METHOD FOR ESTIMATING A MAGNETIC FIELD DEVIATION, A MAGNETIC RESONANCE DEVICE AND A COMPUTER PROGRAM PRODUCT

Abstract

A method for estimating a magnetic field deviation, a magnetic resonance device, and a computer program product are disclosed. In accordance with the method, at least one gradient value is provided, wherein each gradient value describes a gradient strength of the respective gradient magnetic field, e.g., the setpoint gradient magnetic field. The magnetic resonance device generates a main magnetic field in a main magnetic field direction. The at least one value of a deviation is estimated by applying the at least one gradient value to a magnetic field model. In this case, in accordance with a magnetic field model, a deviation of the gradient magnetic field from a setpoint gradient magnetic field is described by at least one vectorial component in a spatial direction deviating from the main magnetic field direction.

Claims

1. A computer-implemented method for estimating at least one value of a deviation, wherein each value of the at least one value of the deviation describes a deviation of a respective actual gradient magnetic field from a respective setpoint gradient magnetic field of a magnetic resonance device, the method comprising: providing at least one gradient value, wherein each gradient value of the at least one gradient value describes a gradient strength of the respective setpoint gradient magnetic field; generating, by the magnetic resonance device, a main magnetic field in a main magnetic field direction; and estimating the at least one value of the deviation by applying the at least one gradient value to a magnetic field model, wherein, in accordance with the magnetic field model, the deviation of the respective actual gradient magnetic field from the respective setpoint gradient magnetic field is described by at least one vectorial component in a spatial direction deviating from the main magnetic field direction.

2. The method of claim 1, wherein the at least one value of the deviation comprises a Maxwell term.

3. The method of claim 1, wherein the at least one vectorial component has a linear dependency on at least one coordinate of the spatial direction.

4. The method of claim 1, wherein a vector field of the main magnetic field is oriented in the main magnetic field direction, wherein an actual vector field of the respective actual gradient magnetic field contains at least one vector comprising at least one vector component that deviates from the main magnetic field direction, and wherein the at least one value of the deviation describes the deviation of the at least one vector component from the main magnetic field direction.

5. The method of claim 1, wherein the respective actual gradient magnetic field comprises: a first actual gradient magnetic field with a magnetic field gradient in a first spatial direction; a second actual gradient magnetic field with a magnetic field gradient in a second spatial direction; and/or a third actual gradient magnetic field with a magnetic field gradient in a third spatial direction, and wherein the first spatial direction, the second spatial direction, and the third spatial direction are orthogonal to one another.

6. The method of claim 5, wherein the first spatial direction is an X direction, the second spatial direction is a Y direction, and the third spatial direction is a Z direction, wherein the Z direction is the main magnetic field direction, wherein, in accordance with the magnetic field model, B.sub.xx=z.Math.GX, B.sub.xy=0 applies for the at least one value of the deviation for the first actual gradient magnetic field, B.sub.yx=0, B.sub.yy=z.Math.GY applies for the at least one value of the deviation for the second actual gradient magnetic field, and/or $B_{zx}=-x\frac{GZ}{2},B_{zy}=-y\frac{GZ}{2}$ applies for the at least one value of the deviation for the third actual gradient magnetic field, and wherein: GX is the gradient strength in the X direction, GY is the gradient strength in the Y direction, GZ is the gradient strength in the Z direction, x is a coordinate in the X direction, y is a coordinate in the Y direction, and z is a coordinate in the Z direction.

7. The method of claim 6, further comprising: correcting magnetic resonance signals using the at least one value of the deviation.

8. The method of claim 7, wherein the correcting of the magnetic resonance signals comprises correcting an encoding of the magnetic resonance signals.

9. The method of claim 7, wherein the correcting comprises calculating a Larmor frequency in dependency on the at least one value of the deviation.

10. The method of claim 1, further comprising: correcting magnetic resonance signals using the at least one value of the deviation.

11. The method of claim 10, wherein the correcting of the magnetic resonance signals comprises correcting an encoding of the magnetic resonance signals.

12. The method of claim 10, wherein the correcting comprises calculating a Larmor frequency in dependency on the at least one value of the deviation.

13. The method of claim 1, further comprising: reconstructing at least one magnetic resonance image using the at least one value of the deviation, wherein, during the reconstructing of the at least one magnetic resonance image, phase errors caused by the deviation of the respective actual gradient magnetic field are corrected using the at least one value of the deviation.

14. The method of claim 1, further comprising: providing at least one parameter which describes the main magnetic field; and estimating a total magnetic field using the at least one parameter, the at least one gradient value, and the at least one value of the deviation.

15. The method of claim 14, further comprising: performing a magnetic resonance scan, wherein, prior to the performing of the magnetic resonance scan, the at least one parameter of the main magnetic field has been calibrated, wherein, during the performing of the magnetic resonance scan, the calibrated at least one parameter is recalibrated, and wherein the estimating of the total magnetic field takes place using the recalibrated at least one parameter.

16. The method of claim 15, wherein the recalibration is conducted in real time during the performing of the magnetic resonance scan.

17. A system control unit of a magnetic resonance device, the system control unit comprising: at least one processor; and at least one memory, wherein the at least one memory and the at least one processor are configured to: receive at least one gradient value, wherein each gradient value of the at least one gradient value describes a gradient strength of a respective setpoint gradient magnetic field; generate a main magnetic field in a main magnetic field direction; and estimate at least one value of a deviation of an actual gradient magnetic field from the respective setpoint gradient magnetic field of the magnetic resonance device by applying the at least one gradient value to a magnetic field model, wherein, in accordance with the magnetic field model, the deviation of the respective actual gradient magnetic field from the respective setpoint gradient magnetic field is described by at least one vectorial component in a spatial direction deviating from the main magnetic field direction.

18. A magnetic resonance device comprising: a system control unit configured to: receive at least one gradient value, wherein each gradient value of the at least one gradient value describes a gradient strength of a respective setpoint gradient magnetic field; generate a main magnetic field in a main magnetic field direction; and estimate at least one value of a deviation of an actual gradient magnetic field from the respective setpoint gradient magnetic field of the magnetic resonance device by applying the at least one gradient value to a magnetic field model, wherein, in accordance with the magnetic field model, the deviation of the actual gradient magnetic field from the respective setpoint gradient magnetic field is described by at least one vectorial component in a spatial direction deviating from the main magnetic field direction.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0060] FIG. 1 shows an example of a magnetic resonance device in a schematic representation,

[0061] FIG. 2 shows an example of subunits of a gradient coil unit of a magnetic resonance device,

[0062] FIG. 3 shows am example of a flow diagram of a method for estimating at least one value of a deviation,

[0063] FIG. 4-10 show examples of the influence of magnetic vector fields representing Maxwell terms,

[0064] FIG. 11 shows an example of an addition of different magnetic field sources, in particular contributions to the total magnetic field.

DETAILED DESCRIPTION

[0065] FIG. 1 schematically shows a magnetic resonance device 10. The magnetic resonance device 10 includes a magnetic unit 11, which has a main magnet 12 for generation of a strong and in particular temporally constant main magnetic field B.sub.0. Furthermore, the magnetic resonance device 10 includes a patient receiving area 14 for receiving a patient 15. The patient receiving area 14 in the present exemplary embodiment is cylindrical in design and in a circumferential direction is cylindrically surrounded by the magnetic unit 11. Running in parallel to the direction of the main magnetic field B.sub.0, the main magnetic field direction 13, is the cylinder axis of the patient receiving area 14, the Z axis in the spatial direction Z. The patient 15 may be pushed into the patient receiving area 14 by a patient positioning device 16 of the magnetic resonance device 10. To this end the patient positioning device 16 has a patient table 17 designed so as to be movable within the patient receiving area 14.

[0066] The magnetic unit 11 furthermore has a gradient coil unit 18 (with multiple gradient coils shown in FIG. 2) for generation of gradient magnetic fields, in particular of actual gradient magnetic fields, which overlap with the main magnetic field B.sub.0 and are used for position encoding during imaging. The gradient coil unit 18 is controlled by a gradient control unit 19 of the magnetic resonance device 10. The magnetic unit 11 furthermore includes a radio-frequency antenna unit 20, which in the present exemplary embodiment is designed as a body coil permanently integrated into the magnetic resonance device 10. The radio-frequency antenna unit 20 is controlled by a radio-frequency antenna control unit 21 of the magnetic resonance device 10 and irradiates radio-frequency magnetic resonance sequences into an examination space, which is substantially formed by a patient receiving area 14 of the magnetic resonance device 10. As a result, an excitation of atomic nuclei occurs in the main magnetic field 13 generated by the main magnet 12. Magnetic resonance signals are generated by relaxation of the excited atomic nuclei. The radio-frequency antenna unit 20 is designed to receive the magnetic resonance signals.

[0067] For control of the main magnet 12 and of the gradient control unit 19 and for control of the radio-frequency antenna control unit 21, the magnetic resonance device 10 contains a system control unit 22. The system control unit 22 controls the magnetic resonance device 10 centrally, for example, the performance of a predetermined imaging gradient echo sequence. Furthermore, the system control unit 22 includes an evaluation unit (not shown in greater detail) for evaluation of the magnetic resonance signals that are captured during the magnetic resonance examination. Further, the magnetic resonance device 10 includes a user interface 23 which is connected to the system control unit 22. Control information such as for example imaging parameters, as well as reconstructed magnetic resonance images, may be displayed on a display unit 24, (for example, on at least one monitor), of the user interface 23 for medical personnel. Furthermore, the user interface 23 contains an input unit 25, by which information and/or parameters may be input by the medical personnel during a scanning procedure.

[0068] FIG. 2 shows three gradient coils 18x, 18y, 18z of the gradient coil unit 18. The gradient coil 18x, XGC, generates a gradient magnetic field, in particular an actual gradient magnetic field, with a gradient of the amount of the magnetic field in the X direction. The gradient coil 18y, YGC, generates a gradient magnetic field, in particular an actual gradient magnetic field, with a gradient of the amount of the magnetic field in the Y direction. The gradient coil 18z, ZGC, generates a gradient magnetic field, in particular an actual gradient magnetic field, with a gradient of the amount of the magnetic field in the Z direction. The vector fields B.sub.gx(x,y,z), B.sub.gy(x,y,z) B.sub.gz(x,y,z) of the three gradient magnetic fields, in particular the associated setpoint gradient magnetic fields, may be oriented (only) in the Z direction; deviations from this ideal field direction may be estimated and/or taken into consideration using the proposed method.

[0069] The magnetic resonance device 10, in particular the system control unit 22, is configured to perform a computer-implemented method, shown in FIG. 3, for estimating at least one value of a deviation, in particular of a Maxwell term. The at least one value of a deviation describes a deviation of an actual gradient magnetic field from a setpoint gradient magnetic field of the magnetic resonance device.

[0070] In act S10, at least one gradient value, for example, the gradient values GX, GY, GZ, is provided. Each of the gradient values GX, GY, GZ describes a gradient strength of the respective gradient magnetic field, in particular of the actual gradient magnetic field and/or of the associated setpoint gradient magnetic field.

[0071] In act S20, at least one value of a deviation is estimated, in that the gradient values GX, GY, GZ are applied to a magnetic field model. In accordance with the magnetic field model, the deviation of the actual gradient magnetic field from the setpoint gradient magnetic field is described by at least one vectorial component in a spatial direction X, Y deviating from the main magnetic field direction Z.

[0072] Optionally, in act S30, an acquisition and/or reconstruction of magnetic resonance signals takes place, having regard to the estimated at least one value of a deviation.

a. Various possible features and advantages of the method for estimating the at least one value of a deviation will be illustrated below. Using the method, in particular the following aspects may be improved compared to the prior art. First, not only may the amount or strength of the magnetic field, in particular of the at least one actual gradient magnetic field, be estimated, but also its direction. Second, for each Cartesian axis, deviations of the field may be estimated separately, depending on which gradient coil is active. Third, an estimation may be performed which does not presuppose that the main magnetic field B.sub.0(x,y,z) is homogeneous (cf. assumption A4 of the Bernstein method). Fourth, no assumptions need be made about the field strength (cf. assumption A5 of the Bernstein method). As a result, estimations may also be made for low strengths of the main magnetic field (for example B.sub.0≤0.5 T) and relatively high gradient strengths (for example G.sub.max≥40 mT/m). The method may further be applied to high strengths of the main magnetic field with very high gradient strengths, for example B.sub.0=3 T, G.sub.max=300 mT/m.

[0073] An especially great potential advantage of the proposed method is that a Taylor series development is no longer necessary, so that no additional simplified assumptions need be made here, in that higher-order terms of the Taylor series are ignored. Further, one great potential advantage is that by selective application of the method as a function of the active gradient coils inadequacies of various conventional assumptions (cf. assumptions A1 . . . A5 of the Bernstein method) may consciously be taken into consideration.

7. Mathematical Principles

[0074] Let A(x,y,z) and B(x,y,z) be two vector fields. For rotation operator and divergence operator the associative law applies:

∇×(A+B)=∇×A+∇×B

∇×(A+B)=∇.Math.A+∇.Math.B

2. Physical Principles

[0075] Displacement currents and convection currents (genuine conduction currents) may be ignored within the FOV of the magnetic resonance device. Thus, it emerges from the Maxwell equations that the magnetic vector field B within the FOV is non-rotational and solenoidal:

[00005]$\{\begin{array}{c}\nabla \times B={\mu }_{0}J+\frac{1}{c^2}\frac{\partial E}{\partial t}=0\\ \nabla .Math.B=0\end{array}$

[0076] Thus the following relationships apply for the Cartesian components B.sub.x, B.sub.y and B.sub.z of the vector field B:

[00006]$\nabla \times B=.Math.\begin{array}{ccc}i& j& k\\ \frac{\partial }{\partial x}& \frac{\partial }{\partial y}& \frac{\partial }{\partial z}\\ B_x& B_y& B_z\end{array}.Math.=0.fwdarw.\frac{\partial B_x}{\partial z}=\frac{\partial B_z}{\partial x},\frac{\partial B_y}{\partial x}=\frac{\partial B_x}{\partial y},\frac{\partial B_z}{\partial y}=\frac{\partial B_y}{\partial z}$$\nabla .Math.B=0.fwdarw.\frac{\partial B_x}{\partial x}+\frac{\partial B_y}{\partial y}+\frac{\partial B_z}{\partial z}=0$

[0077] The total vector field B(x,y,z) in the imaging volume results from an overlap of the main magnetic field B.sub.0(x,y,z) (generated by the main magnet 11) and the actual gradient magnetic fields B.sub.gx(x,y,z), B.sub.gy(x,y,z) and/or B.sub.gz(x,y,z) (generated by the gradient coils 18x, 18y, 18z of the gradient coil unit 18). Because the sources of the overlapping magnetic fields, in other words of the main magnetic field and of the at least one actual gradient magnetic field, do not interact with one another and any transient effects caused by eddy currents may be ignored, the following results, for example, for an overlap of the main magnetic field B.sub.0 and an actual gradient magnetic field B.sub.gx(x,y,z) in the X direction:

[00007]$\{\begin{array}{c}\nabla \times \left(B_0+B_{gx}\right)=\nabla \times B_0+\nabla \times B_{gx}=0+0\\ \nabla .Math.\left(B_0+B_{gx}\right)=\nabla .Math.B_0+\nabla .Math.B_{gx}=0+0\end{array}$

[0078] From this, in the event that two or more gradient coils are active, these equations may be extended to all possible overlaps of magnetic fields; each individual contribution to the total magnetic field B(x,y,z) in the imaging volume (e.g. each actual gradient magnetic field B.sub.gx(x,y,z), B.sub.gy(x,y,z) and/or B.sub.gz(x,y,z) and/or the main magnetic field B.sub.0(x,y,z)) is thus non-rotational and solenoidal. This important finding enables each magnetic field contribution to be considered independently, as a result of which various technical advantages may be derived, as are shown below.

3. Estimation of Maxwell Terms with Active Gradient Coil 18x for Generation of a Magnetic Field Gradient in the X Direction

[0079] When using the expressions from section 2 for the Cartesian components of the actual gradient magnetic field B.sub.gx(x,y,z) and the assumptions A1 to A3, the following results for the vectorial components B.sub.gx,x, B.sub.gx,y and B.sub.gx,z:

[00008]$B_{\mathrm{gx},z}=x.Math.\mathrm{GX}.fwdarw.\left\{\begin{array}{c}\frac{\partial B_{\mathrm{gx},z}}{\partial x}=\mathrm{GX}\\ \frac{\partial B_{\mathrm{gx},z}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gx},z}}{\partial z}=0\end{array}\right\}.fwdarw.\begin{array}{c}\left\{\begin{array}{c}\frac{\partial B_{\mathrm{gx},x}}{\partial x}=\frac{\partial B_{\mathrm{gx},y}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gx},x}}{\partial y}=\frac{\partial B_{\mathrm{gx},y}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gx},x}}{\partial z}=\frac{\partial B_{\mathrm{gx},z}}{\partial x}=\mathrm{GX}\end{array}\right\}.fwdarw.B_{\mathrm{gx},x}=z.Math.\mathrm{GX}\\ \left\{\begin{array}{c}\frac{\partial B_{\mathrm{gx},y}}{\partial x}=\frac{\partial B_{\mathrm{gx},x}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gx},y}}{\partial y}=\frac{\partial B_{\mathrm{gx},x}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gx},y}}{\partial z}=\frac{\partial B_{\mathrm{gx},z}}{\partial y}=0\end{array}\right\}.fwdarw.B_{\mathrm{gx},y}=0\end{array}$

[0080] The deviation of the actual gradient magnetic field from the setpoint gradient magnetic field is described here by the vectorial components B.sub.gx,x and B.sub.gx,y of the spatial directions (X and Y direction) deviating from the main magnetic field direction (Z direction). A gradient coil 18x for generation of a magnetic field oriented in the Z direction with a linear magnetic field gradient in the X direction thus generates an equally large, concomitant orthogonal magnetic field, which is oriented in the X direction and changes linearly with the z coordinate. The vectorial component B.sub.gx,x has a linear dependency on the z coordinate. In contrast, the concomitant orthogonal magnetic field oriented in the Y direction is negligibly small or approximately 0.

[0081] FIGS. 4 and 5 show by way of example a magnetic field B(x,y,z) in each case as a vector field, these confirming the validity of the above theoretical results. In FIG. 4, y=0 and in FIG. 5, z=z.sub.0>0. Whereas, in FIG. 4, the X component of the vectors changes significantly depending on the z coordinate. In FIG. 5, the Y component of the vectors is also negligible where z=z.sub.0>0.

4. Estimation of Maxwell Terms with Active Gradient Coil 18y for Generation of a Magnetic Field Gradient in the Y Direction

[0082] When using the expressions from section 2 for the Cartesian components of the actual gradient magnetic field B.sub.gy(x,y,z) and the assumptions A1 to A3, the following results for the vectorial components B.sub.gy,x, B.sub.gy,y and B.sub.gy,z:

[00009]$B_{\mathrm{gy},z}=y.Math.\mathrm{GY}.fwdarw.\left\{\begin{array}{c}\frac{\partial B_{\mathrm{gy},z}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gy},z}}{\partial y}=\mathrm{GY}\\ \frac{\partial B_{\mathrm{gy},z}}{\partial z}=0\end{array}\right\}.fwdarw.\begin{array}{c}\left\{\begin{array}{c}\frac{\partial B_{\mathrm{gy},x}}{\partial x}=\frac{\partial B_{\mathrm{gy},y}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gy},x}}{\partial y}=\frac{\partial B_{\mathrm{gy},y}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gy},x}}{\partial z}=\frac{\partial B_{\mathrm{gy},z}}{\partial x}=0\end{array}\right\}.fwdarw.B_{\mathrm{gy},x}=0\\ \left\{\begin{array}{c}\frac{\partial B_{\mathrm{gy},y}}{\partial x}=\frac{\partial B_{\mathrm{gy},x}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gy},y}}{\partial y}=\frac{\partial B_{\mathrm{gy},x}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gy},y}}{\partial z}=\frac{\partial B_{\mathrm{gy},z}}{\partial y}=\mathrm{GY}\end{array}\right\}.fwdarw.B_{\mathrm{gy},y}=z.Math.\mathrm{GY}\end{array}$

[0083] The deviation of the actual gradient magnetic field from the setpoint gradient magnetic field is described here by the vectorial components B.sub.gy,x and B.sub.gy,y of the spatial directions (X and Y direction) deviating from the main magnetic field direction (Z direction). A gradient coil 18y for generation of a magnetic field oriented in the Z direction with a linear magnetic field gradient in the Y direction thus generates an equally large, concomitant orthogonal magnetic field, which is oriented in the Y direction and changes linearly with the z coordinate. The vectorial component B.sub.gy,y has a linear dependency on the z coordinate. In contrast, the concomitant orthogonal magnetic field oriented in the X direction is negligibly small or approximately 0.

[0084] FIGS. 6 and 7 show by way of example a magnetic field B(x,y,z) in each case as a vector field, these confirming the validity of the above theoretical results. In FIG. 6, x=0 and in FIG. 7, z=z.sub.0>0. Whereas, in FIG. 6, the Y component of the vectors changes significantly depending on the z coordinate. In FIG. 7, the X component of the vectors is also negligible where z=z.sub.0>0.

5. Estimation of Maxwell Terms with Active Gradient Coil 18z for Generation of a Magnetic Field Gradient in the Z Direction

[0085] When using the expressions from section 2 for the Cartesian components of the actual gradient magnetic field B.sub.gz(x,y,z) and the assumptions A1 to A3, the following results for the vectorial components B.sub.gz,x, B.sub.gz,y and B.sub.gz,z:

[00010]$B_{\mathrm{gz},z}=z.Math.\mathrm{GZ}.fwdarw.\left\{\begin{array}{c}\frac{\partial B_{\mathrm{gz},z}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gz},z}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gz},z}}{\partial z}=\mathrm{GZ}\end{array}\right\}.fwdarw.\begin{array}{c}\left\{\begin{array}{c}\frac{\partial B_{\mathrm{gz},x}}{\partial x}=\frac{\partial B_{\mathrm{gz},y}}{\partial y}=\frac{\mathrm{GZ}}{2}\\ \frac{\partial B_{\mathrm{gz},x}}{\partial y}=\frac{\partial B_{\mathrm{gz},y}}{\partial x}=0\\ \frac{\partial B_{\mathrm{gz},x}}{\partial z}=\frac{\partial B_{\mathrm{gz},z}}{\partial x}=0\end{array}\right\}.fwdarw.B_{\mathrm{gz},x}=-x\frac{\mathrm{GZ}}{2}\\ \left\{\begin{array}{c}\frac{\partial B_{\mathrm{gz},y}}{\partial x}=\frac{\partial B_{\mathrm{gz},x}}{\partial y}=0\\ \frac{\partial B_{\mathrm{gz},y}}{\partial y}=\frac{\partial B_{\mathrm{gz},x}}{\partial x}=\frac{\mathrm{GZ}}{0}\\ \frac{\partial B_{\mathrm{gz},y}}{\partial z}=\frac{\partial B_{\mathrm{gz},z}}{\partial y}=0\end{array}\right\}.fwdarw.B_{\mathrm{gz},y}=-y\frac{\mathrm{GZ}}{2}\end{array}$

[0086] The deviation of the actual gradient magnetic field from the setpoint gradient magnetic field is described here by the vectorial components B.sub.gz,x and B.sub.gz,y of the spatial directions (X and Y direction) deviating from the main magnetic field direction (Z direction). A gradient coil 18z for generation of a magnetic field oriented in the z direction with a linear magnetic field gradient in the Z direction thus generates two half as large, concomitant orthogonal magnetic fields: one is oriented opposite to the X direction and changes linearly with the x coordinate; the other is oriented opposite to the Y direction and changes linearly with the y coordinate. The vectorial component B.sub.gz,x has a linear dependency on the x coordinate; the vectorial component B.sub.gz,y has a linear dependency on the y coordinate.

[0087] FIGS. 8-10 show by way of example a magnetic field B(x,y,z) in each case as a vector field, these confirming the validity of the above theoretical results. In FIG. 8, z=0, in FIG. 9, y=0, and in FIG. 10, x=0.

6. Overview of the Estimations of the Maxwell Terms

[0088] In accordance with the explanations in sections 1-6, a magnetic field model has been developed, in accordance with which the deviation of the actual gradient magnetic field from the setpoint gradient magnetic field is described by at least one vectorial component in a spatial direction deviating from the main magnetic field direction.

[0089] Depending on which of the gradient coils 18x, 18y, 18z is active, the (resultant) gradient magnetic field includes a first actual gradient magnetic field with a magnetic field gradient in the X direction, a second actual gradient magnetic field with a magnetic field gradient in the Y direction and/or a third actual gradient magnetic field with a magnetic field gradient in the Z direction. X direction, Y direction and Z direction are in this case orthogonal to one another.

[0090] The vector field of the main magnetic field is oriented in the main magnetic field direction, the Z direction. The vector field of the first actual gradient magnetic field contains the vectors B.sub.gx(x,y,z) with the vector components B.sub.gx,x, B.sub.gx,y and B.sub.gx,z. The vector field of the second actual gradient magnetic field contains the vectors B.sub.gy(x,y,z) with the vector components B.sub.gy,x, B.sub.gy,y and B.sub.gy,z. The vector field of the third actual gradient magnetic field contains the vectors B.sub.gz(x,y,z) with the vector components B.sub.gz,x, B.sub.gz,y and B.sub.gz,z. The vector components B.sub.gx,x, B.sub.gx,y, B.sub.gy,x, B.sub.gy,y, B.sub.gz,x and B.sub.gz,y may be viewed as values of a deviation, in particular concomitant field components, which describe a deviation of the actual gradient magnetic field from a setpoint gradient magnetic field of the magnetic resonance device 10. The setpoint gradient magnetic field may provide that the vector components B.sub.gx,x, B.sub.gx,y, B.sub.gy,x, B.sub.gy,y, B.sub.gz,x and B.sub.gz,y are equal to zero. In accordance with sections 4 and 5 this is in particular not the case for B.sub.gx,x, B.sub.gy,y, B.sub.gz,x and B.sub.gz,y.

7. Calculation of Field Errors Caused by Maxwell Terms in the Case of a Homogeneous Main Magnetic Field

[0091] FIG. 11 shows by way of example an overlap of various magnetic fields, in that vector components are combined, in particular added, to form a resultant magnetic field. In this case B.sub.0 is the vector of the main magnetic field that is generated by the main magnet 12. B.sub.z is the desired (setpoint) component of the gradient magnetic field along the Z axis. B.sub.x and B.sub.y are concomitant field components along the X and Y axis. If multiple gradient coils are active simultaneously, these concomitant field components may result from a sum of multiple concomitant field components, e.g. B.sub.x=B.sub.gx,x+B.sub.gy,x+B.sub.gz,x and B.sub.y=B.sub.gx,y+B.sub.gy,y+B.sub.gz,y.

[0092] In particular, if the main magnet 12 is properly shimmed, the main magnetic field B.sub.0 may have a very high homogeneity within the FOV of just a few ppm deviation from a target value. In this case the vector B.sub.0 of the main magnetic field has a constant amount B.sub.0 and is parallel to the Z axis, i.e., B.sub.0=B.sub.0.Math.k, wherein k is the unit vector in the Z direction. By using the estimation in accordance with sections 3-5 the following results for vector field B(x,y,z) of the total magnetic field:

[00011]$B\left(x,y,z\right)=B_{x}i+B_{y}j+\left(B_0+B_z\right)k==\left(z.Math.\mathrm{GX}-x\frac{GZ}{2}\right)i+\left(z.Math.\mathrm{Gy}-y\frac{GZ}{2}\right)j+\left(B_0+x.Math.\mathrm{GX}+y.Math.\mathrm{GY}+z.Math.\mathrm{GZ}\right)k$

[0093] In this case, i and j are the unit vectors in the X and Y direction. Thus, following a provision of a parameter which describes the main magnetic field, such as for instance the vector field B.sub.0, the total magnetic field B(x,y,z) may be estimated using the vector field B.sub.0, the gradient values GX, GY, GZ and the concomitant field components.

[0094] The last equation may of course be simplified if only one or two gradient coils are active. For example, if only the gradient coil 18x for generation of a magnetic field gradient in the X direction is active, GY=GZ=0, and the resultant spatial distribution of the vectorial magnetic field may be estimated with the following equation:

B(x,y,z)=(z.Math.GX)i+(B.sub.0+x.Math.GX)k

[0095] It is further conceivable, using the estimated vector field B(x,y,z), to correct encoding errors, induced by Maxwell terms, of magnetic resonance signals. For example, during a readout phase the local frequency is proportionally dependent on the amount of B(x,y,z)—and not for instance as when viewed in a conventionally idealized manner proportionally dependent on BZ(x,y,z)=B.sub.0+x.Math.GX. The actual spatial distribution of the frequency encoding for the local magnetic resonance signal in this case produces:

ω(x,y,z)=γ.Math.|B(x,y,z)|=γ.Math.√{square root over ((z.Math.GX).sup.2+(B.sub.0+x.Math.GX).sup.2)}

[0096] In this case, ω(x,y,z) the local Larmor frequency and γ the gyromagnetic ratio of the nucleus are of interest, mostly of the water protons. This expression may also be used directly to correct the geometric distortions in the magnetic resonance images. The advantage of the new method compared to the prior art is in particular that no development into Taylor series and/or assumptions about the relative strength of the gradient fields (cf. assumption A5 of the Maxwell method) are necessary. Thus the method also works for magnetic resonance examinations with a low or very low field.

[0097] Using the estimated values of a deviation, in particular the concomitant field components, a correction of magnetic resonance signals, in particular of an encoding of magnetic resonance signals, may be performed. In particular, the correction may include a calculation of a Larmor frequency in dependency on the values of a deviation.

8. Calculation of Field Errors Caused by Maxwell Terms in the Case of an Inhomogeneous Main Magnetic Field

[0098] In particular, to be able to produce cost-effective magnetic resonance devices, in particular main magnets, compromises may be required as regards the achievable homogeneity of the static main magnetic field B.sub.0. The proposed method enables the effects of such inhomogeneities to be calibrated and/or corrected, in order to minimize any image artifacts connected thereto.

[0099] Various methods are known in the prior art for creating field maps of an inhomogeneous static magnetic field, such as the main magnetic field B.sub.0(x,y,z), e.g., using a 3D magnetic field camera. It is possible to use such field maps to correct signal encoding errors when concomitant fields exist.

[0100] The total magnetic field B(x,y,z) may result from an overlap of all contributing field sources. If all gradient coils are active, then in accordance with the explanations in sections 2-4 the actual field distribution may be expressed by:

[00012]$B\left(x,y,z\right)=\left[\mathrm{ijk}\right].Math.\left[\begin{array}{c}{B}_{0x}\left(x,y,z\right)+z.Math.\mathrm{GX}-x\frac{\mathrm{GZ}}{2}\\ B_{0y}\left(x,y,z\right)+z.Math.\mathrm{GY}-y\frac{\mathrm{GZ}}{2}\\ B_{0z}\left(x,y,z\right)+x.Math.\mathrm{GX}+y.Math.\mathrm{GY}+z.Math.\mathrm{GZ}\end{array}\right]$

[0101] In this case, B.sub.0x(x,y,z), B.sub.0y(x,y,z), B.sub.0z(x,y,z) are the vector components of the vector field B.sub.0(x,y,z) of the main magnetic field.

[0102] In certain situations, this expression may be simplified. If, for example, the main magnetic field is in fact inhomogeous, but is nevertheless reasonably parallel to the Z axis and only the X gradient coil 18x is active, then:

[00013]$B\left(x,y,z\right)=\left[\mathrm{ijk}\right].Math.\left[\begin{array}{c}z.Math.\mathrm{GX}\\ 0\\ B_{0z}\left(x,y,z\right)+x.Math.\mathrm{GX}\end{array}\right]$

[0103] Accordingly, the following applies for the spatial distribution of the frequency encoding of local magnetic resonance signals:

ω(x,y,z)=γ.Math.|B(x,y,z)|=γ.Math.√{square root over ((z.Math.GX).sup.2+[B.sub.0z(x,y,z)+x.Math.GX].sup.2)}

[0104] The proposed method may advantageously also be used to take into consideration larger inhomogeneities of the main magnetic field, e.g., in the periphery of the FOV.

9. Model-Based Image Reconstruction

[0105] An image reconstruction may advantageously, in accordance with the proposed magnetic field model, take into consideration the phase errors that are induced by the concomitant fields. With this model, an instantaneous frequency of the magnetic resonance signals at a given spatial location may be modeled:

[00014]$\omega \left(x,y,z,t\right)=\gamma .Math..Math.B\left(x,y,z,t\right).Math.==\gamma .Math..Math.\left[\mathrm{ijk}\right].Math.\left[\begin{array}{c}{B}_{0x}\left(x,y,z,t\right)+z.Math.\mathrm{GX}\left(t\right)-x\frac{\mathrm{GZ}\left(t\right)}{2}\\ B_{0y}\left(x,y,z,t\right)+z.Math.\mathrm{GY}\left(t\right)-y\frac{\mathrm{GZ}\left(t\right)}{2}\\ B_{0z}\left(x,y,z,t\right)+x.Math.\mathrm{GX}\left(t\right)+y.Math.\mathrm{GY}\left(t\right)+z.Math.\mathrm{GZ}\left(t\right)\end{array}\right].Math.$

[0106] In this case, B(x,y,z,t) advantageously takes into consideration a temporal drift of the magnetic field, in particular of the main magnetic field, for example, because of floor vibrations or as a result of thermal heating of various components of the magnetic unit 11 (e.g. field coils, shim irons, formers or permanent magnets). This drift may be calibrated in advance, e.g., using a 3D magnetic field camera, and recalibrated during a magnetic resonance scan, e.g., using one or more sensors, in particular temperature sensors and/or vibration sensors, which in particular capture (actual) ambient parameters in real time. The expressions GX(t), GY(t), and GZ(t), in particular, describe gradient waveforms or gradient pulses which are applied and/or used during the magnetic resonance scan.

[0107] In conclusion, it is once again noted that the methods described in detail above and the magnetic resonance device relate solely to exemplary embodiments that may be modified by the person skilled in the art in a variety of ways, without departing from the scope of the disclosure. Further, the use of the indefinite article “a” or “an” does not preclude that the features in question may also be present multiple times. Likewise, the term “unit” does not rule out that the components in question include multiple interacting subcomponents that if appropriate may also be distributed spatially.

[0108] It is to be understood that the elements and features recited in the appended claims may be combined in different ways to produce new claims that likewise fall within the scope of the present disclosure. Thus, whereas the dependent claims appended below depend on only a single independent or dependent claim, it is to be understood that these dependent claims may, alternatively, be made to depend in the alternative from any preceding or following claim, whether independent or dependent, and that such new combinations are to be understood as forming a part of the present specification.

[0109] While the present disclosure has been described above by reference to various embodiments, it may be understood that many changes and modifications may be made to the described embodiments. It is therefore intended that the foregoing description be regarded as illustrative rather than limiting, and that it be understood that all equivalents and/or combinations of embodiments are intended to be included in this description.