An off-centered conical head gradient coil and its design method

Abstract

The present invention relates to an eccentric conical head gradient coil and its design method, including: setting the structure and size of the conical coil, discretizing the current-carrying surface of the conical coil structure into a grid composed of triangles, and calculating the current basis functions of the nodes of each triangle; moving the imaging region a set distance towards the coil inlet end, selecting the magnetic field sampling points in the imaging region, and calculating the target magnetic field values at the magnetic field sampling points; expressing the magnetic field component in the Z direction at the magnetic field sampling points with the node stream function values and the current basis functions; combining the target magnetic field values at the magnetic field sampling points and the magnetic field component in the Z direction, constructing an optimization problem with the minimization of the coil power consumption as the optimization objective and the linearity of the magnetic field in the imaging region as the constraint condition; solving the optimization problem to obtain the stream function distribution of the coil; and using the stream function method to discretize the wire to obtain the winding distribution of the coil. The present invention has the advantages of higher current efficiency, greater openness, and the ability to reduce the local hot spot temperature, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of gradient coils in magnetic resonance imaging systems, and particularly to an eccentric conical head gradient coil and its design method. Background Art

[0002] Magnetic resonance imaging (MRI) technology is widely used in clinical diagnosis and scientific research due to its advantages of non-invasive, high soft tissue contrast and resolution. As one of the core components of the magnetic resonance system, the gradient coil is responsible for generating a gradient magnetic field that linearly changes with spatial position in the imaging area, and spatially encoding the MRI signals from the imaging target as the basis for image reconstruction. The gradient coil usually adopts a cylindrical structure design, and a spherical imaging area, called DSV (Diameter of Spherical Volume), is included at its exact center. When the gradient coil is working, it needs to be supplied with pulsed current of several hundred amperes, which will generate a large amount of heat, and a water cooling system needs to be equipped for cooling.

[0003] Conventional clinical 3T human magnetic resonance imaging systems usually come with a cylindrical whole-body gradient coil, which can be used for human imaging of all parts of the body. For some imaging applications of head magnetic resonance imaging, such as diffusion-weighted imaging (DWI) and echo-planar imaging (EPI), etc., it is required that the gradient coil can achieve higher gradient strength and switching rate to improve the image resolution and imaging speed. For such imaging applications, a head-specific gradient coil is usually used as an insertable coil and loaded into the existing clinical 3T human magnetic resonance imaging system for head imaging. Compared with the whole-body gradient coil, the insertable head gradient coil has more advantages because its coil size is smaller, the distance between the coil and the imaging area is closer, and it can generate higher gradient strength and switching rate.

[0004] For the cylindrical coil structure, in order to obtain a gradient coil with good enough linearity, the ratio of length to diameter should be at least 1.5; in order to improve the current efficiency and reduce the coil size, the coil diameter needs to be as small as possible, so that only the head can enter the coil, but the shoulders cannot. However, this ratio and size will make the distance from the inlet end of the coil to the exact center of the coil much longer than the length from the shoulders to the head, and finally the head cannot enter the imaging area at the exact center of the coil. For this reason, the ratio of the length to the diameter of the cylinder is usually reduced to 1. This shorter cylindrical structure can ensure that the head can enter the imaging area without being blocked by the shoulders for imaging. However, this brings a reduction in magnetic field linearity.

[0005] To enable the head to fully enter the imaging region without reducing the magnetic field linearity, D. Tomasi et al. proposed an asymmetrical cylindrical gradient coil design in the journal article "Asymmetrical Gradient Coil for Head Imaging" in Magnetic Resonance in Medicine. The ratio of the coil length to the diameter is 1.5, and the center of the imaging region is set near the entrance end of the coil to ensure that the head can enter the imaging region. As the imaging region moves, the corresponding winding distribution also moves towards one end of the coil, and the coil winding changes from a symmetric distribution to an asymmetrical distribution. Therefore, this design is also called an asymmetrical cylindrical gradient coil.

[0006] The design goal of the gradient coil is to obtain a coil with a certain spatial distribution, which can generate a linear gradient magnetic field in the imaging region after applying current. The existing gradient coil design method mainly uses the target field method for design. In this method, the current density is expanded based on Fourier-Bessel functions on the cylindrical surface, and the system equation is constructed by establishing the relationship between the target magnetic field and the current density. The unknown Fourier coefficients are solved to obtain the corresponding current density distribution, and then the wire is discretized to obtain the specific winding distribution.

[0007] However, for the existing head gradient coils with an asymmetrical cylindrical structure, the winding at one end of the coil is very dense, which is likely to generate local temperature hotspots and pose safety problems to patients; the dense winding makes it very difficult to further increase the number of winding turns, resulting in low current efficiency of the coil, and the openness of the coil is poor, making it impossible to observe or perform interventional treatment operations on patients during the scanning process. The existing target field design method is only applicable to the design of cylindrical coils, and it is necessary to assume that the length of the coil is infinite. During the design process, the obtained winding distribution needs to be truncated to obtain a coil with a finite length, which will bring about a reduction in magnetic field linearity, and this method is not applicable to the design of irregular coils. Summary of the Invention

[0008] The purpose of the present invention is to overcome the deficiencies of the prior art and provide an eccentric conical head gradient coil with higher current efficiency, greater openness, and capable of reducing the local hotspot temperature.

[0009] To achieve the above purpose, the technical solution provided by the present invention is as follows:

[0010] An eccentric conical head gradient coil, having an eccentric conical structure in the imaging region.

[0011] To achieve the above purpose, the present invention further provides a design method for the above-mentioned eccentric conical head gradient coil, specifically including:

[0012] Set the conical coil structure and dimensions, discretize the current-carrying surface of the conical coil structure into a mesh composed of multiple triangles, and calculate the current basis functions of the nodes of each triangle therein;

[0013] Move the imaging region a set distance towards the coil inlet end, select the magnetic field sampling points in the imaging region, and calculate the target magnetic field values at the magnetic field sampling points;

[0014] Express the magnetic field component in the Z direction at the magnetic field sampling points using the node stream function values and the current basis functions;

[0015] Combine the target magnetic field values at the magnetic field sampling points and the magnetic field component in the Z direction, and construct an optimization problem with the minimization of the coil power consumption as the optimization objective and the linearity of the magnetic field in the imaging region as the constraint condition;

[0016] Solve the optimization problem to obtain the stream function distribution of the coil;

[0017] Use the stream function method to discretize the wire and obtain the winding distribution of the coil, thereby obtaining an off-centered conical head gradient coil.

[0018] Further, discretize the current-carrying surface of the conical coil structure into a mesh composed of multiple triangles, and calculate the current basis functions of the nodes of each triangle therein, including:

[0019] The vertices of the triangle are called nodes. Import the nodes, coordinates, and labels of the triangle into MATLAB software for the calculation of the current basis functions. The specific calculation is as follows:

[0020] Node n is located in six triangles that can form a hexagon. If the coordinate vector r′ is within the i-th triangle, the corresponding current basis function v ni (r′) calculation formula is:

[0021]

[0022] Among them, e ni is the side vector opposite to node n in the i-th triangle, S ni is the area of the i-th triangle Δ ni where node n is located. For non-boundary nodes, N n = 6, and for boundary nodes N n = 3.

[0023] Further, the magnetic field sampling points in the imaging region are uniformly selected through Gaussian distribution sampling.

[0024] Further, multiply the initial target gradient intensity by the abscissa value of the magnetic field sampling points to calculate the target magnetic field values at the magnetic field sampling points in the imaging region.

[0025] Further, expressing the magnetic field component in the Z direction at the magnetic field sampling point in terms of the nodal stream function values and the current basis functions includes:

[0026] First, expressing the current density J(r′) as a linear combination of the nodal stream function values and the current basis function v n (r′):

[0027]

[0028] According to the Biot - Savart law, the magnetic field component B z (r) in the Z direction at the sampling point r can be expressed in terms of the X component J x (r′) and the Y component J y (r′) of the current density J(r′) as:

[0029]

[0030] where μ0 is the magnetic permeability of vacuum, r and r′ are the coordinate vectors at the sampling point and the source point position respectively, x and y are the abscissa and ordinate of the coordinate vector r at the sampling point, x' and y' are the abscissa and ordinate of the coordinate vector r′ respectively, and S is the current - carrying surface;

[0031] Substituting the current density J(r′) into the above formula gives the expression for the magnetic field component B z (r) in the Z direction at the sampling point position r:

[0032]

[0033] where C n (r) is the magnetic field coefficient corresponding to node n, calculated by the following formula:

[0034]

[0035] where N is the number of nodes, S is the current - carrying surface, and μ0 is the magnetic permeability of vacuum; v nx (r′) and v ny (r′) are the x - and y - direction components of the current basis function v n (r′) respectively.

[0036] Further, combining the target magnetic field value at the magnetic field sampling point and the magnetic field component in the Z direction, an optimization problem is constructed with the minimization of the coil power consumption as the optimization objective and the linearity of the magnetic field in the imaging region as the constraint condition, including:

[0037] Constraining the magnetic field non - linearity. There are M magnetic field sampling points, and the magnetic field component in the Z direction at each magnetic field sampling point satisfies the following inequality

[0038]

[0039] Among them, ε is the maximum magnetic field error, is the target magnetic field value at the magnetic field sampling point in the imaging region;

[0040] Writing the constraint conditions composed of M such inequalities in the form of a matrix and a vector, we get:

[0041]

[0042] Finally, the optimization problem is formulated as:

[0043] Minimize:

[0044]

[0045] The constraint conditions are:

[0046]

[0047] Among them, is the column vector of the stream function to be solved, composed of the node stream function values represents the transpose of the vector A is the coefficient matrix composed of the magnetic field coefficients C n (r) at the magnetic field sampling points in the imaging region; t (r) at the magnetic field sampling points in the imaging region; t Bz is the column vector composed of the target magnetic field values [[ID=4D]]at the magnetic field sampling points in the imaging region, and R is the resistance matrix of the coil.

[0048] Furthermore, use the quadprog function of the MATLAB software to solve, and obtain the stream function vector and the stream function distribution.

[0049] Furthermore, use the stream function method to discretize the wire, and obtain the winding distribution of the coil, including:

[0050] The stream function method obtains the specific wire distribution by depicting the contour lines of the stream function. Depicting the contour lines of the stream function is to linearly interpolate in the grid model to obtain the discrete points of the contour line, and then connect the discrete points to form a contour line;

[0051] The stream function value at the position where the nth wire is located is calculated by the following formula:

[0052]

[0053] Among them, and are the maximum and minimum values of the node stream function values Nt For discrete wire turns.

[0054] Furthermore, the number of wire turns N t is determined by continuously increasing the number of turns N t and performing wire discretization until the wiring spacing of the coil just does not exceed the given minimum wiring spacing d min .

[0055] Compared with the prior art, the principle and advantages of this solution are as follows:

[0056] 1. It has higher current efficiency, which is achieved by adopting a conical coil structure and an off-centered imaging area. This structure makes the winding distribution of the coil more uniform on the design surface, which is beneficial to increasing the number of winding turns and thus improving the current efficiency. In addition, the conical structure makes the overall distance between the coil and the imaging area closer, which is also beneficial to improving the current efficiency.

[0057] 2. It has greater openness, which is convenient for patients to enter the coil for scanning and for doctors to observe and perform interventional treatment operations on patients. This advantage is achieved by adopting a conical structure. At the entrance end of the conical coil, it has a larger diameter than the cylindrical head coil, so that the patient's head and shoulders can enter the coil for imaging scanning without obstruction.

[0058] 3. It can reduce the local hot spot temperature, which is achieved by adopting a conical structure and an off-centered imaging area. This structure makes the winding distribution of the coil more uniform on the design surface, reducing the local winding density, thus reducing the generation of local hot spots. In addition, the improvement of current efficiency reduces the current amplitude required to reach the same gradient strength, which is beneficial to reducing the heating of the coil.

[0059] 4. It has higher magnetic field linearity, which is achieved by adopting a coil design method based on the expansion of current basis functions. This method does not require truncating the winding distribution and can maximize the number of winding turns, reducing the magnetic field non-linearity caused by the discretization process. Brief Description of the Drawings

[0060] Figure 1 is a schematic structural diagram of an off-centered conical head gradient coil of the present invention;

[0061] Figure 2 is a grid diagram of an off-centered conical head gradient coil of the present invention;

[0062] Figure 3 is a principle flow chart of a design method for an off-centered conical head gradient coil of the present invention;

[0063] Figure 4(a) Schematic diagram of current basis function, Figure 4 (b) Schematic diagram of the edge vector corresponding to the triangular node;

[0064] Figure 5 Distribution map of magnetic field sampling points in the imaging area;

[0065] Figure 6 Distribution map of the winding of the off-center conical head gradient coil. Specific implementation mode

[0066] The present invention will be further described below in conjunction with specific embodiments:

[0067] As Figure 1 shown, an off-center conical head gradient coil described in this embodiment has an off-center conical structure in the imaging area.

[0068] As Figure 3 shown, in order to obtain the off-center conical head gradient coil described above, this embodiment further provides a design method for the off-center conical head gradient coil, which specifically includes the following steps:

[0069] S1. Set the structure and size of the conical coil, discretize the current-carrying surface of the conical coil structure into a grid composed of multiple triangles, and calculate the current basis function of each node in the triangles;

[0070] The conical coil structure described in this step is as Figure 1 shown. The minimum inner diameter D1 of this structure is 12 cm, the maximum inner diameter D2 is 44 cm, and the coil length L1 is 50.4 cm. Discretize the current-carrying surface of the conical coil structure into a grid composed of multiple triangles, as Figure 2 shown. This grid is established using blender2.9 software. The vertices of the triangles are called nodes, and the coordinates and labels of the triangle nodes are imported into MATLAB software for the calculation of the current basis function. The current basis function corresponding to node n is as Figure 4 (a) shown. This node n is located in 6 triangles. If the coordinate vector r′ is located in the i-th triangle, the corresponding current basis function v ni (r′) calculation formula is:

[0071]

[0072] Among them, e ni is the edge vector opposite to node n in the i-th triangle, S ni is the area of the i-th triangle Δ ni where node n is located, as Figure 4 (b) shown. For non-boundary nodes, N n= 6, for boundary node N n = 3.

[0073] S2. The imaging region (DSV) of the coil is a spherical region with a diameter of 20 cm. Move the imaging region 7 cm along the axis towards the inlet end of the coil, so that the distance L2 from the center of the imaging region to the inlet end of the coil is 16.2 cm, as Figure 2 shown. Then, select the magnetic field sampling points in the imaging region. The magnetic field sampling points in the imaging region are uniformly selected by Gaussian distribution sampling on the sphere with a diameter of 20 cm, a total of 496 points, as Figure 5 shown. Then, calculate the target magnetic field value at the sampling points in the imaging region by multiplying the initial target gradient intensity by the abscissa value of the sampling points. The initial target gradient intensity is set to 80 mT / m.

[0074] S3. Represent the magnetic field component in the Z direction at the magnetic field sampling points with the node stream function value and the current basis function. This step includes:

[0075] First, represent the current density J(r′) as a linear combination of the node stream function value and the current basis function v n (r′):

[0076]

[0077] According to the Biot - Savart law, the magnetic field component B z (r) in the Z direction at the sampling point r can be expressed by the X component J x (r′) and the Y component J y (r′) of the current density J(r′) as:

[0078]

[0079] where μ0 is the vacuum permeability, r and r′ are the coordinate vectors at the sampling point and the source point position respectively, x and y are the abscissa and ordinate of the coordinate vector r at the sampling point respectively, x' and y' are the abscissa and ordinate of the coordinate vector r′ respectively, and S is the current - carrying surface;

[0080] Substitute the current density J(r′) into the above formula to obtain the expression of the magnetic field component B z (r) in the Z direction at the sampling point position r:

[0081]

[0082] where C n (r) is the magnetic field coefficient corresponding to node n, calculated by the following formula:

[0083]

[0084] where N is the number of nodes, S is the current-carrying surface, and μ0 is the magnetic permeability of vacuum; v nx (r′) and v ny (r′) are the x- and y-direction components of the current basis function v n (r′), respectively.

[0085] S4. Combine the target magnetic field value at the magnetic field sampling point and the magnetic field component in the Z direction, and construct an optimization problem with the minimization of the coil power consumption as the optimization objective and the magnetic field linearity in the imaging region as the constraint condition;

[0086] This step specifically includes:

[0087] Constrain the magnetic field non-linearity. There are M magnetic field sampling points, and the Z-direction magnetic field component at each magnetic field sampling point satisfies the following inequality

[0088]

[0089] where ε is the maximum magnetic field error, is the target magnetic field value at the magnetic field sampling point in the imaging region;

[0090] Write the constraint condition composed of M above-mentioned inequalities in the form of a matrix and a vector, and obtain:

[0091]

[0092] The final optimization problem is expressed as:

[0093] Minimize:

[0094]

[0095] The constraint condition is:

[0096]

[0097] where, is the column vector of the stream function to be solved composed of the node stream function values , represents the transpose of the vector , A is the coefficient matrix composed of the magnetic field coefficients C n (r) at the magnetic field sampling points in the imaging region; t Bz is the column vector composed of the target magnetic field values at the magnetic field sampling points in the imaging region, and R is the resistance matrix of the coil.

[0098] S5. Use the quadprog function of the MATLAB software to solve the above optimization problem to obtain the stream function vector and the stream function distribution.

[0099] S6. Discretize the wire using the stream function method to obtain the winding distribution of the coil, thereby obtaining an eccentric conical head gradient coil.

[0100] This step specifically includes:

[0101] The stream function method obtains the specific wire distribution by depicting the contour lines of the stream function. Depicting the contour lines of the stream function is to perform linear interpolation in the grid model to obtain the discrete points of the contour lines, and then connect the discrete points to form a contour line;

[0102] The stream function value at the position of the nth wire is calculated by the following formula:

[0103]

[0104] where and are the maximum and minimum values of the nodal stream function values, and N is the number of wire turns for discretization. t is the number of wire turns for discretization.

[0105] In order to improve the number of winding turns as much as possible to improve the current efficiency, while ensuring that the coil resistance is not too large, the determination method of the number of wire turns N t is: continuously increase the value of the number of turns N t and perform wire discretization until the wiring spacing of the coil just does not exceed the given minimum wiring spacing d min , where d min is set to 5 mm. Select the wire distribution at this time as the final coil design. The winding distribution diagram of the eccentric conical head gradient coil obtained by this method is as shown in Figure 6 shown.

[0106] The above-described embodiments are only the preferred embodiments of the present invention, and do not limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A design method for an eccentric conical head gradient coil, characterized in that, The off-center conical head gradient coil has a conical structure that is off-center in the imaging region. It is designed using a conical structure and an off-center setting in the imaging region, specifically including: Set the conical coil structure and size. Discretize the current-carrying surface of the conical coil structure into a grid composed of multiple triangles, and calculate the current basis functions of the nodes of each triangle therein; Move the imaging region a set distance towards the coil inlet end, select the magnetic field sampling points in the imaging region, and calculate the target magnetic field values at the magnetic field sampling points; Express the magnetic field component in the Z direction at the magnetic field sampling point using the nodal stream function values and current basis functions; Combine the target magnetic field values at the magnetic field sampling points and the magnetic field components in the Z direction, and construct an optimization problem with the minimization of coil power consumption as the optimization objective and the magnetic field linearity in the imaging region as the constraint condition; Solve the optimization problem to obtain the stream function distribution of the coil; Use the stream function method to discretize the wire to obtain the winding distribution of the coil, thereby obtaining the off-center conical head gradient coil.

2. A method for designing an eccentric conical head gradient coil according to claim 1, characterized in that Discretize the current-carrying surface of the conical coil structure into a grid composed of multiple triangles, and calculate the current basis functions of the nodes of each triangle therein, including: The vertices of the triangle are called nodes. Import the nodes, coordinates, and labels of the triangle into MATLAB software for the calculation of the current basis functions. The specific calculation is as follows: The node n is located in six triangles that can form a hexagon. If the coordinate vector r′ is within the i-th triangle, the corresponding current basis function v ni (r′) is calculated by the formula: where e ni is the edge vector opposite to node n in the i-th triangle, and S ni is the area of the i-th triangle Δ ni where node n is located. For non-boundary nodes, N n = 6, and for boundary nodes N n = 3.

3. A design method for an eccentric conical head gradient coil according to claim 1, characterized in that The magnetic field sampling points in the imaging region are uniformly selected through Gaussian distribution sampling.

4. A method for designing an eccentric conical head gradient coil according to claim 1 or 3, characterized in that Multiply the initial target gradient intensity by the abscissa value of the magnetic field sampling point to calculate the target magnetic field value at the magnetic field sampling point in the imaging region.

5. A design method for an eccentric conical head gradient coil according to claim 1, characterized in that, Express the magnetic field component in the Z direction at the magnetic field sampling point using the nodal stream function values and current basis functions, including: First, the current density J(r′) is expressed as a linear combination of the nodal stream function values and the current basis function v n (r′): According to the Biot-Savart law, the Z-direction magnetic field component B at the sampling point r z (r) can be expressed by the X component J of the current density J(r′) x (r′) and the Y component J y (r′) as follows: Among them, μ0 is the vacuum permeability, r and r′ are the coordinate vectors at the sampling point and the coordinate vector of the source point position respectively, x and y are the abscissa and ordinate of the coordinate vector r at the sampling point respectively, x' and y' are the abscissa and ordinate of the coordinate vector r′ respectively, and S is the current-carrying surface; Substituting the current density J(r′) into the above equation yields the expression for the Z-direction magnetic field component B z (r) at the sampling point position r: Among them, C n (r) is the magnetic field coefficient corresponding to node n, which is calculated by the following formula: where N is the number of nodes, S is the current-carrying surface, μ0 is the permeability of free space; v nx (r′) and v ny (r′) are the x- and y-direction components of the current basis function v n (r′), respectively.

6. A method for designing an eccentric conical head gradient coil according to claim 5, characterized in that, Combine the target magnetic field values at the magnetic field sampling points and the magnetic field components in the Z direction, and construct an optimization problem with the minimization of coil power consumption as the optimization objective and the magnetic field linearity in the imaging region as the constraint condition, including: Constrain the magnetic field non-linearity. There are M magnetic field sampling points, and the magnetic field component in the Z direction at each magnetic field sampling point satisfies the following inequality where ε is the maximum magnetic field error, is the target magnetic field value at the magnetic field sampling point in the imaging area; Write the constraint conditions composed of M such inequalities in the form of a matrix and a vector, and get: The final optimization problem is expressed as: Minimize: The constraint condition is: Among them, is the column vector of the stream function to be solved, which is composed of the node stream function values , represents the transpose of the vector . A is the coefficient matrix composed of the magnetic field coefficients C n (r) at the magnetic field sampling points in the imaging region; t Bz is the column vector composed of the target magnetic field values at the magnetic field sampling points in the imaging region . R is the resistance matrix of the coil.

7. A design method for an eccentric conical head gradient coil according to claim 1, characterized in that, Solve using the quadprog function of MATLAB software to obtain the stream function vector and the stream function distribution.

8. A method for designing an eccentric conical head gradient coil according to claim 1, characterized in that Use the stream function method to discretize the wire to obtain the winding distribution of the coil, including: The stream function method obtains the specific wire distribution by depicting the contour lines of the stream function. Depicting the contour lines of the stream function is to perform linear interpolation in the grid model to obtain the discrete points of the contour line, and then connect the discrete points to form a contour line; The stream function value at the location of the nth wire is calculated by the following formula: Among them, and are the maximum and minimum values of the node stream function value , and N t is the number of turns of the wire for discretization.

9. A method for designing an eccentric conical head gradient coil according to claim 8, characterized in that, The number of turns N of the wire t The determination method is as follows: continuously increase the number of turns N t and perform wire discretization until the wiring spacing of the coil just does not exceed the given minimum wiring spacing d min .

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