Design Method Of Magnetic Resonance System Gradient Coil On Non-Developable Surface

Magnetic resonance imaging(MRI)as a medical imaging diagnostic method has been applied increasingly in recent years.Gradient coil is an important part of the MRI system,which generates a gradient magnetic field to spatially encode magnetic resonance signals.The linearity of gradient magnetic generated by the gradient coil has a major influence on the imaging resolution of the MRI system.In addition,when the distance between the current-carrying surface of the gradient coil and the detected object decreases,the coil efficiency and quality of the imaging area is increasing.The smaller the distance between the current carrying surface of the gradient coil and the object to be detected,the more obvious the efficiency of the coil is improved.A gradient coil with an elliptical cylinder as the current carrying surface that is closer to the shape of the human torso has also been proposed.The current carrying surfaces of these gradient coils are all developable surfaces.In order to adapt to more practical needs,such as the MRI system dedicated to the human head,it is necessary to extend the current carrying surface from the developable surface to the non-developable surface.The design of gradient coils is mostly based on the finite element discrete non-intrinsic method,which the normal vectors on the current carrying surface is used multiple times in the calculation.Therefore,the correct expression of the normal vectors has a very important influence on the accuracy of the calculation results.In the previous design and optimization of gradient coil,in order to avoid the problem that the normal vectors of discrete surface can not accurately express and affect the calculation result,a developable surface(cylinder or plane)is usually used as the current carrying surface,and the developable surface is expanded to a plane for calculation when design.For the irregular non-developable surface,how to accurately express the normal vectors is the difficulty of designing the gradient coil on the non-developable surface.In recent years,mathematically proved that the Delaunay triangulation of a surface can converge the discrete elemental normal vectors to the normal vectors of the original smooth surface.According to this conclusion,this paper extends the method of design and optimization gradient coil on the developable surface to the non-developable surface,and guarantees the convergence of numerical results and approximation errors to a certain extent.This paper mainly introduces the stream function method and the topology optimization method for the non-developable surface gradient coil design.For using the stream function method and the finite element method to calculate the electrostatic field Laplace partial differential equations on the surface,a tangential gradient operator is introduced to calculate the gradient and partial derivative of the scalar function on the discrete surface.The final problem comes down to the calculation of surface normal vectors.Using the geodesic Delaunay triangulation to discretize the current-carrying surface ensures that the normal vectors of the discrete surface converges to the original smooth surface.The distribution of surface electric current or potential is obtained by calculating the stream function or solving the electrostatic Laplace equation with the finite element method.The magnetic field distribution of the space is calculated by using the Biot-Savart formula based on the current-carrying surface.Thus,the topology optimization method can also be used to design the configuration of the gradient coil on the non-developable surface.When the MRI system works,the energized gradient coil is subjected to the Lorentz force in the uniform magnetic field of the MRI system and as the current through the coil is pulsed.The Lorentz force will cause deformation and vibration of the coil.Therefore,the support structure of the gradient coil should be optimized in order to improve the mechanical properties of the gradient coil under actual working conditions.In this paper,the stiffness of the support structure of the cylindrical three-directional gradient coil designed by the stream function method is increased to reduce the influence of the Lorentz force on the accuracy of the gradient coil.The SIMP topology optimization method based on the density method under multi-load conditions is used to optimize the mechanical structure of the gradient coil support structure in three directions of x,y and z.The results obtained are more in line with actual stress conditions and can be applied to actual products through various manufacturing methods.