Design MRI Gradient Coils On Super-elliptical Cylindrical Surfaces

Magnetic resonance imaging (MRI) is a commonly used non-invasive techniquein radiology to visualize the structure and function of the body. In an MRI scanner,there are four main parts: a main magnet, the gradient coils system, the radiofrequency transmitter-receiver, and the computer-aided control system. For a testsubstance with the spatial difference, gradient coils spatially encode the positions ofprotons by varying the magnetic field across the imaging volume. The layout ofgradient coils evolved from discrete Maxwell pairs and saddle coils to the surfacecoils wound on bi-planar or cylindrical surfaces, and the design method for thegradient coils evolved from target field method to the currently widely used streamfunction method. Considering the geometric properties of the bi-planar and cylindricalsurfaces, designing gradient coils on super-elliptical cylindrical surface is proposed inthis thesis using the stream function and the developable property of thesuper-elliptical cylindrical surface.A super-elliptical cylindrical surface can shorten the distance between coils andtarget, enhance space utilization, and enlarge the homogeneous imaging volumes.Based on the Biot-Savart law, the relationship between the magnetic flux density andstream function is established firstly, and the objective is chosen as the least-squareform with the additional Tikhonov regularization term. The numerical accuracy of themagnetic flux density in the region of interest is maintained through transforming thesuper-elliptical cylindrical surface to the corresponding flat surface and the value ofregularization coefficient of the dissipated powers is chosen automatically by usingthe L-curve method. Via imposing specified boundary conditions for the streamfunction on the developed surface, the optimization of gradient coils is implementedby directly solving well-posed linear algebraic equations. Numerical examplesillustrate the feasibility of the proposed design method. The designed coils onsuper-elliptical cylindrical surface show that the current and the dissipated powers are adequately optimized under the condition that the linear gradient deviation is less than5%.In order to obtain a better performance in applications, the influence of linearity,switch time, inductance, and eddy current should be considered during the designprocess. A flexible winding pattern can be obtained by substituting magnetic energyfor dissipated power, proving that magnetic energy can also be chosen as theadditional Tikhonov regularization term. Self-shielded coils, which is used to decreaseeddy current, are designed via the multiple-layer coil design. Numerical analysis ofthe designed coils demonstrates that the optimization of inductance and resistance isequivalent to the optimization of magnetic energy and dissipated power, respectively.Finally the advantages and the potential improvement of the proposed numericaloptimization method are discussed for the further research on gradient coils on thesuper-elliptical cylindrical surfaces.