CN103678791B - Magnetic resonance radio frequency coil fast analysis method and system based on method of moments - Google Patents

Abstract

The invention provides a magnetic resonance radio frequency coil fast analysis method based on the method of moments. The method includes: establishing an octree data structure according to parameter information of a magnetic resonance radio frequency coil; selecting a reference layer of the octree data structure and acquiring a first impedance matrix of the reference layer; generating a second impedance matrix of the reference layer according to the first impedance matrix of the reference layer, acquiring a parent layer of a target layer, generating a second impedance matrix of the parent layer according to a first impedance matrix of the target layer, using the parent layer as another target layer, and iterating the step of acquiring the parent layer of the target layer; calculating excitation coefficients of the magnetic resonance radio frequency coil by matrix-vector multiplication. The method has the advantages that memory demand and time calculation can be effectively reduced and the magnetic resonance radio frequency coil is quickly analyzed accordingly. In addition, the invention further provides a magnetic resonance radio frequency coil fast analysis system based on the method of moments.

Description

Method and system for rapidly analyzing magnetic resonance radio frequency coil based on moment method

Technical Field

The invention relates to the field of magnetic resonance radio frequency, in particular to a method and a system for rapidly analyzing a magnetic resonance radio frequency coil based on a moment method.

Background

The magnetic resonance radio frequency mainly excites and collects magnetic resonance signals through a radio frequency coil, and the performance of the radio frequency coil directly influences the quality of a final image, so that a manufacturing element of the magnetic resonance radio frequency coil is repeatedly tested, the excitation coefficient of the manufacturing element is calculated for multiple times, and whether the manufacturing element meets the requirement of non-magnetism or not is judged according to the excitation coefficient.

In recent years, a technique for acquiring an excitation coefficient of a magnetic resonance radio frequency coil by using a computer has been rapidly developed and applied. At present, the excitation coefficient acquisition method of the magnetic resonance radio frequency coil based on a computer is mainly divided into two categories: a differential equation method and an integral equation method. The differential equation method needs to perform mesh subdivision on the whole space where the radio frequency coil is located, and meanwhile, an absorption boundary condition needs to be added, so that the number of finally-subdivided model unknowns is large, and the calculation time is long. The integral equation method only needs to divide the metal surface of the radio frequency coil, the unknown quantity is relatively small, and the method is favorable for quick calculation.

However, in the case of a high field, the operating frequency of the magnetic resonance radio frequency coil is relatively high, the impedance matrix generated by the integral equation based moment method through numerical value dispersion is a full matrix, the memory consumption for storing the dense impedance matrix is large, and the computation complexity of matrix vector multiplication is high, so that the computation time for analyzing the problem of the magnetic resonance radio frequency coil becomes very long.

Disclosure of Invention

In view of the foregoing, there is a need for a method for fast analyzing an mr rf coil based on a moment method that reduces memory requirements and computation time.

A method for rapid analysis of a magnetic resonance radio frequency coil based on a moment method, comprising:

acquiring input parameter information of a magnetic resonance radio frequency coil, and establishing an octree data structure according to the parameter information of the magnetic resonance radio frequency coil;

selecting a reference layer of the octree data structure, and acquiring a first impedance matrix of the reference layer, wherein data stored in the first impedance matrix are impedance matrix sub-blocks corresponding to far-field weak interaction between non-empty sub-groups in the reference layer;

performing singular value decomposition on the first impedance matrix of the reference layer to obtain a base matrix and a coupling matrix of the reference layer;

generating a second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer;

taking a reference layer as a target layer, acquiring a parent layer of the target layer, wherein the parent layer is an upper layer adjacent to the target layer, and if the parent layer is not the maximum layer of the octree data structure, acquiring a base matrix of the parent layer according to the base matrix of the target layer and a first impedance matrix;

acquiring a first impedance matrix of the parent layer, wherein data stored in the first impedance matrix of the parent layer are impedance matrix subblocks corresponding to far-field weak interaction between non-empty subgroups in the parent layer, and generating a coupling matrix of the parent layer according to the first impedance matrix of the parent layer and a base matrix;

and generating a second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer, taking the parent layer as a target layer, and iteratively executing the step of obtaining the parent layer of the target layer.

In one embodiment, after the step of building the octree data structure, the method further includes:

acquiring an input current and/or voltage source and a near-field action impedance matrix of each layer of the octree data structure, and calculating to obtain a near-field action excitation coefficient of each layer of the octree data structure;

calculating the total near-field effect excitation coefficient of the octree data structure according to the near-field effect excitation coefficients of all layers of the octree data structure;

after the step of obtaining the base matrix and the coupling matrix of the reference layer, the method further includes:

selecting any non-empty subgroup from the non-empty subgroups of the reference layer as a specific non-empty subgroup, acquiring input voltage and/or current sources and a base matrix of the specific non-empty subgroup of the reference layer, and calculating to obtain a far-field action excitation coefficient of the specific non-empty subgroup of the reference layer;

calculating to obtain a far-field action excitation coefficient set of the reference layer according to the coupling matrix of the reference layer, and calculating to obtain a far-field action excitation coefficient of the reference layer according to the far-field action excitation coefficient set of the reference layer;

after the step of taking the reference layer as the target layer and acquiring the parent layer of the target layer, the method further includes:

obtaining a transfer matrix of the target layer according to the base matrix and the first impedance matrix of the target layer;

calculating to obtain the far field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer on the parent layer according to the far field action excitation coefficient of the specific non-empty subgroup of the target layer and the transfer matrix of the target layer;

after the step of generating the coupling matrix of the parent layer, the method further includes:

calculating to obtain a far-field action excitation coefficient set of the parent layer according to the far-field action excitation coefficients of the corresponding non-empty subgroups on the parent layer and the coupling matrix of the parent layer, and calculating to obtain the far-field action excitation coefficients of the parent layer according to the far-field action excitation coefficient set of the parent layer;

the method further comprises the following steps: calculating the total far field effect excitation coefficient of the octree data structure according to the far field effect excitation coefficients of all layers in the octree data structure;

and calculating the excitation coefficient of the magnetic resonance radio frequency coil according to the far field action total excitation coefficient and the near field action total excitation coefficient of the octree data structure.

In one embodiment, the step of building an octree data structure according to the parameter information of the magnetic resonance radio frequency coil comprises:

establishing a cubic space coordinate model, wherein the cubic space coordinate model is a minimum cubic space which completely surrounds the magnetic resonance radio frequency coil;

dividing the cubic space coordinate model into eight sub-cubic space coordinate models with equal size;

and carrying out iterative segmentation on the subcube space coordinate model according to the parameter information of the magnetic resonance radio frequency coil, and establishing an octree data structure.

In one embodiment, the step of selecting a reference layer of the octree data structure and obtaining a first impedance matrix of the reference layer further includes:

selecting a reference layer of the octree data structure;

acquiring a specific non-empty subgroup of the reference layer and a non-empty subgroup set corresponding to the specific non-empty subgroup through far-field weak interaction;

and acquiring a first impedance matrix of the reference layer according to the specific non-empty subgroup and the far-field acting non-empty subgroup set corresponding to the specific non-empty subgroup.

In one embodiment, the step of performing singular value decomposition on the first impedance matrix of the reference layer to obtain the base matrix and the coupling matrix of the reference layer includes:

performing singular value decomposition on the first impedance matrix of the reference layer to obtain a first left unitary matrix, a first singular value matrix and a first right unitary matrix of the reference layer;

multiplying the first left unitary matrix by the first singular value matrix and arranging the first left unitary matrix and the first singular value matrix according to rows to obtain a middle matrix of the reference layer;

performing singular value decomposition on the intermediate matrix according to a preset truncation error to obtain a base matrix, a second singular value matrix and a second right unitary matrix of the reference layer;

and generating a coupling matrix of the reference layer according to the base matrix of the reference layer.

In one embodiment, the step of generating the coupling matrix of the reference layer according to the base matrix of the reference layer includes:

according to the formula:

generating a coupling matrix for the reference layer; wherein L represents the reference layer, i represents a non-null subgroup of the reference layer, and j represents any non-null subgroup in a set of far-field-acting non-null subgroups corresponding to the non-null subgroup iA second matrix of singular values representing the reference layer,a second right unitary matrix representing the reference layerThe conjugate transpose of (a) is performed,a first right unitary matrix representing the reference layer,a base matrix representing the reference layerThe conjugate of (a) to (b),a coupling matrix representing the reference layer.

In one embodiment, the step of generating the second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer comprises:

according to the formula:

generating a second impedance matrix for the reference layer; wherein Z (L) represents the referenceA second impedance matrix of the layer is formed,a base matrix representing all of the reference layersThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the reference layer,representing all of the basis matrix composition of the reference layerTranspose of the diagonal matrix of (a).

In one embodiment, the obtaining the base matrix of the parent layer according to the base matrix of the target layer and the first impedance matrix includes:

multiplying the base matrix of the target layer by a first left unitary matrix of a first impedance matrix of the target layer to obtain a transfer matrix of the target layer;

and multiplying the transfer matrix of the target layer by the base matrix of the target layer to obtain the base matrix of the parent layer.

In one embodiment, the obtaining the first impedance matrix of the parent layer, the first impedance matrix of the parent layer storing data corresponding to far-field weak interaction between non-empty subgroups in the parent layer, and the generating the coupling matrix of the parent layer according to the first impedance matrix of the parent layer and the base matrix includes:

according to the formula:

generating a coupling matrix of the parent layer; wherein L-1 represents the parent layer,anda base matrix representing the parent layer,to representThe conjugate transpose of (a) is performed,a first impedance matrix representing the parent layer.

In one embodiment, the generating the second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer includes:

according to the formula:

generating a second impedance matrix of the parent layer; wherein Z (L-1) represents a second impedance matrix of the parent layer,base matrix representing all of the parent layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the parent layer,representing the composition of all base matrices of the parent layerTranspose of the diagonal matrix of (a).

A system for fast analysis of magnetic resonance radio frequency coils based on the moment method, comprising:

the modeling module is used for acquiring input parameter information of the magnetic resonance radio frequency coil and establishing an octree data structure according to the parameter information of the magnetic resonance radio frequency coil;

a reference layer first impedance matrix obtaining module, configured to select a reference layer of the octree data structure, and obtain a first impedance matrix of the reference layer, where data stored in the first impedance matrix is an impedance matrix sub-block corresponding to a far-field weak interaction between non-empty sub-groups in the reference layer;

the reference layer calculation module is used for performing singular value decomposition on the first impedance matrix of the reference layer to obtain a base matrix and a coupling matrix of the reference layer;

the reference layer second impedance matrix generation module is used for generating a second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer;

a parent layer first calculation module, configured to use a reference layer as a target layer, obtain a parent layer of the target layer, where the parent layer is an upper layer adjacent to the target layer, and obtain a base matrix of the parent layer according to the base matrix of the target layer and a first impedance matrix if the parent layer is not a maximum layer of the octree data structure;

the second computation module of the parent layer is used for obtaining a first impedance matrix of the parent layer, the data stored in the first impedance matrix of the parent layer are impedance matrix subblocks corresponding to the far-field weak interaction between the non-empty subgroups in the parent layer, and a coupling matrix of the parent layer is generated according to the first impedance matrix of the parent layer and a base matrix;

the parent layer second impedance matrix generation module is used for generating a second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer;

and the iteration module is used for taking the parent layer as a target layer and iteratively executing the parent layer of the target layer.

In one embodiment, the system further comprises:

the far-field action excitation coefficient acquisition module of the specific non-empty subgroup of the reference layer is used for selecting any non-empty subgroup from the non-empty subgroups of the reference layer as a specific non-empty subgroup, acquiring a base matrix of an input voltage and/or a current source and the specific non-empty subgroup of the reference layer, and calculating to obtain a far-field action excitation coefficient of the specific non-empty subgroup of the reference layer;

a far-field action excitation coefficient acquisition module of a non-empty subgroup corresponding to a parent layer, configured to acquire the parent layer of the target layer by using the reference layer as the target layer, where the parent layer is an upper layer adjacent to the target layer, and if the far-field action excitation coefficient is acquired, the far-field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer on the parent layer is calculated according to the far-field action excitation coefficient of the specific non-empty subgroup of the target layer and the transfer matrix of the target layer;

a far-field action excitation coefficient acquisition module of the non-empty subgroup corresponding to the octree, configured to take the parent layer as a target layer, and iteratively execute the step of acquiring the parent layer of the target layer, so as to obtain a far-field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer in each layer of the octree data structure;

a far-field-effect total excitation coefficient acquisition module, configured to calculate and obtain a far-field-effect excitation coefficient set of each layer in the octree data structure according to the coupling matrix of each layer in the octree data structure, calculate and obtain a far-field-effect excitation coefficient of each layer according to the far-field-effect excitation coefficient set of each layer, and calculate and obtain a far-field-effect total excitation coefficient of the octree data structure according to the far-field-effect excitation coefficient of each layer;

the near-field action total excitation coefficient acquisition module is used for acquiring a near-field action impedance matrix of each layer in the octree data structure, calculating to obtain a near-field action excitation coefficient of each layer in the octree data structure according to input current and/or voltage sources, and calculating to obtain a near-field action total excitation coefficient of the octree data structure according to the near-field action excitation coefficients of each layer;

and the excitation coefficient acquisition module of the magnetic resonance radio frequency coil is used for calculating the excitation coefficient of the magnetic resonance radio frequency coil according to the far field action total excitation coefficient and the near field action total excitation coefficient of the octree data structure.

In one embodiment, the modeling module comprises:

the cubic space coordinate model establishing module is used for establishing a cubic space coordinate model, and the cubic space coordinate model is a minimum cubic space which completely surrounds the magnetic resonance radio frequency coil;

the dividing module is used for dividing the cubic space coordinate model into eight sub-cubic space coordinate models with the same size;

and the octree establishing module is used for carrying out iterative segmentation on the subcube space coordinate model according to the parameter information of the magnetic resonance radio frequency coil and establishing an octree data structure.

In one embodiment, the reference layer first impedance matrix obtaining module includes:

the reference layer selection module is used for selecting a reference layer of the octree data structure;

the specific non-empty subgroup acquisition module is used for acquiring a specific non-empty subgroup of the reference layer and a non-empty subgroup set corresponding to the specific non-empty subgroup through far-field weak interaction;

and the parameter acquisition module is used for acquiring a first impedance matrix of the reference layer according to the specific non-empty subgroup and the far-field acting non-empty subgroup set corresponding to the specific non-empty subgroup.

In one embodiment, the reference layer calculation module comprises:

the first singular value decomposition module is used for performing singular value decomposition on the first impedance matrix of the reference layer to obtain a first left unitary matrix, a first singular value matrix and a first right unitary matrix of the reference layer;

the middle matrix acquisition module is used for multiplying the first left unitary matrix and the first singular value matrix and arranging the first left unitary matrix and the first singular value matrix according to rows to obtain a middle matrix of the reference layer;

the second singular value decomposition module is used for performing singular value decomposition on the intermediate matrix according to a preset truncation error to obtain a base matrix, a second singular value matrix and a second right unitary matrix of the reference layer;

and the coupling matrix generating module is used for generating the coupling matrix of the reference layer according to the base matrix of the reference layer.

In one embodiment, the coupling matrix generation module generates the coupling matrix according to the formula:

generating a coupling matrix for the reference layer; wherein L represents the reference layer, i represents a non-null subgroup of the reference layer, and j represents any non-null subgroup in a set of far-field-acting non-null subgroups corresponding to the non-null subgroup iA second matrix of singular values representing the reference layer,a second right unitary matrix representing the reference layerThe conjugate transpose of (a) is performed,a first right unitary matrix representing the reference layer,a base matrix representing the reference layerThe conjugate of (a) to (b),a coupling matrix characterizing the reference layer is shown.

In one embodiment, the reference layer second impedance matrix generation module generates the reference layer second impedance matrix according to the formula:

generating a second impedance matrix for the reference layer; wherein Z (L) represents a second impedance matrix of the reference layer,a base matrix representing all of the reference layersThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the reference layer,representing all of the basis matrix composition of the reference layerTranspose of the diagonal matrix of (a).

In one embodiment, the parent-layer first computing module comprises:

a transfer matrix obtaining module, configured to multiply the base matrix of the target layer by a first left unitary matrix of a first impedance matrix of the target layer to obtain a transfer matrix of the target layer;

and the parent layer base matrix acquisition module is used for multiplying the transfer matrix of the target layer by the base matrix of the target layer to obtain the base matrix of the parent layer.

In one embodiment, the parent layer second computation module:

generating a coupling matrix of the parent layer; wherein L-1 represents the parent layer,anda base matrix representing the parent layer,to representThe conjugate transpose of (a) is performed,a first impedance matrix representing the parent layer.

In one embodiment, the parent layer second impedance matrix generation module generates the second impedance matrix according to the formula:

generating a second impedance matrix of the parent layer; wherein Z (L-1) represents a second impedance matrix of the parent layer,base matrix representing all of the parent layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the parent layer,representing the composition of all base matrices of the parent layerTranspose of the diagonal matrix of (a).

The method and the system for rapidly analyzing the magnetic resonance radio frequency coil based on the moment method are characterized in that an octree data structure is established for the magnetic resonance radio frequency coil, a reference layer of the octree data structure is selected as a target layer, singular value decomposition is carried out on a far-field weak-acting impedance matrix of the target layer to obtain a base matrix, a coupling matrix and a transfer matrix of the target layer, and then the base matrix and the coupling matrix of a parent layer adjacent to the target layer can be calculated, so that an impedance matrix sub-block corresponding to the far-field weak interaction of the parent layer can be stored and converted into an H-matrix form by a first impedance matrix in an H-matrix form²-a second impedance matrix storage in matrix form, reducing memory requirements. Then selecting the parent layer as a target layer, and continuing to perform iterative computation, thereby converting all far-field weak-acting impedance matrixes of the octree data structure into impedance matrixesH²-matrix form. Computing H from matrix vector multiplication²A second impedance matrix in matrix form, enabling a reduction of the computational complexity even in high field environments, thereby reducing the memory requirements and computation time of the computer, and thus a fast analysis of the magnetic resonance radio frequency coil.

Drawings

FIG. 1 is a schematic flow chart of a method for fast analysis of a magnetic resonance RF coil based on a moment method in one embodiment;

FIG. 2 is a flow chart illustrating a method for fast moment method-based analysis of a magnetic resonance RF coil in one embodiment;

FIG. 3 is a schematic diagram of octree data structure generation;

FIG. 4 is a flow chart illustrating a method for fast moment method based analysis of a magnetic resonance RF coil in one embodiment;

FIG. 5 is an exploded view of an impedance matrix;

FIG. 6 is a flow chart illustrating a method for fast moment method based analysis of a magnetic resonance RF coil in one embodiment;

FIG. 7 is a schematic diagram of a first impedance matrix being transformed into a second impedance matrix;

FIG. 8 is a flow chart illustrating a method for fast moment method based analysis of a magnetic resonance RF coil in one embodiment;

FIG. 9 is a schematic diagram of a system for fast analysis of a magnetic resonance RF coil based on a moment method in one embodiment;

FIG. 10 is a schematic diagram of a system for fast analysis of a magnetic resonance RF coil based on a moment method, according to one embodiment;

FIG. 11 is a schematic diagram of the structure of the modeling module of FIG. 9;

FIG. 12 is a schematic structural diagram of a first impedance matrix obtaining module of the reference layer in FIG. 9;

FIG. 13 is a schematic diagram of a reference layer calculation module shown in FIG. 9;

fig. 14 is a schematic structural diagram of a first calculation module in the parent layer of fig. 9.

Detailed Description

In one embodiment, as shown in fig. 1, a method for fast analysis of a magnetic resonance radio frequency coil based on a moment method includes the steps of:

and S102, acquiring the input parameter information of the magnetic resonance radio frequency coil, and establishing an octree data structure according to the parameter information of the magnetic resonance radio frequency coil.

In this embodiment, the parameter information of the magnetic resonance rf coil may be a volume, a spatial coordinate, an electromagnetic wavelength generated when the coil works, and the like of the magnetic resonance rf coil, and the octree data structure is a spatial stereo model obtained by iteratively dividing a minimum cubic space completely surrounding the magnetic resonance rf coil.

In one embodiment, as shown in fig. 2, step S102 includes:

step S202, a cubic space coordinate model is established, wherein the cubic space coordinate model is the minimum cubic space which completely surrounds the magnetic resonance radio frequency coil.

Specifically, a spatial coordinate model, namely the maximum layer of the octree data structure, is established by using Ansys according to parameter information of the magnetic resonance radio frequency coil. On the premise that the space coordinate model can completely surround the magnetic resonance radio frequency coil, the space volume of the space coordinate model is as minimum as possible, so that the calculation amount and the calculation complexity of a computer are reduced.

And step S204, dividing the cubic space coordinate model into eight sub-cubic space coordinate models with equal size.

Specifically, a triangular mesh based on RWG (Rao-Wilton-Glisson) basis functions is used for segmenting the cubic space coordinate model. And after the cubic space coordinate model is divided for the first time, a first sublayer is obtained, and the number of the cubic space coordinate models in the first sublayer is 8.

And S206, performing iterative segmentation on the sub-cube space coordinate model according to the parameter information of the magnetic resonance radio frequency coil, and establishing an octree data structure.

Specifically, each subcube space coordinate model in the first sublayer is subdivided into eight smaller subcube space coordinate models with the same size, so as to obtain a second sublayer, wherein the number of the smaller subcube space coordinate models in the second sublayer is 8²I.e. 64. The smaller sub-cube space coordinate models are subjected to iterative segmentation according to parameter information of the magnetic resonance radio frequency coil, each segmentation can obtain a sub-layer, and the number of the sub-cube space coordinate models in the nth sub-layer is 8ⁿAnd (4) respectively. Combining all sub-layers creates an octree data structure. In this embodiment, when the side length of the sub-cube space coordinate model in the nth sub-layer is about 10 times of the wavelength of the electromagnetic wave generated by the magnetic resonance radio frequency coil, the optimum octree data structure is obtained.

For example, as shown in FIG. 3, a schematic is generated for an octree data structure. 302 is a cubic spatial coordinate model completely surrounding the magnetic resonance radio frequency coil, i.e. is the largest layer, 304 is a first division of the cubic spatial coordinate model 302, i.e. is the first sublayer, each subcube spatial coordinate model of the first sublayer 304 is divided into eight smaller subcube spatial coordinate models again, and the second sublayer 306 is obtained. And continuously segmenting according to the parameter information of the magnetic resonance radio frequency coil, obtaining one sub-layer by one segmentation, and combining the maximum layer with all the sub-layers to establish an octree data structure.

And step S104, selecting a reference layer of an octree data structure, and acquiring a first impedance matrix of the reference layer, wherein data stored in the first impedance matrix are impedance matrix sub-blocks corresponding to the far-field weak interaction between non-empty sub-groups in the reference layer.

In this embodiment, the reference layer is the layer whose side length of the subcube space coordinate model is the smallest among all layers of the octree data structure. The subgroups are divided into a null subgroup and a non-null subgroup, the null subgroup is a cubic space coordinate model unit of which the internal structure does not contain the magnetic resonance radio frequency coil, and the non-null subgroup is a cubic space coordinate model unit of which the internal structure contains the magnetic resonance radio frequency coil.

In one embodiment, as shown in fig. 4, step S104 includes:

step S402, selecting a reference layer of the octree data structure.

In step S404, a specific non-empty subgroup of the reference layer and a non-empty subgroup set corresponding thereto through a far-field weak interaction are obtained.

Specifically, the interaction between the non-empty and non-empty subgroups is divided into a near field strength interaction and a far field weak interaction. The specific non-empty subgroup may be any non-empty subgroup of the reference layer that has a corresponding set of near/far field active non-empty subgroups at the reference layer.

Further, the set of far-field-acting non-null subsets corresponding to different non-null subsets is different. The interaction between the different non-empty subgroups and their corresponding set of non-empty subgroups is in the form of an impedance matrix.

As shown in fig. 5, the impedance matrix 500 is decomposed in one dimension into a near field strongly acting impedance matrix 502 and a far field weakly acting impedance matrix 504.

Step S406, obtaining the impedance matrix sub-block of the reference layer corresponding to the far-field weak interaction stored in the first impedance matrix according to the specific non-empty sub-group and the far-field acting non-empty sub-group set corresponding to the specific non-empty sub-group.

In this embodiment, the impedance matrix sub-block corresponding to the far-field weak interaction between a particular non-null subgroup of the reference layer and its corresponding set of far-field acting non-null subgroups constitutes the first impedance matrix of the reference layer.

And S106, performing singular value decomposition on the first impedance matrix of the reference layer to obtain a base matrix and a coupling matrix of the reference layer.

In this embodiment, the base matrix is in the form of a non-empty subgroup spatial coordinate, and the coupling matrix is a spatial coordinate relationship between a specific non-empty subgroup and a plurality of non-empty subgroups in the far-field-effect non-empty subgroup set corresponding to the specific non-empty subgroup.

In one embodiment, as shown in fig. 6, step S106 further includes:

step S602, performing singular value decomposition on the first impedance matrix of the reference layer to obtain a first left unitary matrix, a first singular value matrix, and a first right unitary matrix of the reference layer.

In this embodiment, for a specific non-null subgroup i, j of the reference layer, which is any non-null subgroup in the far-field-acting non-null subgroup set corresponding to the specific non-null subgroup i, the first impedance matrix is a far-field weak-acting impedance matrix between the specific non-null subgroup i and the non-null subgroup set where the non-null subgroup j is located. Since the far field weakly acting impedance matrix is a sparse matrix, new forms of storage can be regenerated to reduce memory requirements.

Specifically, according to the formula:

singular value decomposition is performed on the first impedance matrix of the reference layer. Wherein, L represents a reference layer,a first matrix of impedances is represented that is,representing a first left unitary matrix of a first type,representing a first right unitary matrix,representing a first matrix of singular values.

Step S604, the first left unitary matrix is multiplied by the first singular value matrix and arranged in rows to obtain an intermediate matrix of the reference layer.

In this embodiment, a first left unitary matrix corresponding to a specific non-empty subgroup i is multiplied by a first singular value matrix, and the products are arranged in rows to obtain an intermediate matrix of the reference layer. Specifically, according to the formula:

computing an intermediate matrix B_Li。

Step S606, according to the preset truncation error, singular value decomposition is carried out on the intermediate matrix to obtain a base matrix of the reference layer, a second singular value matrix and a second right unitary matrix.

In this embodiment, the truncation error may be determined according to the calculation accuracy requirement, and it is used to determine that the product of the base matrix of the reference layer, the second singular value matrix, and the second right unitary matrix is similar to the accuracy of the middle matrix.

According to a preset truncation error, according to the formula:

the intermediate matrix of the reference layer is subjected to singular value decomposition to obtain a base matrix, a second singular value matrix and a second right unitary matrix of the reference layer. Wherein, B_LiAn intermediate matrix representing the reference layer is shown,a base matrix representing a base layer of the reference layer,and isA second matrix of singular values representing the reference layer,representing a second right unitary matrix.

Specifically, the intermediate matrix is decomposed to obtain a second singular value matrix. When the singular value of the second singular value matrixLess than or equal to the truncation error andwhen the error is larger than the truncation error, selecting a singular valueAnd the corresponding left singular vector and right singular vector form a base matrix and a second right unitary matrix of the reference layer.

In step S608, a coupling matrix of the reference layer is generated based on the base matrix of the reference layer.

In this embodiment, the second right unitary matrix of the reference layer is usedIs shown asAccording to the formula:

a coupling matrix for the reference layer is calculated. Wherein L represents a reference layer, i represents a specific non-null subgroup of the reference layer, and j represents any non-null subgroup in a set of far-field-acting non-null subgroups corresponding to the specific non-null subgroup iA second matrix of singular values representing the reference layer,second right unitary matrix representing reference layerThe conjugate transpose of (a) is performed,a first right unitary matrix representing a reference layer,base matrix representing a reference layerThe conjugate of (a) to (b),representing the coupling matrix of the reference layer.

And step S108, generating a second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer.

In the present embodiment, according to the formulaA second impedance matrix for the reference layer may be generated. Wherein Z (L) represents a second impedance matrix of the reference layer,base matrix representing all non-empty subgroups of reference layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the reference layer is shown,composition of basis matrix representing all non-empty subgroups of reference layerTranspose of the diagonal matrix of (a). At this time, the first impedance matrix of the reference layer is changed from the original H-matrix form to H of the second impedance matrix²-matrix form, reducing memory requirements.

Specifically, fig. 7 is a schematic diagram of a change from the first impedance matrix of the reference layer to the second impedance matrix. 702 is a first impedance matrix of the reference layer, 704 is a second impedance matrix of the reference layer, 706 is a diagonal matrix composed of all the base matrices of the reference layer, 708 is a coupling matrix of the reference layer, and 710 is a transposed matrix of the diagonal matrix composed of all the base matrices of the reference layer.

And step S110, taking the reference layer as a target layer, acquiring a parent layer of the target layer, wherein the parent layer is an upper layer adjacent to the target layer, and if the parent layer is not the maximum layer of the octree data structure, obtaining a base matrix of the parent layer according to the base matrix of the target layer and the first impedance matrix.

Further, in one embodiment, if the parent level is the largest level of the octree data structure, then stop.

In one embodiment, as shown in fig. 8, step S110 includes:

step S111, the base matrix of the target layer is multiplied by the first left unitary matrix of the first impedance matrix of the target layer to obtain a transition matrix of the target layer.

In this embodiment, the first left unitary matrix of the first impedance matrix of the target layer is the first left unitary matrix obtained when the first impedance matrix of the reference layer is subjected to the first singular value decomposition. The transition matrix represents the relationship between the base matrix of the target layer and the base matrix corresponding to the target layer in the parent layer. And calculating a transfer matrix of the base matrix of the specific non-empty subgroup corresponding to the base matrix of the specific non-empty subgroup on the parent layer according to the obtained base matrix of the specific non-empty subgroup of the target layer.

Specifically, according to a calculation formulaAnd calculating a transfer matrix from the specific non-empty subgroup i of the target layer L to the specific non-empty subgroup i corresponding to the parent layer L-1.A transition matrix representing a particular non-empty subgroup i of the target layer L to a particular non-empty subgroup i corresponding to the parent layer L-1,the basis matrix corresponding to a particular non-empty subgroup i representing the target layer L,the first left unitary matrix representing the target layer L (i.e. in equation (1)))。

And step S113, multiplying the transfer matrix of the target layer by the base matrix of the target layer to obtain the base matrix of the parent layer.

In this embodiment, according to the formula:

the base matrix of a particular non-empty subgroup i of the parent layer is computed. Wherein,a base matrix representing a particular non-empty subgroup i of the parent layer,a base matrix representing a particular non-empty subgroup i of the target layer,a transition matrix representing a particular non-empty subgroup i of the target layer.

Step S112, a first impedance matrix of the parent layer is obtained, data stored in the first impedance matrix of the parent layer are impedance matrix subblocks corresponding to the far-field weak interaction between the non-empty subgroups in the parent layer, and a coupling matrix of the parent layer is generated according to the first impedance matrix of the parent layer and the base matrix.

In this embodiment, according toThe coupling matrix of the parent layer can be obtained. Wherein,a coupling matrix between a particular non-empty subgroup i of the parent layer and any non-empty subgroup j of its corresponding set of far-field-effect non-empty subgroups,anda base matrix representing any non-empty subgroup j of the set of specific non-empty subgroups i of the parent layer and the corresponding set of far-field-effect non-empty subgroups,andto representAndthe conjugate transpose of (c).

And step S114, generating a second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer.

In the present embodiment, according to the formulaA second impedance matrix for the parent layer may be derived. Wherein Z (L-1) represents a second impedance matrix of the parent layer,base matrix representing all of parent layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing a parent layer of the device,composition of base matrix representing all of parent layerTranspose of the diagonal matrix of (a).

Further, after the second impedance matrix of the parent layer is generated, the parent layer is used as a target layer, and then the second impedance matrix of the parent layer is generated until the data of all layers of the octree data structure are converted from the form stored by the first impedance matrix to the form stored by the second impedance matrix. The second impedance matrix has a smaller memory space and thus a lower memory requirement than the first impedance matrix.

Further, in one embodiment, after generating the second impedance matrices for each layer of the octree data structure, the corresponding first impedance matrices for each layer may be removed.

In another embodiment, after the step of building the octree data structure, the method further comprises:

and acquiring the input current and/or voltage source and the near-field action impedance matrix of each layer in the octree data structure, and calculating to obtain the near-field action excitation coefficient of each layer in the octree data structure.

In the present embodiment, Z is given by the formula U ═ Z^NFX calculate the near-field effect excitation coefficients for the layers in the octree data structure. U is the near-field effect excitation coefficient of each layer in the octree data structure, Z^NFThe impedance matrix is acted upon for the near field in each layer, and x is the current and/or voltage source drawn.

And calculating the total near-field effect excitation coefficient of the octree data structure according to the near-field effect excitation coefficients of all layers of the octree data structure.

In one embodiment, after the step of obtaining the base matrix and the coupling matrix of the reference layer, the method further includes:

and selecting any non-empty subgroup from the non-empty subgroups of the reference layer as a specific non-empty subgroup, acquiring the input voltage and/or current source and a base matrix of the specific non-empty subgroup of the reference layer, and calculating to obtain a far-field action excitation coefficient of the specific non-empty subgroup of the reference layer.

In this embodiment, according toThe far-field contribution excitation coefficients of a particular non-empty subgroup i of the reference layer are calculated. Wherein, f (L)_i) The far-field-acting excitation coefficient for a particular non-empty subgroup i of the reference layer L, x is the input voltage and/or current source,transposing a base matrix of a particular non-empty subgroup i of the reference layer L, x_iIndicating the limitation of the voltage and/or current source of the input on a particular non-empty subgroup i.

And calculating to obtain a far-field acting excitation coefficient set of the reference layer according to the coupling matrix of the reference layer, and calculating to obtain a far-field acting excitation coefficient of the reference layer according to the far-field acting excitation coefficient set of the reference layer.

In this embodiment, according toAnd calculating a far-field action excitation coefficient set of the reference layer. Wherein u (L)_i) Is the Far-field acting excitation coefficient set of the reference layer, j is the Far-field acting non-null subgroup set Far (L) corresponding to the specific non-null subgroup i of each layer_i) Any one of the non-empty subgroups of (1),is the coupling matrix between specific non-empty subgroups i and j of the reference layer, f (L)_j) The far field contribution excitation coefficients for a particular non-empty subgroup i of the reference layer. Further, the far-field effect excitation coefficient u (L) of the reference layer is determined_i) Base matrix of aggregate and reference layersMultiplying to obtain the far-field action excitation coefficient g (L) of the reference layer_i)。

In one embodiment, the step of taking the reference layer as the target layer and obtaining the parent layer of the target layer further includes:

and obtaining a transfer matrix of the target layer according to the base matrix and the first impedance matrix of the target layer.

Specifically, in this embodiment, the base matrix of the specific non-empty subgroup i of the target layer is multiplied by the first left unitary matrix of the first impedance matrix of the target layer to obtain the transfer matrix of the specific non-empty subgroup i of the target layer, where the transfer matrix represents the transfer relationship between the specific non-empty subgroup i of the target layer and the corresponding non-empty subgroup i of the parent layer.

And calculating the far field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer on the parent layer according to the far field action excitation coefficient of the specific non-empty subgroup of the target layer and the transfer matrix of the target layer.

In the present embodiment, the far-field effect excitation coefficient f ((l +1) of a specific non-empty subgroup i) of the target layer l +1 is determined_i) Transfer matrix with target layer lMultiplying to obtain the far-field action excitation coefficient f (l) of the specific non-empty subgroup i of the parent layer l_i)。

In one embodiment, after the step of generating the coupling matrix of the parent layer, the method further includes:

and calculating to obtain a far-field action excitation coefficient set of the parent layer according to the far-field action excitation coefficients of the corresponding non-empty subgroups on the parent layer and the coupling matrix of the parent layer, and calculating to obtain the far-field action excitation coefficients of the parent layer according to the far-field action excitation coefficient set of the parent layer.

In this embodiment, according toAnd calculating a far-field action excitation coefficient set of each layer. Wherein u (_li) For each layer of the set of Far-field-effect excitation coefficients, j is the set of Far-field-effect non-null subgroups Far (l) corresponding to the specific non-null subgroup i of each layer_i) Any one of the non-empty subgroups of (1),for the coupling matrix between specific non-empty subgroups i and j of each layer, f (l)_j) The excitation coefficients are the far field contributions of the specific non-empty subgroup i of each layer.

Further according to the formulaObtaining the excitation coefficient g (l) of the far field action of the father layer_i)，g[(l+1)_jThe excitation coefficient is applied to the far field of the target layer.

In one embodiment, further comprising: and calculating the far field action total excitation coefficient of the octree data structure according to the far field action excitation coefficients of all layers in the octree data structure.

In this embodiment, according to(wherein, 2)<l<L), obtaining the total excitation coefficient of the far field effect of the octree data structure.

And calculating to obtain the excitation coefficient of the magnetic resonance radio frequency coil according to the far field action total excitation coefficient and the near field action total excitation coefficient of the octree data structure.

Specifically, the total excitation coefficient of the octree data structure far-field effect and the total excitation coefficient of the near-field effect are added to obtain the excitation coefficient of the magnetic resonance radio frequency coil.

The method for fast analyzing the magnetic resonance radio frequency coil based on the moment method in the above embodiments is described as a specific application scenario. Firstly, acquiring input parameter information of the magnetic resonance radio frequency coil, wherein the parameter information can be volume, space coordinates, generated electromagnetic wave wavelength and the like of the coil, and establishing an octree data structure according to the parameter information of the magnetic resonance radio frequency coil.

Further, after the octree data structure is established, a reference layer of the octree data structure is selected, a first impedance matrix of the reference layer is obtained, then a base matrix and a coupling matrix of the reference layer can be obtained according to the first impedance matrix of the reference layer, and then a second impedance matrix of the reference layer is generated by the base matrix and the coupling matrix of the reference layer.

Further, the reference layer is used as a target layer, a parent layer of the target layer is obtained, and a transfer matrix of the target layer can be obtained according to the reference layer of the target layer and the first impedance matrix. And further obtaining the base matrix of the parent layer through the base matrix and the transfer matrix of the target layer. And then, according to the acquired first impedance matrix of the parent layer and the acquired base matrix of the parent layer, obtaining a coupling matrix of the parent layer, and then generating a second impedance matrix of the parent layer by the base matrix of the parent layer and the coupling matrix. And finally, taking the father layer as a target layer, and iteratively executing the step of obtaining the father layer of the target layer to obtain a second impedance matrix of each layer of the octree data structure.

In another embodiment, the input current and/or voltage source and the near-field effective impedance matrix of each layer in the octree data structure can be obtained, and the near-field effective excitation coefficient of each layer of the octree data structure can be calculated. And acquiring the input current and/or voltage source and a base matrix, a coupling matrix and a transfer matrix of each layer of the octree data structure, and calculating to obtain the near-field action excitation coefficient of each layer of the octree data structure.

Further, according to the near/far field effect excitation coefficients of all layers in the octree data structure, calculating to obtain the near/far field effect total excitation coefficient of the octree data structure, and according to the near/far field effect total excitation coefficient of the model, calculating to obtain the excitation coefficient of the magnetic resonance radio frequency coil.

As shown in fig. 9, in one embodiment, the system for fast analyzing a magnetic resonance radio frequency coil based on a moment method includes a modeling module 102, a reference layer first impedance matrix obtaining module 104, a reference layer calculating module 106, a reference layer second impedance matrix generating module 108, a parent layer first calculating module 110, a parent layer second calculating module 112, a parent layer second impedance matrix generating module 114, and an iteration module 116, wherein:

the modeling module 102 is configured to obtain input parameter information of the magnetic resonance radio frequency coil, and establish an octree data structure according to the parameter information of the magnetic resonance radio frequency coil.

The reference layer first impedance matrix obtaining module 104 is configured to select a reference layer of an octree data structure, and obtain a first impedance matrix of the reference layer, where data stored in the first impedance matrix is an impedance matrix sub-block corresponding to a far-field weak interaction between non-empty sub-groups in the reference layer.

And the reference layer calculation module 106 is configured to perform singular value decomposition on the first impedance matrix of the reference layer to obtain a base matrix and a coupling matrix of the reference layer.

And a reference layer second impedance matrix generating module 108, configured to generate a second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer.

And a parent layer first calculation module 110, configured to use the reference layer as a target layer, obtain a parent layer of the target layer, where the parent layer is an upper layer adjacent to the target layer, and obtain a base matrix of the parent layer according to the base matrix of the target layer and the first impedance matrix if the parent layer is not the maximum layer of the octree data structure.

And the parent layer second calculation module 112 is configured to obtain a first impedance matrix of the parent layer, where data stored in the first impedance matrix of the parent layer is an impedance matrix subblock corresponding to a far-field weak interaction between non-empty subgroups in the parent layer, and generate a coupling matrix of the parent layer according to the first impedance matrix of the parent layer and the base matrix.

And a parent layer second impedance matrix generating module 114, configured to generate a second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer.

And the iteration module 116 is configured to take the parent layer as the target layer, and perform iteration to obtain the parent layer of the target layer.

As shown in fig. 10, in another embodiment, the system for fast analyzing a magnetic resonance rf coil based on the moment method further includes a far-field excitation coefficient obtaining module 118 for a specific non-empty subgroup of the reference layer, a far-field excitation coefficient obtaining module 120 for a corresponding non-empty subgroup of the parent layer, a far-field excitation coefficient obtaining module 122 for a corresponding non-empty subgroup of the octree, a far-field total excitation coefficient obtaining module 124, a near-field total excitation coefficient obtaining module 126, and an excitation coefficient obtaining module 128 for a magnetic resonance rf coil, wherein:

and the far-field acting excitation coefficient acquisition module 118 for the specific non-empty subgroup of the reference layer is used for acquiring the input voltage and/or current source and the base matrix of the specific non-empty subgroup of the reference layer, and calculating to obtain the far-field acting excitation coefficient of the specific non-empty subgroup of the reference layer.

And a far-field action excitation coefficient acquisition module 120 of the non-empty subgroup corresponding to the parent layer, configured to acquire the parent layer of the target layer by using the reference layer as the target layer, where the parent layer is an upper layer adjacent to the target layer, and if the far-field action excitation coefficient is acquired, the far-field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer on the parent layer is calculated according to the far-field action excitation coefficient of the specific non-empty subgroup of the target layer and the transfer matrix of the target layer.

And the far-field action excitation coefficient acquisition module 122 of the non-empty subgroup corresponding to the octree is configured to take the parent layer as the target layer, and iteratively execute the step of acquiring the parent layer of the target layer to obtain the far-field action excitation coefficients of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer in each layer of the octree data structure.

And the far-field-effect total excitation coefficient acquisition module 124 is configured to calculate and obtain a far-field-effect excitation coefficient set of each layer in the octree data structure according to the coupling matrix of each layer in the octree data structure, calculate and obtain a far-field-effect excitation coefficient of each layer according to the far-field-effect excitation coefficient set of each layer, and calculate and obtain a far-field-effect total excitation coefficient of the octree data structure according to the far-field-effect excitation coefficient of each layer.

The near-field effect total excitation coefficient obtaining module 126 is configured to obtain a near-field effect impedance matrix of each layer in the octree data structure, calculate a near-field effect excitation coefficient of each layer in the octree data structure according to an input current and/or voltage source, and calculate a near-field effect total excitation coefficient of the octree data structure according to a near-field effect excitation coefficient of each layer.

And the excitation coefficient acquisition module 128 of the magnetic resonance radio frequency coil is configured to calculate an excitation coefficient of the magnetic resonance radio frequency coil according to the far-field effect total excitation coefficient and the near-field effect total excitation coefficient of the octree data structure.

As shown in FIG. 11, in one embodiment, modeling module 102 includes a cube space coordinate model building module 202, a segmentation module 204, and an octree building module 206, wherein:

a cubic space coordinate model establishing module 202, configured to establish a cubic space coordinate model, where the cubic space coordinate model is a minimum cubic space that completely surrounds the magnetic resonance radio frequency coil.

And the dividing module 204 is configured to divide the cube space coordinate model into eight sub-cube space coordinate models with equal sizes.

And the octree establishing module 206 is configured to iteratively partition the sub-cube space coordinate model according to the parameter information of the magnetic resonance radio frequency coil, and establish an octree data structure.

As shown in fig. 12, in one embodiment, the reference layer first impedance matrix obtaining module 104 includes a reference layer selecting module 402, a specific non-empty subgroup obtaining module 404 and a parameter obtaining module 406, wherein:

a reference layer selecting module 402, configured to select a reference layer of the octree data structure.

A specific non-empty subgroup acquisition module 404, configured to acquire a specific non-empty subgroup of the reference layer and a set of non-empty subgroups corresponding thereto through weak far-field interaction.

The parameter obtaining module 406 is configured to obtain a first impedance matrix of the reference layer according to the specific non-empty subgroup and the far-field-acting non-empty subgroup set corresponding to the specific non-empty subgroup.

As shown in fig. 13, in one embodiment, the reference layer calculation module 106 includes a first singular value decomposition module 602, an intermediate matrix acquisition module 604, a second singular value decomposition module 606, and a coupling matrix generation module 608, wherein:

the first singular value decomposition module 602 is configured to perform singular value decomposition on the first impedance matrix of the reference layer to obtain a first left unitary matrix, a first singular value matrix, and a first right unitary matrix of the reference layer.

The intermediate matrix obtaining module 604 multiplies the first left unitary matrix and the first singular value matrix and arranges the multiplied first left unitary matrix and the first singular value matrix in rows to obtain an intermediate matrix of the reference layer.

And a second singular value decomposition module 606, configured to perform singular value decomposition on the intermediate matrix according to the preset truncation error to obtain a base matrix, a second singular value matrix, and a second right unitary matrix of the reference layer.

A coupling matrix generating module 608, configured to generate a coupling matrix of the reference layer according to the base matrix of the reference layer.

In one embodiment, the coupling matrix generation module 608 generates the coupling matrix according to the formula:

generating a coupling matrix of the reference layer; wherein L represents a reference layer, i represents a non-null subgroup of the reference layer, and j represents any non-null subgroup in a set of far-field-acting non-null subgroups corresponding to the non-null subgroup iA second matrix of singular values representing the reference layer,second right unitary matrix representing reference layerThe conjugate transpose of (a) is performed,a first right unitary matrix representing a reference layer,base matrix representing a reference layerThe conjugate of (a) to (b),representing the coupling matrix of the reference layer.

In one embodiment, the reference layer second impedance matrix generation module 108 generates the reference layer second impedance matrix according to the formula:

generating a second impedance matrix of the reference layer; wherein Z (L) represents a second impedance matrix of the reference layer,) Base matrix representing all of the base layersThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the reference layer is shown,representing the composition of all basis matrices of the reference layerTranspose of the diagonal matrix of (a).

As shown in fig. 14, in one embodiment, the parent-layer first computation module 110 includes a transition matrix acquisition module 111 and a parent-layer base matrix acquisition module 113, wherein:

the transfer matrix obtaining module 111 is configured to multiply the base matrix of the target layer by the first left unitary matrix of the first impedance matrix of the target layer to obtain a transfer matrix of the target layer.

A parent layer base matrix obtaining module 113, configured to multiply the transfer matrix of the target layer with the base matrix of the target layer to obtain a base matrix of the parent layer.

In one embodiment, the parent layer second calculation module 112 calculates the value of:

generating a coupling matrix of a parent layer; wherein L-1 represents the parent layer,andthe base matrix representing the parent layer,to representThe conjugate transpose of (a) is performed,a first impedance matrix representing a parent layer.

In one embodiment, the parent layer second impedance matrix generation module 114 generates the impedance matrix according to the formula:

generating a second impedance matrix of the parent layer; wherein Z (L-1) represents a second impedance matrix of the parent layer,base matrix representing all of parent layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing a parent layer of the device,composition of base matrix representing all of parent layerTranspose of the diagonal matrix of (a).

The method and the system for rapidly analyzing the magnetic resonance radio frequency coil based on the moment method are characterized in that an octree data structure is established for the magnetic resonance radio frequency coil, a reference layer of the octree data structure is selected as a target layer, singular value decomposition is carried out on a far-field weak-acting impedance matrix of the target layer to obtain a base matrix, a coupling matrix and a transfer matrix of the target layer, and then the base matrix and the coupling matrix of a parent layer adjacent to the target layer can be calculated, so that an impedance matrix sub-block corresponding to the far-field weak interaction of the parent layer can be stored and converted into an H-matrix form by a first impedance matrix in an H-matrix form²-a second impedance matrix storage in matrix form, reducing memory requirements. Then selecting the parent layer as a target layer, and continuing to perform iterative computation, thereby converting all far-field weak-acting impedance matrixes of the octree data structure into H²-matrix form. Computing H from matrix vector multiplication²A second impedance matrix in matrix form, enabling a reduction of the computational complexity even in high field environments, thereby reducing the memory requirements and computation time of the computer, and thus a fast analysis of the magnetic resonance radio frequency coil.

The above examples only show some embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (14)

1. A method for rapid analysis of a magnetic resonance radio frequency coil based on a moment method, comprising:

acquiring input parameter information of a magnetic resonance radio frequency coil, and establishing an octree data structure according to the parameter information of the magnetic resonance radio frequency coil;

selecting a reference layer of the octree data structure, and acquiring a first impedance matrix of the reference layer, wherein data stored in the first impedance matrix are impedance matrix sub-blocks corresponding to far-field weak interaction between non-empty sub-groups in the reference layer;

performing singular value decomposition on the first impedance matrix of the reference layer to obtain a base matrix and a coupling matrix of the reference layer, including: performing singular value decomposition on the first impedance matrix of the reference layer to obtain a first left unitary matrix, a first singular value matrix and a first right unitary matrix of the reference layer, multiplying the first left unitary matrix and the first singular value matrix and arranging the first left unitary matrix and the first singular value matrix in rows to obtain an intermediate matrix of the reference layer, performing singular value decomposition on the intermediate matrix according to a preset truncation error to obtain a base matrix, a second singular value matrix and a second right unitary matrix of the reference layer, generating a coupling matrix of the reference layer according to the base matrix of the reference layer, and generating a second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer;

taking a reference layer as a target layer, acquiring a parent layer of the target layer, wherein the parent layer is an upper layer adjacent to the target layer, and if the parent layer is not the maximum layer of the octree data structure, acquiring a base matrix of the parent layer according to the base matrix of the target layer and a first impedance matrix;

acquiring a first impedance matrix of the parent layer, wherein data stored in the first impedance matrix of the parent layer are impedance matrix subblocks corresponding to far-field weak interaction between non-empty subgroups in the parent layer, and generating a coupling matrix of the parent layer according to the first impedance matrix of the parent layer and a base matrix, and the method comprises the following steps: according toA coupling matrix for a parent layer can be derived, wherein L-1 denotes the parent layer,a coupling matrix between a particular non-empty subgroup i of the parent layer and any non-empty subgroup j of its corresponding set of far-field-effect non-empty subgroups,a first impedance matrix representing the parent layer,anda base matrix representing any non-empty subgroup j of the set of specific non-empty subgroups i of the parent layer and the corresponding set of far-field-effect non-empty subgroups,andto representAndthe specific non-empty subgroup is any non-empty subgroup of the reference layer, and the specific non-empty subgroup has a corresponding near-field-effect non-empty subgroup set or far-field-effect non-empty subgroup set on the reference layer;

generating a second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer, taking the parent layer as a target layer, and iteratively executing the step of obtaining the parent layer of the target layer, wherein the step of obtaining the parent layer of the target layer comprises the following steps: according to the formula:generating a second impedance matrix of the reference layer, wherein Z (L) represents the second impedance matrix of the reference layer,a base matrix representing all of the reference layersThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the reference layer,representing all of the basis matrix composition of the reference layerTranspose of the diagonal matrix of (a).

2. The method of claim 1, wherein the step of building an octree data structure is followed by the step of:

acquiring an input current and/or voltage source and a near-field action impedance matrix of each layer of the octree data structure, and calculating to obtain a near-field action excitation coefficient of each layer of the octree data structure;

calculating the total near-field effect excitation coefficient of the octree data structure according to the near-field effect excitation coefficients of all layers of the octree data structure;

after the step of obtaining the base matrix and the coupling matrix of the reference layer, the method further includes:

selecting any non-empty subgroup from the non-empty subgroups of the reference layer as a specific non-empty subgroup, acquiring input voltage and/or current sources and a base matrix of the specific non-empty subgroup of the reference layer, and calculating to obtain a far-field action excitation coefficient of the specific non-empty subgroup of the reference layer;

calculating to obtain a far-field action excitation coefficient set of the reference layer according to the coupling matrix of the reference layer, and calculating to obtain a far-field action excitation coefficient of the reference layer according to the far-field action excitation coefficient set of the reference layer;

after the step of taking the reference layer as the target layer and acquiring the parent layer of the target layer, the method further includes:

obtaining a transfer matrix of the target layer according to the base matrix and the first impedance matrix of the target layer;

calculating to obtain the far field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer on the parent layer according to the far field action excitation coefficient of the specific non-empty subgroup of the target layer and the transfer matrix of the target layer;

after the step of generating the coupling matrix of the parent layer, the method further includes:

calculating to obtain a far-field action excitation coefficient set of the parent layer according to the far-field action excitation coefficients of the corresponding non-empty subgroups on the parent layer and the coupling matrix of the parent layer, and calculating to obtain the far-field action excitation coefficients of the parent layer according to the far-field action excitation coefficient set of the parent layer;

the method further comprises the following steps:

calculating the total far field effect excitation coefficient of the octree data structure according to the far field effect excitation coefficients of all layers in the octree data structure;

and calculating the excitation coefficient of the magnetic resonance radio frequency coil according to the far field action total excitation coefficient and the near field action total excitation coefficient of the octree data structure.

3. The method of claim 1, wherein the step of building an octree data structure from the parameter information of the magnetic resonance radio frequency coil comprises:

establishing a cubic space coordinate model, wherein the cubic space coordinate model is a minimum cubic space which completely surrounds the magnetic resonance radio frequency coil;

dividing the cubic space coordinate model into eight sub-cubic space coordinate models with equal size;

and carrying out iterative segmentation on the subcube space coordinate model according to the parameter information of the magnetic resonance radio frequency coil, and establishing an octree data structure.

4. The method of claim 1, wherein the step of selecting a reference layer of the octree data structure and obtaining a first impedance matrix of the reference layer further comprises:

selecting a reference layer of the octree data structure;

acquiring a specific non-empty subgroup of the reference layer and a non-empty subgroup set corresponding to the specific non-empty subgroup through far-field weak interaction;

and acquiring a first impedance matrix of the reference layer according to the specific non-empty subgroup and the far-field acting non-empty subgroup set corresponding to the specific non-empty subgroup.

5. The method of claim 1, wherein the step of generating the coupling matrix for the reference layer from the base matrix for the reference layer comprises:

according to the formula:

${\hat{Z}}_L^{i\&times;j}=\&lsqb;{\hat{S}}_{Li}{\left({\hat{V}}_{Li}\right)}^H\&rsqb;{|}_j{V}^{r_{ij}\&times;j}{\left({\hat{U}}_{Lj}\right)}^C$

generating a coupling matrix for the reference layer; wherein L represents the reference layer, i represents a non-null subgroup of the reference layer, and j represents any non-null subgroup in a set of far-field-acting non-null subgroups corresponding to the non-null subgroup iA second matrix of singular values representing the reference layer,a second right unitary matrix representing the reference layerThe conjugate transpose of (a) is performed,a first right unitary matrix representing the reference layer,a base matrix representing the reference layerThe conjugate of (a) to (b),a coupling matrix representing the reference layer.

6. The method of claim 1, wherein the step of deriving the base matrix of the parent layer from the base matrix of the target layer and the first impedance matrix comprises:

multiplying the base matrix of the target layer by a first left unitary matrix of a first impedance matrix of the target layer to obtain a transfer matrix of the target layer;

and multiplying the transfer matrix of the target layer by the base matrix of the target layer to obtain the base matrix of the parent layer.

7. The method of claim 1, wherein the generating a second impedance matrix for the parent layer from the base matrix and the coupling matrix for the parent layer comprises:

according to the formula:

$Z(L-1)=diag\left({\hat{U}}_{(L-1)i}\right)\&CenterDot;\hat{Z}(L-1)\&CenterDot;{\left(diag\right({\hat{U}}_{(L-1)j}\left)\right)}^T$

generating a second impedance matrix of the parent layer; wherein Z (L-1) represents a second impedance matrix of the parent layer,base matrix representing all of the parent layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the parent layer,representing the composition of all base matrices of the parent layerTranspose of the diagonal matrix of (a).

8. A system for fast analysis of magnetic resonance radio frequency coils based on the moment method, comprising:

the modeling module is used for acquiring input parameter information of the magnetic resonance radio frequency coil and establishing an octree data structure according to the parameter information of the magnetic resonance radio frequency coil;

a reference layer first impedance matrix obtaining module, configured to select a reference layer of the octree data structure, and obtain a first impedance matrix of the reference layer, where data stored in the first impedance matrix is an impedance matrix sub-block corresponding to a far-field weak interaction between non-empty sub-groups in the reference layer;

the reference layer calculation module is used for performing singular value decomposition on the first impedance matrix of the reference layer to obtain a base matrix and a coupling matrix of the reference layer;

the reference layer second impedance matrix generation module is used for generating a second impedance matrix of the reference layer according to the base matrix and the coupling matrix of the reference layer;

a parent layer first calculation module, configured to use a reference layer as a target layer, obtain a parent layer of the target layer, where the parent layer is an upper layer adjacent to the target layer, and obtain a base matrix of the parent layer according to the base matrix of the target layer and a first impedance matrix if the parent layer is not a maximum layer of the octree data structure;

a parent layer second calculation module, configured to obtain a first impedance matrix of the parent layer, where data stored in the first impedance matrix of the parent layer is an impedance matrix subblock corresponding to a far-field weak interaction between non-empty subgroups in the parent layer, and generate a coupling matrix of the parent layer according to the first impedance matrix of the parent layer and a base matrix, where the method includes: according toA coupling matrix for a parent layer can be derived, wherein L-1 denotes the parent layer,a coupling matrix between a particular non-empty subgroup i of the parent layer and any non-empty subgroup j of its corresponding set of far-field-effect non-empty subgroups,a first impedance matrix representing the parent layer,anda base matrix representing any non-empty subgroup j of the set of specific non-empty subgroups i of the parent layer and the corresponding set of far-field-effect non-empty subgroups,andto representAndthe specific non-empty subgroup is any non-empty subgroup of the reference layer, and the specific non-empty subgroup has a corresponding near-field-effect non-empty subgroup set or far-field-effect non-empty subgroup set on the reference layer;

a parent layer second impedance matrix generation module, configured to generate a second impedance matrix of the parent layer according to the base matrix and the coupling matrix of the parent layer, including: according to the formula:generating a second impedance matrix of the reference layer, wherein Z (L) represents the second impedance matrix of the reference layer,a base matrix representing all of the reference layersThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the reference layer,representing all of the basis matrix composition of the reference layerTranspose of the diagonal matrix of (a);

an iteration module for taking the father layer as a target layer and performing the iteration to obtain the father layer of the target layer

The reference layer calculation module includes: the first singular value decomposition module is used for performing singular value decomposition on the first impedance matrix of the reference layer to obtain a first left unitary matrix, a first singular value matrix and a first right unitary matrix of the reference layer; an intermediate matrix obtaining module, configured to multiply the first left unitary matrix and the first singular value matrix and arrange the multiplied first left unitary matrix and the first singular value matrix in rows to obtain an intermediate matrix of the reference layer; the second singular value decomposition module is used for performing singular value decomposition on the intermediate matrix according to a preset truncation error to obtain a base matrix, a second singular value matrix and a second right unitary matrix of the reference layer; and the coupling matrix generating module is used for generating the coupling matrix of the reference layer according to the base matrix of the reference layer.

9. The system of claim 8, further comprising:

the far-field action excitation coefficient acquisition module of the specific non-empty subgroup of the reference layer is used for selecting any non-empty subgroup from the non-empty subgroups of the reference layer as a specific non-empty subgroup, acquiring a base matrix of an input voltage and/or a current source and the specific non-empty subgroup of the reference layer, and calculating to obtain a far-field action excitation coefficient of the specific non-empty subgroup of the reference layer;

a far-field action excitation coefficient acquisition module of a non-empty subgroup corresponding to a parent layer, configured to acquire the parent layer of the target layer by using the reference layer as the target layer, where the parent layer is an upper layer adjacent to the target layer, and if the far-field action excitation coefficient is acquired, the far-field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer on the parent layer is calculated according to the far-field action excitation coefficient of the specific non-empty subgroup of the target layer and the transfer matrix of the target layer;

a far-field action excitation coefficient acquisition module of the non-empty subgroup corresponding to the octree, configured to take the parent layer as a target layer, and iteratively execute the step of acquiring the parent layer of the target layer, so as to obtain a far-field action excitation coefficient of the non-empty subgroup corresponding to the specific non-empty subgroup of the target layer in each layer of the octree data structure;

a far-field-effect total excitation coefficient acquisition module, configured to calculate and obtain a far-field-effect excitation coefficient set of each layer in the octree data structure according to the coupling matrix of each layer in the octree data structure, calculate and obtain a far-field-effect excitation coefficient of each layer according to the far-field-effect excitation coefficient set of each layer, and calculate and obtain a far-field-effect total excitation coefficient of the octree data structure according to the far-field-effect excitation coefficient of each layer;

the near-field action total excitation coefficient acquisition module is used for acquiring a near-field action impedance matrix of each layer in the octree data structure, calculating to obtain a near-field action excitation coefficient of each layer in the octree data structure according to input current and/or voltage sources, and calculating to obtain a near-field action total excitation coefficient of the octree data structure according to the near-field action excitation coefficients of each layer;

and the excitation coefficient acquisition module of the magnetic resonance radio frequency coil is used for calculating the excitation coefficient of the magnetic resonance radio frequency coil according to the far field action total excitation coefficient and the near field action total excitation coefficient of the octree data structure.

10. The system of claim 8, wherein the modeling module comprises:

the cubic space coordinate model establishing module is used for establishing a cubic space coordinate model, and the cubic space coordinate model is a minimum cubic space which completely surrounds the magnetic resonance radio frequency coil;

the dividing module is used for dividing the cubic space coordinate model into eight sub-cubic space coordinate models with the same size;

and the octree establishing module is used for carrying out iterative segmentation on the subcube space coordinate model according to the parameter information of the magnetic resonance radio frequency coil and establishing an octree data structure.

11. The system of claim 8, wherein the reference layer first impedance matrix acquisition module comprises:

the reference layer selection module is used for selecting a reference layer of the octree data structure;

the specific non-empty subgroup acquisition module is used for acquiring a specific non-empty subgroup of the reference layer and a non-empty subgroup set corresponding to the specific non-empty subgroup through far-field weak interaction;

and the parameter acquisition module is used for acquiring a first impedance matrix of the reference layer according to the specific non-empty subgroup and the far-field acting non-empty subgroup set corresponding to the specific non-empty subgroup.

12. The system of claim 8, wherein the coupling matrix generation module generates the coupling matrix according to the formula:

${\hat{Z}}_L^{i\&times;j}=\&lsqb;{\hat{S}}_{Li}{\left({\hat{V}}_{Li}\right)}^H\&rsqb;{|}_j{V}^{r_{ij}\&times;j}{\left({\hat{U}}_{Lj}\right)}^C$

generating a coupling matrix for the reference layer; wherein L represents the reference layer, i represents a non-null subgroup of the reference layer, and j represents any non-null subgroup in a set of far-field-acting non-null subgroups corresponding to the non-null subgroup iA second matrix of singular values representing the reference layer,a second right unitary matrix representing the reference layerThe conjugate transpose of (a) is performed,a first right unitary matrix representing the reference layer,a base matrix representing the reference layerThe conjugate of (a) to (b),a coupling matrix representing the reference layer.

13. The system of claim 8, wherein the parent tier first computing module comprises:

a transfer matrix obtaining module, configured to multiply the base matrix of the target layer by a first left unitary matrix of a first impedance matrix of the target layer to obtain a transfer matrix of the target layer;

and the parent layer base matrix acquisition module is used for multiplying the transfer matrix of the target layer by the base matrix of the target layer to obtain the base matrix of the parent layer.

14. The system of claim 8, wherein the parent layer second impedance matrix generation module generates the impedance matrix according to the formula:

$Z(L-1)=diag\left({\hat{U}}_{(L-1)i}\right)\&CenterDot;\hat{Z}(L-1)\&CenterDot;{\left(diag\right({\hat{U}}_{(L-1)j}\left)\right)}^T$

generating a second impedance matrix of the parent layer; wherein Z (L-1) represents a second impedance matrix of the parent layer,base matrix representing all of the parent layerThe diagonal matrix is formed by the two groups of the diagonal matrix,a coupling matrix representing the parent layer,representing the composition of all base matrices of the parent layerTranspose of the diagonal matrix of (a).