A Finite-difference Method For The Design Of Three Dimensional MRI Gradient Coil

Magnetic resonance imaging(MRI),as an important part of the modern medical imaging system,has been more and more widely used.The gradient coil is one of the indispensable components of an MRI scanner,providing important spatial encoding information for image reconstruction.The design methods of gradient coils are being continuously developed for coils with higher performance,including higher gradient strength,higher slew rate and lower coil impedance,to better satisfy the everincreasing imaging requirements,increasingly complex spatial structures and more stringent engineering restrictions.In order to meet the increasing demand of the gradient coil performance,this thesis tries to propose a simple and efficient gradient coil design method based on the concise numerical finite difference method,and apply it to the area of gradient coil design.Through the finite difference schemes,this method can associate the stream function from which the coil winding patterns can be directly extracted,with the current density that can be used to calculate the performance parameters of gradient coils,and finally obtains the stream function values as well as coil winding data by a regularization,quadratic programming,or nonlinear programming method.To ensure that the proposed method can design gradient coils with complex three-dimensional structures,this thesis further extends the basic finite-difference coil design method.The extended method applies the finite difference schemes along the mutually-orthogonal adjacent edges of a quasi-rectangular element independent of specific coordinates,rather than a specific coordinate direction.In addition,the method unifies the difference results with the Cartesian coordinate system of the imaging region through a transformation of coordinates.Using this method,several gradient coils are designed including a shielded,ultra-short cylindrical coil,partially shielded biplanar coil and asymmetric head coil with 3D geometries,which can verify the wide application range and high design flexibility of the proposed method.In addition,the finite difference method is used to model and simulate the acoustic noise and joule heat generated by gradient coils in this thesis.Equations which describe the coil vibration,noise propagation and heat balance state are established according to the generation and propagation process of the acoustic noise and joule heat.By solving these equations,the acoustic noise and heat distribution of gradient coil can be obtained.Moreover,the coil vibration displacement due to Lorentz force is added as a constraint to the coil optimization process,and a coil with small vibration displacement is then designed for acoustic control.The designed coil can reduce its vibration displacement by half with little performance loss.Based on the proposed finite difference method,this thesis also presents a novel insertable cone-shaped gradient coil matrix for head imaging.By changing the transport current of each coil element,the gradient field along x-,y-,and z-directions can be realized with the same coil matrix,thereby simplifying the entire gradient system.The newly designed structure can not only meet the gradient field requirement on the maximum imaging region,but can generate various magnetic fields according to the imaging requirements over different local imaging regions with higher gradient intensity and lower gradient field deviation.