions in standard MR imaging sequences. Pulse sequences currently 
employed are generally based on the so-called "spin-warp" method, as 
disclosed, for example, in U.S. Pat. No. 4,706,025. A nuclear magnetic 
resonance signal is thereby phase-coded in at least one direction before 
the read-out and is frequency-coded in another direction by a read-out 
gradient during the read-out. Inhomogeneities of the basic magnetic field 
in the phase-coding direction are relatively unimportant since the only 
concern is the signal differences between the individual phase-coding 
steps. The superimposition of the readout gradient with basic field 
inhomogeneities, however, leads to distortions in the direction of the 
read-out gradient. In conventional methods having slice selection during 
the radio-frequency excitation phase, further distortions arise since the 
field inhomogeneities act as a locus-dependent, additional slice selection 
gradient. This leads to bendings of the slice surface as well as a varying 
slice thickness. 
Only linearity deviations of no more than approximately 1 ppm can therefore 
typically be tolerated within the measuring volume for magnets used for 
nuclear magnetic resonance tomography apparatus. 
These demands can only be met with substantial outlay. In particular, 
magnets must be constructed comparatively long, or with a comparatively 
large area (given pole shoe magnets), in relationship to the actual 
measuring volume so that the required uniformity can be achieved. 
For nuclear magnetic resonance tomography in solids having an extremely 
short echo time, for example, the article "SPI--Single Point FID Imaging, 
MRI With Echo Times &lt;50 .mu.s" A. Nauert et al., SMRM Abstracts, 1993, 
p.1215, discloses that only one phase coding be implemented after an 
excitation and that a FID signal be acquired very quickly after the 
excitation without influence of a read-out gradient. By contrast to the 
standard spin-warp method, only one point in the k-space is thereby 
obtained with each signal. In order to produce an image having 
128.times.128 picture elements, thus, 128.times.128 individual 
measurements are required, each having radio-frequency excitation and 
phase coding. When, due to the aforementioned problem of selected 
excitation, a 3-dimensional phase coding is implemented instead then, for 
example, 128.times.128.times.128=2,097,152 individual measurements are 
required. Since the gradient fields must be activated and in turn 
deactivated for each individual measurement, a long measuring time arises, 
particularly particularly due to the required ramp times for the gradient 
pulses. Such a measurement is also extremely inefficient. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide a method for 
MR image acquisition wherein the time expended for the image acquisition 
becomes shorter than in known methods. 
This object is inventively achieved in a method for MR image reconstruction 
wherein a first phase-coding gradient remains activated during a group of 
chronologically contiguous individual measurements, and the first 
phase-coding gradient changes in size from individual 
measurement-to-individual measurement. Since the activation and 
deactivation of the phase-coding gradients in each individual measurement 
is thereby not necessary, the ramp times that are otherwise needed for the 
activation and deactivation of the phase-coding gradient are eliminated 
and the image acquisition can be implemented significantly faster.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The conventional spin-warp sequence of FIGS. 1-6 is merely intended to 
serve the purpose of explaining the problem which is solved by the 
inventive method. In the illustrated example, a frequency-selective 
radio-frequency pulse RF is first emitted under the influence of a slice 
selection gradient G.sub.S. Nuclear spins are thus excited only in one 
slice of the examination subject. Subsequently, the dephasing caused by 
the positive sub-pulse of the slice selection gradient G.sub.S is in turn 
canceled by a negative sub-pulse G.sub.S.sup.-. Further, a phase-coding 
gradient G.sub.P is emitted. Finally, a negative read-out gradient 
G.sub.R.sup.- is also activated. 
Only a positive read-out gradient G.sub.R.sup.+ is activated during the 
following read-out phase. The arising echo signal S--as indicated by 
arrows on the axis AQ--is sampled M times and the M measured values 
acquired in this way are entered into a row of a raw data matrix RD 
according to FIG. 7. 
The illustrated pulse sequence is repeated N times with different values of 
the phase-coding gradient G.sub.P, so that a measured matrix having N rows 
is obtained overall. Usually, the phase-coding gradient is thereby 
advanced from the highest positive to the highest negative value, or vice 
versa, in identical steps from pulse sequence-to-pulse sequence. The raw 
data matrix RD can be considered to be a measured data space, i.e., a 
measured data plane in the 2-dimensional case in the exemplary embodiment. 
This measured data space is referred to as "k-space" in nuclear magnetic 
resonance tomography. 
The information about the spatial origin of signal contributions necessary 
for the imaging is coded in the phase factors, whereby the relationship 
between the locus space having the Cartesian coordinates x, y, z and the 
k-space exists mathematically via a Fourier transformation 
##EQU1## 
The following definitions thereby apply: .gamma.=gyromagnetic ratio 
G.sub.R (t')=momentary value of the read-out gradient (in the x-direction) 
G.sub.P (T')=momentary value of the phase-coding gradient (in the 
y-direction) 
.rho.(xy)=nuclear spin density. 
In the raw data matrix RD shown in FIG. 7, each line corresponds to an 
individual nuclear magnetic resonance signal. Given a step-by-step advance 
of the phase-coding gradient G.sub.P, the scanning in the k-space ensues 
in successive rows. A phase-coding gradient G.sub.P whose gradient 
amplitude increases continuously in steps from subsequence-to-sub-sequence 
is activated before the nuclear magnetic resonance signal S at the 
beginning of every individual measurement. When, for example, each nuclear 
magnetic resonance signal is sampled with 128 measuring points and when 
128 phase-coding steps are implemented, then a raw data matrix having 128 
rows and 128 columns is obtained, i.e., 128.times.128 measured values in 
the k-space. The analog measured signals obtained given the pulse sequence 
of FIGS. 1-6 are thus digitized onto a grid in the k-space. 
An image matrix is then acquired by 2-dimensional Fourier transformation 
from the raw data matrix, or k-space matrix, RD. As previously mentioned, 
two types of distortion occur in a non-uniform basic magnetic field: 
Magnetic field inhomogeneities during the excitation phase lead to bendings 
of the slice surface and to a varying slice thickness. In the read-out 
phase, magnetic field inhomogeneities lead to distortions in the direction 
of the read-out gradient G.sub.R. In the ideal case, the linear 
relationship between the location x in frequency-coding direction and the 
allocated resonant frequency f of the nuclear spins should be achieved as 
a result of the read-out gradient G.sub.R as shown in FIG. 8. Magnetic 
field inhomogeneities, however, lead to non-linearities in this context, 
as shown in FIG. 9. This occurs because gradients that represent the 
inhomogeneities of the basic magnetic field are superimposed on the linear 
read-out gradient G.sub.R. 
With the condition that the magnetic field is constant during the read-out 
phase, inhomogeneities in phase-coding direction do not lead to 
distortions since the principal concern is the signal differences between 
successive phase-coding steps. 
In what is referred to as a SPI sequence (single point imaging), a read-out 
gradient is foregone and phase-coding gradients are applied. Such a 
sequence known from the previously cited article of Nauerth et al. is 
shown in FIGS. 10-14, likewise for explaining the problem. A non-selective 
radio-frequency pulse RF is thereby followed by a phase-coding of the 
nuclear magnetic resonance signal in three directions as a result of the 
three phase-coding gradients GP1, GP2 and GP3 residing perpendicularly 
relative to one another. The arising FID (free induction decay) signal is 
read out a fixed time T1 after the excitation. Whereas a complete row in 
the k-space matrix is always acquired with each signal in the 
above-described, conventional spin-warp method, only a point in the 
k-space is obtained in the method illustrated in FIGS. 10-14, this being 
defined by the gradients GP1-GP3. A corresponding number of individual 
measurements is therefore required for acquiring a data set having 
128.times.128.times.128 k-space points, with all required k-space points 
being covered successively by appropriate switching of the gradients 
GP1-GP3. 
In order to keep the time expenditure within reasonable limits, an attempt 
must be made to make the repetition time of the individual measurements as 
short as possible. The three gradients GP1-GP3, however, must be 
respectively switched on and off in each individual measurement. Since 
gradient coils have an inductance which is not inconsiderable, the 
switching events cannot ensue arbitrarily quickly; on the contrary, 
substantial ramp times that oppose a shortening of the repetition time are 
required for the activation and deactivation. One thus arrives at a 
overall measuring time that cannot be accepted for practical operation. 
Substantially shorter measuring times can be achieved when, according to an 
exemplary embodiment of the invention in FIGS. 15-18, the phase-coding 
gradients are not switched on and off in every individual measurement but 
are left switched on at least for a group of individual measurements. 
FIG. 15 shows a sequence of radio-frequency pulses RF between which the 
data acquisition phases respectively referenced AQ lie. The phase-coding 
gradients GP2 and GP3 according to FIGS. 17 and 18 remain constant during 
the illustrated group of individual measurements, whereas the phase-coding 
gradient GP1 changes linearly from a negative to a positive value. One 
thus obtains N nuclear magnetic resonance signals that are all differently 
phase-coded in the direction of the phase-coding gradient GP1. A complete 
row of the k-space matrix will thus typically be acquired. 
For acquiring the further rows of a k-space matrix having a total of M 
rows, the illustrated measurement is repeated M times with different 
values of the phase-coding gradient GP2. Correspondingly, the entire 
procedure is repeated P times with different values of the phase-coding 
gradient GP3 for acquiring the third direction, so that a total of 
M.multidot.P measurements according to FIGS. 15-18 are required in order 
to cover a 3-dimensional k-space. 
The advantage of the described pulse sequences is that the ramps for the 
gradient pulses during the individual measurements are eliminated, so that 
the individual measurements can be repeated significantly faster. 
The radio-frequency pulses are implemented as "hard" pulses, i.e. broadband 
pulses, so that the simultaneously activated gradients do not undesirably 
lead to a slice selection. Although the gradient GP1 is activated during 
every read-out phase, this does not lead to distortions as in the case of 
conventional data acquisition since only an individual measured point 
having a fixed spacing relative to the radio-frequency pulse RF is 
registered in each measurement, instead of the entire signal being read 
out with the frequency-dependency caused by a read-out gradient. 
For illustration, a part of the sequence of FIGS. 15 and 18 is shown with 
an expanded time scale in FIGS. 19 and 20. One may thereby see that each 
signal S.sub.k is read out at a fixed time interval t.sub.1 following the 
appertaining excitation pulse RF.sub.k. The phase-coding in the direction 
of the phase-coding gradient GP1 is defined by the time integral thereof 
between excitation and read-out time, i.e. over the time span t.sub.1. 
This time integral is shown shaded in FIG. 20. One may thereby see that 
the phase coding increases in the direction of the phase-coding gradient 
G.sub.P1 from individual measurement to-individual measurement. 
Measuring times on the order of magnitude of conventional methods are 
obtained with the described method. For example, a measuring time of 15 
minutes was capable of being achieved for 64.times.128.times.128 measuring 
points. Given a time interval of 500 .mu.s between excitation and read-out 
and a gradient system for a maximum of 10 mT/m.multidot.s, the field 
inhomogeneity over a 300 mm subject expanse that could be tolerated 
without perceptible image artifacts amounted to approximately 1% of the 
main field of 0.3 T. Radio-frequency excitation pulses having a duration 
of 10 .mu.s and an excitation angle of 4.degree. were thereby employed. 
The sampling rate for the nuclear magnetic resonance signals amounted to 
200 kHz. A linear resolution of 2.53 mm for one voxel was achieved. 
Since only one data point is sampled from the nuclear magnetic resonance 
signal in the inventive method as described above, the signal-to-noise 
ratio is rather unfavorable with respect to the overall measuring time. In 
a further embodiment of the inventive method, the resulting nuclear 
magnetic resonance signal is thereby multiply sampled in every individual 
measurement, i.e. at y different time intervals t.sub.i after the 
excitation, as illustrated by the arrows in FIG. 22. Subsequently, a 
complete, separate k-space matrix is produced for each sampling time; 
i.e., a total of y k-space matrices RD1-RDy are obtained. The further 
processing is shown in the block diagram of FIG. 22. Each k-space matrix 
RD1-RDy is separately subjected to a FFT (fast Fourier transform) 
transformation. A corresponding number of the image matrices BD1'-BDY' are 
thus obtained. Due to the phase-coding of different strengths as a result 
of the different time intervals relative to the excitation, however, these 
image matrices have a different zoom factor, this being indicated in FIG. 
22 by the broken lines in the image matrices BD2' and BDY'. 
Real image matrices DB"-DBY" are acquired by magnitude formation from what 
are initially image matrices BD1'-DBY' that are still complex. 
Alternatively, a phase correction could also ensue instead of the 
magnitude formation since what is ultimately involved in this step is to 
eliminate phase errors. 
The image matrices BD1"-DBY" continue to have different zoom factors, that 
are corrected in the next step by corresponding expansion. Interpolations 
are thereby implemented for acquiring the picture elements in a grid 
defined by the image matrix. Finally, the image data are averaged from the 
y image data matrices BD1'"DBY'", so that an image data matrix BD is 
obtained. The image thus acquired has a noticeably improved 
signal-to-noise ratio. Stated more precisely, the signal-to-noise ratio is 
improved by the square root of the number of averaged measured points. The 
measuring time is thereby not lengthened compared to the SPI method with 
the registration of only a single data point. 
Although modifications and changes may be suggested by those skilled in the 
art, it is the intention of the inventors to embody within the patent 
warranted hereon all changes and modifications as reasonably and properly 
come within the scope of their contribution to the art.