Shim method with determination of the target field distribution by optimization in a parameter space

专利摘要:
The invention relates to a method for homogenizing the static magnetic field with a distribution B0 (r) in the working volume of a magnetic resonance device with N shim coils comprising the following steps: (a) mapping (21) of the magnetic field distribution B0 (r), (b) Determining (22) a target field distribution B0T (r), (c) generating (23) the target field distribution B0T (r) in the working volume by adjusting the shim currents, wherein in step (b) an optimization method for optimizing a numerical quality criterion for the target field distribution B0T (r ), which as a result provides values for the N shim currents, and wherein a spatial weighting function is used, is characterized in that a filtering method is used in which filter norms influence a norm of the shim currents and in that the optimization method is in a parameter space with M control parameters, where 2 ≤ M <N, where one of the control parameters is a weighting parameter is used to modify a spatial weighting function and another control parameter to control the filter factors. In this way, the hardware limitations can be taken into account when determining the target field distribution (22), without the computational outlay in the optimization for determining the target field distribution (22) being significantly greater.
公开号:CH708759B1
申请号:CH01552/14
申请日:2014-10-13
公开日:2018-09-14
发明作者:Douwe Van Beek Jacco；Speck Thomas
申请人:Bruker Biospin Ag；
IPC主号:

专利说明:

Description: The invention relates to a method for homogenizing the static magnetic field with a magnetic field distribution BO (r) in the working volume of a magnetic resonance apparatus having a number N shim coils, the method comprising the following steps: (a) mapping of the magnetic field distribution BO (r) the static magnetic field, (b) setting a target field distribution BOT (r), (c) generating the target field distribution BOT (r) in the working volume by adjusting currents in the shim coils, wherein in step (b) an optimization method for Optimization of a numerical quality criterion for the target field distribution BOT (r) is used, the optimization method as a result provides values for the currents through the N shim coils, and wherein in the optimization method, a spatial weighting function is used.
[0002] Such a method is known from Markus Weiger, Thomas Speck, Michael Fey, "Gradient shimming with spectrum optimization"; Journal of Magnetic Resonance 182 (2006) 38-48 (= Reference [5]).
BACKGROUND OF THE INVENTION Many magnetic resonance methods require as homogeneous a static magnetic field as possible, for example in order to achieve a high spectral resolution in the case of a spectroscopic method or in order to obtain a distortion-free and sharp image in the case of an imaging method. A well-known means for adjusting the homogeneity of the static magnetic field are so-called shim coils (see for example reference [2]), which provide adjustable magnetic fields in addition to the main magnetic field in the working volume. Each of these shim coils is powered by its own adjustable current source. By means of different field distributions generated by the different shim coils, a wide range of field distributions can be homogenized. Shim systems with up to 38 independent shim coils or current sources are already known.
In addition to the device for generating the magnetic fields, a method for finding the appropriate current setting is needed. Such a method, which leads in the concrete application to the desired homogeneous magnetic field distribution in the working volume is called shim method. A particular difficulty of such methods is in dealing with the large number of degrees of freedom in the choice of the current setting. In particular, long-known shim methods (see, for example, reference [1]) which progressively improve a global homogeneity measure, such as the amplitude, signal energy or second moment of a resonance line, by making small changes to each current degree of freedom Under the increasing number of degrees of freedom enormously increasing number of required process steps.
A significant improvement over such a method is achieved by the shim method takes into account information about the spatial distribution of the static magnetic field in the working volume. The information about the spatial distribution of the static magnetic field is obtained in a method step in which the magnetic field distribution BO (r) of the static magnetic field is mapped using a suitable measuring method.
Background of the invention Particularly efficient known methods for adjusting the currents in the shim coils comprise the following steps: (a) mapping of the magnetic field distribution BO (r) of the static magnetic field (b) specifying a target field distribution BOT (r) (c ) Generate the target field distribution BOT (r) in the working volume by adjusting currents through the shim coils.
Such a method is described in reference [4]:
The mapping of the magnetic field distribution BO (r) in the working volume of the static magnetic field takes place by means of a method which is based on phase-sensitive magnetic resonance imaging, and whose implementation uses switchable gradient coils for determining the spatial origin of the signals. Examples of such methods are the gradient echo method or the spin-echo method.
When setting the target field distribution BOT (r), a quality criterion is used whose optimum value (minimum or maximum) determines the target field distribution BOT (r). In the method according to reference [4], a quality criterion is used, which is derived from a simulated spectrum. At this predicted spectrum Eigengeschäften such as the half-width of spectral lines and envelopes around spectral lines are determined and combined to a size, which serves as a target for an optimization algorithm. After the optimization algorithm has found an optimum for this target variable, the magnetic field distribution belonging to this optimum is defined as the target field distribution. Subsequently, in this method, the currents in the shim coils are iteratively set and the effect achieved is checked by re-mapping the magnetic field distribution in the working volume until the target field distribution is achieved.
[0009] Many optimization algorithms are suitable for finding the target field distribution. In particular, the Gauss-Newton method, the conjugate gradient method, the simplex method and the simulated annealing may be considered. In general, in all these methods, the computational effort to find an optimum increases with higher dimensionality of the parameter space, in this case with the number of shim coils or the corresponding number of currents.
[0011] The closest prior art to the subject matter of the present invention is described in reference [5] cited at the outset: Here too, an optimization of a quality criterion is carried out to determine the target field distribution, a spatial weighting function being used in the optimization method , Efficient optimization is achieved by reducing the parameter space to one dimension. The optimization in a one-dimensional parameter space is here implemented such that the measured magnetic field distribution BO (r) is in each case subjected to a weighted fit with spatial weighting function W (r, k) = (B1 (r)) Ak, the power k being varied. The fit functions are the field distributions of the shim coils. The role of the only parameter is taken from k. Each choice of the parameter k leads to a list of currents to be set for the shim coils and to a field distribution which is close to a homogeneous distribution.
A small number of analyzes (i.e., a small number of values for k) are often enough to find a very good solution, although it can not be guaranteed that this is the optimal solution. The advantage of this procedure is that an optimization in a high-dimensional parameter space with as many dimensions as shim coils are present can be avoided.
Other Problems and Disadvantages of the Prior Art Another problem of shim methods arises from the fact that the approximation of a magnetic field distribution, as it results from the mapping of the field distribution in the working volume, by a set of field distributions, as of Shim coils can be generated, generally resulting in a mathematically ill-posed problem. The well-known approach, to deal with mathematically ill-posed problems, is the regularization of the problem (see for example reference [6]).
By means of regularization, where it is attempted with the smallest possible filtering effect to prevent high-frequency oscillations, these problems can be largely eliminated. An application of regularization to shimming MRI experiments is described in reference [3j. The shim method described therein aims to remedy the numerical instabilities that arise when using shim coils constructed so that the magnetic fields they produce form an orthogonal set of functions in a spherical volume about a midpoint Working volume to be chamfered, which is not spherical, and whose center is shifted from the center of the shim coils (see reference [3], column 1, lines 56-63).
Is chased in this case up to high orders (ie, a large number of Stromfreiheitsgraden determined), so already affect small, for example due to measurement noise errors in the mapped magnetic fields so that huge shim currents with opposite signs as useless solution result if not regularized. By applying a regularization method, the diverging of the currents can be avoided.
Although in a concrete application the problems with diverging currents described in the last section do not occur, it is generally of great interest to find shim-current settings which are economical with respect to shim power. The reasons for this are the avoidance of the heating of the measuring system and of the sample volume by the adjacent shim coils. Furthermore, it is advantageous to operate the current sources with currents sufficiently far away from hardware limitations. In addition to maximum values for the individual currents, the overall performance of the power supply unit that supplies the power sources as well as the temperature of electronic elements are also relevant limitations.
Restricting the optimization to one dimension in parameter space, as described in reference [5], is too restrictive to accommodate such hardware limitations in current or power. An explicit consideration of these limitations, however, leads again to the fact that the parameter space must be considered in full size, which leads to long-term optimization.
A very primitive way of considering current limitations is simply to first calculate an optimization of the quality criterion without considering the limitation, and then to cut the individual currents for the shim coils to the maximum allowable value. As shown in reference [7], a better result can generally be achieved with the same limitations. The improvement proposed in reference [7] employs a minimization algorithm tailored to the special case of a positive and negative limit for each individual shim stream and a quadratic dependence of the quality criterion on the shim streams. As discussed above, more complex limitations such as shim performance also play a role in practice. There are also desirable quality criteria, which have other than a quadratic dependence on the Shimströmen. In both cases, the algorithm is no longer applicable. Moreover, in the minimization algorithm proposed in reference [7], the parameter space of the full-size shim currents will be taken into account.
In contrast, the application of a regularization process allows at least an indirect influence on the shim power. However, the optimally regularized solutions give no information about the quality of the shim state as a function of the shim current power. There are often many other solutions of comparable shim quality, but which need significantly less power.
OBJECT OF THE INVENTION The present invention is based on the object of presenting a method of the kind defined in the introduction, in which the hardware limitations are taken into account in the determination of the target field distribution, without the computational outlay in the optimization for determining the target field distribution being clear gets bigger.
Furthermore, the invention is intended to effect that more points in the parameter space are tested in order to reduce the probability that the proximity to the optimal solution will be missed. By increasing the number of points in the parameter space an independent direction should be tested.
BRIEF DESCRIPTION OF THE INVENTION [0022] This object is achieved in a surprisingly simple manner and with readily available technical means by a modification of a method having the features mentioned in the introduction, which is characterized in that a filtering method is used as the optimization method, in which a norm of the shim currents is influenced by means of filter factors, and that the optimization method works in a parameter space with M control parameters, where 2 <Μ <N, where one of the control parameters is used as weighting parameter for modifying the spatial weighting function, and another control parameter is the Filter factors controlled.
The above-mentioned object of the invention is achieved in that the control parameter, which controls the norm of the shim currents, defines solutions in the full parameter space, which can be calculated very quickly. The final solution is chosen from a small number of trial solutions spanned by the few (M) control parameters. This is achieved with very little additional effort that a particularly good solution is found, which minimizes the standard of Shimströme.
Operation of the Invention and Further Advantages over the Prior Art With the aid of the method modified according to the invention, the distance between the resulting solutions and the hardware limitations can be influenced in particular in comparison to the closest prior art. The hardware limitations can be expressed in terms of a standard of the currents. This standard can be selectively influenced towards smaller values of the standard of the streams by choosing the control parameter that controls the filter factors in the filtering process. This possibility of deliberately influencing the standard of the currents is completely lacking in the next state of the art.
Compared to the prior art, e.g. According to reference [4], in which the full dimensionality N (namely the number of shim currents) of the task is taken into account in the optimization step for determining the target field distribution, in the method according to the invention the number of control parameters M can be chosen to be significantly smaller than N, and thus the computational effort becomes clear be reduced. The inventive method allows a reduction of the number of control parameters to M = 2.
Preferred Embodiments of the Invention In practice, the method according to the invention will find application in apparatus in which the magnetic resonance apparatus is an NMR spectrometer, an MRI scanner, an EPR apparatus or an ion cyclotron resonance apparatus is. These devices are all used in a manner in which a very homogeneous magnetic field in a working volume is a prerequisite for an optimal measurement result. Furthermore, the adjustment possibilities of the magnetic field homogeneity by means of shim currents are always limited by the available hardware in these devices. In the operation of these devices, one profits in particular from the method according to the invention, which achieves the best possible homogeneity of the magnetic field taking into account these hardware limits. Especially advantageous are developments of the inventive method in which the magnetic resonance device is an NMR spectrometer in which a sample is rotated about one or more axes, wherein the axes may be inclined with respect to the direction of the static magnetic field. Shim systems for NMR spectrometers are usually designed so that an active volume with an axis of rotation parallel to the static magnetic field can be cooled particularly efficiently. If one deviates from this sample geometry, then currents in shim coils may become inefficient
Way used to influence the field homogeneity. The method according to the invention takes into account the standard of the shim currents and is therefore able to efficiently use shim coils which were actually designed for a different sample geometry, in particular a sample geometry with a different axis of rotation.
In further advantageous embodiments of the inventive method, a gradient-echo method or a spin-echo method is used in step (a) for mapping the magnetic field distribution BO (r) of the static magnetic field. These known imaging techniques for mapping a magnetic field distribution allow the mapping of the magnetic field with the use of means such as are already present in the magnetic resonance apparatus anyway, i. Transmit / receive coils and gradient coils. In this embodiment of the method according to the invention, therefore, no additional measuring means are necessary in order to carry out the method. Particular preference is also given to embodiments of the invention in which, when determining the target field distribution in step (b), the adjustment range of the shim currents and the absorbed power of all shim coils are taken into account. The absorbed power of all shim coils is a special case of a standard of shim currents, which has specific technical meanings for the operation of the measuring apparatus. On the one hand, it describes the heat output, which is delivered in the shim coils and thus in the vicinity of the working volume. Many magnetic resonance measurements depend on the temperature of the sample, and an excess of emitted heat output in the vicinity of the working volume can adversely affect the measurement. Considering this effect already in the selection of the target field distribution avoids these negative effects. On the other hand, the absorbed power of all shim coils is an important measure of the load on the power supply and usually this power has a defined upper limit, which can not be exceeded with given means for power supply.
Embodiments of the process according to the invention in which the filtering process used in step (b) is one of the following processes are also particularly preferred:
Tikhonov regularization or
Tikhonov-Phillips regularization or
Truncated-singular-value-decomposition or
Damped-Singular Value Decomposition.
These mentioned methods belong to the most suitable known methods for working on mathematically ill-posed problems (so-called ill-posed problems). The methods use a single regularization parameter, which determines the filter effect. Continuously increasing the value of the regularization parameter makes it possible to find solutions in the full parameter space which correspond to an ever smaller standard of the shim currents. Regularization methods in which the value of the regularization parameter can be varied continuously are particularly advantageous.
Advantageous developments of these embodiments are characterized in that the optimization method in step (b) optimizes a numerical quality criterion, and that a calculation method for calculating the quality criterion is used, wherein the calculation method as input the magnetic field distribution BO (r), the influence of Receiving currents in the shim coils to the magnetic field and a weighting parameter and a regularization parameter, the calculation method producing as output the quality criterion and a list of current settings, and wherein in the optimization process the following steps are performed: (i) selecting a list of values for a first control parameter, the weighting parameter; (ii) choosing a list of values for a second control parameter, the regularization parameter, (iii) forming pairs of weighting parameters and regularization parameters from the list of values from (i) and the list of values from (ii) and computing the quality criterion with input (iv) assessing whether the list of current settings is a viable current setting; (v) selecting the optimal pair of weighting parameters and regularization parameters based on the quality criterion and excluding the unrealisable current settings.
These advantageous developments of the inventive method work with the minimum number of control parameters, with which the inventive idea can be realized, namely with M = 2. Thus, the computational effort in the optimization for determining the target field distribution, insofar as it depends on the number of control parameters depends as much as possible. In addition, in step (iv) an explicit check of the ability to adjust the currents is carried out for each result resulting from the input of a pair of weighting parameters and regularization parameters. In this way, a list of complexly dependent on the individual shim currents conditions in the choice of the targeted target field distribution can be considered.
Particularly preferred variants of these developments are characterized in that in the calculation of the quality criterion, a simulated magnetic resonance spectrum is used. When applying the method to a spectroscopic method, the quality of the resulting spectrum is in the foreground. The connection between the magnetic field distribution in the space, which is adjusted by the method according to the invention, and the resulting spectrum is produced by the simulation of the spectrum. This procedure makes it possible to formulate the quality criterion in the language of the spectroscopist and to explicitly consider the properties of the sample relevant to the planned experiment, the measuring method used and their specific dependence on the homogeneity of the magnetic field. The scope of the present invention also includes an electronically readable data carrier on which a computer program is stored which, when executed, carries out a method according to one of the preceding claims. Such an electronically readable data carrier is a particularly favorable means for enabling a user of a modern, computer-controlled magnetic resonance apparatus to carry out the method according to the invention.
Further advantages of the invention will become apparent from the description and the drawings. The embodiments shown and described are not to be understood as exhaustive enumeration, but rather have exemplary character for the description of the invention.
DETAILED DESCRIPTION OF THE INVENTION AND DRAWING [0033] The invention is illustrated in the drawing and will be explained in more detail by means of exemplary embodiments. It shows:
1 shows a flowchart with optimization in a parameter space with M = 2 control parameters;
FIG. 2 shows a flowchart with the shim method according to the prior art; FIG.
3 shows a flowchart with a possible sequence of a method variant according to the invention;
Figures 4a, 4b illustrate the construction of a set of spatial weighting functions for the varying data width fit
4a shows functions for varying the data width, wherein the weighting functions in FIG. 4b arise by scaling the measured excitation profile with these functions;
FIG. 4b shows in each line the excitation profile scaled with the corresponding functions from FIG. 4a, which is used as the weighting function in the fit; FIG.
5a, 5b, the illustration of the optimization of the quality criterion in a two-dimensional parameter space with
Fig. 5a 2D-plot quality criterion for shims state vs. Log regularization parameters (horizontal) and data width (vertical);
Fig. 5b 2D plot quality criterion for Shimszustand vs. Log of the 2-norm of the shim currents (horizontal) and data width (vertical);
6 shows the quality criterion (Q) for shim state as a function of the data width for solutions obtained by optimal regularization (discrepancy principle or L-plot);
FIGS. 7a-7d illustrate the generation of spatial weighting functions for the fit derived from an MRI image
Fig. 7a prepares for the shimming process taken MRI image, wherein a user-selected
Area (71) in which highest homogeneity requirements are made, further areas (72) with different, symbolized by different hatching signal strength and areas (73) where no signal was received;
FIG. 7b shows a spatial weighting function with values 0 to 1 along the W-axis for the fit in the case of the Shimvor, with a uniform transition from full weight 1 in area 71 to weight 0 in area 73;
FIG. 7c shows a spatial weighting function with values 0 to 1 along the W-axis for the fit in the case of the shim, wherein the weighting function of FIG. 7b has been increased by k, and where 0 <k <1, so that regions close to (71) receive an increased weight;
FIG. 7 d shows a spatial weighting function with values 0 to 1 along the W axis for the fit in the case of the shim, where the weighting function of FIG. 7 b has been increased by k, and k> 1, so that the weight for areas outside of (71 ) drops rapidly;
Fig. 8a, 8b further ways to vary the spatial weighting functions with a parameter, namely
Fig. 8a Variation of the spatial weighting function for the fit, in the form of (B1 (r)) Ak, where k from bottom to top assumes the following values: O.O1,0.2, 0.5, 1,2, 5, 10, 20; and
Figure 8b shows a variation of the spatial weighting function for the fit, varying the z-position of a reduced weight spot.
In carrying out the method according to the invention, the steps of (a) mapping the magnetic field distribution BO (r) of the static magnetic field (b) defining a target field distribution BOT (r) (c) generating the target field distribution BOT (r) in the working volume, by currents are adjusted by the shim coils, fitted to the task in a total process, which may include repetitions of the steps and decisions on the achievement of a goal.
A possible sequence is illustrated in FIG. 3 of reference [5] (reproduced here in FIG. 2). This procedure contains an inner "fit-loop", which was not previously discussed, in which only the difference between the current magnetic field distribution BO (r) and the target field distribution BOT (r) is fit without defining a new target field distribution. Such a loop makes the method more robust in the event that the calculated current change does not exactly result in the predicted change in the magnetic field distribution. Iterative readjustment, without the effort involved in defining a new target field distribution and the optimization required for it, can significantly speed up the entire process. Ultimately, however, with precise knowledge of the reaction of the entire measuring arrangement to current changes in the shim system, this loop is no longer necessary and thus not a compulsory component of the method according to the invention.
For mapping the magnetic field distribution in the working volume, various methods come into question. Phase-sensitive magnetic resonance imaging methods using switchable gradient coils, such as the gradient echo method or the spin-echo method, are particularly suitable for performing the mapping of the magnetic field distribution in the working volume. The information about the local magnetic field is thereby obtained from the phase difference of the signals in two images, which are recorded with different evolution time for the spins.
The advantage of these methods is that the mapping of the magnetic field can be carried out with the same apparatus (i.e., transmitting / receiving coils, gradient coils) with which the experiment which requires homogenization of the magnetic field is also performed. The sample finally used or the object to be imaged, or the patient to be examined, may already be in the measuring position, so that their influence on the homogeneity of the magnetic field can already be taken into account and corrected.
Other known methods for measuring magnetic fields with spatial resolution use a displaceable magnetic field sensor with which the magnetic field can be measured at different positions or an array of magnetic field sensors. Hall sensors or small NMR samples are suitable here. Such a method may e.g. be used in the installation of a main field magnet for generating a basic homogeneity of the magnetic field. After the homogenization of the magnetic field, however, the displaceable magnetic field sensor must be replaced by another measuring device and also the sample to be examined must not be in the working volume during the mapping of the magnetic field.
When determining the target field distribution BOT (r) one or more quality criteria are used, from which a target variable can be derived whose optimal value (minimum or maximum) determines the target field distribution BOT (r). A target variable which can be used to determine the target field distribution is the root of the mean value of the squared deviations from the constant nominal field (root mean squared deviation, RMSD).
Not always this size is suitable to guarantee the quality of the target field. This is the case, for example, with spectra, where the highest possible resolution of the spectral lines is achieved and, at the same time, a splitting into closely adjacent lines, which could be confused with multiplets, must be avoided. In such a case, a method according to reference [4] is suitable, wherein the objective function is calculated by evaluating a prediction of the resulting spectrum. At this predicted spectrum, properties such as the half-width of spectral lines and of envelopes around spectral lines are determined and combined to a size which serves as the target variable for an optimization algorithm.
This approach of using a simulated spectrum allows to formulate the quality criterion in the language of the spectroscopist, as well as to take into account the relevant properties of the sample for the planned experiment, the measurement method used and their specific dependence on the homogeneity of the magnetic field explicitly. Possible quality criteria may be, for example, the half width, the width at a different height or the half width of an envelope (as described in reference [4]) of a spectral line. The natural line width of the sample to be examined is an important experimental parameter which, properly set, avoids inefficient homogenization on a too fine scale. Different pulse sequences, which are sensitive to inhomogeneities of the magnetic field, can be used on the same apparatus. This effect can also be taken into account when simulating the spectrum.
Another quality criterion that is particularly useful for assessing homogeneity in MRI images is that the local gradient of the magnetic field (gradients of all three spatial directions) is squared and summed over all voxels. By minimizing the resulting value, the total signal is maximized, as far as it depends on the homogeneity of the magnetic field, by minimizing the intra-voxel dephasing caused by local gradients.
The key feature of the present invention is the optimization in a parameter space with M control parameters, where 2 <Μ <N, in determining the target field distribution BOT (r). At least one of the control parameters, the weighting parameter, is used to modify the spatial weighting function. This parameter is used to find possible solutions in the high-dimensional parameter space of the shim currents by varying the relative weighting of subregions in the measurement data.
A possible realization of such a weighting parameter is given in the reference [5] with the parameter k: [0045] A k-dependent weighting function W (r, k) = (B1 (r)) Ak is calculated based on the normalized RF Excitation profile B1 (r) constructed. The effect of the choice of k is such that with k = 1 the weighting of the excitation profile is taken over unchanged, that with 0 <k <1 the edge of the excitation profile is weighted more heavily, and that with k> 1 the edge of the excitation profile in the fit is weaker is weighted.
The local effect of k depends on the value of the excitation profile at the respective location. The choice of a spatial weighting function, which closely follows its shape to the excitation profile of the RF coil, is particularly suitable in the case of a spectroscopic method in which a homogeneous sample is examined. In this case, the differential treatment of the regions in the sample that contribute strongly to the received signal and regions in the sample that are at the edge of the excitation profile and that provide only weak contributions and possibly impaired by measurement artifacts is important.
A palette of such weighting functions, which was generated with variation of the power k from the measured excitation profile B1 (z), is shown in FIG. 8a.
A further possibility to obtain a variation of the solutions via the weighting function in the case of fits is achieved when a measured excitation profile is scaled with a function which modulates the effective width of the signal. In addition, this function is also taken into account when analyzing the scaled data.
In Fig. 4b it is shown how a set of weighting functions can be generated from a measured excitation profile, by means of the 14 different functions shown in Fig. 4a, which serve to vary the data width.
By means of an efficient linear analysis, a result is then obtained, as shown in Figs. 5a and 5b, from which then the best solution is chosen. The axis direction 11 in these figures denotes the direction in which the data width is varied.
A third way to vary the spatial weighting function is useful in cases where the fit result is strongly influenced by a localized distortion of the magnetic field distribution. Instead of varying the width of the distribution as above, the spatial position of a zone in which the weighting function is to be locally reduced is varied. A set of such functions is shown in Fig. 8b.
In the case of imaging applications, the choice of a spatial weighting function is required, which takes into account the spatial arrangement of the object to be imaged. For example, a suitable weighting function may be derived based on a pre-recorded image and a user-marked region in which the highest homogeneity requirements are set. Such a region may, for example, be an organ of a patient to be examined.
A compromise between global homogeneity throughout the image and local homogeneity in the selected region can be found by a parameter that continuously affects the weighting function. Such a parameter can be used as a first dimension in the optimization in step (b) of the shim method. A set of weighting functions thus constructed that fit the schematically illustrated MRI image of Figure 7a is shown in Figures 7b, 7c and 7d.
Another control parameter controls the filter factors of the filtering process, in which a norm of the shim currents is influenced by means of these filter factors. The thus-influenced norm of the shim currents may be e.g. to be the total power of all shim coils.
The standard of the shim currents is thereby influenced in an indirect way. By "indirect influence" is meant that the exact value of the norm of the shim currents can not be specified directly, but that, starting from a solution to a parameter value, with the choice of a larger or smaller value for the control parameter controlling the filter factors , a solution can be found specifically whose standard is smaller or larger than the initial value.
A suitable parameter is the regularization parameter of a regularization method, where as regularization method e.g. Discretization, truncated singular value decomposition (TSVD), damped singular value de-composition (DSVD), Tikhonov regularization, Tikhonov-Phillips regularization (see reference [6]) are eligible. With a standard of shim currents, the entire list of currents in the N shim coils is combined into a single measure.
If, above all, the power is of interest, the norm is formed as the root of the sum of squares of the shim currents (the "2 norm"), if necessary with a weighting which corresponds to the different resistances of the shim coils.
If the sum of the currents is important as a limiting variable, alternatively the sum of the amounts of the currents (the "1-norm") can be taken into account.
If one wishes to avoid extreme loads on individual shim coils, the maximum standard is the appropriate size.
A very efficient implementation of the method is achieved by exploiting the regularization parameter λ from the Tikhonov method in order to produce solutions which have a steadily decreasing shim output as the value of λ increases.
Let
the singular value decomposition of the set of shim functions K, then the solution g of the linear analysis can be written from the mapped data s by least squares method
Here, the singular values wh are sorted by decreasing magnitude, so that w-i is the largest and wN is the smallest singular value, where N is the number of available shim functions. The singular values, which drop very rapidly, typically with increasing index I2, provide for the numerical problems which have to be regularized.
In the Tikhonov regularization, the parameter λ has a filtering effect which is described by the equation
However, this equation can also be exploited to efficiently find solutions in the highly complex parameter space by performing analyzes with different values of λ. It is also of great advantage that λ can be varied with arbitrary accuracy, which is not possible with all regularization methods.
A two-dimensional representation of the shim quality as a function of the data width and the parameter λ obtained from a mapped magnetic field distribution BO (r) in the working volume of the static magnetic field is shown in Fig. 5a by means of a practical example of an NMR probe head.
Common methods in regularization methods to determine the optimum value of λ, such as. "Dis-crepancy principle" or L-plot, give a result as shown in Fig. 6 and also in Fig. 5a and Fig. 5b indicated by hexagonal symbols. These locations are optimized to provide the least possible increase in deviation, i. with minimal filtering effect to solve the numerical problems.
At the optimum value of the parameter λ, however, the solution is not found in which an almost optimal result is achieved with the lowest possible shimming power.
In Fig. 5b is shown what is found in the same data when the required Shimleistung is evaluated for each parameter λ and the corresponding data point is entered in a diagram with Shimleistung as a horizontal axis. The two-dimensional space often allows solutions of similar quality to be found at significantly lower shim powers, as found, for example, with the "discrepancy principle". In the example shown, solutions result, which save up to 2 orders of magnitude of shim power compared to the regularized solution.
A relatively small choice of points in two-dimensional space is often sufficient to determine a local optimum and to meet the requirements. An important point in this selection is to consider known hardware limits before setting the shims and experimentally testing whether the expected shim state is achieved.
This can save a lot of time. In particular, in more complicated problems, where the algorithm outputs solutions that exceed the hardware limits, this mechanism is of great advantage. In particular, the second parameter, the regularization parameter, specifies the direction in which a solution must be sought that no longer exceeds the hardware limits.
Problems in which there is an increased risk of exceeding the hardware limits are, for example, highly inhomogeneous samples or samples in short containers (for example MAS rotors).
A concrete implementation of the method according to the invention is shown in FIG. 3 as a flowchart. The weighting parameter used in this case was the data width. A second control parameter for the optimization here is the regularization parameter λ of the Tikhonov regularization. The procedure involves the following steps: (a) mapping the magnetic field distribution BO (r) in the static magnetic field working volume (b) making the selection of data width variations which are considered to scale the theoretical shim functions (c) fits the magnetic field distribution BO (r ) with the scaled shim functions, for all data width variations and for several values of λ (d) defining a target field distribution BOT (r) in the working volume, which corresponds to the requirement for a good shim state at low shim power. (e) generating the target field distribution BOT (r) in the working volume by adjusting currents through the shim coils (f) mapping the magnetic field distribution B0 (r) in the working volume of the static magnetic field (g) repeating steps (b) - (f) until the target field distribution BOT (r) in the working volume is approximately reached
Main Fields of Application The method according to the invention can be used in all known magnetic resonance devices, such as MRI scanners, NMR spectrometers or EPR devices, but is particularly advantageous in high-resolution spectroscopy, where the goal is to have as narrow, serrated as possible Line shape, often not achieved by minimizing the norm of the target field distribution BOT (r).
Particularly preferably, the inventive method for homogenizing the static magnetic field in the working volume of a magnetic resonance device can be used, wherein the magnetic resonance device, an NMR spectrometer, an MRI scanner, an EPR device or an ion cyclotron resonance Device can be.
Inclined Rotational Axis NMR spectroscopy methods in which a specimen is rotated about an axis inclined with respect to the direction of the static magnetic field require high magnetic field uniformity mainly along this inclined rotational axis (n). Magic Angle Spinning (MAS), Variable Angle Spinning (VAS) and Double Rotation (DOR) are examples of such techniques. These methods may suffer because the shim coils are designed to efficiently affect the field distribution on an axis parallel to the static magnetic field. Such methods particularly benefit from a shim method according to the invention, which takes into account the shim quality and the shimming performance required for this purpose.
Also preferably, the inventive method for homogenizing the static magnetic field in the working volume of a magnetic resonance device is used, wherein the magnetic resonance device will be an NMR spectrometer, in which a sample is rotated about one or more axes, with respect may also be inclined to the direction of the static magnetic field.
Computer program All operations in the operation of modern magnetic resonance spectrometers and MRI scanners, such as the transmission of RF pulses, the switching of currents in gradients, the adjustment of shim currents and the reception and digitization of signals, are today triggered by computer control. Therefore, the shim method according to the invention is ideally implemented as a computer program which, when executed on the control computer of the magnetic resonance spectrometer or the MRI scanner, directly triggers the necessary processes in the hardware. Such a computer program is simply transmitted to users of the spectrometer as an electronically readable data carrier containing a computer program which carries out the method according to the invention during its execution.
REFERENCE NUMBER LIST 10 Two interleaved loops with count variables 11 and I2 11 Step (i): select a list of values for a first control parameter, the weighting parameter; choose a list (k (1), ..., k (Hmax)} of weighting parameters 12 Step (ii): choose a list of values for a second control parameter, the regularization parameter, choose a list (λ (1), .. Step (iii): Formation of pairs of weighting parameters and regularization parameters from the list of values from (i) and the list of values from (ii) and calculation of the quality criterion with input of this pair of weighting parameters and regularization parameter; current parameter pair is (k (H), λ (Ι2)}, compute quality criterion Q (I1, I2) and associated current setting J (I1, I2) 14 Step (iv): Evaluate whether the list of current settings is realizable Current setting is, decision is adjustable J If yes, set F (l 1, I2) = 1, otherwise F (l 1,12) = 0. 15 Step (v): Selecting the optimal pair of weighting parameters and regularization parameters based on the quality criterion and under Aussch loss of unrealisable current settings; 11 opt, I2opt, such that Q (I1opt, I2opt) minimally under the constraint that F (I1opt, I2opt) = 1- The magnetic field calculated from BO (r) and J (I1opt, I2opt) is the target field distribution BOT ( r). 16 Input of BO (r) 17 Output of BOT (r) 21 Step in shim procedure: Mapping of the magnetic field distribution BO (r) of the static magnetic field 22 Shim step: Defining a target field distribution BOT (r) 23 Step in Shim procedure: Generating the target field distribution BOT (r) in the working volume, by adjusting currents through the shim coils 51 curve in the 2D plot, on the solutions obtained by optimal regularization ("discrepancy principle" or L-plot) lie 52 region of optimal values for the quality criterion, which found in the search along (51) 53 Other solutions with similar values for the quality criterion and lower shim power than in (52) 71 region in the MRI image, which should achieve the highest possible homogeneity after shimming 72 Other region in the MRI image , with signal strength greater than zero 73 Region in the MRI image, which contains no signal and does not need to be taken into account when shimmering 11 Axial direction of the data width in 2 D-Plot Q Axis direction of the quality criterion W Axis direction of the function value for weighting function w1 Data width of the 1'th weighting function w14 Data width of the 14'th weighting function x spatial x-direction (in the MRI image) y spatial y-direction (in the MRI image) z spatial z-direction (for weighting functions)

权利要求:
Claims (8)
[1]
λ Regularization Parameter (Lambda) Reference List [1] Richard R. Ernst: "Measurement and Control of Magnetic Field Homogeneity"; The Review of Scientific Instruments 39 (1968) 998-1012 [2] RE Gang: US-A 3,287,630 [31] Dong-Hyun Kim, Daniel M. Spielman, Gary H. Glover, Elfar Adalsteinsson: US Pat. No. 6,529,002 [4] Markus Weiger, Michael Fey, Thomas Speck: EP 1 662 270 B1 [5] Markus Weiger, Thomas Speck, Michael Fey: "Gradient shimming with spectrum optimization"; Journal of Magnetic Resonance 182 (2006) 38-48 [6] PC. Hansen: "Rank-Deficient and Discrete Ill-Posed Problems"; SIAM, Philadelphia, 1998 [7] Han Wen, Farouc A. Jaffer: "An In Vivo Automated Shimming Method Taking Into Account Shim Current Constraints"; Magnetic Resonance in Medicine 34 (1995) 898-904 claims
A method for homogenizing the static magnetic field with a magnetic field distribution BO (r) in the working volume of a magnetic resonance apparatus having a number N shim coils, the method comprising the following steps: a) mapping the magnetic field distribution BO (r) of the static magnetic field, b) defining a target field distribution BOT (r), c) generating the target field distribution BOT (r) in the working volume by adjusting currents in the shim coils, wherein in step b) an optimization method for optimizing a numerical quality criterion for the target field distribution BOT (r ), the optimization method yielding as a result values for the currents through the N shim coils, and wherein a spatial weighting function is used in the optimization method, characterized in that a filter method is used as the optimization method, in which a norm of the currents by means of filter factors is affected in the shim coils, and that there s optimization method operates in a parameter space with M control parameters, where 2 <Μ <N, where one of the control parameters is used as a weighting parameter to modify the spatial weighting function, and another control parameter controls the filter factors.
[2]
2. Method according to claim 1, characterized in that a NMR spectrometer, an MRI scanner, an EPR device or an ion cyclotron resonance device is used as the magnetic resonance device.
[3]
A method according to claim 2, characterized in that the magnetic resonance apparatus is an NMR spectrometer in which a sample is rotated about one or more axes, which axes may be inclined with respect to the direction of the static magnetic field.
[4]
4. The method according to any one of the preceding claims, characterized in that in step a) for mapping the magnetic field distribution BO (r) of the static magnetic field, a gradient echo method or a spin-echo Ver-driving is used.
[5]
5. The method according to any one of the preceding claims, characterized in that the filtering method used in step b) comprises one of the following methods: Tikhonov regularization or Tikhonov-Phillips regularization or truncated-singular-value-decomposition or damped-singular-value Decomposition.
[6]
6. The method according to claim 5, characterized in that the optimization method in step b) optimizes a numerical quality criterion, and that a calculation method for calculating the quality criterion is used, wherein the calculation method as input the magnetic field distribution BO (r), the influence of the currents in receiving the shim coils on the magnetic field and the weighting parameter and a regularization parameter, the calculation method producing as output the quality criterion and a list of current settings, and wherein in the optimization process the following steps are performed: i) selecting a list of values for a first one Control parameters, the weighting parameter; ii) selecting a list of values for a second control parameter, the regularization parameter, iii) forming pairs of weighting parameters and regularization parameters from the list of values of i) and the list of values of ii) and calculating the quality criterion with input of this pair of weighting parameters and regularization parameters, iv) judging whether the list of current settings is a realizable current setting, v) selecting the optimum pair of weighting parameters and regularization parameters based on the quality criterion and excluding the unrealisable current settings.
[7]
7. The method according to claim 6, characterized in that in the calculation of the quality criterion, a simulated magnetic resonance spectrum is used.
[8]
8. An electronically readable data carrier, on which a computer program is stored, which causes it to carry out the method according to one of claims 1 to 7 when it is carried out on a control computer.

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法律状态:
2019-10-31| PFA| Name/firm changed|Owner name: BRUKER SWITZERLAND AG, CH Free format text: FORMER OWNER: BRUKER BIOSPIN AG, CH |

优先权:

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申请号 | 申请日 | 专利标题

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DE201310220933|DE102013220933B3|2013-10-16|2013-10-16|Shim method with determination of the target field distribution by optimization in a parameter space of reduced dimension|

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