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    • 专利摘要:
    An inventive measuring arrangement for NMR measurements comprises a sample container (2) with susceptibility χ 2, an environment (1) with susceptibility χ 1, a sample substance (3) with susceptibility χ 3 and volume, wherein the volume of the sample substance (3) from a upper (V 2b), a lower (V 2a) and a central partial volume (V 1), wherein the sample container (2) has a first interface to the environment (1) and a second interface to the sample substance (3), and possibly. there is a further interface between the sample substance (3) and the environment (1), the susceptibility jump at the second interface being so great that the maximum value of | B'G 2 / B 0 | within the volume is at least 0.5 ppm. The geometry of the sample container (2) is selected such that when there is a homogeneous magnetic field B 0 in the volume there is a location-dependent relative field change F that is greater than 20 ppb at least at one point in the middle subvolume (V 1) that the first residual field in the mean subvolume (V 1) is less than 1.6 ppb, and that the second residual field in the lower subvolume (V 2a) is less than 30 ppb.
    公开号:CH704820B1
    申请号:CH00468/12
    申请日:2012-04-03
    公开日:2016-05-13
    发明作者:Wilhelm Dirk；Speck Thomas；Schett Oskar
    申请人:Bruker Biospin Ag；
    IPC主号:
    专利说明:

    The invention relates to a measurement arrangement for NMR measurements, comprising a sample container closed on one side, the material of the sample container having a magnetic susceptibility χ2, an environment with a magnetic susceptibility χ1 in which the sample container is arranged, and a sample substance located in the sample container with a magnetic susceptibility χ3, which takes up a volume within the sample container, the volume of the sample substance consisting of an upper sub-volume, a lower sub-volume and a middle sub-volume, which contains the origin of a spherical coordinate system with a z-axis, the sub-volumes to one another connect, the sample container having a first interface with the environment and a second interface with the sample substance, and optionally (with certain types of construction of the sample container) the sample substance is a further interface between the sample substance and the environment b It sits, with magnetic susceptibility jumps at the interfaces which, when a given external homogeneous magnetic field running parallel to the z-axis is applied, cause location-dependent interference fields in the volume of the sample substance, the susceptibility jump at the second interface being so large that the maximum value of | B ́G2 / B0 | within the volume is at least 0.5 ppm, with a first residual field in the middle partial volume and a second residual field in the lower partial volume when a homogeneous magnetic field B0 is applied,WithBG1:location-dependent z-component of the magnetic field that arises due to the susceptibility jump from χ1 to χ2 at the first interface G1;BG2:position-dependent z-component of the magnetic field that arises due to the susceptibility jump from χ2 to χ3 at the second interface G2;BG3:location-dependent z-component of the magnetic field that arises due to the susceptibility jump from χ3 to χ1 at the further interface G3;F: = (B ́G1 + B ́G2 + B ́G3) / B0:location-dependent relative field change due to the susceptibility jumps at the interfaces G1, G2, G3B ́j: = Bj– Bj:location-dependent deviation of field Bj from mean value Bj
    Bj: mean value of the z-component of the field Bj, where (j = G1, G2, G3)
    first residual field in the middle partial volume (V1);
    second remaining field in the lower partial volume (V2a)F <N>:Development of the relative field change F around the origin of the spherical coordinate system in rotationally symmetrical spherical functions up to order N, where N = 4 to 10;where generally applies
    Average value of any magnetic field A in the sample volume V
    Development of A into rotationally symmetric (i.e. ϕ-independent) spherical functions up to order N, withan: = development coefficientsKn (r, θ) = r <n> Pn (cosθ): = rotationally symmetrical spherical functionsPn (cosθ): = Legendre polynomials
    Background of the invention
    Such a measuring arrangement is known from [6], [8].
    [0003] NMR spectroscopy is a versatile tool in the chemical analysis of samples. For this purpose, a sample is placed in a strong, static magnetic field and exposed to electromagnetic pulses. The reaction of the atomic nuclei in the sample is measured and analyzed. The properties of the static magnetic field influence the quality of the measurement results. In general, the best results are achieved in a large magnetic field with high homogeneity. Field strengths of up to 23T are used for high-resolution NMR spectroscopy. Superconducting magnets are used for this.
    The typical measuring arrangement, as used in modern spectrometers, consists of a cylindrical superconducting coil that generates a strong magnetic field parallel to the axis in the cylindrical interior. In the cylindrical interior there are also shim coils, gradients and radio frequency coils, which are arranged in this interior on different radii around a sample container. The sample container contains the substance to be examined. It must be made of electrically insulating and chemically inert material.
    [0005] The field homogeneity required for high-resolution NMR spectroscopy is in the order of magnitude of parts per billion (ppb). The superconducting magnet coil generates a sufficiently strong, but typically not sufficiently homogeneous magnetic field. The magnetic field needs a fine correction in order to achieve the required homogeneity. It is therefore common to correct the field homogeneity with the aid of a shim coil system. The shim coil system provides a number of coils with different geometrical arrangements. Currents in these coils cause magnetic fields in the space that is used to hold the RF coils and the sample container. These magnetic fields add to the magnetic field of the magnet. With a suitable setting of the currents in the coils of the shim coil system, a largely homogeneous magnetic field can be achieved. Geometric arrangements of shim coils in such shim coil systems are e.g. described in [1].
    In addition to the insufficient basic homogeneity of the magnet, all materials introduced into the magnetic field can cause a distortion of the magnetic field due to their magnetic susceptibility. These materials include in particular the RF coil, but also the sample container and the sample substance itself. These magnetic field inhomogeneities can also be partially compensated for by magnetic fields of the shim coil system.
    The process of setting the currents in the shim coil system with the aim of obtaining a magnetic field that is as homogeneous as possible is called shimming. Various methods of shimming are known, e.g. [2], [3], [4]. What they all have in common is that in the course of the process they receive signals from the sample substance with one of the RF coils in order to draw conclusions about the magnetic field homogeneity and to determine the necessary current changes in the shim coils. Therefore, when shimming, only that volume fraction from the sample substance is taken into account that is in the sensitive area of the RF coil.
    Those coils of the shim coil system which are rotationally symmetrical with respect to the magnet axis play a special role. They generate magnetic fields that are described by the rotationally symmetrical spherical functions. They are necessary for shimming rotationally symmetrical field deviations.
    The sample container can have different shapes depending on the application. Typically it is a long, rotationally symmetrical cylinder. There are two main reasons for choosing the rotationally symmetrical cylinder. First, the cylindrical geometry creates magnetic perturbations only at the two ends, i. a deterioration in the homogeneity of the static magnetic field (B0). Second, rotationally symmetrical sample containers can be rotated during the measurement and thus non-rotationally symmetrical field inhomogeneities can be averaged over time. This reduces their influence on the measurement result.
    Typically, in such an arrangement, only half of the sample volume, namely the portion located in the highly sensitive area of the radio frequency coil, contributes significantly to the measured signal. The additional sample substance serves to reduce the magnetic interference at the upper and lower edge of the sample volume. This additional sample substance has the following disadvantages: If only a small amount of sample substance is available, the sample substance must be diluted to the required volume. However, this reduces the measurement sensitivity in the highly sensitive area of the radio frequency coil.
    Furthermore, the area of additional sample substance can generate undesired NMR signals, for example in the case of the problem of solvent suppression. Often the NMR signal of the substance to be examined (useful signal, e.g. of a protein) is orders of magnitude weaker than that of the solvent (e.g. water). Then it is usually not possible in terms of measurement technology to detect the weak signals in the presence of the undesirably strong solvent signal. The solvent signal can be suppressed by means of suitable pulse sequences. Since the solvent suppression in the upper and lower partial volumes is less efficient, solvent signals from these volumes can be significantly larger than the useful signal (= NMR signal of the nuclei to be examined).
    Both problems can be mitigated if the magnetic interference at the ends of the sample container can be reduced. Smaller magnetic disturbances allow the ends to be closer to the highly sensitive area of the coil. This in turn can reduce the area of additional sample substance. Three strategies are known for this reduction: 1. Adapting the magnetic susceptibility of the sample container to that of the sample substance; 2. Choice of the interface to the sample substance in the form of an ellipsoid of revolution; 3. Choice of the two interfaces (outer space to the sample container; and sample container to the sample substance) in such a way that the magnetic interferences inside the sample substance largely cancel each other out.
    1. Adjustment of the magnetic susceptibility
    If the susceptibility over the interface of the sample substance to the sample container remains constant, there is no inhomogeneity of the magnetic field at this point. This arrangement is described in [5] and [6]. The material of the sample container, e.g. Glass in [6], a sufficiently large amount of a paramagnetic substance is added so that the magnetic susceptibility of the container corresponds precisely to the sample substance to be examined. The outer interfaces are far away from the sample volume in order to minimize the magnetic disturbance in the sample volume due to the change in susceptibility from the sample container to the outside space.
    2. Interface in the form of an ellipsoid of revolution
    It is known [7] that the magnetic field within a body, which has the boundary surface of an ellipsoid and consists of magnetically homogeneous material, is homogeneous inside the body if a homogeneous magnetic field is applied from the outside. The magnetic susceptibility of the body (here the sample substance container) may in this case also differ from the magnetic susceptibility of the sample substance. As in the case of the adjustment of the magnetic susceptibility, the end of the sample substance container remote from the sample substance must be far away from the sample substance so that the field inhomogeneity arising at this end has no influence on the sample volume.
    3. Choice of the two interfaces to minimize the field inhomogeneity
    In [8], the interface between the environment and the sample container and that of the sample container with the sample substance are selected so that the magnetic field within the sample volume remains largely homogeneous when a homogeneous magnetic field B0 is applied. The field disturbance within the sample volume is thus minimized by choosing the interfaces. However, no statement is made about the type of disturbance remaining after the selection of the interface before shimming, except that the field disturbances should be as small as possible in the entire sample volume.
    However, the known devices have significant disadvantages:
    For methods 1 and 2, the ends of the sample containers must be far from the central area in order to achieve the desired effect.
    The technology for producing the glasses with susceptibility correction according to method 2 is demanding and expensive.
    The sample floors produced by method 3 are very thick. This has the disadvantage that, on the one hand, the sample is greatly lengthened and, on the other hand, it is significantly heavier than a standard sample with a base of the thickness of the side walls. Furthermore, method 3 remains for all practical cases, i.e. for sample bottoms that are not infinitely thick, a residual field back after shimming.
    Object of the invention
    The aim of the device according to the invention is to obtain an NMR measuring arrangement and a method for calculating the shape of a sample container, which both interferes with an NMR measurement caused by the field inhomogeneities caused by jumps in susceptibility at the boundary of the sample container to the sample substance can be caused, as well as the required volume of sample substance can be minimized.
    Brief description of the invention
    [0021] This object is achieved by a measuring arrangement according to claim 1 and by methods according to claims 16 and 18.
    According to the invention, the geometry of the sample container is chosen so that when a homogeneous magnetic field B0 due to the susceptibility jumps at the interfaces in the volume before shimming there is a location-dependent relative field change that is greater than 20 ppb at least at one point in the mean partial volume, that the The residual field in the middle partial volume after shimming is less than 1.6 ppb, and that the residual field in the partial volume R2a is less than 30 ppb.
    According to the invention, the structure of the residual field is influenced in such a way that the shim process is also taken into account. For this purpose, larger field changes, which can be developed in rotationally symmetrical spherical functions of low order (N <5, preferably N <11), are permitted in the measuring arrangement according to the invention (in contrast to the prior art [8], in which the field change is minimized). These relative field changes are accepted because they can be compensated for using conventional shim coil systems with rotationally symmetrical coils. This results in greater freedom of design with regard to the shape of the sample container. The development of the field disturbance in rotationally symmetrical spherical coordinates simulates a shim process. The choice of the order of the development in rotationally symmetrical spherical coordinates depends on the shim coil system that is to be used with the measuring arrangement according to the invention.
    The measuring arrangement according to the invention is preferably provided as part of an NMR system with a magnetic coil for generating the homogeneous magnetic field B0, a shim coil system and an RF coil. The shim coil system and the RF coil are arranged around the sample tube so that the coil center of the RF coil (focus of the RF coil profile on the z-axis) and the center of the shim coil system (Fig. 6 in [10]) point to the Origin of the spherical coordinate system, which represents the center (geometric center of gravity) of the first partial volume are positioned. The strongest RF field of the RF coil then prevails in the middle partial volume. The axes of symmetry of the magnetic coil, the HF coil and the shim coil system are oriented parallel to the z-axis. To compensate for the relative field change, a shim coil system is used that can generate a field that can generate a number N of mutually independent shim magnetic fields that are rotationally symmetrical with respect to the z-axis of the spherical coordinate system. In addition, common shim coil systems use coils which also generate fields that are not rotationally symmetrical. N is equal to the order of the development of the relative field change F around the center SZ in rotationally symmetrical spherical functions. These rotationally symmetrical spherical functions can be generated by a suitable combination of the rotationally symmetrical magnetic fields. Such shim coil systems are known [10]. The shim functions of the zeroth, first ..., to Nth order are explicitly taken into account when choosing the geometry of the sample container. The field inhomogeneities caused by the interfaces can then be compensated in such a way that the remaining field inhomogeneities in the central partial volume are minimized.
    The measuring arrangement according to the invention thus enables the field inhomogeneities caused by the interfaces to be minimized with conventional shim coil systems, with greater freedom in the choice of the shape of the sample container than has previously been the case.
    The inventive measuring arrangement can include both a sample container that is open at the top and thus has a further interface G3 between the sample substance and the environment, and a sample container that is closed off from the environment and accordingly no further interface G3 between the sample substance and the environment.
    The sample container of the measuring arrangement according to the invention is not susceptibility-adjusted, i.e. the susceptibility of the sample container differs from that of the sample substance.
    The mean partial volume is the volume in which the highly sensitive area of the RF coil is to be located when using the measuring arrangement with an RF coil, that is to say the area from which the signals are obtained during an MR measurement. It is therefore also referred to as “active volume”. In practice, the mean partial volume is therefore predetermined by the geometry of the RF coil to be used. The lower sub-volume adjoins the middle sub-volume in the direction of the bottom of the sample container. The center of the central partial volume is defined by the geometric center of gravity of the central partial volume located on the z-axis (= axis of rotation in the case of a rotationally symmetrical sample container). In the prior art, without measures to reduce the magnetic interferences at the ends of the sample container (cf. method 1-3, above), the sum of the upper and lower partial volumes is approximately as large as the mean partial volume. With the measuring arrangement according to the invention, the lower and upper volumes and thus also the total volume (V = V1 + V2a + V2b) of the sample substance can be selected to be smaller than in the prior art. The interfaces between the sample container and the environment are then closer to the mean volume than in the prior art (the distance between the interface between the sample substance / sample vessel and the interface V2a / V1 or V2b / V1 is smaller than in the prior art), so that only a small amount of sample substance for the measurement is needed.
    The susceptibility jumps at the interfaces cause field inhomogeneities. The sample container preferably has a constant susceptibility. In principle, however, it is also conceivable that the susceptibility of the sample container varies locally.
    [0030] The sample substance is preferably liquid. Since liquid samples place the highest demands on the spectral line width, the arrangement according to the invention is of great benefit for liquids. However, gaseous and powdery substances are also possible.
    In the volume V there is a location-dependent magnetic field which is composed of the homogeneous magnetic field B0 and the interference fields Bj.
    During shimming, the development F <N> of the relative field change F in rotationally symmetrical spherical functions up to the order N is subtracted from the relative field change F. This changes the field both in the lower partial volume and in the upper partial volume. Depending on the course of the relative field change F and the size of the partial volumes, it can happen that an initially large inhomogeneity in the lower partial volume can be reduced by shimming, but the inhomogeneity in the upper partial volume is indirectly greater. In order to rule out this case, it is advantageous if an additional criterion is observed when selecting the geometry of the sample container, namely that when a homogeneous magnetic field B0 is applied, a third residual field in the upper partial volume applies: R2h ≤ 30 ppb, with the third residual field in the upper partial volume ( V2b).
    In this embodiment, the residual field in the lower partial volume (second residual field) and the residual field in the upper partial volume (third residual field) are simultaneously subject to a restriction. The remaining field in the upper partial volume could be reduced simply by filling the sample container with a sufficient amount of sample liquid. However, this leads to an increase in the upper partial volume and a corresponding deterioration in the ratio of active to passive sample volume. It is therefore desirable to make the residual field in the upper partial volume as small as possible and, according to the invention, to minimize the residual field in the upper partial volume via the geometry of the sample container.
    The sample container preferably has a multiple symmetry with respect to a rotation about the z-axis, preferably a cylindrical shape with e.g. elliptical or rectangular cross-section. It is particularly preferred if the sample container is rotationally symmetrical, in particular circular cylindrical.
    The extent of the upper partial volume and / or the lower partial volume in the z-direction is preferably smaller than the shortest secant of the cross-section of the sample vessel that intersects the z-axis. The shortest secant of the cross-section intersecting the z-axis is, for example, the diameter of the circle in the case of a circular cross-section, the small semi-axis of the ellipse in the case of an elliptical cross-section, and a parallel to the short side of the rectangle in the case of a rectangular cross-section.
    In order to compensate for the interference fields generated by the interfaces, it is advantageous if the sample container is made of a material whose magnetic susceptibility is greater in magnitude than the magnetic susceptibility of the sample substance and of the same sign. Sample containers made of glass meet this requirement for practically all relevant solvents and also meet the requirements to be electrically insulating and chemically inert.
    It is particularly preferred if the sample container is made of glass, in particular of borosilicate glass or quartz glass. Borosilicate glass is easy to process, can be exposed to large temperature fluctuations and has a magnetic susceptibility of –11 ppm. Among the solvents used for NMR, water has one of the highest susceptibilities at -9.05 ppm. At the other end of the scale is acetone at -5.78 ppm. The rather small difference in susceptibility between borosilicate glass and water leads to particularly thick sample bases with the method according to [8]. The combination of sample containers made of borosilicate glass with sample substances dissolved in water, which is important in practice, therefore benefits in particular from a geometry of the sample container according to the present invention.
    Since the susceptibility of the sample substance does not or only slightly differs from that of the solvent, the optimization of the sample container is generally carried out exclusively for a specific solvent. In a particularly preferred embodiment, the magnetic susceptibility of the sample substance is in the susceptibility interval of water and acetone.
    The environment preferably consists of air or nitrogen.
    Particularly preferred is a measuring arrangement in which the sample container is a thin-walled, circular cylindrical tube with a base and a cylinder jacket, the base and the cylinder jacket each having an inner surface and an outer surface. The outer surface of the tube runs parallel to the axis of rotation (z-axis). The inner surface of the bottom and the inner surface of the jacket form the inner surface of the sample tube. When the tube is completely filled, this is covered by the sample substance. The outer jacket surface and the outer bottom surface form an outer surface of the sample tube.
    Preferably, the maximum thickness of the bottom of the tube is 0.4 to 0.6 times the outer tube diameter. The ratio d / D (bottom thickness to outside diameter of the sample container) influences the remaining field in the lower partial volume. For values of d / D between 0.4 and 0.6, small values are achieved for the remaining field in the lower partial volume. In this case one is relatively independent of the exact shape of the second interface (interface between sample container and sample substance). The thickness of the floor is the distance between the inner surface of the floor and the outer surface of the floor. This distance can vary within the floor. If, for example, there is a central curvature of the inner bottom surface, while the outer bottom surface is flat, the thickness of the bottom in the middle (intersection with the z-axis) is maximal (in the case of a hump) or minimal (in the case of a trough) .
    A special embodiment provides that both the inner surface and the outer surface of the bottom of the tube are formed by a flat closure perpendicular to the axis of rotation. This achieves a compact design at the lower end of the sample container. According to the invention, this is made possible by the fact that the geometry of the sample container is determined taking into account the available shim functions (rotationally symmetrical spherical functions of low order). The course of the contours in the sample container according to the invention may have small radii of curvature at the transition to the tube wall. According to the invention, only high order gradients have to be avoided. Low order gradients can be eliminated in the shim process. For a circular cylindrical test tube, the most compact closure is given when both the inner surface and the outer surface are described by a plane perpendicular to the cylinder axis. The optimum base thickness can be adjusted depending on the susceptibility of the sample container material and the sample substance to be used. A flat outer end surface also makes it easier to adjust the base thickness precisely by grinding the outer surface.
    As an alternative to this, the contour of the inner surface of the tube bottom can be described by a curve which has a central curvature. Melting off a cylindrical tube creates inner contours that allow a smooth transition from the cylindrical wall to the end on the cylinder axis. Such an inner contour is defined by a curve which runs horizontally on the axis of rotation of the tube and perpendicular to the wall of the tube. As a degree of freedom, the possibility remains to let this curve run in such a way that a slight curve in the form of a hump or a depression is formed in the middle of the tube. The height of the curvature and the thickness of the base can be coordinated so that the remaining fields are minimal after shimming. A mathematical description is given in a simple manner by a spline function, the direction of which is specified on the axis of rotation and on the sample container wall. The height of the bulge can be controlled with a parameter of the spline function.
    In many NMR experiments it is important that the sample substance has a precisely defined temperature. In order to achieve this, a temperature gas flows around the sample container. Although the most compact closure is achieved by the cylindrical closure described above, the perfect cylindrical shape has the disadvantage of the outer contour that, due to the sharp edge, the gas flow can separate. It can therefore be advantageous if the outer contour of the tube is formed by a flat base in the central area near the axis of rotation and a radius of curvature at the transition to the cylindrical jacket surface. "Flat" here means perpendicular to the axis of rotation and not curved.
    Another possibility of avoiding the occurrence of flow separation of a gas flowing around the sample container is that the outer contour of the tube is formed at the lower end by half of an ellipsoid of revolution whose shortest semi-axis lies in the direction of the tube axis. The described orientation of the semi-axis keeps the closure as compact as possible.
    In order to specifically influence the remaining field in the upper partial volume, it can be advantageous for the sample container to comprise a closure element which is shaped so that it can be introduced from the open end after the sample substance has been filled in and brought into direct contact with the sample substance can. The closure element can be in the form of a stopper and preferably has the same susceptibility as the sample tube.
    The invention also relates to a method for calculating the shape of a rotationally symmetrical sample container closed on one side for a measuring arrangement described above.
    A first variant of the method according to the invention comprises: a) determining the susceptibilities of the surrounding medium, the material of the sample container and the sample substance; Establishing the maximum order N for a development of the relative field change in rotationally symmetrical spherical functions; Establishing a permissible upper limit for the remaining fields in the middle and lower partial volume and, if necessary, in the upper partial volume, b) determining a parameterized starting contour in a spherical coordinate system by determining a part of the shape of the sample container that should remain unchanged during the process; Establishing the dimensions and position of the mean partial volume of the sample substance within the unchangeable part of the sample container; Defining one or more geometric shapes and / or functions which continue the fixed invariable part of the shape into a complete sample container; c) determining the parameters which describe the mass of these geometric shapes and / or functions; d) determining a contour of the sample container by selecting a value for each parameter; e) Establishing a grid of points in the spherical coordinate system and assigning grid points to the partial volumes; f) Calculation of the relative field change that is caused on the grid points when an external homogeneous magnetic field running parallel to the z-axis is applied; g) Developing the relative field change in rotationally symmetrical spherical functions up to order N, where N = 4 to 10, around the origin of the spherical coordinate system; h) Calculation of the remaining fields in the middle and lower partial volume and, if applicable, in the upper partial volume; i) If at least one of the specified upper limits for the calculated residual fields is exceeded: Repeat steps d) -i), with at least one parameter value being changed until a combination of parameter values is found with which none of the specified upper limits for the residual fields is exceeded .
    The determination of the mean partial volume depends on the RF coil with which the sample container is to be used. The middle partial volume is chosen so that it covers the highly sensitive area of a given RF coil. The other two sub-volumes are variable, as the inner contour can change, which leads to a change in the upper and lower sub-volumes.
    As unchangeable parts of the shape of the sample vessel, parts of the sample vessel that are invariant in the z-direction are preferably defined: e.g. a circular cylindrical surface with a certain diameter and a fixed wall thickness. The mean volume is preferably set within this range.
    The approximate shape of the variable parts of the sample vial (e.g. whether the bottom of the vial should be curved or flat) is determined, i.e. geometric shapes are selected from which the contour of the variable parts of the sample vial should be composed. The method according to the invention only varies the values of the parameters that have been assigned to this fixed geometric shape. The variable parts of the sample vessel can also include contours that are composed of several geometric shapes. The parts of the sample vessel determined by the parameters preferably include the parts of the vessel which are not invariant when displaced in the z-direction, that is to say essentially the base and possibly the closure element of the sample vessel. The geometric shapes of the variable parts include, for example (but not limited to) a flat disk (with the thickness of the disk, the radius of the rounding to the outer surface, the ratio of thickness to the diameter of the disk as parameters), a spherical segment as a bulge or indentation (with the radius of the sphere, height of the segment, radius of the intersection of the sphere and the end surface as parameters), an ellipsoid segment of revolution (with large and small semiaxes, height of the segment as parameters).
    By defining the unchangeable parts of the shape of the sample container, the geometric shapes that continue the defined unchangeable part of the shape into a complete sample container, and the parameters, a parameterized contour of the sample container is defined. The contour, in particular the shape of the three interfaces, the shape of the sample container and the size of the upper and lower partial volume (and thus also the total volume of the sample substance) are obtained by choosing the values for the parameters. With the choice of the geometric shapes and the values for the parameters, the upper and lower partial volumes result. The grid points located in the three partial volumes are assigned to these partial volumes. The respective field change and the development of the field change are calculated in spherical coordinates at the assigned grid points. The residual fields brought about by a sample tube with this starting contour in a homogeneous magnetic field B0 are calculated and compared with the permissible upper limits. When calculating the residual fields, the discretization on a grid instead of the integral is the sum of the grid points assigned to the corresponding volume. If one of the upper limits is exceeded, the contour is changed by changing at least one parameter. The method can be carried out with the aid of common optimization algorithms, e.g. by means of a Newton method.
    A second variant of the method according to the invention provides for the following method steps to be carried out: a) Establishing the susceptibilities of the surrounding medium, the material of the sample container and the sample substance. Establishing the maximum order for a development of the relative field change in rotationally symmetrical spherical functions; b) determining a parameterized starting contour in a spherical coordinate system by defining a part of the shape of the sample container which is to remain unchanged during the method; Determining the position and extent of the mean partial volume of the sample substance within the unchangeable part of the sample container; Defining one or more geometric shapes and / or functions which continue the fixed invariable part of the shape into a complete sample container; c) determining the parameters which describe the mass of these geometric shapes and / or functions; d) determining a contour for the sample container by selecting a value for each parameter; e) Establishing a grid of points in the spherical coordinate system and assigning grid points to the partial volumes; f) Calculation of the relative field change that is caused on the grid points when an external homogeneous magnetic field running parallel to the z-axis is applied; g) Developing the relative field changes in rotationally symmetrical spherical functions up to order N, where N = 4 to 10, around the origin of the spherical coordinate system; h) Calculation of the remaining fields in the middle and lower partial volume and, if applicable, in the upper partial volume; i) Definition of a cost function f = - w1 * R1– w2a * R2a– w2b * R2b, where 0 ≤ w1 ≤ 1, 0 ≤ w2a ≤ 1 and 0 ≤ w2b ≤ 1; j) Applying a numerical optimization algorithm to determine a set of parameter values which define a minimum of the cost function f, steps d) to j) being run through with the parameter values determined in this way until an optimum of the cost function f is reached.
    In this variant of the method, the result of a cost function is used as a criterion, according to which it is decided whether the determined contour of the sample container corresponds to the desired requirements, while in the first variant compliance with limit values for the remaining fields in different partial volumes serve as a criterion . The optimum of the cost function is reached at a local or global extreme value of the cost function. The method can be carried out with the aid of common optimization algorithms.
    Both methods are based on the principle that inhomogeneities up to the Nth order in the mean partial volume, which originate from the susceptibility jump at the limit of the sample volume, are deliberately not compensated, since these can be easily eliminated with a conventional shim coil system. This idea leads to the fact that both the residual field in the middle partial volume and the residual field in the lower partial volume can be reduced much more effectively.
    This enables greater freedom in the design of the shape of the sample container. In particular, the upper and lower partial volumes can be selected to be smaller, so that only a small amount of sample substance is required for the measurement. This allows an optimal quality of the NMR signals to be achieved, i.e. The narrowest possible NMR lines, as well as extensive freedom from artifacts or unwanted interference lines, the latter can occur in particular in experiments to suppress the solvent signals.
    The NMR measuring arrangement according to the invention is preferably used in NMR spectroscopy or in magnetic resonance imaging.
    Further advantages of the invention emerge from the description and the drawing. The features mentioned above and those listed below can also be used individually or collectively in any combination. The embodiments shown and described are not to be understood as an exhaustive list, but rather have an exemplary character for describing the invention.
    Drawing and detailed description of the invention
    1 shows a schematic representation of an MR system with a measuring arrangement according to the invention. Fig. 2 shows a coordinate system with origin SZ in which the spherical functions are defined. 3 shows a sample container filled with a sample substance and the division of the entire sample substance volume V into partial volumes V1, V2a, V2b. Fig. 4 shows a sample container filled with a sample substance with the magnetic susceptibilities of the materials and interfaces involved, at which susceptibility jumps occur, the sample container, Fig. 4a, being open at the top so that the sample substance comes into direct contact with the environment, Fig 4b is closed by means of a closure element. Fig. 5 shows a sectional view of different ends of rotationally symmetrical sample containers in the form of a thin-walled, circular cylindrical tube, Fig. 5a wherein the bottom of both the inner surface and the outer surface is formed by a flat closure perpendicular to the cylinder axis, Fig. 5b wherein the outer contour of the tube is formed by a flat bottom in the central area near the axis of rotation and a radius of curvature at the transition to the cylindrical outer surface, Fig. 5c, the inner contour of the tube is defined by a curve which runs horizontally on the axis of rotation of the tube and perpendicular to the wall of the tube and also describes a curvature in the middle of the tube, FIG. 5d wherein the outer contour of the tube at the lower end is formed by half of an ellipsoid of revolution whose shortest semiaxis lies in the direction of the tube axis. 6 shows a representation of a family of curves for describing possible inner interfaces, described by the parameters d (maximum thickness of the bottom) and b (measure of the curvature). Each partial image shows a section through the inner and outer boundary surface of a rotationally symmetrical sample container at its closed, lower end. Fig. 7 shows a representation of the dependence of the residual field R2a in the lower partial volume on the parameters d and b for the shapes of the sample containers shown in Fig. 6, contour lines of the residual field R2a in the lower partial volume are given in ppb. 8 shows an illustration of the iterative method according to the invention for optimizing the sample container. 9 shows sectional views through four different rotationally symmetrical sample containers in the area of the lower end, FIG. 9a with a lens-shaped base according to the prior art, FIG. 9b with constant wall thickness according to the prior art, FIG. 9c with minimized field change according to [8] , FIG. 9d with residual fields minimized according to the invention. 10 shows an illustration of the creation of the residual fields after shimming for sample container geometries according to FIG. 9d, with FIGS. 10a + b bottom thickness d = 0.1 D, FIGS. 10c + d bottom thickness d = 0.48 D, FIGS. 10e + f bottom thickness d = 0.8 D. FIG. 11a shows a graphical representation of the dependence of the remaining field R2a in the lower partial volume on the ratio d / D for a sample container geometry with a lower end with a flat inner and outer contour according to FIG. 11b, FIG. 11b shows a sample container geometry with a lower end with flat inner and outer contour, which has a residual field R2a according to FIG. 11a. 12a shows a graphical representation of the dependence of the remaining field R2a in the lower partial volume on the ratio d / D for a sample container geometry with a lower end with a flat inner contour and an outer contour provided with a radius of rounding according to FIG. 12b, FIG. 12b shows a sample container geometry with a lower end with a flat inner contour and an outer contour provided with a radius of rounding, which has a residual field R2a according to FIG. 12a. 13a shows a graphic representation of the dependence of the residual field R2a in the lower partial volume on the ratio d / D for a sample container geometry with a lower end with an ellipsoidal inner contour and an outer contour provided with a radius of rounding according to FIG. 13b, FIG. 13b shows a sample container geometry with a lower end with an ellipsoidal inner contour and an outer contour provided with a rounding radius, which has a residual field R2a according to FIG. 13a.
    1 shows a schematic representation of an MR system with a magnet 5 for generating a static magnetic field B0, an RF coil 4, a shim coil system 6 and an NMR measurement arrangement according to the invention.
    In an environment 1 there is a sample container 2 filled with a sample substance 3. The sample substance 3 occupies a sample volume V in the sample container 2, which is divided into a middle sub-volume V1, a lower sub-volume V2a and an upper sub-volume V2be, as shown in FIG 3 shown. The mean partial volume V1 represents the active sample volume in the NMR system, that is, the sample container 2 is positioned in the NMR system in such a way that the center of the mean partial volume V1 corresponds to the center of the RF coil, which is through the center of gravity of the RF profile is given, coincides. This center is the origin SZ of a spherical coordinate system (Fig. 2).
    The shape of the sample container shown in FIGS. 1-4 is only exemplary.
    In Fig. 4a a first interface G1 between the sample container 2 and the environment 1, a second interface G2 between the sample substance 3 and the sample container 2 and a third interface G3 between the sample substance 3 and the environment is identified. The sample container 2 is open at the top. To avoid a third interface G3, a closure element 41, e.g. in the form of a stopper, preferably with the same susceptibility as that of the sample container 2, are introduced into the sample container 2, as shown in FIG. 4b.
    In the sample volume V, field inhomogeneities arise that are caused by susceptibility jumps at the interfaces G1, G2, G3. The influence of these field inhomogeneities on the NMR signal quality depends on the distance between the boundaries of the sample volume V and the active sample volume V1ab, in particular on the distance between the base and the interface G3 or the closure element and the active volume V1. By minimizing the sample volume V, this distance is correspondingly reduced according to the invention, i.e. the extent of the lower and / or upper partial volume in the direction of the z-axis can be selected to be smaller.
    While the field homogeneity in the active sample volume V1 is decisive for the line width, field inhomogeneities in the edge area (i.e. in the upper sub-volume V2a and in the lower sub-volume V2b) can generate artifacts or unwanted interference lines. The field inhomogeneity in the active sample volume V1 can be largely compensated for with the aid of the shim coil system 6. In the upper and lower sub-volumes V2a, V2b for samples according to the prior art, however, the field inhomogeneities are difficult to control with the aid of a shim coil system 6, since little information is available for the shim process in these insensitive areas of the RF coil 4. During the shim process, the field inhomogeneities in the inner partial volume V1 are generally optimally corrected and the field inhomogeneities in the outer volumes V2a and V2 are transferred automatically due to the global effect of the shim coil fields.
    In the measuring arrangement according to the invention, the shape of the sample container 2 (in particular the wall thickness of the bottom) is selected so that the proportions of the relative field change F that are not in rotationally symmetrical spherical functions of low order (N <11, in particular N <5) let develop, become as small as possible. When the active sample volume VI is shimmed, the field inhomogeneities in the lower partial volume V2 are minimized at the same time.
    The shape of the sample container 2 is optimized with the aid of an iterative method, as shown in FIG. 8. This begins with a parameterized starting contour of the sample container 2, which is discretized on a suitable grid. The fields resulting from this contour are next developed in rotationally symmetrical spherical functions up to order N (which simulates the shim process). The residual field R1 in the middle partial volume V1, which is essentially a measure of the width of the NMR lines, is then determined. Furthermore, in the present method according to the invention, the remaining field R2a in the lower partial volume V2a is calculated. If neither of the two conditions: R2a <30 ppb and R1 <1.6 ppb is met, the repetitive optimization process is continued with another change to the sample container contour. Known optimization algorithms (e.g. Newton method) are used to change the parameterized contour. The optimization is terminated when both of the above conditions are met.
    The parameterized contour comprises a part of the shape of the sample container 2, which should remain unchanged, and one or more parts that can be changed by changing parameters. The variable part of the contour is generally around the base of the sample container 2 and the transition from the base to the unchangeable part of the sample container 2. The shape of the base of the sample container is therefore essentially optimized. As an alternative or in addition to this, however, this optimization process can also be used for the closure element 41 in the same way as for the sample container base. By parameterizing and optimizing the contour of the closure element 42, the residual field R2b in particular can be minimized in the upper partial volume. The remaining fields R2b and R1 in the upper and middle sub-volumes V2b, V1 are optimized and the termination criterion: R2b <30 ppb and R1 <1.6 ppb are used. The method can thus be used to optimize the container bottom and the closure element 41 in the same way. The remaining field R2a in the lower partial volume V2a (for optimizing the container bottom) or the remaining field R2b in the upper partial volume V2b (for optimizing the closure element 41, together with the remaining field R1 in the middle partial volume V1) is minimized.
    For the variable part of the contour, geometric shapes are defined which describe how the variable parts should look approximately. In Fig. 5 ends of rotationally symmetrical sample containers (here unfilled) are shown, the contours of which contain different geometric shapes. All of the sample containers shown in FIG. 5 have in common a cylindrical basic shape with an outside diameter D.
    In the sample container 51 shown in Fig. 5a, the bottom of both the inner surface and the outer surface is formed by a flat end perpendicular to the cylinder axis, i.e. Both the outer contour and the inner contour of the sample container are described by a circular cylinder, which differ in diameter and height. The height difference corresponds to the thickness d of the floor. The thickness d of the soil, for example, can be used as a parameter for the optimization method according to the invention.
    In Fig. 5b, the outer contour of the tube is formed by a flat bottom in the central area near the axis of rotation and a radius of curvature at the transition to the cylindrical outer surface. The rounding radius is therefore also required to describe the outer contour. The thickness d of the base and the radius of the rounding can serve as parameters for the optimization method according to the invention.
    Fig. 5c shows an embodiment in which the inner contour of the sample container is defined by a curve which runs horizontally on the axis of rotation of the tube and perpendicular to the wall of the tube and also describes a small curvature in the center of the bottom of the sample container . In addition, the outer contour has a rounding radius analogous to FIG. 5b, but here with a larger rounding radius. The thickness d of the bottom, the rounding radii of the inner and outer contour and the radius of the curvature (in the case of a spherical curvature) and height of the spherical segment can serve as parameters for the optimization method according to the invention. In this case, the contour is composed of many geometric shapes and can be described by a spline function.
    5d shows an embodiment in which the outer contour of the tube is formed at the lower end by half of an ellipsoid of revolution, the shortest semiaxis of which lies in the direction of the tube axis (z-direction). The thickness d of the bottom, the radius of the rounding of the inner contour and the semi-axes of the ellipsoid of revolution can serve as parameters for the optimization method according to the invention.
    6 shows a family of curves for the contour of a sample vessel, the inner contour having a central curvature and a radius of curvature at the transition to the wall of the sample vessel. The parameters d (maximum thickness of the floor) and b (measure of the height of the arch) were varied. Each partial image shows a section through the inner and outer interfaces of a rotationally symmetrical sample container at its closed, lower end. For each partial image, the maximum thickness d of the bottom is in a fixed ratio to the diameter D of the sample container 2. The parameter b is varied to generate different curve shapes (from top to bottom: b = -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4). The partial images differ in the maximum thickness d of the soil. The range of values for d and b for the curves shown corresponds to the range of values shown in FIG. The curve shapes designated with 61, 62, 63 correspond to the pairs (b, d) which are marked in FIG. 7 by the points 71, 72, 73.
    The height of the curvature and the thickness of the bottom can be matched to one another so that the remaining fields R1 and R2a become minimal after shimming. The family of curves shown in FIG. 6 was calculated in a simple manner by a spline function, the direction of which is specified on the axis of rotation and on the sample container wall. The height of the bulge can be controlled with a parameter of the spline function.
    In FIG. 7, the dependence of the remaining field R2a on the parameters d and b for the shapes of the sample container shown in FIG. 6 is shown. The numerical values on the contour lines designate the value of the residual field R2a in the lower partial volume V2ain ppb (parts per billion), for the case of water as the sample substance and a sample container made of borosilicate glass. The area of pairs (b, d) with which a residual field R2a <30 ppb can be achieved is indicated by hatching. Those pairs (b, d) which correspond to a curve shape shown in FIG. 6 and which meet the condition R2a <30 ppb are marked by the points 71, 72, 73.
    9a-9c show sectional views through four different rotationally symmetrical sample containers in the area of the lower end according to the prior art: sample container 91 with a lens-shaped bottom (FIG. 9a), sample container 92 with constant wall thickness according to (FIG. 9b) and Sample container 93 with minimized field change according to [8], optimized for the material combination of borosilicate glass and water and hemispherical shape inside (FIG. 9c). FIG. 9d shows a sample container 94 according to the invention with a sample container shape (62) as in FIG. 6. The axis of rotation (z-axis) is shown in dash-dotted lines.
    The commercially available sample container 92 is inserted below the coil center of the RF coil with a predetermined immersion depth (here 20 mm), ie the part of the interface G2 of the sample container 92 to the sample substance furthest away in the z direction is 20 mm below SZ. The sample container 93 according to the prior art [8], method 3, the commercially available sample container 91 with a lens base, the sample container 92 and the sample container 94 according to the invention are arranged in the z-direction so that the volume V or the volumes VI and V2a for all sample containers are the same size. The remaining fields R2a and R1 are compiled for χ2 of borosilicate and χ3 of water in Table 1. The remaining fields R1 and R2a of the sample container 94 according to the invention are approximately one order of magnitude smaller than those of the commercially available sample containers 91, 92, which leads to a clear improvement in the NMR signal quality. The container 94 according to the invention achieves approximately the same values for R1 as the container 93 and, however, has a residual field R2a which is approximately 4 times smaller, which leads to a better NMR signal quality, especially for solvent suppression experiments. more commercially availableContainer withLens base (91) commercially availableContainer withconstant wall thickness (92) sample container (93)according to the state of the art,Method 3 [8] according to the inventionSample container (94) R2a 127 ppb 119 ppb 50 ppb 11 ppb R1 0.04 ppb 0.062 ppb 0.01 ppb 0.008 ppb
    In the sample container according to the invention, the sample base is optimized for the corrections made possible by a conventional shim coil system. This means that a significantly thinner sample bottom can be used. This is clearly evident from the comparison of the sample container 93 with the sample container 94 according to the invention. Furthermore, by optimizing the sample container 94 for the corrections made possible by the shim coil system, smaller magnetic inhomogeneities are achieved. This leads to better results, especially in the case of solvent suppression.
    In the following, a simple example is used to illustrate how the residual fields arise after shimming and how their size can be minimized by a clever choice of the geometry of the sample container.
    In FIGS. 10a, 10c, and 10e, for the form shown in FIG. 11b, the relative field changes F on the sample axis as a function of the z position (solid line) and developments FN of the field change in spherical coordinates up to the order N = 8 (dotted line) for different bottom thicknesses of the sample container. The associated differences (F-F <N>) are shown in FIGS. 10b, 10d, 10f. The z-position is given in units of the sample container diameter D. The zero point is at the origin SZ, in which the coil center of the RF coil should be positioned in an NMR system. The relative field changes are given in ppb.
    The following assumptions are made for the example;
    The middle partial volume V1 is located between the z positions -2.4 D and +2.4 D. The lowest position with sample substance is at z = -3.9 D, the lower partial volume V2a is therefore between -3.9 D and -2.4 D. The boundaries between the partial volume areas are marked by vertical lines. Water with a magnetic susceptibility of –9.05 ppm is assumed as the sample substance. The sample container is made of borosilicate and has a magnetic susceptibility of –11.0 ppm. The wall thickness of the sample container in the area in which the wall runs parallel to the cylinder axis is 0.1 D. The filling height of the sample container is assumed to be sufficiently high (greater than 12 D), so that in this example the influence of the bottom thickness, detached from the influence of field changes originating from the top of the sample can be discussed.
    In FIGS. 10a and 10b, the bottom thickness is d = 0.1 D. Here the two boundary surfaces are so close to one another that there is hardly any compensatory effect on the residual field R2a in the lower partial volume V2a. In FIGS. 10c and 10d the base thickness is d = 0.48 D. This choice leads to the arrangement according to the invention with a minimal residual field R2a in the lower partial volume V2a.
    In FIGS. 10e and 10f, the bottom thickness is d = 0.8 D. This choice leads to a more homogeneous field without taking into account the development in spherical functions (compare FIG. 10e with FIG. 10c). After the subtraction from the development FN of the field change in spherical coordinates, the field in the volume V2a but becomes more inhomogeneous (compare FIG. 10f with FIG. 10d). 10e and 10f correspond to geometries as obtained by means of the method known from [8], namely by minimizing the relative field change F in the entire volume. In the context of the present invention, it was recognized that striving for a minimal field change F in the entire volume in combination with shimming leads to overcompensation.
    A comparison of the numerical values for the remaining fields calculated in the partial volumes V1 and V2a for the three floor thicknesses discussed is given in the following table: d = 0.1 D d = 0.48 D d = 0.8 D R2a 361 ppb 13.6 ppb 90 ppb R1 0.039 ppb 0.0053 ppb 0.0039 ppb
    In the same way, the dependency of the residual field R2a on the ratio d / D was calculated with a finer resolution. The entire course is shown in FIG. 11a. This curve shows that in a range from d = 0.42 D to d = 0.53 D around the minimum, a residual field R2a in the lower partial volume of less than 30 ppb can be achieved.
    The influence of adaptations of the contours by means of rounding radii or ellipsoidal shape of the contours is shown by way of example in FIGS. 12 and 13.
    The inventive combination of the geometric optimization of the sample container with a (simulated) shim process in the form of a development of the relative field change in spherical coordinates is more efficient and produces better results than is the case with sample containers known from the prior art. Because with the method according to the invention, the field inhomogeneity unavoidably generated by the limits of the sample volume V can be constructed in such a way that the essential part can be developed in rotationally symmetrical spherical coordinates. This part can be «shimmed away» and therefore has no negative influence on the signal quality. The remaining remaining fields R1, R2a, R2b are checked with the present optimization method, whereby the required signal quality can be achieved.
    List of reference symbols
    1 environment of the sample container 2 sample container 3 liquid sample substance 4 RF coil, suitable for exciting the spin system of the sample substance and for receiving an NMR signal, the center of which is positioned on SZ 5 magnet for generating the strong static magnetic field B0 8 shim coil system, the center of which is positioned on the SZ 41 closure element that can be inserted from the open end of the sample container and brought into contact with the sample substance 61 inner contour according to parameterization b = -0.6 and d = 0.5 D 62 inner contour according to parameterization b = -0.4 and d = 0.5 D 63 inner contour corresponding to the parameterization b = -0.2 and d = 0.5 D 71 point in area 74, which corresponds to the inner contour parameterized by b = -0.6 and d = 0.5 D 72 point in area 74, which corresponds to the inner contour parameterized by b = -0.6 and d = 0.5 D = –0.4 and d = 0.5 D parameterized inner contour corresponds to 73 point in area 74, which corresponds to the inner cone parameterized by b = –0.2 and d = 0.5 D ture corresponds to 74 area, which includes pairs (b, d) with which a residual field R2a <30 ppb can be achieved B0 static homogeneous magnetic field χ1 susceptibility of the environment (typically air or nitrogen) χ2 susceptibility of the sample container (typically glass) χ3 susceptibility of the Sample substance (e.g. Water) b Parameter with which the development of a bulge in the form of a hump or a depression in the inner contour of the sample can be influenced d Maximum thickness of the bottom of the sample substance container measured on the z-axis D Outside diameter of the sample substance container G1 interface between the environment and the sample container G2 Interface between sample container and sample substance G3 Interface between sample substance and environment SZ Origin of the spherical coordinate system in which the development of the relative field change is carried out. The spherical coordinate system comprises a z-axis which represents the axis of rotation of the sample vessel. V total volume of the sample substance (V = V1 + V2a + V2b) V1 mean partial volumeSample substance volume active in an NMR system (= partial volume of V, in which the RF field of the coil is at least greater than 50% of the maximum RF field) V2a lower partial volume of V (at the lower end of V and then to V1) V2b upper partial volume of V (at the upper end of V and afterwards to V1)
    Reference list
    [1] F. Romeo and D. I. Hoult, "Magnetic Field Profiling and Correcting Coil Design" Magn. Reson. Med. 1, 44-65 (1984) [2] R. R. Ernst, "Measurement and Control of Magnetic Field Homogeneity", Rev. Sci. Instrum. 39, 998-1012 (1968) [3] Van Zijl PCM, Sukumar S, Johnson M, Webb P, Hurd RE., “Optimized shimming for high-resolution NMR using three-dimensional image-based field mapping”, JMR A 111 , 203-207 (1994) [4] M. Weiger, T. Speck, M. Fey, "Gradient shimming with spectrum optimization", J. Magn Reson. 182 (1), 38-48, (2006) [5] US 4 549 136 [6] US 5 831 434 [7] JC Maxwell, A Treatise on Electricity an Magnetism, Dover Publications, New York, 1954, third edition, Vol. 2, pp. 66-70. [8] EP 1 918 731 A1. [9] I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik, BSB Teubner, Leibzig, 1989. [10] US 3,287,630
    权利要求:
    Claims (18)
    [1]
    1. NMR measuring arrangement, comprisinga sample container (2) closed on one side, the material of the sample container (2) having a magnetic susceptibility χ2,an environment (1) with a magnetic susceptibility χ1, in which the sample container (2) is arranged,a sample substance (3) located in the sample container (2) with a magnetic susceptibility χ3, which takes up a volume (V) within the sample container,wherein the volume (V) of the sample substance (3) consists of an upper part volume (V2b), a lower part volume (V2a) and a middle part volume (V1) which contains the origin (SZ) of a spherical coordinate system with a z-axis, the partial volumes (V1, V2a, V2b) adjoining one another,wherein the sample container (2) has a first interface (G1) to the environment (1) and a second interface (G2) to the sample substance (3), and optionally the sample substance (3) has a further interface (G3) between the sample substance (3) and the environment (1),where there are magnetic susceptibility jumps at the interfaces (G1, G2, G3) which, when an external homogeneous magnetic field B0 runs parallel to the z-axis is applied, cause location-dependent interference fields BG1, BG2, BG3 in the volume (V) of the sample substance (3),where the susceptibility jump at the second interface (G2) is so large that the maximum value of | B ́G2 / B0 | within the volume (V) of the sample substance (3) is at least 0.5 ppm,with an applied homogeneous magnetic field B0 in the middle partial volume (V1) a first residual field (R1) and in the lower partial volume (V2a) a second residual field (R2a),in whichBG1:position-dependent z-component of the magnetic field that arises due to the susceptibility jump from χ1 to χ2 at the first interface (G1);BG2:position-dependent z-component of the magnetic field that arises due to the susceptibility jump from χ2 to χ3 at the second interface (G2);BG3:location-dependent z-component of the magnetic field that arises due to the susceptibility jump from χ3 to χ1 at the further interface (G3);F: = (B ́G1 + B ́G2 + B ́G3) / B0:location-dependent relative field change due to the susceptibility jumps at the interfaces (G1, G2, G3)B ́j: = Bj– Bj:location-dependent deviation of the field Bj from the mean value Bj
    Bj: mean value of the z-component of the field Bj, where j = G1, G2, G3
    first remaining field in the middle partial volume (V1)
    second remaining field in the lower partial volume (V2a)F <N>:Development of the relative field change F around the origin (SZ) in rotationally symmetrical spherical functions up to order N, where N = 4 to 10;where generally applies
    Mean value of any magnetic field A in the sample volume V;
    Development of A into rotationally symmetrical spherical functions up to order N, withan: = expansion coefficientsKn (r, θ) = r <n> Pn (cosθ): = rotationally symmetrical spherical functionsPn (cosθ): = Legendre polynomialscharacterized in thatthe geometry of the sample container (2) is chosen sothat when a homogeneous magnetic field B0 is applied, due to the susceptibility jumps at the interfaces (G1, G2, G3) in the volume (V) of the sample substance (3) there is a location-dependent relative field change F, the relative field change F at at least one point in the middle partial volume (V1) is greater than 20 ppb,that the first residual field (R1) is less than 1.6 ppb, andthat the second residual field (R2a) is less than 30 ppb.
    [2]
    2. Measuring arrangement according to claim 1, characterized in that the geometry of the sample container (2) is chosen so that when a homogeneous magnetic field B0 is applied for a third residual field (R2b) in the upper partial volume (V2b): R2b≤ 30 ppb, where
    is the third remaining field in the upper partial volume (V2b).
    [3]
    3. Measuring arrangement according to one of the preceding claims, characterized in that the sample container (2) is rotationally symmetrical with respect to the z-axis.
    [4]
    4. Measuring arrangement according to one of the preceding claims, characterized in that the sample container (2) consists of a material whose magnetic susceptibility χ2 is greater in magnitude than the magnetic susceptibility χ3 of the sample substance.
    [5]
    5. Measuring arrangement according to one of the preceding claims, characterized in that the sample container (2) consists of glass, in particular of borosilicate glass or quartz glass.
    [6]
    6. Measuring arrangement according to one of the preceding claims, characterized in that the magnetic susceptibility χ3 of the sample substance (3) is in the susceptibility interval of water and acetone.
    [7]
    7. Measuring arrangement according to one of the preceding claims, characterized in that the environment (1) consists of air or nitrogen.
    [8]
    8. Measuring arrangement according to one of claims 3 to 7, characterized in that the sample container (2) is a circular cylindrical tube with a base and a cylinder jacket, the base and the cylinder jacket surface each having an inner surface and an outer surface.
    [9]
    9. Measuring arrangement according to claim 8, characterized in that the extent of the upper partial volume (V2b) and / or the lower partial volume (V2a) in the direction of the z-axis is smaller than the diameter of the sample container (2).
    [10]
    10. Measuring arrangement according to claim 8 or 9, characterized in that the maximum thickness of the bottom of the tube is 0.4 to 0.6 times the outer tube diameter (D).
    [11]
    11. Measuring arrangement according to one of claims 9 or 10, characterized in that both the inner surface and the outer surface of the bottom of the tube are formed by a flat closure perpendicular to the z-axis.
    [12]
    12. Measuring arrangement according to one of claims 9 to 10, characterized in that the contour of the inner surface of the tube bottom is described by a curve which has a central curvature.
    [13]
    13. Measuring arrangement according to one of claims 9 to 12 and claim 3, characterized in that the outer contour of the tube is formed by a flat bottom in the central area near the z-axis and a rounding at the transition of the bottom to the cylindrical outer surface.
    [14]
    14. Measuring arrangement according to one of claims 9 to 12, characterized in that the outer contour of the tube on the tube bottom is formed by half of an ellipsoid of revolution, the shortest semiaxis of which lies in the direction of the tube axis.
    [15]
    15. Measuring arrangement according to one of claims 9 to 14, characterized in that the sample container (2) comprises a closure element (41) which is shaped so that it is introduced from the open end after filling the sample substance and in direct contact with the sample substance (3) can be brought.
    [16]
    16. A method for producing a rotationally symmetrical sample container (2) closed on one side for a measuring arrangement according to one of claims 1 to 14, the following method steps being carried out to determine the shape of the sample container (2):a) Establish- The susceptibilities χ1, χ2, χ3 of the surrounding medium (1), the material of the sample container (2) and the sample substance (3);- the maximum order N for a development of the relative field change F in rotationally symmetrical spherical functions;- a permissible upper limit for the first remaining field (R1) and the second remaining field (R2a),b) Determination of a parameterized contour in a spherical coordinate system by definition- Part of the shape of the sample container (2), which should remain unchanged during the process,- of the dimensions and position of the mean partial volume (V1) of the sample substance (3) within the unchangeable part of the sample container (2),- one or more geometric shapes and / or functions which continue the fixed, unchangeable part of the shape to form a complete sample container (2),c) Determination of the parameters that describe the mass of these geometric shapes and / or functions,d) determining a contour of the sample container (2) by selecting a value for each parameter,e) Establishing a grid of points in the spherical coordinate system and assigning grid points to the partial volumes (V1, V2a, V2b),f) Calculation of the relative field change that is caused by applying an external homogeneous magnetic field running parallel to the z-axis on the grid points,g) Developing the relative field change F in rotationally symmetrical spherical functions up to order N, where N = 4 to 10, around the origin (SZ) of the spherical coordinate system;h) Calculation of the first remaining field (R1) and the second remaining field (R2a),i) if at least one of the specified upper limits for the remaining fields (R1, R2a) is exceeded:Repeat steps d) -i), at least one parameter value being changed until a combination of parameter values is found with which none of the established upper limits for the remaining fields (R1, R2a) is exceeded.
    [17]
    17. The method according to claim 16 for producing a rotationally symmetrical sample container (2) closed on one side for a measuring arrangement according to one of claims 2 to 14, characterized in thatIn step a), a permissible upper limit for the third remaining field (R2b) is also specified,in step h) the third remaining field (R2b) is calculatedand steps d) -i) are repeated if at least one of the specified upper limits for the remaining fields (R1, R2a, R2b) is exceeded, at least one parameter value being changed until a combination of parameter values is found that does not match any of the specified Upper limits for the remaining fields (R1, R2a, R2b) is exceeded.
    [18]
    18. A method for producing a rotationally symmetrical sample container (2) closed on one side for a measuring arrangement according to one of claims 2 to 14, the following method steps being carried out to determine the shape of the sample container (2):a) Establish- The susceptibilities χ1, χ2, χ3 of the surrounding medium (1), the material of the sample container (2) and the sample substance (3);- the maximum order N for a development of the relative field change F in rotationally symmetrical spherical functions;b) Determination of a parameterized starting contour in a spherical coordinate system by definition- Part of the shape of the sample container (2), which should remain unchanged during the process,- Position and dimensions of the mean partial volume (V1) of the sample substance (3) within the unchangeable part of the sample container (2),- one or more geometric shapes and / or functions which continue the fixed, unchangeable part of the shape to form a complete sample container (2),c) Determination of the parameters that describe the mass of these geometric shapes and / or functions,d) determining a contour for the sample container (2) by selecting a value for each parameter,e) Establishing a grid of points in the spherical coordinate system and assigning grid points to the partial volumes (V1, V2a, V2b),f) Calculation of the relative field change which is caused by the application of an external homogeneous magnetic field running parallel to the z-axis on the grid points;g) Developing the relative field changes F in rotationally symmetrical spherical functions up to order N, where N = 4 to 10, around the origin (SZ) of the spherical coordinate system;h) calculation of the first remaining field (R1), the second remaining field (R2a) and the third remaining field (R2b),i) Definition of a cost function f = w1 * R1 + w2a * R2a + w2b * R2b, where0 ≤ w1≤ 1, 0 ≤ w2a≤ 1 and 0 ≤ w2b≤ 1,j) Applying a numerical optimization algorithm to determine a set of parameter values which define a minimum of the cost function f, steps d) to j) being run through with the parameter values determined in this way until an optimum of the cost function f is reached.
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    同族专利:
    公开号 | 公开日
    CH704820A2|2012-10-15|
    DE102011007167A1|2012-10-11|
    US20120256632A1|2012-10-11|
    DE102011007167B4|2016-05-19|
    GB2490030B|2017-05-03|
    US8912796B2|2014-12-16|
    GB201206327D0|2012-05-23|
    GB2490030A|2012-10-17|
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    法律状态:
    2016-02-15| PK| Correction|Free format text: BERICHTIGUNG ERFINDER |
    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:
    申请号 | 申请日 | 专利标题
    DE102011007167.9A|DE102011007167B4|2011-04-11|2011-04-11|NMR measuring arrangement with optimized sample container geometry and method for calculating the shape of the sample container|
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