CN112684392A - Design method of non-planar gradient coil - Google Patents
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Abstract
The invention discloses a design method of a non-planar gradient coil, which is composed of two arc surfaces formed by bending two circular surfaces at a certain angle, wherein target points are firstly divided on a sphere, magnetic field values of the gradient coil on the target points are respectively calculated by adopting a spherical harmonic function, then each vertex and each surface of a triangular grid are read, the arrangement sequence of the vertex and the surface is optimized, the size of a wire is set according to a boundary element method, the contribution value of an electrified wire in a source point area to a field point is calculated, the power consumption and the energy storage of the non-planar gradient coil are restrained to be minimum, the power consumption and the energy storage of the non-planar gradient coil are solved to be minimum, the current density distribution on the non-planar gradient coil is solved, and finally the winding shape of the non-planar gradient coil is obtained by a flow function method. The invention adopts the design method of the non-planar gradient coil, can increase the distance between the gradient coil and the pole head, reduce the eddy current generated on the pole head by the gradient coil and improve the image quality of the open MRI system.
Description
Technical Field
The invention relates to the field of magnetic resonance imaging system component design, in particular to a design method of a non-planar gradient coil.
Background
Magnetic Resonance Imaging (magnetic Resonance Imaging MRI) technology is a technology crossed by multiple technologies, including the subjects of electromagnetism, digital signal processing, biomedicine, atomic physics and the like, and compared with other medical Imaging technologies, MRI has the advantages of no radiation, high resolution, clear image quality and the like, so that the MRI technology has important clinical application value in medical examination, because the gradient coil is rapidly sheared, eddy current can be generated on the magnetic pole head, the electromagnetic field generated by the eddy current is superposed in the main magnetic field to influence the uniformity of the main magnetic field, the image quality of MRI is reduced, the eddy current can be effectively reduced by increasing the distance between the gradient coil and the pole head, and the gradient coil adopted by the open MRI imaging system is of a flat plate type structure, because the spacing between the openings of the magnet is limited, the spacing between the flat-plate type gradient coil and the pole heads cannot be too large, and therefore, the eddy current generated by the gradient coil is restrained by adopting more complicated silicon steel sheet laminations.
The invention provides a design method of a non-planar gradient coil, which aims to solve the problem that the open MRI magnet adopts a flat-plate gradient coil to generate large eddy current on a pole head, and can reduce the eddy current generated by the gradient coil on the pole head and improve the image quality of an open MRI system.
Disclosure of Invention
The invention aims to provide a design method of a non-planar gradient coil, which can reduce the eddy current generated on a pole head by the gradient coil and improve the image quality of an open MRI system.
To achieve the above object, the present invention provides a method for designing a non-planar gradient coil, which comprises the following steps.
The method comprises the following steps: and (3) modeling a biplane gradient coil by using MATLAB, and performing triangular mesh division on a coil plane to obtain vertex coordinates and sequence a top surface and a triangular surface.
Step two: and (3) bending the planar gradient coil, multiplying the vertex coordinate by a bending angle eta (0 degrees < eta <180 degrees) to obtain the shape of the non-planar gradient coil after bending, and calculating the vertex coordinate value of the gradient coil after bending.
Step three: coordinates of the target point of the imaging area are defined.
Step four: and calculating the magnetic field value of the non-planar gradient coil at the target point according to the spherical harmonic function.
Step five: and calculating the magnetic field contribution value of the electrified conducting wire in the source point region to the target point in the imaging region by using a Bio Saval formula according to a boundary element method and a given wire size.
Step six: and calculating a power consumption matrix and an energy storage matrix of the source point.
Step seven: according to the Quadratic Programming method, the power consumption of the non-planar gradient coil is constrained to be minimum, and the magnitude and the direction of the current on the gradient coil are calculated.
Step eight: and obtaining the actual winding shape of the non-planar gradient coil by a flow function method.
Step nine: and verifying whether the non-planar gradient coil meets the requirement of the target magnetic field value error or not according to the winding shape of the gradient coil, and if not, modifying the weight coefficients of the power consumption matrix and the energy storage matrix until the magnetic field value meets the requirement of the target magnetic field value error.
Preferably, the method for defining the coordinates of the target point of the imaging area in the third step comprises: dividing the sphere into 16 layers, setting a test point every 11.6 degrees for each layer, and obtaining coordinate values of coordinate points by using MATLAB (matrix laboratory) to obtain a field coordinate point F (x1, y1, z 1).
Preferably, the method for calculating the magnetic field value of the target point in the fourth step comprises: the product of the field coordinate value and the gradient strength, i.e.:
Gx＝G*Cx(x,y,z)
Gy＝G*Cy(x,y,z)
Gz＝G*Cz(x,y,z)
wherein G isx、GyAnd GzThe magnetic field value of the target point in a given target area is given in mT; g is given gradient strength, and the unit is mT/m; c (x, y, z) is coordinate values of the x, y and z directions of the target points, and the unit is m.
Preferably, the biotival formula in the step five is as follows:
wherein the content of the first and second substances,
the contribution value of the source point lead to the field point magnetic induction intensity is obtained; mu.s0Is a vacuum magnetic conductivity; dl is the length of the electrified lead in the source region; r is the distance from the source point to the field point; i is the current value on the source point lead; theta is an included angle between the electrified lead and a connecting line of the source point and the field point.
Preferably, the coil power consumption matrix expression in the sixth step is as follows:
wherein S is a discrete unit surface and comprises n nodes, ImAnd InCurrent values at the m-th and n-th nodes, respectively, p being the resistance of the conductor, drIs the thickness of the conductor. RmnIs a resistance matrix of the gradient coil;
the coil energy storage matrix expression is as follows:
Smand SnAre discrete triangular surfaces and belong to nodes n and m respectively, and the nodes n and m respectively contain WnAnd WmA triangle ImAnd InCurrent values, μ, at the mth and nth nodes, respectively0Is the magnetic permeability of vacuum, rmAnd rnRespectively, the coordinates of the points in the triangular plane. v. ofmaAnd vnbAre basis functions of nodes M and n, respectively, MmnIs the energy storage matrix of the gradient coil.
Preferably, the expression of the quadprog function in the step seven is as follows:
F＝α*I*Rmn*I’+β*I*Mmn*I’
wherein: f is an objective function, I is a current value of a discrete point in a source region, I' is a transposed matrix of I, RmnIs a source region discrete point resistance matrix, MmnFor the source discrete point inductance matrix, alpha and beta, respectivelyIs the resistance matrix and inductance matrix weight coefficients;
the conditions that constrain the non-planar gradient coil to minimize power consumption are:
|A*I|<ε*Bt
wherein: a is a magnetic field coefficient matrix which does not contain a node current value and is calculated by Bio savart at a target point through a source point; epsilon is the magnetic field error, 0.025; b istIs the target magnetic field value; i is the node current value.
Preferably, the expression of the stream function in the step eight is as follows:
wherein: s is equal parallax, max (I) is the maximum value of the node current, min (I) is the minimum value of the node current, and N is the number of winding turns of the non-planar gradient coil.
The invention has the beneficial effects that:
the non-planar gradient coil designed by the invention can reduce the eddy current generated on the pole head by the gradient coil and improve the image quality of the open MRI system.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flow chart of a method of designing a non-planar gradient coil of the present invention.
FIG. 2 is a schematic diagram of source region meshing for a non-planar gradient coil of the present invention.
FIG. 3 is a schematic view of the imaging region target point of the present invention.
FIG. 4 is a schematic diagram of a three-dimensional display source region and imaging region target point of the present invention.
FIG. 5 is an XY plan view of an X gradient coil of a non-planar gradient coil of the present invention.
FIG. 6 is a three-dimensional view of an X-gradient coil of a non-planar gradient coil of the present invention.
FIG. 7 is an XY plan view of a Y gradient coil of a non-planar gradient coil of the present invention.
FIG. 8 is a three-dimensional view of a Y gradient coil of the non-planar gradient coil of the present invention.
FIG. 9 is an XY plan view of a Z gradient coil of a non-planar gradient coil of the present invention.
FIG. 10 is a three-dimensional view of a Z gradient coil of a non-planar gradient coil of the present invention.
Detailed Description
Embodiments of the present invention will be further described with reference to the accompanying drawings.
The following is a design example of the present invention, the design flow chart of which is shown in fig. 1, the design parameters of the non-planar gradient coil are set, the diameter of the non-planar gradient coil is 0.42m, the spacing is 460mm, 480mm and 500mm respectively, the non-planar gradient coil is divided into 16 layers on a sphere with the diameter of 360mm, a test point is set every 11.6 degrees, 496 target points are set in total, the error is not more than 5%, and the specific design steps are as follows.
The method comprises the following steps: according to the design parameters of the set non-planar gradient coil, MATLAB software is adopted to carry out modeling and triangularization mesh division on the circular surface, and the vertex and the surface of the triangularization mesh are sequenced to obtain the source point coordinates S (x, y, z) and the surface number connected with the vertex.
Step two: the vertex numbers and the triangular surface numbers are not changed when the planar gradient coil is wound, and the vertex coordinate values are multiplied by a winding angle η (0 ° < η <180 °), and the winding angle in this embodiment is 120 °, to obtain the vertex coordinate values of the shape of the non-planar gradient coil after winding, as shown in fig. 2.
Step three: dividing spheres with the diameter of 360mm into 16 layers, setting a test point every 11.6 degrees and 496 target points in total, and calculating the x, y and z coordinates of the target points by MATLAB to obtain a field coordinate point F (x1, y1 and z1) as shown in figures 3 and 4.
Step four: and determining a target point magnetic field value according to the target field point coordinate value and the spherical harmonic function, wherein the gradient strength is 15mT/m, and the target point magnetic field value on the spherical surface is the product of the coordinate point coordinate value and the gradient strength. Namely:
Gx＝G*Cx(x,y,z)
Gy＝G*Cy(x,y,z)
Gz＝G*Cz(x,y,z)
in the formula Gx、GyAnd GzThe magnetic field value of the target point in a given target area is given in mT; g is given gradient strength, and the unit is mT/m; c (x, y, z) is coordinate values of the x, y and z directions of the target points, and the unit is m.
Step five: calculating the contribution value of the electrified lead of the source point region to the target field point according to a boundary element method and the size of the set non-planar gradient coil lead, wherein the calculation method comprises the following steps:
according to the biot savart formula:
in the formula
The contribution value of the source point lead to the field point magnetic induction intensity is obtained; mu.s0Is a vacuum magnetic conductivity; dl is the length of the electrified lead in the source region; r is the distance from the source point to the field point; i is the current value on the source point lead; theta is an included angle between the electrified lead and a connecting line of the source point and the field point.
Step six: calculating a power consumption matrix and an energy storage matrix of the non-planar gradient coil,
the coil power consumption expression is as follows:
wherein the surface S is a discrete unit surface comprising n nodes, ImAnd InCurrent values at the m-th and n-th nodes, respectively, p being the resistance of the conductor, drIs the thickness of the conductor, RmnIs a resistive matrix of the gradient coil and,
the coil energy storage expression is as follows:
formula middle surface SmAnd SnAre discrete triangular surfaces and belong to nodes n and m respectively, and the nodes n and m respectively contain WnAnd WmA triangle ImAnd InCurrent values, μ, at the mth and nth nodes, respectively0Is the magnetic permeability of vacuum, rmAnd rnRespectively, the coordinates of the points in the triangular plane, vmaAnd vnbAre basis functions of nodes M and n, respectively, MmnIs the energy storage matrix of the gradient coil.
Step seven: and (3) calculating a current value on a power consumption minimum gradient coil node by adopting a quadrprog function in MATLAB, wherein the quadrprog function is as follows:
F＝α*I*Rmn*I’+β*I*Mmn*I’
wherein F is an objective function, I is a discrete point current value of the source region, I' is a transposed matrix of I, RmnIs a source region discrete point resistance matrix, MmnIs an inductance matrix of discrete points in the source region, alpha and beta are respectively a resistance matrix and an inductance matrix weight coefficient,
constraint conditions
|A*I|<ε*Bt
In the formula, A is a magnetic field coefficient matrix which does not contain a node current value and is calculated by Bio savart at a target point through a source point; epsilon is the magnetic field error, 0.025; b istIs the target magnetic field value; i is the node current value.
Step eight: the winding shape of the non-planar gradient coil is calculated by a flow function method,
wherein S is the equipotential difference, max (I) is the maximum node current, min (I) is the minimum node current, and N is the number of winding turns of the non-planar gradient coil.
Step nine: and (3) solving a magnetic field value of the coil on the target point by utilizing the Bio Saval theorem according to the winding shape of the non-planar gradient coil, judging whether the magnetic field value meets the error requirement of the target magnetic field value, if so, stopping modifying the alpha and beta weighting coefficients, and otherwise, continuing the alpha and beta weighting coefficients until the linearity requirement of the gradient coil is met, and finally obtaining the result shown in the figures 5-10.
Therefore, the invention provides a design method of a non-planar gradient coil, which controls the power consumption and energy storage minimization of the gradient coil, restrains the magnetic field value of the gradient coil on a target point, can effectively increase the distance between the gradient coil and a pole head, reduces the eddy current generated by the gradient coil on the pole head, and improves the image quality of an open MRI system.
Finally, it should be noted that: the above embodiments are not limited to the non-planar gradient coil with a winding angle of 120 ° but are not limited to the non-planar gradient coil with a winding angle of 120 °, and the non-planar gradient coils with various winding angles for use in an open MRI system can be designed by modifying the angle, and the above embodiments are only used for illustrating the technical solution of the present invention and not for limiting the same, although the present invention is described in detail with reference to the preferred embodiments, those skilled in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.
Claims (7)
1. A method of designing a non-planar gradient coil, comprising: the method comprises the following steps:
the method comprises the following steps: modeling a biplane gradient coil by using MATLAB, and carrying out triangular mesh division on a coil plane to obtain vertex coordinates and sequence a top surface and a triangular surface;
step two: bending the planar gradient coil, multiplying the vertex coordinate by a bending angle eta (0 degrees < eta <180 degrees) to obtain the shape of the non-planar gradient coil after bending, and calculating the vertex coordinate value of the gradient coil after bending;
step three: defining coordinates of a target point of an imaging area;
step four: calculating the magnetic field value of the non-planar gradient coil at a target point according to the spherical harmonic function;
step five: calculating the magnetic field contribution value of the electrified conducting wire of the source point region to the target point of the imaging region by a Bio Saval formula according to a boundary element method and a given conducting wire size;
step six: calculating a power consumption matrix and an energy storage matrix of the source point;
step seven: according to a Quadratic Programming method, the power consumption of the non-planar gradient coil is restrained to be minimum, and the magnitude and the direction of the current on the gradient coil are calculated;
step eight: obtaining the actual winding shape of the non-planar gradient coil by a flow function method;
step nine: and verifying whether the non-planar gradient coil meets the requirement of the target magnetic field value error or not according to the winding shape of the gradient coil, and if not, modifying the weight coefficients of the power consumption matrix and the energy storage matrix until the magnetic field value meets the requirement of the target magnetic field value error.
2. A method of designing a non-planar gradient coil as set forth in claim 1, wherein: the method for defining the coordinates of the target points of the imaging area in the third step comprises the following steps: dividing the sphere into 16 layers, setting a test point every 11.6 degrees for each layer, and obtaining coordinate values of coordinate points by using MATLAB (matrix laboratory) to obtain a field coordinate point F (x1, y1, z 1).
3. A method of designing a non-planar gradient coil as set forth in claim 1, wherein: the method for calculating the magnetic field value of the target point in the fourth step comprises the following steps: the product of the field coordinate value and the gradient strength, i.e.:
Gx＝G*Cx(x,y,z)
Gy＝G*Cy(x,y,z)
Gz＝G*Cz(x,y,z)
wherein G isx、GyAnd GzThe magnetic field value of the target point in a given target area is given in mT; g is given gradient strength, and the unit is mT/m; c (x, y, z) is coordinate values of the x, y and z directions of the target points, and the unit is m.
4. A method of designing a non-planar gradient coil as set forth in claim 1, wherein: the biotivall formula in the step five is as follows:
wherein the content of the first and second substances,
the contribution value of the source point lead to the field point magnetic induction intensity is obtained; mu.s0Is a vacuum magnetic conductivity; dl is the length of the electrified lead in the source region; r is the distance from the source point to the field point; i is the current value on the source point lead; theta is an included angle between the electrified lead and a connecting line of the source point and the field point.
5. A method of designing a non-planar gradient coil as set forth in claim 1, wherein: the coil power consumption matrix expression in the sixth step is as follows:
wherein S is a discrete unit surface and comprises n nodes, ImAnd InCurrent values at the m-th and n-th nodes, respectively, p being the resistance of the conductor, drIs the thickness of the conductor. RmnIs a resistance matrix of the gradient coil;
the coil energy storage matrix expression is as follows:
Smand SnAre discrete triangular surfaces and belong to nodes n and m respectively, and the nodes n and m respectively contain WnAnd WmA triangle ImAnd InCurrent values, μ, at the mth and nth nodes, respectively0Is the magnetic permeability of vacuum, rmAnd rnAre respectively triangular surfacesAnd (4) coordinates of the inner points. v. ofmaAnd vnbAre basis functions of nodes M and n, respectively, MmnIs the energy storage matrix of the gradient coil.
6. A method of designing a non-planar gradient coil as set forth in claim 1, wherein: the quadrprog function expression in the step seven is as follows:
F＝α*I*Rmn*I’+β*I*Mmn*I’
wherein: f is an objective function, I is a current value of a discrete point in a source region, I' is a transposed matrix of I, RmnIs a source region discrete point resistance matrix, MmnThe method comprises the steps that a source region discrete point inductance matrix is adopted, and alpha and beta are respectively a resistance matrix and an inductance matrix weight coefficient;
the conditions that constrain the non-planar gradient coil to minimize power consumption are:
|A*I|<ε*Bt
wherein: a is a magnetic field coefficient matrix which does not contain a node current value and is calculated by Bio savart at a target point through a source point; epsilon is the magnetic field error, 0.025; b istIs the target magnetic field value; i is the node current value.
7. A method of designing a non-planar gradient coil as set forth in claim 1, wherein: the expression of the stream function in the step eight is as follows:
wherein: s is equal parallax, max (I) is the maximum value of the node current, min (I) is the minimum value of the node current, and N is the number of winding turns of the non-planar gradient coil.
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Application publication date: 20210420 |