Characterization of Concomitant Field Effects on MR Imaging

Abstract

The present disclosure relates to a method of performing 3D Magnetic Resonance Imaging including applying a magnetic gradient field that causes a concomitant field B.sub.c. A further step of the method includes determining phase accruals due to the self-squared terms of the concomitant field B.sub.c and phase accruals .sub.xz, .sub.yz due to the cross terms of the concomitant field B.sub.c based on an encoding matrix that accounts for the different possible sign combinations of the applied magnetic gradients.

Claims

1. A method for performing 3D magnetic resonance imaging, comprising: applying a magnetic gradient field that causes a concomitant field B.sub.c leading to a phase accrual .sub.c represented as: $_{c} = \frac{T}{2 B_{0}} (\overset{}{G_{x}^{2} z^{2} + G_{y}^{2} z^{2} + G_{z}^{2} \frac{x^{2} + y^{2}}{4}} \underset{}{- G_{x} G_{z} x z - G_{y} G_{z} y z}),$ the terms G.sub.x.sup.2, G.sub.y.sup.2 and G.sub.z.sup.2 comprise self-squared terms, the terms G.sub.xG.sub.z and G.sub.yG.sub.z comprise cross terms, x, y and z represent coordinates in a 3D space, B.sub.0 represents a static magnetic field, G.sub.x, G.sub.y and G.sub.z represent applied magnetic gradients, represents a gyromagnetic ratio characteristic of nuclei, T represents a total time duration for applying the magnetic gradients; determining phase accruals .sub.xz, .sub.yz due to the self-squared terms of the concomitant field B.sub.c and due to the cross terms of the concomitant field B.sub.c, based on an encoding matrix that accounts for different possible sign combinations of the applied magnetic gradients G.sub.x, G.sub.y and G.sub.z; and generating a 2D or 3D image based upon one or more of the phase accruals .sub.xz, .sub.yz.

2. The method according to claim 1, further comprising: performing phase measurements for determining the phase accruals according to an encoding scheme represented by a predetermined invertible encoding matrix.

3. The method according to claim 2, wherein the performing the phase measurements comprises performing five phase measurements for determining the phase accruals based upon the self-squared terms of the concomitant field B.sub.c and the cross terms of the concomitant field B.sub.c, and wherein the predetermined invertible encoding matrix is a 55 matrix.

4. The method according to claim 2, further comprising: performing the phase measurements as six phase measurements represented as m.sub.1 to m.sub.6 for determining: phase accruals .sub.Uz, .sub.Ux, .sub.Uy based upon to a 3D displacement field, phase accruals .sub.xz, .sub.yz due to the cross terms of the concomitant field B.sub.c, and a phase accrual .sub.err based upon to a constant phase error and the self-squared terms of the concomitant field B.sub.c, wherein the predetermined invertible encoding matrix M is a 66 matrix represented as: $[\begin{matrix} m_{1} \\ m_{2} \\ m_{3} \\ m_{4} \\ m_{5} \\ m_{6} \end{matrix}] = M [\begin{matrix} _{U_{z}} \\ _{U_{x}} \\ _{U_{y}} \\ _{err} \\ _{xz} \\ _{yz} \end{matrix}] .$

5. The method according to claim 2, wherein the predetermined invertible encoding matrix only includes elements comprising 1 and/or +1.

6. The method according to claim 2, wherein the predetermined invertible encoding matrix includes elements that reflect amplitudes of the applied magnetic gradients G.sub.x, G.sub.y and G.sub.z.

7. The method according to claim 4, wherein the 66 predetermined invertible encoding matrix M is represented as: $M = [\begin{matrix} - 1 & + 1 & - 1 & + 1 & + 1 & - 1 \\ + 1 & - 1 & - 1 & + 1 & + 1 & + 1 \\ - 1 & - 1 & + 1 & + 1 & - 1 & + 1 \\ + 1 & + 1 & + 1 & + 1 & - 1 & - 1 \\ + 1 & - 1 & + 1 & + 1 & + 1 & - 1 \\ - 1 & + 1 & + 1 & + 1 & + 1 & + 1 \end{matrix}] .$

8. The method according to claim 1, wherein the applied magnetic gradients G.sub.x, G.sub.y, and G.sub.z have equal amplitudes.

9. The method according to claim 1, wherein the applied magnetic gradients Gx, Gy, and Gz have unequal amplitudes.

10. The method according to claim 1, further comprising: applying motion encoding gradients without any overlap with imaging gradients.

11. The method according to claim 4, further comprising: displaying a 2D or 3D image based on one of the phase accruals .sub.Uz, .sub.Ux, .sub.Uy, .sub.xz, .sub.yz.

12. The method according to claim 4, further comprising: displaying a 2D or 3D image based on an amplitude of a temporal Fourier transform of one of the phase accruals .sub.Uz, .sub.Ux, .sub.Uy, .sub.xz, .sub.yz.

13. The method according to claim 1, wherein the 3D magnetic resonance imaging comprises at least part of a 3D magnetic resonance elastography examination.

14. The method according to claim 1, further comprising: performing mechanical excitation at a frequency in a range of 20 to 100 Hz.

15. The method according to claim 1, further comprising: performing mechanical excitation at a frequency in a range of 20 to 60 Hz.

16. A 3D magnetic resonance imaging system, comprising: a magnet configured to apply a magnetic gradient field that causes a concomitant field B.sub.c leading to a phase accrual .sub.c represented as: $_{c} = \frac{T}{2 B_{0}} (\overset{}{G_{x}^{2} z^{2} + G_{y}^{2} z^{2} + G_{z}^{2} \frac{x^{2} + y^{2}}{4}} \underset{}{- G_{x} G_{z} x z - G_{y} G_{z} y z}),$ wherein: the terms G.sub.x.sup.2, G.sub.y.sup.2 and G.sub.z.sup.2 comprise self-squared terms, the terms G.sub.xG.sub.z and G.sub.yG.sub.z comprise cross terms, x, y and z represent coordinates in a 3D space, B.sub.0 represents a static magnetic field, G.sub.x, G.sub.y and G.sub.z represent applied magnetic gradients, represents a gyromagnetic ratio characteristic of nuclei, T represents a total time duration for applying the magnetic gradients; and processing circuitry configured to: determine phase accruals .sub.xz, .sub.yz due to the self-squared terms of the concomitant field B.sub.c and due to the cross terms of the concomitant field B.sub.c, based on an encoding matrix that accounts for different possible sign combinations of the applied magnetic gradients G.sub.x, G.sub.y and G.sub.z; and generate a 2D or 3D image based upon one or more of the phase accruals .sub.xz, .sub.yz.

17. A computer-readable medium having instructions stored thereon that, when executed by a 3D magnetic resonance imaging system, cause the magnetic resonance imaging system to: apply a magnetic gradient field that causes a concomitant field B.sub.c leading to a phase accrual .sub.c represented as: $_{c} = \frac{T}{2 B_{0}} (\overset{}{G_{x}^{2} z^{2} + G_{y}^{2} z^{2} + G_{z}^{2} \frac{x^{2} + y^{2}}{4}} \underset{}{- G_{x} G_{z} x z - G_{y} G_{z} y z}),$ wherein: the terms G.sub.x.sup.2, G.sub.y.sup.2 and G.sub.z.sup.2 comprise self-squared terms, the terms G.sub.xG.sub.z and G.sub.yG.sub.z comprise cross terms, x, y and z represent coordinates in a 3D space, B.sub.0 represents a static magnetic field, G.sub.x, G.sub.y and G.sub.z represent applied magnetic gradients, represents a gyromagnetic ratio characteristic of nuclei, T represents a total time duration for applying the magnetic gradients; and determine phase accruals .sub.xz, .sub.yz due to the self-squared terms of the concomitant field B.sub.c and due to the cross terms of the concomitant field B.sub.c, based on an encoding matrix that accounts for different possible sign combinations of the applied magnetic gradients G.sub.x, G.sub.y and G.sub.z; and generate a 2D or 3D image based upon one or more of the phase accruals .sub.xz, .sub.yz.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present disclosure will now be described in more detail in connection with the attached drawings showing in:

[0035] FIG. 1 illustrates a schematic diagram of an example MRE system, in accordance with the disclosure;

[0036] FIG. 2 illustrates example unwrapped phases and Fourier transforms of phantom measurements without mechanical excitation, in accordance with the disclosure; and

[0037] FIG. 3 illustrates example unwrapped phases and Fourier transforms of the phantom measurement with mechanical excitation, in accordance with the disclosure.

DETAILED DESCRIPTION OF THE DISCLOSURE

[0038] The following embodiments represent preferable examples of the present disclosure.

[0039] The following embodiments relate to MRE systems and methods. However, they can be used for other MR techniques too where additional gradients are applied besides the imaging gradients.

[0040] FIG. 1 illustrates a schematic diagram of an example MRE system, in accordance with the disclosure.

[0041] The MRE-system comprises a magnet unit with an imaging region 2, for example within a patient tunnel for placing an object 8, e.g. a patient, to be imaged. The magnet unit comprises a field magnet 3 (also referred to herein as a main magnet) that generates a main magnet field for aligning nuclear spins of the object, e.g. within the imaging region 2. The imaging region 2 is characterized by a very homogeneous static main magnet field, the homogeneity relating, e.g. to the magnetic field strength. The field magnet 3 may, for example, be a superconducting magnet capable of providing magnetic fields with a magnetic flux density in the order of several Tesla, e.g. in the order of 7 T or more. A patient table 7 may be movable within the patient tunnel.

[0042] Furthermore, the magnet unit comprises a gradient coil arrangement 5 with several gradient coils that are designed to superimpose location-dependent magnetic fields in the three spatial directions on the static main magnet field for spatial differentiation and e.g. slice selection. The gradient coils of the gradient coil arrangement 5 may, for example, be designed as coils of normal conducting wires, which may, for example, generate mutually orthogonal fields or field gradients in the recording region.

[0043] The MRE-system 1, e.g. the magnet unit, comprises a transmission coil arrangement, which contains one or more RF-coils 4. It is noted that the one or more RF-coils 4 of the transmission coil arrangement may, depending on the specific implementation or application, also be used as receiving coils. Optionally, the MRE-system 1 may also comprise one or more local coils (not shown in FIG. 1), which may be arranged in the immediate vicinity of the object 8, for example on the object 8 or in the patient table 7. The local coils may serve as receiving coils and/or transmission coils.

[0044] Furthermore, the MRE-system comprises a (pulse) wave generator 6 for exciting shear waves within the object/patient to be examined.

[0045] The MRE-system 1 also comprises a data processing apparatus 9 including at least one computing unit 10 (also referred to herein as a controller, processing circuitry, or an evaluation device). The at least one computing unit 10 is configured to carry out a computer-implemented method for controlling the MRE-system according to a specific timing scheme. For instance, the time control of the wave generator 6 may be synchronized with the MR imaging. As a result of the computer-implemented method, the at least one computing unit 10 controls the of the MRE-system so that the acquisition is performed in a very efficient way.

[0046] In response to the excitation RF-pulses, the at least one computing unit 10 receives corresponding NMR-signals from the receiving coils and may generate respective MR-images of the object 8 depending on those signals.

[0047] For instance, the at least one computing unit may comprise a readout control unit, which is connected to the at least one RF-coil 4 and/or the local coil. Depending on the detected MR-signals, the readout control unit, which may comprise an analog-to-digital converter (ADC), may generate corresponding MR-data, e.g. in k-space.

[0048] The at least one computing unit 10 may evaluate the MR-data and, for example, carry out a two-dimensional or three-dimensional image reconstruction based on the MR-data. The at least one computing unit 10 also comprises a sending control unit, which is connected to and controls the RF-coil(s) 4 and/or the local coil to emit the excitation RF-pulses and, for example refocusing RF-pulses and other RF-pulses. The at least one computing unit 10 comprises gradient control unit, which is connected to and controls the gradient coil arrangement 5 to apply, for example, slice selecting gradients, gradients for frequency and/or phase encoding, defocusing gradients, and/or readout gradients, and so forth. Additionally, the at least one computing unit 10 comprises a wave generation control unit adapted to control the wave generator.

[0049] It is noted that the described structure of the MRE-system 1 is a non-limiting example only. The different required tasks and functions may also be distributed differently and/or to different units in other applications.

[0050] Concomitant field effects in MRE might become of importance when translating MRE to low field MR systems. To design an experiment that measures the effect of concomitant fields B.sub.c on Hadamard-encoded 3D MRE, we first look at the phase accrual .sub.c of B.sub.c following the work of Bernstein et al.:

[00005] $\begin{matrix} _{c} = \frac{T}{2 B_{0}} (\overset{self - squared terms}{\overset{}{G_{x}^{2} z^{2} + G_{y}^{2} z^{2} + G_{z}^{2} \frac{x^{2} + y^{2}}{4}}} \underset{cross terms}{\underset{}{- G_{x} G_{z} x z - G_{y} G_{z} y z}}) & Eqn . 1 \end{matrix}$

[0051] A Hadamard-encoded MRE measurement consists of unique combinations of motion encoding gradients applied on all gradient axes simultaneously with equal amplitudes. The following 44 Hadamard matrix (H) is typically used in MRE measurement in accordance with Equation 5:

[00006] $\begin{matrix} H = [\begin{matrix} - 1 & + 1 & - 1 & + 1 \\ + 1 & - 1 & - 1 & + 1 \\ - 1 & - 1 & + 1 & + 1 \\ + 1 & + 1 & + 1 & + 1 \end{matrix}] & Eqn . 5 \end{matrix}$

[0052] The first three terms in Eqn. 1, the self-squared terms, are constant throughout the different measurements of Hadamard encoding and are therefore encoded in the same term that encodes constant phase errors such as magnetic field inhomogeneity. However, the last two terms, the cross terms, change signs between the different measurements of Hadamard encoding depending on the polarity of the applied motion encoding gradients. As a result, the cross terms cannot be resolved using a conventional 44 Hadamard encoding matrix.

[0053] A larger squared encoding matrix (e.g. 55, 66, 77 matrix) can resolve the cross terms.

[0054] For instance, the Hadamard encoding can be extended to a 66 encoding matrix M that accounts for the different possible sign combinations of the cross terms, as shown in Equations 3 and 4:

[00007] $\begin{matrix} M = [\begin{matrix} - 1 & + 1 & - 1 & + 1 & + 1 & - 1 \\ + 1 & - 1 & - 1 & + 1 & + 1 & + 1 \\ - 1 & - 1 & + 1 & + 1 & - 1 & + 1 \\ + 1 & + 1 & + 1 & + 1 & - 1 & - 1 \\ + 1 & - 1 & + 1 & + 1 & + 1 & - 1 \\ - 1 & + 1 & + 1 & + 1 & + 1 & + 1 \end{matrix}] & Eqn . 4 \end{matrix}$ $\begin{matrix} [\begin{matrix} m_{1} \\ m_{2} \\ m_{3} \\ m_{4} \\ m_{5} \\ m_{6} \end{matrix}] = M [\begin{matrix} _{U_{z}} \\ _{U_{x}} \\ _{U_{y}} \\ _{err} \\ _{xz} \\ _{yz} \end{matrix}] & Eqn . 3 \end{matrix}$

[0055] Where m.sub.k (k=1, 2, . . . , 6) represents the k-th MRE phase measurement, .sub.U.sub.x, .sub.U.sub.y, and .sub.U.sub.z represent the phase accruals due to the 3D displacement field, .sub.err represents the phase accrual due to constant phase errors and the phase accrual of the self-squared terms, and .sub.xz and .sub.yz represent the phase accrual due to the first and second cross terms, respectively.

[0056] The proposed encoding matrix M is incorporated into a previously published 3D MRE sequence (Guenthner et al.) extending the sequence from 4 to 6 measurements. The motion encoding gradients are applied without any overlap with the imaging gradients.

[0057] The extended 3D MRE sequence can be implemented on a 0.55 T system. Two phantom experiments are conducted: (I) without vibration to verify that M is solving for the cross terms (see FIG. 2). Note that the first cross term (G.sub.xG.sub.zxz) varies with x and z, and the second cross term (G.sub.yG.sub.zyz) varies with y and z, both independent of the vibration. (II) an experiment with 60 Hz mechanical excitation (see FIG. 3) to examine the phase accrual due to B.sub.c with respect to the acquired mechanical wave phase offsets. The phantom used is an ultrasound gel phantom shifted to right of the iso-centre of the bore to increase the apparent effect of the concomitant fields.

[0058] The results of the phantom experiment without mechanical excitation, i.e. without vibrations, are shown in FIG. 2. There is no spatial variation in .sub.U.sub.x (FIG. 1.B). However, we can observe a spatial variation in x (left-right direction) in .sub.xz (FIG. 2.C) and a spatial variation in y (posterior-anterior direction) in .sub.yz (FIG. 2.D). The spatial variation observed in FIG. 2.C-D suggests that the proposed encoding matrix M is solving for the cross terms. The amplitude of the displacement field in the three terms .sub.U.sub.x, .sub.xz, .sub.yz) is very low (0.90.2 um, 1.40.2 um, and 1.60.2 um respectively) (FIG. 2.E-G).

[0059] Specifically, FIG. 2.A shows a magnitude image calculated by averaging the central four slices of the acquisition volume. FIG. 2.B-D show the unwrapped phases .sub.U.sub.x, .sub.xz, and .sub.yz) after decoding of a single slice, and FIG. 2.E-G show the amplitude of the temporal Fourier transform ( custom-character , , ) at the mechanical vibration frequency (.sub.0=60 Hz) of .sub.U.sub.x, .sub.xz, and .sub.yz, respectively averaged over the central four slices.

[0060] The results of the phantom experiments with mechanical excitation are presented in FIG. 3. .sub.U.sub.x (FIG. 3.B) varies with the mechanical excitation, however, .sub.xz (FIG. 3.C) and .sub.yz (FIG. 3.D) only vary spatially in x (left-right direction) and in y (posterior-anterior direction) respectively. In addition, the amplitude of the displacement field in O.sub.U.sub.x (8111 um) is approximately an order of magnitude higher than the amplitudes in .sub.xz (52 um) and .sub.yz (102 um) (FIG. 3.E-G).

[0061] Specifically, FIG. 3.A shows a magnitude image calculated by averaging the central four slices of the acquisition volume. FIG. 3.B-D show the unwarped phases (.sub.U.sub.x, .sub.xz, and .sub.yz) after decoding of a single slice, and FIG. 3.E-G show the amplitude of the temporal fourier transform ( custom-character , , ) at the mechanical vibration frequency (.sub.0=60 Hz) of .sub.U.sub.x, .sub.xz, and .sub.yz respectively averaged over the central four slices.

[0062] The embodiments described herein method may be extended to other MRE measurements on all field strengths, and is not limited only to 0.55 T systems or to Hadamard motion encoding.

[0063] The various components described herein may be referred to as devices or units. Such components may be implemented via any suitable combination of hardware and/or software components as applicable and/or known to achieve their intended respective functionality. This may include mechanical and/or electrical components, processors, processing circuitry, or other suitable hardware components, in addition to or instead of those discussed herein. Such components may be configured to operate independently, or configured to execute instructions or computer programs that are stored on a suitable computer-readable medium. Regardless of the particular implementation, such units and/or devices, as applicable and relevant, may alternatively be referred to herein as circuitry, controllers, processors, or processing circuitry, or alternatively as noted herein.

Characterization of Concomitant Field Effects on MR Imaging

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Cpc classification

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G01R33/385

PHYSICS

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G01R33/56358

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A61B5/055

HUMAN NECESSITIES

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International classification

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PHYSICS

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PHYSICS

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HUMAN NECESSITIES

Abstract

Claims

Description