A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) scanner.In this model,the magnetic field inhomogeneity tolerance and the central value of the magnetic field after shimming are programmed together with the volume of each shim piece as the variables,which increases the degree of freedom and guarantees a better solution.The magnetic field inhomogeneity tolerance after shimming with a weighting coefficient and the total volume of shim pieces are both contained in the objective function of the model.By assigning different values to the weighting coefficient in the objective function,different shimming plans with different emphases can be obtained.A simulation test has been carried out on a small permanent magnet with frame structure.Several solutions are given and compared in this paper,which indicates that a practical shimming plan can be obtained quickly by solving this model.
YOU XiaoFeiWANG ZhengZHANG XiaoBingYANG WenHuiSONG Tao
